Table of Contents
ISRN Materials Science
Volume 2011, Article ID 680785, 8 pages
http://dx.doi.org/10.5402/2011/680785
Research Article

Estimating Free Energies of Formation of Titanate ( M 𝟐 T i 𝟐 O πŸ• ) and Zirconate ( M 𝟐 Z r 𝟐 O πŸ• ) Pyrochlore Phases of Trivalent Lanthanides and Actinides

1Department of Electrical and Biomedical Engineering, M.S. 258, University of Nevada, Reno, NV 89557, USA
2Department of Civil and Environmental Engineering, University of Nevada, Reno, NV 89557, USA

Received 29 March 2011; Accepted 25 May 2011

Academic Editors: C. S. Ha, M. Polverari, and M. C. Somani

Copyright © 2011 Anpalaki J. Ragavan and Dean V. Adams. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A linear free energy relationship was developed to predict the Gibbs free energies of formation ( Ξ” 𝐺 0 𝑓 , M v X , in kJ/mol) of crystalline titanate (M2Ti2O7) and zirconate (M2Zr2O2) pyrochlore families of trivalent lanthanides and actinides (M3+) from the Shannon-Prewitt radius of M3+ in a given coordination state ( π‘Ÿ M 3 + , in nm) and the nonsolvation contribution to the Gibbs free energy of formation of the aqueous M3+ ( Ξ” 𝐺 0 𝑛 , M 3 + ). The linear free energy relationship for M2Ti2O7 is expressed as Ξ” 𝐺 0 𝑓 , M v X = 0 . 0 8 4 π‘Ÿ M 3 + + 8 2 . 3 0 Ξ” 𝐺 0 𝑛 , M 3 + βˆ’ 3 6 4 0 . The linear free energy relationship for M2Zr2O7 is expressed as Ξ” 𝐺 0 𝑓 , M v X = 0 . 0 8 3 π‘Ÿ M 3 + + 8 3 . 1 3 Ξ” 𝐺 0 𝑛 , M 3 + βˆ’ 3 9 2 0 . Estimated free energies were within 0.73 percent of those calculated from the first principles for M2Ti2O7 and within 0.50 percent for M2Zr2O7. Entropies of formation were estimated from constituent oxides (J/mol), based on an empirical parameter defined as the difference between the measured entropies of formation of the oxides and the measured entropies of formation of the aqueous cation.