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.
Afrikaans: ‘n In-diepte studie is uitgevoer om die invloed van die bcc Fe kristal se mikroskopiese eienskappe op die segregasie parameters, naamlik Q, D0, ΔG en Ω, te ondersoek. Hierdie mikroskopiese eienskappe behels die invloed van die oppervlakoriëntasie op die aktiveringsenergie vir diffusie, Q, asook die lagie-afhanklikheid van die segregasieparameters in die oppervlaklaag (atomlaag 1) en naas-oppervlaklae (atoomlae 2- 4) van die kristal. Die vorming van leemtes in die lae-indeks oriëntasies van bcc Fe, naamlik die Fe(100), Fe(110) en Fe(111) oriëntasies, is beskou as die vorming van ‘n Schottky defek. Hierdie meganisme lei tot die oriëntasie-afhanlikheid van die leemte vormings energie en dus ook die aktiveringsenergie van diffusie. Die aktiveringsenergie vir swawel (S) in die bulk van die Fe(100), Fe(110) en Fe(111) oriëntasies, bereken deur gebruik te maak van Digtheids Funksionele Teorie (DFT), is 2.86 eV (276 kJ/mol), 2.75 eV (265 kJ/mol) en 1.94 eV (187 kJ/mol) onderskeidelik. Hierdie berekende oriëntasie-afhankliheid van die aktiveringsenergie is bevestig deur Auger Elektron Spektroskopie (AES) en Vlugtyd Sekondêre Ioon Massa Spektrometrie (“TOF”-SIMS) metings. Die data toon verder ook dat daar ‘n oriëntasie-afhanklikheid in die pre-eksponensiële faktor, D0, die segregasieenergie, ΔG, asook die interaksieparameter, Ω, bestaan. DFT berekeninge is aangewend om die lagie-afkankliheid van die segregasieparameters in atoomlagies 1 tot 4 van die Fe(100) oriëntasie te ondersoek. Hierdie verskynsel was vir die eerste keer in die betrokke studie ondersoek en is benoem as die “oppervlakverskynsel”. Resultate van die segregasieparameters vir beide S en Chroom (Cr) toon ‘n definitiewe lagie-afhankliheid. Die aktiveringsenergie vir elk van hierdie elemente vir segregasie van atoomlaag 2 na 1 is baie klein, met waardes van onderskeidelik 1.39 eV (134 kJ/mol) en 1.62 eV (156 kJ/mol) vir S en Cr. Dus, segregasie van beide S en Cr vanaf atoomlaag 2 na atoomlaag 1 vind teen ‘n baie hoë tempo plaas en dit kan beskou word dat die onderskeidelike elemente vanaf atoomlaag 2 na 1 “oorgestort” is, genoem die “oorstortingseffek”. Segregasie van S vanaf atoomlaag 3 na 2, ondervind ‘n aktiveringsenergie van 2.97 eV (287 kJ/mol), die grootste aktiveringsenergie van al die atoomlagies, en vorm dus die tempo-bepalende stap vir S segregasie in Fe(100). Cr segregasie in Fe(100) ondervind die grootste aktiveringsenergie met ‘n waarde van 4.16 eV (401 kJ/mol) vir segregasie van Cr vanaf atoomlagie 4 na 3, wat tot gevolg het dat hierdie die tempo-bepalende stap vir Cr segregasie in Fe(100) is. Daar is waargeneem dat die segregasie-energie van S toeneem vanaf 0.00 in atoomlaag 5 tot ‘n positiewe waarde van 0.07 eV (6.51 kJ/mol) in atoomlaag 3 en ‘n waarde van 0.21 eV (20.7 kJ/mol) in atoomlaag 2. Vanaf atoomlaag 2 na 1, daal die segregasie-energie egter dramaties na ‘n negatiewe waarde van -1.93 eV (-186 kJ/mol). Cr segregasie toon ‘n soortgelyke verskynsel waarby die segregasie-energie geleidelik toeneem vanaf die bulk en dan skerp afneem in die oppervlaklaag. Die segregasie-energie van Cr in atoomlaag 2 is 0.47 eV (45.3 kJ/mol) en daal dan skerp na ‘n waarde van 0.18 eV (17.6 kJ/mol) vir atoomlaag 1, die oppervlak atoomlaag. Hierdie data dui daarop dat S ‘n sterk segregerende element is, terwyl Cr segregasie nie sal plaasvind nie. Waardes vir die interaksieparameters bevestig die segregasie van S in Fe(100), asook die feit dat Cr segregasie in Fe(100) nie sal plaasvind nie. Inkorporering van die DFT resultate in die “Modified Darken Model” (MDM) toon die segregasieprofiel van S segregasie in Fe(100), asook die desegregasieprofiel van Cr in Fe(100). AES segregasie metings van S in die Fe(100) en Fe(111) enkelkristalle toon ‘n oriëntasie-afhankliheid op elk van die segregasieparameters. Passings op die data was uitgevoer met die konvensionele MDM en daar word gemerk dat hierdie model nie die segregasieprofiel oor die hele temperatuurgebied akkuraat kan beskryf nie. Met inagneming van die lagie-afhanklikheid van elk van die segregasieparameters, die “oppervklakverskynsel”, is ‘n akkurate beskrywing van die eksperimentele segregasieprofiel van S in beide die Fe(100) en Fe(111) oriëntasies verkry. Segregasie van S en Cr in die ternêre Fe-Cr-S allooi is ondersoek deur middel van TOFSIMS en daar is gevind dat Cr segregasie wel plaasvind in die teenwoordigheid van S. Hierdie twee elemente ko-segregeer, met S wat weer desegregeer by hoër temperature (> 900 K) terwyl die Cr oppervlakkonsentrasie toeneem. Hierdie ko-segregasie is deur middel van DFT berekeninge verduidelik as die sterk positiewe interaksie tussen Cr en S in die bulk wat daartoe lei dat S die Cr uit die bulk trek na die oppervlak toe. In die oppervlaklaag is daar egter ‘n sterk afstotende interaksie tussen S en Cr wat lei tot die desegregasie van S. Hierdie resultate bied ‘n verduideliking vir die dubbelsinnigheid wat in die literatuur bestaan oor die segregasie van Cr in Fe, en verder bevestig dit ook die teenwoordigheid van die “oppervlakverskynsel”.
University of the Free State, Cluster program: Material Science and Nanotechnology
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