Week 2

Question 1

Define crystalline

Answer 1

atoms are situated in a repeating or periodic array over large atomic distances; maintain long-range atomic order

Question 2

Define Crystal Structure

Answer 2

properties of crystallin solids depend on crystal structure; manner in which atoms, ions or molecules are spatially arranged

Question 3

Define Unit Cell

Answer 3

small repeat entities; basic structural unit or building block of the crystal structure and defines the crystal structure by virtue of its geometry and the atom positions within

Question 4

Define Lattice

Answer 4

3-D array of points coinciding with atom positions (or sphere centers)

Question 5

How many crystal systems are there and name them

Answer 5

Cubic
Tetragonal 
Orthorhombic
Rhombohedral
Hexagonal
Monoclinic
Triclinic

Question 6

The 14 Crystal (Bravais) Lattices

Answer 6

Simple Cubic, body-centered cubic, Face-centered cubic, simple tetragonal, body-centered tetragonal, simple orthorhombic, body-centered orthorhombic, face-centered orthorhombic, rhombohedral, hexagonal, simple monoclinic, base-centered monoclinic, triclinic

Question 7

What is the Coordination Number

Answer 7

Number of adjacent ions/atoms surrounding a reference ion/atom

Question 8

Atomic Packing Factor

Answer 8

volume of atoms in a unit cell divided by the total unit cell volume

Question 9

Most common crystal structure for elemental metals at room temp

Answer 9

Face centered cubic
Body centered cubic
Hexagonal Close Packed

Question 10

How to calculate theoretical density

Answer 10

[nA] / VcNa
n = # of atoms associated with each cell (atoms)
A = atomic weight (g/mol)
Vc = volume fo unit cell (cm^3)
Na = Avogardro’s number (6.022 x 10^23 atoms/mol)

Question 11

What is polymorphism

Answer 11

Having more than one crystal structure

Question 12

What is Allotropy

Answer 12

When polymorphism exists in elemental solids

Question 13

Lattice Position Coordinates

Answer 13

to specify a particular point within a unit cell
x, y, and z(right-handed)

• axes not mutually perpendicular for hexagonal, rhombohedral, monoclinic and triclinic
• a, b, and c (unit cell lengths)
• p, q and r (fractional lengths)
• point coordinate = (q,r,s)

Question 14

Steps to get cyrstallographic directions

Answer 14

1. construct x,y,z
2. coordinates of two points (x1,y1,z1 and x2,y2,z2)
3. normalize coordinate differences (x2 - x1)/a, …
4. multiply/divide by n with common factor to reduce to smallest integer values
5. represented as [uvw]; u = n(x2-x1)/2; v=n(y2-y1)/b; w=n(z2-z1)/c

Question 15

What are crystallographically equivalent points

Answer 15

points where spacing of atoms along each direction is same

Question 16

Directions in Hexagonal Crystals

Answer 16

U = n(a''1-a'1)/a
V = n(a''2-a'2)/a
W = n(z''-z')/a

[UVW] to [uvtw]
u = (1/3)(2U - V)
v = (1/3)(2V - U)
t = -(u+v)
w = W

Question 17

Crystallographic Planes

Answer 17

1. If plane passes through origin, construct another parallel plane or establish new origin
2. Plane either intersects or parallels each of the three axes; origin is the intersection of each of axes (A,B,C)
3. Reciprocals are normalized and multiple by respective a, b, and c lattice parameters
4. If required, change to smallest integers by multiplications or division by common factor
5. Integer indices (hkl) enclosed within parentheses

h = na/A ; k = nb/B ; l = nc/C

Question 18

Linear Density (equation)

Answer 18

of atoms entered on direction vector divided by length of direction vector

Question 19

Planar Density (equation)

Answer 19

of atoms centered on plane divided by area of plane

Question 20

What are single crystals

Answer 20

• when the repeated arrangement of atoms is perfect and extends throughout the material without interruption
• all unit cells interlock in the same way and have same orientation (flat surfaces)
• exist naturally and can be produced
• applications: electronic microcircuits, semiconductors

Question 21

Polycrystalline Materials

Answer 21

• composed of a collection of many small crystals(grains)
• small crystals form at various positions
• grains grow by successive addition
• extremities of adjacent grain impinge on one another
• atomic mismatch within region where two grains meet (grain boundary)

Question 22

Ceramics

Answer 22

• wide variety of chemical composition is reflected in crystalline structures
• ionic packing factor rather than atomic packing factor

Question 23

Polymers

Answer 23

• most commercial plastics are to a large degree noncrystalline
• chain-like structure of long polymeric molecules
• long-chain molecules folds back and forth on itself

Question 24

Anisotropy

Answer 24

Directionality of properties due to variance of atomic/ionic spacing with crystallographic direction

Question 25

Isotropic

Answer 25

materials in which measured properties are independent of the direction of measurement

Question 26

Diffraction and when does it occur

Answer 26

• scattering of radiation by regular array of scattering centers

Occurs when obstacles:

1. are capable of scattering the wave
2. have spacings that are comparable in magnitude to the wavelength

Question 27

What is Bragg’s equation

Answer 27

n(wavelength) = 2d(hkl) sin(pheta)

n = difference in path length between adjacent beams (whole number)
d = spacing between adjacent crystal planes
pheta = Bragg angle (2pheta: diffraction angle)

Question 28

Semiconductor structure

Answer 28

diamond cubic structure

Question 29

Noncrystalline solids

Answer 29

• solids that lack a systematic and regular arrangement of atoms over relatively large atomic distances (amorphous)
• depends on the ease with which a random atomic structure in the liquid can transform to an ordered state during solidification
• formation favoured by rapid cooling through freezing temp