Experimental and computational study of S segregation in Fe
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Date
2012-06
Authors
Barnard, Pieter Egbert
Journal Title
Journal ISSN
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Publisher
University of the Free State
Abstract
A systematic study was conducted to investigate the diffusion and segregation of S in bcc Fe using (i) DFT modelling and (ii) the experimental techniques Auger Electron Spectroscopy (AES) and XRay diffraction (XRD). The aim of this study was to obtain the activation energies for the segregation of sulfur (S) in bcc iron (Fe), both computationally and experimentally in order to explain the diffusion mechanism of S in bcc Fe as well as the influence the surface orientation has on surface segregation. The Quantum ESPRESSO code which performs plane wave pseudopotential Density Functional Theory (DFT) calculations was used to conduct a theoretical study on the segregation of S in bcc Fe. To determine the equilibrium lattice sites of S in bcc Fe, the tetrahedral-interstitial, octahedralinterstitial and substitutional lattice sites were considered. Their respective binding energies were calculated as -1.464 eV, -1.660 eV and -3.605 eV, indicating that the most stable lattice site for S in bcc Fe is the substitutional lattice site. The following mechanisms were considered for the diffusion of S in bcc Fe: tetrahedral-interstitial, octahedral-interstitial, nearest neighbour (nn) substitutional and next nearest neighbour (nnn) substitutional with migration energies, Em, of respectively 4.438 kJ/mol (0.046 eV), 22.48 kJ/mol (0.233 eV), 9.938±6.754 kJ/mol (0.103±0.007 eV) and 96.49±0.579 kJ/mol (1.000±0.006 eV). According to the binding and migration energy calculations, S will diffuse via a substitutional mechanism with a migration energy of 9.938±6.754 kJ/mol (0.103±0.007 eV). The three low-index planes of bcc Fe were investigated to determine the stability, the vacancy formation energy and the activation energy for each surface. Structural relaxation calculations showed that the surfaces in order of decreasing stability are: Fe(110)>Fe(100)>Fe(111) which is in agreement with surface energy calculations obtained from literature. The formation of a vacancy in bcc Fe was modelled as the formation of a Schottky defect in the lattice. Using this mechanism, the vacancy formation energies, Evac, for the Fe(110), Fe(100) and Fe(111) surfaces were respectively calculated as 267.4 kJ/mol (2.772 eV), 256.8 kJ/mol (2.662 eV) and 178.2 kJ/mol (1.847 eV). The activation energy, Q, of S diffusing via the substitutional mechanism for the Fe(100), Fe(110) and Fe(111) surfaces were respectively calculated as 277.4 kJ/mol (2.875 eV), 266.8 kJ/mol (2.765 eV) and 188.1 kJ/mol (1.950 eV). Thus it was found that the vacancy formation energy is dependent on the surface orientation and thus the structural stability of the Fe crystal. Experimental values for the activation energy of S in bcc Fe (232 kJ/mol (2.40 eV) and 205 kJ/mol (2.13 eV)) were obtained from literature confirming the nearest neighbour substitutional diffusion mechanism of S in bcc Fe. No indication is given regarding the orientation of the crystal in which the value of 232 kJ/mol (2.40 eV) was obtained while the value of 205 kJ/mol (2.13 eV) is for a Fe(111) crystal orientation. For the experimental investigation of the Fe/S system polycrystalline bcc Fe samples were studied. These samples were prepared by a new doping method by which elemental S is diffused into Fe. In order to prepare the samples by this method a new system was designed and build. Auger depth profile analysis confirms the successful doping of Fe with S using the newly proposed doping method. It was found that the S concentration was increased by 89.38 % when the doping time was doubled from 25 s to 50 s. An Fe sample doped for 50 s was annealed at 1073 K for 40 days after which the effects induced by S and the annealing of the sample were investigated by Secondary Electron Detector (SED) imaging. Results showed a 36±11 % decrease in the grain sizes of the polycrystalline Fe sample due to the presence of S. It was found that the re-crystallization rate of Fe is increased due to the presence of S. Using XRD, the Fe (100), Fe(211), Fe(110), Fe(310) and Fe(111) orientations were detected for both the un-doped and the annealed S doped Fe samples. The annealed sample showed the following percentage changes in the concentrations of the respective orientations compared to the un-doped sample: -5.180, +2.030, +16.41, +0.400, -13.66. Taking the calculated trend in surface stability for the three low-index orientations of Fe into consideration, it was found that the more stable Fe(110) orientation had increased in concentration during annealing, while the less stable Fe(100) and unstable Fe(111) orientations had decreased in concentration during annealing. AES measurements on the two samples were performed using the linear programmed heating method. The segregation parameters of S for the un-doped Fe sample are: D0=4.90×10-2 m2/s, Q=190.8 kJ/mol (1.978 eV), ΔG=-134 kJ/mol (-1.39 eV) and ΩFe/S=20 kJ/mol (0.21 eV). The segregation parameters of P obtained for the un-doped Fe sample are: D0=0.129 m2/s, Q=226.5 kJ/mol (2.348 eV). For the S doped Fe sample the segregation parameters of S were determined as: D0=1.79×10-2 m2/s and Q=228.7 kJ/mol (2.370 eV), ΔG=-145 kJ/mol (-1.50 eV) and ΩFe/S=8 kJ/mol (0.08 eV). These results showed that for the doped sample, with an increased concentration in the stable Fe(110) and a decreased concentration in the less stable Fe(100) and unstable Fe(111) orientations, a higher activation energy was obtained. Comparing the measured activation energies to the calculated values indicates that the diffusion of S occurs via a vacancy mechanism, where the S atom occupies a substitutional lattice site. Despite the fact that polycrystalline samples were analysed, the activation energies are still in the same order as the calculated activation energies of the single crystals. This confirms the theoretical prediction of a substitutional diffusion mechanism of S in bcc Fe. During this study the diffusion mechanism of S was determined as the substitutional diffusion mechanism whereby a S atom would diffuse from a substitutional lattice site to a nearest neighbour vacancy. The different Fe orientations considered in the calculations can be arranged from highest to lowest activation energy as Fe(110)>Fe(100)>Fe(111). These calculations are in agreement with the AES results which showed an increased activation energy for the doped sample having a higher Fe(110) concentration and lower Fe(111) and Fe(100) concentrations.
Description
Keywords
Iron -- Surfaces, Density functionals, Auger electron spectroscopy, Segregation (Metallurgy), Activation energy, Auger Electron Spectroscopy (AES), Binding energy, Density Functional Theory (DFT), Diffusion mechanism, Quantum ESPRESSO, Pre-exponential factor, Migration energy, Linear heating, Lattice strain, Guttmann`s model, Guttmann`s model, Fick`s model, Fe(111), Fe(110), Fe(100), Segregation energy, Sulfur (S), Surface stability, Vacancy formation energy, X-Ray Diffraction, Dissertation (M.Sc. (Physics))--University of the Free State, 2012