Anisotropy of thermal expansion of the brannerite-type MnV 2O 6: Effect of doping with MoO 3 and Li 2O; theoretical predictions, verification, new rules

Abstract

Thermal expansion of the brannerite-type phases has been studied with the high temperature X-ray diffraction between room-temperature and the decomposition temperatures of 535–660°C. The studies involved the MnLi = Mn 1− y Li y V 2− y Mo y O 6 (0 ≤ y ≤ 1) solid solutions, including the lateral compounds MnV 2O 6 and LiVMoO 6 and the MnLi∅ = Mn 1− x− y ∅ x Li y V 2−2 x− y Mo 2 x+ y O 6 ( x max between 0.16 and 0.45) solid solutions in which Mo 6+ ions are substituted randomly for V 5+ and similarly Li 1+ and cation vacancies ∅ for Mn 2+. The results were processes with a number of computer programs and the coefficients of linear thermal expansion d 11 > d 33 ≥ d 22 along the main orthogonal X, Y, Z axes have been determined. Y coincides with the crystallographic [010] axis, X lies in the (010) plane and makes an angle α x with the crystallographic [100] of 54–82°C, depending on the temperature and composition. The values of d ii are between 0.2 × 10 −5 and 7.5 × 10 −5. On the assumption of the energy equipartition and using the bond-length-bond-energy concept some predictions concerning the anisotropy of the thermal expansion and the isomorphous substitution effect have been formulated and compared with the experimental data. On this basis the ancient empirical rule that the highest dilatation of a crystal corresponds to a direction of the longest bonds has been replaced with a number of more precise rules including (i) the thermal bond-sensitivity rule (increment ΔR% of the bond length corresponding to a given increment of the bond energy Δe is taken as a measure of the bond sensitivity), (ii) the isomorphous substitution rule, (iii) the weak link rule, (iv) the strong chain rule, and (v) the clathrate rule. A comparison of the presently proposed model of thermal expansion and the classical approaches is offered.