Lattice thermal expansion and anisotropic displacements in 𝜶-sulfur from diffraction experiments and first-principles theory

Abstract

Thermal properties of solid-state materials are a fundamental topic of study with important practical implications. For example, anisotropic displacement parameters (ADPs) are routinely used in physics, chemistry, and crystallography to quantify the thermal motion of atoms in crystals. ADPs are commonly derived from diffraction experiments, but recent developments have also enabled their first-principles prediction using periodic density-functional theory (DFT). Here, we combine experiments and dispersion-corrected DFT to quantify lattice thermal expansion and ADPs in crystalline α-sulfur (S), a prototypical elemental solid that is controlled by the interplay of covalent and van der Waals interactions. We begin by reporting on single-crystal and powder X-ray diffraction measurements that provide new and improved reference data from 10 K up to room temperature. We then use several popular dispersion-corrected DFT methods to predict vibrational and thermal properties of α-sulfur, including the anisotropic lattice thermal expansion. Hereafter, ADPs are derived in the commonly used harmonic approximation (in the computed zero-Kelvin structure) and also in the quasi-harmonic approximation (QHA) which takes the predicted lattice thermal expansion into account. At the PPBE+D3(BJ) level, the QHA leads to excellent agreement with experiments. Finally, more general implications of this study for theory and experiment are discussed.

Orthorhombic sulfur from Cap Garonne, Mine du Pradet

“…The crystal chemistry of orthorhombic S 8 and the various metastable sulfur modifications is summarized in [18] and [19]. The thermal expansion of orthorhombic sulfur has been studied through temperature-dependent X-ray powder and single-crystal diffraction data [10,16]. Our 150 K data show reasonable agreement with these studies.…”

“…One should keep in mind that these studies used sulfur from different sources, i.e. crystals grown by evaporation of a CS 2 solution [10] and microcrystalline α-S 8 that resulted from desulfurization reactions in a biorefinery [16].…”

“…The structure of the low-temperature modification, α-S 8 was first determined in 1935 by Warren and Burwell [3] using crystals grown from CS 2 solution via rotation and oscillation film data. Subsequent studies focused on precise determinations of the lattice parameters, higher accuracy structure refinements, lattice thermal expansion experiments, analyses of thermal vibrations, charge density studies as well as high-pressure experiments up to the amorphization limit [4][5][6][7][8][9][10][11][12][13][14][15][16]. The early work has competently been summarized by Donohue [17], later in reviews on all sulfur modifications by Meyer [18] and Steudel and Eckert [19].…”

Thermal Expansion in Layered Na x MO2

“…The hard-sphere model examined in this paper gives intuitive and easy comprehension of the thermal expansion behavior of the layered oxides. The density-functional-thery (DFT) calculation successfully reproduces the linear thermal expansion coefficients of several materials such as Al 75 , S 76 , 4d transition metals 77,78 , Os 78 , MgO 79 , CaO 79 , and ZnO 80 , which is beyond the scope of this paper.…”

Sublimation Properties of α,ω‐Diamines Revisited from First‐Principles Calculations

“…Although systematic convergence of ab initio cohesive energies of molecular crystals to the sub‐kJ/mol level in particular model cases of methanol, benzene, and carbon dioxide was demonstrated, none of the mentioned methods grants reaching such a high computational accuracy (and affordability at the same time) in a general case. Phenomena such as the thermal expansivity or compressibility of crystals need to be captured realistically to capture finite‐temperature/pressure properties for which the quasi‐harmonic approximation proved to be a reliable tool . Recent studies demonstrate successful applications of the computational methodologies to larger and more flexible molecules, such as selected active pharmaceutical ingredients …”