International
Tables for
Crystallography
Volume D
Physical properties of crystals
Edited by A. Authier

International Tables for Crystallography (2006). Vol. D, ch. 1.4, p. 103

Section 1.4.3.4. Electrical methods

H. Küppersa*

aInstitut für Geowissenshaften, Universität Kiel, Olshausenstrasse 40, D-24098 Kiel, Germany
Correspondence e-mail: kueppers@min.uni-kiel.de

1.4.3.4. Electrical methods

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1.4.3.4.1. Inductance changes (pushrod dilatometry)

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With this method, the expansion of the crystal is transmitted out of the cooled or heated region to an external measuring device by a rod made of a reference material whose thermal expansion is low and well known (usually silica glass) (cf. Gaal, 1998[link]). If this rod is inside a tube of the same material (silica glass), and the specimen is inside as well, then the difference in expansion between the crystal and an equal length of the reference material is measured. Above 1100 K, instead of silica glass, high-purity alumina or single-crystal sapphire or tungsten rods are used.

To measure the displacement of the rods, several techniques are used. The most important are:

  • (1) a ferrite core is moved in a coil to change the inductivity of the coil, which is detected by the change of resonance frequency of an electrical circuit having a fixed capacitance;

  • (2) linear-variable-differential transformers.

Temperature gradients in the rod and the tube can lead to severe complications. For every determination, the system should be calibrated by certified materials (White, 1998[link]), such as α-Al2O3, Cu, Pt, fused silica, Si, W, Mg or Mo.

1.4.3.4.2. Capacitance methods

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In a way similar to the interferometric methods, the change of the gap between the lower surface of P1 and the upper surface of P2 (Fig. 1.4.3.1[link]) is used to determine the thermal expansion of the sample. This gap – with electrically conducting surfaces – is used as the capacitance in an electric circuit with a fixed inductance. The change of capacitance leads to a change of resonance frequency, which is measured.

References

Gaal, P. S. (1998). Pushrod dilatometers. In Thermal expansion of solids, edited by C. Y. Ho, ch. 5. Materials Park, Ohio: ASM International.Google Scholar
White, G. K. (1998). Thermal expansion reference materials. In Thermal expansion of solids, edited by C. Y. Ho, ch. 11. Materials Park, Ohio: ASM International.Google Scholar








































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