P. C. Schmidt

Theoretical investigations of the elastic constants in Laves phases

Abstract The bulk modulus B and the tetragonal shear modulus C ′ of the C15 Laves phases AAl 2 , A = Ca, Sc, Y, La and Gd and ZrB 2 , B = V, Cr, Fe, Co, Zn and Mo; the C14 Laves phases ZrMn 2 , ZrAl 2 , ZrCr 2 , TiCr 2 , NbCr 2 and TaFe 2 and the metals forming these Laves phases are studied theoretically by ab-initio density functional band structure calculations. Additionally, the Poisson ratios, the Young moduli, for cubic systems C 11 and C 12 and for the hexagonal phases C 11 + C 12 , C 13 and C 33 are calculated and compared with the experimental data. We also compare the results of B obtained from the augmented spherical wave method using the local density and atomic sphere approximations and the full potential linear muf-fin-tin orbitals procedure with and without the generalized gradient correction for the crystal potential. All procedures give the right trend in B and the differences between experiment and theory are less than 15% for systems without a transition element and up to 25% for systems with a transition metal component. The correlation between B and the electron density ϱ I in the interstitial region of the crystal found by Moruzzi et al . for metals can be extended to B for the Laves phases and allows rules of mixture for B . For C ′ and the other elastic constants, the agreement between experiment and theory is similar for the non-transition metals but less satisfactory for the transition metals and the Laves phases with a transition metal component.

1H nuclear magnetic resonance (the magnetic susceptibility and the knight shift) in the ternary system NbTiH

Abstract By high resolution 1 H nuclear magnetic resonance Fourier transform spectroscopy on thin polycrystalline foils of 66 different compositions of b.c.c. alloys (α, α′)-Nb 1− y Ti y H x (0 ⩽ y ⩽ 0.5; 0 x ⩽ 1) the hydrogen Knight shift K H and the magnetic susceptibility were studied at T = 180 °C. The molar susceptibility χ m depends only on the valence electron concentration, in agreement with the augmented plane wave band structure calculations and application of the rigid band model. K H = f ( x , y ) cannot be explained within the frame of the rigid band model and is not simply related to the valence electron concentration.

Molecular orbital electronegativity

The molecular orbital electronegativities of a representative set of free radicals of Be, BC, N and O have been calculated for the first time using the transition operator method within the semi-empirical CNDO LCAO MO theory. The significance of the effect of delocalization on electronegativity is discussed.

Slater transition state calculations of electron affinity of heavy atoms

The spin restricted relativistic Hartree‐Fock‐Slater transition‐state method is used to predict the electron affinity of heavy atoms (Z≳54).(AIP)

Orbital electronegativity and electron affinity of rare earth atoms using Xα-theory

Slaters transition state concept and the relativistic numerical Hartree-Fock-Slater theory has been used to calculate the electronegativity and first ionization potential for the rare earth atoms. Based on these results the electron affinity has also been estimated. The theory predicts almost constant values of the electronegativity as ∼2 eV, first ionization potential as ∼8 eV and the electron affinity of ∼ -(4–5) eV respectively.

Electric field gradients in the ionic crystals NaNO2, NaBF4, NaNO3, and Ba(NO3)2

Abstract The electric field gradients (EFG) at the sites of the cations and the “central” atoms of the anions in the ionic crystals NaNO 2 , NaBF 4 , NaNO 3 and Ba(NO 3 ) 2 are calculated by a method based on a combination of the semi-empirical INDO method for the charge distribution and the intramolecular EFG with a lattice summation in the framework of the extended multipole model. At some lattice sites the contribution of the induced dipole and quadrupole moments to the EFG is comparable with the contribution of the point charges. The charge distribution within the molecular ions is found by adjusting either the calculated asymmetry parameter η or the z -component of the EFG to the experimental value deduced from nuclear quadrupole coupling constants. These charge distributions are in good agreement with those gained from INDO calculations. The calculated and experimental quadrupole coupling constants of nuclei in anions and cations are compared.

The ternary systems CuTiAl and CuZrAl around the heusler phase composition Cu2XAl (X ≡ Ti, Zr): Phase diagrams and hydrogen solubility

In the ternary systems CuTiAl and CuZrAl the phase diagrams were evaluated at 600 °C around the Heusler phase composition Cu2XAl (X ≡ Ti, Zr). Under the influence of hydrogen, Cu2TiAl decomposes to titanium hydride and γ-brass Cu8Al4, while Cu2ZrAl forms a quarternary hydride with the composition Cu16Zr6Al7Hx. By hydrogen absorption measurements (p = 1–100 bar) p-c-T diagrams were determined for the two stoichiometric compounds. The partial molar enthalpies of hydrogen absorption at infinite dilution were calculated as − 10.7 kJ (mol H)− 1 and − 12.1 kJ (mol H)− 1 for Cu2TiAl and Cu2ZrAl respectively. Partial molar excess entropies at infinite dilution of − 77.6 J K− 1 (mol H)− 1 and − 80.0 J K− 1 (mol H)− 1 for Cu2TiAl and Cu2ZrAl respectively were found. From the temperature dependence of the plateau pressure the enthalpy and entropy of decomposition of the Cu2TiAl Heusler phase were determined: ΔHd = − 43.8 kJ (mol H)− 1 and ΔSd = − 82.5 J K− 1 (mol H)− 1. From the known formation enthalpies of TiH2 − δ and Cu8 A14 and the enthalpies of hydrogen solution in Cu2TiAl and TiH2 − δ, the enthalpy of formation of the Cu2TiAl Heusler phase was calculated: ΔHf(Cu2TiAl) = − 28.9 kJ(mol M)− 1.

Temperature dependence of 1H knight shift and magnetic susceptibility of (α, α')-NbHx☆

Abstract The magnetic susceptibility χ and the 1H nuclear magnetic resonance shift KH of NbHx (0.10 ⩽ x ⩽ 0.86) were measured in the temperature range 80 °C ⩽ T ⩽ 185 °C. Within this range, χ and KH vary nearly linearly with temperature. The temperature coefficients Δχ ΔT and ΔK H ΔT vary continuously as a function of x from −3.3 × 10−9 K−1 and −2.0 × 10−3 ppm K−1 respectively for x = 0.10 to +1.5 × 10−9 K−1 and +9.5 × 10−3 ppm K−1 respectively for x = 0.86. The density of states (DOS) for niobium metal was calculated by the tetrahedron method from the self-consistent augmented plane wave band structure calculations. From the slope of the DOS curve a contribution to Δχ ΔT can be obtained which is a factor of 7 less than the experimental value. The plots KH = f(χ) for fixed x show that the hyperfine fields at the proton site have different signs for different values of x.

Molecular orbital electronegativities of transition metal fragments: a MO approach based on the transition operator method

Abstract The molecular orbital electronegativities χ of various transition metal fragments have been investigated by means of the “transition operator (TO) method” within a semi-empirical INDO Hamiltonian. The calculated electronegativities χ(TO) are discussed with respect to the donor and acceptor properties of the studied complexes. It is found that the values χ(TO) can be correlated with experimental and theoretical data concerning the nature of the chemical bond in transition metal derivatives.

Hydrogen-supported formation of G phase Cu16Zr6Al7 in the ternary system CuZrAl

The absorption of hydrogen by the alloy Cu2ZrAl leads to a structural transformation from the L21 Heusler-type phase to the quarternary G hydride phase Cu16Zr6Al7Hx(O5h(Fm3m); Z = 116 + 4x atoms). By Rietveld profile analysis of X-ray diffraction diagrams of two samples with well-defined hydrogen concentrations (x = 3.0 and x = 8.2), and by applying both the geometrical model of Westlake and the imaginary binary hydride model of Jacobs et al., information about the hydrogen occupation sequence of interstitial sites in the G phase was obtained: for Cu16Zr6Al7H3.0, a = 1195.2(1) pm, H(1) in 4a, occupation factor n = 1, H(2) in 32f3, x = 0.0901 and n = 0.25; for Cu16Zr6Al7H8.2, a = 1205.8(1) pm H(1) in 4a, n = 0.2, H(2) in 32f3, x = 0.0912 and n = 1. The change in the structure due to the incorporation of hydrogen, x = 3.0 → x = 8.2, is discussed. The results are compared with data from neutron diffraction studies of binary G phase deutendes of the rare earths (Ho6Fe23D1.5 and Y6Mn23D8.3).