材料科学专业英语 (4)
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Phase diagram
-1-
WHY STUDY Phase Diagrams?
➢ Predicting microstructures ➢ Helping designing alloys ➢ Understanding the phase transformation path in forming
P – T phase diagram
aO: solid – vapor boundary bO: solid – liquid boundary cO: liquid – vapor boundary O: trip point
At any point on one of these curves, the two phases on either side of the curve are in equilibrium (or coexist) with one another.
Example: H2O -- vapor, liquid (water) and solid (ice) phases
Equilibrium:
When the free energy of the system is a minimum for a given set of external conditions (pressure, temperature, composition, etc)
2. Given a binary phase diagram, the composition of an alloy, its temperature, and assuming that the alloy is at equilibrium, determine(a) what phase(s) is (are) present, (b) the composition(s) of the phase(s), and (c) the mass fraction(s) of the phase(s).
-12-
BINARY EUTECTIC SYSTEMS
Eutectic reaction
Point E: triple point 3 phase are in equilibrium with each other.
Eutectic isotherm: the horizontal solidus line at TE (line BEG).
ONE-COMPONENT PHASE DIAGRAMS
There are three externally controllable parameters that will affect phase structure—viz. temperature, pressure, and composition— and phase diagrams are constructed when various combinations of these parameters are plotted against one another.
Example: H2O -- 0-100 oC and 1 atm pressure, liquid
G PV TS 1X1 2 X 2 .... i X i
G: Gibbs free energy P: pressure of the system; V: volume of the system i: chemical potential of ith components Xi: mole fraction of ith components
-2-
Learning Objectives
1. (a) Schematically sketch simple isomorphous and eutectic phase diagrams. (b) On these diagrams label the various phase regions. (c) Label liquidus, solidus, and solvus lines.
Ci the composition of i phase Combining the two equations
-9-
Exercises
-10-
-11-
DEVELOPMENT OF MICROSTRUCTURE IN ISOMORPHOUS ALLOYS
Equilibrium
Non-equilibrium
-7-
Determination of Phase Compositions (concerning the two phase region) 1) A tie line is constructed across the two-phase region at the temperature of the alloy. 2) The intersections of the tie line and the phase boundaries on either side are noted. 3) Perpendiculars are dropped from these intersections to the horizontaHale Waihona Puke Baidu composition axis,
Mixing heat and configurational entropy need to be considered Gs GM H TSm
For idea solution, H 0
Gid ,s G M TSm
For regular solution, H 0
Gr,s G M H TSm
-15-
DEVELOPMENT OF MICROSTRUCTURE IN EUTECTIC ALLOYS Microstructural development of Pb-rich phase
Lead – Tin binary eutectic phase diagram
-16-
Formation of a Pd-Sn eutecitc microstructure Microstructure of a PbSn eutectic alloy, 375X
-17-
Microstructural development of hypoeutecitc Pd-Sn alloy
Microstructure of a hypoeutectic Pb-Sn alloy, 400X
-18-
Lever rule in eutectic systems
(b) At what temperature is salt no longer useful in causing ice to melt?
-14-
For a 40 wt% Sn–60 wt% Pb alloy at 150 Celsius degree (a) What phase(s) is (are) present? (b) What is (are) the composition(s) of the phase(s)?
from which the composition of each of the respective phases is read.
-8-
Determination of Phase Amounts (Lever rule) ―based on a mass balance equation
Wi the mass fraction of i phase
-13-
Questions
(a) Using this diagram, briefly explain how spreading salt on ice that is at a temperature below 0 Celsius degree can cause the ice to melt.
-6-
Point A: single α phase region Point B: α+L two phase region
This complete solubility is explained by the fact that both Cu and Ni have the same crystal structure (FCC), nearly identical atomic radii and electronegativities, and similar valences. The copper–nickel system is termed isomorphous because of this complete liquid and solid solubility of the two components.
Phase:
Mass (or part) of system that is uniform chemically and physically and bounded by a surface so that it is mechanically separable from the rest of the system.
-3-
Component:
The smallest number of independently variable chemical constituents necessary and sufficient to express the composition of each phase present. Examples: in Cu-Zn brass, the components are Cu an Zn.
a microstructure ➢ Helping the design and control of heat-treating procedures ➢ Being useful in understanding the development and preservation
of non-equilibrium structures and their attendant properties
In the construction of binary phase diagrams, it is important to understand that one or at most two phases may be in equilibrium within a phase field. Three phases may be in equilibrium, but only at points along the eutectic isotherm.
3. Given the composition of an iron–carbon alloy containing between 0.022 wt% C and 2.14 wt% C, be able to (a) specify whether the alloy is hypoeutectoid or hypereutectoid, (b) name the proeutectoid phase, (c) compute the mass fractions of proeutectoid phase and pearlite, and (d) make a schematic diagram of the microstructure at a temperature just below the eutectoid.
-5-
BINARY PHASE DIAGRAMS BINARY ISOMORPHOUS SYSTEMS
- Thermodynamic consideration
Components: A and B
For simple mechanical mixture
GM X AGA X BGB
XA XB 1
-1-
WHY STUDY Phase Diagrams?
➢ Predicting microstructures ➢ Helping designing alloys ➢ Understanding the phase transformation path in forming
P – T phase diagram
aO: solid – vapor boundary bO: solid – liquid boundary cO: liquid – vapor boundary O: trip point
At any point on one of these curves, the two phases on either side of the curve are in equilibrium (or coexist) with one another.
Example: H2O -- vapor, liquid (water) and solid (ice) phases
Equilibrium:
When the free energy of the system is a minimum for a given set of external conditions (pressure, temperature, composition, etc)
2. Given a binary phase diagram, the composition of an alloy, its temperature, and assuming that the alloy is at equilibrium, determine(a) what phase(s) is (are) present, (b) the composition(s) of the phase(s), and (c) the mass fraction(s) of the phase(s).
-12-
BINARY EUTECTIC SYSTEMS
Eutectic reaction
Point E: triple point 3 phase are in equilibrium with each other.
Eutectic isotherm: the horizontal solidus line at TE (line BEG).
ONE-COMPONENT PHASE DIAGRAMS
There are three externally controllable parameters that will affect phase structure—viz. temperature, pressure, and composition— and phase diagrams are constructed when various combinations of these parameters are plotted against one another.
Example: H2O -- 0-100 oC and 1 atm pressure, liquid
G PV TS 1X1 2 X 2 .... i X i
G: Gibbs free energy P: pressure of the system; V: volume of the system i: chemical potential of ith components Xi: mole fraction of ith components
-2-
Learning Objectives
1. (a) Schematically sketch simple isomorphous and eutectic phase diagrams. (b) On these diagrams label the various phase regions. (c) Label liquidus, solidus, and solvus lines.
Ci the composition of i phase Combining the two equations
-9-
Exercises
-10-
-11-
DEVELOPMENT OF MICROSTRUCTURE IN ISOMORPHOUS ALLOYS
Equilibrium
Non-equilibrium
-7-
Determination of Phase Compositions (concerning the two phase region) 1) A tie line is constructed across the two-phase region at the temperature of the alloy. 2) The intersections of the tie line and the phase boundaries on either side are noted. 3) Perpendiculars are dropped from these intersections to the horizontaHale Waihona Puke Baidu composition axis,
Mixing heat and configurational entropy need to be considered Gs GM H TSm
For idea solution, H 0
Gid ,s G M TSm
For regular solution, H 0
Gr,s G M H TSm
-15-
DEVELOPMENT OF MICROSTRUCTURE IN EUTECTIC ALLOYS Microstructural development of Pb-rich phase
Lead – Tin binary eutectic phase diagram
-16-
Formation of a Pd-Sn eutecitc microstructure Microstructure of a PbSn eutectic alloy, 375X
-17-
Microstructural development of hypoeutecitc Pd-Sn alloy
Microstructure of a hypoeutectic Pb-Sn alloy, 400X
-18-
Lever rule in eutectic systems
(b) At what temperature is salt no longer useful in causing ice to melt?
-14-
For a 40 wt% Sn–60 wt% Pb alloy at 150 Celsius degree (a) What phase(s) is (are) present? (b) What is (are) the composition(s) of the phase(s)?
from which the composition of each of the respective phases is read.
-8-
Determination of Phase Amounts (Lever rule) ―based on a mass balance equation
Wi the mass fraction of i phase
-13-
Questions
(a) Using this diagram, briefly explain how spreading salt on ice that is at a temperature below 0 Celsius degree can cause the ice to melt.
-6-
Point A: single α phase region Point B: α+L two phase region
This complete solubility is explained by the fact that both Cu and Ni have the same crystal structure (FCC), nearly identical atomic radii and electronegativities, and similar valences. The copper–nickel system is termed isomorphous because of this complete liquid and solid solubility of the two components.
Phase:
Mass (or part) of system that is uniform chemically and physically and bounded by a surface so that it is mechanically separable from the rest of the system.
-3-
Component:
The smallest number of independently variable chemical constituents necessary and sufficient to express the composition of each phase present. Examples: in Cu-Zn brass, the components are Cu an Zn.
a microstructure ➢ Helping the design and control of heat-treating procedures ➢ Being useful in understanding the development and preservation
of non-equilibrium structures and their attendant properties
In the construction of binary phase diagrams, it is important to understand that one or at most two phases may be in equilibrium within a phase field. Three phases may be in equilibrium, but only at points along the eutectic isotherm.
3. Given the composition of an iron–carbon alloy containing between 0.022 wt% C and 2.14 wt% C, be able to (a) specify whether the alloy is hypoeutectoid or hypereutectoid, (b) name the proeutectoid phase, (c) compute the mass fractions of proeutectoid phase and pearlite, and (d) make a schematic diagram of the microstructure at a temperature just below the eutectoid.
-5-
BINARY PHASE DIAGRAMS BINARY ISOMORPHOUS SYSTEMS
- Thermodynamic consideration
Components: A and B
For simple mechanical mixture
GM X AGA X BGB
XA XB 1