We used the Rayleigh-Ritz method 14 , 15 , 16 , 17 , 18 , 19 and the basis functions used in the algorithm 20 are expressed in powers of Cartesian coordinates 20 , We collected the MRS spectra between 0. In our non-linear least square fits, we varied the number of resonance modes from 20 to We noticed that the components of the full elastic constant tensors vary significantly if the number of resonance modes considered is less than When more than 35 resonance modes are considered in the determination of the elastic constants, the components of the full elastic constant tensor converge and remain unaffected when additional resonance modes are considered in the non-linear fit.
Concomitant with the convergence of the elastic constant, the error associated with the full elastic constant tensor also reduces significantly when more than 35 resonance modes are considered in the non-linear least square fit. Hence in our study across the temperature range we have included 55 resonance modes to determine the elastic constants. Convergence test and Error analysis. All these elastic constants are for room temperatures i.
Grey shaded area indicates the least number of modes required to have converged elastic constants and errors. This is likely related to a difference in the temperature, i. Temperature dependence of full elastic constant tensor. Shear waves propagating in the crystal are affected by the propagation direction as well as the direction of particle displacement polarization. The elasticity and the elastic anisotropy of topaz can be understood in terms of the crystal structure. We observed a significantly high stiffness along b -axis, i. This could be due to several factors including the difference in the OH-F content, approximations made in the first principles simulation and difference in the room temperature experiments and static conditions for the simulation.
The temperature derivative i.
Hence, the temperature derivatives of sound wave velocity for topaz lies somewhat in-between the various aluminosilicates and mantle phases. Open symbols represent first principles simulations with varying OH and F content The sound wave velocity is also sensitive to the chemistry of topaz. In particular, the F and OH content of topaz is known to affect elasticity However, the effect is very nonlinear, the first principles simulations across the F and OH end member of topaz indicate that the sound velocity gradually decreases up to the composition.
In contrast to the recent first principles simulations 12 , the sound velocity fluorine end member topaz determined by plate-resonance technique is significantly softer The sound velocity of fluorine and OH bearing topaz from the present study also deviates from the first principles simulations 11 , 12 Fig. To our knowledge, there are no experimental results on the sound velocity for the OH end member of topaz. The sound velocities for the OH end member from two different first principles simulation exhibit good agreement 11 , However, these simulations are at static conditions i.
We compared thermally corrected first principles sound velocity results with experimentally determined sound velocity from previous 10 , 13 and present studies Fig.
This is likely to have implications for high pressures where topaz tends to incorporate OH component as observed in ultra high pressure metamorphic rocks 2 , 5. The estimate for the compositional derivative of the velocity could be significantly improved by having more results across the F and OH end members. So care must be taken when interpreting the effect of composition on the sound velocity. We examined the effect of resonance mode on the elasticity and sound velocity Fig. Based on the effect of temperature, pressure, and chemistry, we note that, 0.
In order to understand how the physical properties such as sound velocity vary across the mineral phases in hydrated subducting sediments, we examined sound velocity and anisotropy of mineral phases in the Al 2 O 3 -SiO 2 -H 2 O ternary system, which includes andalusite, diaspore, kaolinite, quartz, phase-pi, pyrophyllite, and topaz.
This is consistent with the observations in major mantle mineral phases We investigated the elasticity of natural single crystal topaz with a stoichiometry of Al 2 SiO 4 F 1. In topaz, the sound velocity varies as a function temperature and composition i. We note that topaz has one of the lowest temperature derivatives among aluminosilicates and other major mantle phases.
Elasticity results indicate that topaz is quite anisotropic and comparable with other mantle phases and aluminosilicate minerals. We also note that the sound velocity, Debye temperature of mineral phases vary as a function of density in the hydrous aluminosilicates phases belonging to the Al 2 O 3 -SiO 2 -H 2 O ternary system that are relevant for the hydrated subducted sediments.
All data generated or analyzed during this study are included in this published article and its Supplementary Information files. Barton, M. The thermodynamic properties of fluor-topaz. Alberico, A. X-ray single-crystal structure refinement of an OH-rich topaz from Sulu UHP terrane Eastern China -Structural foundation of the correlation between cell parameters and fluorine content. Barkley, M. The effects of F-OH-Substitution on the crystal structure of pegmatitic topaz. Zhang, R. Hydroxyl-rich topaz in high-pressure and ultrahigh-pressure kyanites quartzites, with retrograde woodhouseite, from the Sulu terrane, eastern China.
Wunder, B. High-pressure synthesis and properties of OH-rich topaz. Schreyer, W.
- Keith Richards: The Biography.
- Diffusion-Controlled Solid State Reactions, in Alloys, Thin-Films, and Nano Systems.
- Encyclopedic Dictionary of Archaeology.
- Verb Clusters: A Study of Hungarian, German and Dutch (Linguistik Aktuell Linguistics Today).
- Crow Mountain!
Ultradeep metamorphic rocks: the retrospective viewpoint. Ono, S. Stability limits of hydrous minerals in sediment and mid-ocean ridge basalt compositions: Implications for water transport in subduction zones. Thermoelastic properties of beryl, topaz, diaspore, sanidine and periclase. Mookherjee, M.www.hiphopenation.com/mu-plugins/usa/free-dating-sites-in-2.php
New insight into crystal chemistry of topaz: A multi-methodological study
Earth Planet. Ulian, G. Sema, F. Determination of elastic constants of a single-crystal topaz and their temperature dependence via sphere resonance method. Anderson, O.
Composition of Topaz
Rectangular parallelepiped resonance-A technique of resonance ultrasound and its applications to the determination of elasticity at high temperatures. Leisure, R. Resonant ultrasound spectroscopy. Li, G. High Temperature Resonant Ultrasound. Spectroscopy: A Review. Migliori, A. Implementation of a modern resonant ultrasound spectroscopy system for the measurement of the elastic moduli of small solid specimens.
Ohno, I. Free vibration of a rectangular parallelepiped crystal and its application to determination of elastic constants of orthorhombic crystals. Visscher, W. On the normal modes of free vibration of inhomogeneous and anisotropic elastic objects. Resonant ultrasound spectroscopy: applications to physics, materials measurements, and nondestructive evaluation. Experimental Methods in the Physical Sciences 39 , — Komatsu, K. Hearmon, R. The elastic constants of anisotropic materials.
Topaz: Properties, colour and information
Press, Cambridge, Massachusetts, and London, Englend Chung, D. Some elastic constant data on minerals relevant to geophysics. A simplified method for calculating the debye temperature from elastic constants. Suzuki, Y. The thermodynamic properties of topaz solid solutions and some petrologic applications. Hemingway, B. Revised heat capacity values for topaz and stauroliti based upon a better analysis of the water content of the samples. Jaeken, J. Solving the Christoffel equation: Phase and group velocities.
Gatta, G. Elastic behaviour and structural evolution of topaz at high pressure. Elastic behavior and pressure-induced structure evolution of topaz up to 45 GPa. Ribbe, P. The crystal structure of topaz and its relation to physical properties.
The crystal structure of topaz - CaltechAUTHORS
Stixrude, L. Thermodynamics of mantle minerals- II. The blue topaz that is often confused with aquamarine is rarely natural and is produced by irradiating and then heating clear crystals. Golden Topaz is the November Birthstone , and Blue Topaz is an acceptable and popular alternate birthstone for December. The structure of Topaz is controlled by a chain like structure of connected irregular octahedrons. These octahedrons have an aluminum in the middle surrounded by four oxygens.
Above and below the aluminum are the hydroxide or fluoride ions. The chains of octahedrons are held together by individual silicate tetrahedrons but it is the octahedron chains that give topaz its crystalline shape.
Topaz is the hardest silicate mineral and one of the hardest minerals in nature. However it has a perfect cleavage which is perpendicular to the chains and is caused by planes that break the weaker Al-O, Al-OH and Al-F bonds. None of the stronger Si-O bonds cross these planes.
Topaz crystals can reach the incredible size of several hundred pounds. Topaz can make very attractive mineral specimens due to their high luster, nice colors and well formed and multifaceted crystals. Luster is adamantine to vitreous. Transparency crystals are transparent to translucent. The termination is typically capped by a dome forming a roof like top. Another dome can modify the termination producing a point at the juncture of the two domes. A basal pinacoid can flatten the prisms termination or truncate the top of the domes.