High pressure elastic properties of minerals from ab initio simulations: the case of pyrope, grossular and andradite silicate garnets

Crucial Role of Ni Point Defects and Sb Doping for Tailoring the Thermoelectric Properties of ZrNiSn Half-Heusler Alloy: An Ab Initio Study

In the wide group of thermoelectric compounds, the half-Heusler ZrNiSn alloy is one of the most promising materials thanks to its thermal stability and narrow band gap, which open it to the possibility of mid-temperature applications. A large variety of defects and doping can be introduced in the ZrNiSn crystalline structure, thus allowing researchers to tune the electronic band structure and enhance the thermoelectric performance. Within this picture, theoretical studies of the electronic properties of perfect and defective ZrNiSn structures can help with the comprehension of the relation between the topology of defects and the thermoelectric features. In this work, a half-Heusler ZrNiSn alloy is studied using different defective models by means of an accurate Density Functional Theory supercell approach. In particular, we decided to model the most common defects related to Ni, which are certainly present in the experimental samples, i.e., interstitial and antisite Ni and a substitutional defect consisting of the replacement of Sn with Sb atoms using concentrations of 3% and 6%. First of all, a comprehensive characterization of the one-electron properties is performed in order to gain deeper insight into the relationship between structural, topological and electronic properties. Then, the effects of the modeled defects on the band structure are analyzed, with particular attention paid to the region between the valence and the conduction bands, where the defective models introduce in-gap states with respect to the perfect ZrNiSn crystal. Finally, the electronic transport properties of perfect and defective structures are computed using semi-classical approximation in the framework of the Boltzmann transport theory as implemented in the Crystal code. The dependence obtained of the Seebeck coefficient and the power factor on the temperature and the carrier concentration shows reasonable agreement with respect to the experimental counterpart, allowing possible rationalization of the effect of the modeled defects on the thermoelectric performance of the synthesized samples. As a general conclusion, defect-free ZrNiSn crystal appears to be the best candidate for thermoelectric applications when compared to interstitial and antisite Ni defective models, and substitutional defects of Sn with Sb atoms (using concentrations of 3% and 6%) do not appreciably improve electronic transport properties.

Efficient calculation of derivatives of integrals in a basis of non-separable Gaussians

A computational procedure is developed for the efficient calculation of derivatives of integrals over non-separable Gaussian-type basis functions, used for the evaluation of gradients of the total energy in quantum-mechanical simulations. The approach, based on symbolic computation with computer algebra systems and automated generation of optimized subroutines, takes full advantage of sparsity and is here applied to first energy derivatives with respect to nuclear displacements and lattice parameters of molecules and materials. The implementation in the Crystal code is presented, and the considerably improved computational efficiency over the previous implementation is illustrated. For this purpose, three different tasks involving the use of analytical forces are considered: (i) geometry optimization; (ii) harmonic frequency calculation; and (iii) elastic tensor calculation. Three test case materials are selected as representatives of different classes: (i) a metallic 2D model of the Cu(111) surface; (ii) a wide-gap semiconductor ZnO crystal, with a wurtzite-type structure; and (iii) a porous metal-organic crystal, namely the ZIF-8 zinc-imidazolate framework. Finally, it is argued that the present symbolic approach is particularly amenable to generalizations, and its potential application to other derivatives is sketched.

Mg3Al2Si3O12 jeffbenite inclusion in super-deep diamonds is thermodynamically stable at very shallow Earth's depths

Jeffbenite (having the same chemical composition of pyrope, ~ Mg₃Al₂Si₃O₁₂, and also known as TAPP phase) is a mineral inclusion only found in diamonds formed between about 300 and 1000 km depth) and is considered a stable phase in the transition zone (410-660 km depth) and/or in the shallowest regions of the lower mantle (around 660-700 km depth). This rare and enigmatic mineral is considered to be a pressure marker for super-deep diamonds and therefore it has a key role in super-deep diamond research. However, the pressure-temperature stability fields for Mg₃Al₂Si₃O₁₂ jeffbenite is unknown and its actual formation conditions remain unexplored. Here we have determined the thermodynamic pressure-temperature stability field for the jeffbenite Mg-end member and surprisingly discovered that it is stable at low pressure-temperature conditions, i.e., 2-4 GPa at 800 and 500 °C. Thus, Mg₃Al₂Si₃O₁₂ jeffbenite is not the high-pressure polymorph of pyrope and is likely a retrogressed phase formed during the late ascent stages of super-deep diamonds to the surface.

Chemical Bonding Effects and Physical Properties of Noncentrosymmetric Hexagonal Fluorocarbonates ABCO3F (A: K, Rb, Cs; B: Mg, Ca, Sr, Zn, Cd)

The present work applied the methods of density functional theory and the van der Waals interaction PBE + D3(BJ) on the basis of localized orbitals of the CRYSTAL17 package. It featured the effect of interactions between structural elements of fluorocarbonates ABCO₃F (A: K, Rb, Cs; B: Mg, Ca, Sr, Zn, Cd) on their elastic and vibrational properties. The hexagonal structures proved to consist of alternating ···B-CO₃··· and ···A-F··· layers in planes ab, interconnected along axis c by infinite chains ···F-B-F···, where cations formed polyhedra AO_nF₃ and BO_mF₂. The calculations included the band energy structure, the total and partial density of electron states, the energy and band widths of the upper ns- and np-states of alkali and alkaline-earth metals, as well as nd-zinc and nd-cadmium. For hydrostatic compression, we calculated the parameters of the Birch–Murnaghan equation of state and the linear compressibility moduli along the crystal axes and bond lines. We also defined the elastic constants of single crystals to obtain the Voigt–Reuss–Hill approximations for the elastic moduli of polycrystalline materials. The study also revealed the relationship between the elastic properties and the nature of the chemical bond. Hybrid functional B3LYP made it possible to calculate the modes of normal long-wavelength oscillations, which provided the spectra of infrared absorption and Raman scattering. Intramolecular modes ν1 and ν4 with one or two maxima were found to be intense, and their relative positions depended on the lengths of nonequivalent C–O bonds.

Maximizing completeness in single-crystal high-pressure diffraction experiments: phase transitions in 2°AP

Sufficiently high completeness of diffraction data is necessary to correctly determine the space group, observe solid-state structural transformations or investigate charge density distribution under pressure. Regrettably, experiments performed at high pressure in a diamond anvil cell (DAC) yield inherently incomplete datasets. The present work systematizes the combined influence of radiation wavelength, DAC opening angle and sample orientation in a DAC on the completeness of diffraction data collected in a single-crystal high-pressure (HP) experiment with the help of dedicated software. In particular, the impact of the sample orientation on the achievable data completeness is quantified and proved to be substantial. Graphical guides for estimating the most beneficial sample orientation depending on the sample Laue class and assuming a few commonly used experimental setups are proposed. The usefulness of these guides has been tested in the case of luminescent 1,3-diacetylpyrene, suspected to undergo transitions from the α phase (Pnma) to the γ phase (Pn21 a) and δ phase (P1121/a) under pressure. Effective sample orientation has ensured over 90% coverage even for the monoclinic system and enabled unrestrained structure refinements and access to complete systematic extinction patterns.

Discovery of new boron-rich chalcogenides: orthorhombic B6X (X=S, Se)

New boron-rich sulfide B₆S and selenide B₆Se have been discovered by combination of high pressure – high temperature synthesis and ab initio evolutionary crystal structure prediction, and studied by synchrotron X-ray diffraction and Raman spectroscopy at ambient conditions. As it follows from Rietveld refinement of powder X-ray diffraction data, both chalcogenides have orthorhombic symmetry and belong to Pmna space group. All experimentally observed Raman bands have been attributed to the theoretically calculated phonon modes, and the mode assignment has been performed. Prediction of mechanical properties (hardness and elastic moduli) of new boron-rich chalcogenides has been made using ab initio calculations, and both compounds were found to be members of a family of hard phases.

Experimental charge density of grossular under pressure - a feasibility study

X-ray diffraction studies of crystals under pressure and quantitative experimental charge density analysis are among the most demanding types of crystallographic research. A successful feasibility study of the electron density in the mineral grossular under 1 GPa pressure conducted at the CRISTAL beamline at the SOLEIL synchrotron is presented in this work. A single crystal was placed in a diamond anvil cell, but owing to its special design (wide opening angle), short synchrotron wavelength and the high symmetry of the crystal, data with high completeness and high resolution were collected. This allowed refinement of a full multipole model of experimental electron distribution. Results are consistent with the benchmark measurement conducted without a diamond-anvil cell and also with the literature describing investigations of similar structures. Results of theoretical calculations of electron density distribution on the basis of dynamic structure factors mimic experimental findings very well. Such studies allow for laboratory simulations of processes which take place in the Earth's mantle.

Anharmonic motions versus dynamic disorder at the Mg ion from the charge densities in pyrope (Mg3Al2Si3O12) crystals at 30 K: six of one, half a dozen of the other

The possible occurrence of static/dynamic disorder at the Mg site in pyrope (Mg₃Al₂Si₃O₁₂), with or without anharmonic contribution to the thermal vibrations even at low temperatures, has been largely debated but conclusions were contrasting. Here a report is given on the experimental charge density distribution, ρ_EXP, of synthetic pyrope at T = 30 K, built through a Stewart multipolar expansion up to l = 5 and based on a very precise and accurate set of in-home measured single-crystal X-ray diffraction amplitudes with a maximum resolution of 0.44 Å. Local and integral topological properties of ρ_EXP are in substantial agreement with those of ρ_THEO, the corresponding DFT-grade quantum charge density of an ideal pyrope crystal, and those derived from synchrotron investigations of chemical bonding in olivines. Relevant thermal atomic displacements, probably anharmonic in nature, clearly affect the whole structure down to 30 K. No significant (> 2.5σ) residual Fourier peaks are detectable from the ρ_EXP distribution around Mg, after least-squares refinement of a multipole model with anharmonic thermal motion at the Mg site. Experimental findings were confirmed by a full analysis of normal vibration modes of the DFT-optimized structure of the perfect pyrope crystal. Mg undergoes wide displacements from its equilibrium position even at very low temperatures, as it is allocated in a ∼ 4.5 Å large dodecahedral cavity and involved in several soft phonon modes. Implications on the interplay among static/dynamic disorder of Mg and lattice vibrational degrees of freedom are discussed.

On combining temperature and pressure effects on structural properties of crystals with standard ab initio techniques

A general-purpose, fully automated, computationally efficient implementation is presented of a series of techniques for the simultaneous description of pressure and temperature effects on structural properties of materials, by means of standard ab initio simulations. Equilibrium volume, bulk modulus, thermal expansion coefficient, equation-of-state, Grüneisen parameter, constant-pressure and constant-volume specific heats are computed as a function of temperature and pressure for the simple crystal of diamond and compared with accurate experimental data. Convergence of computed properties with respect to super-cell size is critically discussed. The effect on such properties of the adopted exchange-correlation functional of the density-functional-theory is discussed by considering three different levels of approximation (including hybrids): it is found to be rather small for the temperature dependence of equilibrium volume and bulk modulus, whereas it is quite large as regards their absolute values.

Assessing thermochemical properties of materials through ab initio quantum-mechanical methods: the case of α-Al2O3

Accurate ab initio calculations of thermodynamic and structural thermal properties of corundum demonstrate its quasi-harmonic nature up to the melting temperature.

Katoite under pressure: an ab initio investigation of its structural, elastic and vibrational properties sheds light on the phase transition

Structural, elastic and vibrational properties of the katoite hydrogarnet are investigated as a function of pressure, up to 65 GPa, with an ab initio simulation. A group-subgroup phase transition is found to occur in the 5–15 GPa range of pressure.