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Ab Initio Calculations of the Main Crystal Surfaces of Baryte (BaSO) Erica Bittarello, Marco Bruno, and Dino Aquilano Cryst. Growth Des., Just Accepted Manuscript • DOI: 10.1021/acs.cgd.8b00460 • Publication Date (Web): 24 Apr 2018 Downloaded from http://pubs.acs.org on May 8, 2018
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Crystal Growth & Design
Ab Initio Calculations of the Main Crystal Surfaces of Baryte (BaSO4) BITTARELLO Erica,*1 BRUNO Marco,2 AQUILANO Dino2
1
Dipartimento di Chimica, Università degli Studi di Torino, Via Pietro Giuria 7, 10125 Torino, Italy
2
Dipartimento di Scienze della Terra, Università degli Studi di Torino, Via Valperga Caluso 35, 10125 Torino, Italy *Corresponding author
[email protected] ABSTRACT
In this work, we revisited the theoretical morphology of baryte for determining the character (Flat, Stepped and Kinked) and the different profiles (or terminations) of the crystal faces, and presented an accurate ab initio study of the structures and surface energies at 0 K of the low-index (001), (011), (210), (101), (100), (010), (201), (012) and (211) baryte faces, by using the hybrid Hartree−Fock/density functional B3LYP Hamiltonian. According to the surface energy values, the stability order of the baryte faces was found to be (210) ≅ (001) < (211) < (101) < (010) < (011) < (201) ≅ (100) < (012). Then, the equilibrium shape of baryte was drawn and compared with the previous ones obtained at an empirical level. This is a preliminary work, which is necessary to successively evaluate the influence of water and/or impurities adsorption on the most important baryte surfaces, both at equilibrium and during growth. Indeed, to evaluate these adsorption effects on the crystal morphology, it is fundamental an in-depth analysis of the structure and energetics of the crystal faces acting as substrates.
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1. INTRODUCTION Baryte, BaSO4, is an orthorhombic sulfate, named after the Greek βαρ́ ς (heavy), due to its unusual heaviness for a non-metallic mineral.1 Baryte is a common gangue mineral in low-temperature hydrothermal veins and is typical in deposits derived from weathered baryte-bearing limestones; it is also an accessory mineral in igneous rocks and a primary component of submarine volcanogenic sulfide deposits. Baryte is commonly in association with fluorite, calcite, dolomite, rhodochrosite, gypsum, sphalerite, galena and stibnite. Usually found as thin to thick tabular {001} crystals, bounded by {210} alone or in combination with {101}, {011} or other forms. It also can display flattened {001}, and elongated to prismatic [010] or [100], and more rarely prismatic [001], or equant. Often baryte appears as massive aggregates or clusters of tabular crystals with edges projecting into crest-like forms, or as rosettes-like aggregates. Baryte is isostructural with celestine (SrSO4) and anglesite (PbSO4), its crystal structure being first determined by James and Wood.2 Sahl,3 Colville and Staudhammer4 and Hill5 refined the structural model in space group Pnma. The unit-cell parameters5 for baryte are: a0 = 8.8842(12), b0 = 5.4559(8), c0 = 7. 1569(9) Å, V = 346.904Å3, Z = 4. The structure of the baryte-celestine series was successively refined by Miyake et al.6, Jacobsen et al.7 and Antao8 to determine the structural trends that are expected across the series and the structure refinements were carried out in space group Pbnm. In this work we choose to use the crystallographic parameters by Hill 5. Commonly, baryte is used in the industries for the production of barium-hydroxide for sugar refining and as a white pigment for paper, textiles and paint.9 It is also suitable for other purposes due to its high specific gravity, opaqueness to X-rays, inertness, and whiteness10. Recently, controlled morphology and crystal growth of massive production of BaSO4 micro- and nanoparticles have been closely studied for multiple applications in medical area, in oil industry,11 electronics, TV screen, glass, car filters, paint industry and ceramics.12 Moreover, baryte is also used as space filler in automotive brake friction materials.13 The amount, the morphology and size of the baryte crystals affect the tribological properties of these materials. Therefore, the ability to control the size and morphology of the baryte crystals is of fundamental importance to produce highly efficient materials for the industry. The rich literature on baryte can be roughly divided in two large domains: experimental and theoretical. The experimental works can be, in turn, sub-divided in: I. precipitation and growth, including an averaged mass morphology14-23 2 ACS Paragon Plus Environment
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II. detailed nucleation and growth processes, including surface morphology (during both growth and dissolution)24-32 III. influence by organic and inorganic additives,33-37 or surfactants38 on the growth features of baryte. The theoretical works are mainly devoted to predict the equilibrium and growth morphology of baryte, both at 0 K and room temperature, either with or without surface relaxation.39-48 Special attention should be deserved as well to a kind of papers in which an accurate surface microtopography has been integrated by theoretical aspects concerning both the overall growth morphology and the kinetics of the steps building up the surface patterns (spirals and/or 2Dnuclei).49-55 In this work we aim at revising the theoretical morphology of baryte, (i) by applying the Hartman and Perdok39 analysis to determine the character (Flat, Stepped and Kinked) and the different profiles (or terminations) of the crystal faces, and (ii) by performing quantum-mechanical calculations to obtain their optimized structure and surface energy at 0 K and in the vacuum. We employed a hybrid Hartree-Fock (HF)-density functional theory (DFT) approach that, notably, has never before been applied to the study of baryte surfaces; in particular, the B3LYP functional was used. The following crystal faces were taken into account: (001), (011), (210), (101), (100), (010), (201), (012) and (211). This preliminary work is necessary to successively evaluate the influence of water and/or impurities adsorption on the most important baryte surfaces, both at equilibrium and during growth. Indeed, to evaluate these adsorption effects on the crystal morphology, it is fundamental an in-depth analysis of the structure and energetics of the crystal faces acting as substrates. The optimized surfaces structures to be determined in this work will be used as well, in a forthcoming paper, to calculate the adsorption energies released when water molecules or specific impurities are placed in contact with the crystal faces. This article is structured as follows: section 2 provides an outline of the computational methodology. In sections 3: (i) the Hartman and Perdok39 analysis on the main crystal faces of barite is performed, and (ii) their optimized structures and surface energies obtained at ab initio level are described and compared with the results of previous computational studies.
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2. COMPUTATIONAL DETAILS The calculations were performed with the ab initio CRYSTAL14 code56-59 and at the DFT (Density Functional Theory) level with the B3LYP Hamiltonian.60-62 In CRYSTAL14, the multi-electronic wave-function is constructed as an anti-symmetrized product (Slater determinant) of mono-electronic crystalline orbitals (COs) which are linear combinations of local functions (i.e.: atomic orbitals, AOs) centred on each atom of the crystal. In turn, AOs are linear combinations of Gaussian-type functions (GTF, the product of a Gaussian times a real solid spherical harmonic to give s-, p- and d-type AOs). In this study, oxygen was described by (8s)(411sp)-(1d) contraction63: the exponents (in bohr−2 units) of the most diffuse sp-shells are 0.59 and 0.25; the exponent of the single Gaussian d-shell is 0.5. For barium atoms, we used the pseudopotential by Hay and Wadt 64 in combination with the tightest sp-contraction from Piskunov et al.,65 and three sp-shells with exponent 0.95, 0.45, 0.17, and two d-shells with exponents 0.4 and 0.15.66 In order to test the effect of the basis set of sulphur on the geometry and energy of the crystal surfaces, we performed the calculations by using: I.
BS1: a pseudopotential67 to describe the first ten electrons and (31sp)-(1d) contraction to describe the remaining six electrons; the exponent of the diffuse sp-shell is 0.13 and that of the d-shell is 0.21.
II.
BS2: an all Gaussian-type basis sets recently developed68; it consists of a TZVP contraction that has been systematically derived for solid state systems starting from def2-TZVP69-70 basis sets devised for molecular cases.
It is important to highlight that others basis set for Ba and O were tested before to choose those above reported. Unfortunately, not one was able to reproduce in a satisfactory way the bulk structure of barite: the distances in the SO4 tetrahedra obtained at quantum-mechanical level are on average ∼7% higher than those experimentally measured. Therefore, we choose a combination of basis set that better reproduces the bulk structure and, at the same time, allows to perform the calculations in a reasonable time, compatibly with the resources of calculus actually in our hand. Further computational details (e.g., thresholds controlling the accuracy of the calculations) are given as Supporting Information. The CRYSTAL14 output files, listing the optimized fractional coordinates and optimized 2D cell parameters of the (001), (011), (210), (101), (100), (010), (201), (012) and (211) slabs, are freely available at http://mabruno.weebly.com/download. All of these slabs are charge neutral and retain either the centre of inversion or the mirror plane parallel to the (hkl) face, to ensure that the dipole 4 ACS Paragon Plus Environment
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moment perpendicular to the slab is equal to zero. The calculations were performed by considering 2D slabs56-57 with a thickness sufficient to obtain an accurate description of the surfaces. The slab thickness is considered appropriate when the bulk-like properties are reproduced at the centre of the slab. Further details are given as Supporting Information. The specific surface energy γ (J/m2) at T = 0 K was calculated by means of the relation:56-57
γ = lim Es(n) = lim →∞
→∞
()
(1)
where E(n) and Ebulk are the energy of a n-layer slab and of the bulk, respectively; A is the area of the primitive unit cell of the surface; the factor 2 in the denominator accounts for both upper and lower surfaces of the slab. Es(n) is thus the energy (per unit area) required for the formation of the surface from the bulk. When n → ∞, Es(n) will converge to the surface energy per unit area (γ). The number of dhkl layers to be considered in each slab, n, was set to values such that the relative difference between Es(n) and Es(n − 1) was
