The system thorium-palladium-boron: A DFT study on the stability and properties of Th2Pd15B5

Abstract Phase relations in the Th-Pd-B system were determined via electron microprobe and X-ray powder diffraction analyses of ∼20 ternary alloys. Phase equilibria are dominated by the two high-melting thorium borides ThB4, Th1-yB6 and one ternary compound, namely τ1-Th2Pd14+xB5, with a structure deriving from the Sc4Ni29B10-type. Th1-yB6 is the binary starting point of a continuous solid solution up to ThPd0.53B4.28 closely corresponding to the superconducting phase Th1-yPdxB6-2x (x ≤ 0.65; 0 ≤ y ≤ 0.22 at x = 0; TC = 21 K), which was described by Zandbergen et al., in 1995 for x = 0.65 from high resolution electron microscopy. All thorium-rich palladium compounds from 0 to 75 at.% Pd form stable two-phase equilibria with ThB4 without any significant mutual solid solubilities. The solubility of Th in βB has been determined for the first time from a single crystal X-ray study of ThB99: Th atoms occupy sites A1 (occ. = 13%), D (occ. = 11%), and rather small amount of 2.9% in site 18f (Dd-hole). To shed light on the physical properties of the ternary compound, DFT (density functional theory) calculations were performed for two idealized representatives of the τ1-phase, namely for Th2Pd14B5 and Th2Pd15B4. The calculations cover ionic relaxation, electron density of states, band structure and Fermi surfaces, elastic constants (computed via the linear response method) and the phonon density of states. Furthermore the thermodynamic stability (energy of formation) as well as the phonon contribution of the thermodynamic properties, such as the specific heat have been calculated clearly indicating Th2Pd15B4 as the composition thermodynamically more stable than Th2Pd14B5. At the Fermi energy the Pd-d contribution is dominant for both structures, but the number of states is higher for Th2Pd15B4 with DOS(EF) = 13 states/eV/f.u. than for Th2Pd14B5 with DOS(EF) = 8.5 states/eV/f.u. The corresponding Sommerfeld constants γe = DOS(EF)kBπ2/3 = 30.55 mJ/molK2 for Th2Pd15B4 and 19.98 mJ/molK2 for Th2Pd14B5, clearly indicate metallic behavior of the τ1-phase. In addition, mechanical properties were measured for Th2Pd15B5 and compared with calculated values and data from the literature. Th2Pd15B5 on account of its high content of Pd is only slightly harder than the rather soft and almost ductile binary Pd-borides.