Elasticity and Anisotropy of Common Crustal MineralsAlex Teel; Earth and Space Sciences, Physics Mentor: J. Michael Brown; Earth and Space Sciences

What is Elasticity? What is Anisotropy? What are Common Crustal Minerals?

Experiment

Plagioclase Results Amphibole Results

Conclusions

•A pulsed laser creates surface waves on polished surfaced of oriented single crystals.  •The acoustic wave velocities are measured as a function of direction.•These velocities are inverted to determine the elastic constants.

For materials which return to their original shape after deformation, elasticity is a measure of how much the material will deform given an applied stress. Examples of elastic behavior are diving boards, springs and tennis balls. Elasticity can be quantified with a linear relationship between deformation (strain) and stress. These linear constants can be put into a matrix called the elastic constants tensor.

I experimented on plagioclase feldspars and amphiboles. The table above lists common literature values for the volumetric percentage of the crust by mineral group. Plagioclase feldspars range from the Sodium rich end-member albite to the Calcium rich end-member anorthite. Amphiboles come in many different compositions featuring a wide range of elemental variation.

Mineral % VolumePlagioclase ~40%K-Feldspar 15-20%

Quartz ~20%Amphibole 10-20%

Biotite 5-10%Chlorite 0-5%Other 0-5%

These figures plot maximum and minimum observed velocity for the three amphibole compositions studied. The purple lines represent the prior isotropic average velocities. The most remarkable feature of the amphiboles is their anisotropy. For example the sodic-calcic amphibole’s compressional velocities range from about 6.25 km/s to 9 km/s. This is a range characteristic of upper crust to mantle transition zone velocities.

Shown above are composition ranging from albite to anorthite on the x-axis and velocity in km/s on the y-axis. Plotted are velocities from previous elasticity data and from my data. The vertical lines are not error bars – they are the maximum and minimum velocity values observed at each respective composition studied. In the case of plaioclases, shear wave velocities differ by about 15% and compressional waves differ by about 7%. In both cases my new data is higher than the old data. Important to notice is the velocity anisotropy. Velocity variations due to anisotropy dwarf velocity variations due to composition in plagioclase feldspars.

Anisotropy is directional dependence. The opposite is isotropy which is the same in every direction. Water is isotropic because it is the same no matter how you look at it. Most Earth materials are anisotropic to some degree and in the case of plagioclase feldspars and amphiboles the anisotropy is very large.

This plot shows acoustic wave speed with changing angle for a simulated rock made entirely of Sodium rich plagioclase. If this rock was isotropic the lines would all be flat because they would not change with direction.

PremiseSeismology is the best tool for probing Earth’s interior. Using a technique called seismic tomography, velocity profiles of Earth’s interior can be created. Velocity profiles provide valuable information regarding the structure, mechanical behavior and composition of Earth. A current issue is the link between seismic velocity and composition is poorly determined. The mineral elasticity data is necessary to determine composition from velocity however the elasticity of many minerals has never been calibrated and in some cases these calibrations are biased. I performed these calibrations on several common mineral compositions in Earth’s crust.

This is a velocity profile below Seattle from Preston et al. 2004. Some structural and compositional features are marked.

•New plagioclase feldspar and amphibole elasticity data

•Higher seismic velocities

•These minerals are highly anisotropic

•Anisotropy is a large effect and will need to be calculated into the next generation of seismic models