Materials Science and Engineering/Doctoral review questions/Crystallography
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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]
- Central Forces
- Each atom at center of symmetry
- No initial stress
