Materials Science and Engineering/Doctoral review questions/Crystallography

Tensor 1

edit

Propagation of Waves Along One-Dimensional Crystal with Two Kinds of Atoms

edit
  • Force-balance equations
  • Trial solution
  • With a given value of k, there are two different waves of angular frequency that may be propagated

Interpretation of the Solutions

edit
Solutions of Small k
edit
Solutions with positive sign at k = 0
edit
Solutions with negative sign at k = 0
edit

Acoustic and optic branch

Solutions with k = kmax
edit
Displacements at kmx
edit

Correspondence to the Identical-Atom Problem

edit

The optical mode is not present in the case with one kind of atom.

Tensor 2

edit

Wave Propagation in a Continuous One-Dimensional Medium

edit

The wave velocity is independent of  

  

Wave Motion on a Row of Identical Atoms

edit

Total Number of Vibrational Modes that May be Supported by the Crystal

edit

The number of vibration modes that can be supported is equal to the number of atoms in the crystal

Tensor 3

edit

Propagation of Elastic Waves in Crystals

edit

Relation of stress and strain in a cubic crystal

Tensor 4

edit

Tensor 5

edit

Conventions of Relabeling Stress, Strain, Stiffness, and Compliance in Matrix Notation

edit

Condensation of Tensor to Matrix Notation

edit

Strain in Terms of Stress

edit

Stress in Terms of Strain

edit

Tensor 6

edit

Property Tensors

edit

Triclinic

edit

Monoclinic

edit

Orthorhombic

edit

Tetragonal

edit

Tetragonal

edit

Cubic

edit

Isotropic

edit

Cauchy Relation

edit
  1. Central Forces
  2. Each atom at center of symmetry
  3. No initial stress

Tensor 7

edit

Some Basic Relations in Electromagnetism

edit