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
Problem 1
In[107]:=
Clear"Global`*"
Part a
Similar to the free energy curve, the phase boundaries will have a common miminum at x = 0.5. The
slopes of the phase boundaries at this point will be equal.
Part b
In[108]:=
R = 8.3144598 1000;
TmNa = 1240;
TmK
Mat Sci 103 Phase Transformations and Kinetics
Spring Semester, 2017
Homework Assignment 3
Posted: February 3, 2017
Due: Friday, February 10, 2017 by 11:59 pm on the bCourses website.
Instructions:
Please complete all parts of all problems.
All homework a
Mat Sci 103 Phase Transformations and Kinetics
Spring Semester, 2017
Homework Assignment 4
Posted: February 10, 2017
Due: Friday, February 17, 2017 by 11:59 pm on the bCourses website.
Instructions:
Please complete all parts of all problems.
All homework
Mat Sci 103 Phase Transformations and Kinetics
Spring Semester, 2017
Homework Assignment 5
Posted: February 17, 2017
Due: Friday, February 24, 2017 by 11:59 pm on the bCourses website.
Instructions:
Please co
Mat Sci 103 Phase Transformations and Kinetics
Spring Semester, 2017
Homework Assignment 6
Posted: Friday, March 3, 2017
Due: Friday, March 11, 2017 by 11:59 pm on the bCourses website.
Instructions:
Please
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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
Mat Sci 103 Phase Transformations and Kinetics
Spring Semester, 2017
Homework Assignment 1
Posted: January 20, 2017
Due: Friday, January 27, 2017 by 11:59 pm on the bCourses website.
Instructions:
Please complete all parts of all problems.
All homework
Mat Sci 103 Phase Transformations and Kinetics
Spring Semester, 2017
Homework Assignment 2
Posted: January 27, 2017
Due: Friday, February 3, 2017 by 11:59 pm on the bCourses website.
Instructions:
Please complete all parts of all problems.
All homework
E 115
A. M. Glaeser
Chapter 9:
Equilibrium in Multicomponent Systems - Solution Behavior
Phase equilibrium in single component systems
Reactions involving gases
Reactions between gases and pure solids
Equilibrium in multicomponent systems (solution behavi
Problem 1
Clear"Global`*"
Part a
Using the diffusion couple solution from the handout, calling the first block 1 and the second 2, and using
concentration of B. Assuming (volume per atom) is constant, we can use mole fraction instead of
concentration. For
Problem 1
Clear"Global`*"
Part a
Looking at Figure 5.3 we can see that Gn is given by:
Gn [x * ] = x * B [x0 ] + (1 - x * ) A [x0 ] - x * B [x * ] + (1 - x * ) A [x * ]
Assume that x* x. Then by the common tangent construction we can also write:
B [x ] =
Problem 1
Part a
Method (note not all the same points as assignment):
Part b
At pure B corner, XA= 0,
XB= 1, and XC= 0
At point 7,
XA= 0.15, XB= 0.70, and XC= 0.15
2
assignment5_solutions.nb
So XA= XC and XA + XB + XC = 1
XA = XC = 0.5 (1 - XB)
Part c
At
Clear"Global`*"
Problem 1
Part a
gesT_, x_ := R T Log1 - x
gelT_, x_ := R T Log1 - x + GmgeT
sisT_, x_ := R T Log[x]
silT_, x_ := R T Log[x] + GmsiT
The above equations define the chemical potentials. As in the first assignment, when the chemical
potentia
Problem 1
Clear"Global`*"
Part a
ri (t - i ) is radius at time t for grain that nucleated at i , it has area
Ai = ri (t - i )2
assume constant interface velocity v.
df = v2(t - i )2 N d (1 - f )
df
= v2(t - i )2 N d
1-f
-d ln(1 - f ) = v2(t - i )2 N d
Int
E 115
A. M. Glaeser
Chapter 9:
Equilibrium in Multicomponent Systems - Solution Behavior
Phase equilibrium in single component systems
Reactions involving gases
Reactions between gases and pure solids
Equilibrium in multicomponent systems (solution behavi
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