Chapter 1: Crystal Structures

Question 1

Ideal Crystal

Answer 1

an infinite repetition of identical structural elements described by a structural unit, basis, and repetition rule, lattice

crystal = lattice + basis

Question 2

Bravais Lattice

(6 points)

Answer 2

• Mathematical concept that contains only the geometry of lattice
• Independent of basis
• Invariant with respect to translations
• Two points always connected by a translation
• Primitive lattice vectors not unique
• 14 in 3D space

Question 3

Primitive Unit Cell

(4 points)

Answer 3

• Parallelpiped formed by primitive lattice vectors
• Volume V = (a₁ x a₂) · a₃
• Not unique
• Must contain only one lattice point

Question 4

Conventional Unit Cell

(2 points)

Answer 4

• Reflects symmetry of lattice
• Usually larger than primitive unit cell

Question 5

Wigner-Seitz Cell

(3 points)

Answer 5

• Contains full symmetry of bravais lattice
• Around single point
• All points within cell are closer to enclosed point than any other lattice point

Question 6

Miller Indices

(4 points)

Answer 6

• Define a crystal plane
• Determine intersecting points of plane and lattice vectors
• Take reciprocal
• Find smallest integer with same ratio

Question 7

Surfaces

(4 points)

Answer 7

• Net force in center is zero
• Non-zero net force at surface towards center
  
  • Creates surface relaxation, where surface is pulled towards center
  • Dangling bonds cause surface reconstruction

Question 8

Structural Disorder

(7 points)

Answer 8

• Depends highly on temperature
• Intrinsic defects occur at equilibrium temperature
  
  • Vacancies, interstitial atoms, etc.
• Extrinsic defects occur away from equilibrium temperature and require high temperature
  
  • Dislocations, grain boundaries
• Point defects
• Line/plane defects

Question 9

Creating/Annealing Defects

(4 points)

Answer 9

• Quenching: rapid temperature cooling
• Annealing: heat quickly to nearly the melting point and then allow to cool gradually
• Bombard with heavy particles
• Plastic deformation

Question 10

Point Defects

(6 points)

Answer 10

• Vacancy: missing atom
• Interstitial atom: extra atom
• Foreign atom: non-native atom

NOTE: Usually come in pairs to maintain electrically neutral structure

• Schottky defect: vacancy at two adjacent sites
• Frenkel defect: vacancy at A and interstitial atom near A