Temperature variation of elastic constants of quartz across the α - β transition |
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| Authors: | Ichiro Ohno Kazumi Harada Chihiro Yoshitomi |
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| Institution: | (1) Department of Earth Sciences, Ehime University, 2-5 Bunkyou-cho, Matsuyama 790-8577, Japan |
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| Abstract: | The α − β transition of quartz was successfully observed with using a single sample by means of the rectangular parallelepiped
resonance (RPR) method. An oriented rectangular parallelepiped of α-quartz single crystal was prepared and the resonant frequencies
of 30–11 vibrational modes were measured from room temperature to 700°C. The softening of quartz crystal was observed as the
significant reduction of resonant frequencies near the α–β transition. The present study is the first application of the RPR
method to the study of phase transition. The complete set of elastic constants of α- and β-quartz were determined as a function
of temperature by the least-squares inversion of the measured frequency data obtained by a single run. This is a merit yielded
by the RPR method. It is shown near the α − β transition in both α- and β-quartz that the elastic parameters decrease proportionally
to |T−T
0|−n
, where T is temperature and T
0 is the transition temperature, 573.0°C for α-quartz and 574.3°C for β-quartz. It was also seen that linear incompressibilities
K
1 = (C
11
+C
12
+C
13)/3 and K
3 = (C
33
+2C
13)/3 decrease rapidly toward the transition, whereas, shear moduli C
44, C
S1 = (C
11
+C
33
-2C
13)/4 and C
S3 = (C
11
-C
12)/2 = C
66 decrease only slightly. The shear modulus C
S3 = C
66 increased slightly in α-quartz. The elastic properties of isotropic aggregate of quartz were calculated, and it is shown
that the longitudinal wave velocity significantly decreases at the α − β transition, whereas, the shear wave velocity decreases
only slightly. |
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| Keywords: | |
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