Anisotropic thermodynamics and $Tsqrt H$ scaling of d-wave superconductors in the vortex st

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On Microscopic Thermodynamic

On Microscopic Thermodynamic Mechanisms of Damage Evolution LawsQ IANG Y ANG,*X IN C HEN AND W EI-Y UAN Z HOUDepartment of Hydraulic EngineeringTsinghua UniversityBeijing100084,PR ChinaABSTRACT:Most existing phenomenological damage evolution laws can be covered by phenomenological equations or linear irreversible thermodynamics. In this paper,general microscopic thermodynamic mechanisms leading to nonlinear phenomenological equations are explored within the framework of‘normality structures’by Rice(Rice,J.R.(1971).Inelastic Constitutive Relations for Solids: An Internal Variable Theory and its Application to Metal Plasticity,Journal of the Mechanics and Physics of Solids,19:433–455,Rice,J.R.(1975).Continuum Mechanics and Thermodynamics of Plasticity in Relation to Microscale Deformation Mechanisms,In:Argon,A.S.(ed.),Constitutive Equations in Plasticity,MIT Press, Cambridge,MA,pp.23–79.)at the level of microstructural rearrangements.Rice’s kinetic rate laws of local internal variables,with each rate being stress dependent only via its conjugate thermodynamic force,are cornerstones of the normality structure. It is revealed in this paper that nonlinear phenomenological equations and Onsager reciprocal relations emerge naturally from the normality structures if each rate is a homogeneous function of degree q in its conjugate force.Furthermore,the nonlinear phenomenological coefficient matrix is identical to the Hessian matrix of the flow potential function in conjugate forces scaled by q.Finally,as an application and demonstration,some fundamental issues on damage evolution laws for microcracked solids have been addressed based on the revealed remarkable properties.It is shown that the deduced flow potential functions of microcracked solids can be expressed in the forms of well-established Hill(Hill,R.(1950).The Mathematical Theory of Plasticity,Clarendon Press,Oxford.)anisotropic yield function and Karafillis and Boyce(Karafillis, A.P.and Boyce, D.B.(1993).A General Anisotropic Yield Criterion Using Bounds and a Transformation Weighting Tensor,Journal of the Mechanics and Physics of Solids,46:85–113.)isotropic yield surface.KEY WORDS:thermodynamic mechanism,damage evolution,microcracking, microstructure.*Author to whom correspondence should be addressed.E-mail:yangq@ International Journal of D AMAGE M ECHANICS,Vol.14—July20052611056-7895/05/030261–33$10.00/0DOI:10.1177/1056789505050356ß2005Sage Publications262Q.Y ANG ET AL.INTRODUCTIOND AMAGE EVOLUTION LAWS,especially for anisotropic damagingbehaviors,have been the most elusive part of continuum damage mechanics,owing to their complex tensorial and high-degree nonlinear properties,see e.g.,Krajcinovic(2000)and Lemaitre et al.(2000).It is usually assumed that there exists a scalar damage dissipation potential Q in phenomenological damage models,and then the damage evolution laws are derived from it by normality condition,_:¼@Qð1Þ@Ywhere_:denotes a damage variable and is considered as a second-order tensor here without a loss of generality,and Y is the generalized thermodynamic force conjugate to_:.If further assuming that Q is a quadratic function in the conjugate force Y e.g.,_:¼Y:J:Y/2,the phenomenological equation or linear irreversible thermodynamics appears from Equation(1),_:¼J:Yð2Þwhere J is termed damage characteristic tensor of rank four by Chow and Lu(1989).The damage characteristic tensor should be symmetric and semipositive definite required by Onsager(1931)reciprocal relations and the second law of thermodynamics.Chow and Lu(1989)have shown that many classical damage evolution laws can be covered by Equation(2), e.g., Chaboche(1979),Lee et al.(1985),Murakami and Ohno(1980)and Cordebois and Sidoroff(1980),etc.The latest damage model of Soh et al. (2003)also follows this line.There are two cruxes related to this type of damage evolution laws.The first one is:whether does the normality condition(1)hold unconditionally? Furthermore,linear irreversible thermodynamics is not sufficient to cover wide nonlinear damaging phenomena.It is evident that the linear phenomenological equation(2)is not consistent with microscopic damaging mechanism, e.g.,cracking where the propagating rate of cracks possesses a high-degree nonlinear relation with the cracking drive force,stress intensity factors,or energy release rates.Thus,the nonlinear phenomenological equation(2)with conjugate-force-dependent damage characteristic tensor J¼J(Y,:,...)is more appealing than linear ones. Then the second crux is that:under what conditions does the normality condition(1)reduce to the nonlinear phenomenological equation(2)? Obviously,the cruxes cannot be answered definitely from a macroscopicThermodynamic Mechanisms of Damage Evolution Laws263 point of view,and microscopic thermodynamic mechanisms must be taken into account.In this paper,the thermodynamic framework developed by Rice(1971, 1975)is taken as a starting point.In this framework briefed in the section on ‘‘Normality Structure,’’structural rearrangements of material elements on the microscale can be related to corresponding increments of macroscopic plastic strain,and finally the thermodynamic forces and fluxes are related by certain‘normality structures.’Rice’s kinetic rate laws of local internal variables,with each rate being stress dependent only via its conjugate thermodynamic force,are cornerstones of the normality structure and represent a wide class of inelastic behaviors.Then the first crux is answered, see also Equations(11)and(14).The aim of this paper is to explore the general microscopic thermo-dynamic mechanisms leading to the nonlinear phenomenological equations within the framework of Rice(1971,1975).In this paper,it is revealed in the section on‘‘Normality Structures with Homogeneous Kinetic Rate Laws’’that nonlinear phenomenological equations and Onsager reciprocal relations emerge naturally from the normality structure if each rate is a homogeneous function of degree q in its conjugate force.Furthermore, the phenomenological coefficient matrix is identical to the Hessian matrix of the flow potential function in conjugate forces only scaled by q,and the homogeneous property transfers exactly from local internal variables to global average internal variables.The properties of damage evolution laws based on such homogenous kinetic rate laws are given in‘‘Damage Evolution basd on Homogenous kinetic Rate laws.’’The remarkable properties were first indicated by Yang et al.(2002),and further investigated from different viewpoints by Yang et al.(2004a,c,d).The idea that the normality structure of Rice(1971,1975)could be taken as the foundation of damage evolution laws,has been proposed and emphasized by Krajcinovic et al.(1991)and Krajcinovic(2000).Most existing damage evolution laws can be covered by phenomenological equations.However,it is difficult or impossible to determine fully the damage characteristic tensors without considering microscopic damaging mechanisms.The normality structure by Rice(1971,1975)furnishes such an excellent thermodynamic framework of micro–macro transition.Swoboda and Yang(1999a,b)and Yang et al.(1999)explore the structure of anisotropic damage evolution laws within the normality structure to determine analytic damage characteristic tensors for second-order crack tensors as damage variables.To do so,it is necessary to answer the second crux but their answers are plausible.Finally,as an application and demonstration,some fundamental issues on damage evolution laws for microcracked solids have been addressedbased on the revealed remarkable properties.The general structure of the damage evolution laws based on homogenous kinetic rate laws is established in the same section of this paper.The analytic damage characteristic tensors for zero-,second-,and fourth-order fabric tensors of microcracks have been deduced in the section on‘‘Damage Evolution Laws of Fabric Tensors.’’The properties of the deduced damage characteristic tensors and flow potentials functions have been discussed in the next section with the help of orientation distribution functions (Onat,1984;Lubarda and Kracinovic,1993;Yang et al.,1999,2001b, 2004b).It is shown that the deduced flow potential functions of microcracked solids can be expressed in the forms of well-established Hill(1950)anisotropic yield function and Karafillis and Boyce(1993) isotropic yield surface.NORMALITY STRUCTUREConsider a material sample of size V.Introduce the specific free energy and its Legendre transform with respect to strain¼ ðe,#,HÞ,¼ðr,#,HÞ¼e:@@eÀ ð3Þwhere#denotes temperature;"denotes any strain tensor,objective and symmetric,that measures deformation from an arbitrary reference state; denotes the symmetric conjugate stress such that :d"is the work per unit volume of the adopted reference state in any virtual deformation d";H denotes symbolically the current pattern of microstructural rearrangement of constituent elements of the materials.At fixed H,variations of and #necessarily induce a purely elastic response.Then the first law of thermodynamics leads to the stress–strain relations,r¼@ ðe,#,HÞ@e,e¼@ ðr,#,HÞ@r:ð4ÞConsider two neighboring patterns of microstructural rearrangement denoted by H,HþdH for the sample of size V.It is assumed that a set of incremental internal variables d 1,d 2,...,d n characterizes the specific local rearrangements,which are represented collectively by d H,at sites throughout the material sample.The d s and dH are related by1 V f d ¼Àd p ¼d pð5Þ264Q.Y ANG ET AL.where1d p ¼ ðe,#,Hþd HÞÀ ðe,#,HÞ,d p¼ðr,#,Hþd HÞÀðr,#,HÞ:ð6ÞEquation(5)also defines the thermodynamic forces f1,f2,...,f n(collectively f)conjugate to the variables,f¼fðr,#,HÞor f¼fðe,#,HÞ:ð7ÞThe corresponding set of total internal variables,n¼ 1, 2,..., nf g,ð8Þgenerally are not state variables in the sense that thermodynamic state functions are not direct functions of n,but instead depend on the path history of n.Only if the n is one set of explicit state variables,the conjugate forces can be determined as:f ¼V @@¼ÀV@@, ¼ ðe,#,nÞ,¼ðr,#,nÞ:ð9ÞFollowing the second law of thermodynamics,the entropy production rate should be always non-negative,1Vf _ !0:ð10ÞIn the normality structure,a key assumption is that the kinetic rate laws of the internal variables take the form_¼_ ðf ,#,HÞ,ð ¼1,2,...,nÞ:ð11ÞTherefore,the kinetic rate laws can be related to a flow potential Q and be recast as:_ ¼V@Q@,Q¼Qðf,#,HÞ¼1VZ f_ðf,#,HÞd f ,ð12Þ1In this paper,Einstein’s summation convention is adopted for repeated indexes.However,if an index range is listed like in Equation(11),the index is considered as a free index without the summation convention. The superscript denotes‘plastic.’Thermodynamic Mechanisms of Damage Evolution Laws265where the integration is carried out at fixed#and H,and defines a direct function Q of f since each term in the integrand is a total differential. The inelastic part of a strain increment is,due to Equations(4)–(6),d p e¼eðr,#,Hþd HÞÀeðr,#,HÞ¼@ðd pÞ@r¼1V@f@rd :ð13ÞTherefore,the following normality structure holds,noting f¼fðr,#,HÞ,d pe d t ¼@Q@r,Q¼Qðr,#,HÞ¼Qðf,#,HÞð14Þwhere t denotes time,since,due to Equation(12b)@Q @r ¼1V@f@r_:ð15ÞIntroduction of Averaging Internal Variables fThe set n generally contains numerous elements.One set of much reduced internal variables f can be introduced as the average measurements of n f¼ 1, 2,..., mf g, ¼ ð 1, 2,..., n;VÞð ¼1,2,...,m(nÞð16Þwhere V indicates averaging over the volume.The thermodynamic forces acting on the averaging variables n are g1,g2,...,g m(collectively g).Only if the n is one set of explicit state variables,the conjugate forces can be determined as:g ¼@@¼À@@, ¼ ðe,#,fÞ,¼ðr,#,fÞ:ð17ÞThe equivalence that the averaging variables f can describe the thermodynamic system characterized by n,is achieved by requiring the equality for all ng ¼1Vf :ð18ÞDue to Equation(16),one obtains¼@@, ¼ ðn,VÞ:ð19Þ266Q.Y ANG ET AL.Substituting Equation(19)into Equation(18)leads tof ¼Vg @ ðn,VÞ@¼f ðg,#,HÞ)@ ðn,VÞ@¼1V@f ðg,#,HÞ@g:ð20ÞTherefore,_ ¼@@_¼1V_@f ðg,#,HÞ@g¼@Qðg,#,HÞ@gð21ÞwhereQðg,#,HÞ¼1VZ fðg,#,HÞ_ðf,#,HÞd f ¼Qðf,#,HÞ:ð22ÞIncremental Dependence of f on nThere do not always exist direct relations between f and n like Equation(16).However,since the set of incremental internal variables d n determines fully the internal rearrangement d H,a proper set of incremental averaging internal variables d f can also describe d H with sufficient accuracy. Thus,it is reasonable to assume such a linear dependence between d f and d n,d f¼RÁd n or d ¼R d ð23Þwhich implies that the setf depends on not only the set n but also its path history.Here it is only assumed that the transformation operator R exists uniquely for a given internal rearrangement H.Evidently,the direct relations Equation(16)can also be written as Equation(23)withR ¼@@:ð24ÞNo matter what the relations between f and n are,the dissipation relation Equation(18)should always hold.Therefore,the following relations are obtained,similar to Equation(20)f ¼Vg R )R ¼1V@f@gð25ÞThermodynamic Mechanisms of Damage Evolution Laws267Therefore,with the potential function Qðg,#,HÞdefined in Equation (22),the normality condition similar to Equation(21)still holds,_ ¼R _ ¼1V_@f ðg,#,HÞ@g¼@Qðg,#,HÞ@g:ð26ÞIn the following discussion,the incremental relations like Equation(23) are generally assumed between f and n,and the direct relations like Equation(16)are just considered as a special case of the incremental relations with Equation(24).NORMALITY STRUCTURES WITH HOMOGENEOUSKINETIC RATE LAWSLet us define the dissipation functions at both microscopic and macro-scopic levels,Èðf,#,HÞ¼1Vf _ ,Èðg,#,HÞ¼g _ :ð27ÞEvidently,we have the following relations,È¼Àd pdt¼d pdt:ð28ÞIn fact,È=#is just the entropy production rate.The introduction of Rice (1971,1975)kinetic rate laws implies that the dissipation functionÈðf,#,HÞis well-defined.On the other hand,Equation(18)is just the requirement that the microscopic dissipation function should be equal to the macroscopic one,i.e.,Èðf,#,HÞ¼Èðg,#,HÞð29ÞDue to Equations(12)and(21),the dissipation and flow potential functions are related byÈðf,#,HÞ¼f @Qðf,#,HÞ@f,Èðg,#,HÞ¼g@Qðg,#,HÞ@gð30ÞThe Rice(1971,1975)kinetic rate laws of the internal variables, Equation(11),with each rate being stress dependent only via its conjugate thermodynamic force,are cornerstones of the normality structure.However, they should be thought of only as an approximation and not as a physical law,as remarked by Rice(1975).In this paper,we are interested in a special 268Q.Y ANG ET AL.type of kinetic rate laws that each rate_ is a homogeneous function of degree q in its conjugate force f ,@_ ðf ,#,HÞ@ff ¼q_ ðf ,#,HÞð ¼1,2,...,nÞð31Þwhere Euler’s Theorem on homogeneous functions is adopted as a definition.It is emphasized that all kinetic rate laws possess the same homogeneous degree q.With the homogeneous property Equation(31)and integration by parts, the flow potential Q defined in Equation(12)can be recast as:Qðf,#,HÞ¼1VZ f_d f ¼1V_f À1VZ fq_ d f¼Èðf,#,HÞÀqQðf,#,HÞð32Þwhich leads toÈðf,#,HÞ¼ðqþ1ÞQðf,#,HÞ)Èðg,#,HÞ¼ðqþ1ÞQðg,#,HÞ,ð33Þdue to Equations(22)and(29).This equation along with Equation(30) indicate that bothÈðf,#,HÞ,Qðf,#,HÞ,andÈðg,#,HÞ,Qðg,#,HÞare homogeneous functions of degree qþ1in f and g,respectively.@È@f f ¼@È@gg ¼ðqþ1ÞÈ,@Q@ff ¼@Q@gg ¼ðqþ1ÞQ:ð34ÞNonlinear Phenomenological Equations Differentiating Equation(30b)by g ,it follows that@Èðg,#,HÞ@g ¼@Qðg,#,HÞ@gþg@2Qðg,#,HÞ@g @gð35Þwith the summation convention for ( ¼1,2,...,m).Using Equations(21) and(33b),one obtains_ ¼J g ,J ¼1q@2Qðg,#,HÞ@g @g¼J ð36ÞThermodynamic Mechanisms of Damage Evolution Laws269which are exactly the phenomenological equations and Onsager reciprocal relations (Onsager,1931).The phenomenological equations can be written in matrix form_f ¼J Ág ,_f ¼_ 1,_ 2,...,_ m ÈÉT ,g ¼g 1,g 2,...,g m ÈÉT ð37Þwhere the nonlinear phenomenological coefficient matrix J is a m Âm square matrix,and its element at th row and th column is J .Note that the Hessian matrix of the flow potential Q in g is denoted by H (Q ,g )and defined as:H ðQ ,g Þ¼@2Q@g 1@2Q @g 1@g 2ÁÁÁ@2Q @g 1@g m @2Q @g 2@g 1@2Q @g 2ÁÁÁ@2Q @g 2@g m (2)@g m @g 1@2Q @g m @g 2ÁÁÁ@2Q @g m 2666666666666666437777777777777775ð38ÞEvidently,the matrix J is identical to the Hessian matrix scaled by 1/q ,i.e.,J ¼1q H ðQ ,g Þor J ¼1q ðq þ1ÞH ðÈ,g Þð39Þdue to Equation (33).Since Hessian matrices are always symmetric,the Onsager reciprocal relations are incorporated implicitly.Similarly,Equation (31)directly leads to the phenomenological equations at the microscopic level,_¼J f ,J ¼1q @_ @f ¼1q @2Q @f 2 ð ¼1,2,...,n Þð40Þor in matrix form_n ¼~J Áf ,_n ¼_ 1,_ 2,...,_ n ÈÉT ,f ¼f 1,f 2,...,f n ÈÉT ð41Þ270Q.Y ANG ET AL .where,the nonlinear phenomenological coefficient matrix~J is a nÂn square matrix and associated with the Hessian matrix of Q orÈby~J¼1q HðQ,fÞ¼1qðqþ1ÞHðÈ,fÞ:ð42ÞNote that all the three square matrices are diagonal matrices since the off-diagonal elements of H(Q,f)are@2Q @f @f ¼@_@f¼0,ð ¼ Þ:ð43ÞObviously,the th diagonal element of~J is just J .Convexity of DissipationLet us discuss the restriction of the second law of thermodynamics on the nonlinear phenomenological coefficient matrices,see Equation(10).In view of Equations(37)and(41),it is requiredÈ¼g T Jg¼f T~J f!0ð44Þfor any g or f.Thus,J and~J should be positive semidefinite,and then H(Q,f),H(Q,g),H(È,f),and H(È,g)should also be positive semidefinite. Obviously,if anyone of the six matrices is positive semidefinite,the other ones are all positive semidefinite.Note that,if the Hessian matrix of a scalar function,say Q(f),is positive semidefinite,the function is convex,see e.g., Maugin(1999).The analytic formulation of the convexity is given byQ f1þð1À Þf2½ Qðf1Þþð1À ÞQðf2Þð45Þwhere f1,f2are two sets of arbitrary conjugate forces and0 1. Therefore,the convexity of the flow potential Q or dissipation functionÈis required by the second law of thermodynamics.Note that~J is a diagonal matrix,and it is positive semidefinite ifJ ¼1q@2Q@f¼1q@_@f!0,ð ¼1,2,...,nÞð46Þwhich require that_ is a monotonic increasing function of the conjugate force f .The requirement can be recast,due to Equation(31),J ¼1q@_@f¼_f!0,ð ¼1,2,...,nÞð47Þwhich is equivalent to,in the sense of non-negativeness,f _ !0,ð ¼1,2,...,nÞð48ÞAs compared with Equation(10),it is evident that the homogeneous conditions equation(31)require that the intrinsic dissipation inequality hold for each internal variable or locally.Due to Equations(27)and(33),one obtains,g _ ¼Èðg,#,HÞ¼ðqþ1ÞQðg,#,HÞ:ð49ÞDifferentiating Equation(49)by g and using Equation(21),the global homogeneous conditions emerge,@_ @g g ¼q_ ,or@_f@gÁg¼q_fð50Þwhich shows that the homogeneous property transfers exactly from local internal variables n to global internal variables f,as compared with Equations(50)and(31).It should be emphasized that all deduction in this section is fully independent of the specific relation between f and n,so all results hold for both direct and incremental relations between them.DAMAGE EVOLUTION BASED ON HOMOGENOUSKINETIC RATE LAWSIn phenomenological damage models,it is usually assumed that the current microstructure of the material sample is uniquely characterized by the current damage variable:.In this sense,the damage variable:is equivalent to H,the parameter denoting the current pattern of micro-structural rearrangement of constituent elements of the materials. Therefore,the conjugate force Y is determined byY¼@@:¼À@@:, ¼ ðe,#,:Þ,¼ðr,#,:Þ:ð51ÞEvidently,the homogeneous local rate laws,Equation(31),lead to the following properties,in view of Equations(36),(50),and(34),_:¼@Q@Y¼J:Y,ð52ÞJ¼1q@2Q@Y2,ð53Þ@Q@Y:Y¼ðqþ1ÞQ,ð54Þ@_:@Y:Y¼q_:ð55ÞIt should be emphasized that these properties are irrelevant to the specific physical meanings and tensorial characters of the damage tensor.The damage tensor may be net area reduction(Murakami and Ohno,1980;Lemaitre et al., 2000),or elasticity or compliance tensors(Ju,1989;Lubarda et al.,1994),or crack fabric tensors(Lubarda and Kracinovic,1993;Swoboda et al.,1999a,b; Yang et al.,1999,2001a),but the constitutive equations keep the same form as soon as the local rate laws are homogeneous functions of degree q. Furthermore,the quadratic assumption,:¼Y:J:Y/2,is unnecessary.APPLICATION TO MICROCRACKED SOLIDThe essential properties of the normality structures with homogeneous kinetic rate laws have been revealed in the preceding sections.In this section, some further discussions are made from different viewpoints.One of the interesting results is that the refined normality structure directly leads to the restriction on quasi-static extension or healing of Griffith cracks by Rice (1978),which has been briefed by Yang et al.(2004a).Based on the discussions,it may be concluded that the homogeneous kinetic rate laws can really be considered as an intrinsic property of certain materials,especially for microcracked solids.Rice(1975)has applied the normality structure to a material sample containing some distribution of Griffith cracks.Let the locus of all crack fronts be denoted by L and let d a be a function of position along L describing the amount of local advance of the cracks,and hence constituting the structural rearrangements.It is assumed that the surfaces of cracking have continuously turning tangent planes,without abrupt forking or branching.Therefore,Equation(5)becomesd p¼Àd p ¼1f d !1ZL½F d a d Lð56Þwhere F denotes the thermodynamic crack extension force per unit length along L.Here the discrete expression of Equation(5)is replaced by the continuous expression.Similarly,the flow potential defined in Equation(12) is rewritten asQ¼1VZLZ F_a d F d Lð57ÞThe requirement by the second law of thermodynamics is,in view of Equation(10),1 V ZL½F d a d L!0:ð58ÞAs pointed by Rice(1975),at any local crack front,F¼GÀ2 ð59Þwhere G is the Irwin energy release rate and is the surface free energy. Rather than the more usually cited condition that G¼2 for the onset of crack extension,Rice(1978)proposed the restriction on quasi-static extension or healing of Griffith cracks,ðGÀ2 Þ_a!0ð60Þat any local crack front.Evidently,the inequality(60)is only a sufficient condition for the requirement of the second law of thermodynamics, Equation(58),but not a necessary condition for the requirement.In other words,the Rice(1978)restriction is not a thermodynamic requirement which can only take the form,Equation(58).However,this inequality can be considered as the result of the homogeneous kinetic rate laws.The homogeneous crack kinetic rate laws in the sense of Equation(31)can be written as:@_a @F F¼q_a or_a¼Fq@_a@Fð61Þat each local crack front.The homogeneous kinetic rate laws lead to the local intrinsic dissipation inequality(48)which,in this case,can be rewritten as,at any local crack front,F_a!0orðGÀ2 Þ_a!0ð62Þwhich is just the Rice(1978)restriction on quasi-static growth of Griffith cracks.It is indicated in the following parts that the homogeneous condition equation(61)really holds for cracking due to the widely used power laws. The time-dependent subcritical crack growthÁ at a local crack front can often be covered by the following power-law,_a/K nð63Þwhere K is the stress intensity factor at the crack front.For example,n¼13 for the nickel-based superalloy Nimonic80A at a temperature of650 C (Delph,1999).The fatigue crack growth can also be described by similar power laws if taking cycle number N as the generalized time,e.g.,the simple Paris equation da=dN/ðÁKÞn,where the exponent n can take values as high as15–50in ceramics(Ritchie et al.,2000).Due to G/K2,the power law can be written as:_a/G q,or_a¼hG qð64Þwhere h and q(¼n/2)are material parameters.Except for an‘ideal’brittle cracking,the surface free energy is generally much smaller than the required energy release rate G,i.e., (G)G%F.Thus,the following crack kinetic rate law possesses a solid physical basis,_a¼hF qð65Þwhich is consistent with the homogeneous condition(61).Inserting Equation(65)into Equation(57),then yieldsQ¼1VZLZ_a d F d L¼hðqþ1ÞVZLF qþ1d L for_a¼hF qð66ÞDAMAGE CHARACTERISTIC TENSORSOF MICROCRACKED SOLIDSIn this part,microcracks and their propagation are considered as the dominant microdefects and energy dissipation mechanism in a solid.Indeed, microcracks attracted,and still attract,most interest due to its relevance to the structural reliability and failure,as remarked by Krajcinovic (2000).With the microcracks described in the section on‘‘Application。

Thermodynamics 课件

Adiabatic System: can exchange work with its surroundings, but not heat or matter -----------------------------------------------------------Property of a System: an observable characteristic of the system Extensive Property: a characteristic whose value depends on the quantity of matter considered (e.g.,mass, volume, energy)
Definitions (cont.) State Function: • a parameter that depends only on the change in the properties between an initial state and a final state (not on the path traversed from the initial to the final state) • a parameter that is a perfect differential Consider a property A that depends on the variables x and y, so that the function dA is given by: dA = [∂A/∂x|y]dx + [∂A/∂y|x]dy = L(x,y)dx + M(x,y)dy where L(x,y) and M(x,y) are also functions of x and y. dA is a perfect differential if and only if: ∂(∂A/∂x|y)/∂y|x = ∂(∂A/∂y|x)/∂x|y or ∂L/∂y|x = ∂M/∂x|y

化学及化工专业词汇英语翻译(A-C)2

化学及化工专业词汇英语翻译(A-C)2- -is 氨基分解aminonaphthol 氨基萘酚aminonaphthol sulfonic acid 氨基萘磺酸aminopeptidase 氨基胜胨酵素aminophenol 氨基苯酚aminophenylarsonic acid 氨基苯胂酸aminophosphorylase 淀粉磷酸化酶aminophylline 氨苯碱aminopolypeptidase 氨基多胜酵素aminoprotease 氨蛋白酶aminopterin 氨基蝶呤aminopyridine 氨基吡啶aminopyrin 氨基吡啉aminoquinoline 氨基喹啉aminosalicylic acid 氨基水杨酸aminosuccinic acid 氨基琥珀酸aminosulfonic acid 氨基磺酸aminotoluene 氨基甲苯ammeter 电另ammonal 阿芒拿ammonia 氨ammonia compressor 氨气压缩机ammonia gas 氨气ammonia poisoning 氨中毒ammonia still 氨气塔ammonia synthesis 氨合成ammonia water 氨水ammoniacal brine 氨盐水ammoniacal fermentation 氨发酵ammoniacal latex 氨胶乳ammoniameter 氨量计ammoniasoda process 氨碱法ammoniated superphosphate 含铵过磷酸钙ammoniator 氨化器ammoniometry 氨量测定法ammonite 阿芒炸药ammonium 铵ammonium acetate 乙酸铵ammonium alum 铵茂ammonium benzoate 安息香酸铵ammonium bifluoride 氟化氢铵ammonium borate 硼酸铵ammonium carbamate 氨基甲酸铵ammonium carbonate 碳酸铵ammonium chloride 氯化铵ammonium chromate 铬酸铵ammonium cyanate 氰酸铵ammonium dichromate 重铬酸铵ammonium fluoride 氟化铵ammonium formate 甲酸铵ammonium hydrogen carbonate 碳酸氢铵ammonium hydroxide 氢氧化铵ammonium iodate 碘酸铵ammonium iron sulfate 硫酸铁铵ammonium metavanadate 偏钒酸铵ammonium molybdate 钼酸铵ammonium nitrate 硝酸铵ammonium nitrate explosive 硝铵炸药ammonium nitrate fertilizer 硝铵肥料ammonium oxalate 草酸铵ammonium perchlorate 高氯酸铵ammonium persulfate 过硫酸铵ammonium phosphate 磷酸铵ammonium phosphite 亚磷酸铵ammonium phosphomolybdate 磷钼酸铵ammonium picrate 苦味酸铵ammonium polysulfide 多硫化铵ammonium rhodanide 硫氰酸铵ammonium salt 铵盐ammonium selenate 硒酸铵ammonium stearate 硬脂酸铵ammonium sulfate 硫酸铵ammonium sulfite 亚硫酸铵ammonium thiocyanate 硫氰酸铵ammonium thiosulfate 硫代硫酸铵ammonium uranate 铀酸铵ammonium vanadate 钒酸铵ammonobase 氨基金属ammonolysis 氨解ammophos 安福粉amobarbital 戊巴比妥amodiaquine 阿莫待喹amorphism 无定形amorphous carbon 无定形碳amorphous graphite 无定型石墨amorphous material 无定形材料amorphous metal 无定形金属amorphous phosphorus 无定形磷amorphous polymer 非晶态聚合物amorphous state 无定形状态amorphous sulfur 无定形硫ampere 安amperemeter 电另amperometric titration 电廖定amperometry 电廖定amphetamine 苯异丙胺amphibole 闪石amphipathic molecule 两亲水脂分子amphiphilic molecule 两亲水脂分子ampholyte 两性电解质ampholytic active agent 两性表面活性剂ampholytic surfactant 两性表面活性剂ampholytoid 两性胶体amphoteric 两性的amphoteric character 两性特征amphoteric colloid 两性胶体amphoteric compound 两性化合物amphoteric ion 两性离子amphoteric oxide 两性氧化物amphoteric resin 两性尸amphotericeledrolyte 两性电解质amplifier 放大器ampule 安瓿amygdalin 扁桃苷amyl 戊基amyl acetate 醋酸戊酯amyl alcohol 戊醇amyl bromide 戊基溴amyl butyrate 丁酸戊酯amyl ether 戊醚amyl formate 甲酸戊酯amyl mercaptan 戊硫醇amyl nitrite 亚硝酸戊酯amyl oleate 油酸戊酯amyl propionate 丙酸戊酯amylamine 戊胺amylase 淀粉酶amylbenzene 戊基苯amylene 戊烯amylo process 淀粉发酵法amylodextrin 淀粉糊精amyloid 淀粉状朊amylolysis 淀粉分解amylopectin 支链淀粉amylopsin 胰淀粉酶amylose 直链淀粉amytal 戊巴比妥anabasine 安纳巴松anabolism 同化酌anaerobe 厌氧微生物anaerobic glycolysis 无氧糖酵解analcime 方沸石analgesic 镇痛药analog digital conversion 模拟数字转换analog signal 模拟信号analogue 类似analogue computer 模拟计算机analysis 分析analysis line 分析线analysis with ion selective electrodes 离子选择电极分析法analyte 分析物analytic function 解析函数analytical balance 分析天平analytical chemistry 分析化学analytical extraction 分析抽出analytical method 分析法analytical reaction 分析反应analytically pure 分析纯anapaite 斜磷钙铁矿anaphoresis 阴离子电泳anatase octahedrite 锐钛矿anchor agitator 锚式搅拌器anchor stirrer 锚式搅拌器andalusite 红柱石andesite 安山岩andreasen pipet 安德烈森型吸管androsin 雄素androstane 雄烷androstendione 雄烯二酮androsterone 雄酮andrussow process 安德卢梭法anelasticity 滞弹性anemometer 风速计anemonin 白头翁脑aneroid barometer 空盒气压计anesthesin 氨基苯甲酸乙酯anesthetic 麻醉剂anethole 茴香脑aneurin 硫胺素angelica lactone 当归内酯angelica oil 当归油angiotensin 血管紧张肽angle of polarization 偏振光角angle of refraction 折射角angle of repose 休止角anglesite 硫酸铅矿angstrom 埃angular momentum 角动量anhalonine 老头掌碱anhydride 酐anhydrite 硬石膏anhydrone 无水高氯酸镁anhydrous 无水的anhydrous acid 无水酸anhydrous alcohol 无水酒精anhydrous ammonia 无水氨anhydrous salt 无水盐anileridine 氨苄哌替啶anilide 酰替苯胺aniline 苯胺aniline black 苯胺黑aniline blue 苯胺蓝aniline dye 苯胺染料aniline formaldehyde resin 苯胺甲醛尸aniline hydrochloride 盐酸苯胺aniline point 苯胺点aniline red 苯胺红aniline resin 苯胺尸aniline yellow 苯胺黄anilol 酒精苯胺混合液animal biochemistry 动物生化学animal charcoal 骨炭animal chemistry 动物化学animal dye 动物染料animal fat 动物脂animal fiber 动物纤维animal glue 动物胶animal oil 动物油anime 硬尸anion 阴离子anion active agent 阴离子表面活性剂anion exchange 阴离子交换anion exchange resin 阴离子交换尸anion exchanger 阴离子交换剂anionic polymerization 阴离子聚合anionic surfactant 阴离子表面活性剂anionoid reagent 类阴离子试剂anionotropy 阴离子移变现象anisaldehyde 茴香醛anise oil 茴香油anisic acid 茴香酸anisic alcohol 茴香醇anisidine 茴香胺anisole 茴香醚anisometric crystal 不等轴晶体anisotropic body 蛤异性体anisotropic liquid 蛤异性液体anisotropic membrane 蛤异性膜anisotropy 蛤异性anisoyl chloride 茴香酰氯anisyl acetate 醋酸茴香酯anisyl alcohol 茴香醇ankerite 铁白云石annabergite 镍华annealing 退火annealing furnace 退火窑annealing temperature 退火温度annulene 环轮烯anode 阳极anode effect 阳极效应anode process 阳极过程anode slime 阳极淀渣anodic oxidation 阳极氧化anodic polarization 阳极极化anodic reaction 阳极反应anodization 阳极化anodizing 阳极化anolyte 阳极电解液anomalous dispersion 异常弥散anomalous magnetic moment 异常磁矩anomalous skin effect 反常囚效应anomer 异头物anone 环己酮anorthoclase 钠斜微长石antagonism 拮抗酌antazoline 安他唑啉anthelmintics 驱肠虫剂anthocyan 花青素anthocyanidin 花色素anthocyanin 花色素苷anthophyllite 直闪石anthracene 蒽anthracene oil 蒽油anthracite 无烟煤anthracite duff 无烟煤粉anthralin 蒽啉anthranil 氨茴内酐anthranilate 邻氨基苯甲酸盐anthranilic acid 邻氨基苯酸anthranol 蒽酚anthranone 蒽酮anthrapurpurin 蒽红紫anthraquinone 蒽醌anthraquinone dye 蒽醌染料anthrarufin 蒽绛酚anthraxylon 结焦素anthrone 蒽酮anti allergic drug 抗过敏性药anti fouling paint 防污涂料anti tack agent 防粘剂antiacid 解酸药antiacid additive 抗酸添加剂antiager 抗老剂antiaromaticity 反芳香性antibiosis 抗生antibiotics 抗生物质antibody 抗体antibonding orbital 反键轨道anticarcinogen 抗癌物anticatalyst 抗催化剂anticathode 对阴极antichlor 脱氯剂anticholinesterase 抗胆碱酯酶剂anticoagulant 抗凝剂anticoagulating action 阻凝酌anticonvulsant 镇痉剂anticorrosion 抗腐蚀anticorrosive agent 防腐蚀剂anticorrosive paint 防腐涂料antidetonant 抗爆剂antidote 解毒剂antienzyme 抗酶antifertilizin 抗受精介体antifibrinolysin 抗纤维蛋白酶antifoamer 抗泡剂antifoaming agent 抗泡剂antifouling paint 防污漆antifreezing agent 阻冻剂antigen 抗原antihistamine 抗组胺剂antihistaminic agent 抗组胺剂antiknock agent 抗爆剂antiknock gasoline 抗爆汽油antiknocking fuel 抗爆燃料antimetabolite 抗代谢物antimonate 锑酸盐antimonial lead 锑铅antimonic acid anhydride 锑酸酐antimonide 锑化物antimonite 亚锑酸盐antimony 锑antimony chloride 氯化锑antimony electrode 锑电极antimony hydride 氢化锑antimony oxide 氧化锑antimony pentachloride 五氯化锑antimony potassium tartrate 酒石酸锑钾antimony red 锑红antimony sulfate 硫酸锑antimony sulfide 硫化锑antimony trisulfide 三硫化二锑antimony vermillon 锑朱antimony white 锑白antineuralgic 治神经痛药antinucleon 反核子antioxidant 抗氧化剂antiozonant 抗臭氧剂antiparticle 反粒子antipode 对映体antiproton 反质子antipyretic and analgesic 解热镇痛药antipyrine 安替吡啉antiscorbutic vitamin 抗坏血病维生素antiscorcher 防焦剂antiscorching agent 防焦剂antisepsis 防腐antiseptics 防腐剂antispasmodic 镇痉剂antistat 抗静电剂antistatic agent 抗静电剂antitermination factor 抗终止因素antithrombin 抗凝血酶antitoxin 抗毒素antivitamin 抗维生素apatite 磷灰石aphthitalite 硫酸钾石apiin 芹实苷apiose 洋芹糖aplysiopurpurin 海螺紫apocodeine 阿朴可特因apoenzyme 酶朊apoferritin 脱铁铁蛋白apomorphine 阿朴吗啡apoprotein 脱辅基蛋白apozymase 酒化酶原apparatus 装置apparent activation energy 表观活化能apparent density 表观密度apparent equilibrium 表观平衡apparent specific gravity 表观比重apparent viscosity 表观粘度applied chemistry 应用化学applied thermodynamics 应用热力学approximate calculation 近似计算approximate value 近似值aprotic solvent 非质子溶剂aqua ion 水合离子aqua regia 王水aquagel 水凝胶aquametry 测水法aqueous emulsion 水乳状液aqueous medium 水介质aqueous phase 水相aqueous solution 水溶液aqueous vapor 水蒸汽arabic acid 阿糖酸arabic gum 阿拉伯胶arabinose 阿拉伯糖arabitol 阿糖醇arabonic acid 阿糖酸arachic acid 花生酸arachidonic acid 花生四烯酸arachis oil 花生油aragonite 霰石aralkyl 芳烷arbutin 熊果苷arc furnace 电弧炉arc process 电弧法arc spectrum 弧光谱arch brick 拱砖archeochemistry 考古化学arecoline 槟榔素areometer 比重计areometry 比重测定法argentite 辉银矿argentometry 银量滴定argillaceous sand 粘质砂土argillite 泥质板岩arginase 精氨酸酶arginine 精氨酸argol 粗酒石argon 氩aristolochic acid 马兜铃酸arnicin 由金车苦素aroma 香味aromatic acid 芳族酸aromatic aldehyde 芳族醛aromatic amine 芳香胺aromatic compound 芳族化合物aromatic hydrocarbon 芳香烃aromatic nucleus 芳香环aromatic series 芳香系aromaticity 芳香度aromatization 芳香化aromatization reaction 芳香化反应aroylation 芳酰基化arrhenius equation 阿雷尼厄斯方程arsanilic acid 阿散酸arsenate 砷酸盐arsenazo i 偶氮胂arsenblende 雄黄arsenic 砷arsenic acid 砷酸arsenic butter 三氯化砷arsenic glass 砷玻璃arsenic hydride 砷化三氢arsenic mirror 砷镜arsenic sulfide 硫化砷arsenic trichloride 三氯化砷arsenic trioxide 三氧化二砷arsenic trisulfide 三硫化二砷arsenide 砷化物arsenite 亚砷酸盐arseno compound 偶砷化合物arsenobenzene 偶砷苯arsenometry 亚砷酸滴定法arsenopyrite 砷黄铁矿arsenous anhydride 亚砷酸酐arsine 胂arsonic acid 胂酸arsonium 氢化砷arsonium compound 胂化合物arsphenamine 胂凡纳明art glass 艺术玻璃art paper 加工印刷纸artemisin 蒿属素arthropodin 节肢蛋白artiad 偶价元素artificial abrasive 人造磨料artificial aging 人工老化artificial almond oil 人造扁桃油artificial asphalt 人造地沥青artificial atmospher 人工气氛artificial butter 人造奶油artificial camphor 人造樟脑artificial corundum 人造金刚砂artificial diamond 人造金刚石artificial dye 人造染料artificial fertilizer 人造肥料artificial fiber 人造纤维artificial intelligence 人工智能artificial lattice 人工晶格artificial leather 人造革artificial musk 人造香artificial perfume 人造香料artificial radioactivity 人工放射性artificial resin 人造尸artificial rubber 人造橡胶artificial silk 人造丝artificial stone 人造石aryl compound 芳基化合物aryl halide 芳基卤arylamine 芳基胺arylation 芳基化arylide 芳基化物aryloxy compound 芳氧基化合物arylsulphonate 芳基磺酸盐asarin 细辛脑asarone 细辛脑asbestine 滑石棉asbestos 石棉asbestos board 石棉纸板asbestos cement 石棉水泥asbestos cloth 石棉布asbestos felt 石棉毛毯asbestos fiber 石棉纤维asbestos filter 石棉滤器asbestos insulation 石棉绝热体asbestos paper 石棉纸asbestos powder 石棉粉asbestos slate 石棉板asbestos wire gauze 石棉衬网asbestos yarn 石棉丝asbolane 钴土矿asbolite 钴土矿ascaridol 驱蛔脑ascending method 上行法ascorbic acid 抗坏血酸asepsis 防腐ash 灰ash bath 灰浴ash collector 除尘器ash content 灰分含量ash ejector 灰喷射器ash pit door 灰坑门ash softening point 灰熔温度ashing 灰化ashless filter paper 无灰滤纸asparaginase 天门冬酰胺酶asparagine 天门冬酰胺aspartase 天门冬氨酸酶aspartate 天冬氨酸盐aspartic acid 天冬氨酸aspartokinase 天冬氨酸激酶aspartyl phosphate 天冬氨酰磷酸aspergillic acid 曲霉酸asphalt 沥青asphalt cement 沥青膏asphalt emulsion 地沥青乳液asphalt mastic 地沥青砂胶asphalt varnish 沥青油漆asphaltene 沥青烯asphaltic road oil 沥青质铺路油asphaltogenic acid 沥青酸asphaltous acid 沥青酸asphyxia 窒息asphyxiant 窒息剂asphyxy 窒息aspirator 吸气器aspirin 阿司匹林assay 试金assay balance 试金天平assay flask 试验瓶assayer's tongs 试金钳assili cotton 阿嘻棉assimilation 同化assimilation starch 同化淀粉assistant 助剂associated liquid 缔合液体association 缔合assortment 分类astacin 虾红素astatine 砹astaxanthin 虾青素astringency 收敛性astringent 收敛剂astrochemical 天体化学的astrochemist 天体化学家astrochemistry 天体化学astrogeochemical 天体地球化学的astrogeochemistry 天体地球化学asymmetric atom 不对称原子asymmetric carbon atom 不对称碳原子asymmetric oxidation 不对称氧化asymmetric structure 不对称结构asymmetric synthesis 不对称合成asymmetric system 不对称系asymmetry 不对称asymptotic freedom 渐近自由性atactic 无规立构的atactic polymer 无规聚合物atebrine 疟涤平atmolysis 微孔分气法atmosphere 大气atmospheric air 大气空气atmospheric corrosion 大气腐蚀atmospheric nitrogen 大气氮atmospheric pressure 大气压atom 原子atomic absorption spectrometry原子吸收分光光度法atomic arrangement 原子排列atomic battery 原子电池atomic beam 原子束atomic bomb 原子弹atomic bond 原子键atomic charge 原子电荷atomic clock 原子钟atomic core 原子核atomic dispersion 原子分散atomic energy 原子能atomic fluorescence spectrometry 原子荧光光谱法atomic form factor 原子散射因子atomic group 原子团atomic heat 原子热atomic hydrogen 原子氢atomic hydrogen welding 原子氢焊接atomic hypothesis 原子假说atomic lattice 原子晶格atomic magnetism 原子磁性atomic mass 原子质量atomic mass unit 原子质量单位atomic model 原子模型atomic molecular theory 原子分子论atomic nucleus 原子核atomic number 原子序atomic orbital 原子轨道atomic polarization 原子极化atomic properties 原子特性atomic radius 原子半径atomic refraction 原子折射atomic scattering factor 原子散射因子atomic spectrum 原子光谱atomic structure 原子结构atomic susceptibility 原子磁化率atomic symbol 原子符号atomic theory 原子论atomic unit 原子单位atomic volume 原子体积atomic weight 原子量atomicity 原子数atomism 原子论atomistics 原子论atomization 喷雾atomizer 喷雾器atophan 阿托方atrazine 阿特拉津atropic acid 阿托酸atropine 阿托品atropine sulfate 硫酸阿托品atropisomer 阿托异构体attachment 附件attrition 磨损aufbau principle 构造原理augmentation distance 扩增距离auramine 金胺aurantia 金橙黄aurantin 橙色菌素aurate 金酸盐aureomycin 金霉素aureusidin 金色草素auric acid 金酸auric compound 正金化合物auric oxide 氧化金auric salt 正金盐aurin 金精aurin tricarboxylic acid 铝试剂auripigment 雄黄aurothioglucose 金硫葡萄糖aurous chloride 氯化亚金aurous compound 亚金化合物aurous oxide 氧化亚金aurous salt 亚金盐austenite 奥氏体auto condensation 自动缩合autocatalysis 自动催化autocatalyst 自动催化剂autocatalytic reaction 自动催化反应autoclave 压热器autocomplex 自动合成物autocorrelation function 自相关函数autofermentation 自动发酵autogenous ignition 自动着火autoionization 自电离autolysis 自溶酌autolytic enzyme 自溶酶automatic analyser 自动分析计automatic balance 自动天平automatic buret 自动滴定管automatic control 自动控制automatic regulation 自动控制automatic temperature controller 自动温度控制器automatic thermoregulator 自动温度控制器automatic titration 自动滴定automatic weighing machine 自动秤automation 自动化autometer 汽车速度表autopolymerization 自动聚合autoprotolysis 自质子解autoracemization 自动外消旋autotetraploid 同源四倍体autotransformer 单卷变压器autovulcanization 自动硫化autoxidation 自氧化autunite 钙铀云母auxiliary air 辅助空气auxiliary electrode 辅助电极auxiliary unit 辅助单位auxiliary valency 副价auximone 茁长激素auxin 茁长素auxochrome 助色团availability 有效性available chlorine 有效氯available energy 有效能available phosphoric acid 有效磷酸avenin 燕麦蛋白average boiling point 平均沸点average degree of polymerization 平均聚合度average error 平均误差average life 平均寿命average mean molecular weight 平均分子量average molecular weight 平均分子量average particle diameter 平均粒子直径average sample 平均试样average speed 平均速度average value 平均值aviation gasoline 航空汽油aviation mix 航空汽油抗爆液avidin 抗生物素蛋白avocado oil 鳄梨油avogadro number 阿伏伽德罗数avogadro's hypothesis 阿伏伽德罗假说avogadro's law 阿伏伽德罗定律axial bond 贮axial flow pump 轴撩axiomatic quantum field theory 公理的量子场理论axis 轴axis of rotation 旋转轴azaserine 重氮丝氨酸azelaic acid 杜鹃花酸azeotrope 共沸混合物azeotropic copolymer 共沸共聚物azeotropic distillation 共沸蒸馏azeotropic mixture 共沸混合物azeotropic point 共沸点azeotropy 共沸性azide 叠氮化物azimuthal 方位的azimuthal quantum number 角量子数azine 吖嗪azine dye 吖嗪染料aziridine 氮杂环丙烷azlactone 吖内酯azlon 人造蛋白质纤维azo compound 偶氮化合物azo coupling 偶氮耦合azo dye 偶氮染料azo group 偶氮基azobenzene 偶氮苯azodicarbonamide 偶氮甲酰胺azoimide 叠氮化氢azole 唑azolitmin 石蕊精azotometer 氮素计azoxy compound 氧化偶氮化合物azoxybenzene 氧化偶氮苯azulene 甘菊环烃azurite 蓝铜矿b stage resin b 阶尸baby dryer 小烧缸bacillus 杆菌bacitracin 杆菌肽back bond 反向键back flow condenser 回龄凝器back mixing 逆向混合back pressure 反压back reaction 逆反应back sweetening 返回脱硫法back titration 回滴定backfire 回火backflash 反闪backscattering 后方散射backward motion 反向运动backwash 回洗bacteria 细菌bacterial fertilizer 细菌肥料bacterial incubator 细菌培育箱bactericide 杀细菌剂bacteriochlorophyll 菌叶绿素bacteriolysis 溶菌酌bacteriostasis 抑菌酌baddeleyite 斜锆石baeyer reaction 拜尔反应baeyer reagent 拜尔试药baeyer villiger rearrangement 拜尔维利格重排baffle 挡板bag filter 袋滤器bagasse 甘蔗渣bakelite 酚醛塑料baking 烧制baking enamel 烘烤搪瓷baking powder 发粉baking varnish 烤漆balance 平衡balance bar 平衡杆balance beam 平衡杆balance pan 天平盘balance rider 游码balata 巴拉塔矢ball clay 块状粘土ball hardness 钢球硬度ball mill 球磨机ball valve 球阀ball viscosimeter 落球式粘度计balloon tire 低压轮胎balsam 香脂banana oil 香蕉油band brake 带式制动器band dryer 带式干燥机band spectrum 带光谱barbital 巴比妥barbituric acid 巴比土酸barilla 海草灰苏打barite 重晶石barium 钡barium acetate 醋酸钡barium bioxide 二氧化钡barium carbonate 碳酸钡barium chlorate 氯酸钡barium chloride 氯化钡barium chromate 铬酸钡barium crown glass 钡钙玻璃barium cyanate 氰酸钡barium dioxide 二氧化钡barium flint glass 钡火石玻璃barium fluoride 氟化钡barium hydroxide 氢氧化钡barium manganate 锰酸钡barium nitrate 硝酸钡barium nitrite 亚硝酸钡barium oxide 氧化钡barium perchlorate 高氯酸钡barium peroxide 过氧化钡barium sulfate 硫酸钡barium sulfide 硫化钡barium thiosulfate 硫代硫酸钡barium titanate 钛酸钡barium yellow 钡黄barkometer 液比重计barley malt 大麦芽barley sugar 大麦糖barm 酒母barometer 气压计barometric condenser 气压冷凝器barrel 桶;卷筒barrier penetration 势垒穿透barrier separation 膜分离baryta 氧化钡baryta paper 钡地纸baryta water 氢氧化钡水溶液baryta yellow 钡黄baryte 重晶石basal metabolic rate 基础代谢率basal metabolism 基础代谢basalt 玄武岩base 碱base catalysis 碱催化酌base exchange 碱交换base line 基线base metal 贱金属base solution 底液basic acetate 碱式乙酸盐basic bismuth carbomate 碱式碳酸铋basic bismuth nitrate 碱式硝酸铋basic converter 碱性转炉basic dye 碱性染料basic function 基础函数basic lead carbonate 碱式碳酸铅basic material 基本材料basic open hearth process 碱性平炉法basic oxide 碱性氧化物basic reaction 碱性反应basic refractory 碱性耐火材料basic salt 碱性盐basic slag 碱性炉渣basicity 碱度basil 罗勒basket strainer 篮过滤器bast fiber 韧皮纤维batch distillation 分批蒸馏batch extraction 分批萃取batch mixer 分批混合器batch process 分批法batch rectification 分批精馏batchwise operation 分批操作bath ratio&n。

化工热力学英文词汇

thermodynamics n. 热力学 system n. 体系 thermodynamic state 热力学状态 dimension 量纲 SI= International System of Units 国际单位制强度（热力学）变量广度（热力学）变量celsius scale 摄氏刻度 → fahrenheit scale 华氏刻度 kelvin scale 开尔文刻度 → Rankine scale dead-weight gauge 静压、压力表 mano meter （流体）压力计 product 乘积 kinetic energy 动能 221mu E k = potential energy 势能mgz E P =conservation守恒* Terms in chapter 2sublimation curve 升华线 fusion curve 熔融线vaporization curve （蒸发）汽化线single-phase region 单相区 triple point 三相点univariant 单变量 divariant 多变量critical point 临界点 critical pressure 临界压力critical temperature 临界温度dome-shaped curve 圆拱形曲线saturated vapors at their condensation temperatures 露点的饱和蒸汽 saturated liquids at their vaporization(boiling) temperatures 泡点的饱和液体vapor pressure 蒸汽压subcooled-liquid region 过冷液体区 superheated-vapor region 过热蒸汽区partial derivative 偏导数differentiate v . 求微分，求导 differentiation n. derivate n. 求导数 derivation 求导数，求解incompressible fluid 不可压缩流体 ideal-gas理想气体simple fluid简单流体（argon 、krypton 、xenon ）virial expansion维里展开式 virial coefficients 维里系数 virial equation维里方程equation of state状态方程compressibility factor 压缩因子 RTPVZ = volume expansivity体积膨胀系数PT V V ⎪⎭⎫ ⎝⎛∂∂=1βisothermal compressibility 等温压缩系数 TP V V ⎪⎭⎫ ⎝⎛∂∂=1κ acentric factor偏心因子isothermal process 等温过程 isobaric process 等压过程 isochoric process等容过程 adiabatic process 绝热过程 polytropic process 多变过程throttling process节流过程 0=∆Htruncate equation to two terms 截断方程前二项 cubic equation of state 立方型状态方程reduced pressure 对比压力 reduced temperature 对比温度 reduced density对比密度corresponding-state parameters 对应态参数 generalized correlations 普遍化关联nonpolar非极性的 slightly polar 弱极性的 highly polar高极性的volumetric properties 容积性质 realistic 现实主义的，逼真的dashed line虚线dotted line 点线 straight line 实线Terms in chapter 3internal energy 内能 transport across kinetic energy 动能 221mu E t =potential energy 势能 m g z E p = conservation 守恒operator 算符，运算符（such as “Δ”） system 体系 surroundings 环境 closed system 封闭体系 open system 开放体系finite change 有限的变化 infinitesimal change 无限的变化 differential change 微分（小）的变化 intensive property 强度性质 extensive property 广度性质specific or molar property 单位（比）性质或摩尔性质 property — variable — functionthermodynamics state of the system 体系热力学状态 thermodynamics properties 热力学性质 state function(s) 状态函数equilibrium 平衡 (the) phase rule 相率reversible process 可逆过程irreversible process 不可逆过程mechanically reversible 机械可逆thermostate 恒温箱constant—temperature bath 恒温浴efficiency 效率，（有效）系数enthalpy 焓heat capacity 热容constant—volume heat capacity 恒容热容constant—pressure heat capacity 恒压热容vector quantity 矢量scalar magnitude 数量，纯量continuity equation 连续方程steady state (flow process) 移去（流动过程）datum level 基准面shaft work 体积功stirring work 搅拌功work associated with moving the flow streams 流动功expansion work 膨胀功surface work 表面功electricity work 电功calorimeter 量热计(测定焓)intensive property 强度性质extensive property 广度性质shaft work 轴功enthalpy 焓entropy 熵heat-capacity 热容Gibbs energy (G) 吉布斯自由能Helmholtz energy (A) 亥姆霍茨自由能internal energy 内能system 系统，体系close system 封闭体系equilibrium state 平衡态total differential of F F的全微分exact differential expression 全微分表达式Maxwell equations 麦克斯威尔方程homogeneous fluid 均相流体residual property 剩余性质real gas 真实气体actual gasideal gas 理想气体explicit function 显函数volume explicit 体积显函数pressure explicit 压力显函数isentropic process 等熵过程reversible adiabatic process 绝热可逆过程pseudocritical parameter 虚拟临界参数path variables 过程变量state variables 状态变量constant pressure heat capacity CP 等压热容constant volume heat capacity C V 等容热容residual property 剩余性质reference state 参比态reference conditionpartial derivative 偏导数total derivative 全导数β volume expansivity 体积膨胀系数κ isothermal compressibility 等温压缩系数quality 干度fugacity 逸度fugacity coefficient 逸度系数*Terms in Chapter 4chemical potential 化学势，化学位partial property 偏性质partial molar property 偏摩尔性质ideal solution 理想溶液real solution 真实溶液excess property 超额/过量性质excess Gibbs energy 超额/过量自由焓partial excess property 偏摩尔超额/过量性质activity 活度activity coefficient 活度系数standard state 标准态property change of mixing 混合性质regular solution 正规溶液atherpical solution 无热溶液local-composition 局部组成local molar fraction 局部摩尔分数*Terms in Chapter 5First Law of thermodynamics（energy conservation law）热力学第一定律steady-state flow processes 稳定状态流动过程control volume 控制体heat Engines 热机Carnot engine 卡诺热机thermal efficiency 热效率thermodynamic efficiency 热力学效率isentropic efficiency 等熵效率ideal work and lost work 理想功和损耗功exergy 火用available Energy, availability, utilizable Energy 有效能*Terms in Chapter 6steam Power cycle 蒸汽动力循环Carnot-engine cycle 卡诺循环cycle with feed water heaters 抽气回热循环heat-power cycle 热电循环exhaust steam 乏气heat reservoir 热源working substance of the engine 工质specific steam consumption 汽耗率SSCrefrigeration Cycle 制冷循环vapor-compression cycle 蒸汽压缩（制冷）循环absorption refrigeration 吸收式制冷Carnot refrigeration 卡诺冷机reversed heat-engine cycle 逆热机循环multi-stage compression refrigeration多级压缩制冷heat pump 热泵throttling expansion process 节流膨胀过程reversible adiabatic expansion process 可逆绝热膨胀过程inversion curve and inversion point 转变曲线和转变点condenser 冷凝器expander 膨胀机compressor 压缩机evaporator 蒸发器supheater 过热器turbine 透平机boiler 锅炉pump 泵*Statements of the second lawstatement1: No apparatus can operate in such a way that its only effect (in system and surrounings) is to convert heat absorbed by a system completely into work done by the system。

Thermodynamics培训课件.ppt

pick any two points on the equilibrium curve dDG = 0 = DVdP - DSdT
Thus dP = DS dT DV
Figure 27.1. Temperature-pressure phase diagram for the reaction: Albite = Jadeite + Quartz calculated using the program TWQ of Berman (1988, 1990, 1991). Winter (2010) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.
G P2 - G P1 = RT
P2 1 P1 P
dP
Gas Pressure-Volume Relationships
z1
And since
dx = ln x
x
GP2 - GP1 = RT ln P2 - ln P1 = RT ln (P2/P1)
Thus the free energy of a gas phase at a specific P and T, when referenced to a standard atate of 0.1 MPa becomes:
Thermodynamics
For other temperatures and pressures we can use the equatig DX for now)
where V = volume and S = entropy (both molar)
How do you know which side has which phases?

StochasticProcessesinPhysicsandChemistry

PY542INFORMATION Fall2008Instructor:Sidney Redner(321SCI,x2618)Oﬃce Hours:Tues.&Fri.9-10:30am,and by appointment.General:This course treats non-equilibrium statistical mechanics and transport phenom-ena.Because of the rapid developments in theﬁeld,the breadth of topics,and the lack of an established formalism,most of the classic texts no longer seem appropriate for this course.For this reason,the“unoﬃcial”course text is a book that I am currently writing with2co-authors.It is continuously being updated and individual chapters are posted on the course website.Other books that should be helpful during the semester include:(i)N.G.Van Kampen,Stochastic Processes in Physics and Chemistry(North-Holland). This gives an excellent treatment of stochastic processes.Buy it used if you can.I would have assigned this as the text if the price was a factor2smaller.(ii)S.Redner,A Guide to First-Passage Processes(Cambridge University Press).This book gives background on random walks and diﬀusion processes,as well as a reference for the portion of the course onﬁrst-passage phenomena.If you purchase the hardcover version,I will refund you my royalty(approximately$5.50per book),but the paperback version is much cheaper.I will also post relevant excerpts on the course website. (iii)F.Reif,Statistical and Thermal Physics(McGraw-Hill).A standard advanced un-dergraduate text for statistical mechanics.The last few chapters provide a particularly useful introduction to various aspects of non-equilibrium processes.(iv)K.Huang,Statistical Mechanics2nd edition(Wiley).Relevant chapters are3and 5that deal with kinetic theory and transport phenomena.(i)N.Wax(editor),Selected Papers on Noise and Stochastic Processes(Dover).This book contains reprints of some of the most important classic research articles on stochas-tic processes.Although out of print,it may be possible to obtain used somewhere.How-ever,the book contains reprints of articles that are generally available on the web.The most useful is“Stochastic Problems in Physics in Astronomy”by S.Chandrasekhar, Rev.Mod.Phys.15,1–89(1943).Other useful articles include“On the Theory of the Brownian Motion”,by G.E.Uhlenbeck and L.S.Orenstein,Phys.Rev.26,823–41(1930)&“On the Theory of the Brownian Motion II”by M.C.Wang and G.E. Uhlenbeck,Rev.Mod.Phys.17,323–42(1945).(v)R.Kubo,M.Toda and N.Hashitsume,Statistical Physics II(Springer-Verlag). Contains a particularly good discussion of linear response theory and theﬂuctuation-dissipation theorem.(vi)J.A.McLennan,Introduction to Non-Equilibrium Statistical Mechanicsi(Prentice-Hall).This book contains a thorough discussion of the Boltzmann transport equation. (vii)H.J.Kreuzer,Non-Equilibrium Thermodynamics and its Statistical Foundations (Oxford University Press).Comprehensively treats transport theory from the macro-scopic viewpoint and has an excellent discussion of the Rayleigh-B´e nard instability.Course organization:Lectures:Lectures will be held on Tuesdays and Thursdays from2:00—3:30in SCI B58.The accompanying outline represents a rough approximation to the material that will be covered this semester.Discussion:Sections will be held weekly starting Wed.Sept.3at2:00pm in PRB365.Homework:Approximately10assignments will be handed out.While some collab-oration on homework is acceptable,what is turned in should represent your personal eﬀort.Exams and Grading:The average of the homeworks will count approximately30±5% of the total class grade.I will give one midterm exam(exact format to be determined) that will count approximately30±5%of the total class grade.For theﬁnal,I am currently planning a take-home but time-limitedﬁnal exam that will count for the approximately remaining40%of the total course grade.。

On Phantom Thermodynamics

a rXiv:086.682v1[gr-qc]4J un28On Phantom Thermodynamics S.H.Pereira ∗and J.A.S.Lima †Departamento de Astronomia,Universidade de S˜a o Paulo Rua do Mat˜a o,1226-05508-900,S˜a o Paulo,SP,Brazil Abstract The thermodynamic properties of dark energy ﬂuids described by an equation of state parameter ω=p/ρare rediscussed in the context of FRW type geometries.Contrarily to previous claims,it is argued here that the phantom regime ω<−1is not physically possible since that both the temperature and the entropy of every physical ﬂuids must be always positive deﬁnite.This means that one cannot appeal to negative temperature in order to save the phantom dark energy hypothesis as has been recently done in the literature.Such a result remains true as long as the chemical potential is zero.However,if the phantom ﬂuid is endowed with a non-null chemical potential,the phantom ﬁeld hypothesis becomes thermodynamically consistent,that is,there are macroscopic equilibrium states with T >0and S >0in the course of the Universe expansion.PACS numbers:Dark energy models,phantom cosmologyI.INTRODUCTIONSeveral kinds of complementary astronomical observations indicate that the Universe is expanding in an accelerated form and that the transition(from a decelerating to an accelerating regime)occurred at a redshift of the order of unity[1,2].In the context of general relativity,an accelerating stage and the associated dimming of type Ia Supernovae are usually explained by assuming the existence of an exotic substance with negative pressure sometimes called dark energy.Actually,for dark energy dominated models,the scale factor evolution is governed by the equation3¨a/a=−4πG(ρ+3p),and means that a hypothetical component with negative pressure satisfying p<−ρ/3may accelerate the Universe(¨a>0).There are many candidates to represent this extra non-luminous relativistic component. In the case of XCDM cosmologies,for instance,it can be phenomenologically described by an equation of state(EoS)of the form[3]p=ωρ,(1)where p andρdenotes the pressure and energy density,respectively,andωis a constant negative parameter.The caseω=−1corresponds to a positive cosmological constant,or vacuum energy,while forω<−1we have the so called phantom dark energy regime[4],or phantomﬂuids1.The case for a phantom dominated Universe has beenﬁrst suggested with basis on SN-Ia analysis alone which favorω<−1more than cosmological constant or quintessence[5].A more precise observational data analysis(involving CMB,Hubble Space Telescope,type Ia Supernovae,and2dF data sets)allows the equation of state p=ωρwith a constantωon the interval[-1.38,-0.82]at the95%C.L.[6].From a theoretical point of view,the study of phantom regime is also a very interesting subject mainly due to a long list of pathologies.Initially,it was criticized by several authors due to issues of stability[7,8,9]which must be added to some weird properties,like the possibility of superluminal sound speed,as well as the violation of some classical energy conditions[10].In particular,since(p+ρ<0)one may see that it violates the strong and dominant energy conditions.Further,the energy density of a phantomﬁeld increasesalong the cosmic evolution thereby causing a super accelerating universe which will end in a doomsday state dubbed Big Rip[11]which is of type I singularity according to the Barrow classiﬁcation scheme[12].Such a Big Rip singularity corresponds toρ→∞at aﬁnite time in the future which presumably will be avoided only if one considers possible eﬀects from quantum gravity.Another interesting point concerns the study of the spectral distribution and some related thermodynamical properties of the phantomﬂuid,like their temperature and entropy.We have two diﬀerent approaches to study the thermodynamic of phantomﬂuids.Theﬁrst, based on a somewhat ambiguous thermodynamic deduction[14](see discussion in section II),was given by Gonz´a lez-D´ıaz and C.L.Sig¨u enza[13],which claimed that the temperature of phantomﬂuids in a Friedmann-Robertson-Walker(FRW)geometry should be negative and deﬁned by the scaling lawT∼(1+ω)a−3ω,(2) where a(t)is the scale factor(note the negative prefactor,1+ω,multiplying the power of the FRW scale function).By adopting such a temperature reinterpretation,it was possible to keep the entropy of the phantomﬁeld positive deﬁnite as required by its probabilistic deﬁnition in the context of statistical mechanics.In a second approach,a group of authors [15,16]have advocated that the temperature of any dark energy component is always positive deﬁnite obeying the evolution lawT∼a−3ω,(3)and,more important,that the existence of phantomﬂuids is not thermodynamically con-sistent because its co-moving entropy is negative since S∼(1+ω)T1/ωa3.In this approach, a possible way to save the phantom regime is to introduce a negative chemical potential to theﬂuid[17],so that the phantom hypothesis is recovered.In this note we have the intention to shed some light on this discussion,by favoring a phantom component with positive temperature,and,under certain thermodynamic condi-tions,with positive entropy.II.THERMODYNAMIC ANALYSIS OF DARK ENERGY FLUIDS For simplicity,let us now consider that the homogeneous and isotropic FRW universemodel is dominated by a separately conserved dark energyﬂuiddescribed by the EoS(1).Following standard lines(see,for instance,Kolb and Turner[18]),the combination of the ﬁrst and the second law of thermodynamics applied to a co-moving volume element of unit coordinate volume and physical volume V=a3,implies thatT dS=d(ρV)+pdV≡d[(ρ+p)V]−V dp,(4)whereρand p are the equilibrium energy density and pressure.The integrability condition,∂2S∂V∂T.(5)leads to the following relation between the energy density and pressure(ρand p depends only on the temperature)dp=ρ+pT d[(ρ+p)V]−(ρ+p)VdTT+C ,(7)where C is a constant(from now onﬁxed to be zero).Therefore,up to an additive constant, the entropy per co-moving volume must be deﬁned byS≡(ρ+p)T =0,(9) which means that the entropy S per co-moving volume is conserved.The same deﬁnition of entropy follows from the energy conservation law,d(ρV)+pdV=0,which can be rewritten asd[(ρ+p)V]=V dp.(10)As expected,by inserting(6)into(10)one obtains(9).Now,using the equation of state (1),we may write the entropy density on the forms≡ST=(1+ω)ρnamics.More important still for the discussion here,the temperature as deﬁned by1∂U V,N,(14) is always positive deﬁnite for the equilibrium states.Therefore,if the energy density in the cosmological FRW context is positive(weak energy condition)one may conclude from(8), or directly from(11),that the entropy for a phantomﬂuid(ω<−1)is negative deﬁnite, and,therefore,such a component is thermodynamically forbidden.Note also that all dark energyﬂuids withω>−1have positive entropies,a result obtained before the Supernovae observations[15].In addition,once the dependence of the energy density on the scale factor ρ(a)is established for an expanding adiabatic Universe,the expression for the entropy itself determines the temperature evolution law as happens for the cosmic background radiation (ω=1/3).Naturally,this approach to determine the temperature law is not valid if the system evolves trough a sequence of non-equilibrium states as happens when bulk viscosity [21]or irreversible matter creation[22]mechanisms are taken into account.It should also be remarked that the temperature evolution law can also be obtained even when the hypothesis that the energy density and pressure are functions only on the temperature and does not need to be explicitly used as discussed above.This approach will be discussed in the next section by using only local variables in the FRW background.III.TEMPERATURE EVOLUTION LA W IN THE FR W GEOMETRY The equilibrium thermodynamic states of a relativistic simpleﬂuid obeying theω-EoS can be completely characterized by the conservation laws of energy,the number of particles, and entropy.In terms of speciﬁc variables,ρ,n(particle number density)and s(entropy density)the above quoted laws for a FRW type background can be expressed as˙ρ+3(1+ω)ρ˙aa=0,˙s+3s˙aa 3(1+ω),n=n0 a0a 3,(16)whereρ0,n0,s0and a0are present day(positive)values of the corresponding quantities.On the other hand,the quantities p,ρ,n and s are related to the temperature T by the GibbslawnT d s n dn,(17) and from the Gibbs-Duhem relation(13)there are only two independent thermodynamic variables,say n and T.Therefore,by assuming thatρ=ρ(T,n)and p=p(T,n),one may show that the following thermodynamic identity must be satisﬁedT ∂p∂n T,(18) an expression that remains locally valid even for out of equilibrium states[23].Now,inserting the above expression into the energy conservation law as given by(15)one may show thatthe temperature satisﬁes˙T∂ρ n˙n a,(19) and assumingω=0a straightforward integration yieldsn=n0 Tω⇔T=T0 aωV remains constant and must char-acterize the equilibrium states(adiabatic expansion).At this point,the above temperature law,T∼a−3ω,should be compared with the one proposed in Refs.[13,14],namely, T∼(1+ω)a−3ω.It shows that the prefactor(1+ω)in the temperature law is completely artiﬁcial,and,therefore,it has no physical meaning.Moreover,the entropy expression as given by the Euler relation(8)withµ=0,is just telling us that the phantomﬂuid is ther-modynamically forbidden because the entropy of a dark energyﬂuid becomes negative for ω<−1.In an attempt to turn acceptable a phantomﬂuid with negative temperature,the authors of Ref.[13]comment on some quantum mechanical systems with negative temperatures. Actually,the possibility of negative values of temperature has been discussed by several authors[24,25,26].From Eq.(14)one may conclude that the temperature may be negative if the entropy diminishes while the internal energy grows.This may happens,for instance, in some condensed matter system when the energy spectrum is limited from above therebypresenting population inversion phenomenon as required for the operation of semiconductor lasers[27].Such an eﬀect for paramagnetic systems of nuclear moments in a crystal were studied in detail by by Purcell and Pound[28].However,as remarked by Izquerdo and Pav´o n [29],all models of phantom energy models proposed so far in literature assume some type of scalarﬁeld with no upper bound on their energy spectrum.Moreover,while population inversion is a rather transient phenomenon,the phantom regime is supposed to last for many eons.In a point of fact,bodies of negative temperature would be completely unstable and in principle they cannot exist naturally in the Universe,except in some singular states of a system[30].Such states are out of equilibrium(diﬀerent from the analysis assumed in Refs. [13,14]).They can be produced only in certain very unique systems,speciﬁcally in isolated spin systems,and they spontaneously decay away[20].The considerations presented in the two previous sections may induce someone to think that phantomﬂuids cannot exist in nature or that the statistical mechanics and thermo-dynamics need to be somewhat generalized,as for instance,by adopting the non-extensive framework proposed by Tsallis[31].However,it should be recalled that all the results above discussed are valid only if the chemical potential of the phantomﬂuid is identically zero.IV.SA VING THE PHANTOM HYPOTHESISAs we have argued,the concept of negative temperature is not a reasonable physical or mathematical solution to save the phantom hypothesis.Therefore,the important question now is how a phantomﬂuid may exist with temperature and entropy positives.In principle, it should be nice if such a problem might be solved in the framework of the standard thermo-dynamics and statistical mechanics.As far as we know,the unique possibility available to us is to introduce a new thermodynamic degree of freedom,namely,the chemical potential, a quantity appearing naturally in the Euler and Gibbs-Duhem relations.Actually,ifµis diﬀerent from zero,one may show that the entropy(8)must be replaced by(see also Eq.(12))S(T,V)= (1+ω)ρ0−µ0n0T0 1/ωV,(21) whereµ0and n0are the present day value of the chemical potential and particle number density.However,in order to keep the entropy positive deﬁnite,the following constraintmust be satisﬁed[17]:µ0n0ω≥ωmin=−1+Research Agencies).[1] A.G.Riess et al.,Astron.J.116,1009(1998);S.Perlmutter et al.,Astrophys.J.517,565(1999);P.Astier et al.,Astron.Astrophys.447,31(2006);A.G.Riess et al.,Astro.J.659, 98(2007).[2] D.N.Spergel et al.Astrophys.J.Suppl.Ser.170,377(2007);S.W.Allen et.al.,arXiv:0706.0033v1(2007).[3]T.Padmanabhan,Phys.Rept.380,235(2003);P.J.E.Peebles and B.Ratra,Rev.Mod.Phys.75,559(2003);J.A.S.Lima,Braz.Jour.Phys.34,194(2004),[astro-ph/0402109];J.S.Alcaniz,Braz.J.Phys.36,1109(2006);V.Sahni and A.Starobinsky,IJMP D15,2105 (2006);E.J.Copeland,M.Sami and S.Tsujikawa,Int.J.Mod.Phys.D15,1753(2006). [4]R.R.Caldwell,Phys.Lett.B545,23(2002);S.M.Carroll,M.Hoﬀman and M.Trodden,Phys.Rev.D68,023509(2003);B.McInnes,astro-ph/0210321;V.Faraoni,Int.J.Mod.Phys.D11,471(2002);P.F.Gonzalez-Diaz,Phys.Rev.D68,021303(2003);S.Nojiri and S.D.Odintsov,Phys.Lett.B562,147(2003);Phys.Lett.B565,1(2003);Y.-S.Piao and E.Zhou, Phys.Rev.D68,083515(2003);M.Sami and A.Toporensky,gr-qc/0312009;J.M.Cline,S.Jeon,G.D.Moore,hep-ph/0311312;R.Silva,J.S.Alcaniz and J.A.S.Lima,Int.J.Mod.Phys.D16,469(2007).[5]P.S.Corasaniti,M.Kunz,D.Parkinson,E.J.Copeland,and B.A.Bassett,Phys.Rev.D70,083006(2004);U.Alam,V.Sahni,T.D.Saini,and A.A.Starobinsky,Mon.Not.R.Astron.Soc.354,275(2004).[6] A.Melchiorri,L.Mersini-Houghton,C.J.Odman,and M.Trodden,Phys.Rev.D68,043509(2003).[7]S.M.Carroll,M.Hoﬀman and M.Trodden,Phys.Rev.D68,023509(2003).[8]P.H.Frampton,hep-th/0302007.[9]J.M.Cline,S.Y.Jeon and G.D.Moore,Phys.Rev.D70,043543(2004).[10] A.E.Schulz,M.J.White,Phys.Rev.D64,043514(2001);J.G.Hao and X.Z.Li,Phys.Rev.D67,107303(2003);S.Nojiri and S.D.Odintson,Phys.Lett.B562,147(2003);Phys.Lett.B565,1(2003);J.Santos,J.S.Alcaniz and M.J.Reboucas,Phys.Rev.D74,067301 (2006).[11]R.R.Caldwell,M.Kamionkowski,N.N.Weinberg,Phys.Rev.Lett.91,071301(2003);J.A.S.Lima,J.V.Cunha and J.S.Alcaniz,Phys.Rev.D68,023510(2003),J.Santos andJ.S.Alcaniz,Phys.Lett.B619,11(2005);M.Szydlowski,O.Hrycyna and A.Krawiec, JCAP0706,010(2007);R.C.Santos and J.A.S.Lima,Phys.Rev.D7*******(2008).[arXiv:0803.1865].The possibility of a solution with a Big-Rip wasﬁrst noticed by P.C.W.Davies,Ann.H.Poicar´e,43,297(1988).[12]J.D.Barrow,Class.Quant.Grav.21,L79(2004).See also S.Nojiri,S.D.Odintsov,and S.Tsujikawa,Phys.Rev.D71,063004(2005).[13]P.F.Gonz´a lez-D´ıaz and C.L.Sig¨u enza,Nucl.Phys.B697,363(2004);Phys.Lett.B589,78(2004).[14] D.Youm,Phys.Lett.B531,276(2002).[15]J.A.S.Lima and A.Maia Jr.,Phys.Rev.D52,56(1995);ibdem,Int.J.Theor.Phys,34,9(1995),[gr-qc/9505052];J.A.S.Lima and J.Santos,Int.J.Theor.Phys.34,143(1995);J.A.E.Carrillo,J.A.S.Lima,A.Maia Jr.,Int.J.Theor.Phys.35,2013(1996),[hep-th/9906016].[16]J.A.S.Lima and J.S.Alcaniz,Phys.Lett.B600,191(2004),[astro-ph/0402265].[17]J.A.S.Lima and S.H.Pereira,[arXiv:0801.0323].[18] E.W.Kolb and M.S.Turner,The Early Universe,Addison-Wesley(1990).[19]J.A.Freitas Pacheco and J.E.Horvath,Class.Quant.Grav.24,5427(2007).[20]H.B.Callen,Thermodynamics and an Introduction to Thermostatistics,2nd ed.,John Wiley&Sons,New York,(1985).[21]G.L.Murphy,Phys.Rev.D48,4231(1973);J.D.Barrow,Phys.Lett B180,335(1986);M.Morikawa and M.Sasaki,Phys.Lett.B165,59(1985);T.Padmanabhan and S.M.Chitre, Phys.Lett.A120,433(1987);J.A.S.Lima,R.Portugal and I.Waga,Phys.Rev.D37,2755 (1988);J.A.S.Lima and A.S.Germano,Phys.Lett.A170,373(1992);J.Casas-Vazquez and D.Jou,Rep.Prog.Phys.43,1937(2003).[22]I.Prigogine et al.,Gen.Rel.Grav.,21,767(1989);M.O.Calvao,Lima,J.A.S.and Waga,Phys.Lett.A162,233(1992);W.Zimdhal and D.Pav´o n,Phys.Lett.A176,57(1993);W.Zimdahl and D.Pav´o n,Mon.Not.R.Astr.Soc.266,872(1994);W.Zimdahl and D.Pav´o n, GRG26,1259(1994);J.Gariel and G.Le Denmat,Phys.Lett.A20011(1995);J.A.S.Lima,A.S.M.Germano and L.R.W.Abramo,Phys.Rev.D53,4287(1996),[gr-qc/9511006];J.A.S.Lima and L.R.W.Abramo,Class.Quant.Grav.13,2953(1996),[gr-qc/9606067];J.A.S.Lima,Gen.Rel.Grav.29,805(1997),[gr-qc/9605056];J.S.Alcaniz and J.A.S.Lima,Astron.and Astrophys.349,729(1999),[astro-ph/9906410];W.Zimdahl,D.J.Schwarz,A.B.Balakin and D.Pavon,Phys.Rev.D6*******(2001),[astro-ph/0009353];P.Gopakumarand G.V.Vijayagovindan,IJMPD15,321(2006);Y.Quinang,T-J.Zhang and Z-L Yi, Astrop.Spac.Sci.311,407(2007).[23]S.Weinberg,Astrop.J.168,175(1971);R.Silva,J.A.S.Lima and M.O.Calv˜a o,Gen.Rel.Grav.34,865(2002),gr-qc/0201048.[24]N.F.Ramsey,Phys.Rev.103,20(1956).[25]ndsberg,Phys.Rev.115,518(1959).[26]N.Bloembergen,Am.J.Phys.41,325(1973).[27]ndsberg,Thermodynamics and Statistical Mechanics,Dover,New York,(1990).[28] E.M.Purcell and R.V.Pound,Phys.Rev.81,279(1951).[29]G.Izquierdo and D.Pav´o n,Phys.Lett.B633,420(2006).[30]ndau and E.M.Lifshitz,Statistical Physics Part1,3rd ed.,Pergamom Press,NewYork,(1985).[31] C.Tsallis,J.Stat.Phys.52,479(1988);J.A.S.Lima,R.Silva and A.R.Plastino,Phys.Rev.Lett.86,2938(2001),[cond-mat/0101030];J.A.S.Lima,R.Silva and J.Santos,Astron.Astrophys.396,309(2002),[astro-ph/0109474].。

2-1 Thermodynamics

ThermodynamicsThermodynamicsThermodynamics is a branch of physics which deals with the energy and work of a system Thermodynamics is the study of the effect of work, heat, and energy on the system.Power (W) = Rate at which energy is being transferred Work (J) ‐ amount of energy transferred from one system to another2ThermodynamicsThere are three principal laws of thermodynamics. Each law leads to the definition of thermodynamic properties which help us to understand and predict the operation of a physical system - Zeroth Law - First Law; Work, Heat, and Energy - Second Law; Entropy3The The Zero(th) Zero(th) Law LawThis law states that if object A is in thermal equilibrium with object B, and object B is in thermal equilibrium with object C, then object C is also in thermal equilibrium with object A. This law allows us to build thermometers.“C” for methane at +15C = 2.2 kJ/kg KThe concept of thermodynamic equilibrium, in which two objects have the same temperature. If we bring two objects that are initially at different temperatures into physical contact, they eventually achieve thermal equilibrium. During the process of reaching thermal equilibrium, heat is transferred between the objects. The amount of heat transferred delta Q is proportional to the temperature difference delta T 5 between the objects and the heat capacity c of the object.The amount of heat transferred delta Q is proportional to the temperature difference delta T between the objects and the heat capacity c of the object.6First First Law Law of of Thermodynamics ThermodynamicsThe first law introduces the concept that heat and work are equivalent. It states that: The heat lost from a source is equal to the total heat gained and work done on bodies that receive that heat.Second Second Law Law of of Thermodynamics ThermodynamicsThe second law introduce the concept of directional heat flow. It states that: Heat always flows from the hot body to a cooler one.Heat Heat Engine EngineForward Heat EngineA forward heat engine has a positive work output such as Rankine or Brayton cycle. Applying the first law of thermodynamics to the cycle gives: Q1 - Q2 - W = 0 The second law of thermodynamics states that the thermal efficiency of the cycle η has an upper limit (the thermal efficiency of the Carnot cycle), i.e. It can be shown that: Q1 > W, which means that it is impossible to convert the whole heat input to work and Q2 > 0, which means that a minimum of heat supply to the cold reservoir is necessary.Heat Heat Engine EngineForward Heat EngineHeat engine is defined as a device that converts heat energy into mechanical energy or more exactly a system which operates continuously and only heat and work may pass across its boundaries. The operation of a heat engine can best be represented by a thermodynamic cycle.Heat Heat Engine EngineReverse Heat EngineA reverse heat engine has a positive work input such as heat pump and refrigerator. Applying the first law of thermodynamics to the cycle gives: - Q1 + Q2 + W = 0 In case of a reverse heat engine the second law of thermodynamics is as follows: It is impossible to transfer heat from a cooler body to a hotter body without any work input i.e. W>0 which means that the co-efficiency of performance for a heat pump is greater than unity.Heat Heat Engine EngineReverse Heat EngineThe effectiveness of a reversed heat engine is defined in terms of a coefficient of performance (COP). The COP for a refrigerator is defined as: COP2 = Q2 / W and for a heat pump as: COP1 = Q1 / WEnthalpy Enthalpy Enthalpy is a thermodynamic measure of the total heat content of a liquid or vapor at a given temperature and is expressed in energy per unit mass (k Joules per 1 kg) from absolute zero. Therefore, for a liquid/vapor mixture, it will be seen that it is the sum of the enthalpy of the liquid plus the latent heat of vaporizationhx = h′+ χ（h″- h″) χ: Dryness factorEnthalpy Enthalpy -- Pressure Pressure In the previous examples the transition temperatures of water were 0° C and 100° C at atmospheric pressure. By altering pressure, we will affect the transitional temperature. When the relationship of enthalpy to pressure is plotted on a chart the resulting diagram is known as Mollier diagram.Enthalpy EnthalpyFrom a study of the FIRST LAW of thermodynamics, we find that the internal energy of a gas is also a state variable. - For a gas, a useful additional state variable is the enthalpy which is defined to be the sum of the internal energy E plus the product of the pressure p and volume V. Using the symbol H for the enthalpy: H=E+p*V - Propulsion engineers use the specific enthalpy in engine analysis more than the enthalpy itself. For a system with heat transfer Q and work W, the change in internal energy E from state 1 to state 2 is equal to the difference in the heat transfer into the system and the work done by the system: E2 - E1 = Q - W15Enthalpy Enthalpy- For the special case of a constant pressure process, the work done by the gas is given as the constant pressure p times the change in volume V: W = p * [V2 - V1] - Substituting into the first equation, we have: E2 - E1 = Q - p * [V2 - V1] - Let's group the conditions at state 2 and the conditions at state 1 together: (E2 + p * V2) - (E1 + p * V1) = Q - The (E + p * V) can be replaced by the enthalpy H; H2 - H1 = Q16Enthalpy EnthalpyFrom our definition of the heat transfer, we can represent Q by some heat capacity coefficient Cp times the temperature T. (H2 - H1) = Cp * (T2 - T1) -The SPECIFIC HEAT CAPACITY cp is called the specific heat at constant pressure and is related to the universal gas constant of the equation of state. This final equation is used to determine values of specific enthalpy for a given temperature. - Enthalpy is used in the energy equation for a fluid. Across shock waves, the total enthalpy of the gas remains a constant.17Entropy Entropy- Entropy, like temperature and pressure, can be explained on both a macro scale and a micro scale. Since thermodynamics deals only with the macro scale, the change in entropy delta S is defined here to be the heat transfer delta Q into the system divided by the temperature T: delta S = delta Q / T, dS = dQ / T - For gases, there are two possible ways to evaluate the change in entropy. We begin by using the first law of thermodynamics: dE = dQ - dW - If we use the definition of the enthalpy H of a gas: H = E + p * V, Then, dH = dE + p dV + V dp18Entropy Entropy- Substitute into the first law equation: dQ = dH - V dp - p dV + p dV - dQ = dH - V dp is an alternate way to present the first law of thermodynamics. For an ideal gas, the equation of state is written: p * V = R * T ; R is the gas constant - The heat transfer of a gas is equal to the heat capacity times the change in temperature; in differential form: dQ = C * dT - If we have a constant volume process, the formulation of the first law gives: dE = dQ = C (constant volume) * dT19Entropy Entropy- If we assume that the heat capacity is constant with temperature, we can use these two equations to define the change in enthalpy and internal energy. If we substitute the value for p from the equation of state, and the definition of dE in the first energy equation, we obtain: dQ = C (constant volume) * dT + R * T dV / V - Similarly substituting the value of V from the equation of state, and the definition of dH we obtain the alternate form: dQ = C (constant pressure) * dT - R * T dp / p - Substituting these forms for dQ into the differential form of the entropy equation gives: dS = C (constant volume) * dT / T + R * dV / V, and dS = C (constant pressure) * dT / T - R * dp / p20Entropy Entropy- These equations can be integrated from condition "1" to condition "2" to give: S2 - S1 = Cv * ln ( T2 / T1) + R * ln ( V2 / V1), and S2 - S1 = Cp * ln ( T2 / T1) - R * ln ( p2 / p1) - If we have a constant volume process, the second term in the equation is equal to zero, since v2/v1 = 1. We can then determine the value of the specific heat for the constant volume process. But if we have a process that changes volume, the second term in the equation is not zero. We can think of the first term of the equation as the contribution for a constant volume process, and the second term as the additional change produced by the change in volume. A similar type of argument can be made for the equation used for a change in pressure.21Operation Operation of of a a Simple Simple Cargo Cargo Reliq Reliq System System• There are two main types of liquefaction plants, namely: • Direct Reliquefaction Cycle; and Indirect Reliquefaction Cycle.In a Direct Reliquefaction Cycle, the evaporated or displaced cargo vapour is compressed, condensed and returned to the tank. This is the most commonly used system.••In an Indirect Reliquefaction Cycle, an external refrigeration system is employed to condense the cargo vapour without it being compressed. This cycle requires a very cold refrigerant and large surfaces. Enthalpy is a thermodynamic measure of the total heat content of a liquid or vapour at a given temperature and is expressed in energy per unit mass (k Joules per 1 kg) from absolute zero. Therefore, for a liquid/vapour mixture, it will be seen that it is the sum of the enthalpy of the liquid plus the latent heat of vaporisation.22Operation Operation of of a a Simple Simple Cargo Cargo System SystemVapour from cargo tankbCondensera dCompressorSeawaterTankcExpansion ValveReceiverHeatWith an understanding of the gas laws and the law of thermodynamics, the operation of the simple cargo system on board a liquefied gas ship can be followed. The cargo tank contains cold liquid, although it is insulated, some heat will still come through from outside. This is a consequence of second law of thermodynamics. This heat will overcome the latent heat of vaporisation and so some of the cargo will boil off. The vapour formed will raise the pressure in the tank. The vapour is drawn off and passed to a compressor.Operation Operation of of a a Simple Simple Cargo Cargo System SystemVapour from cargo tankbCondensera dCompressorSeawaterTankcExpansion ValveReceiverHeatThe work done by the compressor raises the temperature of the vapour according to the first law of thermodynamics. This temperature rise necessary so that it becomes hotter than the cooling medium that is subsequently used to cool it again.Operation Operation of of a a Simple Simple Cargo Cargo System SystemVapour from cargo tankbCondensera dCompressorSeawaterTankcExpansion ValveReceiverHeatThe hot gas or vapour now passes to a condenser where it is cooled by seawater. The removal of heat means that the molecules slow down and the vapour condenses to form a warm liquid. This liquid is also under pressure. The liquid is then passed through an expansion valve that reduces the pressure. This results in a partial evaporation, which causes the temperature of the bulk liquid to fall back down to tank temperature.Operation Operation of of a a Simple Simple Cargo Cargo System SystemVapour from cargo tankbCondensera dCompressorSeawaterTankcExpansion ValveReceiverHeatSo cold condensate is returned to the tank. These valves are also referred as JouleThompson valves, the physicist who discovered the cooling-expansion phenomenon. It is important to note that the joule-Thompson expansion results in cooling because the small amount of gas generated absorbs its latent heat of vaporisation from some of liquid.Operation Operation of of a a Simple Simple Cargo Cargo System SystemVapour from cargo tankbCondensera dCompressorSeawaterTankcExpansion ValveReceiverHeatJoule-Thompson expansion takes place at constant Enthalpy. The real cooling effect of this cycle is the removal of sensible heat and the latent heat of vaporisation from the full flow of gas as it condensed and cooled.28Operation Operation of of a a Simple Simple Cargo Cargo Reliq Reliq System SystemPressurecb aEnthalpyd29Ammonia Reliq Proces – direct single stage+33C 11.7 bar+140C 11.7 barCondenserExpansion valve Cargo Tank-33C 1.031 barCompressor-33C 1.031 bar3031Mollier Mollier Chart Chart of of Methane MethaneThe thermodynamic calculation of various gases or the liquids is done by using the thermodynamic diagram in general. Five (5) values of:1.pressure p, 2.specific volume v, 3.temperature T, 4.heat content h or i (enthalpy) 5.entropy sare used for the thermodynamic calculation. The p - i diagram is a so-called Mollier diagram, and “pressure p” is shown on VERICAL Axis and the “heat content h” (enthalpy i) on horizontal axisEnthalpyMollier Mollier Chart Chart of of Methane MethaneIsoEnthalpyMollier Mollier Chart Chart of of Methane MethaneThe following characteristics are included in this diagram:connected.）① Iso-bar（It is the horizontal in the line where the point of the same pressure was② Iso-enthalpy line （The normal in the line where the point of same was connected. ）liquid and the right side are moist steam at the left of this line. ）③ Saturated liquid line （In the line where the saturated liquid is shown, the under cooling ④ Saturated vapor line （In the line where the saturated vapor is shown, moist steamthe right side are superheated steam at the left of this line. ） andnormal in the liquid, and the line of a right descending in moist steam in the horizon and superheated steam as well as the isobar. ）⑤ Iso-thermal （In the line where the same point of the temperature is shown, near the⑥ Iso-entropy curve （Line where point of the same entropy was connected） ⑦ Iso-specific volume line （Line where point of the same bulkiness was connected） ⑧ Iso-Dryness line （Line where point of constant dryness was connected. Dryness X = 0.1,it means that 10% dry saturated steam in moist steam.） 34Mollier Mollier Chart Chart of of Methane MethaneK Kj/K j/KgK gKCR I TI CA LC Con onst stan ant tT Tem empe pera ratu ture re oC oCTEConstant Constant Enthalpy Enthalpy kcal/kg kcal/kg or or Kj/kg Kj/kgC Con onst stan ant tE Ent ntro ropy pyGAS AREAM PE RA TURE=-82 .5C)CRITICAL PRESSURE (ie. CH4 = 43 Bar)IsoSUB COOLED LIQUIDS SA AT TU UR RA AT TE ED DV VA AP PO OU UR RL LI IN NE EL LII Q QU UII D DS SA AT TU UR RA AT TE ED Di spec o s IS CON e olum fi c VL LII N NE Ekg m3/ E M OLU V T TANSUPERHEATED VAPOURArea of PV=mRTSATURATED REGION – LIQUID / VAPOR MIXTURELATENT HEAT OF VAPORISATIONEnthalpyPRACTICAL USE OF MOLLIER DIAGRAM361ST EXAMPLE DIFFERENCE IN VOLUME BETWEEN LNG LIQUID AND LNG VAPOR AT SAME TEMPERATURE37Specific Volume 0.00235 m3/kgFor Density 425 kg/m3 (1/425 = 0.00235)s e ime m lu 55 t o V 2 ic ce f i ec ren p S iffe D.66 ity 1 s n e For Dfic V i c e Sp3/kg m 0 .600 0 e olum 001/ 1 m3 ( 0.6 .66 = kg/LNG Liquid >>> LNG Vapour at Boiling temp – 160 C1.4 51. LNG liquid2. LNG Vapour38Specific Volume 0.00235 m3/kgFor Density 425 kg/m3 (1/425 = 0.00235)Specific Volume change from LNG Liquid – 160 C >>> LNG Vapour at 20 C = Difference 619 timesSpecific Volume 1.45000 m3/kg @ 20CFor Density 0.69 kg/m3 (1/0.696 = 1.45 m3/kg1.4 51. LNG Liquid 3. LNG Vapour @ 20C 39LATENT HEAT REQUIRED FROM LIQUID to VAPOR KJ / KGLNG liquidLNG VapourLNG Latent Heat = 675 – 164 kj/kg = 511 kj/kgEnthalpy 164 kj/kg Enthalpy 675 kj/kg 40SENSITIVE HEAT KJ / kg C (K)Sensitive Heat from – 160 C to – 100 = 800 kj/kg ‐ 675 kj/kg = 125 kj/kg For 1 kg temperature to increase 60 C required 125 kj i.e. 125 kj / 60 C = Cp = 2.083 kJ/kg/CLNG VapourLNG VapourEnthalpy 675 kj/kgEnthalpy 800 kj/kg 41Mollier Mollier Chart ChartIn summary, it can be seen that the heat flowing into the tank has been returned to the environment via the seawater, together with the additional work done by Mollier chart. Point ‘a’ represents the vapour in the dome of the tank. As it passes to the compressor it picks up some heat. The compressor raises the temperature and pressure of the gas to point ‘b’ it is then cooled and condensed and becomes a saturated liquid at point ‘c’ in the condenser. The expansion valve then produces cold liquid with a proportion of vapour and this is returned to the tank at point ‘d’.Pressurecb aEnthalpyd。

Principles of Plasma Discharges and Materials Processing第1章

CHAPTER 1INTRODUCTION1.1MATERIALS PROCESSINGChemically reactive plasma discharges are widely used to modify the surface prop-erties of materials.Plasma processing technology is vitally important to several of the largest manufacturing industries in the world.Plasma-based surface processes are indispensable for manufacturing the very large scale integrated circuits (ICs)used by the electronics industry.Such processes are also critical for the aerospace,automotive,steel,biomedical,and toxic waste management industries.Materials and surface structures can be fabricated that are not attainable by any other commer-cial method,and the surface properties of materials can be modiﬁed in unique ways.For example,0.2-m m-wide,4-m m-deep trenches can be etched into silicon ﬁlms or substrates (Fig.1.1).A human hair is 50–100m m in diameter,so hundreds of these trenches would ﬁt endwise within a human hair.Unique materials such as diamond ﬁlms and amorphous silicon for solar cells have also been produced,and plasma-based hardening of surgically implanted hip joints and machine tools have extended their working lifetimes manyfold.It is instructive to look closer at integrated circuit fabrication,which is the key application that we describe in this book.As a very incomplete list of plasma pro-cesses,argon or oxygen discharges are used to sputter-deposit aluminum,tungsten,or high-temperature superconducting ﬁlms;oxygen discharges can be used to grow SiO 2ﬁlms on silicon;SiH 2Cl 2=NH 3and Si(OC 2H 5)4=O 2discharges are used for the plasma-enhanced chemical vapor deposition (PECVD)of Si 3N 4and SiO 2ﬁlms,1Principles of Plasma Discharges and Materials Processing ,by M.A.Lieberman and A.J.Lichtenberg.ISBN 0-471-72001-1Copyright #2005John Wiley &Sons,Inc.respectively;BF 3discharges can be used to implant dopant (B)atoms into silicon;CF 4=Cl 2=O 2discharges are used to selectively remove silicon ﬁlms;and oxygen dis-charges are used to remove photoresist or polymer ﬁlms.These types of steps (deposit or grow,dope or modify,etch or remove)are repeated again and again in the manufacture of a modern IC.They are the equivalent,on a micrometer-size scale,of centimeter-size manufacture using metal and components,bolts and solder,and drill press and lathe.For microfabrication of an IC,one-third of the tens to hundreds of fabrication steps are typically plasma based.Figure 1.2shows a typical set of steps to create a metal ﬁlm patterned with sub-micrometer features on a large area (300mm diameter)wafer substrate.In (a ),the ﬁlm is deposited;in (b ),a photoresist layer is deposited over the ﬁlm;in (c ),the resist is selectively exposed to light through a pattern;and in (d ),the resist is developed,removing the exposed resist regions and leaving behind a patterned resist mask.In (e ),this pattern is transferred into the ﬁlm by an etch process;the mask protects the underlying ﬁlm from being etched.In (f ),the remaining resist mask is removed.Of these six steps,plasma processing is generally used for ﬁlm deposition (a )and etch (e ),and may also be used for resist development (d )and removal (f ).The etch process in (e )is illustrated as leading to vertical sidewalls aligned with the resist mask;that is,the mask pattern has been faithfully transferred into the metal ﬁlm.This can be accomplished by an etch process that removes material in the vertical direction only.The horizontal etch rate is zero.Such anisotropic etches are easily produced by plasma processing.On the other hand,one mightimagineFIGURE 1.1.Trench etch (0.2m m wide by 4m m deep)in single-crystal silicon,showing the extraordinary capabilities of plasma processing;such trenches are used for device isolation and charge storage capacitors in integrated circuits.2INTRODUCTIONthat exposing the masked ﬁlm (d )to a liquid (or vapor phase)etchant will lead to the undercut isotropic proﬁle shown in Figure 1.3a (compare to Fig.1.2e ),which is produced by equal vertical and horizontal etch rates.Many years ago,feature spa-cings (e.g.,between trenches)were tens of micrometers,much exceeding required ﬁlm thicknesses.Undercutting was then acceptable.This is no longer true with submicrometer feature spacings.The reduction in feature sizes and spacings makes anisotropic etch processes essential.In fact,strictly vertical etches are some-times not desired;one wants controlled sidewall angles.Plasma processing is the only commercial technology capable of such control.Anisotropy is a critical process parameter in IC manufacture and has been a major force in driving the development of plasma processing technology.The etch process applied to remove the ﬁlm in Figure 1.2d is shown in Figure 1.2e as not removing,either the photoresist or the underlying substrate.This selectivity is another critical process parameter for IC manufacture.Whereas FIGURE 1.2.Deposition and pattern transfer in manufacturing an integrated circuit:(a )metal deposition;(b )photoresist deposition;(c )optical exposure through a pattern;(d )photoresist development;(e )anisotropic plasma etch;(f )remaining photoresist removal.1.1MATERIALS PROCESSING 3wet etches have been developed having essentially inﬁnite selectivity,highly selec-tive plasma etch processes are not easily designed.Selectivity and anisotropy often compete in the design of a plasma etch process,with results as shown in Figure 1.3b .Compare this to the idealized result shown in Figure 1.2e .Assuming that ﬁlm-to-substrate selectivity is a critical issue,one might imagine simply turning off the plasma after the ﬁlm has been etched through.This requires a good endpoint detection system.Even then,variations in ﬁlm thickness and etch rate across the area of the wafer imply that the etch cannot be stopped at the right moment every-where.Hence,depending on the process uniformity ,there is a need for some selectivity.These issues are considered further in Chapter 15.Here is a simple recipe for etching silicon using a plasma discharge.Start with an inert molecular gas,such as CF 4.Excite the discharge to sustain a plasma by electron–neutral dissociative ionization,e þCF 4À!2e þCF þ3þFand to create reactive species by electron–neutral dissociation,e þCF 4À!e þF þCF 3À!e þ2F þCF2FIGURE 1.3.Plasma etching in integrated circuit manufacture:(a )example of isotropic etch;(b )sidewall etching of the resist mask leads to a loss of anisotropy in ﬁlm etch;(c )illustrating the role of bombarding ions in anisotropic etch;(d )illustrating the role of sidewall passivating ﬁlms in anisotropic etch.4INTRODUCTIONThe etchant F atoms react with the silicon substrate,yielding the volatile etch product SiF4:Si(s)þ4F(g)À!SiF4(g)Here,s and g indicate solid and gaseous forms,respectively.Finally,the product is pumped away.It is important that CF4does not react with silicon,and that the etch product SiF4is volatile,so that it can be removed.This process etches siliconisotropically.For an anisotropic etch,there must be high-energy ion(CFþ3)bombard-ment of the substrate.As illustrated in Figures1.3c and d,energetic ions leaving the discharge during the etch bombard the bottom of the trench but do not bombard the sidewalls,leading to anisotropic etching by one of two mechanisms.Either the ion bombardment increases the reaction rate at the surface(Fig.1.3c),or it exposes the surface to the etchant by removing passivatingﬁlms that cover the surface(Fig.1.3d).Similarly,Cl and Br atoms created by dissociation in a discharge are good etch-ants for silicon,F atoms and CF2molecules for SiO2,O atoms for photoresist,and Cl atoms for aluminum.In all cases,a volatile etch product is formed.However,F atoms do not etch aluminum,and there is no known etchant for copper,because the etch products are not volatile at reasonable substrate temperatures.We see the importance of the basic physics and chemistry topics treated in this book:(1)plasma physics(Chapters2,4–6,and18),to determine the electron and ion densities,temperatures,and ion bombardment energies andﬂuxes for a given dis-charge conﬁguration;and(2)gas-phase chemistry and(3)surface physics and chem-istry(Chapters7and9),to determine the etchant densities andﬂuxes and the etch rates with and without ion bombardment.The data base for theseﬁelds of science is provided by(4)atomic and molecular physics,which we discuss in Chapters3 and8.We also discuss applications of equilibrium thermodynamics(Chapter7)to plasma processing.The measurement and experimental control of plasma and chemical properties in reactive discharges is itself a vast subject.We provide brief introductions to some simple plasma diagnostic techniques throughout the text.We have motivated the study of the fundamentals of plasma processing by exam-ining isotropic and anisotropic etches for IC manufacture.These are discussed in Chapter15.Other characteristics motivate its use for deposition and surface modi-ﬁcation.For example,a central feature of the low-pressure processing discharges that we consider in this book is that the plasma itself,as well as the plasma–substrate system,is not in thermal equilibrium.This enables substrate temperatures to be relatively low,compared to those required in conventional thermal processes, while maintaining adequate deposition or etch rates.Putting it another way,plasma processing rates are greatly enhanced over thermal processing rates at the same sub-strate temperature.For example,Si3N4ﬁlms can be deposited over aluminumﬁlms by PECVD,whereas adequate deposition rates cannot be achieved by conventional chemical vapor deposition(CVD)without melting the aluminumﬁlm.Chapter16 gives further details.Particulates or“dust”can be a signiﬁcant component in processing discharges and can be a source of substrate-level contamination in etch and deposition1.1MATERIALS PROCESSING56INTRODUCTIONprocesses.One can also control dust formation in useful ways,for example,to produce powders of various sizes or to incorporate nanoparticles during deposition to modifyﬁlm properties.Dusty plasmas are described in Chapter17.The nonequilibrium nature of plasma processing has been known for many years, as illustrated by the laboratory data in Figure1.4.In time sequence,this showsﬁrst, the equilibrium chemical etch rate of silicon in the XeF2etchant gas;next,the tenfold increase in etch rate with the addition of argon ion bombardment of the sub-strate,simulating plasma-assisted etching;andﬁnally,the very low“etch rate”due to the physical sputtering of silicon by the ion bombardment alone.A more recent application is the use of plasma-immersion ion implantation(PIII)to implant ions into materials at dose rates that are tens to hundreds of times larger than those achievable with conventional(beam based)ion implantation systems.In PIII,a series of negative high-voltage pulses are applied to a substrate that is immersed directly into a discharge,thus accelerating plasma ions into the substrate.The devel-opment of PIII has opened a new implantation regime characterized by very high dose rates,even at very low energies,and by the capability to implant both large area and irregularly shaped substrates,such asﬂat panel displays or machine tools and dies. This is illustrated in Figure1.5.Further details are given in Chapter16.1.2PLASMAS AND SHEATHSPlasmasA plasma is a collection of free charged particles moving in random directions that is,on the average,electrically neutral(see Fig.1.6a).This book deals withweakly Array FIGURE1.4.Experimental demonstration of ion-enhanced plasma etching.(Coburn and Winters,1979.)ionized plasma discharges,which are plasmas having the following features:(1)they are driven electrically;(2)charged particle collisions with neutral gas mol-ecules are important;(3)there are boundaries at which surface losses are important;(4)ionization of neutrals sustains the plasma in the steady state;and (5)the electrons are not in thermal equilibrium with the ions.A simple discharge is shown schematically in Figure 1.6b .It consists of a voltage source that drives current through a low-pressure gas between two parallel conduct-ing plates or electrodes.The gas “breaks down”to form a plasma,usually weakly ionized,that is,the plasma density is only a small fraction of the neutral gas density.We describe some qualitative features of plasmas in this section;discharges are described in the following section.Plasmas are often called a fourth state of matter.As we know,a solid substance in thermal equilibrium generally passes into a liquid state as the temperature is increased at a ﬁxed pressure.The liquid passes into a gas as the temperature is further increased.At a sufﬁciently high temperature,the molecules in the gas decompose to form a gas of atoms that move freely in random directions,except for infrequent collisions between atoms.If the temperature is furtherincreased,FIGURE 1.5.Illustrating ion implantation of an irregular object:(a )In a conventional ion beam implanter,the beam is electrically scanned and the target object is mechanically rotated and tilted to achieve uniform implantation;(b )in plasma-immersion ion implantation (PIII),the target is immersed in a plasma,and ions from the plasma are implanted with a relatively uniform spatialdistribution.VFIGURE 1.6.Schematic view of (a )a plasma and (b )a discharge.1.2PLASMAS AND SHEATHS 7then the atoms decompose into freely moving charged particles(electrons and positive ions),and the substance enters the plasma state.This state is characterized by a common charged particle density n e%n i%n particles/m3and,in equilibrium, a temperature T e¼T i¼T.The temperatures required to form plasmas from puresubstances in thermal equilibrium range from roughly4000K for easy-to-ionize elements like cesium to20,000K for hard-to-ionize elements like helium.The fractional ionization of a plasma isx iz¼n i n gþn iwhere n g is the neutral gas density.x iz is near unity for fully ionized plasmas,and x iz(1for weakly ionized plasmas.Much of the matter in the universe is in the plasma state.This is true because stars,as well as most interstellar matter,are plasmas.Although stars are plasmas in thermal equilibrium,the light and heavy charged particles in low-pressure proces-sing discharges are almost never in thermal equilibrium,either between themselves or with their surroundings.Because these discharges are electrically driven and are weakly ionized,the applied power preferentially heats the mobile electrons,while the heavy ions efﬁciently exchange energy by collisions with the background gas. Hence,T e)T i for these plasmas.Figure1.7identiﬁes different kinds of plasmas on a log n versus log T e diagram. There is an enormous range of densities and temperatures for both laboratory and space plasmas.Two important types of processing discharges are indicated on the ﬁgure.Low-pressure discharges are characterized by T e%1–10V,T i(T e,and n%108–1013cm23.These discharges are used as miniature chemical factories in which feedstock gases are broken into positive ions and chemically reactive etch-ants,deposition precursors,and so on,which thenﬂow to and physically or chemi-cally react at the substrate surface.While energy is delivered to the substrate also, for example,in the form of bombarding ions,the energyﬂux is there to promote the chemistry at the substrate,and not to heat the substrate.The gas pressures for these discharges are low:p%1mTorr–1Torr.These discharges and their use for processing are the principal subject of this book.We give the quantitative frame-work for their analysis in Chapter10.High-pressure arc discharges are also used for processing.These discharges have T e%0.1–2V and n%1014–1019cm23,and the light and heavy particles are more nearly in thermal equilibrium,with T i.T e.These discharges are used mainly to deliver heat to the substrate,for example,to increase surface reaction rates, to melt,sinter,or evaporate materials,or to weld or cut refractory materials.Opera-ting pressures are typically near atmospheric pressure(760Torr).High-pressure discharges of this type are beyond the scope of this book.Figure1.8shows the densities and temperatures(or average energies)for various species in a typical rf-driven capacitively coupled low-pressure discharge;for example,for silicon etching using CF4,as described in Section1.1.We see that the feedstock gas,etchant atoms,etch product gas,and plasma ions have roughly 8INTRODUCTIONthe same temperature,which does not exceed a few times room temperature (0.026V).The etchant F and product SiF 4densities are signiﬁcant fractions of the CF 4density,but the fractional ionization is very low:n i 10À5n g .The electron temperature T e is two orders of magnitude larger than the ion temperature T i .However,we note that the energy of ions bombarding the substrate can be 100–1000V,much exceeding T e .The acceleration of low-temperature ions510152025log 10 T (V)el o g 10n (c m –3)FIGURE 1.7.Space and laboratory plasmas on a log n versus log T e diagram (after Book,1987).l De is deﬁned in Section 2.4.1.2PLASMAS AND SHEATHS 9across a thin sheath region where the plasma and substrate meet is central to all pro-cessing discharges.We describe this qualitatively below and quantitatively in later chapters.Although n i and n e may be ﬁve orders of magnitude lower that n g ,the charged particles play central roles in sustaining the discharge and in processing.Because T e )T i ,it is the electrons that dissociate the feedstock gas to create the free radicals,etchant atoms,and deposition precursors,required for the chemistry at the substrate.Electrons also ionize the gas to create the positive ions that sub-sequently bombard the substrate.As we have seen,energetic ion bombardment can increase chemical reaction rates at the surface,clear inhibitor ﬁlms from the surface,and physically sputter materials from or implant ions into the surface.T e is generally less than the threshold energies E diss or E iz for dissociation and ionization of the feedstock gas molecules.Nevertheless,dissociation and ionization occur because electrons have a distribution of energies.Letting g e (E )d E be the number of electrons per unit volume with energies lying between E and E þd E ,then the distribution function g e (E )is sketched in Figure 1.9.Electrons having ener-gies below E diss or E iz cannot dissociate or ionize the gas.We see that dissociation and ionization are produced by the high-energy tail of the distribution.Although the distribution is sketched in the ﬁgure as if it were Maxwellian at the bulk electron temperature T e ,this may not be the case.The tail distribution might be depressed below or enhanced above a Maxwellian by electron heating and electron–neutral collision processes.Two temperature distributions are sometimes observed,with Te 1081010n (c m –3)T or ·Ò (V)FIGURE 1.8.Densities and energies for various species in a low-pressure capacitive rf discharge.10INTRODUCTIONfor the bulk electrons lower than T h for the energetic electron tail.Non-Maxwellian distributions can only be described using the kinetic theory of discharges,which we introduce in Chapter 18.SheathsPlasmas,which are quasi-neutral (n i %n e ),are joined to wall surfaces across thin positively charged layers called sheaths .To see why,ﬁrst note that the electron thermal velocity (e T e =m )1=2is at least 100times the ion thermal velocity (e T i =M )1=2because m =M (1and T e &T i .(Here,T e and T i are given in units of volts.)Consider a plasma of width l with n e ¼n i initially conﬁned between two grounded (F ¼0)absorbing walls (Fig.1.10a ).Because the net charge density r ¼e (n i Àn e )is zero,the electric potential F and the electric ﬁeld E x is zero every-where.Hence,the fast-moving electrons are not conﬁned and will rapidly be lost to the walls.On a very short timescale,however,some electrons near the walls are lost,leading to the situation shown in Figure 1.10b .Thin (s (l )positive ion sheaths form near each wall in which n i )n e .The net positive r within the sheaths leads to a potential proﬁle F (x )that is positive within the plasma and falls sharply to zero near both walls.This acts as a conﬁning potential “valley”for electrons and a “hill”for ions because the electric ﬁelds within the sheaths point from the plasma to the wall.Thus the force ÀeE x acting on electrons is directed into the plasma;this reﬂects electrons traveling toward the walls back into the plasma.Conversely,ions from the plasma that enter the sheaths are accel-erated into the walls.If the plasma potential (with respect to the walls)is V p ,then we expect that V p a few T e in order to conﬁne most of the electrons.The energy of ions bombarding the walls is then E i a few T e .Charge uncovering is treated quan-titatively in Chapter 2,and sheaths in Chapter 6.Figure 1.11shows sheath formation as obtained from a particle-in-cell (PIC)plasma simulation.We use PIC results throughout this book to illustrate various dis-charge phenomena.In this simulation,the left wall is grounded,the right wall is ﬂoating (zero net current),and the positive ion density is uniform and constant in time.The electrons are modeled as N sheets having charge-to-mass ratio Àe =mFIGURE 1.9.Electron distribution function in a weakly ionized discharge.1.2PLASMAS AND SHEATHS 1112INTRODUCTION(b)FIGURE1.10.The formation of plasma sheaths:(a)initial ion and electron densities andsheath.potential;(b)densities,electricﬁeld,and potential after formation of the Array FIGURE1.11.PIC simulation of positive ion sheath formation:(a)v x–x electron phase space,with horizontal scale in meters;(b)electron density n e;(c)electricﬁeld E x;(d)potential F;(e)electron number N versus time t in seconds;(f)right hand potential V r versus time t.that move in one dimension (along x )under the action of the time-varying ﬁelds pro-duced by all the other sheets,the ﬁxed ion charge density,and the charges on the walls.Electrons do not collide with other electrons,ions,or neutrals in this simu-lation.Four thousand sheets were used with T e ¼1V and n i ¼n e ¼1013m À3at time t ¼0.In (a ),(b ),(c ),and (d ),we,respectively,see the v x –x electron phase space,electron density,electric ﬁeld,and potential after the sheath has formed,at t ¼0.77m s.The time history of N is shown in (e );40sheets have been lost to form the sheaths.Figures 1.11a –d show the absence of electrons near each wall over a sheath width s %6mm.Except for ﬂuctuations due to the ﬁnite N ,the ﬁeld in the bulk plasma is near zero,and the ﬁelds in the sheaths are large and point from the plasma to the walls.(E x is negative at the left wall and positive at the right wall to repel plasma electrons.)The potential in the center of the discharge is V p %2:5V and falls to zero at the left wall (this wall is grounded by deﬁnition).The potential at the right wall is also low,but we see in (f )that it oscillates in time.We will see in Chapter 4that these are plasma oscillations .We would not see them if the initial sheet positions and velocities were chosen exactly symmetrically about the midplane,or if many more sheets were used in the simulation.If the ions were also modeled as moving sheets,then on a longer timescale we would see ion acceleration within the sheaths,and a consequent drop in ion density near the walls,as sketched in Figure 1.10b .We return to this in Chapter 6.The separation of discharges into bulk plasma and sheath regions is an important paradigm that applies to all discharges.The bulk region is quasi-neutral,and both instantaneous and time-averaged ﬁelds are low.The bulk plasma dynamicsare FIGURE 1.11.(Continued ).1.2PLASMAS AND SHEATHS 1314INTRODUCTIONdescribed by diffusive ion loss at high pressures and by free-fall ion loss at low pressures.In the positive space charge sheaths,highﬁelds exist,leading to dynamics that are described by various ion space charge sheath laws,including low-voltage sheaths and various high-voltage sheath models,such as collisionless and collisional Child laws and their modiﬁcations.The plasma and sheath dynamics must be joined at their interface.As will be seen in Chapter6,the usual joining condition is to require that the mean ion velocity at the plasma-sheath edge be equal to the ion-sound(Bohm)velocity:u B¼(e T e=M)1=2,where e and M are the charge and mass of the ion,respectively,and T e is the electron temperature in volts.1.3DISCHARGESRadio Frequency DiodesCapacitively driven radio frequency(rf)discharges—so-called rf diodes—are commonly used for materials processing.An idealized discharge in plane parallel geometry,shown in Figure1.12a,consists of a vacuum chamber containing two planar electrodes separated by a spacing l and driven by an rf power source.The sub-strates are placed on one electrode,feedstock gases are admitted toﬂow through the discharge,and efﬂuent gases are removed by the vacuum pump.Coaxial discharge geometries,such as the“hexode”shown in Figure1.12b,are also in widespread use. Typical parameters are shown in Table1.1.The typical rf driving voltage is V rf¼100–1000V,and the plate separation is l¼2–10cm.When operated at low pressure,with the wafer mounted on the powered electrode,and used to remove substrate material,such reactors are commonly called reactive ion etchers (RIEs)—a misnomer,since the etching is a chemical process enhanced by energetic ion bombardment of the substrate,rather than a removal process due to reactive ions alone.For anisotropic etching,typically pressures are in the range10–100mTorr, power densities are0.1–1W/cm2,the driving frequency is13.56MHz,and mul-tiple wafer systems are common.Typical plasma densities are relatively low, 109–1011cm23,and the electron temperature is of order3V.Ion acceleration ener-gies(sheath voltages)are high,greater than200V,and fractional ionization is low. The degree of dissociation of the molecules into reactive species is seldom measured but can range widely from less than0.1percent to nearly100percent depending on gas composition and plasma conditions.For deposition and isotropic etch appli-cations,pressures tend to be higher,ion bombarding energies are lower,and fre-quencies can be lower than the commonly used standard of13.56MHz.The operation of capacitively driven discharges is reasonably well understood. As shown in Figure1.13for a symmetrically driven discharge,the mobile plasma electrons,responding to the instantaneous electricﬁelds produced by the rf driving voltage,oscillate back and forth within the positive space charge cloud of the ions.The massive ions respond only to the time-averaged electricﬁelds.Oscil-lation of the electron cloud creates sheath regions near each electrode that containnet positive charge when averaged over an oscillation period;that is,the positive charge exceeds the negative charge in the system,with the excess appearing within the sheaths.This excess produces a strong time-averaged electric ﬁeld within each sheath directed from the plasma to the electrode.Ions ﬂowing out of the bulk plasma near the center of the discharge can be accelerated by the sheath ﬁelds to high energies as they ﬂow to the substrate,leading to energetic-ion enhanced processes.Typical ion-bombarding energies E i can be as high as V rf =2for symmetric systems (Fig.1.13)and as high as V rf at the powered electrode for asymmetric systems (Fig.1.12).A quantitative description of capacitive discharges is given in Chapter11.FIGURE 1.12.Capacitive rf discharges in (a )plane parallel geometry and (b )coaxial “hexode”geometry (after Lieberman and Gottscho,1994).1.3DISCHARGES 15。

光学专业词汇单词

AAmorphous 无定性的，无组织的Amplitude 广阔，丰富，振幅Analyte 分析物Anisotropic 各项异性的Annihilation 湮灭Anode 阳极Antenna 天线Angstrom 埃Alignment 对准，调整，定位Aliasing 混淆现象Aperture 孔，穴，缝隙，光圈，孔径Aperture 孔，穴，缝隙，光圈，孔径Attenuation 变薄，稀薄化，变细，衰减Airbome 空运的，空气传播的，空降的Azimuth angle 方位角Avalanche 雪崩；雪崩Acronym 只取首字母缩写词BBarium titanate 钛酸钡Bandgap 能带隙Bandpass 通频带，带通Bulk 大批的，大量的Built-in 内置的，固定的，嵌入的；内置Burst 爆裂，炸破，急于，爆发；突然破裂，爆发，脉冲Bioluminescence 生物发光Bilinear 双线性的Bombard 炮轰，轰击BER 误码率CCompound 混合物，化合物Covalent 共价的Constructive interference 相厂干涉Conserve 保存，保藏Coil 线圈，线阻，感应器Compromise 妥协，折中；妥协，折中，危及....的安全Convolution 回旋，盘旋，卷绕Cosecant 余割Congestion 拥挤Congruent 适合的，一致的，全等的，叠合的，同余的Constraint 约束，强制，局促Convolution 卷积Counterpart 副本，对应物Centrosymmetric 中心对称的Ceramic 陶瓷的Cross-section 横截面Crosstalk 色度亮度干扰Cumulative 累积的Cumbersome 讨厌的，麻烦的，笨重的Curvature 弯曲，曲率Chemiluminescence 化学发光Chebyshev transform 切比雪夫转换Closed loop 闭环Clutter 杂乱回波Cylindrical 圆柱的Cathode 阴极CRT 阴极射线管Circulator 循环器DDeformed 变形的，形状上被扭曲的，畸形的Depletion 损耗Derivative 引出的，系出的；派生的事物，派生词Derive 得自，起源Degenerate 退化的Depletion 损耗Deliver 交付，输送，投递Demanding 过分要求的，苛求的Demultiplexer 信号分离器，多路输出选择器Destructive interference 相消干涉Decibel 分贝Decimation 十中抽一，抽选Dedicated 专注的，献身的，专用，指定Depict 描述，描写Dielectric 电介质，绝缘体，非传导性的Differentiating 求........的微分，计算导数或微分Dilute 冲淡，稀释；稀释的Dimensionless 无量纲的，无一次的Dipoles 双极子，偶极Distortion 扭曲，变形，曲解，失真Dispersed 被驱散的，被分散的，散布的Dispersion 散布，驱散，传播，散射Dielectric 电介质，绝缘体；非传导性Disciplinary 训练的，训诫的，规律的规程，学科Discrete 不连续的，离散的Dominant 有统治权的，占优势的，支配的Donor 施主Doped 掺杂质的Duality 二元性Ducting 大气波导现象EElectroluminescence 电场发光Elevation angle 升运角，倾斜角，仰角Enzyme 酶End-to-end 端到端Envelope 包络线，包络面Extract 萃取物，浓缩物Extrinsic 非本征Equilibrium 平衡Etching 蚀刻Essentially 本质上，本来Evaluate 评价，估计，求.....的值；评价FFerroelectricity 铁电现象Feedback 回授，反馈，反应Foe 反对者，敌人，危害物Foil 箔，金属薄片，叶形片，烘托，衬托；衬托，阻止，挡开，挫败，贴箔于Forward-bias 正向偏压Formidable 强大的，令人敬畏的，可怕的，艰难的Fluorescent 荧光的Flux 涨潮，变迁，流量，通量；熔化，流出；使熔融，用焊剂处理Flashlight 手电筒，闪光灯Flock 羊群，群，大量，众多；聚结Fluctuation 波动，起伏Finite 有限的，有穷的，限定的Finite 有限的，有穷的，限定的Fringing 边缘现象，散射现象Facilitate 推动，帮助，使容易，促使Fundamental 原理GGauge 标准尺，规格，量规，量表，测量Germanium 锗Gigahertz 千兆赫Glancing 方向上是斜的，倾斜的或偏斜的HHerein 于此，在这里Humidity 湿气，潮湿，湿度，沼泽中的肥沃高地Hand in hand 手拉手，联合Histogram 直方图，条形图，矩形图IIncentive 动机，激励的Induce 劝诱，促使，导致，引起，感应Inherently 天性地，固有地Infinite 无限的东西，无穷大；无穷的，无限的，无数的，极大的Inserted 插入的，嵌入的，着生的，附着的Invert 转化的；使颠倒，使转化；颠倒的事物Intercept 中途阻止，截取Interleave 交错，隔行扫描，插帧Inter 埋葬，葬，埋Interdisciplinary 各学科间的Interpolation 插入，内插，插值法，内插法，移植Intrinsic 固有的，内在的，本质的Invoke 调用Incoherent 不连贯的，语无伦次的Indices 指数，index的复数Insulating 绝缘的Interdigitate 相间错杂，互相交叉Incident 事件，事变；附带的，易于发生的Inevitably 不可避免的Intensity 强烈，剧烈，强度，亮度Interfere 干涉，干预，妨碍，打扰Intergalactic 银河间的Impedance 阻抗，全电阻，阻抗Implantation 培植，灌输Implantation 注入Impedance 阻抗，全电阻，阻抗Ion 离子Ionization 电离化Isothermal 等温的，等温线的；等温线Identical 同一的，同样的LLinearize 使线性化Lithium 锂Limes limites边境或边界的防线，尤其罗马帝国的Line of sight 视线，瞄准线Luciferin 虫荧光素，荧光素Luminescent 发冷光的Longitudinal 经度的，纵向的Lattice 格子Lengthy 冗长的，过分的MMacroscopic 肉眼可见的，巨观的Magnetic 磁的，有磁性的，有吸引力的Mask 屏蔽码Mainframe 主机，主机柜，大型机Mapping 映射，绘制.....之地图，计划Mechanism 机械装置，机构，机制Membrane 膜，隔膜Mean square 均方Methodology 方法论，方法学Megahertz 兆赫MESFET 金属半导体场效应晶体管Microscopy 显微镜方法Miniscule 极小的，细微的Mitigate 减轻Monolithic 单片电路，单块集成电路Moot 未决议的，无实际意义的Modulated 已调整的，被调制的Momentum 动量Module 模数，模块Monopulse 单脉冲Motivated 有根据的，有动机的，由.....推动的MOSFET 金属氧化物半导体场效应管NNoteworthy 值的注目的，显著的Node 节点Noninverting 放大器Necessitate 成为必要Niobate 铌酸盐OOpaque 不透明物；不透明的，不传热的，迟钝的Opto-coupler 光耦合器Opto-isolator 光隔离器Optimal 最佳的，最优的Overshadow 使显得不重要，遮蔽Overlap 交叠，复合Ominated 受控的Oscillation 振动PPolycrystalline 多晶的Polymer 聚合体Polyvinylidene fluoride 聚氟乙烯Potential 潜在的，可能的，势的，位的；潜能，潜力，电压Porous 多孔的，有孔的Potential 潜在的，可能的，势的，位的；潜能，潜力，电压Polarization 偏振，极化，两极化，分化Postprocessing 后加工，后处理Photolithographic 照相平版印刷Phosphor 磷光体Photoconductive 光敏的Photon 光子Phototransistor 光电晶体管Photons 光子，光量子Photodiode 光敏二极管，光电二极管Phased 定相的Phase-lock 锁相Permittivity 介电常数Perovskite 钙钛矿Perturbation 扰动，扰乱，干扰，摄动Piezoelectric 压电的Piezojunction 偏振极化Propagate 繁殖，传播，宣传，扩散Proportional 比例的，成比例的，相称的，均衡的Prominent 卓越的，显著的，突出的Plankton 浮游生物Plasma 等离子体Pyroelectricity 焦热电PET 正电子X射线层析术Pseudorandom 伪随机的Parasitic 寄生的QQuantum 量，额，量子，量子论Quanta 量子Quantization 量子化RReciprocally 相互地，相反地Redeeming 补偿的，弥补的Resistivity 抵抗力，电阻系数Resonators 谐振器Reversible 可逆的Refined 精制的，优雅的，精确的Resolution 分辨率Resonator 谐振器，振荡电路Retract 缩合，缩进，所卷，收回，取消，撤销Rearrange 再排列，重新整理Resistor 电阻器Refine 提纯，变优雅，推敲，琢磨，改善，改进Repertoire 节目，保留剧目，指令表，指令系统SSpatial 空间的Spectral 光谱的，频谱，光谱Spill 溢出，溅出，摔下，木片，小塞子，暴跌，溢出量；使溢出，使散落，洒，使流出，使摔下，倒出；溢出，涌流，充满Spontaneous 自发的，自然产生的Sputtered 阴极真空喷镀，阴极溅镀Splice 接合，连接Sporadic 零星的Substrates 底层，下层Substrate 基片，衬底，基底Superposition 重叠，重合，叠合Superheterodyne 超外差式，收音机；超外差的Surveillance 监视，监督Standpoint 立场，观点Steep 陡峭的，险峻的，急剧升降的，不合理的；悬崖，峭壁，浸渍，浸渍液；浸，泡，沉浸Stack 叠加Steer 导引，引入，操纵Straddle 跨骑Stochastic 随机的Saturation 饱和Sag 松弛，下陷，下垂，下跌，漂流；下垂，下陷，物价下跌，随风漂流，垂度sinusoidal 正弦曲线，窦状小管，窦状隙Sidelobe suppression 旁瓣抑制Searchlight 探照灯Series 连续，系列，丛书，级数Synthetic aperture radar 合成孔径雷达Synchronization 同一时刻，同步Scaling 缩放比例Solvent 溶解的，有偿付能力的，有溶解力的；溶媒，溶剂，解决方法Shifter 移位器，移相器Swath 收割的刈痕，细长的列SNR 信噪比，信号噪声比TTemporal 时间的，当时的，暂时的Terminal 终点站，终端，接线端；末期，每期的，每学期的Terminology 术语学Tenuous 纤细的Terrain 地形Trapping 截留，俘获Trigonometry 三角法Trough 槽，水槽，饲料槽，木钵Transition 转变，转换，跃迁，过滤，变调Transverse 横向的，横断的Tractable 易驾驭的，驯良的，易管教的，易处理的Trade-off 权衡，折中，折中方案，综合Transient 短暂的，瞬时的；瞬时现象Tolerance 公差，宽容，忍受，容忍；给规定公差Topology 拓扑，布局，拓扑学Thermodynamics 热力学Throughput 吞吐量，通过量，解题能力，吞吐率Tapering 尖端细的Tade off 权衡Titanate 钛酸盐UUnderlying 在下面，根本的，潜在的，优先的Unity 团结，联合，统一，一致Unmodulated 未调整的，未压低的，未调制的Ubiquitous 到处存在的，普遍存在的VVirtual 虚的，实质的，有效的，事实上的Violate 违犯，亵渎，冒犯，干扰，违反，妨碍Valence 价，原子价Vehicle 交通工具，车辆，媒介物，传达手段ZZirconate 锆酸盐Zenith 顶点，顶峰，天顶，最高点。

A New Equation of State for Carbon Dioxide Covering the Fluid Region

1514
1514 1516 1516 1516 1516 1517 1517 1518 1518
3.3 3.4 3.5 3.6 3.7 3.8 4.
Melting Pressure. . . . . . . . . . . . . . . . . . . . . . .. Sublimation Pressure. . . . . . . . . . . . . . . . . . . .. Vapor Pressure ....................... " Saturated Liquid Density. . . . . . . . . . . . . . . .. Saturated Vapor Density. . . . . . . . . . . . . . . . .. Caloric Data on the Liquid-Vapor Phase Boundary. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Experimental Basis of the New Equation of State. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 4.1 Thermal Properties .................... " 4.2 Specific Isobaric Heat Capacity. . . . . . . . . . .. 4.2.1 Experimental Results for the Specific Isobaric Heat Capacity. . . . . . . . . . . . .. 4.2.2 Results for the Specific Isobaric Heat

Biochemical Thermodynamics

Biochemical Thermodynamics
Andy Howard Biochemistry, Fall 2009 IIT
08/27/2009 Biology 401: Thermodynamics 1
Thermodynamics matters!
• Thermodynamics tells
Biology 401: Thermodynamics p. 7 of 45
08/27/2009
… but first: iClicker quiz!
• 1. Which of the following statements
is true?
– (a) All enzymes are proteins. – (b) All proteins are enzymes. – (c) All viruses use RNA as their transmittable genetic material. – (d) None of the above.
Biology 401: Thermodynamics p. 13 of 45
•
• •
08/27/2009
That makes sense if…
• It makes sense
Boltzmann Gibbs
• • •
•
provided that we understand the words! Energy. Hmm. Capacity to do work. Entropy: Disorder. (Boltzmann): S = klnW Isolated system: one in which energy and matter don’t enter or leave An organism is not an isolated system: so S can decrease within an organism!

Energy release due to antineutrino untrapping from hot quark stars

a rXiv:as tr o-ph/4273v13Fe b24February 2,20089:6Proceedings Trim Size:9in x 6in AGUI˙Korea ENERGY RELEASE DUE TO ANTINEUTRINO UNTRAPPING FROM HOT QUARK STARS ∗D.N.AGUILERA,†Fachbereich Physik,Universit¨a t Rostock,Universit¨a tsplatz 1,18051Rostock,Germany Instituto de F´ısica Rosario,Bv.27de febrero 210bis,2000Rosario,Argentina E-mail:deborah@darss.mpg.uni-rostock.de D.BLASCHKE Fachbereich Physik,Universit¨a t Rostock,Universit¨a tsplatz 1,18051Rostock,Germany Bogoliubov Laboratory for Theoretical Physics,JINR,141980Dubna,Russia email:david@thsun1.jinr.ru H.GRIGORIAN Fachbereich Physik,Universit¨a t Rostock,Universit¨a tsplatz 1,18051Rostock,Germany Department of Physics,Yerevan State University,Alex Manoogian Str.1,375025Yerevan,Armenia email:hovik@darss.mpg.uni-rostock.deAn equation of state for 2-ﬂavor quark matter (QM)with diquark condensation un-der the conditions for compact stars -β-equilibrium,charge and color neutrality-is presented.Trapped antineutrinos prevent the formation of the diquark condensate at moderate densities above a critical value of the antineutrino chemical potential µc ¯νe .The following consequences are presented:1)The star develops a 2-phase structure (µ¯νe ≥µc ¯νe ):a color superconducting QM core and a normal QM shell.2)During the cooling,when the temperature is small enough (T <1MeV)the antineutrino mean free path becomes larger than the thickness of the normal QM shell and the antineutrinos get untrapped in a sudden burst.The energy release is estimated as ≃1052erg and an antineutrino pulse is expected to be observed.February2,20089:6Proceedings Trim Size:9in x6in AGUI˙Korea21.IntroductionIt has been proposed that cold dense quark matter should be in a su-perconducting state with the formation of a diquark condensate1,2.Theconsequences of the diquark condensation for the conﬁguration and thecooling behaviour of compact stars have been broadly studied3,4,5,6andthe question if this phase can be detected by the signatures still remains7.Also the engine for the most energetic phenomena in the universe like supernova explosions and gamma ray burst does not have a satisfactoryexplanation yet8and it has been proposed that the energy involved couldbe related with the occurence of the color superdonductivity phase9,10.Since the pairing energy gap in quark matter is of the order of the Fermi energy,the diquark condensation gives a considerable contributionto the equation of state(EoS)that is estimated of the order of(∆/µ)2.Disregarding relativistic eﬀects,the total binding energy release in the coreof a cooling protoneutron star has been estimated as(∆/µ)2M core≃1052erg.But,if relativistic eﬀects are considered,the gravitational mass defectof the cooling star decreases when diquark condensation is included andthere is no explosive process6possible since the color superconductivitytransition is second order.In this work a new mechanism of releasing the energy in an explosive way is presented(for the original idea see11).During the collapse of a pro-toneutron star antineutrinos are produced by theβ-processes and remaintrapped due to the small mean free path.This increases the asymmetry inthe system and therefore the diquark condensation is inhibited at moderatedensities.So,a two-phase structure developes in the star:a superconduct-ing interior and a sorrounding shell of normal quark matter,the latterbeing opaque to antineutrinos for T≥1MeV12.In the cooling process theantineutrino mean free path increases above the size of this normal mat-ter shell and an outburst of neutrinos occurs releasing an energy of about1051−1052erg.Thisﬁrst order phase transition leads to an explosivephenomenon in which a pulse of antineutrinos could be observed.1.1.Equation of state for2-ﬂavour quark matterA nonlocal chiral quark model for2-ﬂavour{u,d}and three color{r,b,g}superconducting(2SC)quark matter in the meanﬁeld approximation isused,for details see6,13.The order parameters are the mass gapφf andthe diquark gap∆for the chiral and superconducting phase transitionsrespectively.As in13,the following chemical potentials are introduced:February2,20089:6Proceedings Trim Size:9in x6in AGUI˙Korea3µq=(µu+µd)/2for quark number,µI=(µu−µd)/2for isospin asymmetryandµ8for color charge asymmetry.The deviation in the color space isconsideredµ8≪µq,so the eﬀect of consideringµ8is neglected.The quark thermodynamic potential is expresed as14Ωq(φ,∆;µq,µI,T)+Ωvac=φ24G2−22π2 ∞dqq2{E++E−+ω[E−φ−µI,T]+ω[E−φ+µI,T]+ω[E+φ−µI,T]+ω[E+φ+µI,T]}(1)withω[E,T]=T ln[1+exp(−E/T)].(2) The dispersion relations for the quarks of unpaired and paired colors are respectively,Eφ2=q2+(m+F2(q)φ)2(3)E±φ2=(Eφ±µ)2+F4(¯q)∆2(4)The interaction between the quarks is implemented via a Gaussian form-factor function F(q)in the momentum space(Gaussian types give stable hybrid conﬁgurations7)as F(q)=exp(−q2/Λ2).The parametersΛ=1.025GeV,G1=3.761Λ2and m u=m d=m= 2.41MeV areﬁxed by the pion mass,pion decay constant and the con-stituent quark mass at T=µ=015.The constant G2is a free parameter of the approach and isﬁxed as G2=0.86G1.1.1.1.Stellar matter conditionsThe stellar matter in the quark core of compact stars is considered to consists of u and d quarks and leptons(electrons e−and antineutrinos ¯νe)under the following conditions•β-equilibrium d←→u+e−+¯νe,µe+µ¯νe=−2µI,•Charge neutrality23n d−n e=0,n B+n I−2n e=0,•Color neutrality n8=0,2n qr−n qb=0,February2,20089:6Proceedings Trim Size:9in x6in AGUI˙Korea4where n j=∂Ω12π2µ4−1180π2T4(5)are added to the quark thermodynamical potentialΩ(φ,∆;µq,µI,µe,T)=Ωq(φ,∆;µq,µI,T)+Ωe(µe,T)+Ω¯νe (µ¯νe,T).(6)The baryon chemical potentialµB=3µq−µI is introduced as the conjugate of the baryon number density n B.TheΩfunction can have several minima in theφ,∆plane,an example is shown is Fig.1.The global minimum represents the stable equilibrium of the system and the minima search is perfomed solving the gap equations∂Ω∂∆φ=φ0;∆=∆0=0(7)under the conditions that are mentioned above for the stellar interior.The thermodynamics of the system,e.g.pressure P,energy densityǫ, number density n and entropy density s,is deﬁned via this global minimumΩ(φ0,∆0;µB,µI,T)=ǫ−T s−µB n B−µI n I=−P.(8) To fulﬁll the charge neutrality condition(see Fig.2,right)a mixed phase between a subphase with diquark condensation(subscript∆>0) and normal quark matter subphase(subscript∆=0)is deﬁned via the Glendenning construction.The Gibbs condition for equilibrium atﬁxed T andµB is that the pressure of the subphases should be the sameP=P∆>0(µB,µI,µe,T)=P∆=0(µB,µI,µe,T).(9) The volume fractionχthat is occupied by the subphase with diquark condensation is deﬁned by the charge Q in the subphases,χ=Q∆>0/(Q∆>0−Q∆=0),(10) and is plotted on the right panel in Fig.2for diﬀerent antineutrino chemical potentials as a function ofµB.In the same way,the numberFebruary 2,20089:6Proceedings Trim Size:9in x 6in AGUI˙Korea51×102×10Ω[GeV4]×10-4×10-4φ [MeV]-4×10-2×102×10Ω[GeV 4]∆ [MeV]×10-4×10-4×10-4µB = 933 MeVµB = 1100 MeV Figure 1.Cuts of the thermodynamic potential Ω(φ,∆;µB ,µI ,T =0)in the planes ∆=const (on the left)and φ=const (on the right)for two diﬀerent constant values of µB and the corresponding µI .For µB =933MeV (upper panel)two degenerate minima can coexist at the values:φ=331MeV,∆=0(solid lines)and φ=107MeV,∆=98MeV (dashed lines).For µB =1100MeV (lower panel)the minimum with a nonvanishing diquark ∆=121MeV and φ=54.8MeV (dashed lines)is preferable.This corresponds to a ﬁrst order transition from the vacuum to a superconducting phase.In this example G 2/G 1=1was taken.densities for the diﬀerent particle species j and the energy density are given byn j =χn j ∆>0+(1−χ)n j ∆=0,(11)ǫ=χǫ∆>0+(1−χ)ǫ∆=0.(12)1.1.2.Equation of state with trapped antineutrinosIncreasing the antineutrino chemical potential µ¯νe increases the asymme-try in the system and this shifts the onset of the superconducting phase transition to higher densities.Above a critical value of µ¯νe ≥µc¯νe ≃30MeV (see critical value in Fig.February 2,20089:6Proceedings Trim Size:9in x 6in AGUI˙Korea6µe [MeV]µI[M e V ]µB = 1 GeVµB [MeV]χ=V ∆/[V ∆+V ∆=0]Figure 2.Left :Solutions of the gap equations and the charge neutrality condition (solid black line)in the µI vs.µe plane.Two branches are shown:states with diquark condensation on the upper right (∆>0)and states from normal quark matter (∆=0)on the lower left.The plateau in between corresponds to a mixed phase.The lines for the β-equilibrium condition are also shown (solid and dashed red lines)for diﬀerent values of the (anti)-neutrino chemical potential.The stellar matter should satisfy both conditions (intersection of the corresponding lines)and therefore for µ¯νe =0a mixed phase is preferable.Right :Volume fraction χof the phase with nonvanishing diquark condensate obtained by a Glendenning construction of a charge-neutral mixed phase.Results are shown for two diﬀerent values of µ¯νe .2,on the left)ﬁrst a normal quark matter phase occurs and then the phase transition to superconducting matter takes place,see Fig.3,on the left.The consequences for the equation of state can be seen on the right of the Fig.3:the onset of the superconductivity in quark matter is shifted to higher densities and the equation of state becames harder.1.2.Quark stars and antineutrino trappingThe conﬁgurations for the quark stars are obtained by solving the Tolman-Oppenheimer-Volkoﬀequations for a set of central quark number densities n q for which the stars are stable.In Fig.4the conﬁgurations for diﬀerent antineutrino chemical poten-tials are shown.The equations of state with trapped antineutrinos are softer and therefore this allows more compact conﬁgurations.The presence of antineutrinos tends to increase the mass of the star for a given centralFebruary 2,20089:6Proceedings Trim Size:9in x 6in AGUI˙Korea7µB [MeV]µI [M e V ]φ, ∆ [M e V ]µB [MeV]P [M e V /fm 3]ε [MeV/fm 3]P[M e V/f m3]Figure 3.Left :Solutions of the gap equations and µI as a function of µB .Increasing the antineutrino chemical potential increases the asymmetry in the system and the su-perconducting phase is inhibited at moderates densities.Right :Equation of state for diﬀerent values of µ¯νe of trapped antineutrinos.As µ¯νe increases the equation of state becomes harder.density.A reference conﬁguration with total baryon number NB =1.51N ⊙(where N ⊙is the total baryon number of the sun)is chosen and the case with (conﬁgurations A and B in Fig.4)and without antineutrinos (f in Fig.4)are compared.A mass defect can be calculated between the conﬁgurations with and without trapped antineutrinos at constant total baryon number and the result is shown on the right panel of Fig.4).The mass defect could be interpreted as an energy release if the conﬁgurations A,B with antineutrinos are initial states and the conﬁguration f without them is the ﬁnal state of a protoneutron star evolution.1.2.1.Protoneutron star evolution with antineutrino trappingAfter the collapse of a protoneutron star the star cools down by surface emission of photons and antineutrinos.Antineutrinos are trapped because they were generated by the direct β-process in the hot and dense matter and could not escape due to their small mean free path.The region of the star where the temperature falls below the density dependent critical value for diquark condensation,will transform to the color superconducting stateFebruary 2,20089:6Proceedings Trim Size:9in x 6in AGUI˙Korea8R [km]M[M s un]n q [n 0]M [M s u n ]M f [M sun ]∆ M [% M s u n ]∆E[1052e r g ]Figure 4.Left :Quark star conﬁgurations for diﬀerent antineutrino chemical potentials µ¯νe =0,100,150MeV.The total mass M in solar masses (M sun ≡M ⊙in the text)is shown as a function of the radius R (left panel)and of the central number density n q in units of the nuclear saturation density n 0(right panel).Asterisks denote two diﬀerent sets of conﬁgurations (A,B,f)and (A’,B’,f’)with a ﬁxed total baryon number of the set.Right :Mass defect ∆M and corresponding energy release ∆E due to antineutrino untrapping as a function of the mass of the ﬁnal state M f .The shaded region is deﬁned by the estimates for the upper and lower limits of the antineutrino chemical potential in the initial state µ¯νe =150MeV (dashed-dotted line)and µ¯νe =100MeV (dashed line),respectively.which is almost transparent to (anti)neutrinos.But nevertheless due to the trapped antineutrinos there is a dilute normal quark matter shell which prevents neutrino escape from the superconducting bulk of the star,see Fig.5and Fig.6.The criterion for the neutrino untrapping transition is to cool the star below a temperature of about 1MeV when the mean free path of neutrinos becomes larger than the shell radius 16.If at this temperature the antineutrino chemical potential is still large then the neutrinos can escape in a sudden outburst.If it is small then there will be only a gradual increase in the luminosity.An estimate for the possible release of energy within the outburst scenario can be given via the mass defect deﬁned in the previous subsection between an initial conﬁguration with trapped neutrinos (state A or B )and a ﬁnal conﬁguration without neutrinos (state f ).February 2,20089:6Proceedings Trim Size:9in x 6in AGUI˙Korea9µνe = 100 MeVµνe<= 100 MeVµνeFigure 5.Left graph:Quark star cooling by antineutrino and photon emission from the surface.Middle graph:Two-phase structure developes due to the trapped antineutrinos:a normal quark matter shell and a superconducting interior.Right graph:Antineutrino untrapping and burst-type release of energy.µB [MeV]T [M e V ]Figure 6.Star evolution corresponding to Fig.5plotted in the phase diagram2.ConclusionsThe eﬀects of trapped antineutrinos on the diquark condensates in quark star conﬁgurations are investigated.At ﬁxed baryon number the energy release in the antineutrino untrapping transition is of the order of 1052erg.This is a ﬁrst order transition and leads to an explosive release of energy that could help to explain energetic phenomena in the universe like gamma ray bursts or supernova explosions.February2,20089:6Proceedings Trim Size:9in x6in AGUI˙Korea10AcknowledgmentsD.N.A and D.B.thank the organizers of the KIAS-APCTP InternationalSymposium in Astro-Hadron Physics of Compact Stars for their invitationand in particular D.K.Hong and the staﬀof the Department of Physics atPusan National Univertity for their hospitality and interest in this work.D.N.A acknowledges the DAAD-HOST programm D/03/31497and the lo-cal Department of Physics for theﬁnancial support of the visit to PusanUniversity.The authors enjoyed the wonderful atmosphere and lively dis-cussions with all colleagues during the conference.References1.M.Alford,J.A.Bowers and K.Rajagopal,J.Phys.G27(2001)541[Lect.Notes Phys.578(2001)235][arXiv:hep-ph/0009357].2. D.Blaschke,N.K.Glendenning and A.Sedrakian,“Physics Of Neutron StarInteriors.”Springer Lecture Notes in Physics578(2001).Prepared for ECT*International Workshop on Physics of Neutron Star Interiors(NSI00),Trento,Italy,19Jun-7Jul20003. D.Blaschke,T.Klahn and D.N.Voskresensky,Astrophys.J.533(2000)406[arXiv:astro-ph/9908334].4. D.Page,M.Prakash,ttimer and A.Steiner,Phys.Rev.Lett.85(2000)2048[arXiv:hep-ph/0005094].5. D.Blaschke,H.Grigorian and D.N.Voskresensky,Astron.Astrophys.368(2001)561[arXiv:astro-ph/0009120].6. D.Blaschke,S.Fredriksson,H.Grigorian and A.M.Oztas,[arXiv:nucl-th/0301002].7. D.Blaschke,H.Grigorian,D.N.Aguilera,S.Yasui and H.Toki,AIP Conf.Proc.660(2003)209[arXiv:hep-ph/0301087].8.T.Piran and E.Nakar,arXiv:astro-ph/0202403.9.R.Ouyed and F.Sannino,Astron.Astrophys.387(2000)725[arXiv:astro-ph/0103022].10. D.K.Hong,S.D.H.Hsu and F.Sannino,Phys.Lett.B516,(2001)362[arXiv:hep-ph/0107017].11. D.Aguilera,D.Blaschke and H.Grigorian,[arXiv:astro-ph/0212237].12.S.Reddy,M.Prakash and ttimer,Phys.Rev.D58(1998)013009[arXiv:astro-ph/9710115].13.H.Grigorian,D.Blaschke and D.N.Aguilera,arXiv:astro-ph/0303518.14.O.Kiriyama,S.Yasui and H.Toki,Int.J.Mod.Phys.E10(2001)501[arXiv:hep-ph/0105170].15.S.M.Schmidt,D.Blaschke and Y.L.Kalinovsky,Phys.Rev.C50(1994)435.16.M.Prakash,ttimer,R.F.Sawyer and R.R.Volkas,Ann.Rev.Nucl.Part.Sci.51(2001)295[arXiv:astro-ph/0103095].。

Kinetics and Thermodynamics of Phase Transitions

Kinetics and Thermodynamics of PhaseTransitions相变的动力学和热力学相变，即物质从一个稳定的相态转变为另一个稳定的相态。

对于单一物质的相变，有两个重要的理论：动力学理论和热力学理论。

动力学理论研究相变发生的速度和机制，热力学理论则研究相变发生的原因和过程。

在相变中，热力学和动力学相互联系，共同控制着相变的发生和进行。

一、热力学理论热力学是研究体系宏观状态及其变化的学科，其中相变也是研究的重要内容之一。

相变是由于能量的变化引起的。

在相变过程中，物质体系的各种物理量如温度、压力、物质摩尔数等都发生了变化。

这些变化可以用相变的热力学理论来解释。

1. 热力学参数热力学参数是描述相变过程的关键指标，其中最主要的是相变热。

相变热是在相变过程中吸收或放出的热量，也称为潜热。

相变的热流量为：q = ΔH × n其中，q为相变释放或吸收的热量，ΔH为物质的相变潜热，n为物质摩尔数。

另外，热力学参数还包括相变温度、相变压力、相变熵等。

这些参数与物质的性质、外界条件等有关，不同物质的相变参数也存在差异。

2. 热力学过程相变过程中，热力学过程也是非常重要的。

热力学过程可以分为两类：等温过程和等熵过程。

在等温过程中，相变的压强与热力学参数有关，当达到相变某一温度时，压强会突然发生变化，这时相变会发生。

而在等熵过程中，相变的熵与热力学参数有关。

热力学过程中的熵是体系中无序程度的量度，随相变而发生变化。

3. 热力学状态图热力学状态图是热力学研究中常用的工具，用于描述相变状态的改变。

最常用的状态图是温度-压强图（P-T图）。

P-T图是由温度作为横坐标，压强作为纵坐标，画出不同温度和压强下物质的相变状态。

二、动力学理论动力学理论是研究物质相变过程中的机制和速度的学科，它描述了相变的时间演化过程和物质微观结构的变化。

相变的动力学过程与物质的分子运动、晶格结构和表面缺陷等因素有关。

ReX2(X=S,Se):二维各向异性材料发展的新机遇

ReX2(X=S,Se)：二维各向异性材料发展的新机遇王人焱;甘霖;翟天佑【摘要】二维材料因其不同于体相的超薄原子结构、大的比表面积和量子限域效应等受到了人们的广泛关注.二维各向异性材料作为二维材料家族的一员,其取向依赖的物理和化学性质,使得对该类材料性能的选择性优化成为可能.过渡金属Re基硫属化合物作为各向异性材料的典型代表,具有可调的可见光波段吸收带隙,极弱的层间耦合作用力,以及各向异性的光学、电学性能,现已成为电子和光电子领域的研究热点之一.本文主要介绍了ReX2(X=S,Se)的晶体结构和基本性质,总结目前该材料体系主流的合成方法,研究其各向异性物理特性及优化的手段和条件,并对ReX2的制备和发展进行了展望.%Two dimensional (2D) materials have attracted wide attention due to their ultrathin atomic structure, large specific surface area and quantum confinement effect which are remarkably different from their bulk counterparts.Anisotropic materials are unique among reported 2D materials.Their orientation-dependent physical and chemical properties make it possible to selectively improve the performance of materials.As representative examples, Re-based transition metal dichalcogenides (Re-TMDs) have tunable bandgaps in visible spectrum, extremely weak interlayer coupling, and anisotropic properties in optics and electronics, which make them attractive in the application areas of electronics and optoelectronics.In this riviev, the unique crystal structures and intrinsic properties of the Re-based TMDs semiconductors are introduced firstly, and then the synthetic method is introduced, followed by discussion on the unique physical characterizations and optimized means.Finally,prospects and suggestions are put forward for the preparation and research of ReX2.【期刊名称】《无机材料学报》【年(卷),期】2019(034)001【总页数】16页(P1-16)【关键词】各向异性;ReS2;ReSe2;综述【作者】王人焱;甘霖;翟天佑【作者单位】华中科技大学材料科学与工程学院, 材料成型与模具技术国家重点实验室, 武汉 430074;华中科技大学材料科学与工程学院, 材料成型与模具技术国家重点实验室, 武汉 430074;华中科技大学材料科学与工程学院, 材料成型与模具技术国家重点实验室, 武汉 430074【正文语种】中文【中图分类】TQ174超薄的原子结构和巨大的比表面积赋予二维材料不同于体相的光学、电子学、磁学等方面独特的物理性质。

用于寡核苷酸二级结构预测的热力学数据库研究进展

用于寡核苷酸二级结构预测的热力学数据库研究进展刘哲言;屈武斌;张成岗【摘要】基于核酸分子杂交的生物技术（如PCR）在病原微生物检测、临床诊断等诸多领域中应用广泛，此类技术的可靠性在于寡核苷酸分子与其靶点结合的高稳定性与特异性，而精确预测寡核苷酸与靶分子结合的二级结构是分析其稳定性与特异性的关键。

其中，基于热力学的最近邻模型是寡核苷酸二级结构预测最为可靠的计算方法，但其精确性强烈依赖于精确的热力学参数。

由于寡核苷酸分子二级结构的复杂性，除了完美匹配外，还需要错配、内环、膨胀环、末端摇摆、CNG重复、GU摆动等特殊结构的热力学数据。

本文综述了近年来用于寡核苷酸二级结构预测的有效热力学数据库及相关计算方法，并指出当前热力学数据库的局限及未来发展方向。

%The nucleotide hybridization based molecular biological technologies like PCR have been widely used in many fields, such as pathogenic microorganism detection, clinical diagnosis. And the accurate prediction of secondary structures between oligonucleotide and its binding sites is the key to these technologies. The Nearest-Neighbor Model based on thermodynamics is the most accurate method to predict oligonucleotide secondary structure, and the precision mainly depends on the thermodynamic parameters. Meanwhile, the diversity of secondary structure requires different thermodynamic parameters for different motifs, including perfect matches, mismatches, internal loops, bulge loops, dangling ends, CNG repeats, and GU wobble base pairs. Therefore, this review summarized the current parameter sets available for oligonucleotide secondary structure prediction. We also pointed out thelimitations and future development directions of the thermodynamic database.【期刊名称】《生物信息学》【年(卷),期】2014(000)003【总页数】10页(P196-205)【关键词】寡核苷酸二级结构;热力学数据库;热力学计算【作者】刘哲言;屈武斌;张成岗【作者单位】军事医学科学院放射与辐射医学研究所，蛋白质组学国家重点实验室，全军军事认知与心理卫生研究中心，北京100850;军事医学科学院放射与辐射医学研究所，蛋白质组学国家重点实验室，全军军事认知与心理卫生研究中心，北京100850;军事医学科学院放射与辐射医学研究所，蛋白质组学国家重点实验室，全军军事认知与心理卫生研究中心，北京100850【正文语种】中文【中图分类】Q522近年来，以核酸分子杂交为基础的生物技术如聚合酶链反应、DNA印迹、RNA印迹、芯片杂交等在病原微生物检测、临床诊断中应用广泛，其可靠性依赖于寡核苷酸分子与其靶点结合的高稳定性与特异性，而分析这种结合特性的关键在于寡核苷酸与靶分子结合的二级结构的精确预测，否则会导致假阴性或假阳性的检测结果［1－4］。

03Chapter17 heat and the first law of Thermodynamics(公开课)

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isobaric (Constant-pressure) process adiabatic process adiabatic free expansion specific heat molar specific heats
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P410 P409 P412 P407 P413

Thermodynamics from Monte Carlo Hamiltonian

a rXiv:h e p-la t/2216v111Fe b221Thermodynamics from Monte Carlo Hamiltonian L.A.Caron a H.Kr¨o ger a ∗G.Melkonyan a X.Q.Luo b K.J.M.Moriarty c a D´e partement de Physique,Universit´e Laval,Qu´e bec,Qu´e bec G1K 7P4,Canada b Department of Physics,Zhongshan University,Guangzhou 510275,China c Department of Mathematics,Statistics and Computer Science,Dalhousie University,Halifax,Nova Scotia B3H 3J5,Canada AbstractWe construct an eﬀective low-energy Hamiltonian from the clas-sical action via Monte Carlo with importance sampling.We use Monte Carlo (i)to compute matrix elements of the transition am-plitude and (ii)to construct stochastically a basis.The MC Hamil-tonian allows to obtain energies and wave functions of low-lying states.It allows also to compute thermodynamical observables in some temperature window (starting from temperature zero).We present examples from lattice ﬁeld theory (Klein-Gordon model).2L.A.Caron,H.Kr¨o ger,G.Melkonyan,X.Q.Luo,K.Moriarty1IntroductionThe most interesting phenomena in physics occur in many-body systems. The diﬃculty lies in solving models of such systems.A brilliant idea to do this is the renormalisation group approach`a la Kadanoﬀ,Wilson,Migdal and others.It suggests to compute critical phenomena by constructing an eﬀective(renormalized)Hamiltonian,by thinning out degrees of free-dom in an appropriate manner.Here we suggest to adapt this idea for the pupose to construct an eﬀective Hamiltonian in a low-energy window. The basic idea to thin out degrees of freedom is taken over from lattice ﬁeld theory,where inﬁnite-dimensional integrals(path integrals)are suc-cessfully simulated by a small number of representative conﬁgurations.In analogy to the representative conﬁgurations of path integrals,we construct a representative basis of Hilbert states via a Monte Carlo algorithm with importance sampling.Furthermore we use the Monte Carlo algorithm to compute matrix elements of the transition amplitude.In standard Lagrangian latticeﬁeld theory,one is used to construct a corresponding lattice Hamiltonian via the transfer matrix,which corre-sponds to the transition amplitude for inﬁnitesimal short time(when the lattice spacing a t goes to zero).As a result,oneﬁnds a Hamilton operator (on the lattice)which still has the character of a many-body Hamiltonian. In contrast to that,we start out from the transition amplitude for aﬁ-nite time(in imaginary time corresponding to someﬁnite temperature). We compute the transition matrix for all transitions,where the states are taken from theﬁnite stochastically generated basis.As a result,weﬁnd an eﬀective Hamiltonian,i.e.its spectrum and eigen states.It is evident that such Hamiltonian covers only a window of physics,which in this case is a temperature window,starting from temperature zero.From the viewpoint of the enormous success of standard Lagrangian latticeﬁeld theory,one may ask:Do we need such an eﬀective Hamil-tonian?To give an example:Spectrum and wave functions of excited states.Wave functions in conjunction with the energy spectrum contain more physical information than the energy spectrum alone.Although lat-tice QCD simulations in the Lagrangian formulation give good estimates of the hadron masses,one is yet far from a comprehensive understand-ing of hadrons.Let us take as example a new type of hardrons made of gluons,the so-called ttice QCD calculations[1]predict the mass of the lightest glueball with quantum number J P C=0++,toThermodynamics from Monte Carlo Hamiltonian3 be1650±100MeV.Experimentally,there are at least two candidates: f0(1500)and f J(1710).The investigation of the glueball production and decays can certainly provide additional important information for experi-mental determination of a glueball.Therefore,it is important to be able to compute the glueball wave function.The standard Lagrangian lattice for-mulation has made slow progress also in some other areas,like on hadron structure functions(not only moments)in particular at small Q2and at small x B,as well as on scattering amplitudes.2Eﬀective HamiltonianLet us discuss the construction of the eﬀective Hamiltonian in several steps[2].First,consider in quantum mechanics in1-dim the motion of a single particle of mass m under the inﬂuence of a local potential V(x).Its classical action is given byS= dt m4L.A.Caron,H.Kr¨o ger,G.Melkonyan,X.Q.Luo,K.Moriartythe matices U and D have the following meaning,U†ik=<x i|E eff k>D k(T)=e−E ef f k T/¯h,(5)i.e.,the k−th eigenvector|E effk >of the eﬀective Hamiltonian H eff can beidentiﬁed with the k−th column of matrix U†and the energy eigenvaluesE eff k of H eff can be identiﬁed with the logarithm of the diagonal matrixelements of D(T).This yields an eﬀective Hamiltonian,H eff=Nk=1|E eff k>E eff k<E eff k|.(6)Note that in the above we have been mathematically a bit sloppy.The states|x i are not Hilbert states.We have to replace|x i by some”lo-calized”Hilbert state.This can be done by introducing box states.We associate to each x i some box state b i,deﬁned byb i(x)= 1/√x i+1x i dy x j+1x j dz [dx]exp[−S0[x]/¯h] y,T z,0,(9)Thermodynamics from Monte Carlo Hamiltonian5 Here e−S0/¯h is the weight factor and e−S V/¯h is the observable.M(0)ij(T) stands for the transition amplitude of the noninteracting system,which is(almost)known analytically.For details see ref.[2].Carrying out these steps allows to construct an eﬀective Hamiltonian,which reproduces well low energy physics,provided that the box functions cover an interval large enough(depending on the range of the potential)and the resolution∆x is small enough.This can be achieved with a small numerical eﬀort for a one-body system in1dimension.Our goal is,however,to solve many-body systems.For such purpose,the above regular basis fails.What to do in such systems is the subject of the following section.4Stochastic basisIt is evident that the regular basis deﬁned above becomes prohibitively large when applied to a many-body system.For example,in a spin model of a1-dimensional chain of30atoms with spin1/2,the Hilbert space has the dimension D=230=1073741824.For such situations we wish to construct a smaller basis which gives an eﬀective Hamiltonian reproducing well low-energy observables.Why should such a basis exist in theﬁrst place?The heuristic argument is the Euclidean path integral,which,when evaluated via Monte Carlo with importance sampling,gives a good answer for the transition amplitude.In particular,this is possible by taking into account a”small”number of conﬁgurations(e.g.in the order of100-1000).In a crude way the conﬁgurations correspond to basis functions. Thus we expect that suitably chosen basis functions exist,the number of which is in the order of100-1000,which yields a satisfactory eﬀective low energy Hamiltonian.How can we construct such a”small”basis?As example consider a free particle in D=1dimension.Recall:For the free system the transition amplitude readsG Eucl(x,T;y,0)= 2π¯h T exp[−mG Eucl(x,T;0,0),Z6L.A.Caron,H.Kr¨o ger,G.Melkonyan,X.Q.Luo,K.MoriartyZ = dx G Eucl (x,T ;0,0).(11)Then we deﬁne a selection process as follows:Using a random process with probability density P (x )one draws a ”small”set of samples {x ν|ν∈1,...,N eff }.In the case of the free particle,P (x )is a Gaussian,P (x )=12πσexp[−x 2¯h T+∞−∞dx [dy ]exp[−S E [y ]/¯h ] x,T 0,0.(13)Using a Monte Carlo algorithm with importance sampling (e.g.,Metropo-lis)one generates representative paths,which all start at x =0,t =0and arrive at some position x at time t =T .Let us denote those paths (conﬁgurations)by C ν≡x ν(t ).We denote the endpoint of path C νat time t =T by x ν≡x ν(T ).Those form the stochastically selected nodes,which deﬁne the stochastic basis.5NumericalresultsThermodynamics from Monte Carlo Hamiltonian75.1Quantum mechanics The Monte Carlo Hamiltonian has been tested on a number of quantum mechanical potential models,by computing the spectrum,wave functions and thermodynamical observables in some temperature window [2,3,4,5].Although the results from the Monte Carlo Hamiltonian agree well with the exact results,low-dimensional models in Q.M.are not the target of this method.The target is rather high-dimensional models or models with a large number of degrees of freedom.The reason for this is based on the same principle which applies to numerical integration with Monte Carlo:The Monte Carlo method is not the most eﬃcient method when doing low-dimensional integrals.However,it is most eﬃcient when doing integrals in high dimensions (e.g.path integrals).5.2Klein-Gordon modelWe consider in D=1a chain of coupled harmonic oscillators,which is equivalent to the Klein-Gordon ﬁeld on a 1+1lattice.Here we consider a chain of oscillators.The model is given byS =dt T −V T =Nn =112N n =1Ω2(q n −q n +1)2+Ω20q 2n .(14)The parameters have been chosen as m =1,Ω=1,Ω0=2,N osc =9,a =1,T =2and ¯h =1.For the adjustable parameter σin the stochastic basis,we choose σ=E and speciﬁc heat C .8L.A.Caron,H.Kr¨o ger,G.Melkonyan,X.Q.Luo,K.MoriartyTable1:Spectrum of Klein-Gordon model on the lattice,MC Hamiltonian (stochastic basis)versus exact result.n E exactn10.90466319216812.95683055733412.98502357873713.04431158264713.29996734124213.34548063839413.55219513368713.58579498636113.68013674893313.74491908747714.98473701138515.01235380314515.0572********15.10890465202015.12535671356115.18741329003915.30853649010215.39625568658715.42070803141215.4328238107892sinh(β¯hωl/2),Z Tr(H exp(−βH))=−∂log Z2coth(β¯hωl/2),C(β)=k B ∂∂T=−k Bβ2∂∂β=k BN oscl=1 β¯hωl/2Ω20+4Ω2sin2(p l∆x/2),Thermodynamics from Monte Carlo Hamiltonian9∆p=2π/(N osc∆x),x j=[−(N osc−1)/2+(j−1)]∆x,p l=[−(N osc−1)/2+(l−1)]∆p.(16) Here j and l run from1to N osc(number of oscillators).∆x=a=1is the lattice spacing,β=T/¯h,the temperature is related toβvia T=1/(βk B), and k B is the Boltzmann constant.Since we have approximated H by H eﬀ,MC Hamiltonian∆∆∆∆∆∆∆∆∆∆∆∆∆∆∆∆∆∆∆∆∆Analytical resultFigure1:Speciﬁc heat(C/k B)of the Klein-Gordon model on a1+1dimensional lattice.we can express those thermodynamical observables via the eigenvalues of the eﬀective HamiltonianZ eﬀ(β)=Nn=1e−βE eﬀn,Z eﬀ(β),C eﬀ(β)=k Bβ2 N n=1(E eﬀn)2e−βE eﬀn E eﬀ(β) 2 .(17)Since this is a static system,the eigenvalues should in principle not vary withβ.This is observed numerically within statistical errors whenβand10L.A.Caron,H.Kr¨o ger,G.Melkonyan,X.Q.Luo,K.MoriartyN stoch are not too ing this assumption and the spectrum at β=2,we can compute thermodynamical quantities for other values ofβ. The speciﬁc heat as a function ofβis shown in Fig.[1].Again,the results from the MC Hamiltonian are in good agreement with the analytical ones whenβ>1.Preliminary results for larger N osc indicate that it is not necessary to increase N stoch accordingly.This property is very important for an application of the algorithm to many-body systems and QFT.6SummaryIn this paper,we have extended the eﬀective Hamiltonian method with a stochastic basis to QFT,and taken the Klein-Gordon model as an ex-ample.The results are very encouraging.We believe that the application of the algorithm to more complicated systems will be very interesting.It will allow a non-perturbative investigation of physics beyond the ground state.AcknowledgementsH.K.and K.M.are grateful for support by NSERC Canada.X.Q.L.has been supported by NSF for Distinguished Young Scientists of China,by Guangdong Provincial NSF and by the Ministry of Education of China. References[1]X.Q.Luo and Q.Z.Chen,Mod.Phys.Lett.A11(1996)2435;X.Q.Luo,Q.Chen,S.Guo,X.Fang and J.Liu,Nucl.Phys.B(Proc.Suppl.)53(1997)243.[2]H.Jirari,H.Kr¨o ger,X.Q.Luo and K.J.M.Moriarty,Phys.Lett.A258(1999)6.[3]X.Q.Luo,C.Q.Huang,J.Q.Jing,H.Jirari,H.Kr¨o ger and K.J.M.Mo-riarty,Physica A281(2000)201.[4]C.Q.Huang,J.Q.Jiang,X.Q.Luo,H.Jirari,H.Kr¨o ger andK.J.M.Moriarty,High Energy Phys.Nucl.Phys.24(2000)478.Thermodynamics from Monte Carlo Hamiltonian11 [5]J.Q.Jiang,H.C.Qing,X.Q.Luo,H.Jirari,H.Kr¨o ger and K.J.M.Mo-riarty,Comm.Theor.Phys.34(2000)723.。