C6-thermodynamics of phase transformation(1)
正极相变和石墨相变
正极相变和石墨相变英文回答：Positive phase transition and graphite phase transition are two different types of phase transitions that occur in different materials. Positive phase transition refers to the transition from a solid phase to a liquid phase, while graphite phase transition refers to the transition from a graphite phase to a different phase, such as diamond or amorphous carbon.Positive phase transition, also known as melting, occurs when a solid material is heated to a certain temperature, known as the melting point. At this temperature, the intermolecular forces holding the solid together weaken and the solid starts to transform into a liquid. This transition is characterized by an increase in entropy and a decrease in the lattice structure of the material. An example of positive phase transition is the melting of ice into water when heated.Graphite phase transition, on the other hand, occurs when graphite, a form of carbon consisting of layers of hexagonal rings, undergoes a structural transformation into a different phase. This can happen under high pressure or high temperature conditions. One example of graphite phase transition is the transformation of graphite into diamond, which occurs under extreme pressure and temperature conditions deep within the Earth's crust. Another example is the transformation of graphite into amorphous carbon, which occurs when graphite is heated to high temperatures in the absence of oxygen.Both positive phase transition and graphite phase transition are important in various fields of study. Positive phase transition is of great significance in materials science, as it affects the properties and behavior of materials. For example, the melting point of a substance determines its ability to be used as a solid or a liquid in various applications. Graphite phase transition, on the other hand, is important in understanding the properties and behavior of carbon-based materials. Thetransformation of graphite into diamond, for instance, results in a material with very different properties, such as increased hardness and thermal conductivity.In conclusion, positive phase transition and graphite phase transition are two different types of phasetransitions that occur in different materials. Positive phase transition refers to the transition from a solidphase to a liquid phase, while graphite phase transition refers to the transformation of graphite into a different phase. Both types of phase transitions have significant implications in materials science and the study of carbon-based materials.中文回答：正极相变和石墨相变是发生在不同材料中的两种不同类型的相变。
CALPHAD软件介绍
Abstract
The phase-field method has become an important and extremely versatile technique for simulating microstructure evolution at the mesoscale. Thanks to the diffuse-interface approach, it allows us to study the evolution of arbitrary complex grain morphologies without any presumption on their shape or mutual distribution. It is also straightforward to account for different thermodynamic driving forces for microstructure evolution, such as bulk and interfacial energy, elastic energy and electric or magnetic energy, and the effect of different transport processes, such as mass diffusion, heat conduction and convection. The purpose of the paper is to give an introduction to the phase-field modeling technique. The concept of diffuse interfaces, the phase-field variables, the thermodynamic driving force for microstructure evolution and the kinetic phase-field equations are introduced. Furthermore, common techniques for parameter determination and numerical solution of the equations are discussed. To show the variety in phase-field models, different model formulations are exploited, depending on which is most common or most illustrative. c 2007 Elsevier Ltd. All rights reserved.
Thermodynamics培训课件.ppt
Gibbs free energy for a phase:
G = H - TS
Where:
G = Gibbs Free Energy H = Enthalpy (heat content) T = Temperature in Kelvins S = Entropy (can think of as randomness)
Thermodynamics
Begin with a brief review of Chapter 5
Natural systems tend toward states of minimum energy
Energy States
• Unstable: falling or rolling
Stable: at rest in lowest energy state
Gas Pressure-Volume Relationships
Since
z GP2 - GP1 =
P2
VdP
P1
z we can substitute RT/P for V (for a single mole of gas), thus:
G P2 - G P1 =
P2 RT dP
P P1
z and, since R and T are certainly independent of P:
The form of this equation is very useful
GP, T - GTo = RT ln (P/Po)
For a non-ideal gas (more geologically appropriate) the same form is used, but we substitute fugacity ( f ) for P
MolecularThermodynamicsPDF：分子热力学的PDF
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一种热解炭在金属钠中的相变
一种热解炭在金属钠中的相变徐子颉*吉涛王玮衍夏炳忠马超甘礼华(同济大学化学系,上海200092)摘要：通过酚醛树脂的裂解和碳化所形成的热解炭与金属钠在氩气保护气氛中加热,得到一种无定形碳在常压和较低温度下进行石墨化的方法,并研究了热解炭在金属钠熔体中的相变.对所得样品用X 射线粉末衍射(XRD)、光散射拉曼光谱、透射电子显微镜(TEM)以及Brunauer-Emmett-Teller (BET)法氮气吸附进行表征与分析.结果表明:热解炭在金属钠熔体中于800°C 加热24h,发生明显的石墨化;于900°C 加热24h,所得样品的石墨化度为40%,石墨化碳的平均厚度约为40nm,孔结构由微孔转变为介孔.探讨了金属钠在无定形碳中的渗透扩散导致其相变的原因.关键词：酚醛树脂;热解炭;石墨化;金属钠;相变中图分类号：O642;O792Phase Transformation of Pyrocarbon in Molten Sodium MetalXU Zi-Jie *JI TaoWANG Wei-YanXIA Bing-ZhongMA ChaoGAN Li-Hua(Department of Chemistry,Tongji University,Shanghai 200092,P .R.China )Abstract ：A method to graphitize amorphous carbon was carried out by annealing pyrocarbon from crackedphenolic resin in molten sodium metal at a lower temperature and ambient pressure and the phase transformation of pyrocarbon from amorphous carbon to crystallized carbon was studied.X-ray diffraction (XRD),Raman scattering spectroscopy,transmission electron microscopy (TEM),and nitrogen gas physisorption by the Brunauer-Emmett-Teller (BET)method were used to probe the prepared samples for carbon composition,particle size,and morphology.The graphitization of amorphous carbon was obvious when being annealed in molten sodium metal in argon atmosphere at 800°C for 24h.For the sample annealed at 900°C for 24h,the degree of graphitization was 40%and the average thickness of the graphitized carbon layers was about 40nm.The effect of sodium metal infiltration into the matrix of amorphous carbon on the graphitization is also discussed.Key Words ：Phenol resin;Pyrocarbon;Graphitization;Sodium metal;Phase transformation[Article]物理化学学报(Wuli Huaxue Xuebao )Acta Phys.⁃Chim.Sin .,2011,27(1)：262-266JanuaryReceived:August 9,2010;Revised:September 12,2010;Published on Web:November 15,2010.∗Corresponding author.Email:xuzijie-tj@;Tel:+86-21-65982654-8430ⒸEditorial office of Acta Physico ⁃Chimica Sinica炭/炭复合材料是一种多相非均质混合物,因其具有高比强度、高比模量等显著的材料结构性能,逐渐成为新一代航空航天材料的发展方向.然而炭/炭复合材料的石墨化,会影响该类材料的力学性能、物理性能和化学性能,是最重要的结构控制因素之一,通过调整该类材料的石墨化状态,可改善其综合性能,从而满足不同的使用要求.因此,开展无定形碳材料在较低温度下的石墨化研究对炭/炭复合材料的应用具有重要的意义.无定形碳的石墨化就是在一定的二维平面范围内有序的乱层结构碳的残片进行定向重排的相变过程.由于在该相变过程中,无定形碳容易形成亚稳态,使得这种相变的阻力增大,因此商品化石墨的生产一般都在2700°C 左右进行.但是,在如此高温条件下进行石墨化,使得材料的力学和电学性能受到损害,如无定形碳材料在2700°C 经石墨化262No.1徐子颉等：一种热解炭在金属钠中的相变所得样品的放电容量为74mAh·g-1,而在1000℃温度条件下石墨化后,所得样品的放电容量为250 mAh·g-1[1].目前,基于溶解再析出和碳化物转化机理的催化石墨化方法可以有效地降低石墨化温度,具体方法主要有两类:其一,在碳基质中加入过渡金属及其氧化物,如Fe、Mn、Cr等过渡金属及其氧化物[2-3];其二,在碳基质中形成三组分的插层化合物,如Tanaike等[4]将金属Li、Na和K溶于四氢呋喃中,获得相应的有机金属化合物,结果表明所得材料的石墨化度很低.Rojas-Cervantes[5]和Oya[6]等合成了分别含有金属Na、K、Mg和Zr的碳的干凝胶,在1000°C氮气气氛中烧结,没有发现这些金属的催化活性,得到的仍然是无定形碳.由于酚醛树脂产碳量高,常被用作制备先进碳材料的先驱物.选用酚醛树脂类物质作为碳源,经热解后得到热解炭,开展其石墨化的研究近年来已引起人们的重视.张福勤等[7]研究了化学气相沉积热解炭的可石墨化性;王永刚等[8]采用化学气相渗透对泡沫碳进行复合处理,在2500°C得到石墨化泡沫碳;周德凤等[9]报道了在酚醛树脂中加入氯化锌,可以改变热解炭的微观结构及石墨化程度;Chen等人[10-11]使用硝酸镨作催化剂研究其对酚醛树脂热解炭的石墨化作用,在催化剂含量为15%(w)以及2400°C时获得最优化的石墨化条件,他们还用含量为29%(w)的石墨氧化物作催化剂在2400°C时获得较完整的石墨结构;Cai等[12]使用含量为5%(w)的铁镍催化剂,在外加磁场以及1200°C时实现酚醛树脂的石墨化.除此之外,还有文章报道[13]使用金属钇作催化剂研究酚醛树脂的催化石墨化.本文通过将酚醛树脂裂解和碳化后形成的热解炭与金属钠在氩气保护下加热,开展无定形碳在金属钠熔体中的相变研究.采用X射线粉末衍射(XRD)以及激光散射拉曼光谱技术,对所得样品碳组成的相态以及层内、层间碳原子的状态进行表征;通过透射电子显微镜(TEM)观察碳组成的形貌,通过比表面积分析研究热解炭在石墨化前后孔结构特征的变化.探讨了金属钠在无定形碳基质中的渗透与扩散对无定形碳相变产生的影响.该方法可用于新型结构的炭/炭复合材料的石墨化研究中.1实验1.1热解炭的制备将市售酚醛树脂(2130型,无锡久耐防腐材料有限公司)放入烘箱(102A-2型,上海试验仪器总厂)中,调节温度到80°C,保温10h,再升温至120°C,保温10h,继续升温至140°C并保温24h,使酚醛树脂完全固化.将固化后的酚醛树脂放入管式炉(SK2-15-13T型,上海实验电阻炉厂)中,通入氩气保护,以10°C·min-1的升温速率升温至200°C,保温3 h,再以相同的升温速率升温至800°C并保温4h,得到热解炭.1.2石墨化方法称取5g按上述方法制备的热解炭,放入带盖的坩埚中,在充有氩气的手套箱(ZKX1型,南京南大仪器厂)内切割金属钠块,并称取3g放置其表面,再将坩埚置于管式炉(SK2-15-13T型,上海实验电阻炉厂)中并通入氩气保护,以10°C·min-1的升温速率升温至所设定温度并保温24h,本实验所设定的温度分别是600、700、800和900°C;将所得样品用蒸馏水超声清洗,直至洗液的pH值为7,再将清洗后的用品在烘箱(102A-2型,上海试验仪器总厂)内于120℃干燥.1.3表征方法使用D8FOCUS型X射线粉末衍射仪(德国, Bruker AXS)对样品进行XRD表征,测试条件为40 kV,40mA,Cu Kα射线;使用Renishaw inVia激光拉曼光谱仪(英国,Renishaw)对所得样品进行拉曼光谱分析;使用S-TWIN F20型场发射透射电镜(荷兰, FEI)对样品进行TEM形貌表征;使用Micromeritics Tristar3000比表面积测定仪(美国,Micromeritics),采用Brunauer-Emmett-Teller(BET)法分析样品的比表面积、孔径分布以及孔结构特征.2结果与讨论选用酚醛树脂作为碳源,经800°C热解、碳化后得到热解炭,用以研究无定形碳材料在金属钠熔体中的相变.由于残存于样品中的金属钠在样品的后处理中遇到空气被氧化,形成的氧化钠成分在XRD检测时会产生很强的衍射峰,干扰了对碳组成的表征,因此,样品在表征前必须经蒸馏水洗涤,去除氧化钠组分.2.1不同温度条件下热解炭在金属钠中的相变图1是热解炭在不同温度条件下进行热处理所得样品的XRD谱.图谱(1)为在没有金属钠存在的条件下,将热解炭在900°C保温24h,所得样品的碳组成仍然是典型的无定形碳,表明无定形碳在此温263Vol.27Acta Phys.⁃Chim.Sin.2011度时没有发生相变.当热解炭与金属钠在600°C 加热24h,得到谱(2),根据文献[6]的解释,表明金属粒子已经渗透和扩散在无定形碳的基质中,使得其中的乱碳结构残片开始在局部进行重新取向,导致2θ分别在25°和45°附近出现较为明显的漫衍射峰.当热解炭与金属钠中的加热温度为700°C 时,得到谱(3),从中可见其特征衍射峰已经明显锐化,表明此时热解炭中的无定形碳已经晶格化.当加热温度升高至900°C ,得到谱(4),显示石墨化碳的特征衍射峰更加锐化.当样品的加热温度从700°C 升高至900°C 时,样品的衍射数据也相应发生变化,其中2θ值从25.9°增加至26.3°,相应的d 002值从0.3433nm 变为0.3406nm.根据Mering 和Maire 公式[14],样品的石墨化度可由G =((0.3440-d 002)/(0.3440-0.3354))×100%计算得到,当加热温度从700°C 升高至900°C 时,所得样品的石墨化度分别从8.5%增加至40%.对一系列样品的XRD 表征结果的分析表明,在金属钠熔体中,无定形碳的碳组成发生明显的变化,随着加热温度的升高,热解炭的石墨化特征愈加明显.图2是所选样品的拉曼谱图.在1350、1570和2700cm -1处的谱峰被分别称为D 、G 和G ′峰.图谱中D 峰是发生于相同碳原子间的拉曼振动模式,G 峰则表示两种不同碳原子之间的光子振动模式,而G ′峰表示一种源自晶面之间的碳原子所发生的光子振动模式,是一种二阶拉曼散射过程.谱图(1)是酚醛树脂裂解碳在没有金属钠存在的条件下,经过900°C 加热后所得样品的拉曼谱图,图谱中D 峰强度高于G 峰并且两峰没有完全分离,另外,图谱中无G ′峰,表明样品对激光的漫散射分别在乱碳结构残片内部的碳原子以及乱碳结构残片间进行,这种光子振动模式证明了热解炭中的无定形碳含有二维有序的乱碳结构而且呈现杂乱无章地堆积.图谱(2)是热解炭在金属钠中,经过700°C 加热所得样品的拉曼谱图,此时D 峰强度降低,G 峰强度增加并呈现两峰分离的迹象,表明激光在样品中不同碳原子间的光子振动模式加强.另外,图谱中同时呈现一个明显的G ′峰,表明光子振动发生在石墨化层间的碳原子之间,进一步说明乱碳结构残片在此时已经发生明显的定向重排.图谱(3)是热解炭在金属钠中,经过900°C 加热所得样品的拉曼谱图,此时D 峰强度明显降低,G 峰强度明显增加而且两峰完全分离,表明光子的振动模式主要发生在晶面之间的碳原子中,说明该样品中的碳原子已经转变为石墨结构.2.2金属钠在无定形碳中的渗透与扩散对其相变的影响根据对所得样品进行的XRD 和拉曼谱分析知,在没有金属钠存在时,热解炭在900°C 加热条件下没有发生相变,而有金属钠存在的条件下,无定形碳在700°C 加热24h 后,观察到无定形碳开始向结晶态碳转化,随着加热温度的升高,这种相态转化更加明显.因此,金属钠的存在是导致热解炭在加热条件下发生相变的必要因素.虽然目前对金属钠与碳组成的相互作用机制进行原位的实时表征和分析还比较困难,但是,根据XRD 和拉曼的表征结果,不仅证实了这种相变的发生,而且揭示金属钠对该相变的重要影响,即金属钠原子在无定形碳中的渗透与扩散引起了其中乱碳结构残片的重排与取向.当金属图1热解炭在不同条件下退火24h 的XRD 图谱Fig.1XRD patterns of pyrocarbons annealed at differentconditions for 24h(1)900°C without sodium metal;(2)600°C,(3)700°C,and(4)900°C in molten sodiummetal2热解炭在900°C (1)以及在金属钠中于700°C (2)和900°C (3)加热24h 的拉曼图谱Fig.2Raman spectra of pyrocarbons annealed at 900°Cwithout sodium metal (1)and at 700°C (2),900°C(3)in molten sodium metal for 24hNo.1徐子颉等：一种热解炭在金属钠中的相变钠原子渗入到乱碳结构残片间,钠原子外层电子的高活泼性,影响了残片中碳原子周围的电场环境,同时渗透与扩散在其中的钠原子可以形成金属钠的连续相,并充当优良的导热介质,使得无定形碳在石墨化过程中的结晶潜热能够通过导热介质及时地向周围环境释放,从而有利于无定形碳在较低温度条件下发生相变.金属钠在无定形碳中的渗透、扩散与加热温度密切相关.随着加热温度的升高,对所得样品的XRD 和拉曼表征结果都表现出了高度的一致性,即石墨化度增加.无定形碳在金属钠中的相变过程示意图如图3所示.对样品形貌学的观察进一步证实了金属钠对热解炭在其中发生相变的影响.图4(a)是热解炭与金属钠在700°C 加热24h 所得样品的TEM 照片,图中“A ”所在区域为无定形碳,“T ”所在区域显现出湍流碳的形貌特征,“G ”区域则显现出石墨化碳的形貌特征.通过对样品不同区域进行TEM 观察,发现湍流碳总是出现在无定形碳和石墨化碳的过渡区域,其形貌特征显示出无定形碳中的乱碳结构残片已在有限范围内进行了定向重排,但不够完整.在700°C 加热条件下,金属钠在无定形碳中的渗透与扩散不完全,没有形成均匀的金属钠连续相,使得乱碳结构残片的定向重排过程不能在长程范围内连续进行.湍流碳的出现使得无定形碳向石墨化碳转化的阻力增加,这也是商品化石墨必须在高温条件下生产的主要原因.图4(b)是热解炭与金属钠在900°C 加热24h 所得样品的TEM 照片,随着加热温度的升高,石墨化碳的厚度与长度显著增加,所得样品中石墨化碳的平均厚度约为40nm,显然升高温度加速了金属钠在碳基质中的渗透与扩散,有利于无定形碳向石墨化碳的转化.2.3在金属钠作用下热解炭中孔结构特征的变化图5是热解炭在金属钠中发生相变前后样品的对氮气的吸附-脱附等温线.从图中可见,热解炭样品的吸附-脱附等温线属于类型I,插图所示的孔分布曲线表明热解炭中存在大量孔径小于2nm 的微孔,等温线中很小的滞后环表明热解炭中的微孔对氮气的吸附与脱附具有良好的可逆性,这些孔结构特征反映出热解炭中的微孔分布在无定形的乱碳结构残片之间并具有良好的连通性.然而当热解炭与金属钠在900°C 加热24h 所得石墨化热解炭样品的氮气吸附-脱附等温线出现一个较大的滞后环(如等温线2所示),插图中的孔分布曲线显示样品中的孔径尺寸主要集中在4-5nm 之间,属于介孔尺寸,表明热解炭在石墨化前后孔结构发生由微孔向介孔发生转变.导致孔结构转化的原因是由于热解炭中图3无定形碳在金属钠中的相变过程示意图Fig.3Sketch map of the phase transformation of amorphous carbons in molten sodium metalThe conditions of (1)-(4)are the same as those inFig.1.图4热解炭与金属钠在700(a)和900°C (b)加热24h 所得样品的TEM 照片Fig.4TEM image of pyrocarbons annealed in molten sodium metal at 700°C (a)and 900°C (b)for 24hArea A denotes amorphous carbons,aera T denotes turbostraticcarbons,and area G denotes graphitic carbons.图5样品的氮气吸附-脱附等温线Fig.5Nitrogen adsorption desorption isotherms ofselected samplesIsotherm 1represents the sample of pyrocarbon and isotherm 2represents the sample of graphitized pyrocarbon.Inset is pore sizedistributioncurve.265Vol.27 Acta Phys.⁃Chim.Sin.2011的乱碳结构残片在金属钠原子的作用下定向重排,使得原先分布在其中的相互连通的微孔发生合并增大,形成了分布在石墨化碳层间的插层状孔,由于此时毛细管作用力的增强,导致样品对氮气的脱附滞后.另外,从图中可见,热解炭发生石墨化后,随着乱碳结构残片的定向重排使得石墨化热解炭样品的比表面积有所下降.酚醛树脂热解炭在金属钠作用下,其孔结构特征的改变是碳组成发生相变的结果,同时也进一步证实了金属钠原子在乱碳结构残片间的渗透与扩散有利于其发生定向重排,从而导致热解炭能够在较低的温度条件下实现石墨化.催化石墨化是通过在碳基质中引入催化剂,以降低石墨化温度,但是,目前的方法对于一些新型碳材料的石墨化显现出一定的缺陷.首先,在材料的制备阶段必须将催化剂加到碳材料的基质中,这势必增加了材料制备的难度,甚至对材质特性产生不良影响.例如,对碳气凝胶材料的石墨化,如果采用现有的催化石墨化方法,就需要在碳气凝胶制备所必经的溶胶-凝胶过程中加入催化剂,它可能改变胶体离子的微环境,继而影响了碳气凝胶的结构特性.其次,目前所采用的催化剂多数是过渡金属的氧化物,在碳材料石墨化以后,很难将催化剂从碳材料的基质中去除干净,这可能对转型后碳材料的电学特性或电化学催化特性等产生影响.再者,现有催化石墨化方法[4-6]对于碳气凝胶的石墨化效果仍不理想.酚醛树脂热解炭在金属钠作用下发生相变进行石墨化,该方法不仅具有操作简单的特点,而且可以避免在碳基质中加入催化剂给材质纯度、特性带来的不利影响并且可以降低材料的制备难度.另外,该方法有利于一些新型多孔性碳材料的石墨化,因为多孔性结构十分有利于金属钠在碳基质中的渗透与扩散.而实现这类材料的低温石墨化,可以使无定形碳材料的多孔特性与石墨晶体材料的材质特性相结合,有助于扩展碳材料在传感器、探测器、航天以及新能源电池等领域的应用范围.我们以自制的碳气凝胶通过文中方法进行石墨化研究,初步结果表明在800°C实现了碳气凝胶的石墨化,相关研究工作正在进行中.3结论由酚醛树脂经过裂解碳化后得到的热解炭,通过与金属钠一起在氩气保护下,在800°C加热24h 可以观察到明显的石墨化现象.金属钠在无定形碳中的渗透与扩散引起乱碳结构残片的定向重排,湍流碳的形成是金属钠在其中的渗透与扩散不均匀所致,是无定形碳向石墨化碳转化的中间相态,通过升高加热温度,可以改善金属钠在其中的扩散,从而提高了石墨化程度.热解炭在金属钠作用下发生石墨化使得样品中的孔结构由微孔转化为介孔,在900°C时石墨化度达到40%,样品中石墨化碳层的平均厚度达到40nm.致谢:本文实验研究过程中的部分分析测试工作得到同济大学化学系实验中心的支持.References1Skowroński,J.M.;Knofczyński,K.;Inagaki,M.Solid State Ionics,2007,178:1372Oya,A.;Otani,S.Carbon,1979,17:1313Curtis,B.J.Carbon,1966,4:4834Tanaike,O.;Inagaki,M.Carbon,1997,35:8315Rojas-Cervantes,M.L.;Alonso,L.;Díaz-Terán,J.;López-Peinado,A.J.;Martín-Aranda,R.M.;Gómez-Serrano,V.Carbon,2004,42:15756Oya,A.;Mochizuki,M.;Otani,S.;Tomizuka,I.Carbon,1979, 17:717Zhang,F.Q.;Huang,Q.Z.;Zou,L.H.;Huang,B.Y.;Xiong,X.;Zhang,C.F.Journal of Inorganic Materials,2004,19(5):1118[张福勤,黄启忠,邹林华,黄伯云,熊翔,张传福.无机材料学报,2004,19(5):1118]8Wang,Y.G.;Lin,X.C.;Yang,H.J.;Zhang,J.S.;Xu,D.P.Journal of Materials Science&Engineering,2008,26(3):365[王永刚,林雄超,杨慧君,张江松,许德平.材料科学与工程学报,2008,26(3):365]9Zhou,D.F.;Xie,H.M.;Zhao,Y.L.;Wang,R.S.Journal of Functional 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C6-thermodynamics of phase transformation(1)概述
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G G T p T p G s T p
6.1 相变分类(按原子迁移特征分类) (3)按原子迁移特征分类 扩散型相变：依靠原子扩散进行 •原有的原子邻居关系被破坏； •溶体成分发生变化。 无扩散型相变：无原子扩散，或虽存在扩散，但不是 相变所必需的或不是主要过程。 •相邻原子的移动距离不超过原子间距，不 破坏邻居关系； •不改变溶体成分。 马氏体相变
铁磁-顺磁转变(Ferromagnetic-paramagnetic transition) Fe、Ni、Co及其合金，各种铁氧体，Mn-Al合物，稀土过渡族元素化合物等 反铁磁(Anti-ferromagnetic)-顺磁转变 Fe、Mn、Cr及部分稀土元素等 超导-常导转变(Superconduct-generally conduct transition) In、Sn、Ta、V、Pb、Nb等纯金属和Nb-Ti、Nb-Zr、 V3Ga、Nb3Sn、Nb3AlGe、Nb3Ge等金属间化合物以及Y-BaCu-O等氧化物超导体等 合金中有序-无序的转变 Au-Cu、Ti-AI、AI-Mn、Cr-AI、Cu-Zn、Cu-Pd、Cu-Pt、 Fe-Co、Fe-AI、Fe-Si、Fe-Ni、Fe-Pt、Ni-V等合金系
Maxwell 方程
V , S p T p T
V V
V V , S S
表现：体积和熵(焓)的突变
二级相变（Second order phase transitions）
在相变过程中，化学势对T,P的一阶偏微分相等，而 二阶偏微分在相变过程中发生突变的相变称为二级相 变。属于二级相变的有：
耦合光热发电储热-有机朗肯循环的先进绝热压缩空气储能系统热力学分析
第 12 卷第 12 期2023 年 12 月Vol.12 No.12Dec. 2023储能科学与技术Energy Storage Science and Technology耦合光热发电储热-有机朗肯循环的先进绝热压缩空气储能系统热力学分析尹航1，王强1，朱佳华2，廖志荣2，张子楠1，徐二树2，徐超2（1中国广核新能源控股有限公司，北京100160；2华北电力大学能源动力与机械工程学院，北京102206）摘要：先进绝热压缩空气储能是一种储能规模大、对环境无污染的储能方式。
为了提高储能系统效率，本工作提出了一种耦合光热发电储热-有机朗肯循环的先进绝热压缩空气储能系统(AA-CAES+CSP+ORC)。
该系统中光热发电储热用来解决先进绝热压缩空气储能系统压缩热有限的问题，而有机朗肯循环发电系统中的中低温余热发电来进一步提升储能效率。
本工作首先在Aspen Plus软件上搭建了该耦合系统的热力学仿真模型，随后本工作研究并对比两种聚光太阳能储热介质对系统性能的影响，研究结果表明，导热油和太阳盐相比，使用太阳盐为聚光太阳能储热介质的系统性能更好，储能效率达到了115.9%，往返效率达到了68.2%，㶲效率达到了76.8%，储电折合转化系数达到了92.8%，储能密度达到了5.53 kWh/m3。
此外，本研究还发现低环境温度、高空气汽轮机入口温度及高空气汽轮机入口压力有利于系统储能性能的提高。
关键词：先进绝热压缩空气储能；聚光太阳能辅热；有机朗肯循环；热力学模型；㶲分析doi： 10.19799/ki.2095-4239.2023.0548中图分类号：TK 02 文献标志码：A 文章编号：2095-4239（2023）12-3749-12 Thermodynamic analysis of an advanced adiabatic compressed-air energy storage system coupled with molten salt heat and storage-organic Rankine cycleYIN Hang1, WANG Qiang1, ZHU Jiahua2, LIAO Zhirong2, ZHANG Zinan1, XU Ershu2, XU Chao2(1CGN New Energy Holding Co., Ltd., Beijing 100160, China; 2School of Energy Power and Mechanical Engineering,North China Electric Power University, Beijing 102206, China)Abstract:Advanced adiabatic compressed-air energy storage is a method for storing energy at a large scale and with no environmental pollution. To improve its efficiency, an advanced adiabatic compressed-air energy storage system (AA-CAES+CSP+ORC) coupled with the thermal storage-organic Rankine cycle for photothermal power generation is proposed in this report. In this system, the storage of heat from photothermal power generation is used to solve the problem of limited compression heat in the AA-CAES+CSP+ORC, while the medium- and low-temperature waste heat generation in the organic Rankine cycle power收稿日期：2023-08-18；修改稿日期：2023-09-18。
热动力学英语
热动力学英语Thermodynamics: The Fundamental Science of Energy TransformationThermodynamics is a branch of physics that deals with the study of energy, its transformation, and its relationship with matter. It is a fundamental science that underpins our understanding of various natural phenomena and the functioning of many technological devices. Thermodynamics is a complex and multifaceted field, but it can be broadly divided into four main laws that govern the behavior of energy and its interactions with the physical world.The First Law of Thermodynamics states that energy can neither be created nor destroyed, but it can be transformed from one form to another. This means that the total energy of an isolated system is constant; it cannot be created or destroyed, but it can be changed in form. For example, when you burn a piece of wood, the chemical energy stored in the wood is converted into heat and light energy. The total amount of energy before and after the burning process remains the same, but its form has changed.The Second Law of Thermodynamics, on the other hand, deals withthe direction and efficiency of energy transformations. It states that energy transformations are not perfectly efficient, and that some energy is always lost as heat during the process. This heat is often referred to as "waste heat" or "entropy," and it cannot be fully recovered or used to do useful work. The Second Law also states that heat naturally flows from hotter objects to cooler objects, and that the entropy of an isolated system always increases over time.The Third Law of Thermodynamics deals with the behavior of matter at extremely low temperatures, near absolute zero. It states that as a system approaches absolute zero, its entropy approaches a constant, usually zero. This means that at absolute zero, a system has the lowest possible energy and disorder, and its properties become increasingly well-defined and predictable.The Fourth Law of Thermodynamics, also known as the Zeroth Law, establishes the concept of temperature and its relationship to the thermal equilibrium of systems. It states that if two systems are in thermal equilibrium with a third system, then they are also in thermal equilibrium with each other. This law is the foundation for the measurement of temperature and the development of thermometers.Thermodynamics has numerous applications in various fields, including physics, chemistry, engineering, and even biology. In physics, it is used to understand the behavior of gases, the efficiencyof engines and refrigeration systems, and the properties of materials at different temperatures and pressures. In chemistry, it is used to study chemical reactions, the stability of compounds, and the behavior of solutions. In engineering, it is used to design and optimize a wide range of systems, from power plants and refrigeration systems to aerospace and automotive technologies.In biology, thermodynamics is used to understand the energy transformations that occur in living organisms, such as the process of photosynthesis, the production of ATP in cellular respiration, and the regulation of body temperature in warm-blooded animals. The principles of thermodynamics also underlie the functioning of many biological systems, such as the transport of molecules across cell membranes and the folding of proteins.One of the key applications of thermodynamics is in the field of energy conversion and storage. The efficiency of energy conversion processes, such as the conversion of chemical energy to electrical energy in a battery or the conversion of thermal energy to mechanical energy in a steam turbine, is governed by the principles of thermodynamics. Understanding these principles is crucial for the development of more efficient and sustainable energy technologies, which are essential for addressing the global challenges of climate change and resource depletion.Another important application of thermodynamics is in the study of the Earth's climate and the global carbon cycle. The greenhouse effect, which is responsible for the warming of the Earth's atmosphere, is a direct consequence of the principles of thermodynamics. The absorption and emission of infrared radiation by greenhouse gases, such as carbon dioxide and methane, are governed by the laws of thermodynamics, and understanding these processes is crucial for predicting and mitigating the effects of climate change.In conclusion, thermodynamics is a fundamental science that underpins our understanding of a wide range of natural and technological phenomena. Its four laws provide a comprehensive framework for understanding the behavior of energy and its interactions with matter, and its applications span a diverse range of fields, from physics and chemistry to engineering and biology. As we continue to face global challenges related to energy, climate, and resource sustainability, the principles of thermodynamics will remain crucial for the development of innovative and sustainable solutions.。
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。
二元金属合金及其相图(7)
Landolt-BörnsteinNew Series IV/5ThermodynamicsPool et al. [67Poo1] have determined thermodynamic activities in the β-phase at several temperatures using a Knudsen effusion technique. Analogous measurements have been performed for the Laves phases.Results obtained by Rolinski et al. [72Rol1] for ternary Ti-Cr-V alloys agree with those reported by Pool et al. [67Poo1]. Activity measurements by Rubatsov et al. [70Rub1] (1023 K…1123 K) are less precise.Thermodynamic activities reported by Pool et al [67Poo1] are presented as isotherms in Fig. 4 (a Ti S ) and Fig. 5 (a Cr S ). From the temperature dependence of the activities enthalpies of formation and entropies of formation of solid Cr-Ti alloys have been calculated [67Poo1]. The results are given in Fig. 6 and Fig. 7,respectively.The enthalpy of transformation for theβ-transition at 94 at% Ti amounts to ∆H T = 1880 (210)J g-atom −1 (Gertsriken et al. [62Ger1]).Thermodynamic calculations of phase equilibria have been performed by Molokanov et al. [75Mol1]and Kaufman et al. [70Kau1, 78Kau1].Fig. 4. Cr-Ti. Thermodynamic activity of Ti in solid solutions at 1523 K and 1633 K.Landolt-BörnsteinNew Series IV/5Fig. 5. Cr-Ti.Thermodynamic activity of Cr in solid solutions at 1523 K and 1633 K.Fig. 6. Cr-Ti. Enthalpy of formation for (Cr, β-Ti) solid solution at 1653 K.Landolt-BörnsteinNew Series IV/5Fig. 7. Cr-Ti. Entropy of formation for (Cr, β-Ti) solid solution at 1653 K.References40Vog1Vogel, R., Wenderott, B.: Arch. Eisenhüttenwes. 14 (1940) 279.50Cra1Craighead, C.M., Simmons, O.W., Eastwood, L.W.: Trans. AIME 188 (1950) 485.51Mcp1McPherson, D.J., Fontana, M.G.: Trans. ASM 43 (1951) 1098.51Mcq1McQuillan, A.D.: Aeronaut. Res. Lab., Dept. of Supply, Australia, Report SM-165, January (1951).52Cuf1Cuff, F.B., Grant, N.J., Floe, C.F.: Trans. AIME 194 (1952) 848.52Duw1Duwez, P., Martens, H.: Trans. 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Rept. AFML-TR-65-2 (1969) 21, 127.69Rud4Rudy, E.: Techn, Rept. AFML-TR-65-2 Part V, Wright Patterson Air Force Base (1969). 70Kau1Kaufman, L., Bernstein, H.: "Computer Calculation of Phase Diagrams", New York: Acad.Press. (1970) p. 188.70Rub1Rubatsov, A.N., Olesov, Yu.G., Cherkashin, V.I., Suchkov, A.B.: Izv. Akad. Nauk SSSR Met. 6 (1970) 84; Russ. Metall. 6 (1970) 56.70Sve1Svechnikov, V.N., Kobzenko, G.F., Ivanchenko, V.G.: Dopov. Akad. Nauk Ukrain. RSR, Ser. A; Fiz. Tekh. Mat. Nauki (1970) 758.70Sve3Svechnikov, V.N., Teslyuk, M.Yu., Kocherzhinskii, Yu.A., Petkov, V.V., Debizha, E.V.: Dopov. Akad. Nauk Ukr. RSR A 32 (1970) 837.71Min1Minaeva, S.B., Budberg, P.B., Gavze, A.L.: Izv. Akad. Nauk SSSR Met. (1971) 205; Russ.Metall. (1971) 145.71Miy1Miyagi, M., Shin. S.: J. Jpn. Inst. Met. 35 (1971) 716.72Rol1Rolinski, E.J., Hoch, M., Oblinger, C.J.: Metall. Trans. 3 (1972) 1413.73Fed1Fedotov, S.G.: Sci. Technol. Appl. Titanium, Proc. Int. Conf., Jaffee, R.I. (ed.), (1973) 871. 74Don1Donohue, J.: "The Structure of the Elements", J. Wiley, New York (1974).74Sve2Svechnikov, V.N., Kocherzhinskii, Yu.A., Kobzenko, G.F., Pan, V.M., Shurin, A.K.: Akad.Nauk. Ukr. SSSR, Metallofiz. 52 (1974) 3.75Mol1Molokanov, V.V., Budberg, P.B., Alisova, S.P.: Dokl. Akad. Nauk. SSSR 223 (1975) 1184; Dokl. Phys. Chem. 223 (1975) 847.Landolt-BörnsteinNew Series IV/578Kau1Kaufman, L., Nesor, H.: CALPHAD 2 (1978) 55.81Mur1Murray, J.L.: Bull. Alloy Phase Diagrams 2 (1981) 174.83Lyn1Lynch, J.F., Johnson, J.R., Bowman, R.C.: NATO Conf. Series 6 (1983) 437. 87Hel1Hellstern, E., Schultz, L.: Mater. Sci. Eng. 93 (1987) 213.Landolt-BörnsteinNew Series IV/5Landolt-BörnsteinNew Series IV/5Cr-Th (Chromium-Thorium)Phase diagramWilhelm et al. [46Wil1] has stated that the phase diagram is a simple eutectic one with the eutectic at 75 at% Th and 1508 K. There are no intermediate phases and the mutual solubility of the components in the solid state is rather small. For a short discussion see Venkatraman et al. [85Ven5], from where the speculative phase diagram has been redrawn (Fig. 1).Fig. 1. Cr-Th. Tentative phase diagram.References46Wil1Wilhelm, H.A., Newton, A.S., Daane, A.H., Neher, C.: "Thorium Metallurgy", U.S.Atomic Energy Comm. Rept. CT-3714 (1946) 42.85Ven5Venkatraman, M., Neumann, J.P., Peterson, D.E.: Bull. Alloy Phase Diagrams 6 (1985)423.Cr-Te (Chromium-Tellurium)Phase diagramThe first more thoroughly performed investigations concerning the equilibria in this system have been done by Haraldsen et al. [37Har2] who applied magnetic measurements and X-ray diffractography. Then the work by Galperin [49Gal1, 49Gal2] should be mentioned. The crystallographic structure of intermediate phases has been determined relatively often. To get information on the homogeneity range of the intermediate phases metallographic investigations have been done, too. There should be mentioned the work by Berg [50Ber1], Gaidukov et al. [60Gai1], Dudkin et al. [61Dud1], Chevreton et al. [63Che1], Jellinek [57Jel1], Chevreton et al. [61Che1], Con et al. [63Con1], Suchet et al. [66Suc1].Cr7Te8 occurs in two modifications: ordered monoclinic at low temperatures and disordered hexagonal at high temperatures (Hashimoto et al. [69Has1]). From C p measurements Gronvold [73Gro1] found a λ-transition at 903 K. CrTe3 has been found by Klepp et al. [79Kle1], and this has been confirmed by [82Kle1] who stated that CrTe3 is a polyanionic compound (see also Gunia [79Gun1]).The phase equilibria were investigated by Ipser et al. [83Ips1] by differential thermal analysis and X-ray diffractography. Constructing the phase diagram, vapor pressure measurements performed by Ipser et al. [80Ips1] have been regarded, too. From there information was taken to draw Fig. 1.In the concentration range between 46 and 63 at% Te not all results obtained were included in Fig. 1. This part of the phase diagram is given on an enlarged scale and in completed form in Fig. 2 (for temperatures below 1200 K, as given by Ipser et al. [83Ips1]).For the range in the neighbourhood of the congruently melting intermediate phase, Ipser et al. [83Ips1] have given two possible interpretations of the thermal effects obtained (see Fig. 3 and Fig. 4). In Fig. 3 a phase transition of the NiAs-related phases to a modification γ' is assumed. The phase γ means Cr3Te4 (h) or Cr5Te8 (m). For Fig. 4 the γ-phase is assumed to be stable up to the melting point. Possibly, the impurities of oxygen or nitrogen affect the phase transitions.Landolt-BörnsteinNew Series IV/5Landolt-BörnsteinNew Series IV/5Fig. 1. Cr-Te.Phase diagram.Fig. 2. Cr-Te. Partial phase diagram (50…64 at % Te).Landolt-BörnsteinNew Series IV/5Fig. 3. Cr-Te. Partial phase diagram (45…65 at % Te) showing the phase transition γγ'.Fig. 4. Cr-Te. Partial phase diagram (45…65 at % Te) with the γ-phase stable up to the melting point.Crystal structureFour different crystallographic structures are distinguishable in the concentration range between 52.5 and 61.5 at% Te (at higher temperatures; see Ipser et al. [83Ips1]). These are: Cr 1-x Te (hexagonal), Cr 3Te 4-h (monoclinic), Cr 5Te 8-m (monoclinic) and Cr 5Te 8-tr (trigonal). At low temperatures Cr 3Te 4-l (monoclinic)and Cr 2Te 3 (trigonal) exist. The structures are defect derivatives of the NiAs-type. Lattice parameters as a function of concentration are given in Fig. 5 to Fig. 8. Fig. 9 gives the lattice parameters of the hexagonal (Cr 2S 3-type) Cr 2Te 3 phase. The phase richest in Te, CrTe 3, has monoclinic structure (a = 0.7887 nm;b = 1.122 nm; c = 1.156 nm; β = 118.4° [83Ips1]; see also [79Kle1]).Ipser et al. [83Ips1] stated that the "CrTe" phase mentioned and investigated very often, does not exist in reality. Instead a two phase mixture with Cr is stable at 50 at% Te at all temperatures up to 1450 K.Fig. 5. Cr-Te. Lattice parameters for hexagonal (NiAs-type) solid solution (Cr1-x Te).Landolt-BörnsteinNew Series IV/5Fig. 6. Cr-Te. Lattice parameters for monoclinic (Cr3S4-type) solid solution (Cr3Te4).Landolt-BörnsteinNew Series IV/5Fig. 7. Cr-Te. Lattice parameters for monoclinic (V5Sc8-type) for solid solution (Cr5Te8)-m.Landolt-BörnsteinNew Series IV/5Landolt-BörnsteinNew Series IV/5Fig. 8. Cr-Te. Hexagonal unit cell parameters for trigonal (Cr 5Te 8)-tr solid solution.Fig. 9. Cr-Te. Lattice parameters for hexagonal (Cr 2S 3-type) solid solution (Cr 2Te 3).ThermodynamicsGoncharuk et al. [74Gon1, 76Gon1] have determined thermodynamic data by EMF measurements. More reliable results were obtained by Ipser et al. [80Ips1] using the isopiestic method to determine partial vapor pressure of tellurium above Cr-Te alloys. The latter investigation has been performed in the concentration range between 55 and 62 at% Te and from 800 K to 1300 K. From the results obtained the authors calculated for Te thermodynamic activities, partial enthalpies of formation and partial entropies of formation of solid alloys. As standard states solid Cr and liquid Te have been taken. The results are givenin Fig. 10 (ln a Te S ), Fig. 11 (∆H Te S ), and Fig. 12 (∆S Te S ).Fig. 10. Cr-Te. Thermodynamic activity of Te in solid solutions at 1073 K. Standard states: solid Cr and liquid Te.Landolt-BörnsteinNew Series IV/5Landolt-BörnsteinNew Series IV/5Fig. 11. Cr-Te. Partial enthalpy of formation for Te in solid solutions at 1073 K. Standard states: solid Cr and liquidTe.Fig. 12. Cr-Te. Partial entropy of formation for Te in solid solutions at 1073 K. Standard states: solid Cr and liquid Te.References37Har2Haraldsen, H., Neuber, A.: Z. Anorg. Chem. 234 (1937) 353.49Gal1Galperin, F.M., Perekalina, T.M.: Zhur. Eksptl. Theoret. Fiz. 19 (1949) 470.49Gal2Galperin, F.M., Perekalina, T.M.: Dokl. Akad. Nauk SSSR 69 (1949) 19.50Ber1Berg, A.: Thesis, University of Oslo, (1950).57Jel1Jellinek, F.: Acta Crystallogr. 10 (1957) 620.60Gai1Gaidukov, L.G., Novogrudskii, V.N., Fakidov, I.G.: Phys. Met. Metallogr. (USSR) 9 (1960) 131.61Che1Chevreton, M., Bertaut, E.F.: C.R. Acad. Sci. 253 (1961) 145.61Dud1Dudkin, L.D., Vaidanich, V.I.: Voprosy Metallurgii i Fiziki Poluprovodnikov, Akad. Nauk SSSR, Moscow (1961).63Che1Chevreton, M., Bertaut, E.F., Jellinek, F.: Acta Crystallogr. 16 (1963) 431.63Con1Con, K.V., Suchet, J.: C.R. Acad. Sci. 256 (1963) 2823.66Suc1Suchet, J.P., Druille, R., Loriers, J.: Inorg. Mater. (USSR) 2 (1960) 796.69Has1Hashimoto, T., Yamaguchi, M.: J. Phys. Soc. Jpn. 27 (1969) 1121.73Gro1Gronvold, F.: J. Chem. Thermodyn. 5 (1973) 545.74Gon1Goncharuk, L.V., Lukashenko, G.M.: Poroshkov. Met. 9 (1974) 45.76Gon1Goncharuk, L.V., Lukashenko, G.M.: Zhur. Fiz. Khim 50 (1976) 2787.79Gun1Gunia, P.G.: Thesis, Gesamthochschule Siegen (1979).79Kle1Klepp, K.O., Ipser, H.: Monatsh. Chem. 110 (1979) 499.80Ips1Ipser, H., Klepp, K.O., Komarek, K.L.: Monatsh. Chem. 111 (1980) 761.82Kle1Kleppa, O.J., Watanabe, S.: Metal. Trans. B 13 (1982) 391.83Ips1Ipser, H., Komarek, K.L.: J. Less-Common Met. 92 (1983) 265.Landolt-BörnsteinNew Series IV/5Landolt-BörnsteinNew Series IV/5Cr-Tc (Chromium-Technetium)Phase diagramNo experimentally determined phase diagram is available.Using X-ray diffraction techniques, Darby Jr. et al. [61Dar1] and Darby Jr. et al. [62Dar1] have found and investigated an intermediate phase in the concentration range from 60 to 75 at% Tc (σ-phase as it occurs in the Cr-Mn and the Cr-Re systems, too). Assuming that the Cr-Tc system should be similar to the Cr-Re system, Venkatraman et al. [86Ven3] have proposed a speculative phase diagram, which has been taken as a basis for Fig. 1.Fig. 1. Cr-Tc. Tentative phase diagram.Crystal structureAs mentioned above, Darby Jr. et al. [61Dar1, 62Dar1] have determined crystallographic data for the σ-phase occurring in this system. Its structure is tetragonal (Cr-Fe-type). The lattice parameters as a function of concentration are plotted in Fig. 2 (see [91Vil2]).Landolt-BörnsteinNew Series IV/5Fig. 2. Cr-Tc. Lattice parameters for the tetragonal σ-phase. Samples annealed at 973 K.ThermodynamicsThe enthalpy of formation of CrTc 2 (or σ) has been estimated by de Boer et al. [82Boe1] using Miedema's model to be ∆H S = − 10 kJ g-atom −1.References61Dar1Darby jr., J.B., Lam, D.J.: US Atomic Energy Comm., Argonne Nat. Lab., Rept. ANL-6516 (1961) 254.62Dar1Darby jr., J.B., Lam., D.J., Norton, L.J., Downey, J.W.: J. Less-Common Met. 4 (1962)558.82Boe1de Boer, F.R., Boom, R., Miedema, A.R.: Physica B 113 (1982) 18.86Ven3Venkatraman, M., Neumann, J.P.: Bull. Alloy Phase Diagrams 7 (1986) 573.91Vil2Villars, P., Calvert, L.D.: "Pearson's Handbook of Crystallographic Data for IntermetallicPhases", Second Edition, Vol. 3, Amer. Soc. Metals International., Materials Park, Ohio(1991).Tm-Yb 1Landolt-BörnsteinNew Series IV/5Tm-Yb (Thulium-Ytterbium)Phase diagramAn experimentally obtained phase diagram is not known.Moffatt [81Mof1] has assumed similarity to Gd-Yb and Lu-Yb systems (Beaudry et al. [74Bea1]). On this basis he sketched the Tm-Yb phase diagram, which has been redrawn by Massalski [90Mas1] and which, also, has been taken as the main information to construct Fig. 1.Fig. 1. Tm-Yb. Phase diagram.References74Bea1Beaudry, B.J., Spedding, F.H.: Metall. Trans. 5 (1974) 163181Mof1Moffatt, W.G.: "The Handbook of Binary Phase Diagrams", Schenectady, N.Y.: General Electric Comp. (1981)90Mas1Massalski, T.B. (editor-in-chief): "Binary Alloy Phase Diagrams", Second Edition, Vol. 3,T.B. Massalski (editor-in-chief), Materials Information Soc., Materials Park, Ohio (1990)Th-Tl 1Landolt-BörnsteinNew Series IV/5Th-Tl (Thorium-Thallium)Phase diagramUsing differential thermal analysis and X-ray diffraction experiments, Palenzona et al. [85Pal1] have determined the phase diagram and Massalski [90Mas1] has redrawn it. From the latter compilation information has been taken to draw Fig. 1.Fig. 1. Th-Tl. Phase diagram.Crystal structureCrystallographic data of intermediate phases are listed in Table 1.Th-Tl2 Table 1. Th-Tl. Crystal structure and lattice parameters of intermediate phases [85Pal1].Phase Structure Type a [nm]b [nm]c [nm]Th2Tl tetr Al2Cu0.77080.6212Th5Tl3hex Mn5Si30.93880.6420ThTl orth ThIn 1.07700.99320.6554Th3Tl5orth Pu3Pd5 1.02490.8260 1.0419ThTl3cub AuCu30.4751References85Pal1Palenzona, A., Cirafici, S., Canepa, F.: J. Less-Common Met. 114 (1985) 31190Mas1Massalski, T.B. (editor-in-chief): "Binary Alloy Phase Diagrams", Second Edition, Vol. 3, T.B. Massalski (editor-in-chief), Materials Information Soc., Materials Park, Ohio (1990) Landolt-BörnsteinNew Series IV/5。
Emulsions乳剂
Section 10EmulsionsBy Drs. Pardeep K. Gupta, Clyde M. Ofner and Roger L. SchnaareTable of Contents Emulsions (1)Table of Contents (1)Introduction and Background (3)Definitions (3)Types of Emulsions (3)Formation of an Emulsion (4)Determination of Emulsion Type (4)Miscibility or Dilution Test (4)Staining or Dye Test (4)Electrical Conductivity Test (4)Physical State of Emulsions (5)Pharmaceutical Application of Emulsions (5)Formulations (6)Typical Ingredients (6)Drug (6)Oil Phase (6)Aqueous Phase (6)Thickening Agents (6)Sweeteners (6)Preservative (6)Buffer (7)Flavor (7)Color (7)Sequestering Agents (7)Humectants (7)Antioxidants (7)Emulsifiers (7)Guidelines (7)Type of Emulsion Desired (7)Toxicity (8)Method of Preparation (8)Typical Formulas (8)Cod Liver Oil Emulsion (polysaccharide emulsifier) (8)Protective Lotion (divalent soap emulsifier) (8)Benzoyl Benzoate Emulsion (emulsifying wax emulsifier) (8)Barrier Cream (soap emulsifier) (9)Cold Cream (soap emulsifier) (9)All Purpose Cream (synthetic surfactant emulsifier) (9)Emulsifiers (10)Natural Products (10)Polysaccharides (10)Sterols (10)Phospholipids (10)Surfactants (10)Anionic Surfactants (11)Soaps (11)Detergents (11)Cationic Surfactants (11)Nonionic Surfactants (11)Finely Divided Solids (12)Methods to Prepare Emulsions (13)Classical Gum Methods (13)Dry Gum Method (13)Wet Gum Method (13)“In Situ” Soap Method (13)Lime Water/Vegetable Oil Emulsions (13)Other Soaps (13)With Synthetic Surfactants (13)Required HLB of the Oil Phase (14)HLB of Surfactant Mixtures (14)Emulsion Stability (15)Sedimentation or Creaming (15)Factors - Stoke’s Law (15)Droplet Size (15)Density Difference (15)The Gravitational Constant, g (15)Viscosity (15)Breaking or Cracking (16)Thermodynamics of Emulsions (17)Microemulsions (18)References (19)Selected Readings (19)Introduction and BackgroundDefinitionsEmulsions are pharmaceutical preparations consisting of at least two immiscible liquids.Due to the lack of mutual solubility, one liquid is dispersed as tiny droplets in the other liquid to form an emulsion. Therefore,emulsions belong to the group of prepara-tions known as disperse systems.The USP also defines several dosage forms that are essentially emulsions but historically are referred to by other names. For example;Lotions are fluid emulsions orsuspensions intended for external application.Creams are viscous liquid or semi-solid emulsions of either an oil-in-water (O/W) or the water-in-oil (W/O) type. They are ordinarily used topically. The term cream is applied most frequently to soft, cosmetically acceptable types of preparations.Microemulsions are emulsions withextremely small droplet sizes and usually require a high concentration of surfactant for stability. They can also be regarded as isotropic, swollen micellar systems.Multiple emulsions are emulsions that have been emulsified a second time,consequently containing three phases. They may be water-in-oil-in-water (W/O/W) or oil-in-water-in-oil (O/W/O).Fluid emulsions are generally composed of discrete, observable liquid droplets in a fluid media, while semi-solid emulsions generally have a complex, more disorganized structure.The liquid which is dispersed as droplets iscalled as the dispersed , discontinuous or internal phase, and the liquid in which thedispersion is suspended is the dispersion medium or the continuous or external phase.For example, if olive oil is shaken with water,it breaks up into small globules andbecomes dispersed in water. In this case the oil is the internal phase, and water is the external phase.The dispersed particles or globules can range in size from less than 1 µm up to 100 µm. An emulsion is rarely a monodis-perse system, e.g., all the particles are rarely of the same size. A typical emulsion contains a distribution of many sizes, making it a polydisperse system.Types of EmulsionsBased on the nature of the internal (or exter-nal) phase, emulsions are of two types; oil-in-water (O/W) and water-in-oil (W/O). In an O/W type the oil phase is dispersed in the aqueous phase, while the opposite is true in W/O emulsions. Figure 1 depicts these two types of emulsions.Figure 1: Representation of Two Types of EmulsionsO/W Emulsion W/O Emulsion (water black)(oil white)When two immiscible phases are shaken together, either type of emulsion can result.However, this result is not random, but is dependent primarily on two factors; most importantly the type of emulsifier used and secondly the relative ratio of the aqueous and oil phases (phase volume ratio). The emulsifiers and their role in the type of emulsion are discussed in detail later in this chapter.In terms of the phase volume ratio, the percent of the internal phase is generally less than 50%, although emulsions can have internal phase volume percent as high as 75%. Uniform spheres, when packed in a rhombohedral geometry occupy approxi-mately 75% of the total volume. Phase volumes higher than 75% require that the droplets of dispersed phase be distorted into geometric shapes other than perfect spheres. Although it is rare to find emulsions with higher than 75% internal volume, phase volumes of over 90% have been reportedin literature.Formation of an EmulsionWhen two immiscible liquids are placedin contact with each other, they form two separate layers. The liquid with higher density forms the lower layer and the one with lower density forms the upper layer. When this two-layer system is shaken vigorously, one of the layers disperses in the other liquid forming an unstable emul-sion. If left unstirred, the dispersed phase comes together and coalesces into larger drops until the layers become separate again. If no other ingredient is added, this process of separation is usually completein a matter of a few minutes to a few hours. Therefore, a liquid dispersion is inherently an unstable system.However, when an emulsifier is present in the system, it reduces the interfacial tension between the two liquids and forms a physical barrier between droplets, hence lowers the total energy of the system(see discussion on Thermodynamics of Emulsions), thereby reducing the tendency of the droplets to come together and coalesce. Consequently, the globules ofthe internal phase may remain intact for long periods of time, forming a “stable”emulsion. It should be noted, however,that even with an emulsifier, an emulsionis a thermodynamically unstable system and will eventually revert to bulk phases. The time required for this process is determined by kinetics.Determination of Emulsion TypeSeveral tests can be used to determine whether a given emulsion is an O/W or W/O type. These are as follows:Miscibility or Dilution TestThis method is based on the fact that an emulsion can be diluted freely with a liquid of the same kind as its external phase. Typically, a small amount of the emulsion is added to a relatively large volume of water and the mixture is stirred. If the emulsion disperses in water, it is considered to bean O/W type emulsion. If, however, the emulsion remains undispersed, it is a W/O type emulsion.Staining or Dye TestThis test is based on the fact that if a dye is added to an emulsion and the dye is soluble only in the internal phase, the emulsion contains colored droplets dispersed inthe colorless external phase. This can be confirmed by observing a drop of emulsion under a low power microscope. An example of such a dye is scarlet red, which is an oil soluble dye. When added to an O/W type emulsion, followed by observation under the microscope, bright red colored oil drops in an aqueous phase can be seen clearly. Electrical Conductivity TestThis test is based on the fact that onlythe aqueous phase can conduct electrical current. Thus, when a voltage is applied across a liquid, a significant amount of electrical current will flow only when the path of the current is through a continuous aqueous phase. Since oil is a non-conductor of electricity, when tested for conductivity, a W/O type emulsion will show insignificant current flow.Often times a single test may not be conclu-sive. In such circumstances, more than one test may need to be carried out to confirm the emulsion type.Physical State of EmulsionsMost emulsions are either liquid or semi-solid at room temperature. In general, due to their high viscosity, the semi-solid emulsions are relatively more physically stable. Liquid emulsions are more commonly compounded for internal use, while semisolids are usually for external use or for use in body cavities (rectal or vaginal).Other terms commonly used to describe emulsions are lotion and cream . The term lotion refers to a disperse system that flows freely under the force of gravity. A cream is a product that does not flow freely under the force of gravity. It should be noted, however,that these terms are meaningful only when the product is at room temperature. A cream product may behave like a lotion with a temperature increase of a few degrees. The physical state of the final product is also influenced by its intended use. For example suntan lotions are dispensed as lotions instead of creams because they need to be applied on large body surface. Lotion form makes it easy to pour and spread the product. For application over a small portion of skin, a cream is the preferred form of an emulsion.Pharmaceutical Applications of Emulsions There are several reasons for formulation of a product as an emulsion. These include the following:•To disguise the taste or smell of oils or oil soluble drugs. These emulsions are normally O/W types with the aqueous phase containing sweeteners and flavoring agents to mask the poor taste of oils. An O/W type of emulsionalso makes it easy to rinse off the residual dose from the mouth and does not leave an oily taste. Mineral oil and cod liver oil are emulsified for this reason.•To improve the absorption of poorly soluble drugs. Oil soluble drugs may not be soluble enough to be absorbed efficiently. An example of such a drug is cyclosporin, which is dispensed as a microemulsion. •To deliver nutrients and vitamins by intravenous injection. Intralipid is an emulsion product for administering an oil by the IV route.•To serve as a vehicle for the topical administration of a variety of drugs.Kb is the binding constant of the preservative with the surfactantSweeteners are added to emulsions to produce a more palatable preparation, toand sorbitol.AntioxidantsAntioxidants are often added to prevent oxidation of vegetable oils and/or the active drug.Table 1. Typical AntioxidantsEmulsifiersEmulsifiers are substances that have the ability to concentrate at the surface of a liquid or interface of two liquids, many of them reducing the surface or interfacial tension. Those emulsifiers that reduce surface tension are also called surfactants .Emulsifiers in general are discussed inmore detail in a later section of this chapter.GuidelinesBefore selecting a formula for an emulsion,one needs to consider several factors.These are listed below.Type of Emulsion DesiredSince O/W emulsions are more pleasant to touch and swallow, they are generally preferred. Preparations for internal use are almost always O/W type products.Externally used emulsions may be of either type. Creams and lotions that are used primarily to provide oil to the skin need to be W/O due to high concentration of oils in these preparations.The equation shows that the effective concentration in the aqueous phase will always be a fraction of the total concentration.Solvents such as alcohol, glycerin and propylene glycol are often used as apreservative at concentrations approaching 10%. See Table 5, Typical Preservatives in Section 9 of this manual.BufferMany chemical buffer systems have been used in emulsions to control the pH. The optimal pH is chosen to ensure activity of the emulsifier, control stability of the drug and to ensure compatibility and stability of other ingredients.FlavorFlavoring agents enhance patient accept-ance of the product, which is particularly important for pediatric patients.ColorColorants are intended to provide a more aesthetic appearance to the final product.Emulsions are generally not colored with the exception of some topical products. Sequestering AgentsSequestering agents may be necessary to bind metal ions in order to control oxidative degradation of either the drug or other ingredients. HumectantsHumectants are water soluble polyols that prevent or hinder the loss of water from semi-solid emulsions, i.e., topical creams.They also contribute to the solvent proper-ties of the aqueous phase and contribute to the sweetness of oral preparations. The most common are glycerin, propylene glycolToxicityMost emulsifiers are not suitable for internal use. For orally given emulsions, acacia is commonly used as an emulsifying agent.Taste is another factor in selection ofingredients. In this regard, most polysaccha-rides are tasteless and, hence, suitable from a taste standpoint.Method of PreparationSoaps and acacia are excellent forextemporaneous preparations. While soaps allow the preparation to be made by simply mixing the ingredients and shaking, acacia can be used in a pestle and mortar to prepare emulsions.Typical FormulasCod Liver Oil Emulsion (polysaccharide emulsifier)Preparationing a ratio of 4:2:1 for oil, water and gums(both combined), prepare a primary emulsion by dry gum method. (See Methods to Prepare Emulsions on page 13.)2.Dilute with water to a flowable consistency andpour in a measuring device.3.Add alcohol diluted with equal volume of water,followed by the benzaldehyde and saccharin sodium.4.Dilute to volume (200 mL) with waterPreparation1.Add benzyl benzoate to the wax in a beakerand heat in a water bath until the wax melts and the temperature reaches 60°C.2.In a separate beaker, add an appropriate volumeof water and heat to the same temperature.3.Add the water to the oil phase with continuousstirring.4.Continue to stir until the mixture begins tothicken and cools to room temperature.Preparation1.Mix the two powders in a mortar and trituratewell, taking care that all the lumps and large particles have been reduced.2.Then add oil slowly with constant trituration untilall the oil has been added. Triturate to form a smooth paste.3.Then add the limewater and triturate briskly toform the emulsion.Note: The emulsifier, calcium oleate (from limewater and olive oil), preferentially forms O/W emulsions.Protective Lotion (divalent soap emulsifier)Benzyl Benzoate Emulsion (emulsifying wax emulsifier)Preparation1.Mix the paraffins, cetostearyl alcohol andstearic acid in a beaker and heat in a water bath to about 60°C.2.Heat water and chlorocresol together to thesame temperature.3.Add the aqueous phase to the oil phase andstir until congealed and cooled to room temperature.Note:The emulsifier is triethanolamine stearate formed in situ.Preparation1.Melt the sorbitan monostearate and stearicacid in the liquid paraffin and cool to 60°C. 2.Mix the sorbitol solution, preservatives,polysorbate 60 and water and heat to the temperature of the oil mixture.3.Add the aqueous solution to the oil phase andstir until it has congealed and cooled to room temperature.Note:Propylene glycol serves as a solvent for the preservatives.Preparation1.Mix and melt the wax and paraffin together.2.Dissolve borax in water and heat both containerson a water bath to 70°C.3.Add the aqueous phase to the oil phase andstir until it has congealed and cooled to room temperature.Note:The fatty acid in white beeswax reacts with borax (sodium borate) to make a sodium soap which acts as an W/O type emulsifier.Barrier Cream (soap emulsifier)All Purpose Cream (synthetic surfactant emulsifier)Cold Cream (soap emulsifier)Surfactants or surface active agents are molecules that consist of two distinct parts,a hydrophobic tail and a hydrophilic head group. They are generally classified based on the hydrophilic properties of the head group (ionic charge, polarity, etc.). Since the hydrophobic chains do not vary much in their properties, the nature of surfactants is dependent mainly on the head group structure.A common problem with sterol-containing emulsifiers is that being complex mixtures of natural substances, they are prone to variability in their quality and, hence, performance. Also, these agents usually contain some degree of an odor, which varies with the purity and source. Some semi-synthetic substitutes are available that seek to overcome some of the problems associated with these agents.There are of basically three types of emulsifiers: natural products, surface active agents (surfactants), and finely divided solids. Based on whether a stable emulsion can be produced, emulsifiers are also classified either as primary emulsifying agents which produce stable emulsions by themselves, or secondary emulsifying agents (stabilizers) which help primary emulsifiers to form a more stable emulsion.of cholesterol. Cholesterol itself is a very efficient emulsifier and produces W/O type emulsions. Consequently, its use is limited to topical preparations such as Hydrophilic Petrolatum USP which readily absorbs water forming a W/O cream. Woolfat or lanolin contains a considerable amount of choles-terol esters and can absorb up to 50% of its own weight of water.This group of emulsifiers, which numbers in the hundreds, contain a polyoxyethylene chain as the polar head group. They arenonionic and, thus, are compatible with ionic compounds and are less susceptible to pH changes. There are several such surfactants official in the USP/NF , typified by sorbitan monooleate (a partial ester of lauric acid with sorbitol), polysorbate 80(polyoxyethyl-ene 20 sorbitan monooleate) which contains 20 oxyethylene units copolymerized sorbitanAmine soaps consist of an amine, such as triethanolamine, in the presence of a fatty acid. These surfactants are viscous solutions and produce O/W type emulsions. They offer the advantage that the final pH of the preparations is generally close to neutral,and, therefore, allows their use on skin for extended periods of time.monooleate) and polyoxyl 40 stearate(a mixture of stearic acid esters with mixed poloxyethylene diols equivalent to about40 oxyethylene units).The large number of nonionic emulsifiers results from the large number of possible combinations of various alkyl groups with polyoxyethylene chains of varying lengths. Compounds with saturated and/or large alkyl groups, such as stearyl, tend to be solids or semisolids while oleyl (also large, but unsaturated) compounds tend to be liquids. Also, the longer the polyoxyethylene chain, the higher the melting point.To characterize such a large number of compounds, they are each assigned an HLB number. The HLB number or hydrophile-lipophile balance, is a measure of the relative hydrophilic vs lipophilic character of the molecule as determined by the relative size of the polyoxyethylene chain vs the alkyl group. HLB numbers range from 0 for a pure hydrocarbon to 20 for a pure poly-oxyethylene chain. Some typical valuesare listed in Table 3.Ionic surfactants, such as sodium lauryl sulfate, were not included in the original definition of the HLB system but have been included as the HLB system was developed. The HLB number of 40 for sodium lauryl sulfate is outside of the range of 0 to 20 and simply means that sodium lauryl sulfate is much more soluble or hydrophilic thana pure polyoxyethylene chain.Table 3. Typical HLB Numbersof EmulsifiersFinely Divided SolidsFinely divided solids function as emulsifiers because of their small particle size. Fine particles tend to concentrate at a liquid-liquid interface, depending on their wetability, and form a particulate film around the dispersed droplets. They are seldom used as the primary emulsifier.phase. The emulsion type will depend on the type of soap formed.Basically the formula is divided into anoil phase and an aqueous phase with the ingredients dissolved in their proper phases (oil or water). The surfactant(s) is added to the phase in which it is most soluble. The oil phase is then added to the aqueous phase with mixing, and the coarse mixture passed through an homogenizer.When waxes or waxy solids are included in the formulation, the use of heat is necessary,as described above.Required HLB of the Oil Phase.It has been found that various oils and lipid materials form stable emulsions withsurfactants that have a certain HLB value.This HLB value is called the required HLB of the oil or lipid. Theoretically, any surfac-tant with the required HLB would produce a stable emulsion with the indicated oil or lipid. Some examples are given in Table 4.Table 4. Required HLB Values for Typical Oils and LipidsHLB of Surfactant MixturesIt may be difficult to find a surfactant with the exact HLB number required for a given oil phase in an emulsion. Fortunately, the HLB numbers have been shown to be additive for a mixture of surfactants. Thus, if one required a surfactant with a HLB of 10, one could use a mixture of sorbitan monooleate (HLB = 4.7) and polysorbate 80 (HLB = 15.6). Such a mixture can be calculated on the basis of a simple weighted average as follows.Suppose 5 g of surfactant mixture is required. Let = the g of sorbitanmonooleate, then 5 = the g of polysorbate 80 required.(4.7)+(5- )(15.6) = 10(5)4.7 + 78.0- 15.6= 10(5)10.9= 28= 2.57 and 5- = 2.43Thus a mixture of 2.57 g of sorbitanmonooleate and 2.43 g of polysorbate 80would have a HLB of 10.Griffin 2described an experimental approach for the formulation of emulsions using synthetic emulsifiers.1.Group the ingredients on the basis of theirsolubilities in the aqueous and oil phases.2.Determine the type of emulsion required andcalculate an approximate required HLB value.3.Blend a low HLB emulsifier and a high HLBemulsifier to the required HLB.4.Dissolve the oil soluble ingredients and the lowHLB emulsifier in the oil phase. Heat, if necessary,to approximately 5 to 10°over the melting point of the highest melting ingredient or to a maximum temperature of 70 to 80°C.5.Dissolve the water soluble ingredients (exceptacids and salts) in a sufficient quantity of water.6.Heat the aqueous phase to a temperature whichis 3 to 5°higher than that of the oil phase.7.Add the aqueous phase to the oil phase withsuitable agitation.8.If acids or salts are employed, dissolve them inwater and add the solution to the cold emulsion.9.Examine the emulsion and make adjustments inthe formulation if the product is unstable. It may be necessary to add more emulsifier, change to an emulsifier with a slightly higher or lower HLB value or to use an emulsifier with different chemical characteristics.In addition to chemical degradation of various components of an emulsion, which can happen in any liquid preparation, emulsions are subject to a variety of physical instabilities. Sedimentation or Creaming Factors - Stoke’s LawCreaming usually occurs in a liquid emulsion since the particle size is generally greater than that of a colloidal dispersion. The rate is described by Stoke’s Law for a single particle settling in an infinite container under the force of gravity as follows:d =d 2(2- 1)gdt 18where:d /d t= the sedimentation rate in distance/time d = droplet diameter 2= droplet density1= emulsion medium density g = acceleration due to gravity = viscosity of the emulsion mediumSince for most oil phases, 2< 1, then sedimentation will be negative, i.e., the oil droplets will rise forming a creamy whitelayer. While Stoke’s Law does not describe creaming quantitatively in an emulsion, it does provide a clear collection of factors and their qualitative influence on creaming.Droplet SizeReducing droplet size can have a significant effect on creaming rate. Since the diameter is squared in Stoke’s Law, a reduction in size by ¹⁄₂will reduce the creaming rate by (¹⁄₂)2or a factor of 4.Emulsion StabilityDensity DifferenceIf the difference in density between the emulsion droplet and the external phase can be matched, the creaming rate could be reduced to zero. This is almost impossi-ble with most oils and waxy solids used in emulsions.The Gravitational Constant, gThis parameter is not of much interest since it can not be controlled or changed unless in space flight.ViscosityViscosity turns out to be the most readily controllable parameter in affecting the creaming rate. While the viscosity in Stoke’s Law refers to the viscosity of the fluid through which a droplet rises, in reality the viscosity that controls creaming is the viscosity of the entire emulsion. Thus, doubling the viscosity of an emulsion will decrease the creaming rate by a factor of 2.There are three major ways to increase the viscosity of an emulsion:•Increase the concentration of the internal phase•Increase the viscosity of the internal phase by adding waxes and waxy solids to the oil phase.•Increase the viscosity of the external phase by adding a viscosity building agent. Most of the suspending agents described in the Suspensions Section in this manual have been used for this purpose.Creaming does not usually occur in a semi-solid emulsion.Breaking or CrackingThis problem arises when the dispersed globules come together and coalesce to form larger globules. As this process continues, the size of the globules increases, making it easier for them to coalesce. This eventually leads to separation of the oil and water phases. For cracking to occur, the barrier that normally holds globules apart has to break down. Some of the factorsthat contribute to cracking are as follows:•Insufficient or wrong kind of emulsifier in the system.•Addition of ingredients that inactivate the emulsifier. Incompatible ingredients may show their effect over a period of time.An example of such an incompatibilitywill be to use large anions in thepresence of cationic emulsifier.•Presence of hardness in water. The calcium and magnesium present in hard water can replace a part of the alkalisoap with divalent soap. Since thesesoaps form different kinds of emulsions, phase inversion usually takes place.•Low viscosity of the emulsion •Exposure to high temperatures can also accelerate the process of coalescence.This is due to the fact that at an elevated temperature, the collisions between theglobules can overcome the barrier tocoalescence, thereby increasing thechance that a contact between twoparticles will lead to their fusion.Temperature may have an adverse effect on the activity of emulsifiers, particularly if these are proteinaceous in nature.However, this usually happens at temper-atures higher than 50°C. Conversely, areduction in temperature to the point that the aqueous phase freezes also will break the emulsion.•An excessive amount of the internal phase makes an emulsion inherently less stable because there is a greater chance of globules coming together.Cracking is the most serious kind of physical instability of an emulsion. Cracking of an emulsion usually renders it useless. In creams, the problem of cracking may show up as tearing. This is a process where one phase separates and appears like drops on top of the cream.The basic difference between creamingand cracking is that the globules in creaming do not coalesce to form larger particles. Therefore, creaming is a less serious problem and most preparations that show creaming can be shaken to redisperse the internal phase to its original state. A com-mon example of creaming is the formation of cream on top of whole milk due to collection of emulsified fat of the milk. This problem is solved by homogenizing the milk to reduce the particle size of dispersed fat, thereby reducing the rate at which they travel tothe surface.。
热力学词汇——精选推荐
Part 1-1Thermodynamics 热力学热力学是物理学中力学的分支。
热力学研究热力做功，水力学研究水力做功，风力学研究风力做功，电力学研究电力做功。
相关术语词汇Dynamics 动力学Kinetics 运动学Classical mechanics 经典力学Statistical mechanics 统计力学Classical thermodynamics 经典热力学Statistical thermodynamics 统计热力学Chemical thermodynamics 化学热力学Chemical engineering thermodynamics 化工热力学Engineering thermodynamics 工程热力学Chemical and engineering thermodynamics 化学和工程热力学Molecular thermodynamics 分子热力学Nonequilibrium thermodynamics 非平衡态热力学Chemical engineering thermodynamics 化工热力学化工热力学研究过程的方向和限度。
化工热力学是化学工程的一个分支，是热力学基本定律应用于化学工程领域中而形成的一门学科。
主要研究化工过程中各种形式的能量之间相互转化的规律及过程趋近平衡的极限条件，为有效利用能量和改进实际过程提供理论依据。
Steam engine 蒸汽机蒸汽机是众多热机中的一种，是以蒸汽作为工作介质的热机Heat engine 热机，热力发动机In thermodynamics, a heat engine is a system that performs the conversion of heat or thermal energy to mechanical work. It does this by bringing a working substance from a high temperature state to a lower temperature state. A heat "source" generates thermal energy that brings the working substance in the high temperature state. The working substance generates work in the "working body" of the engine while transferring heat to the colder "sink" until it reaches a low temperature state. During this process some of the thermal energy is converted into work by exploiting the properties of the working substance. The working substance can be any system with a non-zero heat capacity, but it usually is a gas or liquid.In general an engine converts energy to mechanical work. Heat engines distinguish themselves from other types of engines by the fact that their efficiency is fundamentally limited by Carnot's theorem. Although this efficiency limitation can be a drawback, an advantage of heat engines is that most forms of energy can be easily converted to heat by processes like exothermic reactions (such as combustion), absorption of light or energetic particles, friction, dissipation and resistance. Since the heat source that supplies thermal energy to the engine can thus be powered by virtually any kind of energy, heat engines are very versatile and have a wide range of applicability.Heat engines are often confused with the cycles they attempt to mimic. Typicallywhen describing the physical device the term 'engine' is used. When describing the model the term 'cycle' is used.Power developed from heat 热力做功The first law of thermodynamics 热力学第一定律The second law of thermodynamics 热力学第二定律Primitive law 基本定律A network of equations 一整套方程式Physical process 物理过程Chemical process 化学过程相关术语词汇Biological process 生物过程A biological process is a process of a living organism. Biological processesare made up of any number of chemical reactions or other events that results in a transformation.热力学和化工热力学不涉及生物过程Equilibrium conditions 平衡条件Chemical species 化学物种Chemical species are atoms, molecules, molecular fragments, ions, etc., subjected to a chemical process or to a measurement. Generally, a chemical species can be defined as an ensemble of chemically identical molecular entities that can explore the same set of molecular energy levels on a characteristic or delineated time scale. The term may be applied equally to a set of chemically identical atomic or molecular structural units in a solid array.简言之，在热力学里化学物种指纯物质，包括化合物和元素Driving force 驱动力Resistance 阻力Thermodynamic variable 热力学变量描述热力学体系状态的变量称为热力学变量，常见的热力学变量有温度，压力，体积，内能，焓，熵，和吉布斯自由能。
磁场对镍基Ni_Mn_Ga铁磁合金相变温度影响的热力学分析_赵容兵
文章编号：1674-9669（2012）01-0001-04收稿日期：2011-12-16基金项目：国家自然科学基金资助项目（50965008）作者简介：赵容兵（1966-），男，博士后，主要从事有色金属功能材料及应用方向研究，E-mail:zhaoyerongbin@.磁场对镍基Ni-Mn-Ga 铁磁合金相变温度影响的热力学分析赵容兵1，赵运才2（1.江西恒大高新技术股份有限公司，南昌330096；2.江西理工大学机电工程学院，江西赣州341000）摘要：通过测量磁化曲线、电阻-温度关系和热分析等手段，研究了磁场对镍基铁磁合金试样Ni-Mn-Ga 相变的影响.结果表明：在磁场作用下相变温度升高了约1.5K ，具有明显的磁场影响特征.利用马氏体相变热力学理论，研究了磁场对镍基铁磁合金化学自由能和非化学自由能与温度的变化关系，建立了其作用的数理模型，并与实验结果比较后基本吻合.关键词：磁场；镍基铁磁合金；相变温度；热力学分析中图分类号：TG156文献标志码：AThermodynamic analysis of phase transformation temperature affected bymagnetic field on nickel-base Ni-Mn-Ga ferromagnetic alloyZHAO Rong-bing 1,ZHAO Yun-cai 2(1.Jiangxi HengDa Hi-tech Industry Co.Ltd.,Nanchang 330096,China;2.School of Mechanic and ElectronicEngineering,Jiangxi University of Science and Technology,Ganzhou 341000,China ）Abstract:Nickel -base ferromagnetic alloy Ni -Mn -Ga was investigated for phase transformation temperature affected by magnetic field by measuring magnetization curve,temperature dependence of the resistance,and thermal analysis.The results show that magnetic field application can increase phase transformation temperature 1.5K with distinctive behavioral affected by field.Meanwhile,thermodynamic theory of martensitic phase transformation is applied to study temperature dependence of the chemical free energy and non-chemical free energy on nickel-base ferromagnetic alloy;a mathematical model is built and agrees well with experimental result.Key words:magnetic field;nickel -base ferromagnetic alloy;phase transformation temperature;thermodynamic analysis0引言镍基铁磁合金作为一种新型的软磁材料，正在许多领域内得到日益广泛的应用，如作为传感器的NiMnGa 、NiFeGa 、NiCoA1、NiFeMnGa 、NiFeCoGa 等磁致伸缩材料[1-4].然而，和实际应用密切相关的一个重要问题是镍基铁合金相变温度受磁场影响的问题.为此，通过测定Ni-Mn-Ga 镍基铁磁合金在磁场中相变温度的改变，并根据铁磁学的有关原理进行热力学计算分析，从中了解自由能差为相变驱动力对母相和马氏体相自由能相等时的平衡温度的影响；同时结合对化学自由能和弹性应变能是可逆性及塑性应变能的不可逆性过程的分析，以期找到马氏体与母相之间的化学自由能变化与温度之间的某种联系，这有可能为弄清磁场影响镍基铁磁合金相变温度的物理机制，以及为如何通过合金化而研究和开发出具有磁致伸缩效应的性能优异的镍基铁磁合金有色金属科学与工程第3卷第1期2012年2月Vol.3，No.1Feb.2012Nonferrous Metals Science and EngineeringDOI:10.13264/ki.ysjskx.2012.01.013提供理论依据.1实验方法1.1试样制备实验采用常用的镍基铁磁合金Ni-Mn-Ga 作为试样.首先，将Ni 52Mn 24Ga 23多晶试样制作成尺寸为3mm ×3mm ×3mm 的小块作为磁化曲线测量备用.其次，电阻-温度关系测量，相变样品采用Ni 52Mn 24Ga 23多晶，试样尺寸为80mm ×2mm ×0.8mm.由于钮扣锭尺寸限制，我们将同一成分的两个40mm 长试样通过银焊连接起来而得.最后，示差扫描量热法热分析测量样品使用10mg 左右的合金碎屑.1.2检测方法试样称重后，采用振动磁强计(VSM)测量试样的磁化曲线.电阻-温度关系测量，采用四端电阻法，实验电路如图1所示.试样的AD 两端通以恒定的24V 电压，电阻变化则通过BC 两端的电流来显示.电压测量电路中串联入一电位差计，调节其输出电势以抵消BC 段试样起始的电位降，这是为了提高温度变化时BC 段试样上电阻变化引起的电位降变化的灵敏度.试样由电炉加热，冷却时采用断电随炉冷却到室温的方法.分别在试样的两端不加磁场和加0.7T 的直流磁场状态下进行冷却.在试样中部E 处点焊上热电偶，用冰水混合物保持冷端温度0℃.通过X-Y 记录仪的X 端来测量温度变化时热电偶所产生的电压变化，显示了试样的温度.通过X-Y 记录仪的Y 端来记录温度变化时BC 段试样由于电阻变化而产生的电流变化.X-Y 记录仪的X 、Y 端都取0.5mA/cm 档，放大器放大倍数为3.热分析实验设备为日本TITC 株式会社产2910型Modulated DSC 分析仪，加热／冷却速率为10K ／min.2实验结果Ni 52Mn 24Ga 23多晶试样的磁化曲线见图2.Ni 52Mn 24Ga 23多晶试样的电阻-温度关系曲线图见图3，电阻测量的温度范围为从室温至400K 左右，再冷至室温.由于马氏体相变及其逆相变的开始和终了温度M s 、M f 、A s 和A f 应分别对应于曲线与直线的切点.从实验结果来看，在磁场冷却状态下相变温度升高了约1.5K ，具有明显的磁场影响特征.Ni 52Mn 24Ga 23多晶试样的热分析其热焓变化量为2.657×107J/m3.3热力学分析根据马氏体相变热力学理论，在没有外磁场的情图1四端电阻法实验电路图1.稳压电源；2.试样；3.热电偶；4.加热炉；5.电位差计；6.放大器；7.记录仪；8.冷端DA65A3DA124V7X-Y 记录仪B2BE 4C图2试样的磁化曲线8000600040002000040000080000012000001600000磁场强度/（A ·m -1）磁化强度/（A ·m -1）图3电阻-温度关系曲线图加热加热无磁场有磁场290300310320330340温度/K24181260电阻比有色金属科学与工程2012年2月2况下，马氏体相变的驱动力由化学自由能与非化学自由能提供[5].图4是母相和马氏体相自由能随温度变化规律的示意图[6]，其中T 0表示母相和马氏体相自由能相等时的平衡温度，由于要克服非化学自由能，马氏体相变需要过冷，发生相变这个温度即为马氏体相变的起始温度M s ，在此温度下马氏体自由能与母相自由能之差△G P →M＜0，即马氏体相具有较低的自由能时，母相才能转变为马氏体.这个自由能差称为相变驱动力(实际上是负值).为表示方便，一般所说的相变驱动力大小指其绝对值而言.马氏体逆相变需要在T 0以上一个温度才开始，即图4中的A s ，逆相变同样需要一定的驱动力，即△G M →P.马氏体相变时的非化学自由能或相变阻力主要包含应变能和界面能[7].马氏体相变驱动力的热力学公式可用式（1）表示：△G=△GP →M（T ）=△G P →M chem （T ）+△G P →Mnon-chem （T ）=△G P →M chem （T ）+△G P →M stra +△G P →Mint（1）式（1）中，△G P →M chem （T ）是由相变而引起的化学自由能变化，△G P →Mstra 是伴随相变的弹性应变能，包括切变和膨胀应变能等，△G P →Mint 是伴随母相与马氏体相界迁移的界面能，包括摩擦、内耗等能量.在从母相到马氏体的正相变和马氏体到母相的逆相变中，化学自由能和弹性应变能是可逆的，而塑性应变能是不可逆的[8].基于这3项能量，可以得到总的自由能与温度变化关系的示意图5.假定马氏体与母相之间的化学自由能变化与温度呈线性关系（图5），△G P →M stra +△G P →Mint 为常数，那么就可以利用相变开始温度M s 、逆相变结束温度A f 和马氏体相变的热焓变化△H ，求得非化学自由能项.结合图5，由式（1）△G =△GP →M（T ）=△G P →Mchem （T ）+△G P →Mnon-chem （T ）可知，当T =T 0（两相平衡温度）时，△G P →Mchem （T 0）＝0，则△G P →M（T 0）=△G P →M chem （T 0）+△G P →Mnon-chem （T 0）＞0未发生相变；当T =M s （相变开始温度）时，△GP →M（M S ）=0，有式（2）：△G P →Mchem （M s ）=-△G P →Mnon-chem （T ）=-（△G P →Mstra +△G P →Mint ）（2）假定相变时，降温1K 所发生的热焓变化量为△H /T 0，那么相变点附近化学自由能与温度的变化关系可以近似用式（3）表示，即△G P →Mchem （M s ）=（T -T 0）×△H /T 0（3）其中△H 是相变总的热焓变化量，其值可利用Ni 52Mn 24Ga 23合金试样热分析得出，测试为2.657×107J/m 3，这与Chernenko 等[9]报导的Ni 52.6Mn 24.4Ga 23.0合金相变总的热焓变化量2.683×107J/m 3比较一致.两相平衡温度T 0可通过该合金的T 0=(M s +A f )/2得到T 0=320K.那么由式（2）得△G P →Mnon-chem （T ）=-（M s -T 0）×△H /T 0=9.53×105J/m 3(M s <T 0)外加磁场后，磁场产生的静磁能对自由能的变化有较大的影响，因此在温度为T ，外加磁场为H 0时，自由能的表达形式可写为式（4）：△GP →M（T ，H 0）=G P →M chem （T ）+△G P →Mnon-chem （T ）+△G magnetic （H 0）（4）Shimizu [10]和Kakeshita 等[11]对Fe-Ni 合金磁场诱发马氏体相变研究表明，磁场对马氏体相变的影响不仅是由于Zeeman 效应，还有高磁场磁化率和磁致伸缩效应.对Ni 52Mn 25Ga 23合金（非Invar 合金），因其磁致伸缩率很低，后两种因素可忽略.因此，在磁场作用下，△G magnetic （H 0）是外磁场施加给试样的磁场能，其值用Satur乙H d M 表达.从图2的磁化曲线可知，对于Ni 52Mn 24Ga 23合金，当外加磁场为H 0～0.7T 时，该合金已达到饱和，磁能所产生的相变驱动力由外磁场施加给试样的磁场能图4马氏体相变中两相化学自由能随温度变化规律的示意图G P△G P －M G MM ST 0吉布斯自由能△G M －PA S温度图5母相和马氏体相自由能随温度变化规律的示意图△G M →Pstra+△G intT 0M s△G ch =0吉布斯自由能温度第3卷第1期赵容兵，等：磁场对镍基Ni-Mn-Ga 铁磁合金相变温度影响的热力学分析△G ch3提供.由于没有测定母相的磁化曲线，近似取相关文献[12]中所测得的Ni 2MnGa 母相和马氏体相的磁化曲线，外磁场施加给马氏体相的磁场能为1.17×105J/m 3，外磁场施加给母相的磁场能为2.7×104J/m 3.由此可知相变时，磁场对试样增加的自由能改变为9×104J/m 3，见示意图6.从图6可见，由于外磁场降低了马氏体的自由能，根据几何关系可得△ACT ’∽△DFT ’那么，有DT ’AT ’=DF AC而AC =DE （磁场作用前后，非化学自由能不改变），所以有DT ’=DF 同时FT ’∥ET ，AC ⊥DT ’和ED ⊥DT ’，即△DET 0≌△ACT ’AT ’=DT 0所以有DT ’DT 0=DF DE ，并可变换为DE DF =DT 0DT ’，置换对应的热力学参数，则△G （T ）△G （T ）+△G magnetic（H 0）=T 0-M sT ’-M s代入相应的数据，可得T ’=321.59K ，则T ’-T 0=1.59K ，也即在M s ’时，△G P →Mchem （T ）+△G magnetic （H 0）=△G P →Mnon-chem （T ），有M s ’=M s +1.59K.所以得出结论，当外加磁场为H 0～0.7T 时，相变温度升高了约1.59K ，这与实验结果，Ni 52Mn 24Ga 23试样中发现的磁场作用下使相变温度出现了1.5K 的升高比较吻合.由于Ni 52Mn 24Ga 23试样塑性差而不能轧制，铸态合金难免存在织构，影响其磁性能；另外，实验过程中也会产生精度误差，测试相变温度与理论计算值有0.09K 偏差是能接受的.4结论（1）磁场对镍基铁磁合金相变温度有适当提高.试样在H 0～0.7T 时，Ni 52Mn 24Ga 23的相变温度提高了1.5K.（2）利用马氏体相变热力学理论，分析了磁场对镍基铁磁合金化学自由能和非化学自由能与温度的变化关系，建立了其作用的数理模型.（3）通过测量磁化曲线、电阻-温度关系和热分析等手段，利用其实验结果，采用数理模型计算了磁场对镍基铁磁合金相变温度影响的大小，并与实验值基本吻合.马氏体相变热力学为研究镍基Ni-Mn-Ga 铁磁合金在磁场中的相变影响提供了合适的计量方法.可供同类型的镍基铁磁合金在其它外加能量场分析判定相变温度改变时参考.参考文献：[1]K.Oikawa ，T.Ota ，F.Gejima ，et a1.Phase equilibria and phasetransformations in new B2-type ferromagnetic shape memory alloys of Co-Ni-Ga and Co-Ni-A1systems[J]．Mater ．Trans ．,2001,42(11):2472-2475.[2]Z.H.Liu ，J.L.Chen ，H.N.Hu ，et al.The influence of heat treatment on the magnetic and phase transformation properties of quaternary Heusler alloy Ni 50Mn 8Fe 17Ga 25ribbons[J]．Scripta Mater ．,2004,51(10):1011-1015.[3]K.Oikawa,T.Ota,Y.Sutou,et a1.Magnetic and martensitic phase transformation in a Ni 54Ga 27Fe 19alloy[J]．Mater.Trans ．,2002，43（9）:2360-2362.[4]K.Oikawa,T.Ota,T.Ohmori,et a1.Magnetic and martensitic phase transtions in ferromagnetic Ni -Ga-Fe shape memory alloys [J]．Appl ．Phys ．Eett ．,2002,81(27):5201-5203.[5]徐祖耀,李麟.材料热力学：第2版[M].北京:科学出版社,2000:198.[6]周如松.金属物理（下）[M].北京:高等教育出版社,1992:131.[7]徐祖耀.马氏体相变与马氏体：第2版[M].北京:科学出版社,1999:431-432.[8]S.Zhang,P G.McCormick.Thermodynamic analysis of shape memory phenomena -I.Effect of transformation plasticity on elastic strain energy [J].Acta Materialia,2000,48（12）:3081-3089.[9]V.A.Chernenko,E.Cesari,V.V.Kokorin,et al.The development of new ferromagnetic shape memory alloys in Ni-Mn-Ga system[J].Scripta Metallurgica et Materialia,1995,33(8):1239-1244.[10]K.Shimizu ，S.Kijima ，Z.Yu.Magnetic field-induced martensitictranformations in Fe-Ni-C invar and non-invar alloys[J].Transactions of the Japan Institute of Metals,1985,26(9):630-637.[11]T.Kakeshita,T.Saburi,K.Shimizu.Effects of hydrostatic pressureand magnetic field on martensitic transformations[J].Materials Science and Engineering A,1999,273-275:21-39.[12]K.Ullakko,J.K.Huang,C.Kanter,et rge magnetic -field -induced strains in Ni 2MnGa single crystals [J].Appl.Phys.lett.,1996，69(13):1996-1968.P →Mnon-chem P →Mnon-chem 图6在磁场能作用下自由能随温度变化关系的示意图△G Treatment in zero field△G Treatment in magnetic field T 0A D M SB EM ’S (H 0=0.7T ）C F△G mag （H 0）T ’温度吉布斯自由能有色金属科学与工程2012年2月4。
磁共振成像技术中英文名词对照之欧阳育创编
Region of interest , ROI
感兴趣区
Spin echo , SE
自旋回波
Spin echo-echo planar imaging , SE-EPI
自旋-平面回波成像
SENSitivity encoding ,SENSE
敏感度编码
siMultaneous acquisition of spatial harmony ,SMASH
磁化准备快速梯度回波
Magnetization prepared rapid gradient echo imaging, MP-RAGE
磁化准备快速梯度回波成像
Magnetic resonance angiograghy ,MRA
磁共振血管成像
Magnetic resonance cholangiopancreatography,MRCP
空间协调同步采集
Signal-to-noise ratio，SNR
信噪比
Spoiled gradient recalled echo , SPGR
扰相梯度回波
Statistical parametric mapping , SPM
统计参数绘图
Saturation recovery , SR
饱和恢复
Saturation recovery fast gradient recalled echo , SR-FGRE
快速小角度激发
Field of view，FOV
视野
Fast spin echo，FSE
快速自旋回波
Generalized autocalibrating partially parallel acquisition, GRAPPA
Thermodynamics_Chap_1
Phase of a substance : a quantity of matter that is uniform throughout.
A substance may exist in one or more phases : solid, liquid, vapor (i.e., water : ice , liquid water , steam). Each phase may exist at various temperature and pressure called states.
Cycle
When a thermodynamic system in a given initial state goes through a number of different changes of state or processes and finally returns to its initial state, the system has undergone a cycle. Therefore at the conclusion of a cycle all of the properties have the same value they had initially.
change with time when the system is isolated from its surroundings.
Thermodynamic equilibrium : A system is in thermodynamic
equilibrium if it is not capable of a spontaneous change to another state without a finite change in its surroundings or when a system is in equilibrium with regards to all possible changes of state Recall we said it is only in the equilibrium state that we can assign values to the thermodynamic properties.
Thermodynamics培训课件
指系统从某一初始状态出发，经历一系列变 化后又回到初始状态的过程。
03
第一定律
定义和内容
定义
第一定律又称为热力学第一定律，是指能量守恒定律在系统 和环境间的应用。
内容
能量不能被创造或消失，只能从一种形式转化为另一种形式 ，系统的总能量保持不变。
热力学能和焓
热力学能
热力学能是指系统在一定压力和温度下的总能量，包括内能和动能。
Understand energy conversion: 了解能量 转换过程
Understand the design of systems: 了 解系统设计中的热力学 应用
Understand the behavior of the environment: 了解环 境中热力学avior of matter in the universe: 了解宇宙 中物质在热力学下的行 为
状态变量
描述系统状态的物理量或化学量，称为状态变量 。
基本状态变量
温度、压力、体积、物质的量等。
过程与循环
过程
热过程
指系统从某一初始状态出发，通过输入或输 出物质或能量，变为另一状态的过程。
指只涉及温度变化的过程，热过程中不发生 化学反应和相变。
平衡过程
循环过程
指系统中所有位置上的物理量和化学量都保 持恒定的过程。
3
该定律有几种表述方式，如克劳修斯表述、开 尔文表述、熵增加原理等。
熵和熵增加原理
熵是描述系统“不可用”能量的一个物理量，可以表示能量的“混乱度”或“无 序度”。
熵增加原理是指，封闭系统中的熵永不减少，只能增加或保持不变。
热力学第二定律指出，在一个封闭系统中，过程总是朝着熵增加的方向进行，即 系统的熵永不减少。
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6.1 相变分类(按原子迁移特征分类) (3)按原子迁移特征分类 扩散型相变：依靠原子扩散进行 •原有的原子邻居关系被破坏； •溶体成分发生变化。 无扩散型相变：无原子扩散，或虽存在扩散，但不是 相变所必需的或不是主要过程。 •相邻原子的移动距离不超过原子间距，不 破坏邻居关系； •不改变溶体成分。 马氏体相变
6.2 新相的形成和形核驱动力
第二相β的形核驱动力Δ*Gm的计算：
Gm Gm F Gm E
dG m Gm x Gm x0 ( x x0 ) dx x0 dGm G x G x ( x x ) m 0 0 m dx x
a a A ( xa ) B ( xa ) RT 1 x ln x ln a A( x0 ) aB ( x0 )
i 0Gi RT ln ai
6.2 新相的形成和形核驱动力
6.2 新相的形成和形核驱动力
d 2G 0 2 dX B
，固溶体自由能升高
d 2G 0 2 dX B
，固溶体自由能降低
6.2 新相的形成和形核驱动力
亚稳区(Metastable range) ： 单相固溶体的自由能高于 两相混合物的白由能。
固溶体要发生分解， 不能以失稳分解的机制 发生，而要通过普通的形 核长大机制进行。
dG G n G G x x n x P x O OQ 2 2 dx x 2 n OP OQ n QP 2 2
如果出现浓度为xβ的核胚，其 ΔG/n2=-QP，如界面能很小，核胚 就会在驱动力QP的作用下发展成 为β相的临界核心.
Maxwell 方程
V , S p T p T
V V
V V , S S
表现：体积和熵(焓)的突变
二级相变（Second order phase transitions）
在相变过程中，化学势对T,P的一阶偏微分相等，而 二阶偏微分在相变过程中发生突变的相变称为二级相 变。属于二级相变的有：
6.2 新相的形成和形核驱动力
G1 G x2 x G n1 G1 G n2 G2 G n2 G2 G x x 1 以n2代表核胚的摩尔数，设xl很接近x，核胚 只占整个体系中很小的部分，即n1远大于n2.
Thermodynamics of Materials
Lecture 6
Thermodynamics of Phase Transformation
第 6章
相变热力学
6.1 相变分类 6.2 新相的形成和形核驱动力 6.3 第二相析出的相变驱动力 6.4 析出相的表面张力效应 6.5 晶间偏析 6.6 固溶体的磁性转变自由能 6.7 有序-无序转变自由能 6.8 二级相变对相平衡的影响
6.2 新相的形成和形核驱动力
固溶体稳定性： 如果将自由能曲线分成若干段，则每个成分段固溶体的性质与 这段曲线的形状有关。
d 2G 0 2 dX B
d 2G 0 2 dX B
固溶体稳定 固溶体将发生失稳分解 (Spinodal decomposition)
原因： 发生浓度起伏(Concentration undulate) 时，
6.2 新相的形成和形核驱动力 热力学指明某一新相的形成是否可能。 材料发生相变时，在形成新相前往往出现浓度起伏， 形成核胚，再成为核心、长大。 在相变过程中，所出现的核胚，不论是稳定相或亚稳 相，只要符合热力学条件，都可能成核长大，因此相变中 可能会出现一系列亚稳定的新相。 这些亚稳定的过渡相在—定的条件下再向稳定相转化
第 6章
相变热力学
Phase Transformation
Melt
Crystal
Melt
Lowering Temp.
相变： 在均匀单相内, 或在几个混合相中，出现了不同成分或不 同结构（包括原子、离子或电子位置位向的改变）、不同 组织形态或不同性质的相。
6.1 相变分类 相变种类繁多,可按不同方式分类： (1)按热力学分类 •一级相变 •二级相变 (2)按相变方式分类 •不连续相变 •连续相变 (3)按原子迁移特征分类 •扩散型相变 •无扩散型相变
二级相变中，定压热容Cp、膨胀系数与压缩系数发生突变。
Cp Cp
C C p p
6.1 相变分类(按相变方式分类) (2)按相变方式分类 不连续相变（形核长大型）：形核、长大型两阶段进行， 新相和母相有明显相界面。 （小范围原子发生强烈重排的涨落） 连续型相变（无核型）：原子较小的起伏，经连续扩展 而进行，新相和母相无明显相界面。（大范围原子发生 轻微重排的涨落） 发生在转变前后晶体结构都相同的系统中。 特点：发生区域大；无形核位垒；上坡扩散 例：调幅分解；有序/无序转变
铁磁-顺磁转变(Ferromagnetic-paramagnetic transition) Fe、Ni、Co及其合金，各种铁氧体，Mn-Al合物，稀土过渡族元素化合物等 反铁磁(Anti-ferromagnetic)-顺磁转变 Fe、Mn、Cr及部分稀土元素等 超导-常导转变(Superconduct-generally conduct transition) In、Sn、Ta、V、Pb、Nb等纯金属和Nb-Ti、Nb-Zr、 V3Ga、Nb3Sn、Nb3AlGe、Nb3Ge等金属间化合物以及Y-BaCu-O等氧化物超导体等 合金中有序-无序的转变 Au-Cu、Ti-AI、AI-Mn、Cr-AI、Cu-Zn、Cu-Pd、Cu-Pt、 Fe-Co、Fe-AI、Fe-Si、Fe-Ni、Fe-Pt、Ni-V等合金系
如果不考虑相界面能，此时体系 总自由能增量为：
n1 G1 G n2 G2 G n1 x1 n2 x2 n1 n2 x 根据质量守恒： n1 x x1 n2 x2 x
G n1G1 n2G2 n1 n2 G
H C p ( ) p T ( 2 ) p T T
2
Cp 2 2 T T p 2 V T p T 2 2 V p T
Cp Cp
二级相变
6.2 新相的形成和形核驱动力 For example: 材料凝固时往往出现亚稳相，甚至得到非晶态。
自由能最低的相最稳定(稳定相) 相对稳定相(亚稳相)具有较高的自由能，但只要亚稳相的 形成会使体系的自由能降低，亚稳相的形成也是可能的。
液相L、稳定相α、亚 稳定相β、γ和δ
如过冷至Tmγ以下，由液相 凝固为α、β和γ都是可能的， 都引起自由能的下降。
O
6.2 新相的形成和形核驱动力
※ 如果浓度起伏小区的自由能为过x点切线上的一点
dG G n2 G2 G x2 x dx x
Nucleation Driving Force 图解法确定形核驱动力的方法： 过α相自由能曲线上相应母相的 成分点作切线； 过相应析出新相核胚的成分点 作垂线； 垂线与切线的交点到垂线与新 相自由能曲线的交点间线段的长 度为新相形核驱动力。
V V , S S
表现：体积和熵(焓)的突变
一级相变（First-order phase transformations）
G G
i i
S S
i i i i , p p T T T p T p
6.2 新相的形成和形核驱动力
原始亚稳α固溶体的浓度为x，其相应的自由能为G。当均匀的α固 溶体出现较大的浓度起伏时，起伏也可作为新相的核胚。
For example: 在浓度为x的α固溶 体出现： 由n1摩尔组成的、浓度为x1的 原子集团,其自由能为G1； 由n2摩尔组成的、浓度为x2的原 子集团，其自由能为G2.
G n2 Ax2 Bx2 BE n2 AB BE n2 AE
G n2 AE
摩尔自由能的变化（形核驱动力）Leabharlann 6.2 新相的形成和形核驱动力
形核驱动力(Nucleation Driving Force) ：由起伏或核胚形成新相核 心的自由能变化 。 程度较小的浓度起伏，引起的自由能变化使体系的自由能提 高→无形核驱动力 → 这种浓度起伏是不稳定的。 当浓度起伏很强，即偏离x很大，而新相的自由能又较低时， 则ΔG就变成负值 →具有形核驱动力 → 形成新相。
0
OR,
Gm Gm F Gm E
1 x x 1 x x A ( xa ) B ( xa ) A( x0 ) B ( x0 )
1 x A( xa ) A( x0 ) x B ( xa ) B ( x0 )
二级相变（Second order phase transitions）
G G
i i
i i i i , p p T T T p T p
V V , S S
G1 G dG dx x x1 x
dG G n2 G2 G x2 x dx x G2 Ax2 G Bx2
dG x2 x BE dx x