A critical assessment of interatomic potentials for modelling lattice defects in forsterite Mg$$_2$$SiO$$_4$$ from 0 to 12 GPa

Five different interatomic potentials designed for modelling forsterite Mg$$_2$$ 2 SiO$$_4$$ 4 are compared to ab initio and experimental data. The set of tested properties include lattice constants, material density, elastic wave velocity, elastic stiffness tensor, free surface energies, generalized stacking faults, neutral Frenkel and Schottky defects, in the pressure range $$0-12$$ 0 - 12 GPa relevant to the Earth’s upper mantle. We conclude that all interatomic potentials are reliable and applicable to the study of point defects. Stacking faults are correctly described by the THB1 potential, and qualitatively by the Pedone2006 potential. Other rigid-ion potentials give a poor account of stacking fault energies, and should not be used to model planar defects or dislocations. These results constitute a database on the transferability of rigid-ion potentials, and provide strong physical ground for simulating diffusion, dislocations, or grain boundaries.

Excess heat capacity and entropy of mixing along the hydroxyapatite-chlorapatite and hydroxyapatite-fluorapatite binaries

The heat capacity, Cp, of synthetic hydroxyapatite [Ca5(PO4)3OH–OH-Ap], as well as of ten compositions along the OH-Ap-chlorapatite (Cl-Ap) join and 12 compositions along the OH-Ap-fluorapatite (F-Ap) join have been measured using relaxation calorimetry (heat capacity option of the Physical Properties Measurement System—PPMS) and differential scanning calorimetry (DSC) in the temperature range of 5–764 K. Apatites along the Cl-OH and F-OH joins were synthesized at 1100 °C and 300 MPa in an internally heated gas pressure vessel via an exchange process between synthetic fluorapatite or chlorapatite crystals (200–500 μm size) and a series of Ca(OH)2-H2O solutions with specific compositions and amounts relative to the starting apatite. The standard third-law entropy of OH-Ap, derived from the low-temperature heat capacity measurements, is S° = 386.3 ± 2.5 J mol−1 K−1, which is ~ 1% lower than that resulting from low-temperature adiabatic calorimetry data on OH-Ap from the 1950’s. The heat capacity of OH-Ap above 298.15 K shows a hump-shaped anomaly centred around 442 K. Based on published structural and calorimetric work, this feature is interpreted to result from a monoclinic to hexagonal phase transition. Super ambient Cp up to this transition can be represented by the polynomial: $$C_{p}^{{\text{OH - Ap}}} {}_{{298K - 442K}}\left( {{\text{J mol}}^{ - 1} {\text{K}}^{- 1}} \right) = {1013.7-13735.5T^{{ - 0.5}}} + 2.616718\,10^{7} T^{{ - 2}} - 3.551381\,10^{9} T^{{ - 3}} .$$ C p OH - Ap 298 K - 442 K J mol - 1 K - 1 = 1013.7 - 13735.5 T - 0.5 + 2.616718 10 7 T - 2 - 3.551381 10 9 T - 3 . . The DSC data above this transition were combined with heat capacities computed using density functional theory and can be given by the Cp polynomial: $$C_{p}^{{\text{OH - Ap}}} {}_{{ >\,442K}}\left( {{\text{J mol}}^{ - 1} {\text{K}}^{- 1}} \right) = {877.2-11393.7 T^{ - 0.5}} + {5.452030\,10^{7}} \,T^{- {2}} - {1.394125\,10^{10}} \,T^{- {3}}$$ C p OH - Ap > 442 K J mol - 1 K - 1 = 877.2 - 11393.7 T - 0.5 + 5.452030 10 7 T - 2 - 1.394125 10 10 T - 3 . Positive excess heat capacities of mixing, ∆Cpex, in the order of 1–2 J mol−1 K−1, occur in both solid solutions at around 70 K. They are significant at these conditions exceeding the 2σ-uncertainty of the data. This positive ∆Cpex is compensated by a negative ∆Cpex of the same order at around 250 K in both binaries. At higher temperatures (up to 1200 K), ∆Cpex is zero within error for all solid solution members. As a consequence, the calorimetric entropies, Scal, show no deviation from ideal mixing behaviour within a 2σ-uncertainty for both joins. Excess entropies of mixing, ∆Sex, are thus zero for the OH-Ap–F-Ap, as well as for the OH-Ap–Cl-Ap join. The Cp–T behaviour of the OH-Ap endmember is discussed in relation to that of the F- and Cl-endmembers.

Characterisation of contact twinning for cerussite, $$\hbox {PbCO}_3$$, by single-crystal NMR spectroscopy

Cerussite, $$\hbox {PbCO}_3$$ PbCO 3 , like all members of the aragonite group, shows a tendency to form twins, due to high pseudo-symmetry within the crystal structure. We here demonstrate that the twin law of a cerussite contact twin may be established using only $$^{207}$$ 207 Pb-NMR spectroscopy. This is achieved by a global fit of several sets of orientation-dependent spectra acquired from the twin specimen, allowing to determine the relative orientation of the twin domains. Also, the full $$^{207}$$ 207 Pb chemical shift tensor in cerussite at room temperature is determined from these data, with the eigenvalues being $$\delta _{11} = (-2315\pm 1)$$ δ 11 = ( - 2315 ± 1 ) ppm, $$\delta _{22} = (-2492 \pm 3)$$ δ 22 = ( - 2492 ± 3 ) ppm, and $$\delta _{33} = (-3071 \pm 3)$$ δ 33 = ( - 3071 ± 3 ) ppm.