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Browsing Physics by Author "Barnard, Pieter Egbert"

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    ItemOpen Access
    Experimental and computational study of S segregation in Fe
    (University of the Free State, 2012-06) Barnard, Pieter Egbert; Terblans, J. J.; Swart, H. C.; Hoffman, M. J. H.
    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.
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    ItemOpen Access
    An investigation on surface segregation of S in Fe and a Fe-Cr alloy using computational models and experimental methods
    (University of the Free State, 2014-11) Barnard, Pieter Egbert; Terblans, J. J.; Swart, H. C.
    English: A systematic investigation is conducted to determine the influence of the microscopic effects of the bcc Fe lattice on the segregation parameters, Q, D0, ΔG and Ω. These microscopic effects include the dependence of the surface orientation on the activation energy of diffusion, Q, and the layer dependence of the segregation parameters in the surface (atomic layer 1) and near surface atomic layers (atomic layers 2-4). The formation of vacancies in the low-index orientations of bcc Fe namely: Fe(100), Fe(110) and Fe(111) were considered to form via the Schottky defect mechanism. This mechanism resulted in an orientation dependence of the vacancy formation energy and also the activation energy of diffusion. Bulk activation energies for the segregation of Sulphur (S), as calculated by Density Functional Theory (DFT), for the Fe(110), Fe(100) and Fe(111) orientations are 2.86 eV (276 kJ/mol), 2.75 eV (265 kJ/mol) and 1.94 eV (187 kJ/mol) respectively. Experimental data obtained by Auger Electron Spectroscopy (AES) and Time-of-Flight Secondary Ion Mass Spectrometry (TOF-SIMS) confirmed the orientation dependence of the activation energy of diffusion. Furthermore, AES results revealed the orientation dependence of the pre-exponential factor (D0), the segregation energy (ΔG) and interaction parameter (Ω). DFT calculations are performed to investigate the layer dependence of the segregation parameters in the first 4 atomic layers of Fe(100), a phenomenon termed the “surface effect”. Results indicate that all the segregation parameters depend on the atomic layer in which either the S or Chrome (Cr) impurities reside. Both S and Cr have very small activation energies of respectively 1.39 eV (134 kJ/mol) and 1.62 eV (156 kJ/mol) for segregation from atomic layer 2 to 1. These low activation energies are responsible for the surface “dumping effect”, whereby S and Cr were “dumped” into the surface layer. S segregated from atomic layer 3 to 2 with an activation energy of 2.97 eV (287 kJ/mol), the highest activation energy value for the crystal and the rate limiting factor for S segregation in Fe(100). Cr had the highest activation energy for segregation from atomic layer 4 to 3 with a value of 4.16 eV (401 kJ/mol) forming the rate limiting step for Cr segregation in Fe(100). Segregation energies of S are observed to increase from a 0.00 value in atomic layer 5 to a positive value of 0.07 eV (6.51 kJ/mol) in atomic layer 3 and a value of 0.21 eV (20.7kJ/mol) in atomic layer 2. Atomic layer 1, the surface layer, has a negative segregation energy of -1.93 eV (-186 kJ/mol) indicating the favourable segregation of S to the Fe(100) surface. Cr segregation energies increase monotonically from the bulk up to atomic layer 2, with a value of 0.47 eV (45.3 kJ/mol), and then decrease to a value of 0.18 eV (17.6 kJ/mol) in the surface layer. Thus, segregation of Cr in Fe is observed to be unfavourable due to the positive segregation energies. The interaction energies obtained for S and Cr confirms the behaviour predicted by the segregation energies, with S being a strong segregant and Cr segregation being unfavourable. Simulations incorporating the segregation parameters, calculated by DFT, in combination with the Modified Darken Model (MDM) reveals the macroscopic segregation of S in Fe(100) and the desegregation of Cr in Fe(100). Segregation experiments performed by AES on the Fe(100) and Fe(111) single crystals confirms the layer dependence of the segregation parameters. Fitting of the MDM to the segregation data of S in Fe(100) and Fe(111) shows that the conventional MDM fails to provide a truly accurate description of the segregation profile. Incorporation of the layer dependence, the “surface effect”, of the segregation parameters provides an accurate description of the observed segregation data. Segregation of S and Cr is studied in the ternary Fe-Cr-S alloy by TOF-SIMS measurements. Results reveal the segregation of Cr as a result of Cr and S co-segregating towards the surface. At high temperatures (> 900 K) S desegregates into the bulk lattice while the concentration of Cr in the surface layer is observe to increase. This observed cosegregation of Cr and S in Fe is explained by the interaction parameters between Cr and S as calculated by DFT. In the bulk lattice Cr and S experience a strong positive interaction resulting in S “drawing” Cr from the bulk towards the surface. In the surface layer these two species however experience a strong negative interaction resulting in the desegregation of S. These results provide a possible explanation of the observed discrepancies that exist in literature concerning the desegregation of Cr in Fe. Furthermore it provides evidence for the presence of the “surface effect” responsible for the layer dependency of the segregation parameters.