Garnet structural simulation

Table 5.20 Equations for structural simulation of garnet (Basso, 1985).

Static simulations of perfect lattices give the lattice energy and crystal structure of the garnets at 0 K. In the static limit, the lattice stmcture is determined by the condition 9 //9A = 0, where U is the internal energy, and the variables A define the structure (i.e., the lattice vectors, the atomic positions in the garnet unit cell, and the oxygen shell displacements). 

Simulated structures for pyrope, ahnandine, spessartme, and grossular were used as the basis for calculations of the energies required to introduce various trace-element defects. In every computational run, one or more defects are introduced into the crystaL e.g., for homo-valent (same-charge) substitution, one divalent cation at the X-site of a perfect garnet lattice is replaced by one trace-element divalent cation. Initial, unrelaxed defect energies were... 

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