Integrated intensities of Bragg reflections from a clear natural quartz (SiOz) were measured at five temperatures below and above the a-S transition (Tc* ), using Mo Ka radiation. All symmetrically independent reflections up to 25 =so' were used in least-squares refinements, which were based on the Gram-Charlier expansion.The atomic. positions for 3 quartz were constrained on the sites with symmetry 222 for Si and with 2 for 0. The Rw values in the refinements of the model including terms· up to the fourth-order were imoroved as shown below with those of the second-order refi~ements in oarentheses : 0.0377 (0.0520) at Tc+l4 K, 0.0366 (0.053i! at Tc+4 K, 0.0413 (0.0528) at Tc-10 K, 0.0374 (0.0478) at Tc-60 K and 0.0302 (0.0356) at room temperature.Of the 38 thirdand fourth-order coefficients, 13 were nearly zero for the room temperature data, while only a few were zero for the high temperature data. Atomic probability density functions (pdf) obtained from the high-order calculations were all unimodal at the five temperatures.A split-atom model for B quartz, where 0 and Si respectively split into two sets of positions corresponding to a quartz, related each other by the Dauphine twin law, was also fitted to the (Tc+4 K) data. This calculation converged at Rw=U.0439 for the positional parameters in good agreement with those obtained by neutron diffraction data at Tc+60 K (Wright & Lehmann, 1981, J. Solid State Chem., 36, 371). The pdf's obtained from the highorder refinements and the split-atom refinement will be discussed. ~Although Gouhara et al. (1983) (J. Phys. Soc. Japan, 52, 3697) have found an incommensurate phase in the range of 1.8 K between a and B we will continue our discussion, for the present, on the basis of the transition scheme traditionally adopted.The three high-pressure phases of MgSiO,, garnet ( maj ori te) , ilmenite and perovski te, are considered to be the major constituents of the deep mantle.The purpose of this investigation is to develop a realistic potential energy model, which is applicable to characterizing and predicting the structural and elastic properties of these three highpressure phases, as a function of pressure.The computational techniques are based on energy minimization with respect to the structural variables. The potential energy of the crystal is aooroxlmat:ed to be the sum of Coulomb interaction, van der Waals attraction and short-range repulsive interaction between atoms.The energy parameters required to model the three phases are determined from a best fitting of the parameters to the observed zero-pressure structures of the ilmenite and perovskite phases as well as to the measured single-crystal elastic constants of the ilmenite phase.The resulting potential model is applied to simulating (1) the zero-pressure structure and elasticity of the garnet phase,( 2) the zero-pressure elasticity of the perovski te phase, and ( 3) the high-pressure behaviors of the structures and elastic constants of the three phases.
