Doctoral Degrees (Physics)

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Browsing Doctoral Degrees (Physics) by Author "Barnard, Pieter Egbert"

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    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.