Advances in the accuracy and efficiency of first-principles electronic structure calculations have allowed detailed studies of the energetics of materials under high pressures. At the same time, improvements in the resolution of powder x-ray diffraction experiments and more sophisticated methods of data analysis have revealed the existence of many new and unexpected high-pressure phases. The most complete set of theoretical and experimental data obtained to date is for the group-IVA elements and the group-IIIA--VA and IIB--VIA compounds. Here the authors review the currently known structures and high-pressure behavior of these materials and the theoretical work that has been done on them. The capabilities of modern first-principles methods are illustrated by a full comparison with the experimental data.

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High-pressure phases of group-IV, III–V, and II–VI compounds

Predictions of observable properties by density-functional theory calculations (DFT) are used increasingly often by experimental condensed-matter physicists and materials engineers as data. These predictions are used to analyze recent measurements, or to plan future experiments in a rational way. Increasingly more experimental scientists in these fields therefore face the natural question: what is the expected error for such a first-principles prediction? Information and experience about this question is implicitly available in the computational community, scattered over two decades of literature. The present review aims to summarize and quantify this implicit knowledge. This eventually leads to a practical protocol that allows any scientist—experimental or theoretical—to determine justifiable error estimates for many basic property predictions, without having to perform additional DFT calculations. A central role is played by a large and diverse test set of crystalline solids, containing all ground-state...

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Error Estimates for Solid-State Density-Functional Theory Predictions: An Overview by Means of the Ground-State Elemental Crystals

Silicon wafers subject to depth-sensing indentation tests have been studied using Raman microspectroscopy. We report a strong correlation between the shape of the load-displacement curve and the phase transformations occurring within a nanoindentation. The results of Raman microanalysis of nanoindentations in silicon suggest that sudden volume change in the unloading part of the load-displacement curve (“pop-out” or “kink-back” effect) corresponds to the formation of Si–XII and Si–III phases, whereas the gradual slope change of the unloading curve (“elbow”) is due to the amorphization of silicon on pressure release. The transformation pressures obtained in nanoindentation tests are in agreement with the results of high pressure cell experiments.

Effect of phase transformations on the shape of the unloading curve in the nanoindentation of silicon

mentally. In this report, we present in situ TEM observation of the elastic-plastic-fracture processes of a single Si NW recorded at atomic resolution. The study directly shows the strain-induced structural evolution process of Si NWs and its largestrain plasticity (LSP). Our results indicate that the LSP of Si NWs via a brittle-ductile transition originates from a dislocation-initiated amorphization. This behavior is in contrast to the mechanical behavior of bulk Si. Our observation reveals a phenomenon and mechanism of the Si NW mechanics and is fundamentally important for Si-NW-based nanotechnology. The in situ Si NW elastic, elastic-plastic, and plastic deformation investigations were carried out by ultrahigh-resolution TEM (UHRTEM) by axially extending the Si NWs by means of a mechanical force created by a TEM specimen-supporting grid under electron beam irradiation, as reported in detail elsewhere [17,18] (also see the Experimental section and Sup

http://www.nanoscience.gatech.edu/zlwang/paper/2007/07_AM_7.pdf

Low-Temperature In Situ Large-Strain Plasticity of Silicon Nanowires

This paper discusses the phase transformation of diamond cubic silicon under nano-indentation with the aid of molecular dynamics analysis using the Tersoff potential. By monitoring the positions of atoms within the model, the microstructural changes as silicon transforms from its diamond cubic structure to other phases were identified. The simulation showed that diamond cubic silicon transforms into a body-centred tetragonal form (β-silicon) upon loading of the indentor. The change of structure is accomplished by the flattening of the tetrahedron structure in diamond cubic silicon. Upon unloading, the body-centred tetragonal form transforms into an amorphous phase accompanied by the loss of long-range order of the silicon atoms. By performing a second indentation on the amorphous zone, it was found that the body-centred-tetragonal-to-amorphous phase transformation could be a reversible process.

http://iopscience.iop.org/article/10.1088/0957-4484/11/3/307/pdf

Molecular dynamics simulation of phase transformations in silicon monocrystals due to nano-indentation

X-ray-diffraction data have been obtained on Si in a diamond anvil cell to pressures of \ensuremath{\sim}50 GPa. Crystallographic data are presented in phase I (cubic, diamond), II (tetragonal, \ensuremath{\beta}-Sn), V (simple hexagonal), VII (hexagonal close-packed), and the metastable phase III [body-centered-cubic (BC8)] and on the coexistence of the phases. Comparison is made between these data and the predictions of ab initio calculations for these structures and their equations of state.

Crystal data for high-pressure phases of silicon

X-ray diffraction experiments have been carried out on germanium in a diamond anvil cell to 26 GPa. The pressure at the transition to the metallic phase (II) has been studied in different pressurizing media, giving 10.6\ifmmode\pm\else\textpm\fi{}0.05 GPa in a quasihydrostatic medium (4:1 methanol:ethanol mixture), 9.8\ifmmode\pm\else\textpm\fi{}0.1 GPa in NaCl, and 8.1\ifmmode\pm\else\textpm\fi{}0.3 GPA when the sample was compressed directly between the anvils. The compression curve for phase II has been fitted to a modified Murnaghan equation. Upon release of pressure the transformation from phase II to III (tetragonal) was found at 7.6\ifmmode\pm\else\textpm\fi{}0.05 GPa. It was found that the details of the transition depended on the stress condition and rate of decompression.

Germanium at high pressures.

GaP at ultrahigh pressure

X-ray diffraction experiments have been carried out on Ge, Si, GaP, InAs at ultrahigh pressure in the diamond anvil high pressure apparatus. Three phases of Si (3-Sn, simple hexagonal, hep) have been found on increase of pressure, with bec phase on release. Only one phase of Ge (g-Sn) has been found to 25 GPa, with tetragonal phase on release. InAs transforms to NaCl phase at high pressure, with some hysteresis in the transformation back to the original zinc-blend phase. Experiments on GaP in a quasi-hydrostatic medium place the transition pressure well above 22 GPa, in agreement with previous work of Pinceaux, Besson, Rimsky, and Weill.

Jing Zhu Hu

Papers

Crystal data for high-pressure phases of silicon

Germanium at high pressures.

GaP at ultrahigh pressure

New phases of semiconductors at ultrahigh pressure