Theoretical studies of the ground state properties of the first-row transition metals (Sc to Zn) are conducted using the Stuttgart TB-LMTO ESC program. The standard deviation of the calculation precision errors (CPE's) and the magnitude of the systematic calculation errors (SCE's) in the output of the TB-LMTO ESC program are estimated. The ground state lattice parameters, local atomic magnetic moment magnitudes and bulk moduli of the first-row transition metals are calculated. Lattice parameters are found to be within 5% to 10% of experimental values, and magnetic moment magnitudes are found to be within 10% to 20% of experimental values. Bulk moduli are found to be within 60% of experimental values. Lattice parameter and magnetic moment magnitude calculations are most accurate when the non-local exchange-correlation functional of Hu and Langreth is used. Bulk modulus calculations are most accurate when conducted using the exchange-correlation functional of Perdew and Yue. The TB-LMTO ESC program is also used to study the volume-controlled low-moment to high-moment (LM-HM) transition of the first-row transition metals (Sc to Ni) when they are constrained to take the FCC crystal structure. A LM-HM transition is predicted to occur in all FCC first-row transition metals if their lattice parameter is sufficiently increased. FCC Fe is found to occupy a unique position in the first-row transition metal series, as its LM-HM transition occurs when its lattice parameter is less than 2.5% larger than its ground state value. The LM-HM transition of the other FCC first-row transition metals occur when their lattice parameters are much larger or much smaller than their ground state values. It is argued that when the lattice parameters of the FCC first-row transition metals are too small, the energy bands of their valence electrons are too wide to allow magnetic moments to form within these metals. A method is proposed for calculating the Helmholtz' free energy of non-magnetic, bulk, crystalline solids consisting of a single chemical species. The method assumes only that an inter-atomic interaction potential can be derived from the minimum total energy versus lattice parameter curve of a solid using results published by Chen, Chen and Wei, and that this potential can accurately reproduce the energy increase that occurs when the atomic nuclei of the solid move away from their equilibrium positions as they undergo small amplitude thermal oscillations. The method is entirely theoretical as the minimum total energy versus lattice parameter curve of a solid can be calculated entirely from first principles using an ESC program. Within the method, the atomic nuclei of a solid are treated in a quasi-harmonic approximation, either as independent harmonic oscillators, or as coupled harmonic oscillators. The thermal expansion of metallic Cu is studied using the proposed method for calculating the Helmholtz' free energy of solids in conjunction with the TB-LMTO ESC program. The lattice parameter versus temperature curve of metallic Cu can be accurately calculated using the method, but its accuracy is sensitive to the functional form of the calculated minimum total energy versus lattice parameter curve of FCC Cu and to the range of the inter-atomic interaction potential. The results of these calculations suggest that the range of the inter-atomic interaction potential extends only to first nearest neighbour atomic nuclei in the metallic Cu solid. These results also suggest that the curvature of the minimum total energy versus lattice parameter curve of FCC Cu is most accurate when the curve is calculated using the exchange-correlation functional of Perdew and Yue even though the ground state lattice parameter of metallic Cu is most accurately predicted using the exchange-correlation functional of Hu and Langreth. However, it may be that imposing a short range to the inter-atomic interaction potential and that using the minimum total energy versus lattice parameter curve obtained with the exchange-correlation functional of Perdew and Yue simply better cancels the errors introduced in the calculation as a result of the quasi-harmonic approximation, as a result of not knowing the correct range of the inter-atomic interaction potential, and as a result of inaccuracies in the calculated minimum total energy versus lattice parameter curve of FCC Cu. Future research efforts should be focussed on the evaluation of the effect of these three factors on the accuracy of the method. We also recommend a direct evaluation of the accuracy of the energy increase that occurs when the atomic nuclei of the solid are displaced slightly from their equilibrium positions, as reproduced using the inter-atomic interaction potential constructed using the results of Chen, Chen and Wei.
| Identifer | oai:union.ndltd.org:uottawa.ca/oai:ruor.uottawa.ca:10393/29881 |
| Date | January 2009 |
| Creators | Prevost, Jean-Paul L |
| Publisher | University of Ottawa (Canada) |
| Source Sets | Université d’Ottawa |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | 307 p. |
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