Pseudopotentials pressure

Figure Al.3.23. Phase diagram of silicon in various polymorphs from an ab initio pseudopotential calculation [34], The volume is nonnalized to the experimental volume. The binding energy is the total electronic energy of the valence electrons. The slope of the dashed curve gives the pressure to transfomi silicon in the diamond structure to the p-Sn structure. Otlier polymorphs listed include face-centred cubic (fee), body-centred cubic (bee), simple hexagonal (sh), simple cubic (sc) and hexagonal close-packed (licp) structures.

The main problem related to the use of pseudopotentials in studies of solids under pressure is to make sure that the overlap of ionic cores does not increase significantly when interatomic distances decrease. The present study is certainly not affected by this potential pitfall since Ti-O distances typically change by no more than 0.1 A over the pressure range investigated. However, theoretical studies of fluorite and related phases at pressures of around 100 GPa should be performed with added caution. 

For ice X and the (fee) antifluorite structure the quantification of various aspects of their structural and chemical character and their dependence with pressure was found using AIM in a novel approach. Metallic character was found to be present in the antifluorite structure, but did not persist with increased pressure since the BCPs then fell within the pseudopotential core radii. In future studies on the antifluorite structure it will be necessary to replace the core with the true all electron distribution. In addition we present a hypothesis for the physical meaning of the O—O bonding interactions, namely that they indicate the onset of, soft phonon modes that are known to accompany structural changes. The fact that there are no O—O interactions in the antifluorite structure is consistent with this hypothesis, since to date there aren t any higher pressure phases of ice than antifluorite ice and so no pressure induced phase change can occur in this structure. Thus our hypothesis would explain why there are no O—O interactions in the antifluorite structure. 

Zakharov and Cohen predicted a pressure of about 550 GPa for the )8-Po to hcc transition on the basis of pseudopotential ab-initio calculations [190]. In addition, a critical temperature of 15 K for the superconducting transition in the vicinity of the ji-Bo to bcc transition was estimated. This relatively high value was attributed to an enhancement of the electron-phonon coupling near the structural transition. Although the lattice parameters of bco and )8-Po sulfur have fairly been reproduced by the calculations, the model failed in reproducing the experimentally observed bco to 8-Po transition. At 145 GPa, the calculated total energy of the bco structure was found higher than that of the 8-Po structure. 

Van Camp et al [13] also calculated the first and second pressure derivatives by the ab-initio norm-conserving non-local pseudopotential method of the energy differences between the T X-, and L-states of the valence and lowest conduction band and the top of the valence band in ri5 for 3C-SiC. The first-order pressure coefficients for the direct (ri5v-ric) and indirect (T15v - Xu) bandgaps are 61.7 meV GPa 1 and -1.1 meV GPa 1, respectively. The signs of these values are the same for all semiconductors by Paul s rule. However, the magnitudes are quite different from those of other semiconductors. 

Fig. 3 23. (a) Grofh of energy vs volume (scale normalised to the diamond structure) for eleven phases of silicon (b) Enthalpy-pressure plot for the same eleven phases relative to the body-centred cubic phase (Figures redrawn from Needs R f and A Mujica 1995. First-principles pseudopotential study of die structural phases of silicon. Physical Review B51-9652-9660.)... 

The effect of s—d hybridization on the relative stability of the structures of metallic Ca and Sr has been studied as a function of temperature and pressure within the context of the pseudopotential theory for metals. The inclusion of hybridization is found to favour the f.c.c. structure at all pressures and, in particular, is necessary to explain the observed f.c.c. structure in these metals at zero temperature and pressure. Phase boundaries are calculated by equating the free energy of the f.c.c. structure to that of the b.c.c. structure. Temperature-induced phase transitions are predicted to occur at 555 K in Ca and 625 K in Sr as compared with the actual temperatures of 721 and 830 K. From the changes in free energy of the reactions of the alkaline-earth metals with gases as a function of temperature, it is confirmed that at 298— 1400 K almost all of the residual gases in electrovacuum devices combine with the metals to form stable compounds. The dehydration of calcium... 

Fig. 3.53 Theoretical energy-volume (a) and enthalpy-pressure (b) diagrams for various structures of TaON on the basis of pseudopotential GGA calculations.

Summarizing, the pseudopotential GGA calculations allow the prediction of unknown phases for the oxynitrides of V, Nb, and Ta, and they also allow the provision of quantitative data for the required synthetic conditions in terms of pressure. Similar predictions would have been impossible to make using purely traditional approaches. 

Several theoretical and experimental studies assess the vibrational properties of the high-pressure phases of silicon. A group-theoretical analysis of lattice vibrations in the -tin structure has been made by Chen [98]. In the vicinity of the F point, the optical modes consist of one longitudinal optical (LO) branch and at higher frequencies of a doubly degenerate transverse optical (TO) branch, both of which are Raman active. Zone-center phonon frequencies of Si-11 have been calculated as a function of pressure using the ab initio pseudopotential method... 

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