Chapter 3

Question 1

Unit cell

Answer 1

fundamental repeating structure that is found in all crystalline structures

Question 2

lattice parameters

Answer 2

a - define a unit cell’s size and shape

Question 3

unit cell shapes

Answer 3

1. cubic
2. tetragonal
3. orthorhombic
4. rhombohedral
5. hexagonal
6. monoclinic
7. triclinic

Question 4

Bravais lattices

Answer 4

expands number of lattices to 14 because you have to take into account location of atoms

Question 5

BCC Lattice definition

Answer 5

body centered cubic - atoms at corner of cell and one in the middle - a = 4R/sqrt(3)

Question 6

bcc lattice characteristics

Answer 6

at room temp is quite open so not in lowest energy state

Question 7

bcc lattice number of atoms

Answer 7

of interior atoms = 1
# of corner atoms = 8 * 1/8 = 1
total = 2

Question 8

fcc lattice definition

Answer 8

face centered cubic - atoms at corners and centered on each cube face - a = 2Rsqrt(2)

Question 9

fcc lattice number of atoms

Answer 9

of face-centered atoms = 6*1/2 = 3

of corner atoms = 8 *1/8 = 1
total = 4

Question 10

hcp definition

Answer 10

hexagonal close packed - two hexagons with atoms at each corner and one in the faces’ centered stacked on top of each other with three interior atoms - a/c = 1.63333 (a = edge length of hexagon, c = height of prism)

Question 11

hcp number of atoms

Answer 11

of corner atoms = 12 * 1/6 = 2
# of face atoms = 2 * 1/2 = 1
# of interior atoms = 3
total = 6

Question 12

theoretical density of a material

Answer 12

rho = nA/V(c)N(a)
n = number of atoms in a unit cell
N(a) = Avogadro’s number
A = atomic weight
V(c) = volume of cell

Question 13

Miller - Bravais

Answer 13

four axis system for representing hcp - a1, a2, a3, evenly spaced axis in xy plane and z is same - [uvtw] - can convert from [UVT] using formulas

Question 14

crystal planes rules

Answer 14

1. pick origin
2. determine intercepts of plane with respect to the axis
3. take inverse numbers of intercepts
4. make these numbers integers
5. these are your (h k l) indices

Question 15

important notes for crystal plane indices

Answer 15

no intercept - infinity (1/infinity = 0)
-1 = 1 bar (1 with line above it)

Question 16

crystal directions for cubic crystals

Answer 16

n is usually 1
use starting point and end point
since unit cell, a=b=c=1

Question 17

APF

Answer 17

atomic packing factor
volume of atoms - use sphere formula (4piR^3/3) and number of atoms
volume of cell - use ‘a’ parameter and formula of cube volume

Question 18

LD

Answer 18

linear density - number of atoms per unit length whose centers lie on the direction vector - must take into account proportion of atoms in that unit cell

Question 19

PD

Answer 19

planar density - number of atoms per unit length on a plane

Question 20

the higher the density, the more likely _______

Answer 20

it is for electrons and atoms to interact with each other - (111) plane is more active than (100) for fcc

Question 21

fcc pattern

Answer 21

ABCABC

Question 22

hcp pattern

Answer 22

ABAB

Question 23

what are the most important planes

Answer 23

highest density planes or close packed planes

Question 24

x-ray diffraction principle

Answer 24

like skipping rocks, if the speed (energy) and direction (angle) are right then we diffract the incoming x-ray beam

Question 25

bragg’s law

Answer 25

nlamda = 2d*sin(theta)
n is usually 1
d is spacing between planes

Question 26

spacing between planes for cubic

Answer 26

d = a/sqrt(h^2+k^2+l^2)

Question 27

allowed reflections for BCC

Answer 27

h+k+l must be even

Question 28

allowed reflections for FCC

Answer 28

h,k,l must all be even or all be odd