MSE 103
Midterm 1
A. M. Glaeser
1.
free energy curves and solution behavior (25 points)
Shown below are five curves that represent the molar free energy of mixing, Gmixing normalized by RT
where R is the gas constant and T is the temperature in Kelvin. Th
MSE 103
1.
Deja vu all over again
A. M. Glaeser
Ordering (25 points)
Elements A and B have the same bcc crystal structure when pure, and form solid solutions. As in the case
discussed in class, when the alloys are disordered, they have a bcc structure. Wh
mse 103
Phase Transformations and Kinetics University of California
Spring 2009
Problem set 1 Solution Due: Wednesday, January 28th, by 11:10am before lecture begins; late homework will not be accepted 1. The schematic below shows a hypothetical P-T diagr
mse 103
Phase Transformations and Kinetics
University of California
Spring 2012
Problem set 14
Due: Wednesday, March 7th at the beginning of discussion
1.
(40 points)
The prior problem set dealt with some aspects of phase equilibrium in ternary systems. T
mse 103
Phase Transformations and Kinetics
University of California
Spring 2012
Problem set 15
Due: Monday, March 12th at the beginning of lecture
1.
(40 points)
In lecture and in the handout, we considered system of one mole of material in the form of a
mse 103
Phase Transformations and Kinetics
University of California
Spring 2012
Problem set 13
Due: Monday, March 5th at the beginning of lecture
1.
(40 points)
A sound understanding of ternary phase diagrams and the solution behavior in ternary systems i
mse 103
Phase Transformations and Kinetics
University of California
Spring 2012
Problem set 17
Due: Monday, March 19th at the beginning of lecture
(40 points)
In the last homework, you made use of knowledge that the Wulff theorem is based on is minimizati
mse 103
Phase Transformations and Kinetics
University of California
Spring 2012
Problem set 18
Due: Wednesday, March 21st at the beginning of discussion
1.
(40 points)
You should now be very comfortable with the idea that the Wulff theorem is based on is
mse 103
Phase Transformations and Kinetics
University of California
Spring 2012
Problem set 19
Due: at the beginning of lecture, Friday, March 23rd
1. (25 points)
In discussing steady-state diffusion and Ficks First Law, we discussed situations where the
mse 103
Phase Transformations and Kinetics
University of California
Spring 2012
Problem set 20
Due: Monday, April 2nd, at the beginning of lecture
Ficks first law relates a flux, J, to the product of a diffusion coefficient and the negative of the
concent
mse 103
Phase Transformations and Kinetics
University of California
Spring 2012
Problem set 16
Due: Friday, March 16th at the beginning of lecture
1.
(40 points)
In Wednesdays lecture, the Wulff theorem will be presented. The Wulff theorem relates the
equ
mse 103
Phase Transformations and Kinetics
University of California
Spring 2012
Problem set 22
Due: Wednesday, April 11th at the start of Wednesday discussion
(40 points)
The purpose of this problem set is to show you that it can be convenient and informa
mse 103
Phase Transformations and Kinetics
University of California
Spring 2012
Problem set 21
Due: Monday, April 9th at the start of lecture, but accepted without penalty until Wednesday discussion
Please note that a second problem set will most likely a
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mse 103
Phase Transformations and Kinetics
University of California
Spring 2012
Problem set 27
Due: at the start of discussion, Wednesday, April 25th
In lecture, we considered the effect of a heterogeneity, e.g., a mould or container, on the nucleation pr
mse 103
Phase Transformations and Kinetics
University of California, Berkeley
Spring 2012
Problem set 26
Due: Monday, April 23rd at the start of lecture
1.
In todays lecture, we examined the impact of surfaces and interfaces (heterogeneities) as possible
mse 103
Phase Transformations and Kinetics
University of California
Spring 2012
Problem set 25
Due: at the beginning of lecture, Friday, April 20th
In lecture, we discussed a formulation for nucleation of a spherical solid particle in a matrix of a
superc
mse 103
Phase Transformations and Kinetics
University of California
Spring 2012
Problem set 24
Due: at the beginning of discussion, Wednesday, April 18th
In Fridays lecture, we reviewed the development of an expression for the diffusivity that included a
mse 103
Phase Transformations and Kinetics
University of California
Spring 2012
Problem set 23
Due: Friday, April 13th, at the beginning of lecture
In a prior problem set you were asked to take diffusivity data for a variety of fcc metals and to
develop a
mse 103
Phase Transformations and Kinetics
University of California
Spring 2012
Problem set 8
Due: Monday, February 13th, at the start of lecture
In the past few lectures and problem sets, the effects of varying the thermodynamic characteristics
of the so
mse 103
Phase Transformations and Kinetics
University of California
Spring 2012
Problem set 2
Due: Friday, January 27th, at the beginning of lecture
Many of you have been exposed to one-component phase diagrams previously. Perhaps some of you have
calcula
MSE 103 Lecture Supplement: 02-03-12
Assessing the condition of equilibrium using equality of the vapor pressures:
1x10
Equilibrium Vapor Pressure (atm)
PB (l )
-6
6x10
-6
PA (s )
4x10
ls
-6
PA (l )
PB (s )
ss
PB (s )
2x10
-6
8x10
PB (l )
-6
6x10
-6
PA (s
MSE 103
Lecture Supplement
A. M. Glaeser
Constant surface composition, semi-infinite body
In lecture, we used the solution for bidirectional (x) diffusional exchange between two semi-infinite
materials to describe the unidirectional diffusion of material
MSE 103
Lecture Supplement
A. M. Glaeser
The curves shown are for a temperature of 1000K, and the parameter that scales the heat of mixing has been set to 1500R.
4000
2000
mechanical
mixture
1
o
GB
o
GA
0.8
-2000
0.6
Activity of B
Molar free energy (joule
Ternary Liquidus Projection
Example of a
liquidus for the
Nb-Ti-Zr system
Ternary Liquidus Projection
Example of a
solidus for the
Nb-Ti-Zr system
Ternary Liquidus Projection
Superposition of
the liquidus and
solidus projections
for the
Nb-Ti-Zr system
Te
Introduction to Grains, Phases, and Interfacesan
Interpretation of Microstructure, Trans. AIME, 1948,
vol. 175, pp. 1551, by C.S. Smith
GREGORY S. ROHRER
DOI: 10.1007/s11661-010-0215-5
The Minerals, Metals & Materials Society and ASM International 2010
S
Chapter 2:
Equilibrium in Multicomponent Systems - Solution Behavior
Phase equilibrium in single-component systems
Equilibrium in multicomponent systems (solution behavior)
Binary phase diagrams
Ternary phase diagrams
Quaternary phase diagrams
Introductio