The mineral has tetragonal crystal symmetry and the same structure as scheelite ( calcium tungstate, CaWO 4 ), but can be metamict ( amorphous ) due to radiation damage from its small content of thorium.
32.
A similar variation was observed for the M 2 PaF 7 fluorides, namely the crystal symmetry was dependent on the cation and differed for Cs 2 PaF 7 and M 2 PaF 7 ( M = K, Rb or NH 4 ).
33.
However, introducing any defect ( even " very symmetrical ", such as N-N substitutional pair ) breaks the crystal symmetry resulting in defect-induced infrared absorption, which is the most common tool to measure the defect concentrations in diamond.
34.
Moreover, crystal symmetry leads to valley dependent optical selection rules : a right circular polarized photon ( ? + ) initialize a carrier in the K + valley and a left circular polarized photon ( ?-) initialize a carrier in the K-valley.
35.
Piezoelectricity may then manifest in a variation of the polarization strength, its direction or both, with the details depending on : 1 . the orientation of " "'P " "'within the crystal; 2 . crystal symmetry; and 3 . the applied mechanical stress.
36.
C12A7 has a cubic crystal symmetry; Ca 12 Al 14 O 33 has a lattice constant of 1.1989 nm and a density of 2.680 g�cm " 3 while Ca 6 Al 7 O 16 ( OH ) has 1.1976 nm and 2.716 g�cm " 3.
37.
Interestingly, all three derivations ( Hessel's, Bravais', and Gadolin's ), which established a small finite number of possible crystal symmetries from first principles, were based on external crystal morphology rather than a crystal's internal structural arrangement ( i . e . lattice symmetry ).
38.
Where P x, P y, and P z are the components of the polarization vector in the x, y, and z directions respectively, and the coefficients, \ alpha _ i, \ alpha _ { ij }, \ alpha _ { ijk } must be consistent with the crystal symmetry.
39.
These crystals have the necessary properties of being strongly birefringent ( necessary to obtain phase matching, see below ), having a specific crystal symmetry, being transparent for both the impinging laser light and the frequency-doubled wavelength, and having high damage thresholds, which makes them resistant against the high-intensity laser light.
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