Thermodynamics of Mineral Phases
Mineral vibrational spectra can be used to obtain vital thermodynamic data of phases relevant to geological processes. If there are no other contributions to the energetics of the material (such as electronic or configurational, which can be accounted for separately), it is assumed all the energy in the material is stored in the bonds. The magnitude of the stored energy is obtained by adding up the energy of the bonds: εi = Σ hνi, where εi represents the energy sum, h Planck's constant and νi the ith vibrational frequency.
The energy is summed using statistical methods by assuming a Boltzmann distribution. To do this summation, one needs to establish a total frequency spectrum. Neither infrared or Raman spectroscopy can provide this because each method selects out only certain vibrations (that follow certain rules which are different for each method). This is not a fatal problem since symmetry rules allow a good accounting of the number of modes and motions related to these modes. Combining results from one or both spectroscopies with the symmetry rules, one can construct a complete frequency spectrum (density of states) for use in the statistical calculations.
Once the energy is summed, the following relationships can be obtained:
Cv = (∂E/∂T)v
CP = Cv (1 + αγT),
where α is the thermal expansion coefficient and γ the
thermal Grüneisen paramater which is γ = αKTV/Cv
Entropy can be obtained from ∫CP/T dT and thermal expansion
from 1/V(∂V/∂T)P = -1/V(∂S/∂P)T
As you can see from the equations, one needs to obtain volume data. A table summarizing the references for much of the available spectroscopic, volumetric, and calorimetric data for certain minerals is found HERE.
Coming soon, computation of thermodynamics of minerals