결정화학

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"결정화학"에 대한 내용입니다.

목차

1. Effect of symmetry
2. Thermal expansion measurements
3. Structure-property relations
4. Temperature dependence

본문내용

11.1 Effect of symmetry

Thermal expansion relates a second rank tensor (strain) to a scalar (temper- ature change).
It is a symmetric second rank tensor because the strain tensor symmetric.(Fig. 11.1)

Therefore thermal expansion and the dielectric constant are the same of tensor, and the effect of symmetry is the same.
This means that type for the general case (a triclinic crystal), six measurements are required to find the three principal thermal expansion coefficients and the three angles needed to orient the principal axes.
The appropriate matrices for other symmetries are given in Table 9.1. Four measurements are needed for monoclinic crystals, three for orthorhombic, two for trigonal, tetragonal, and hexagonal crystals, and only one for cubic crystals.
When referred to principal axes, the thermal expansion coefficient arbitrary direction is

where 0 and are the spherical coordinate angles.
When all three principal coefficients are positive numbers, the resulting surface is shaped like a peanut.(Fig. 11.2)

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