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We outline recent developments of theoretical methodology for first-principles simulations of alloys at high pressure. Particular attention will be paid to the techniques for a treatment of solution phases. Limitations of the present-stage theory are discussed, and a necessity of having a close collaboration between theory and experiment are emphasized. We show several examples where the collaboration leads to new discoveries important for physical and geophysical communities. [ABSTRACT FROM AUTHOR]

In this lecture we review high-pressure phase transition sequences exhibited by simple elements, looking at the examples of the main group I, II, IV, V, and VI elements. General trends are established by analyzing the changes in coordination number on compression. Experimentally found phase transitions and crystal structures are discussed with a brief description of the present theoretical picture. [ABSTRACT FROM AUTHOR]

We review recent developments in the field of ab initio electronic structure theory and its application for studies of phase stability of alloy systems. Basic ideas behind state-ofthe- art techniques for first-principles theoretical simulations of the phase stabilities and properties of intermetallic compounds and alloys based on the density functional theory are outlined. We concentrate on methods that allow for an efficient treatment of disorder effects, and illustrate their predictive power for the case of Fe-Cr system. We show that in the ferromagnetic alloys there are peculiarities of the mixing enthalpy in the low-Cr region in the bcc phase. Thus the stability of the Cr containing steels stems from the negative mixing enthalpy at low concentrations of chromium. We explain the effect by the strong concentration dependence of the interatomic interactions in Fe-Cr system. [ABSTRACT FROM AUTHOR]