Calculated Equilibrium Volume Research Articles

Excitation spectra and ground-state properties from density-functional theory for the inverted band-structure systemsβ-HgS, HgSe, and HgTe

We have performed a systematic density-functional study of the mercury chalcogenide compounds $\ensuremath{\beta}$-HgS, HgSe, and HgTe using an all-electron full-potential linear muffin-tin orbital method. We find that, in the zinc-blende structure, both HgSe and HgTe are semimetals whereas $\ensuremath{\beta}$-HgS has a small spin-orbit-induced band gap. Our calculated relativistic photoemission and inverse photoemission spectra reproduce very well the most recently measured spectra, as do also our theoretical optical spectra. In contrast to the normal situation, we find that the local density approximation to the density functional gives calculated equilibrium volumes in much better agreement with experiment than does the generalized gradient corrected functional. We also address the problem of treating relativistic p electrons with methods based on a scalar-relativistic basis set and show that the effect is rather small for the present systems.

High pressure behaviour of TbN: an X-ray diffraction and computational study

In the present work, we report an X-ray powder diffraction study of TbN up to an applied hydrostatic pressure of 43 GPa. TbN was found to be stable in the B1 (NaCl structure) within the examined pressure interval, and the zero pressure bulk modulus was determined to be 176(7) GPa. The electronic structure of ferromagnetic TbN has been studied using the linearized augmented plane-wave method. The calculated equilibrium volume and equation of state (EOS) for TbN agree poorly with experiment when the LDA and GGA versions of DFT were used. The agreement between the experimental and theoretical EOS is greatly improved by introducing an orbital dependent U term into the energy-functional. The 4f electrons in TbN-B1 are atomic like and highly correlated, and ferro-magnetic TbN-B1 is found to be a magnetic half-metal. Calculations find the spin-down f-electrons in a hypothetical TbN-B2 (CsCl) structure to be itinerant and well described by standard DFT functionals. No pressure-induced phase transitions were found below 250 GPa with the LDA+ U and GGA+ U methods.

Theoretical atomic volumes of the light actinides

The zero-pressure zero-temperature equilibrium volumes and bulk moduli are calculated for the light actinides Th through Pu using two independent all-electron, full-potential, electronic-structure methods: the full-potential linear augmented-plane-wave method and the linear combinations of Gaussian-type orbitals-fitting function method. The results produced by these two distinctly different electronic-structure techniques are in good agreement with each other, but differ significantly from previously published calculations using the full-potential linear muffin-tin-orbital (FP-LMTO) method. The theoretically calculated equilibrium volumes are in some cases nearly 10% larger than the previous FP-LMTO calculations, bringing them much closer to the experimentally observed volumes. We also discuss the anomalous upturn in equilibrium volume seen experimentally for $\ensuremath{\alpha}\ensuremath{-}\mathrm{Pu}.$

Electronic structure and bonding in garnet crystalsGd3Sc2Ga3O12,Gd3Sc2Al3O12,andGd3Ga3O12compared toY3Al3O12

The electronic structure and bonding of ${\mathrm{Gd}}_{3}{\mathrm{Sc}}_{2}{\mathrm{Ga}}_{3}{\mathrm{O}}_{12}$ (GSGG), ${\mathrm{Gd}}_{3}{\mathrm{Sc}}_{2}{\mathrm{Al}}_{3}{\mathrm{O}}_{12}$ (GSAG), and ${\mathrm{Gd}}_{3}{\mathrm{Ga}}_{5}{\mathrm{O}}_{12}$ (GGG) crystals with a garnet structure are studied by means of first-principles local-density calculations. The results are compared with a similar calculation on yttrium aluminum garnet [${\mathrm{Y}}_{3}{\mathrm{Al}}_{5}{\mathrm{O}}_{12}$ (YAG)]. The calculated equilibrium volumes of the three crystals are close to the measured volumes with a slight overestimation for GGG. GGG also has a smaller bulk modulus than the other three crystals. The calculated density of states and their atomic and orbital decompositions are presented and contrasted. All four crystals show very similar band structures and interatomic bonding. However, it is found that in GSGG and GSAG crystals, the Sc atom at the octahedral site shows a higher covalent character and an increased bond order in comparison to Ga or Al at the same site. This result may provide some insight into the significant difference in the radiation hardness of ${\mathrm{Cr}}^{3+}{:\mathrm{N}\mathrm{d}}^{3+}:\mathrm{G}\mathrm{S}\mathrm{G}\mathrm{G}$ as compared to ${\mathrm{Nd}}^{3+}:\mathrm{Y}\mathrm{A}\mathrm{G}.$

Correcting overbinding in local-density-approximation calculations

We introduce a semiempirical method to correct the systematic equilibrium lattice parameters underestimation present in first principles calculations based on the local density approximation. The method consists in performing calculations under a negative pressure such that the calculated equilibrium volume matches the experimentally observed one. We find that elastic properties obtained under these conditions are typically in better agreement with experiment. We also observe that the negative pressure which needs to be applied to crystalline compound can be reliably interpolated by taking the concentration-weighted average of the pressures determined from pure crystals made of each of the elements present in the compound. In a large class of materials, the knowledge of one pressure per element is thus sufficient to correct most of the bias in lattice constants and elastic properties. We finally propose a simple model of the nonlocal contribution to the exchange-correlations energy that is able to explain the observed linear dependence between the required negative pressure and concentration.

Crystallographic phase transitions in actinide metals as a function of pressure

We present first-principles calculations of the equilibrium volumes and crystal structures of the light actinides (ThPu). The calculated equilibrium volumes for f.c.c. Th, b.c.t. Pu, α-U, and β-Np are found to agree reasonably well with the experimental data, and when comparing the total energies of the b.c.c., f.c.c., b.c.t., α-U, and β-Np structures we obtain the correct crystal structures for all studied systems. Also, the calculated equilibrium volumes for ThPu, using a hypothetical f.c.c. structure, have been calculated and it is demonstrated that although spin—orbit coupling is included in these calculations the calculated equilibrium volume of Pu is smaller than for Np, in disagreement with experiment. Moreover, the calculated tetragonal elastic constant, C ′, is shown to be negative for b.c.c. U, b.c.c. Np, b.c.c. Pu and f.c.c. Pu. Thus, our zero temperature calculations suggest that the b.c.c. structure is unstable for these elements and that f.c.c. Pu is also unstable. This is in conflict with experiment and we are led to the conclusion that temperature effects must be of crucial importance for stabilizing cubic structures in U, Np, and Pu. Further, as a function of decreasing volume we predict a crystal structure sequence f. c. c. → b. c. t. → f. c. c. in Th, a sequence α- U → b. c. t. → b. c. c. in U, and a sequence β- Np → b. c. t. → b. c. c. in Np. Also, a sequence of transitions in Sc as a function of decreasing volume have been calculated, namely h. c. p. → f. c. c. → ω → β- Np → b. c. c.

First‐Principles Calculation of Electronic, Optical, and Structural Properties of α‐Al2O3

The electronic structure, the linear optical properties, and the structural properties of α‐Al2O3 in the corundum structure are studied by means of first‐principles local density calculations. An indirect band gap of 6.29 eV is obtained, which is almost the same as the direct band gap of 6.31 eV at Γ. The calculated density of states are compared with X‐ray photoemission and photoabsorption measurements. Real space charge density analysis shows Al,2O3 to be highly ionic with an effective charge formula of Al2+2.75O3−1.83. The calculated dielectric function is in general agreement with the experimental vacuum ultraviolet data. It is shown that the component with c‐direction polarization is in better agreement with the experimental data because it is less affected by the exciton formation near the absorption edge. The intrinsic difference between the calculated local density approximation gap and the measured optical gap is pointed out. Various careful test calculations indicate that the remaining discrepancy in the optical spectra may be in the LDA approximation of the electronic structure theory. The total energy calculation for the ground‐state structural properties of α‐Al2O3 shows excellent agreement with experimental data: the calculated equilibrium volume, c/a ratio, bulk modulus, and internal parameters for Al and O atoms differ from measured values by 0.0, −4.3, −4.0,0.85, and 1.96 percent, respectively. The calculations for the electronic structure and the optical properties are repeated with crystal parameters obtained at 2000°C. The result shows only a slight reduction in the band gap (to 5.76 eV at Γ), with the optical spectra essentially unchanged.

Electronic, optical, and structural properties of some wurtzite crystals.

Using the first-principles orthogonalized linear-combination-of-atomic-orbitals method in the local-density approximation, the electronic structures and the linear-optical properties of ten wurtzite crystals, BeO, BN, SiC, AlN, GaN, InN, ZnO, ZnS, CdS, and CdSe are investigated. Results on band structures, density of states, effective masses, charge-density distributions, and effective charges are presented and compared. Optical properties of the ten wurtzite crystals up to a photon energy of 40 eV are calculated and the dielectric functions are resolved into components perpendicular and parallel to the z axis. The calculated results are compared with the available experimental data and other recent calculations. The structural properties of the wurtzite crystals are also studied by means of local-density total-energy calculations. It is shown that the calculated equilibrium volume and the bulk modulus are in good agreement with recent experimental data.

Electronic structure and magnetism of YFe11Ti

Self-cosistent band calculations for YFe11Ti have been performed with LMTO-ASA method in the frame of local spin density functional formalism. The electronic total energy calculations predict that the system is most stable when the Ti atoms are located at the 8f sites, while experimental results suggest the 8i sites for the Ti atoms. On the other hand, the calculated equilibrium volume of the unit cell exhibits fair agreement with the measured value. It is also shown that the unit cell volume increases with the Ti concentration, X in YFe12−XTiX, with a rate ΔV/ΔX=10 (Å3/unit cell), and the magnetic moment decreases with X with a rate ΔM/ΔX=−4μB. The total magnetic moment of YFe11Ti (X=1) is given as about 21.7μB. With a inclusion of the spin–orbit interaction in the LMTO Hamiltonian, the orbital magnetism and the magnetocrystalline anisotropy were further examined. The orbital magnetic moment per Fe atom is about 0.06μB and the anisotropy energy is obtained as 97μRy/f.u. The value leads to about 12.1×106 erg/cc, which is about the half of the measured value, 23×106 erg/cc at 1.5 K.

Pressure dependence of the band structure, density of states, Fermi surfaces, and optical properties of superconducting K3C60.

The electronic, the structural, and the optical properties of the fcc ${\mathrm{K}}_{3}$${\mathrm{C}}_{60}$ crystal and their dependence on isotropic pressure are studied theoretically by means of first-principles local-density calculations. The calculated equilibrium volume and the pressure coefficients are in good agreement with experimental measurements. The changes in the band structure, the density of states (DOS), the Fermi-surface topology, and the optical-absorption spectrum with pressure are analyzed in detail and compared with other recent theoretical calculations and available measurements. With an increased pressure, the DOS at the Fermi level decreases, the gap diminishes, and the bands widen and eventually merge. The change in the band structure has resulted in the merging of the absorption peaks in the optical spectrum and in the decrease of the static dielectric constant. The linear dependence of the DOS at the Fermi level due to pressure is found to have a smaller slope than that due to the expansion of the lattice by introducing different alkali-metal intercalates of varying ionic radii. The pressure dependence of the superconducting temperature in ${\mathrm{K}}_{3}$${\mathrm{C}}_{60}$ is estimated by the use of the McMillan formula and a set of optimized parameters obtained earlier in the study of ${\mathit{T}}_{\mathit{c}}$ in five alkali-metal-doped fullerites. The agreement with the measured data is not as good as that for the other alkali-metal-doped fullerites but shows the correct trend. The effective Coulomb repulsion in ${\mathrm{K}}_{3}$${\mathrm{C}}_{60}$ is also estimated and found to be small.

Volume effects on the magnetic properties of cubic isostructural intermetallics of Ce.

We compare the magnetic behavior of CeAg, CeZn, and CeCd in the ferromagnetic phase under pressure, using total-energy electronic-structure calculations within the local-spin-density approximation. While the calculated magnetic moments at ambient pressure reflect the trend of the unit-cell volumes as the pressure is increased, an instability of the magnetic phase occurs in isovalent CeCd and CeZn at much lower applied pressure than in CeAg, as found by experiments. Results with use of a rigid-band model to fill in the density of states of CeAg with the same number of electrons as CeCd show that the different magnetic behavior of the two compounds is essentially due to a more effective screening of the complete 6s shell of Cd. Analogous conclusions are valid for CeZn; the calculated equilibrium volume of the ferromagnetic phase of CeZn is found within the experimental pressure range in which the observed order-order magnetic phase transition takes place.

Theoretical determination of the pressure dependence of the electronic and the optical properties of fcc C60.

The electronic, optical, and structural properties of fcc ${\mathrm{C}}_{60}$ crystal are studied as a function of cell volume by means of first-principles local-density calculations. The calculated equilibrium volume, bulk modulus, and the pressure-versus-volume relation are in good agreement with experimental measurements. Changes in the band structure, density of states, bonding pattern, dielectric constant, and optical spectrum with pressure are analyzed and discussed. It is found that the band gap and the absorption threshold energy decrease with increasing pressure while the static dielectric constant increases with increasing pressure. The charge-density map shows that at a pressure of 13 GPa covalent bonding between C atoms in different ${\mathrm{C}}_{60}$ molecules may form and metallization of ${\mathrm{C}}_{60}$ at ultrahigh pressure is unlikely. These results are in line with some very recent experimental observations.

Crystal structure, phase stability, and electronic structure of Ti-Al intermetallics: Ti3Al.

The structural phase stability and electronic properties of the intermetallic compound ${\mathrm{TiAl}}_{3}$ are investigated with use of the self-consistent all-electron total-energy linear muffin-tin orbitals band-structure method within the local-density-functional approximation. The calculated equilibrium volumes have a Wigner-Seitz radius of 2.92 a.u. for the D${0}_{22}$ and D${0}_{19}$ structures, and 2.91 a.u. for the L${1}_{2}$ structure, showing the expected consistency in the volume among the different structures. The calculated value also agrees with experiment for the D${0}_{22}$ structure to within 2%. The calculated heats of formation are 0.42, 0.37, and 0.28 eV/atom for the D${0}_{22}$, L${1}_{2}$, and D${0}_{19}$ lattices, respectively. The D${0}_{22}$ structure is calculated to be the most stable phase, as observed experimentally. The calculated bulk moduli are 1.2, 1.5, and 1.1 Mbar for D${0}_{22}$, L${1}_{2}$, and D${0}_{19}$, respectively. Among the three structures, the density of states at the Fermi energy, N(${\mathit{E}}_{\mathit{F}}$), is lowest in D${0}_{22}$ and so is consistent with the inverse relation between N(${\mathit{E}}_{\mathit{F}}$) and stability found for other aluminum intermetallic compounds.

Crystal structure, phase stability, and electronic structure of Ti-Al intermetallics: TiAl3.

The structural phase stability and electronic properties of the intermetallic compound ${\mathrm{TiAl}}_{3}$ are investigated with use of the self-consistent all-electron total-energy linear muffin-tin orbitals band-structure method within the local-density-functional approximation. The calculated equilibrium volumes have a Wigner-Seitz radius of 2.92 a.u. for the D${0}_{22}$ and D${0}_{19}$ structures, and 2.91 a.u. for the L${1}_{2}$ structure, showing the expected consistency in the volume among the different structures. The calculated value also agrees with experiment for the D${0}_{22}$ structure to within 2%. The calculated heats of formation are 0.42, 0.37, and 0.28 eV/atom for the D${0}_{22}$, L${1}_{2}$, and D${0}_{19}$ lattices, respectively. The D${0}_{22}$ structure is calculated to be the most stable phase, as observed experimentally. The calculated bulk moduli are 1.2, 1.5, and 1.1 Mbar for D${0}_{22}$, L${1}_{2}$, and D${0}_{19}$, respectively. Among the three structures, the density of states at the Fermi energy, N(${\mathit{E}}_{\mathit{F}}$), is lowest in D${0}_{22}$ and so is consistent with the inverse relation between N(${\mathit{E}}_{\mathit{F}}$) and stability found for other aluminum intermetallic compounds.

Density functional theory total energies and equilibrium volumes of La2CuO4 and La1.5Sr0.5CuO4

The authors have calculated the total energy and equilibrium volumes of La2CuO4 and La1.5Sr0.5CuO4 using the local density approximation to density functional theory (DFT). The calculations were performed using the ASA LMTO method under the constraint of a fixed c/a ratio. The calculated equilibrium volumes are in good agreement with experiment indicating that DFT provides a useful starting point for a discussion of the energetics of this class of superconductor. In the strontium compound they find local charge redistributions that result in holes in the p band of the out-of-plane oxygen atoms. These local charge rearrangements invalidate the use of the rigid band and virtual crystal models for describing alloying.

Electronic structure of the uranium-3d transition metal laves phases

Electronic structure calculations within the linearized muffin-tin orbital (LMTO) method have been performed for the uranium-3d metal Laves phases. Calculated equilibrium volumes show very good agreement with experimental data. The spin-only magnetic properties of UFe 2 were also considered and the calculated Fe spin moment agrees quite well with measurements. It is noteworthy that the uranium 5f spin moment is found to be antiparallel to the iron moment. The spin magnetism of UFe 2 was also calculated as a function of pressure. The 3d spin moment is found to initially decrease by 1.5 μ B/Mbar. Around 500 kbar the magnetism is calculated to disappear. For UCo 2 a paramagnetic ground state was obtained, which, however, in agreement with data, is enhanced quite substantially. Finally, for UMn 2 the Stoner criterion for magnetism was found to be just fulfilled. This is somewhat in disagreement with experiments where only enhanced magnetic properties have been reported. The possibility of metamagnetism in UMn 2 is suggested. The bulk modulus for these Laves phase systems has been calculated. Total and partial densities-of-states are also reported.