Homework #4
Professor Estrada
ENGR 245: Intro to Materials Science & Engineering
February 9, 2016
In order to receive full credit, all work MUST be shown and appropriate units must
be specified. Working together is encouraged, however, all work that you turn in must be
YOUR OWN work.
Exercise 1. Derive Bragg’s Law. You should find n? = 2d sin(?). In order to receive full
credit, explain the justification for each step.
Exercise 2. Calculate the spacing between the (111) plane in BCC Fe. Cite the source you
used to look up the lattice constant, a.
Exercise 3. Given the following set of experimental data for the number of vacancies (Nv)
in copper as function of temperature, plot Nv on a logarithm scale (or the natural log of Nv)
as a function of T
-1
(i.e., 1/T) for a temperature range of 500K to 1250K.
T(K) Nv(cm-3
)
500 7.23e13
600 1.75e15
700 3.86e16
800 1.094e17
900 8.83e17
1000 2.475e18
1100 6.97e18
Exercise 4. The equilibrium vacancy concentration, Nv, is given by equation 4.1 in the 9th
edition of Callister and Rethwisch. Given the density (?) and atomic weight (ACu) of copper
are 8.4 g/cm3 and 63.5 g/mol, find the activation energy of vacancy formation in copper
(Qv) by fitting equation 4.1 to the experimental data in exercise 3. Show at least three of
your fits on the same plot as the data points.
1

Homework 4

The task is:

A) to finish reading your resources, and

B) to organize your thoughts for the research paper by CONSTRUCTING AN OUTLINE FOR THE PAPER.

Outline is a map for your final paper and is a key for having a successful research experience and achieving an A paper. When you make an outline for your research paper, you organize your thoughts and make a plan for a strong, focused argument.

Your homework should consist of your full introduction and topic headings for your outline, and your survey questions and plan (if you have not included them with your Homework 2).

How to write an Outline?

Outline of your paper should have following parts that answer indicated questions:

Introduction:
What is your research question?
Define key concepts in your question.
Why is this question interesting? Why did you choose this question?
What is the answer? (Even if you are not sure yet, write an answer. This will be your hypothesis).
What is the support (proof) for your answer?
2. Background/Review of previous research and approaches

-What is the history of this issue/concept?
-What are different explanations for this problem?
3. Presentation of the findings (Support of the answer)

-Using literature (for those of you who use existing research)
-Survey results (for those of you doing surveys/interviews)
4. Conclusions

Homework 4

The task is:

A) to finish reading your resources, and

B) to organize your thoughts for the research paper by CONSTRUCTING AN OUTLINE FOR THE PAPER.

Outline is a map for your final paper and is a key for having a successful research experience and achieving an A paper. When you make an outline for your research paper, you organize your thoughts and make a plan for a strong, focused argument.

Your homework should consist of your full introduction and topic headings for your outline, and your survey questions and plan (if you have not included them with your Homework 2).

How to write an Outline?

Outline of your paper should have following parts that answer indicated questions:

Introduction:
What is your research question?
Define key concepts in your question.
Why is this question interesting? Why did you choose this question?
What is the answer? (Even if you are not sure yet, write an answer. This will be your hypothesis).
What is the support (proof) for your answer?
2. Background/Review of previous research and approaches

-What is the history of this issue/concept?
-What are different explanations for this problem?
3. Presentation of the findings (Support of the answer)

-Using literature (for those of you who use existing research)
-Survey results (for those of you doing surveys/interviews)
4. Conclusions