Material science HW

ENGR 1210 HW 3

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Homework 3 on chapter 3; (Total points: 100)

Reading assignments: Chapter 3 from textbook, notes and slides

Student Name: _______________________________ MTSU ID: ____________________

Honor pledge: I _______________________________ acknowledge that I have neither received nor given any unauthorized help/aid during this assignment.

Part 1 Key Engineering Terms: fill in the blanks – 25 points

1. Crystal structure: The manner in which atoms, ions and molecules are

_____________________________________ arranged.

2. Lattice: A three dimensional array of points coinciding with

________________________________ positions.

3. Unit cell: A ____________________ of lattice into small _________________________

entities still retaining overall characteristics of the entire lattice.

4. Basis or motif: a group of atoms associated with _____________________________.

5. Crystalline material: A crystalline material is one in which the atoms are situated in a

_____________________________________ or periodic array over

________________________________ atomic distances.

6. Coordination number: number of ________________________________ neighbors of an

atom in a crystal structure.

7. Lattice parameter: The unit cell ___________________________ and the

_________________________ between the edges.

8. Closed packed direction: direction in a crystal lattice along which atoms are in

_________________________________.

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9. Bravais lattices: _______________________________ possible lattices arrangements

using lattice points in 3 dimensional space.

10. Atomic packing fraction: a fraction of a plane, volume or direction that is

_____________________________ occupied with atoms.

11. Allotropy or Polymorphism: a property of an element to coexist in more than

________________________________ crystal structures.

12. Amorphous Materials: Materials including glasses that have

______________________________ long range order or crystal structure.

13. Isotropic: Having _________________________________ properties in all directions.

14. Anisotropic: Having _________________________________ properties in different

directions.

15. Miller Indices of Directions: Are _____________________________ components of the

directions resolved along each of the coordinate axes.

16. Miller Indices of Planes: Are _____________________________ of fractional

_________________________________ that plane makes with coordinate axes.

17. Linear density: It is defined as the number of lattice points or atomic diameters per unit

____________________________________ of the direction.

18. Planar density: The number of atoms whose ________________________________ are

intersected by the plane per unit _____________________________.

19. X-ray diffraction: A technique to analyze the _____________________________ of

materials using a beam of X-rays as source.

20. Metallic glass: Metals with ____________________________ crystal structure.

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Part 2 Learning concepts/reflections/problems – 65 points

1. Sketch the unit cells of Simple Cubic, Body Centered Cubic and Face Centered Cubic

lattices and determine and show calculations for following:

A. Number of atoms per unit cell

B. Equation/relation for radius and lattice parameter (unit cell edge length)

C. Atomic Packing Fraction (APF) 15 points

2. Calculate the radius of a palladium (Pd) atom, given that Pd has an FCC crystal structure,

a density of 12.0 g/cm3, and an atomic weight of 106.4 g/mol. Assume Avogadro’s

number = 6.022 x 1023 atoms/mol 5 points

3. Determine the Miller Indices of directions A, B, C and D as shown in figure below:

10 points

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4. Determine Miller Indices of planes as shown in figure below:

10 points

5. Determine Miller Bravais Indices [hkil] of directions as shown in figure below:

10 points

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6. Determine Miller Bravais Indices (hkil) of planes as shown in figure below:

10 points

7. Define diffraction. Write an expression for Bragg’s law of diffraction and explain the

terms of the equation. 5 points

Part 3 Materials design – 10 points

1. Why metallic crystal structure are dense? Explain. 5 points

2. Give 2 materials examples of each of the following crystal structures:

a. Simple cubic (SC)

b. Body Centered Cubuc (BCC)

c. Face Centered Cubic (FCC)

d. Hexagonal Closed Packed (HCP) 5 points

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Bonus questions:

1. Explain why the properties of polycrystalline materials are most often isotropic?

5 points

2. Explain two differences between an optical microscope and a scanning electron

microscope (SEM). 5 points

3. Calculate theoretical density of Chromium which has Body Centered Cubic structure and

atomic weight of 52 g/mol and atomic radius of 0.125 nm. Assume Avogadro’s number =

6.022 x 1023 atoms/mol 5 points

Note: Please use extra sheets wherever necessary to answer the questions. All HW must be uploaded via D2L Dropbox system. Students are highly encouraged to refer textbook, notes and slides.