Structure property relationships in the design of alloy composition: Moving beyond electron to atom ratios
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G.B. Olson Department of Materials Science, Northwestern University, Evanston, Illinois 60208-3108 (Received 18 October 2004; accepted 18 February 2005)
A model explaining the variability of oxygen solubility in the transition metals is proposed in this article. It assumes that the energy of solution can be represented as the sum of the work required to embed an oxygen atom in the electron gas of the host lattice, plus the energy generated through the formation of an oxygen anion. The latter term is treated as nearly constant across the transition metal series, leaving the work term to account for the observed variations in oxygen solubility. This work, we argue, can be approximated by the ratio of the number of metal electrons excluded from the region around the oxygen atom to the Fermi energy density of states. In turn, the number of electrons excluded by oxygen is assumed to be proportional to the charge density at the octahedral interstitial site. These assumptions allow us to define a solubility parameter that is easily determined with first-principles methods. This parameter is shown to correlate well with experimental findings regarding oxygen solubility in transition metals. Supported by these findings, we use first principle methods to identify alloying elements likely to reduce the solubility of oxygen in niobium.
I. INTRODUCTION
As in all aspects of design, alloy design begins by identifying a set of properties necessary to satisfy predefined performance goals. Once identified, the designer relies on process–structure–property relationships to devise an alloy composition and processing regime that will yield properties closest to those desired. These relationships associate a particular structure with properties and a process with structure. Through their use, it is possible to identify the structure that will give rise to a desired property and the process that will produce this structure. In essence, process–structure–property relationships allow the designer to move from desired properties to a composition and process that will produce these. Knowledge of relationships has transformed alloy development, with its dependence on expensive and time-consuming trial and error empiricism, into design. Given their importance, it is not surprising that so much effort is expended in attempts to extend our understanding of process–structure–property relationships. Structure–property relationships used in the design of
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Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/JMR.2005.0167 1330
J. Mater. Res., Vol. 20, No. 5, May 2005
alloy composition include those that correlate properties with electron to atom ratios, e/a. Hume-Rothery was among those to first stress the importance of this structural parameter, observing a correlation between e/a and the phase stability of binary alloys.1,2 However, as noted in a recent review,3 the literature is replete with references to relationships between e/a and the physical properties of metals and alloys. Included in this list are r
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