Materials Science and Engineering/Doctoral review questions/Crystallography
Tensor 1
editPropagation 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
editSolutions of Small k
editSolutions with positive sign at k = 0
editSolutions with negative sign at k = 0
editAcoustic and optic branch
Solutions with k = kmax
editDisplacements at kmx
editCorrespondence to the Identical-Atom Problem
editThe optical mode is not present in the case with one kind of atom.
Tensor 2
editWave Propagation in a Continuous One-Dimensional Medium
editThe wave velocity is independent of
Wave Motion on a Row of Identical Atoms
editTotal Number of Vibrational Modes that May be Supported by the Crystal
editThe number of vibration modes that can be supported is equal to the number of atoms in the crystal
Tensor 3
editPropagation of Elastic Waves in Crystals
editRelation of stress and strain in a cubic crystal
Tensor 4
editTensor 5
editConventions of Relabeling Stress, Strain, Stiffness, and Compliance in Matrix Notation
editCondensation of Tensor to Matrix Notation
editStrain in Terms of Stress
editStress in Terms of Strain
editTensor 6
editProperty Tensors
editTriclinic
editMonoclinic
editOrthorhombic
editTetragonal
editTetragonal
editCubic
editIsotropic
editCauchy Relation
edit- Central Forces
- Each atom at center of symmetry
- No initial stress