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Monocrystalline silicon, more often called single-crystal silicon, in short mono c-Si or mono-Si, is the base material for silicon-based discrete components and integrated circuits used in virtually all modern electronic equipment. Mono-Si also serves as a photovoltaic, light-absorbing material in the manufacture of solar cells. It consists of silicon in which the crystal lattice of the. SingleCrystal provides real-time, interactive simulation of key single-crystal diffraction techniques in gorgeous high-DPI graphics. Diffraction geometries include Transmission Electron Microscope (TEM) - with optional Kikuchi Lines - plus Precession, Laue (Front-Plate, Rear-Plate or Cylindrical geometries), in addition to standard or weighted Reciprocal Lattice Sections (at user-specified heights). Various single crystals, such as semiconductor single crystals (e.g., Si, GaAs, InP) and oxide single crystals (e.g., LiNbO3, LiTaO 3, Al 2 O 3) are used as materials for electronic/optical devices.

Single-Crystal Elasticity Links

• COMPRES
  

Introduction

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.

Thomas Duffy, duffy@princeton.edu
Renee Delamater-Droungas, reneed@princeton.edu
Department of Geosciences Princeton University

The Single-Crystal Elastic Moduli Are Fundamental Properties Of Minerals

• Mechanical properties

  • Stress-stain, compressibility
  • Hardness, brittle-ductile behavior, damage, mechanical stability
    

• Elastic wave propagation, anisotropy, interpretation of seismic data

• Thermodynamic properties

  • Equations of state
  • Phase stability
  • Debye temperature, specific heat, Gruneisen parameter

• Interatomic interactions, lattice dynamics, nature of bonding

Anisotropic Elasticity

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

Oxides includes hydroxides; Carbonates includes nitrates, Sulfates includes molybdates and tungstates; carbides includes carbon, nitrides, phosphides.

Single Crystal X-ray Diffraction

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.
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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.
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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.
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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.

Acknowledgements:

Single Crystal X-ray Diffraction

This project is supported by COMPRES, the Consortium for Materials Properties Research in Earth Sciences under NSF Cooperative Agreement EAR 1606856.