MET 3100 (Applied Physical Metallurgy) - Chapter 2: Crystal Structures

What is a Motif?

An atom or a group of atoms associated with each lattice point - WHAT is repeated in the crystal

Crystals have a translationally periodic arrangement of these

What is a Lattice?

The underlying periodicity of the crystal - HOW the crystal repeats

It is a translationally periodic arrangement of points

What is the Basis of a crystal?

The entity associated with each lattice point

3D Lattices

Infinite in three dimensions / distances (a, b, c), and contain angles (alpha, beta, and gamma)

What are the Bravais Lattices?

The 14 distinct lattices possible in 3D space

What are the 4 different “center types” of unit cells

Simple cubic, Base-centered Cubic, Body-centered Cubic, Face-centered Cubic

What is the Seven Crystal System? (and what are the seven types?)

Based on symmetry, crystals are classified into seven types;

1. simple cubic

2. tetragonal

3. orthorhombic

4. hexagonal

5. rhombohedral

6. monoclinic

7. triclinic

What are the parameters of a “Simple Cubic” crystal system?

side a = b = c
angle alpha = beta = gamma = 90 degrees

What are the parameters of a “Tetragonal” crystal system?

side a = b /= (does not equal) c
angle alpha = beta = gamma = 90 degrees

What are the parameters of a “Orthorhombic” crystal system?

side a /= b /= c
angle alpha = beta = gamma = 90 degrees

What are the parameters of a “Hexagonal” crystal system?

side a = b /= (does not equal) c
angle alpha = beta = 90 degrees, and gamma = 120 degrees

What are the parameters of a “Rhombohedral” crystal system?

side a = b = c
angle alpha = beta = gamma /= 90 degrees

What are the parameters of a “Monoclinic” crystal system?

sides a = b /= c
angles alpha = gamma = 90 degrees, beta /= 90 degrees

What are the parameters of a “Triclinic” crystal system?

sides a /= b /= c
angles alpha /= beta /= gamma /= 90 degrees

What is the Coordination Number?

It is defined as the total number of nearest neighboring atoms

What are the Coordination Numbers for the different lattices?

SC = 6
BCC = 8
FCC = 12
HCPS = 12

What is the mathematical definition of the Packing Fraction?

___ = Volume occupied by atoms / Volume of Cell

What are Miller Indices used for in crystallography?

Miller Indices are used to express the orientation of crystal directions and planes in terms of their intercepts on the three axes.

What are the conventions for Miller Indices?

There are NO COMMAS between numbers, Negative values are expressed with a bar over the number

x, y, z are the axes, a, b, c are the lattice parameters, h, k, l are the miller indices for planes ( ) and directions [ ]

What is the significance of knowing crystal directions and planes in materials science?

Understanding crystal directions and planes is essential for predicting modes of failure and how materials deform under loading.

How can properties like electrical and thermal conductivity vary in a crystal?

These properties can vary based on the orientation of the crystal.

What is the relationship between slip direction and crystal structure?

Slip direction is critical for understanding how deformation occurs in specific crystalline planes and directions.

What is the importance of crystal structure in applied physical metallurgy?

Crystal structure is crucial as it influences material properties and behavior under stress.

What type of crystal structure does the letter 'P' represent?

'P' represents a Triclinic structure in crystal systems.

What are crystallographic defects?

Crystallographic defects are imperfections in the crystal structure that can affect material properties.

What is the role of deformation in crystal structures?

Deformation occurs on specific crystalline planes and directions, influencing how materials respond to stress.

What does the term 'unit cells' refer to in crystallography?

Unit cells are the smallest repeating units in a crystal lattice that define the crystal structure.

What are the (four) 0D, or “point,” defects?

• vacancy

• impurity

• Frenkel Defect

• Schottky defect

What are the (three) 1D, or “Line,” defects?

• dislocation

• Disclination

• Dispiration

What are the (five) 2D, or “Surface / Interface,” defects?

• Surface

• Interphase boundary

• Grain Boundary

• Twin Boundary

• Stacking faults

What are the (five) 3D, or “Volume,” Defects?

• Twins

• Precipitate

• Faulted region

• Voids / Cracks

• Thermal Vibration