SINGLE-CRYSTAL ELASTICITY OF MINERALS AND RELATED MATERIALS
This web site provides an introduction to the single-crystal second-order elastic moduli of minerals and related materials. The goal is to collect and systematize the large literature of single-crystal elasticity data reported on such materials over the past eight decades or so. A database is currently under development that contains data for more than 400 mineral compositions. In addition to the single-crystal elastic moduli, related quantities computed from the single-crystal elastic moduli (aggregate elastic properties, sound velocities, anisotropy factors, etc.) are compiled. A brief overview of the importance of mineral elasticity, statistics on the distribution of literature measurements, and some examples of overall trends in mineral elasticity are provided below, as well as links for many other resources. A preliminary version of the complete database is available upon request.
Poisson’s ratio in (001) plane of cassiterite
Poisson's ratio in (010) plane of quartz at 500 C
The Single-Crystal Elastic Moduli Are Fundamental Properties Of Minerals
- Stress-stain, compressibility
- Hardness, brittle-ductile behavior, damage, mechanical stability
Elastic wave propagation, anisotropy, interpretation of seismic data
- Equations of state
- Phase stability
- Debye temperature, specific heat, Gruneisen parameter
Interatomic interactions, lattice dynamics, nature of bonding
Single-crystal elastic moduli are a 4th rank tensor with 3-21 independent, non-zero coefficients, depending on the crystal system.
Distribution of Single-Crystal Elasticity Data Among Mineral Groups and Crystal Systems
Bulk Modulus vs Shear Modulus For Minerals
Aggregate bulk modulus vs shear modulus for minerals according to Nickel-Strunz class. Several trends are apparent. K/G typically ~1.5 up to K~200 GPa with K/G tending to decrease for higher values of K. Above K=100 GPa, oxides and silicates are dominant with other mineral classes generally have K<100 GPa. Oxides generally exhibit a higher K/G than silicates, reflecting a higher degree of ionic bonding. Selected minerals are labeled.
Poisson’s Ratio vs Shear Modulus
Aggregate Poison’s ratio vs shear modulus, G, for the dataset. K/G values representative of different bonding types are shown. Maximum values of Poisson’s ratio for a given value of the shear modulus decreases with increasing G as shown by the solid red line.
Elastic Anisotropy of Crust and Mantle Minerals
Elastic anisotropy of selected crust and mantle minerals at ambient conditions based on the universal anisotropy index, AU, which is determined from the Voigt and Reuss bounds of the bulk and shear moduli. The large difference in anisotropy between crustal and subduction zone minerals and those expected in the Earth’s mantle is clearly evident.
Elasticity of SiO2 Polymorphs: Poisson’s Ratio
The aggregate Poisson’s ratio of SiO2 polymorphs is plotted as a function of density. Poisson’s ratio for SiO2 shows extreme variations as a function of pressure and temperature especially in the vicinity of martensitic phase transitions(a-b quartz, stishovite-CaCl2-type). Filled symbols are experimental data while solid lines with pluses show theoretical calculations. Both high pressure/ambient temperature and ambient pressure/high temperature data are shown. Below the horizontal dashed line at n=0 is the region of bulk auxetic behavior (negative Poisson’s ratio). The horizontal dashed line at 0.5 corresponds to the maximum Poisson’s ratio for a solid aggregate. The open circles in light grey show values of Poisson ratio values for other silicates at ambient conditions.
This project is supported by COMPRES, the Consortium for Materials Properties Research in Earth Sciences under NSF Cooperative Agreement EAR 1606856.