Calculated Transition Pressure Research Articles

Optical and structural properties of III-nitrides compounds

Self-consistent linear muffin-tin-orbital band-structure calculations are used to investigate the optical and structural properties of III-V semiconducting nitrides under hydrostatic pressure. The pressure behavior of the energy band structures is discussed in the context of the postulated chemical trends in III-V semiconductors. The regions in k space of dominant interband contributions to the elements of structure in the dielectric functions are identified. The total-energy calculations suggest that all the nitrides under pressure transform to the semiconducting rocksalt phase. The calculated transition pressures are 21.6 GPa (InN), 51.8 GPa (GaN), 16.6 GPa (AlN), and 850 GPa (BN). Experimental values that agree well with this have been found for the first three compounds. The fact that GaN and AlN have such different transition pressures in spite of their very similar ionicities is explained by the presence of 3d states on Ga.

Thermodynamic Properties of Fe-Bearing Wadsleyite and Determination of the Olivine-Wadsleyite Phase Transition Boundary in (Mg,Fe)2SiO4 System

The self-consistent molar volumes, elastic properties and thermodynamic properties of β-(Mg0.87,Fe0.13)2SiO4wadsleyite have been determined over a wide temperature and pressure range based on an iterative numerical approach and experimental data from the literature. The obtained molar volumes, adiabatic bulk modulus, and shear modulus generally agree with the available experimental and theoretical results. The thermodynamic properties of α-(Mg0.9,Fe0.1)2SiO4were also reinvestigated. Comparisons on thermodynamic properties show that the thermal expansions, heat capacities, and entropies of both β-(Mg0.87,Fe0.13)2SiO4and α-(Mg0.9,Fe0.1)2SiO4exhibit negative and nonlinear behavior with increasing pressure. Besides, the pressure plays a more important role in thermodynamic properties of the α-(Mg0.9,Fe0.1)2SiO4than that of the β-(Mg0.87,Fe0.13)2SiO4. Using the Clausius-Clapeyron equation combined with molar volumes and entropies of both compositions, the phase transition boundary of Fe-bearing olivine and wadsleyite is estimated. The calculated transition pressure shows a nonlinear relationship with increasing temperature, and the value is generally lower than the previous studies on Fe-free olivine and wadsleyite at the same temperature. On the basis of our phase relation, the temperature at the 410 km discontinuity is estimated as 1795 ± 70 K under anhydrous conditions. The results not only confirm the feasibility of the Clausius-Clapeyron equation in obtaining the solid-solid phase transition, but also suggest that the existence of Fe might decrease the transition pressure of olivine-wadsleyite, which would consequently cause a higher temperature at the 410 km discontinuity.

High-pressure structural systematics in neodymium up to 302 GPa

Angle-dispersive x-ray powder diffraction experiments have been performed on neodymium metal to a pressure of 302 GPa. Up to 70 GPa we observe the $hP4\ensuremath{\rightarrow}cF4\ensuremath{\rightarrow}hR24\ensuremath{\rightarrow}oI16\ensuremath{\rightarrow}hP3$ transition sequence reported previously. At 71(2) GPa we find a transition to a phase which has an orthorhombic structure ($oF8$) with eight atoms in the unit cell, space group $Fddd$. This structure is the same as that recently observed in samarium above 93 GPa, and is isostructural with high-pressure structures found in the actinides Am, Cf, and Cm. We see a further phase transition at 98(1) GPa to a phase with the orthorhombic $\ensuremath{\alpha}$-U ($oC4$) structure, which remains stable up to 302 GPa, the highest pressure reached in this study. Electronic structure calculations find the same structural sequence, with calculated transition pressures of 66 and 88 GPa, respectively, for the $hP3\ensuremath{\rightarrow}F8$ and $oF8\ensuremath{\rightarrow}oC4$ transitions. The calculations further predict that $oC4$-Nd loses its magnetism at 100 GPa, in agreement with previous experimental results, and it is the accompanying decrease in enthalpy and volume that results in the transition to this phase. Comparison calculations on the $oF8$ and $oC4$ phases of Sm show that they both retain their magnetism to at least 240 GPa, with the result that $oC4$-Sm is calculated to have the lowest enthalpy over a narrow pressure region near 200 GPa at 0 K.

Relative stability of Cu, Ag, and Pt at high pressures and temperatures from ab initio calculations

The paper presents ab initio studies into the relative stability of the crystalline structures of copper, silver, and platinum up to high pressures at $T\ensuremath{\ge}0$ K. Our calculations in quasiharmonic approximation suggest that not the fcc structure of Cu and Ag, but the body-centered cubic one, is thermodynamically most favorable at $P\ensuremath{\gtrsim}100$ GPa and $T>3$ kK. The shock Hugoniot of Cu and Ag crosses the fcc-bcc phase boundary and the calculated transition pressures agree well with the result of recent laser shock experiments by Sharma et al. The advantage of the bcc structure comes from its softer low-frequency phonon modes and the smaller contribution of lattice vibrations to free energy at high temperatures, as compared to close-packed structures. The compression of platinum crystal also causes the $\mathrm{fcc}\ensuremath{\rightarrow}\mathrm{bcc}$ transition but at much higher pressures, $P>1.4$ TPa.

Structural, electronic, mechanical, and dynamical properties of scandium carbide

We report results of first-principles calculations for the structural, mechanical, dynamical and electronic properties of Scandium Carbide (ScC) compound, using a Full-Potential Linearized-Augmented Plane Wave (FP-LAPW) method based on density functional theory, within the generalized gradient approximation (GGA). The computed ground states properties; lattice constants, bulk modulus and the pressure derivative of the bulk modulus (a0, B and B') are in good agreement with former works. The calculated transition pressures from the rocksalt (NaCl) structure to the CsCl structure and from the NiAs to CsCl are found to be 111.0 GPa and 27.15GPa, respectively. It was found, that NaCl and NiAs are mechanically and dynamically the stable phases, with NaCl considered as the ground state phase. In contrast, the Zincblende (ZB) and CsCl are both unstable phases mechanically and dynamically. Wurtzite (WZ) phase was found mechanically stable and dynamically not, which might be a possible indication for a metastable phase. The electronic structures reveal that all the considered structures have a metallic character. Upon our best knowledge, for the first time, the mechanical and dynamical properties of the studied structures beside NaCl were calculated.

Parametric study of supersonic film cooling in dual bell nozzle for an experimental air–kerosene engine

Numerical analysis is performed on a dual bell nozzle designed for an experimental semi-cryogenic rocket engine application to predict the effect of film injection on nozzle flow characteristics and transitional behavior. Both start-up and high-altitude operation regimes are simulated to predict actual flight conditions of a dual bell nozzle. Coolant is injected at two locations and at different operating conditions to study the effect of various parameters on flow behavior. Changes in shock interaction and shock patterns during startup flow with and without the injection of coolant are analyzed. An empirical relation for conventional nozzles has been applied to determine the transition pressure ratio. Actual transition flow from base to extension nozzle is found to be different from the calculated transition pressure ratio and flow transition occurs early in case of secondary injection. A large reduction in wall temperature is observed with the film flowing along the nozzle wall and it does not have any adverse effect on flow transition. Instead of efficiency, a film cooling effectiveness for high temperature flow is used to understand the effect of coolant temperature on reduction of heat flux and mixing characteristics. Mass flow rate of coolant is seen to have significant effect on mixing and flow separation.

Comparison of approximations in density functional theory calculations: Energetics and structure of binary oxides

High-throughput first-principles calculations based on density functional theory (DFT) are a powerful tool in data-oriented materials research. The choice of approximation to the exchange-correlation functional is crucial as it strongly affects the accuracy of DFT calculations. This study compares performance of seven approximations, six of which are based on Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA) with and without Hubbard U and van der Waals corrections (PBE, PBE+U, PBED3, PBED3+U, PBEsol, and PBEsol+U), and the strongly constrained and appropriately normed (SCAN) meta-GGA on the energetics and crystal structure of elementary substances and binary oxides. For the latter, only those with closed-shell electronic structures are considered, examples of which include $\mathrm{C}{\mathrm{u}}_{2}\mathrm{O}$, $\mathrm{A}{\mathrm{g}}_{2}\mathrm{O}$, MgO, ZnO, CdO, SnO, PbO, $\mathrm{A}{\mathrm{l}}_{2}{\mathrm{O}}_{3}$, $\mathrm{G}{\mathrm{a}}_{2}{\mathrm{O}}_{3}$, $\mathrm{I}{\mathrm{n}}_{2}{\mathrm{O}}_{3}$, $\mathrm{L}{\mathrm{a}}_{2}{\mathrm{O}}_{3}$, $\mathrm{B}{\mathrm{i}}_{2}{\mathrm{O}}_{3}$, $\mathrm{Si}{\mathrm{O}}_{2}$, $\mathrm{Sn}{\mathrm{O}}_{2}$, $\mathrm{Pb}{\mathrm{O}}_{2}$, $\mathrm{Ti}{\mathrm{O}}_{2}$, $\mathrm{Zr}{\mathrm{O}}_{2}$, $\mathrm{Hf}{\mathrm{O}}_{2}$, ${\mathrm{V}}_{2}{\mathrm{O}}_{5}$, $\mathrm{N}{\mathrm{b}}_{2}{\mathrm{O}}_{5}$, $\mathrm{T}{\mathrm{a}}_{2}{\mathrm{O}}_{5}$, $\mathrm{Mo}{\mathrm{O}}_{3}$, and $\mathrm{W}{\mathrm{O}}_{3}$. Prototype crystal structures are selected from the Inorganic Crystal Structure Database (ICSD) and cation substitution is used to make a set of existing and hypothetical oxides. Two indices are proposed to quantify the extent of lattice and internal coordinate relaxation during a calculation. The former is based on the second invariant and determinant of the transformation matrix of basis vectors from before relaxation to after relaxation, and the latter is derived from shifts of internal coordinates of atoms in the unit cell. PBED3, PBEsol, and SCAN reproduce experimental lattice parameters of elementary substances and oxides well with few outliers. Notably, PBEsol and SCAN predict the lattice parameters of low dimensional structures comparably well with PBED3, even though these two functionals do not explicitly treat van der Waals interactions. SCAN gives formation enthalpies and Gibbs free energies closest to experimental data, with mean errors (MEs) of 0.01 and \ensuremath{-}0.04 eV, respectively, and root-mean-square errors (RMSEs) are both 0.07 eV. In contrast, all GGAs including those with Hubbard U and van der Waals corrections give 0.1 to 0.2 eV MEs and at least 0.11 eV RMSEs. Phonon contributions of solid phases to the formation enthalpies and Gibbs free energies are estimated to be small at less than \ensuremath{\sim}0.1 eV/atom within the quasiharmonic approximation. The same crystal structure appears as the lowest energy polymorph with different approximations in most of the investigated binary oxides. However, there are some systems where the choice of approximation significantly affects energy differences between polymorphs, or even the order of stability between phases. SCAN is the most reasonable regarding relative energies between polymorphs. The calculated transition pressure between polymorphs of ZnO and $\mathrm{Sn}{\mathrm{O}}_{2}$ is closest to experimental values when PBED3, PBEsol (also PBED3+U and PBEsol+U for ZnO), and SCAN are employed. In summary, SCAN appears to be the best choice among the seven approximations based on the analysis of the energetics and crystal structure of binary oxides, while PBEsol is the best among the GGAs considered and shows a comparably good performance with SCAN for many cases. The use of PBEsol+U alongside PBEsol is also a reasonable choice, given that U corrections are required for several materials to qualitatively reproduce their electronic structures.

Pressure-induced spin-state transition of iron in magnesiowüstite (Fe,Mg)O

We present a detailed theoretical study of the electronic, magnetic, and structural properties of magnesiow\"ustite Fe$_{1-x}$Mg$_x$O with $x$ in the range between 0$-$0.875 using a fully charge self-consistent implementation of the density functional theory plus dynamical mean-field theory (DFT+DMFT) method. In particular, we compute the electronic structure and phase stability of the rock-salt B1-structured (Fe,Mg)O at high pressures relevant for the Earth's lower mantle. We obtain that upon compression paramagnetic (Fe,Mg)O exhibits a spin-state transition of Fe$^{2+}$ ions from a high-spin to low-spin (HS-LS) state which is accompanied by a collapse of local magnetic moments. The HS-LS transition results in a substantial drop of the lattice volume by about 4$-$8 %, implying a complex interplay between electronic and lattice degrees of freedom. Our results reveal a strong sensitivity of the calculated transition pressure $P_{\rm tr.}$ upon addition of Mg. While for Fe-rich magnesiow\"ustite, Mg $x < 0.5$, $P_{\rm tr.}$ exhibits a rather weak variation at $\sim$80 GPa, for Fe-poor (Fe,Mg)O it drops, e.g., by about 35 % to 52 GPa for Mg $x=0.75$. This behavior is accompanied by a substantial change of the spin transition range from 50$-$140 GPa in FeO to 30$-$90 GPa for $x=0.75$. In addition, the calculated bulk modulus (in the HS state) is found to increase by $\sim$12 % from 142 GPa in FeO to 159 GPa in (Fe,Mg)O with Mg $x=0.875$. We find that the pressure-induced HS-LS transition has different consequences for the electronic properties of the Fe-rich and poor (Fe,Mg)O. For the Fe-rich (Fe,Mg)O, the transition is found to be accompanied by a Mott insulator to (semi-) metal phase transition. In contrast to that, for $x>0.25$, (Fe,Mg)O remains insulating up to the highest studied pressures, implying a Mott insulator to band insulator phase transition at the HS-LS transformation.

FPLMTO study of new phase changes in CuX (X = Cl, Br, I) compounds under hydrostatic pressure

We study the ground-state properties of copper halides CuX (X = Cl, Br, I) and the behavior under pressure using a recent version of the full potential linear muffin-tin orbitals method (FPLMTO). It predicts the possibility of an additional local minimum in the tetragonal PbO phase for CuBr and CuI at 0.7 GPa and 01.53 GPa with a direct energy gap at Γ of about 0.678 eV and 1.265 eV respectively. The use of GGA in this work is more appropriate than LDA and correctly predicts the cubic B3 phase as ground state structure for the three binaries. Importantly, calculated transition pressure Pt revealed also the presence of PbO phase at 5.333 GPa for CuCl which is consistent with experimental reports. Other important results are that concerned with the possibility of phase transition from B3 to the hexagonal B8 phase at lower pressures (3.43, 4.11 and 6.23) GPa and from B3 to B2 at (22.96, 22.66 and 24.83) GPa respectively for CuBr, CuI and CuCl.

Theoretical study of B3-to-B1 phase transition in ZnS

The pressure-induced phase transformation from B3 to B1 structures in ZnS using first-principle projector-augmented wave method is studied. To understand the nature and driving force behind the transition, the interesting properties in both phases, including enthalpy, phonon dispersion curves and elastic constants, are systematically investigated. The results show that the calculated transition pressure is within the range of 16.33 GPa to 19.04 GPa, which is in good agreement with the available experimental and theoretical data. The transition process can be viewed as the appearance and disappearance of very slight lattice distortion accompanied by the movement of Zn and S atoms along the [111] crystallographic axis. The physical driving force of the B3–B1 phase transition is confirmed to be a coupling effect between the mechanical instability of B3 phase under pressure and the softening acoustic phonon mode resulting from the pressure-induced lattice deformation. For B1 phase, it is further predicted that a new phase transition takes place at about 59.9 GPa.

High-pressure X-ray diffraction, Raman, and computational studies of MgCl2 up to 1 Mbar: Extensive pressure stability of the β-MgCl2 layered structure.

Magnesium chloride (MgCl2) with the rhombohedral layered CdCl2-type structure (α-MgCl2) has been studied experimentally using synchrotron angle-dispersive powder x-ray diffraction and Raman spectroscopy using a diamond-anvil cell up to 100 GPa at room temperature and theoretically using first-principles density functional calculations. The results reveal a pressure-induced second-order structural phase transition to a hexagonal layered CdI2-type structure (β-MgCl2) at 0.7 GPa: the stacking sequence of the Cl anions are altered resulting in a reduction of the c-axis length. Theoretical calculations confirm this phase transition sequence and the calculated transition pressure is in excellent agreement with the experiment. Lattice dynamics calculations also reproduce the experimental Raman spectra measured for the ambient and high-pressure phase. According to our experimental results MgCl2 remains in a 2D layered phase up to 100 GPa and further, the 6-fold coordination of Mg cations is retained. Theoretical calculations of relative enthalpy suggest that this extensive pressure stability is due to a low enthalpy of the layered structure ruling out kinetic barrier effects. This observation is unusual, as it contradicts with the general structural behavior of highly compressed AB2 compounds.

High-pressure structural study ofMnF2

Manganese fluoride $({\mathrm{MnF}}_{2})$ with the tetragonal rutile-type structure has been studied using a synchrotron angle-dispersive powder x-ray diffraction and Raman spectroscopy in a diamond anvil cell up to 60 GPa at room temperature combined with first-principles density functional calculations. The experimental data reveal two pressure-induced structural phase transitions with the following sequence: rutile $\ensuremath{\rightarrow} {\mathrm{SrI}}_{2}$ type (3 GPa)$\ensuremath{\rightarrow} \ensuremath{\alpha}\ensuremath{-}{\mathrm{PbCl}}_{2}$ type (13 GPa). Complete structural information, including interatomic distances, has been determined in the case of ${\mathrm{MnF}}_{2}$ including the exact structure of the debated first high-pressure phase. First-principles density functional calculations confirm this phase transition sequence, and the two calculated transition pressures are in excellent agreement with the experiment. Lattice dynamics calculations also reproduce the experimental Raman spectra measured for the ambient and high-pressure phases. The results are discussed in line with the possible practical use of rutile-type fluorides in general and specifically ${\mathrm{MnF}}_{2}$ as a model compound to reveal the HP structural behavior of rutile-type ${\mathrm{SiO}}_{2}$ (Stishovite).

A coupled cluster and Møller-Plesset perturbation theory study of the pressure induced phase transition in the LiH crystal.

We employ Hartree-Fock, second-order Møller-Plesset perturbation, coupled cluster singles and doubles (CCSD) as well as CCSD plus perturbative triples (CCSD(T)) theory to study the pressure induced transition from the rocksalt to the cesium chloride crystal structure in LiH. We show that the calculated transition pressure converges rapidly in this series of increasingly accurate many-electron wave function based theories. Using CCSD(T) theory, we predict a transition pressure for the structural phase transition in the LiH crystal of 340 GPa. Furthermore, we investigate the potential energy surface for this transition in the parameter space of the Buerger path.

High Pressure Structural Phase Transition and Elastic Properties of Europium Chalcogenides

The high pressure induced structural phase transition and elastic properties of three Europium chalcogenides (EuX; X = S, Se, Te) have been studied using a two body potential approach. The calculated compression curves of EuS, EuSe and EuTe obtained so has been compared with recently measured three body potential data. The calculated transition pressures are in good agreement with the experimental data. The phase transition pressure for EuS, EuSe and EuTe going from the NaCl phase to CsCl phase have been observed are 22 GPa, 15 GPa, 10 GPa respectively, close the theoretical and experimental data. We have also calculated bulk modulas and second order elastic constants at high pressure which show partly ionic nature of theses compounds. The B1 (NaCl) phase is found to be higher in energy than the B2 (CsCl) phase and more stable at zero pressure.

Phase transitions in rare earth tellurides under pressure

Using first-principles calculations we have studied the valence and structural transitions of the rare earth monotellurides RTe (R = Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm and Yb) under pressure. The self-interaction corrected local spin-density approximation is used to establish the ground state valence configuration as a function of volume for the RTe in both the NaCl (B1) and CsCl (B2) structures. We find that in ambient conditions all the RTe are stabilized in the B1 structure. A trivalent (R3+) rare earth ground state is predicted for the majority of the RTe, with the exception of SmTe, EuTe, DyTe, TmTe and YbTe, where the fully localized divalent (R2+) rare earth configuration is found to be energetically most favourable. Under pressure, the trivalent RTe undergo structural transitions to the B2 structure without associated valence transition. The divalent RTe on the other hand are characterized by a competition between the structural and electronic degrees of freedom, and it is the degree of f-electron delocalization that determines the sequence of phase transitions. In EuTe and YbTe, where respectively the half-filled and filled shells result in a very stable divalent configuration, we find that it is the structural B1 → B2 transition that occurs first, followed by the R2+ → R3+ valence transition at even higher pressures. In SmTe, DyTe and TmTe, the electronic transition occurs prior to the structural transition. With the exception of YbTe, the calculated transition pressures are found to be in good agreement with experiment.

Vibrational and elastic properties as a pointer to stishovite to CaCl2 ferroelastic phase transition in RuO2

The high pressure behavior of RuO2 has been investigated using the first principles calculations based on the density functional theory. Here, we report the calculated properties on structure, electronic, elastic, phonon and electron–phonon coupling of rutile and CaCl2 type RuO2. Our calculated lattice constants and bulk modulus agree reasonably well with the available theoretical and experimental data. Results of our calculations of zone center phonon modes at ambient and high pressures are in good agreement with Raman scattering measurements. Elastic (shear) modulus and phonon analysis confirm the ferroelastic phase transition from rutile to CaCl2 phase in RuO2. It is clearly illustrated that the first transition is associated with macroscopic shear instability which arises from the strong coupling between elastic constants and softening of Raman active B1g mode. The observed pressure of phase transition in experimental measurements was reproduced more accurately than in previous calculations and the difference between observed and calculated transition pressure is only of the order of few percentage. We have also analyzed the rotation angle for O-R-O corresponding to B1g mode and found that the rotation of bond about 80 is required for transition from rutile to CaCl2 phase in RuO2. In addition, the mode Grüneisen parameter is discussed. The electron–phonon interaction in both rutile and CaCl2 type RuO2 at high pressure is also discussed.

New Ab Initio Based Pair Potential for Accurate Simulation of Phase Transitions in ZnO

A set of interatomic pair potentials is developed for ZnO based on the partially charged rigid ion model (PCRIM). The derivation of the potentials combines lattice inversion, empirical fitting, and ab initio energy surface fitting. We show that, despite the low number of parameters in this model (8), a wide range of physical properties is accurately reproduced using the new potential model. The calculated lattice parameters and elastic constants of ZnO in the wurtzite (WZ) phase, as well as the lattice parameters and stabilities of ZnO in other high-pressure and metastable phases, agree well with experiments and with density functional theory (DFT) calculations. The calculated transition pressure of the wurtzite-to-rocksalt (WZ-to-RS) transition is 12.3 GPa. A wurtzite-to-honeycomb (WZ-to-HC) phase transition induced by uniaxial pressure along the c-axis is simulated by means of molecular dynamics (MD) simulations. The WZ-to-HC transition takes place at an uniaxial pressure of 8.8 GPa while the reverse transition takes place at 2.9 GPa, which is consistent with DFT calculations. Other physical properties, including phonon dispersion, phonon density of states, and melting point calculated using our ZnO potential model are in good agreement with experimental and DFT data. Limitations of the novel ZnO potential model are also discussed.

Simulation of uranium dioxide polymorphs and their phase transitions

In this article first-principles DFT calculations and molecular dynamics simulations using empirical potentials have been used to study four different polymorphs of uranium dioxide that appear under high compressive and tensile deformations. It has been found, as expected, that the ground-state structure is the fluorite-type structure (space group $Fm\overline{3}m$). Under high compressive deformation urania transforms into cotunnite-type structure (space group $Pnma$), as already known experimentally. The calculated transition pressure is 28 GPa in agreement with the experimental data. Under tensile deformation urania transforms into either scrutinyite-type structure (space group $Pbcn$) or rutile-type (space group $P{4}_{2}/mnm$) structure. These two phases are almost energetically degenerate; hence it is impossible to distinguish which phase is the most favorable. The transition pressure for both phases is found to be equal to $\ensuremath{-}10$ GPa. Subsequently, assessment of four of the most used empirical potentials for ${\mathrm{UO}}_{2}$---Morelon, Arima, Basak, and Yakub---have been carried out comparing the equations of state with those found with DFT calculations. The Morelon potential has been found to be the most accurate to describe the different urania polymorphs. Using this empirical potential and a dedicated minimization procedure, complete transition pathways between the ground state ($Fm\overline{3}m$) and both tensile structures ($Pbcn$ or $P{4}_{2}/mnm$) are described. Finally, uniaxial tensile load molecular dynamics simulations have been performed. It has been found that for load in the $\ensuremath{\langle}100\ensuremath{\rangle}$ direction urania transforms into the $Pbcn$ structure while for load in the $\ensuremath{\langle}110\ensuremath{\rangle}$ direction it transits towards the $P{4}_{2}/mnm$ structure.

Electronic structure and stability of hyperstoichiometric UO2+xunder pressure

Electronic-Structure and high-pressure phase transitions of stoichiometric uranium dioxide (UO${}_{2}$) and hyperstoichiometric UO${}_{2.03}$ were investigated using first-principles calculations. Density functional theory calculations using the generalized gradient approximation and the projector-augmented wave method with the on-site Coulomb repulsive interactions were applied in order to reasonably calculate the equilibrium volume, total and partial density of states, band gap of UO${}_{2+x}$, and energetics of the high-pressure phase transitions. Structure optimizations were completed with and without the Hubbard $U$-ramping method separately. The $U$-ramping method was intended to remove the metastable states of the 5$f$ electrons of both stoichiometric and hyperstoichiometric UO${}_{2+x}$. Using the Hubbard $U$ parameters ($U$ $=$ 3.8, $J$ $=$ 0.4), whose values are based on the experimental band gap width of 2.1 eV as a reference, the calculated cell parameter for the stoichiometric UO${}_{2}$ with cubic fluorite structure is about 1$%$ greater than the experimental unit cell parameter; in contrast, it is about 1$%$ smaller than the experimental value without the on-site Coulomb repulsive interactions. For hyperstoichiometric UO${}_{2.03}$ with the cubic fluorite structure, the interstitial oxygen at the octahedral interstitial site induces new bands at the top of the band gap of the stoichiometric UO${}_{2}$, similar to those of the high-pressure phase with orthorhombic cotunnite structure. The orbitals associated with the charge transfers to the interstitial oxygen in hyperstoichiometric UO${}_{2.03}$ are partially delocalized and partially localized in both the cubic fluorite structure and orthorhombic cotunnite structure. The energy required for the incorporation of an interstitial O atom is 0.3 eV higher for the orthorhombic phase than for the cubic phase at ambient pressure and increases to 0.5 eV at 10 GPa. The calculated transition pressures from the cubic to the orthorhombic structure are 18 and 27 GPa for UO${}_{2}$ and UO${}_{2.03}$, respectively. The dramatic increase in the calculated transition pressure for the hyperstoichiometric UO${}_{2}$ is related to structural incompatibility of the interstitial oxygen in the cotunnite structure (high-pressure phase), which is less in the case of the fluorite structure. These results suggest that experimentally determined pressure values for the phase transition can be significantly affected by small compositional deviations off the ideal stoichiometric UO${}_{2}$. Comparisons of the results using the $U$-ramping method and without using the $U$-ramping method suggest that the electronic metastability of UO${}_{2}$ affects the calculated total energy and electronic structure and could lead to a different local defect configuration for the hyperstoichiometric orthorhombic phase. However, the metastability has a negligible effect on the calculated phase transition pressure.

Electron Momentum Density and Phase Transition in ZnS

The electron momentum density distribution and phase transition in ZnS are reported in this paper. The calculations are performed on the basis of density functional theory (DFT) based on the linear combination of atomic orbitals (LCAO) method. To compare the theoretical Compton profile, the measurement on polycrystalline ZnS has been made using a Compton spectrometer employing 59.54 keV gamma rays. The spherically averaged theoretical Compton profile is in agreement with the measurement. On the basis of equal valence-electron-density Compton profiles, it is found that ZnS is less covalent as compared to ZnSe. The present study suggests zincblende (ZB) to rocksalt (RS) phase transition at 13.7 GPa. The calculated transition pressure is found in good agreement with the previous investigations.