Reconstructing polar surfaces of crystals represents the pathway needed to obtain both surface stability and minimum of surface free energy. Knowing these equilibrium conditions is, in turn, necessary to interpret surface kinetics, especially when foreign adsorption or epitaxial phenomena are involved. Here we reconstructed the {00.1} dipolar surfaces of a centre-symmetrical crystal, calcite (CaCO3), either by removing one half of the ions in the outermost layer of the face, or by applying calcite to the octopolar Lacmann's model, already proposed for NaCl-like lattices. This second way respects the bulk symmetry of the crystal and was carried out by removing ¾ of the ions in the outermost layer and ¼ in the second to last one, respectively. Relaxed and athermal surface energies were determined at the empirical level and the octopolar CO3 terminated {00.1} form was the most stable. Moreover, calculation shows that the {00.1} form, along with the {10.4} and {01.2} rhombohedra, can enter the athermal equilibrium morphology of the calcite crystal. Finally, when recollecting our results on the reconstructed {01.2} form of calcite and {111} NaCl octahedron, it can be stressed that the bulk crystal symmetry has to be considered if one aims to achieve the self consistency of the surface reconstruction (Curie's principle).
24 June 2011 in American Mineralogist: Journal of Earth and Planetary Materials
Powder X-ray diffraction patterns between 90 and 935 K have been collected for nine plagioclase samples, with different compositions and degree of Al-Si order. The refined volumes have been modeled using the Wallace and Suzuki formulations based on the Mie-Grüneisen EOS. No significant difference has been found between the Suzuki and Wallace formulations, and between the Einstein and Debye approximations of lattice energy. A Wallace model with the first derivative of the bulk modulus constrained to the experimentally determined values leads to refined Grüneisen parameters between 0.49 and 0.41, without any definite trend between albite and anorthite; the Einstein temperature in intermediate plagioclase is 𝛉E ~650 K, but it is lower in albite [𝛉E = 453(5) K]. A good fit with experimental heat capacity data for the An60Ab40 composition has been found using two Einstein-like oscillators with 𝛉E1 = 230(3) K and 𝛉E2 = 952(7) K, X????E1 = 0.391(5). The change with temperature in An60Ab40 of the Grüneisen parameter is small at T > 150 K, with a slight decrease with temperature. Similar results could be obtained by independent refinement of an Einstein model with two oscillators to the volume data for the same composition [𝛉E1 = 205(30) K, 𝛉E2 = 873(52) K, and X = 0.36(4)]. The components of the thermal strain tensor with temperature have been calculated and confirm that the greatest deformation is along the a* axis, i.e., along the extension direction of the crankshaft chains of the feldspar structure. Anomalous behavior of the strain tensor components in the a-c plane has been observed in albite and An27Ab73, and is related to an increase in the c unit-cell parameter with decreasing temperature.