American Mineralogist, Volume 84, pages 650–664, 1999 The Gibbs free energies and enthalpies of formation of U6+ phases: An empirical method of prediction FANRONG CHEN,1,* RODNEY C. EWING,1,2,† AND SUE B. CLARK3 1Department of Nuclear Engineering and Radiological Sciences, University of Michigan, Ann Arbor, Michigan 48109-2104, U.S.A. 2Department of Geological Sciences, University of Michigan, Ann Arbor, Michigan 48109-1063, U.S.A. 3Department of Chemistry, Washington State University, Pullman, Washington 99164, U.S.A. ABSTRACT Uranyl minerals form as a result of the oxidation and alteration of uraninite, UO2+x. These uranyl phases are also important alteration products of the corrosion of UO2 in used nuclear fuels under oxidizing conditions. However, the thermodynamic database for these phases is extremely limited. The Gibbs free energies and enthalpies for uranyl phases are estimated based on a method that sums 0 0 polyhedral contributions. The molar contributions of the structural components to ∆Gf and ∆Hf are derived by multiple regression using the thermodynamic data of phases for which the crystal struc- tures are known. In comparison with experimentally determined values, the average residuals associ- 0 0 ated with the predicted ∆Gf and ∆Hf for the uranyl phases used in the model are 0.08 and 0.10%, respectively, well below the limits of uncertainty for the experimentally determined values. To ana- 0 lyze the reliability of the predicted ∆Gf values, activity-activity diagrams in SiO2-CaO-UO3-H2O and 0 CO2-CaO-UO3-H2O systems at 298.15 K and 1 bar were constructed using the predicted ∆Gf,298.15 values for the relevant U6+ phases. There is good agreement between the predicted mineral stability 0 relations and field occurrences, thus providing confidence in this method for the estimation of ∆Gf 0 6+ and ∆Hf of the U phases. INTRODUCTION during the alteration and matrix corrosion of the UO2. Some of UO2 under oxidizing conditions is not stable and rapidly the radionuclides are incorporated into the secondary uranyl forms a wide variety of uranyl oxyhydroxides, silicates, phos- phases (Frondel 1958; Finch and Ewing 1991, 1992; Burns et phates, carbonates, and vanadates depending on groundwater al. 1997a, 1997c) and, in fact, these phases may become the compositions (Langmuir 1978; Finch and Ewing 1992). The primary source term for the release of radionuclides. Thus, the paragenesis and stability of these phases have long been of paragenesis, structures, and stabilities of these phases are of interest with many studies emphasizing the role of oxidation critical importance in evaluating the long-term behavior of and reduction reactions in the formation of uranium deposits spent nuclear fuel in a repository under oxidizing conditions. (McKelvey et al. 1955; Garrels and Christ 1959; Garrels and Unfortunately, the thermodynamic database for these ura- Weeks 1959). However, there has been renewed interest in these nyl phases is limited and in some cases contradictory (Grenthe phases because they form as alteration products in uranium et al. 1992). There is an immediate need to be able to estimate tailings and on used nuclear fuel under oxidizing conditions thermodynamic parameters and solubility constants. This pa- (Wronkiewicz et al. 1992). The nuclear fuel consists predomi- per represents an effort to estimate by regression analysis the 0 0 nantly of UO2, but fission and neutron-capture reactions result standard Gibbs free energies (∆Gf ) and enthalpies (∆Hf ) of in approximately 4% fission products and actinides after a burn- formation of U6+ phases based on their structural components. up of 40 MWd/kgU (Barner 1985; Johnson and Shoesmith Although the present experimental data are limited and the dif- 1988; Johnson and Werme 1994; Oversby 1994). In the pres- ferent types of uranyl polyhedra were not treated separately in ence of an oxidizing aqueous phase, especially involving this analysis, this approach allows one to utilize all data pres- radiolytically produced oxidants, the alteration rate of spent ently available and will allow for the immediate refinement of fuel is appreciable (Shoesmith and Sunder 1992; Sunder et al. estimated thermodynamic values as new experimental data 1998). A critical issue is the fate of the released radionuclides become available. We also identify phases for which future structural analysis and additional thermodynamic data will pro- vide the greatest impact on the development of the required *Permanent address: Guangzhou Institute of Geochemistry, database. Additionally, the estimated values may be used when Chinese Academy of Sciences, Wushan, Guangzhou 510640, suitable samples are not available for experimental determina- P.R. China. tions (i.e., uranyl phases that commonly occur as fine-grained †E-mail: [email protected] mixtures of variable composition). 0003-004X/99/0004–0650$05.00 650 CHEN ET AL.: STABILITY OF U6+ PHASES 651 For silicate minerals, many approaches exist for estimating vations for the occurrences of these minerals. However, be- 0 0 ∆Gf (Karpov and Kashik 1968; Chen 1975; Nriagu 1975; Tardy cause this method used the ∆Gf of a specific mineral to derive and Garrels 1974, 1976, 1977; Mattigod and Sposito 1978; the gi of a constituent oxide (except UO3 and H2O), the errors 0 0 Sposito 1986) and ∆Hf (Hemingway et al. 1982; Vieillard and in the ∆Gf values propagate through the derived gi, and the gi 0 Tardy 1988). Most of these methods are based on the observa- derived in this way depends, partly, on the selected ∆Gf and the 0 0 tion that the ∆Gf and ∆Hf of minerals can be estimated by sum- sequence by which each gi is derived. ming, in stoichiometric proportions, the contributions of sim- In addition, hexavalent uranium, U6+, is almost always com- 2+ pler constituent components. Because the contributions of the bined with two O atoms to form an independent UO2 uranyl 0 0 oxide and hydroxides to ∆Gf and ∆Hf largely depend on the cation (Evans 1963). This approximately linear “dioxocation” coordination numbers of the cations involved, the oxide or is the only form of hexavalent uranium in solution (Baran 1992) hydroxide of the same cation with different coordination num- and also predominates in solid phases (Burns et al. 1997b). In 0 0 4+ ber should be treated differently. In this study, the ∆Gf and ∆Hf contrast to Si , which almost always occupies tetrahedral sites of U6+ minerals are considered to be the sum of oxide polyhe- in silicate structures, the uranyl cation is coordinated by four, dral contributions that were determined by multiple linear re- five, or six anions in an approximately coplanar arrangement gression. This method is similar to that developed by Chermak (Burns et al. 1996, 1997b) to form Urφ4, Urφ5, or Urφ6 bipyramidal 0 0 and Rimstidt (1989) for estimating the ∆Gf and ∆Hf of silicate polyhedra (Ur: uranyl ion; φ: anion) with the oxygen atoms that minerals. are part of the uranyl ion located at the opposing apices. These uranyl polyhedra are proposed to be treated as different struc- PREVIOUS WORK tural components in this paper. Moreover, molecular water and The empirical method developed by Chen (1975) was structural hydroxyl must be treated differently due to their dis- 0 tinctive structural functions. The previous methods did not con- adopted by Hemingway (1982) to estimate the ∆Gf of uranyl silicates. For silicate minerals, the error of estimation made by sider the different coordinations of the cations and, thus, are best this method is, in most cases, <0.6% and seems slightly larger used within a group of structurally similar phases. for uranyl silicates. Van Genderen and Van Der Weijden (1984) The approach proposed in this paper offers the following applied the method developed by Tardy and Garrels (1976) to advantages over previous estimation techniques. (1) The struc- uranyl phases. It is based upon the linear relationship between tural component-summation technique provides smaller uncer- two parameters, ∆O and ∆F (∆O is the difference of the Gibbs tainty relative to the oxide-summation technique if the coordi- ∆ 0 ∆ 0 free energies of formation of the oxide and the aqueous cation nation of the cation is considered. (2) The Gf and Hf may be for a specific element in the mineral; ∆F is the Gibbs free en- estimated even though data for representative phases in simi- ergy of the formation reaction of a mineral from the constitu- lar structural classes are not available because each type of ent oxides and the acids). This method is applicable only within cation polyhedron is considered to possess a set of well-de- a mineral group with the same structure (i.e., coordinations for fined properties (Hazen 1985, 1988). (3) Small errors in indi- all the cations are the same in the structure) because minor vidual data of the reference phases can be reduced through the differences in the structure of the same mineral group can have averaging provided by multiple regression. Although different appreciable influences on the empirical relationships between types of uranyl polyhedra were treated as a single structural ∆O and ∆F. Considering the complexity of uranyl phases and component owing to the present limitations of the thermody- the scarcity of reliable thermodynamic data for these phases, namic database, the predicted results using this approach are the application of this approach is limited. in better agreement with geological observations than those of 0 6+ previous studies and will facilitate further improvement as more Recent attempts to estimate ∆Gf for U minerals have been made by Finch (1997) and Clark et al. (1998). Both used a accurately determined thermodynamic data for uranyl phases method similar to that developed by Tardy and Garrels (1974) with uranium in different coordinations become available. 0 for estimating the ∆Gf for silicate minerals. This method is based on the assumption that a particular constituent oxide makes the FICTIVE STRUCTURAL COMPONENTS 0 same contribution to the ∆Gf for all minerals considered; thus, A fictive structural component is a cation coordination poly- 0 the ∆Gf of a mineral is the arithmetic sum of its constituent hedron with a similar structural function, and it may be ex- oxide contributions.