Vacancies in transition metals: Formation energy and formation volume

This work describes a calculation of the formation energy and volume for a vacancy in transition metals. One uses a tight-binding scheme for the d band and a Born-Mayer type potential to account for the repulsive part of the energy at small distances. The results show that the relaxation energy is small in all cases, less than 0.1 eV. This seems to be coherent with the good agreement obtained for the theoretical and experimental values of the formation energy E_f^v of the vacancy, without including relaxation. The center of the transitional series is found to give a contraction (formation volume of order ?0.4 at. vol.) whereas the edges are found to produce dilatations.     

Binding-energy reference in X-ray photoelectron spectroscopy of insulators

The surface potential of a sample in XPS depends on the flux and energy of incident electrons and on the resistance, R, between the surface and the spectrometer. When R is very low, the kinetic energy E_m of the ejected photoelectron, relative to the spectrometer vacuum level, is given by the well known relation E_m=hν φ_Bφ_S, where hv is the photon energy, φ_B the binding energy relative to the sample Fermi level, and φ_S the work-function of the spectrometer. However, when R is very high and the residual charge left by the ejected photoelectron is solely compensated by a sufficient flux of low-energy monoenergetic electrons of energy φ_e, the sample charges to φ_e. The measured kinetic energy is now given by E_m = hνφ_Bφ_R+φ_e, where φ_R, is the work-function of the sample. Consequently, binding energies on insulated samples are measured relative to the vacuum level, not the Fermi level, since E_m now depends on gf_R. A good conductor can be examined both shorted and insulated. The difference in measured kinetic energy is E_m (shorted)E_m (insulated) = φ_Rφ_Sφ_e. This may provide a method for measuring changes in the work-function while monitoring surface composition.     

Calculations of vacancy formation energies and divacancy binding energies for noble metals using pseudopotential formalism

Vacancy formation energies (E^f_1v) and divacancy binding energies (E^B_2v) for noble metals have been calculated using the Moriarty's pseudopotential. While the calculated E^f_1v are coincident with the experimental values except Cu, E^B_2v agree with them for all the metals tolerably.     

Vacancy induced changes in the electronic structure of titanium carbide—I. Band structure and density of states

Results of a self-consistent “Augmented Plane Wave” (APW) band-structure calculation are presented for substoichiometric titanium carbide with 25% vacancies on the carbon sublattice sites (TiC_{0 75}) assuming a model structure with ordered vacancies Comparison with an earlier APW study on stoichiometric TiC reveals that the carbon vacancies induce two pronounced peaks in the density of states (DOS), 0.4 eV below and 0.8 eV above the Fermi energy E_γ, thus forming electronic states in a region where the DOS for stoichiometric TiC exhibits a minimum So-called “vacancy states” with an important amount of charge on the vacancy site are found to be derived from Ti 3d states extending into the vacancy muffin tin sphere An angular momentum decomposition with respect to the center of the vacancy muffin tin sphere shows that the s character predominates for the occupied and the p character for the unoccupied “vacancy states” The theoretical findings explain features near E_γ, observed in recently published X-ray emission spectra Furthermore, we find a slight increase of electronic charge in the carbon muffin tin spheres as compared with stoichiometnc TiC.     

Dirac quasiparticle tunneling in a NG/ferromagnetic barrier/SG graphene junction

We study the tunneling conductance in a spin dependent barrier NG/F_B/SG graphene junction, where NG, F_B and SG are normal graphene, gate ferromagnetic graphene barrier with thickness d and the graphene s-wave superconductor, respectively. In our work, the quasiparticle scattering process at the interfaces is based on quasi particles governed by the Dirac Bogoliubov–de Gennes equation with effective speed of light v_F ∼ 10⁶ m/s. The conductance of the junction is calculated based on Blonder–Tinkham–Klapwijk (BTK) formalism. The oscillatory conductance under varying gate potential and exchange energy in F_B and the conductance induced by specular Andreev reflection are studied. By taking into account both effects of barrier strengths due to the gate potential χ_G∼V_Gd/?v_F${\chi }_{\text{G}}\sim V_{\text{G}}d/?v_{\text{F}}$ and the exchange energy χ_ex∼E_exd/?v_F${\chi }_{\text{ex}}\sim E_{\text{ex}}d/?v_{\text{F}}$ in the F_B region, we find that the zero bias conductance of junction depends only on the ferromagnetic barrier strength χ_ex in F_B, when the Fermi energy in SG is very much larger than that the Fermi energy in NG (E_FS ? E_FN). The oscillatory conductance peaks can be controlled by either varying χ_ex or χ_G. In the limiting case, by setting E_ex = 0, the conductance in a NG/N_B/SG graphene junction, where SG is the s-wave superconductor, is also studied in order to compare with two earlier contradicted data. Our result agrees with what was obtained by Linder and Sudbo [J. Linder, A. Sudbo, Phys. Rev. B 77 (2008) 64507], which confirms the contradiction to what was given by Bhattacharjee and Sengupta [S. Bhattacharjee, K. Sengupta, Phys. Rev. Lett. 97 (2006) 217001].     

An investigation of the adsorption of oxygen and oxygen containing species on platinum by photoelectron spectroscopy

It is shown that XPS can detect 0.01 monolayers of adsorbed carbon or oxygen and can identify the chemical state of the adsorbed atom(s). Two states of adsorbed oxygen were resolved by thermal desorption spectroscopy and by XPS. The O 1s binding energies (^FE_B) were 530.2 and 533 eV below the platinum Fermi level for the strongly and weakly adsorbed states respectively. (^FE_B) did not vary with coverage. The resulting apparent variation of (^VE_B), the vacuum level referenced value, is discussed in terms of a simple model for the work function Φ which was measured in situ. UPS indicated that the weakly adsorbed state is probably molecular, with levels at 6.1, 9.3, 10.4 and l2.4 eV below the Fermi level. The main change in the UPS spectra produced by the strongly adsorbed state was a reduction of a peak close to the Fermi level.     

Vacancy formation energy related to liquid structure in a nonlinear scaled potential theory

Summary A scaling relation is derived for the vacancy formation energyE _v in a family of homologous systems at their melting temperatureT _m, using a pair potential theory which relatesE _v atT _m to liquid structure under the assumption that atomic relaxation round the vacancy can be neglected.

---

Riassunto Il lavoro deriva una relazione di scala per l’energiaE _v di formazione di un posto vacante in una famiglia di sistemi omologhi alla loro temperatureT _m di fusione, nell’ambito di una teoria a potenziale di coppia che legaE _v aT _m alla struttura della fase liquida nell’ipotesi che rilassamenti atomici attorno al posto vacante possano essere trascurati.

     

NMR study of hydrogen diffusion in uranium hydride

The diffusion of hydrogen in uranium hydride is studied employing the NMR technique. From measurements of spin-spin relaxation time T₂, the activation energy for hydrogen diffusion in β-UH₃ is determined to be $\text{E}{}_{\mathrm{a}}\text{= (19.25 ± 0.4)}\text{kcal}\text{mole}$ and the preexponential factor to be A₀ ≈ 5 × 10¹⁴ Hz. It is shown that these results are in fair agreement with spin-lattice relaxation time T₁ data. Assuming that hydrogen diffusion proceeds via vacancies whose concentration is temperature dependent, it is concluded that E_a is the sum of the energies of vacancy formation and barrier height, and that A₀ contains an entropy change factor. Using vacancy concentration data calculated by Libowitz, we estimate the barrier height energy to be E_b ≈7 kcal/mole. Using a value for the frequency of hydrogen vibration v₀ determined from inelastic neutron scattering by Rush et al., we estimate the entropy change due to vacancy formation and the hydrogen atom jump to be about $\text{S}\text{k}{}_{\mathrm{B}}\text{≈3}$. Similar measurements on samples containing less hydrogen than is needed to compose stoichiometric UH₃, show that the rate of diffusion is enhanced by the presence of excess metal in the sample. The jump frequency at 500°K in UH₃ is found to be approximately 10⁶ Hz while for the two-phase samples of H/U = 2.8 and 2.5, it is larger by a factor of about 3 and 3.5, respectively.     

On the vacancy in a metal

The self-consistent calculations of spatial distributions of electrons and potentials in an isolated spherical cavity (with atomic radius R _WS) of the Wigner-Seitz cell, the energy of the vacancy formation, and the vacancy contribution to the electrical resistance have been performed in terms of the modified Kohn-Sham method and the stabilized jellium model. The energy shift of the ground state of electrons in the Wigner-Seitz cell with radius R _v ? R _WS (where R _v is the average distance between vacancies), the contribution of vacancies to the electron work function, and the effective mass of electrons have been found using the calculated phase shifts of the scattering wave functions and the representation of a system of vacancies as a “superlattice” in a metal.     

Self-diffusion at grain boundaries with a disordered atomic structure

A change in the free energy of a grain boundary is analyzed in the case when lattice vacancies come to the boundary and are then delocalized in its disordered atomic structure. It is shown that the free energy of the boundary is minimized at some excess atomic volume Δv _b =Δv _b ^* , whose value depends on the energy of vacancy formation in the crystal lattice and the boundary energy. The formation of a metastable localized grain-boundary vacancy as a result of thermal fluctuations of the density in a group of n ₀=\gM_v/Δv _b atoms (\gM_v is the vacancy volume), followed by the jump of an adjacent atom into this vacancy, is taken as an elementary event of grain-boundary diffusion. Expressions for the activation energy of diffusion and the diffusion coefficient are derived for equilibrium (Δv _b =Δv _b ^* ) and nonequilibrium (Δv _b >Δv _b ^* ) boundaries.     

Structure,electronic and magnetic properties of hexagonal boron nitride sheets doped by 5d transition metal atoms: First-principles calculations and molecular orbital analysis

A first-principles calculation based on density functional theory is carried out to reveal the geometry, electronic structures and magnetic properties of hexagonal boron nitride sheets (h-BNSs) doped by 5d transitional mental atoms (Lu, Hf, Ta, W, Re, Os, Ir, Pt, Au and Hg) at boron-site (B_5d) and nitrogen-site (N_5d). Results of pure h-BNS, h-BNS with B vacancy (V_B) and N vacancy (V_N) are also given for comparison. It is shown that all the h-BNSs doped with 5d atoms possess a C_3v local symmetry except for N_Lu and N_Hg which have a clear deviation. For the same 5d dopant, the binding energy of B_5d is larger than that of N_5d, which indicates the substitution of a 5d atom for B is preferred. The total densities of states are presented, where impurity energy levels exist. Besides, the total magnetic moments (TMMs) change regularly with the increment of the 5d atomic number. Theoretical analyses by molecular orbital under C_3v symmetry explain the impurity energy levels and TMMs.     

Final state effect for Au 4f line from gold-nano-particles grown on oxides and HOPG supports

The effect of a positive charge left to a small metal particle immediately after photoemission, so called the final state effect is studied for Au 4f binding energy (E_B) shifts. The size and shape of Au nano-particles were determined by high-resolution medium energy ion scattering combined with scanning electron microscopy of a field emission type. The shape of Au nano-particles is well approximated by a partial sphere with diameter d and height h. It is found that the E_B shift is well expressed as number of atoms per particle (n_A) and independent of support species. The E_B shift changes dramatically at a critical n_A value of ∼70 atoms, where metal-nonmetal transition takes place. In the nonmetal region, the E_B shift increases steeply almost exponentially with decreasing n_A and in contrast, gradually decreases with increasing n_A in the metallic region. The effect of the positive charge of an Au 4f vacancy created by photoemission is expressed by the relaxation time τ and the effective charge +αe when the photoelectron just leaves the Au particle surface (e: electron charge, α < 1).     

Amino wagging and inversion in hydrazines: RR branch of the antisymmetric wagging band of NH2NH2

Infrared absorption spectrum of undeuterated hydrazine in the gaseous state has been observed with a resolving power better than 0.06 cm^?1 in the 1024 ～ 961 cm^?1 region, where the ^RR- and ^RQ-branch lines of the antisymmetric wagging band (v_a = 1 ← 0) appear. It has been found that every line belonging to the ^RR branch as well as every ^RQ peak of the band splits into four components, a, b, c, and d. This is explained by considering that the v_a = 0 state splits into A_I, E, and B₂ substates and the v_a = 1 state into B₁, E, and A₂ substates, because of the four equivalent potential minima (D₄) of the hydrazine molecule which are reached by inversions of the two amino groups. From the observed wave numbers of the ^RR lines, effective values of the rotational constants of the B₁, E, and A₂ sublevels of the v_a = 1 state were obtained. On the basis of these values and the ones for the A₁, E, and B₂ sublevels of the ground vibrational state, obtained from a previous microwave study, a discussion of the antisymmetric wagging-inversion coordinate is given.     

Pressure effect on structural,electronic and thermodynamic investigations of europium filled skutterudite EuFe4Sb12: LDA and LSDA approximations

Numerical calculations based on the full potential muffin-tin orbitals method (FP-LMTO) within the local density approximation (LDA) and the local spin-density approximation (LSDA) to investigate the structural, electronic and thermodynamic properties of filled skutterudite EuFe₄Sb₁₂ are presented. The electronic band structure and density of states profiles prove that this material is a conductor. The present investigation is also extended to the elastic constants, such as the bulk modulus B, anisotropy factor A, shear modulus G, young's modulus E, Poisson's ratio ν, and the B/G ratio with pressure in the range of 0–40 GPa. The sound velocities and Debye temperatures are also predicted from the above constants. The variations of the primitive cell volume, expansion coefficient α, bulk modulus B, heat capacity (C_p and C_v), Debye temperature θ_D, Helmholtz free energy A, Gibbs free energy G, entropy S, and internal energy U with pressure and temperature in the range 0–3000 K are calculated successfully.     

Camel's back induced stabilization of electron-hole liquids : GaP

A camel's back-like nonparabolicity of the longitudinal electron mass enhances the density of states and strongly stabilized an electron-hole-liquid. In GaP therefore the EHL density is doubled to 8.6 × 18¹⁸cm^?3 and the Fermi energy ratio E_F^h/E_F^e changes from 1.9 to 4.9. The theoretical binding energy agrees with the experimental E_B=17.5±3meV interpreting the luminescence at 2.30 eV as a superposition of liquid and plasma recombination radiation.     

Monte Carlo calculation of the concentration of lattice vacancies by the method of overlapping distributions

The free energy of formation of vacancies in rare gas crystals is evaluated directly from Monte Carlo simulation of a perfect crystal and a crystal containing a vacancy, without the help of intermediate systems. For solid argon at high temperature we find ΔG_v = 1970 cal/mole - 3.1 k_BT.     

Magnetic susceptibility of titanium diselenide intercalated with copper

The temperature dependence of the magnetic susceptibility of Cu _x TiSe₂ polycrystalline samples has been measured. The electron density of states near the Fermi level N(E _F) in the Pauli model of paramagnetism has been calculated and discussed. The concentration dependences of the density of states N(E _F) and the unit cell parameter in the direction perpendicular to the layers in Cu _x TiSe₂ correlate with the concentration of centers V-Ti-Cu and Cu-Ti-V (V is the vacancy).     

Comparative photoemission study of the electronic properties of L-CVD SnO2 thin films

In this work we present the results of comparative XPS and PYS studies of electronic properties of the space charge layer of the L-CVD SnO₂ thin films after air exposure and subsequent UHV annealing at 400 °C, with a special emphasis on the interface Fermi level position.From the centre of gravity of binding energy of the main XPS Sn 3d_5/2 line the interface Fermi level position E_F − E_v in the band gap has been determined. It was in a good correlation with the value estimated from the offset of valence band region of the XPS spectrum, as well as from the photoemission yield spectroscopy (PYS) measurements. Moreover, from the valence band region of the XPS spectrum and PYS spectrum two different types of filled electronic band gap states of the L-CVD SnO₂ thin films have been derived, located at 6 and 3 eV with respect to the Fermi level.     

Vacancy formation energies from positron trapping measurements

The threshold temperatureT _t at which thermally generated vacancies produce measurable positron trapping is a linear function of the energy of self-diffusionQ. SinceQ is also linearly related to the vacancy formation energyE _1v ^f , a measurement ofT _t leads directly to a determination of the latter. It is possible to make a precise determination ofE _1v ^f without approaching the melting point—a major advantage in dealing with refractories or with metals having a high vapour pressure in the solid state.