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J. Chem. Thermodynamics 39 (2007) 568–575

Thermodynamic properties of soddyite from solubilityand calorimetry measurements

Drew Gorman-Lewis a,*, Lena Mazeina b, Jeremy B. Fein a, Jennifer E.S. Szymanowski a,Peter C. Burns a,c, Alexandra Navrotsky b

a University of Notre Dame, Department of Civil Engineering and Geological Sciences, 156 Fitzpatrick Hall, Notre Dame, IN 46556, United Statesb NEAT ORU and Thermochemistry Facility, 4411 Chemistry Annex, One Shields Avenue,

University of California at Davis, Davis CA 95616-8779, United Statesc Chemistry Division, Argonne National Laboratory, Argonne, IL 60439, United States

Received 27 July 2006; received in revised form 6 September 2006; accepted 7 September 2006Available online 14 September 2006

Abstract

The release of uranium from geologic nuclear waste repositories under oxidizing conditions can only be modeled if the thermody-namic properties of the secondary uranyl minerals that form in the repository setting are known. Toward this end, we synthesized soddy-ite ((UO2)2(SiO4)(H2O)2), and performed solubility measurements from both undersaturation and supersaturation. The solubilitymeasurements rigorously constrain the value of the solubility product of synthetic soddyite, and consequently its standard-state Gibbsfree energy of formation. The log solubility product (lgKsp) with its error (1r) is (6.43 + 0.20/�0.37), and the standard-state Gibbs freeenergy of formation is (�3652.2 ± 4.2 (2r)) kJ mol�1. High-temperature drop solution calorimetry was conducted, yielding a calculatedstandard-state enthalpy of formation of soddyite of (�4045.4 ± 4.9 (2r)) kJ Æ mol�1. The standard-state Gibbs free energy and enthalpyof formation yield a calculated standard-state entropy of formation of soddyite of (�1318.7 ± 21.7 (2r)) J Æ mol�1 Æ K�1. The measure-ments and associated thermodynamic calculations not only describe the T = 298 K stability and solubility of soddyite, but they also canbe used in predictions of repository performance through extrapolation of these properties to repository temperatures.� 2006 Elsevier Ltd. All rights reserved.

Keywords: Soddyite; Uranyl silicate; Gibbs free energy; Enthalpy; Entropy; Solubility; Supersaturation; Solubility product; Calorimetry

1. Introduction

Uranyl silicates are common constituents of the alteredportions of U deposits, and are important for understand-ing the genesis of such deposits as well as the mobility ofuranium in the environment [1]. Uranyl silicate mineralsconsist of three structurally and chemically distinct groups[2,3]. The uranophane group is the most abundant, andeach of their structures contains sheets of uranyl polyhedraand silicate tetrahedra, with lower-valence cations and H2Ogroups located in the interlayer regions. The weeksite

0021-9614/$ - see front matter � 2006 Elsevier Ltd. All rights reserved.

doi:10.1016/j.jct.2006.09.005

* Corresponding author. Present address: Argonne National Labora-tory, CHM 200, 9700 S Cass Avenue, Argonne, IL 60439, United States.Tel.: +1 630 252 3653.

E-mail address: gorman-lewis@anl.gov (D. Gorman-Lewis).

group also corresponds to minerals with sheet structures,but the sheets contain more silicate that those of the urano-phane group. In contrast, soddyite, the chemically simplesturanyl silicate with formula (UO2)2SiO4(H2O)2, has aframework structure composed of uranyl polyhedra andsilicate tetrahedra that share vertices.

The performance of geologic nuclear waste repositorieswill be influenced by interactions between the spent nuclearfuel and the environment in which it is placed. Oxidativeweathering of commercial spent nuclear fuel under oxidiz-ing conditions, such as those expected at the proposedrepository at Yucca Mountain, will likely result in the for-mation of U(VI) mineral phases [1,2,4]; consequently, theformation and stability of U(VI) minerals will impact therelease of U(VI) from the waste package, and potentiallyalso from the repository. Uranyl minerals that form in a

D. Gorman-Lewis et al. / J. Chem. Thermodynamics 39 (2007) 568–575 569

geological repository may also incorporate radionuclidessuch as Np into their structures, potentially having a pro-found impact on the release of such radionuclides [5–7].

Finch et al. [4] examined the alteration products thatformed after groundwater dripped onto the spent nuclearfuel in a laboratory setting for six years at T = 363 K.The experiments used two pressurized-water-reactor fuels,ATM103 and ATM106, with corresponding burn-uphistories of �30 MWd Æ kg�1 U and �45 MWd Æ kg�1 U,respectively. The groundwater used was from well J-13 atthe Yucca Mountain site, and was reacted with crushedTonopah Springs tuff at T = 363 K for 80 days prior touse (designated EJ-13 water). Alteration of the spent fuelin four experiments with different water injection ratesresulted in mostly uranyl compounds. These included sev-eral uranyl oxide hydrates as well as the uranyl silicatessoddyite, b-uranophane, Ca(UO2)2(SiO3OH)2(H2O)5 andNa-boltwoodite, (Na,K)(UO2)(SiO3OH)(H2O)1.5. In simi-lar experiments, Wronkiewicz et al. [8,9] examined non-irradiated UO2 placed under dripping EJ-13 water atT = 363 K for more than 10 years. Wronkiewicz et al. [9]found that the alteration phases that formed initially wereuranyl oxide hydrates, followed by uranyl silicates, a para-genetic sequence which is generally consistent with naturalanalogues.

Despite the potential importance of U(VI) silicate min-erals in the performance of a geologic nuclear waste repos-itory under oxidizing conditions, reliable thermodynamicdata are lacking for most of these minerals. In order topredict the stability and solubility of U(VI) silicate mineralsas a function of solution composition (pH, ionic strength,etc.) and temperature, it is necessary to know thestandard-state Gibbs free energy, enthalpy, and entropyof formation for each phase of interest. These thermody-namic parameters are crucial for predicting repositoryperformance.

Soddyite is a common uranyl silicate in nature, and hasbeen found as an alteration product of spent nuclear fuelunder moist oxidizing conditions [4]. Previous studies ofthe solubility of soddyite have produced a wide range ofsolubility product values. Nguyen et al. [10] and Mollet al. [11] reported lgKsp (solubility product) values of(5.74 ± 0.21) and (6.15 ± 0.53), respectively, for batch dis-solution experiments. Perez et al. [12] reported a wide rangeof values for the lgKsp, with values from 2.58 to 6.36, forexperiments conducted in the presence of dissolved Naand Si. Despite three separate studies measuring the solu-bility of soddyite, there is a lack of an accepted value forthe solubility product. Part of the problem stems from defi-ciencies in the previous studies. Reliable thermodynamicparameters can be derived from solubility studies onlywhen the following conditions are met: (1) the mineral ofinterest is stable under the experimental conditions, (2) atrue equilibrium state is attained during the experiments,and (3) the pH and metal concentrations present in theequilibrium state are measured. The first condition shouldbe established by characterizing the mineral phase both

before and after the solubility experiment using X-ray dif-fractometry (XRD) and/or other spectrometry approaches.The attainment of equilibrium can only be demonstratedvia reversibility experiments; that is, approaching the equi-librium state from supersaturated as well as from undersaturated conditions with respect to the dissolved speciesof interest. All previous studies of the solubility of soddyitehave neglected to demonstrate at least one of the abovethree conditions.

The Gibbs free energy of formation of a phase, coupledwith the enthalpy of formation of that phase, can be usedto calculate the standard entropy of formation. With thesethermodynamic parameters, the stability and solubility ofthe phase can be calculated as a function of temperature.High-temperature oxide-melt solution calorimetry has beenapplied successfully in order to determine the standardenthalpies of formation of some uranyl minerals [13–15].In this study, we synthesized soddyite using mild hydro-thermal conditions and thoroughly characterized the min-eral using X-ray diffractometry (XRD), Fouriertransform infrared (FT-IR) spectroscopy, thermogravime-try, and chemical analysis. Using batch experiments, wemeasured the solubility of soddyite from undersaturationand supersaturation between pH 3.0 and 3.6, and we char-acterized the post-experimental mineral residue. High-tem-perature oxide-melt solution calorimetry was used toobtain the heat of drop solution of soddyite in moltensodium molybdate. Although the early studies of uranylminerals by high-temperature calorimetry were successful,the same method cannot be applied to uranyl silicatesbecause of the lack of solubility of SiO2 in sodium molyb-date. Thus, a slightly modified calorimetric method, inwhich the solvent is saturated with SiO2 prior to the exper-iment, was developed. Using the calorimetric and solubilitymeasurements, we calculate the T = 298 K standard-stateGibbs free energy, enthalpy, and entropy of formationfrom the elements of soddyite.

2. Experimental materials and methods

2.1. Syntheses

Soddyite for the solubility experiments was synthesizedby placing 0.42 g UO2(CH3COO)2(H2O)2 (prepared fromheating �0.5 g UO3 (Strem Chemicals) with �600 cm3 gla-cial acetic acid (Fisher ACS grade)), 0.25 cm3 of 1 MNa2SiO2(H2O)5 (Fisher Chemicals ACS grade), and4.75 cm3 of 18 MX H2O in a 23 cm3 Teflon-lined Parr reac-tion vessel. This method yielded a run product thatincluded both soddyite and amorphous silica, so a secondapproach was used to produce solids for the drop solutioncalorimetry in order to eliminate as much amorphous silicafrom the run product as possible. The calorimetry solidswere synthesized by placing 0.21 g UO2(CH3COO)2(H2O)2,0.25 cm3 of 1 M Na2SiO2(H2O)5, and 4.75 cm3 of 18 MXH2O in a 23 cm3 Teflon-lined Parr reaction vessel. For bothtypes of syntheses, the reactants were heated to T = 389 K

570 D. Gorman-Lewis et al. / J. Chem. Thermodynamics 39 (2007) 568–575

for 7 days. The products were recovered by filtration andrinsed 4 times with boiling 18 MX H2O. The syntheses wererepeated multiple times to produce enough powder for theexperiments. Soddyite containing amorphous silica wasused to determine the final state of soddyite in the calori-metric solvent sodium molybdate. The pure soddyite sam-ple was used for calorimetric measurements withoutadditional treatment.

Cristobalite used in high-temperature calorimetry wassynthesized by heating quartz (Fluka, 0.999 mass fractionpurity of metal basis) at T = 1773 K for 60 h. XRD showedcomplete conversion to cristobalite.

2.2. Characterization

The X-ray powder diffraction patterns were collectedfor each batch of soddyite by finely grinding �5 mg ofpowder and depositing the paste onto a zero-backgroundorientated quartz slide. Diffraction patters were collectedusing a Bruker D8 Discovery diffractometer equippedwith Cu Ka radiation and a solid-state detector. Allpowder diffraction patterns exhibited sharp profiles andno extraneous peaks, and they confirmed the presenceof soddyite as the only crystalline phase in the syntheses.FT-IR analyses were performed using an IlluminatIRFT-IR micro-spectrometer with a diamond total attenu-ated reflectance (ATR) objective in an open atmosphere,background spectra taken prior to measurement, over afrequency range of (400 to 4000) cm�1 using �(5 to10) mg of powder placed on a glass slide. The IR spectrawere in good agreement with previously published spectrafor soddyite by Cjeka and Urbanec [16] and amorphoussilica (determined from FT-IR analysis of silica gel).Thermogravimetry (t.g.a.) and differential scanning calo-rimetry (d.s.c.) analyses were carried out by heating thepowder to T = 983 K at 10 K Æ min�1 under flowing argonat 50 cm3 Æ min�1. Two consecutive runs were performedwith the sample mass between 12 mg and 14 mg. Watercontent was calculated from the weight loss. Soddyitedehydrates at approximately T = 673 K. The water con-tent calculated from the weight loss upon heating was(5.52 ± 0.15) wt%, which represents (2.05 ± 0.06) H2Omolecules per mole of soddyite, consistent within experi-mental error with the ideal stoichiometry for soddyite of(UO2)2SiO4 Æ 2H2O. The molecular weight correspondingto the ideal stoichiometry is used for further calculations.Chemical analyses were performed by dissolving �(50 to100) mg of powder in �17 cm3 of 2 M HCl and analyzingfor U and Si concentrations by inductively coupledplasma-optical emission spectrometry (ICP-OES) with ananalytical uncertainty of 3.5%. The chemical analysis ofthe soddyite that was synthesized for the solubility exper-iments indicated a slight excess (�7.1%) of Si that weattribute to the presence of an amorphous silica phase.The parallel ICP-OES analysis of the soddyite that wassynthesized for the drop solution calorimetry did not exhi-bit excess Si.

2.3. Solubility experiments

All solubility measurements were batch experimentsconducted in Teflon reaction vessels. An Orion combina-tion pH electrode that was calibrated daily with 4 NISTstandards was used for pH measurements. Although theionic strength of the buffers was not perfectly matchedto the ionic strength of the experiments the additionalerror associated with pH measurements as a result ofthe difference in ionic strength and liquid-junction erroris likely much smaller than experimental error whichdominates the stated uncertainties for the calculated ther-modynamic parameters. All the experiments were con-ducted at pH values less than 3.9 in order to increasedissolution reaction kinetics. The low pH conditions alsoenabled us to operate under conditions where UO2þ

2 is thedominant uranium species in solution [17,18], therebyeliminating the complexities in aqueous uranium specia-tion that occur under higher pH conditions. In order tofurther decrease the time necessary to reach equilibrium,we started the experiments in solutions containing dis-solved U and Si. The initial experimental solutions wereprepared by taking aliquots of silica atomic absorptionspectroscopy standard and uranyl nitrate stock solution,prepared from adding uranyl nitrate hexahydrate to18 MX Æ cm3 H2O, and diluting to the desired concentra-tions. Approximately �350 mg of soddyite were addedto �7 cm3 of the prepared U and Si starting solution.The pH of the batch experiments was adjusted using min-ute quantities of 15 M HNO3 (0.999 mass fraction purityof metal basis), and was continuously monitored through-out each experiment. Reaction vessels were sealed andagitated slowly end over end. Aliquots of the experimentalsolution were taken at various intervals, filtered with0.1 lm nylon filters, and diluted for ICP-OES analysisof U and Si concentrations with an analytical uncertaintyof 3.5%. In order to verify the composition of the mineralresidue after 7 days of reaction, and at the end of theexperiment, �10 mg of residue was taken for XRD andFT-IR analyses. Control experiments, performed withoutmineral phases present, indicated that the loss of U andSi due to adsorption or precipitation reactions under theexperimental conditions was negligible. Initial experimen-tal results indicated that soddyite was stable under theexperimental conditions, but that amorphous silica wasalso forming in the reactors. Consequently, we preparedsubsequent experiments as described above and added(200 to 300) mg of amorphous silica gel in order toincrease the kinetics of the amorphous silica precipitationreaction. The co-existence of two phases (soddyite andamorphous silica) in the experimental systems is consis-tent with the Gibbs phase rule for a two-component sys-tem such as these. As long as both phases are stable underthe experimental conditions and we measure all dissolvedelement concentrations, the experimental measurementsrigorously constrain the value of the solubility productsfor each phase present.

TABLE 1Calorimetric cycle for calculation of enthalpy of formation of soddyite

Reaction Heat effect (values are in table 2)

(UO2)2(SiO4) Æ 2H2Oxl,298 K = 2UO3sln,976 K + SiO2xl,976 K + 2H2Og,976 K DH1 = DHds(soddyite)

UO3xl,298 K = UO3sln,976 K DH2 = DHds(UO3)

SiO2cristobalite,298 K = SiO2xl,976 K DH3 = DHds(cristobalite)

H2Ol,298 K = H2Og,976 K DH4 = DHds(H2O)

2UO3xl,298 K + SiO2xl,298 K + 2H2Ol,298 K = (UO2)2(SiO4) Æ 2H2Oxl,298 K DH6 ¼ DH �f ;oxðsoddyiteÞ ¼ �DH 1 þ 2DH 2 þ DH3 þ 2DH4

Uxl,298 K + 3/2O2g,298 K = UO3xl,298 K DH7 ¼ DH �fðUO3ÞSixl,298 K + O2g,298 K = SiO2cristobalite,298 K DH8 ¼ DH �fðSiO2ÞH2g,298 K + O2g,298 K = H2Ol,298 K DH9 ¼ DH �fðH2OÞ2Uxl,298 K + Sixl,298 K + 2H2g,298 K + 5O2g,298 K = (UO2)2(SiO4) Æ 2H2Oxl,298 K DH10 ¼ DH�fðsoddyiteÞ ¼ DH 6 þ 2DH7 þ DH8 þ 2DH9

xl, solid material; g, gaseous; sln ,solution; and l, liquid.

30

40

50

60

70

80

500 10 20 30 40

m (SiO2 / mg

ΔHso

ln /

(kJ.

mo

l-1)

)

FIGURE 1. Plot of enthalpy of solution for cristobalite against the massof SiO2 in the solvent. At approximately (25 to 30) mg the value of dropsolution reaches the value of heat content of cristobalite (43 kJ Æ mol�1

[21]).

D. Gorman-Lewis et al. / J. Chem. Thermodynamics 39 (2007) 568–575 571

2.4. High-temperature oxide-melt solution calorimetry

The calorimetry of soddyite was performed using a cus-tom-built Tian-Calvet high-temperature micro-calorimeter[19,20]. Pellets were dropped into a Pt crucible containinga melt of composition 3Na2O Æ 4MoO3 at T = 976 K. Toprovide stirring, prevent local saturation, speed the dissolu-tion, and to maintain an oxidizing atmosphere, oxygen wasflushed over the solvent (30 cm3 Æ min�1) and bubbledthrough the solvent (3 to 3.5) cm3 Æ min�1. To accelerateprecipitation of SiO2 (see discussion below) and to obtainconsistent values of DHds, 50 mg of cristobalite were addedto the solvent prior to dropping the samples. The measuredenthalpies of drop solution, DHds, were used to calculateenthalpies of formation using the calorimetric cycledepicted in table 1. References phases were cristobalite(dropped into sodium molybdate at the same conditionsas described above for soddyite), H2O [21] and UO3 [30].

We have observed previously that silica does not dis-solve readily in sodium molybdate, and that the oxidativedissolution of silicon nitride precipitates as cristobalite.To further constrain the final state of SiO2 in sodiummolybdate (necessary for writing a well-defined thermody-namic cycle for the heat of formation of soddyite), a seriesof experiments was performed. In these experiments, amor-phous silica (SiO2 Æ xH2O with x = 1.2 to 1.6, Alfa Aesar,0.995 mass fraction purity on metals basis), quartz, cristo-balite (synthesized as described above) and soddyite(containing �7 wt% amorphous SiO2) were dissolved intomolten sodium molybdate. The solvent was then quenchedand dissolved in an abundance of water. The collected pre-cipitates were then checked by XRD to determine thephase(s) present.

3. Results and discussion

3.1. High-temperature oxide-melt solution calorimetry

Recovery of a silicate-rich precipitate from the sodiummolybdate indicated the presence of cristobalite underexperimental conditions, demonstrating the instability ofamorphous silica under these conditions. After quartz reac-tion, the run sediment contained quartz as a major phase

and cristobalite as a minor admixture, indicating a slowtransition of quartz to cristobalite during the experiment.Measured values of DHds for cristobalite (see figure 1)and quartz gradually decreased, indicating that the appar-ent value of DHds strongly depends on SiO2 concentrationin the solvent and that the solvent is saturated whenapproximately (25 to 30) mg of SiO2 are dropped. The heateffect after the solvent was saturated showed values close tothe heat content of SiO2, indicating that no silica dissolved.Calorimetry of cristobalite in sodium molybdate that wasinitially saturated with amorphous silica (�500 mg in20.0 g of sodium molybdate) exhibited nearly constant val-ues with an average for six drops of (40.7 ± 0.6) kJ Æ mol�1,which is close to the heat content of cristobalite atT = 976 K (43.0 kJ Æ mol�1, [21]).

The XRD analysis of the precipitate after recovery ofsoddyite dissolved in sodium molybdate soddyite showedthat SiO2 from soddyite also precipitates as cristobalite,indicating that the final state of SiO2 from soddyite disso-lution is cristobalite. Thus, cristobalite was used as the ref-erence phase in the calorimetric cycle (table 1) to calculatethe enthalpy of formation of soddyite from elements, DH �f ,

TABLE 2Calorimetric data at T = 976 K in sodium molybdate. Enthalpies offormation of materials and reference phases

Material DHds/(kJ Æ mol�1) DH�f =ðkJ �mol�1ÞUO3 9.49 ± 2.3b �1223.8c

Water, H2O 69.0a �285.8 ± 0.1a

Cristobalite,SiO2 (dropped in solventpreliminary saturatedwith SiO2)

40.7 ± 0.6 (6) �908.4 ± 2.1a

Compare: 43.0a

Soddyite, (UO2)2(SiO4) Æ 2H2O 315.4 ± 3.6 (11) From oxides:�117.8 ± 4.3From elements:�4045.4 ± 4.9

a Reference [21].b Reference [31].c Reference [32].

-3.50

-3.00

-2.50

-2.00

-1.50

-1.00

0 10 20 30 40 50

t/days

lg M

FIGURE 2b. Plot of logarithm of solubility of soddyite against time forexperiments at pH 3.40 from supersaturation (filled diamonds U and opendiamonds Si) and undersaturation (filled triangles U and open trianglesSi). Silica gel was added to the experiment.

-5.00

-4.50

-4.00

-3.50

-3.00

-2.50

-2.00

-1.50

-1.00

-0.50

0.00

0 10 20 30 40 50

t/days

lg M

FIGURE 2c. Plot of logarithm of solubility of soddyite against time forexperiments at pH 3.21 (days 19 to 25) and 3.01 (days 26 and beyond)from supersaturation (filled diamonds U and open diamonds Si) andundersaturation (filled triangles U and open triangles Si). Silica gel wasadded to the experiment.

572 D. Gorman-Lewis et al. / J. Chem. Thermodynamics 39 (2007) 568–575

and oxides, DH �f ox. We used the enthalpy of drop solutionof cristobalite obtained from our work (40.7 ±0.6 kJ Æ mol�1) in these calculations.

The calculated enthalpy of formation from the binaryoxides is (�117.8 ± 4.3) kJ Æ mol�1 (table 2). Soddyite ismore stable than the mechanical mixture of its constituentoxides by 117.8 kJ Æ mol�1. Previously published values forthe enthalpies of formation from the binary oxides forrutherfordine and metaschoepite are �99.1 kJ Æ mol�1 and4.4 kJ Æ mol�1 [13,14], respectively. Soddyite is more stablethan rutherfordine and metaschoepite with respect to theenthalpy of formation from the binary oxides. The stan-dard-state enthalpy of formation from the elements ofsoddyite is (�4045.4 ± 4.9) kJ Æ mol�1.

3.2. Solubility experiments

Equilibrium was achieved within 20 days in all experi-ments as shown in figure 2. Our initial experiment (figure2a, diamond symbols) contained only soddyite added toa solution containing aqueous U and Si. The equilibriumSi concentration was 10�2.63±0.08, suggesting that Si wasbuffered in solution by amorphous silica, which has

-5.00

-4.50

-4.00

-3.50

-3.00

-2.50

-2.00

-1.50

-1.00

0 5 10 15 20 25 30 35 40

t/days

lg M

FIGURE 2a. Plot of logarithm of solubility of soddyite against time forexperiments at pH 3.67 from supersaturation (filled diamonds U and opendiamonds Si) and undersaturation (filled triangles U and open trianglesSi). Silica gel was not added to the experiment.

reported solubility values varying from 10�2.38 to 10�2.71

molal [22,23]. Subsequent XRD analysis of the mineral res-idue from this initial experiment indicated that soddyitewas the only crystalline phase present. However, FT-IRresults demonstrated the presence of amorphous silica. Inlight of these results, we chose to add silica gel, in additionto aqueous Si, to all subsequent experiments to ensure thatthe amorphous silica precipitation/dissolution reactionreached equilibrium within �20 days. Figure 2 illustratesthat the Si concentrations in all subsequent experimentswere in the range reported for the solubility of amorphoussilica. As the pH of the experiments decreased, the U con-centrations in solution increased and the Si concentrationsremained constant at a value within the range of reportedamorphous silica solubility values. The XRD and FT-IRanalyses of all subsequent experimental mineral residuesverified that soddyite was the only crystalline phase presentand that amorphous silica remained present and stable aswell.

We based our solubility calculations on the followingstoichiometry for the soddyite dissolution reaction:

TABLE 3

Solubility data used for Ksp calculations

lgU/M lgSi/M lg NO�3 =M pH Days

�1.41 �2.56 �2.46 3.12 20

�1.41 �2.57 �2.46 3.15 21

�1.39 �2.56 �2.46 3.24 22

�1.40 �2.57 �2.46 3.21 25

�1.40 �2.57 �2.46 3.23 24

�1.22 �2.45 �2.46 2.92 26

�1.20 �2.53 �2.46 2.98 31

�1.21 �2.54 �2.46 3.03 33

�1.19 �2.54 �2.46 3.02 38

�1.18 �2.52 �2.46 3.09 40

�1.18 �2.52 �2.46 3.14 43

�1.19 �2.54 �2.46 3.12 44

�1.50 �2.55 �1.97 3.19 20

�1.50 �2.56 �1.97 3.19 21

�1.49 �2.55 �1.97 3.25 22

�1.49 �2.53 �1.97 3.25 25

�1.45 �2.55 �1.97 3.25 24

�1.28 �2.42 �1.97 2.97 26

�1.27 �2.53 �1.97 3.03 31

�1.28 �2.54 �1.97 3.04 33

�1.29 �2.55 �1.97 3.06 38

�1.26 �2.53 �1.97 3.11 40

�1.20 �2.48 �1.97 3.14 43

�1.27 �2.52 �1.97 3.17 45

�2.18 �2.61 �2.05 3.44 9

�2.20 �2.62 �2.05 3.41 18

�2.17 �2.62 �2.05 3.39 22

�2.19 �2.60 �2.05 3.43 30

�2.20 �2.61 �2.05 3.43 32

�2.19 �2.61 �2.05 3.44 35

�2.21 �2.62 �2.05 3.41 38

�2.20 �2.60 �2.05 3.43 45

�2.10 �2.48 �1.84 3.34 1

�2.09 �2.53 �1.84 3.38 3

�2.10 �2.59 �1.84 3.40 8

�2.08 �2.61 �1.84 3.41 15

�2.14 �2.67 �1.84 3.42 18

�2.07 �2.58 �1.84 3.40 22

�2.10 �2.62 �1.84 3.37 30

�2.11 �2.61 �1.84 3.38 32

�2.11 �2.61 �1.84 3.40 35

�2.12 �2.61 �1.84 3.34 38

�2.13 �2.59 �1.84 3.40 45

�2.44 �2.48 �2.45 3.62 20

�2.43 �2.46 �2.45 3.63 21

�2.45 �2.51 �2.45 3.58 26

�2.48 �2.52 �2.45 3.57 27

�2.60 �2.52 �2.45 3.62 31

�2.60 �2.52 �2.45 3.62 38

�2.60 �2.50 �2.45 3.63 51

�2.62 �2.54 �2.45 3.64 73

�2.61 �2.69 �2.22 3.77 6

�2.62 �2.68 �2.22 3.75 7

�2.94 �2.67 �2.22 3.82 10

�2.61 �2.64 �2.22 3.67 11

�2.58 �2.64 �2.22 3.68 12

�2.88 �2.68 �2.22 3.77 14

�2.93 �2.62 �2.22 3.72 15

�2.61 �2.63 �2.22 3.68 16

�2.70 �2.64 �2.22 3.68 17

�2.66 �2.59 �2.22 3.60 18

�2.59 �2.58 �2.22 3.63 25

�2.50 �2.57 �2.22 3.66 32

�2.44 �2.56 �2.22 3.67 33

�2.50 �2.58 �2.22 3.67 34

D. Gorman-Lewis et al. / J. Chem. Thermodynamics 39 (2007) 568–575 573

4Hþ þ ðUO2Þ2SiO4ðH2OÞ2ðsoddyiteÞ ¼2UO2þ

2 þ SiO2ðaqÞ þ 4H2O ð1Þ

For each solubility measurement on the equilibrium con-centration plateau (compiled in table 3), we calculatedthe ionic strength of the solution from the concentrationof U and Si, the pH measurement for each sample, andthe known amount of acid added for pH adjustments.We used the extended Debye–Huckel equation to calculatethe activity coefficients, ci, for each experimental condition:

lg ci ¼�Az2

i I1=2

1þ aBI1=2þ bI ; ð2Þ

where I and zi represent the ionic strength and ionic charge,respectively, A and B are constants with values of 0.5105and 0.3285, respectively, and a and b are values for RbNO3

from Helgeson et al. [24] of 5.22 and 0.062, respectively.Parameters a and b take unique values for a particular elec-trolyte. Because we did not buffer ionic strength in theseexperiments with such an electrolyte, and because valuesof a and b have not been determined for uranyl-dominatedsystems, RbNO3 was chosen as the most reasonableapproximation to the experimental solutions, based on cat-ion size, of those for which extended Debye–Huckelparameters are calculated [24]. The standard-states em-ployed in this study for solid phases and for H2O are thepure mineral or fluid, respectively. The standard-state foraqueous species is defined as a hypothetical one molal solu-tion whose behavior is that of infinite H2O dilution. Molalactivity coefficients of neutral aqueous species are assumedto be unity. Using these standard-states, and assuming thatthe solid phase is pure and that the activity of water is unityunder the experimental conditions, the solubility productfor each data point was calculated based on the followingmass action equation:

Ksp ¼a2

UO2þ2

aSiO2ðaqÞ

a4Hþ

: ð3Þ

When calculating the solubility product, the aqueous com-plexation reactions listed in table 4 were taken into consid-eration in order to calculate the activity of the aqueousuranyl cation under each experimental condition fromour measurement of total aqueous uranium concentration.The calculated solubility product, averaged for all of theequilibrium measurements (table 3), with its 1r error is(6.43 + 0.20/�0.37). Our solubility product is within errorof some of the previously published values; however, ourstudy is the first to rigorously demonstrate attainment ofequilibrium from both supersaturation and undersatura-tion and to measure equilibrium pH and fully characterizethe final run product identification. With our calculatedsolubility product value, in conjunction with the aqueouscomplexation reactions and K values listed in table 4, weextrapolate our results to calculate uranium concentrationsin equilibrium with (soddyite + amorphous silica) at higherpH values of environmental interest (figure 3). Figure 3 de-

picts classical solubility behavior as a function of pH, withuranium concentrations reaching a minimum of approxi-mately 10�6 molal between pH 6 and 7. Calculated uranium

TABLE 4Aqueous phase U(VI) reactions considered in the calculations in this workwith PCO21/4 32 Pa

lgK

I = 0.0, T = 298 K

UO2þ2 þH2O ¼ UO2OHþ þHþ �5.20

UO2þ2 þ 2H2O ¼ UO2ðOHÞ02 þ 2Hþ �12.0a

UO2þ2 þ 3H2O ¼ UO2ðOHÞ�3 þ 3Hþ �19.2

2UO2þ2 þ 2H2O ¼ ðUO2Þ2ðOHÞ2þ2 þ 2Hþ �5.62b

3UO2þ2 þ 5H2O ¼ ðUO2Þ3ðOHÞþ5 þ 5Hþ �15.55

3UO2þ2 þ 7H2O ¼ ðUO2Þ3ðOHÞ�7 þ 7Hþ �31.0

4UO2þ2 þ 7H2O ¼ ðUO2Þ4ðOHÞþ7 þ 7Hþ �21.9

UO2þ2 þ CO2�

3 ¼ UO2CO03 9.70

UO2þ2 þ 2CO2�

3 ¼ UO2ðCO3Þ2�2 17.0UO2þ

2 þ 3CO2�3 ¼ UO2ðCO3Þ4�3 23.63

2UO2þ2 þ CO2�

3 þ 3OH� ¼ ðUO2Þ2ðCO3ÞðOHÞ�3 40.82c

H4SiO4ðaqÞ ¼ H3SiO�4 þHþ �9.83d

H4SiO4ðaqÞ ¼ H2SiO2�4 þ 2Hþ �23.0d

UO2þ2 þH4SiO4ðaqÞ ¼ UO2H3SiOþ4 þHþ �2.5e

All other stability constants from reference [36].a Reference [17].b Reference [33].c Reference [18].d Reference [34].e Reference [35].

574 D. Gorman-Lewis et al. / J. Chem. Thermodynamics 39 (2007) 568–575

concentrations would be correspondingly higher through-out the pH range if we considered the aqueous phase toequilibrate with (soddyite + quartz) due to the lower activ-ities of silica in equilibrium with quartz. These calculationsdemonstrate that soddyite is less soluble than metaschoepiteand rutherfordine in the circumneutral pH range, butconsiderably more soluble than uranyl phosphate phases[25–27].

The standard-state Gibbs free energy of formation ofsoddyite was calculated for each equilibrium measurementfrom equation the following equation:

DG�fðsoddyiteÞ ¼ 2 � DG�fðUO2þ

2Þ þ DG�fðSiO2ðaqÞÞ þ 4 � DG�fðH2OÞ � DG�r :

ð4Þ

Literature values for DG�fðUO2þ

2Þð�953:5 kJ �mol�1Þ,

DG�fðSiO2ðaqÞÞð�833:411 kJ �mol�1Þ, and DG�fðH2OÞð�237:129

-7

-6

-5

-4

-3

-2

3 4 5 6 7 8 9pH

lg U

/M

FIGURE 3. Plot of logarithm of solubility against pH for (soddy-ite + amorphous silica), determined with the Ksp value from this study andthe aqueous reactions listed in table 3.

kJ �mol�1Þ were obtained from Wagman et al. [28] andJohnson et al. [29], and DG�r for each data point was calcu-lated from the corresponding Ksp value with the followingequation:

DG�r ¼ �2:303RT � lg Ksp; ð5Þwhere R is the universal gas constant and T is absolute tem-perature. The average standard-state Gibbs free energy offormation with its 2r error is (�3652.2 ± 4.2) kJ Æ mol�1.Chen et al. [30] predicted the standard-state Gibbs freeenergy of formation of soddyite from an empirical methodthat derives the molar contributions of the structural com-ponents to DG�f and DH �f from thermodynamic data ofphases for which the crystal structures are known. Theirvalue, �3653.0 kJ Æ mol�1, agrees with our value based onour solubility measurements.

3.3. Entropy calculations

The standard-state entropy of formation of soddyite,DS�f , can be calculated from the standard-state Gibbs freeenergy and enthalpy of formation:

DG�f ¼ DH �f � TDS�f ; ð6Þ

where DG�f is the standard-state Gibbs free energy of for-mation of soddyite, as determined from the solubility mea-surements, and DH �f is the standard-state enthalpy offormation of soddyite, as determined from the calorimetrymeasurements. The calculated standard-state entropy offormation of soddyite, with propagated 2r uncertainty, is(�1318.7 ± 21.7) J Æ mol�1 Æ K�1.

Alteration of spent nuclear fuel in a geological reposi-tory under oxidizing conditions is expected to result inthe formation of a variety of uranyl minerals, and the sol-ubilities of these minerals will impact the release of ura-nium and other radionuclides that they incorporate.Therefore, it is crucial to augment the sparse thermody-namic dataset that exists for uranyl minerals in order topredict repository performance. Standard-state Gibbs freeenergies, enthalpies, and entropies of formation for envi-ronmentally important uranyl minerals can be used to esti-mate mineral stabilities and solubilities under the elevatedtemperatures of a repository setting. In this study, we cal-culated the standard-state enthalpy of formation of soddy-ite from drop solution calorimetric measurements. Wemeasured the solubility of soddyite as well, using solubilityreversals to rigorously demonstrate that equilibrium wasattained during the experiments. The solubility measure-ments were used to calculate the standard-state Gibbs freeenergy of formation of soddyite, and together with theenthalpy value, we calculated the standard-state entropyof formation of soddyite. This study demonstrates thepower of combining solubility and calorimetry measure-ments to produce reliable and internally consistent thermo-dynamic data for uranyl minerals. The results of this andfuture similar studies of other environmentally relevanturanyl phases will enable predictions of uranyl mineral

D. Gorman-Lewis et al. / J. Chem. Thermodynamics 39 (2007) 568–575 575

stabilities and solubilities under realistic repositoryconditions.

Acknowledgements

Funding for this research was provided by a US Depart-ment of Energy, Office of Science and Technology andInternational (OST&I) grant under the Source TermThrust program. Journal reviews and the comments madeby the Editor were particularly helpful in improving thepresentation of this work.

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JCT 06-203