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A tensorial representation of the dissolution slowness: Application to etched singly rotated quartz plates

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Abstract

A tensorial method is used to determine the equation of the representative surface of the dissolution slowness vector from a vectorial analysis of the dissolution which in three dimensions is described in terms of an orientation dependent dissolution slowness vector. Calculations are derived for the trigonal class 32 and applied to singly rotated quartz crystals for which coefficients are evaluated up to the 16th order. The polar diagram of the dissolution slowness is presented for orientations,θ, in the range [−60°, 60°]. A numerical simulation of the dissolution based on the vectorial analysis is used to undertake a systematic comparison of the shape of the theoretical dissolution profiles with the experimentalZ′ traces of differently oriented singly rotated quartz plates. For BT-cut plates an excellent agreement is found between theoretical and experimental results. For the AT-cut plates withθ < 29° the agreement is not so good. However, since these AT plates are cut in various quartz crystals the deviation may be attributed to dispersion in the measurement of the etch rate. Thus combining the vectorial analysis of the dissolution with a tensorial representation of the slowness surface provides a useful method for accurately determining the shape of the dissolution profiles of quartz crystals.

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Tellier, C.R., Vaterkowski, J.L. A tensorial representation of the dissolution slowness: Application to etched singly rotated quartz plates. J Mater Sci 24, 1077–1088 (1989). https://doi.org/10.1007/BF01148802

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Keywords

  • Polymer
  • Quartz
  • Excellent Agreement
  • Quartz Crystal
  • Etch Rate