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Anisotropy of thermal expansion is a result of the anisotropy of the intermolecular forces, and has its origin in the distribution of the particular type/types of bonds within the given crystal. 1. LATTICE CONTRIBUTION TO THERMAL EXPANSION The normal modes of vibration of a crystal lattice are plane waves in the harmonic approximation. Each wave is characterised by a wave vector q and a frequency co^q). If there are p atoms in the unit cell of the crystal, there are 3p different normal modes denoted by the index; running from 1 to 3p.

Optical Interferometric Techniques Interferometric methods are most widely used, even today, for the measurement of a of several materials in various laboratories. This method is based on the principle of converting the variations of the length of the specimen into variations of the optical path difference between the monochromatic interfering light beams, in such a way as to produce a shift in interference fringes with respect to a reference mark in the field of view. There are a few different methods of interferometry that are in vogue in these dilatometers.

An amplitude modulated UHF oscillator and a signal amplifier constitute an ultrasonic continuous wave spectrometer. The amplitude modulated UHF energy is fed into the transmission line. When this energy is transferred into the resonance probe a transducer converts it into ultrasonic energy. These longitudinal ultrasonic waves are propagated through the specimen, of a single crystal, and cause a flow of heat accompanied by a dissipation of ultrasonic energy. In other words, attenuation of the amplitude of ultrasonic waves takes place in the crystal.

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