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
- Central Forces
- Each atom at center of symmetry
- No initial stress