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Calculation of the magnetization and total energy of vandium as a function of lattice parameter
vi
ABSTRACTS OF ARTICLES TO APPEAR IN J. PHYS. CHEM. SOLIDS Received 24 August 1972 Revised 1 November 1972
4.
NON-STOICHIOMETRY IN URANIUM SESQUINITRIDE T. Fujino and H. Tagawa, Japan Atomic Energy Research Institute, Tokai-mura, Ibaraki, Japan.
A statistical model is proposed for analyzing thermodynamic properties of non-stoichiometric uranium sesquinitride. It consists of the combination of the site exclusion mechanism and cluster formation reactions. The model was applied to the three ionic possibilities of L4~U1672Nt, LJ4~U5N3 and U~N 2. By fitting the theoretical equations to the 3 experimentally observed data, it was found that the set U~7 2U~72N~,13 = 2, 1: 2 cluster gave the most satisfactory results. From 13 = 2, the upper limit of non-stoichiometry is expected to be N/U = 1.75. The result that the 1:2 clusters predominantly exist in U2 N3+~suggests the existence of UN1..~phase. The energy required for nitrogen atom for occupying the lattice site of the crystal, E, was calculated to be —209.9 kcal/mole, and the interaction energy to form clusters, E~,was —11 .O7kcal/mole. Received 18 July 1972
5.
CALCULATION OF THE MAGNETIZATION AND TOTALOF ENERGY OFPARAMETER VANDIUM AS A FUNCTION LATTICE Thomas M. Hattox, J.B. Conklin, Jr., J.C. Slater and S.B. Trickey, Williamson Hall, Department of Physics and Astronomy, University of Florida, Gainesville, Florida 32601.
Self-consistent spin-polarized APW calculations have been performed to determine the energy band structure of metallic vanadium in an assumed ferromagnetic b.c.c. structure as a function of lattice parameter. The statistical exchange (‘Xa’) and muffin-tin approximations were used. At each lattice parameter for which a calculation was performed, the Xci cohesive energy, the pressure, and the magnetization were calculated. The calculated cohesive energy and pressure agree fairly well with experiment. The calculations also correctly predict the absence of a magnetic moment for vanadium at its equilibrium lattice constant.
Vol. 12, No. 4
However, a nonmagnetic-to-magnetic transition is found to occur abruptly at a lattice constant which is about a factor of 1.25 larger than the equilibrium value, and which is in good qualitative agreement with the appearance of a local magnetic moment in certain vanadium alloys. Received 14 August 1972
6.
FORCE CONSTANT ANALYSIS OF MOLECULAR GROUPS IN APATITE SOLIDS S.R. Levitt and R.A. Condrate, Sr., Department of Ceramic Science, State University of New York College of Ceramics at Alfred University, Alfred, New York 14802. The results of normal coordinate analyses
demonstrate that the simple Urey—Bradley force field gives a reasonable representation of the potentialenergy function of PO~in pyromorphite (Pb10 (P04 )6 Cl2 but is unsatisfactory for AsO~and VO~in mimetite (Pb10 (As04)6C12) and vanad.inite (Pb10(VO4)6Cl2), respectively. Theoretical band assignments are made for PO~in pyromorphite using single Urey—Bradley force field and based on a good frequency fit, a physically reasonable set of molecular force constants and some experimental confirmation. The general order of magnitude and trends in force constants are physically realistic, The theoretical -
analysis provides additional confirmation for the 1 in the assignment of the v2 bending mode to a higherfrequency, lower-intensity bond atallow 436 cm infrared. Eigenvector calculations determination of which internal coordinates are major contributors to the various normal modes. Received 4 March 1971 Revised 31 October 1972
7.
STRUCTURAL, MAGNETIC AND NEUTRON DIFFRACTION STUDIES ON TbFe 2 —ThAI2, ThCo2 —ThAi2 AND HoCo2 —HoA12 Hans Oesterreicher, Oregon Graduate Center, 19600 N.W. W~erRd., Beaverton, OR 97005.
Both pseudobinary systems exhibit large homogeneous regions of cubic and hexagonal Laves phases. Ordering tendencies on crystallographic sites between Al and the transition metals are observed in the hexagonal type.
ABSTRACTS OF ARTICLES TO APPEAR IN J. PHYS. CHEM. SOLIDS Received 24 August 1972 Revised 1 November 1972
4.
NON-STOICHIOMETRY IN URANIUM SESQUINITRIDE T. Fujino and H. Tagawa, Japan Atomic Energy Research Institute, Tokai-mura, Ibaraki, Japan.
A statistical model is proposed for analyzing thermodynamic properties of non-stoichiometric uranium sesquinitride. It consists of the combination of the site exclusion mechanism and cluster formation reactions. The model was applied to the three ionic possibilities of L4~U1672Nt, LJ4~U5N3 and U~N 2. By fitting the theoretical equations to the 3 experimentally observed data, it was found that the set U~7 2U~72N~,13 = 2, 1: 2 cluster gave the most satisfactory results. From 13 = 2, the upper limit of non-stoichiometry is expected to be N/U = 1.75. The result that the 1:2 clusters predominantly exist in U2 N3+~suggests the existence of UN1..~phase. The energy required for nitrogen atom for occupying the lattice site of the crystal, E, was calculated to be —209.9 kcal/mole, and the interaction energy to form clusters, E~,was —11 .O7kcal/mole. Received 18 July 1972
5.
CALCULATION OF THE MAGNETIZATION AND TOTALOF ENERGY OFPARAMETER VANDIUM AS A FUNCTION LATTICE Thomas M. Hattox, J.B. Conklin, Jr., J.C. Slater and S.B. Trickey, Williamson Hall, Department of Physics and Astronomy, University of Florida, Gainesville, Florida 32601.
Self-consistent spin-polarized APW calculations have been performed to determine the energy band structure of metallic vanadium in an assumed ferromagnetic b.c.c. structure as a function of lattice parameter. The statistical exchange (‘Xa’) and muffin-tin approximations were used. At each lattice parameter for which a calculation was performed, the Xci cohesive energy, the pressure, and the magnetization were calculated. The calculated cohesive energy and pressure agree fairly well with experiment. The calculations also correctly predict the absence of a magnetic moment for vanadium at its equilibrium lattice constant.
Vol. 12, No. 4
However, a nonmagnetic-to-magnetic transition is found to occur abruptly at a lattice constant which is about a factor of 1.25 larger than the equilibrium value, and which is in good qualitative agreement with the appearance of a local magnetic moment in certain vanadium alloys. Received 14 August 1972
6.
FORCE CONSTANT ANALYSIS OF MOLECULAR GROUPS IN APATITE SOLIDS S.R. Levitt and R.A. Condrate, Sr., Department of Ceramic Science, State University of New York College of Ceramics at Alfred University, Alfred, New York 14802. The results of normal coordinate analyses
demonstrate that the simple Urey—Bradley force field gives a reasonable representation of the potentialenergy function of PO~in pyromorphite (Pb10 (P04 )6 Cl2 but is unsatisfactory for AsO~and VO~in mimetite (Pb10 (As04)6C12) and vanad.inite (Pb10(VO4)6Cl2), respectively. Theoretical band assignments are made for PO~in pyromorphite using single Urey—Bradley force field and based on a good frequency fit, a physically reasonable set of molecular force constants and some experimental confirmation. The general order of magnitude and trends in force constants are physically realistic, The theoretical -
analysis provides additional confirmation for the 1 in the assignment of the v2 bending mode to a higherfrequency, lower-intensity bond atallow 436 cm infrared. Eigenvector calculations determination of which internal coordinates are major contributors to the various normal modes. Received 4 March 1971 Revised 31 October 1972
7.
STRUCTURAL, MAGNETIC AND NEUTRON DIFFRACTION STUDIES ON TbFe 2 —ThAI2, ThCo2 —ThAi2 AND HoCo2 —HoA12 Hans Oesterreicher, Oregon Graduate Center, 19600 N.W. W~erRd., Beaverton, OR 97005.
Both pseudobinary systems exhibit large homogeneous regions of cubic and hexagonal Laves phases. Ordering tendencies on crystallographic sites between Al and the transition metals are observed in the hexagonal type.