Deliquescence of NaCl–NaNO3, KNO3–NaNO3, and NaCl–KNO3 salt mixtures from 90 to 120°C

We conducted reversed deliquescence experiments in saturated NaCl–NaNO3–H2O, KNO3–NaNO3–H2O, and NaCl–KNO3–H2O systems from 90 to 120°C as a function of relative humidity and solution composition. NaCl, NaNO3, and KNO3 represent members of dust salt assemblages that are likely to deliquesce and form concentrated brines on high-level radioactive waste package surfaces in a repository environment at Yucca Mountain, NV. Discrepancy between model prediction and experiment can be as high as 8% for relative humidity and 50% for dissolved ion concentration. The discrepancy is attributed primarily to the use of 25°C models for Cl–NO3 and K–NO3 ion interactions in the current Yucca Mountain Project high-temperature Pitzer model to describe the nonideal behavior of these highly concentrated solutions.


I. INTRODUCTION
Yucca Mountain, NV is the designated geologic repository for permanent disposal of high-level nuclear waste. Current waste package design calls for double walled containers with an inner wall of stainless steel and an outer wall of highly corrosion resistant Ni-Cr-Mo alloy, which are protected with Ti shields to prevent rocks and seepage water from contacting the containers. 1 Of concern are the corrosion resistance and long-term integrity of these metal barriers. If the Yucca Mountain site license is approved, the waste packages will be placed in tunnels several hundred meters below the ground surface in partially saturated volcanic tuff, but still well above the groundwater table. A likely source of brines that may potentially corrode metal containers and drip shields are those formed by the absorption of water by hygroscopic salts found in local and regional dust deposited during repository construction and ventilation stages.
Accurate prediction of brine formation is important for the safe disposal of radioactive waste, because brine composition is an indicator of the corrosiveness of the aqueous environment and the relationship between deliquescence relative humidity and temperature is an indicator of ''repository dryness.'' Deliquescence refers to the formation of an aqueous solution by the absorption of water by hygroscopic salt minerals. This process allows brines to form above 100°C at standard atmospheric pressure of 1.013 25 bar ͑or above 96°C and 0.9 bar at the repository elevation of 1039-1107 m; BSC, 2004a, Sec. 6.7.2.1͒. The relative humidity at which salts deliquesce is dependent on temperature and is characteristic to each salt mineral or assemblage of salt minerals. For example at 90°C, MgCl 2 deliquesces at 24% relative humidity and KCl deliquesces at 78.5% relative humidity. 2 Generally, the deliquescence relative humidity for a salt mixture is lower than the deliquescence relative humid-ity for its pure salt components. Salt deliquescence data are largely limited to 25°C for mixed salts [3][4][5] but are widely available for single salts at higher temperatures. 2 The range of brines formed by the deliquescence of hygroscopic salts found in dusts can be calculated from mixtures of the pure phases using equilibrium thermodynamics, because relative humidity is related to the activity of water and solution composition. Wolery and Wang 6 used the EQ3/6 geochemical code and the Yucca Mountain Project hightemperature Pitzer model to predict the deliquescence of salt mixtures found in Yucca Mountain dust samples collected from exploratory tunnels. The modeling results predict that mixtures of NaCl, KNO 3 , and/or NaNO 3 are the most prevalent mineral assemblages, and that inclusion of KNO 3 ͑s͒ lowers the deliquescence relative humidity from values near 70% at 25°C to values as low as 20% at 160°C. This analysis implies that concentrated brines may contact the metal container and drip shield surfaces at low relative humidity and high temperature.
In this paper we compare model predictions and experimental results of relative humidity and solution compositions for saturated NaCl-NaNO 3 -H 2 O, KNO 3 -NaNO 3 -H 2 O, and NaCl-KNO 3 -H 2 O systems from 90 to 120°C. These are benchmark experiments that can be used to assess the validity of the model calculations and Pitzer parameters that account for nonideal ion interactions in these highly concentrated solutions.

II. MODEL CALCULATIONS
Relative humidity is thermodynamically tied to solution composition through the activity of water. For water, its activity, a w , is the product of its mole fraction, x w , and its mole fraction activity coefficient, ␥ w : The mole fraction of water is dependent on the solution composition: a͒ Author to whom correspondence should be addressed; electronic mail: carroll6@llnl.gov where n w and n i are the number of moles of water and of dissolved ionic constituent i, respectively. The concentrations of the dissolved constituents are limited by the solubilities of the thermodynamically stable salt minerals. If we use halite ͑NaCl͒ as an example, then the solubility product, K NaCl , at a given temperature is dependent on the Na ϩ and Cl Ϫ concentrations and activity coefficients according to the mass balance reaction: where m i and ␥ i indicate the molality and activity coefficient of species i, with unit activity implied for the solid ͑NaCl͒. Relative humidity, RH frac , is related to activity of water through the partial pressure of water vapor, and is equivalent to where p w is the partial pressure of water vapor over an aqueous solution and p w 0 is the partial pressure of water vapor over pure water. Similarly, the activity of water is equivalent to where f w is the fugacity of water vapor over an aqueous solution and f w 0 is the fugacity of water vapor over pure water. Equating fugacity with its partial pressure: The activity of water is commonly expressed in decimal form and RH is commonly expressed as a percentage; thus RH%ϭ100ϫa w . In hydrologically unsaturated environments, the partial pressure of water cannot exceed the total pressure. The partial pressure of water is related to the vapor pressure of pure water and the activity of water by p w ϭ p w 0 a w . Both the vapor pressure of pure water and the partial pressure of water over a salt solution increase strongly with temperature above 100°C. Brines cannot exist at temperatures above the dry-out temperature, where the partial pressure of water equals the total pressure. Above the dry-out temperature only solid salt minerals and water vapor occur. Since this process is reversible, the dry-out temperature is also the deliquescence temperature for the same assemblage of salt minerals ͑note: at much lower temperature, generally 25°C or less, dry-out or ''efflorescence'' is controlled by salt mineral nucleation instead of equilibrium thermodynamics. 5 The deliquescence temperature is also equivalent to the boiling point for the saturated solution.
Brines formed by the absorption of water by deliquescent minerals are thermodynamically equivalent to brines that are saturated with respect to the same deliquescent minerals. Figures 1-5 show the model calculations of relative humidity and solution composition from 90 to 120°C versus X NO3 or X Na for the NaCl-NaNO 3 -H 2 O, the KNO 3 -NaNO 3 -H 2 O, and the NaCl-KNO 3 -H 2 O systems. For the NaCl-NaNO 3 -H 2 O system, this is done by adding soda niter (NaNO 3 ) to a halite ͑NaCl͒ saturated solution until the solution is saturated with both soda niter and halite. This represents the eutonic point for the NaCl-NaNO 3 salt assemblage. The calculation for this assemblage is completed by a complementary run in which halite is added to a soda niter saturated solution until the same eutonic point is reached. An identical approach is used for the KNO 3 -NaNO 3 -H 2 O and NaCl-KNO 3 -H 2 O systems. We use the EQ3/6 geochemical code 7 and the Yucca Mountain Project high-temperature Pitzer model. 8 Table I.

B. Reverse deliquescence experiments
We measured brine composition at controlled relative humidity for NaCl-NaNO 3 , KNO 3 -NaNO 3 , and NaCl-KNO 3 salt mixtures from 90 to 120°C as a function of X NO3 or X Na . Our experimental design mimics the model calculations in that one salt in the binary system will completely dissolve and the dissolution of the other will be limited by its solubility. We approached the equilibrium brine composition by placing identical mole fractions of dissolved ͑with about 150 g H 2 O) and solid salt mixtures in an environmental chamber ͑Ecosphere, Despatch͒ at controlled relative humidity and temperature. Under these conditions the dissolved salt mixture evaporates concentrating the solution and precipitating one of the two salts, and the solid salt mixture absorbs water dissolving the salts until equilibrium is reached.
For each run, four Teflon™ beakers containing the dissolved salts and four beakers containing the solid salts were placed into the chamber and sequential pairs of initially aqueous and initially solid beakers were sampled over time. Figure 6 shows that steady-state relative humidity and solution composition are achieved with in the first 200 h of reaction and that solution composition of initially dissolved and initially solid samples converge over the time period of the experiments. Samples were typically taken every one to three days. Calibrated temperature ͑Ϯ1°͒ and relative humidity probes ͑Vaisala Inc., model HMP243 or HMP233͒ were placed just above the solutions in the beakers, because microenvironments within the beakers differed from the environmental chamber relative humidity by as much as 5% relative humidity. Relative humidity probe calibration checks were conducted in saturated KNO 3 solutions from 90 to 110°C. Statistical analysis of these RH measurements together with vapor pressure measurements for KNO 3 ͑Ref. 12͒ yield an average standard deviation of about 1.6 RH units. Uncertainty reported in the tables and figures is calculated as 2 ͑3.1% RH units͒. TABLE I. Pitzer interaction parameters used with EQ3/6 to calculate relative humidity and solution composition in saturated brines containing Na, K, Cl, and NO 3 . Temperature dependence of each of these ion interaction parameters is derived from Eq. ͑11͒: (T)ϭa 1 ϩa 2 /(TϪT r )ϩa 3 ln(T/T r )ϩa 4 (TϪT r ). Samples were taken when there was at least 10 g of solution in each beaker. The exact amount of solution was dependent on relative humidity and solubility of the salt mixture. About 1 g of solution was collected from each beaker and filtered through a 0.45 m syringe-less filter into a sampling bottle, the bottle was sealed and weighed to determine sample amount, and then diluted with about 250 g of distilled and de-ionized water. All dilution factors were determined gravimetrically. Each time a pair of samples was taken, the temperature and relative humidity probes were moved to monitor the next pair of beakers. Solids from the fourth pair of samples were separated from the remaining solution by filtration ͑0.45 m pore size͒, dried, and stored in a desiccator until analyzed by powder x-ray diffraction.

C. Analytical techniques
All aqueous samples were analyzed by inductively coupled plasma-atomic emission spectrometry ͑ICP-AES͒ for sodium, and by ion chromatography ͑IC͒ for chloride, nitrate, potassium, and ͑for some samples͒ sodium. Analyti-cal uncertainty for the ICP-AES and the IC is less than 2%. Solids were analyzed using powder x-ray diffraction for detection of halite, sylvite, soda niter, and niter. Trace amounts of a specified solid phase indicate that the intensity of major peak was generally less than 5% of the most intense peak. We suspect that the small amount of the minor component represents solution trapped during the filtration process and not an equilibrium solid.

IV. RESULTS
The deliquescence of NaCl-NaNO 3 , KNO 3 -NaNO 3 , and NaCl-KNO 3 salt mixtures from 90 to 120°C is summarized in Tables II-VI and in Figs. 1-5. Figures 1 and 2 compare the experimental results of the reversed deliquescence experiments with the model calculations for the NaCl-NaNO 3 -H 2 O system at 90 and 110°C. Equilibrium is shown by the convergence of the measured relative humidity and solution composition for the initially dissolved and initially solid salt mixtures. At 90°C, we also show previous solubility data by Linke,13 which agrees with our results.  to the model prediction of 59% RH (X NO3 ϭ0.92). Similarly at 110°C, the experimental data suggest a deliquescence relative humidity of 52% RH (X NO3 ϭ0.9) compared to the model prediction of 56% RH (X NO3 ϭ0.97).
Although there are discrepancies in the absolute RH and solution composition, both experiment and model exhibit similar trends. Relative humidity decreases from a high value near 75% at low X NO3 to a minimum near the eutonic point. Above the eutonic point, the relative humidity increases with increasing X NO3 as the deliquescence point of pure soda niter is approached. The higher solubility of soda niter generates nitrate concentrations that are substantially higher than the chloride concentrations above X NO3 ϭ0.5. Chloride concentrations decrease with increasing X NO3 , because chloride solubility is limited by the increasing sodium concentrations from dissolving soda niter ͑the common ion effect͒.
The solids consisted of halite with trace soda niter below the eutonic and of soda niter with trace halite above the eutonic. Trace amounts of soda niter and halite probably represent residual solution that was trapped in pore spaces during the filtration process when the salts were dried. Halite should be the only solid phase present below the eutonic because the solution is saturated with respect to halite and undersaturated with respect to soda niter. Above the eutonic, soda niter should be the only solid phase present, because the solution is saturated with respect to soda niter and undersaturated with respect to halite. Only at the eutonic, where both minerals are saturated, would one expect to find both halite and soda niter. Figure 3 compares the experimental results of the re-versed deliquescence experiments with the model calculations for the KNO 3 -NaNO 3 -H 2 O system at 90°C. Similar to the NaCl-NaNO 3 -H 2 O system, the convergence between the measured relative humidity and solution composition for initially dissolved and initially solid salt mixtures indicates that equilibrium was achieved. However, there is poor agreement between experiment and model for both the relative humidity and solution composition. Experimental relative humidity values are as much as eight percentage points higher than those predicted by the model on the niter side of the eutonic (X Na Ͻ0.2). Trends in the experimental data indicate that the deliquescence relative humidity of about 42% agrees with the model prediction, but yields a more KNO 3 rich brine ͑about X Na 0.5͒ than predicted by the model. A large discrepancy between experiment and model is seen in the solution composition. Dissolved potassium, sodium, and nitrate concentrations follow similar trends as the model predictions, but the absolute concentrations are significantly higher. In the most extreme case, solution compositions are roughly twice the model prediction with experimental sodiumϭ20 molal, potassiumϭ22 molal, and nitrateϭ42 molal. The high experimental molal concentrations are not an artifact of deriving the values from solution analyses ͑see Sec. III D͒. A test of the analytical methodology using highly concentrated solutions showed that analytically and gravimetrically determined values were generally within 4% of each other. The solids consisted of niter with trace soda niter, below the experimental eutonic and of soda niter with trace niter, above the experimental eutonic. Trace amounts of soda niter or niter probably represent residual solution that was trapped in pore spaces during the filtration process when the salts were dried. Figures 4 and 5 compare the experimental results of the reversed deliquescence experiments with the model calculations for the NaCl-KNO 3 -H 2 O system at 90 and 120°C. Similar to the other salt systems studied here, the convergence between the measured relative humidity and solution composition for initially dissolved and initially solid salt mixtures indicates that equilibrium was achieved. Values for the deliquescence relative humidity are in agreement at both temperatures. This agreement at the eutonic relative humidity appears to be fortuitous, because there is poor agreement between experiment and model for relative humidity and all solution composition. The extent of the mismatch is much greater at 120°C than at 90°C. At 90°C, the greatest mismatch occurs in KNO 3 -rich solutions where the model underpredicts relative humidity by as much as five percentage points and underpredicts solution composition by as much as 4 molal ͑about 30%͒. In solutions dominated by NaCl (X Na Ͼ0.5), there is reasonable agreement between model and experiment. At 120°C, the mismatch between experiment and model relative humidity is similar to that at 90°C. However, at this higher temperature, the model significantly underpredicts the solution composition. In the most extreme case, solution compositions are roughly twice the model prediction with experimental sodiumϭ11 molal, potassiumϭ28 molal, chlorideϭ6 molal, and nitrateϭ33 molal. At 120°C, atmospheric pressure limits the experiments to 50% relative humidity, so we cannot determine if the model adequately predicts relative humidity and solution composition in NaClrich solutions.
Analysis of the solids show that sylvite ͑KCl͒ is an important solubility control near the experimental eutonic in agreement with the results of model calculations at these temperatures. At 90°C, niter, sylvite and minor amounts of halite were detected just to the left of the eutonic (0.28 рX Na р0.31), and halite, sylvite and minor amounts of niter were detected to the right side of the eutonic (0.35рX Na р0.40). As is expected, the solids consisted of niter (X Na р0.25) and halite (X Na у0.60) on their respective limbs of the phase diagram. At 120°C, solutions were saturated with repect to niter, sylvite, and halite between most of samples between 0.15рX Na у0.30. One sample at X Na ϭ0.14 contained only niter, two samples at X Na ϭ0.16 and X Na ϭ0.30 contained niter and halite, but no sylvite. Any trace amounts of salt detected probably represent residual solution that was trapped in pore spaces during the filtration process when the salts were dried.

A. Na-Cl, Na-NO 3 , and K-NO 3 high-temperature Pitzer models
The comparison of model predictions and experimental results of relative humidity and solution compositions for the NaCl-NaNO 3 -H 2 O, KNO 3 -NaNO 3 -H 2 O, and the NaCl-KNO 3 -H 2 O systems from 90 to 120°C indicate that some parameters used in the current high-temperature Pitzer model do not adequately describe brine chemistry formed by deliquescence of these salt mixtures. Before we discuss the specific data needs to resolve discrepancies between experimental results and model predictions, we review the basic high-temperature Pitzer model used in these simulations. 8 The Pitzer model is derived by first defining an expression for the excess Gibbs free energy (G ex ) of the total solution ͓Ref. 9, Eq. ͑23͔͒: where G ex is the difference or ''excess'' in the Gibbs free energy between a real solution and an ideal solution defined on the molality composition scale, R is the universal gas constant, T is the absolute temperature, w w is the mass ͑kg͒ of solvent water, f is a Debye-Hückel function that depends on the ionic strength (Iϭ1/2͚ i m i z i 2 ), i j is a second-order interaction coefficient ͑also a function of I͒, i jk is a thirdorder interaction coefficient, n denotes the number of moles of a species, and i, j, and k denote solute species. Here m denotes molality and z the charge number. Note that molality is defined as m i ϭn i /w w . Upon substitution of m i w w for n i ͑and so forth for the j and k cases͒ in Eq. ͑8͒, the ionic solute activity coefficient (␥ i ) and the solvent osmotic coefficient ͑͒ may be calculated as the partial derivatives with respect to the molality of the ionic solute and the mass of water, respectively: Ϫ1ϭϪ͑‫ץ‬G ex /‫ץ‬w w ͒ n i /RT ͚ i m i ͑10͒ ͓Ref. 9, Eqs. ͑34͒ and ͑35͔͒. The activity of water is closely related to the osmotic coefficient (ln a w ϭϪ(͚ i m i /⍀), where ⍀ is the number of moles of water comprising a 1 kg mass, approximately 55.51͒. Substitution of Eq. ͑8͒ into Eqs. ͑9͒ and ͑10͒ followed by differentiation yields the fundamental Pitzer equations for the solute activity coefficient and the osmotic coefficient ͑or alternative forms for the activity of water or the activity coefficient of water͒. See BSC 8 or Pitzer 9 for full details of the applied forms of the Pitzer equations and the corresponding practical interaction coefficients. Values for the practical interaction coefficients are generally obtained by fitting physical property measurements, such as the osmotic coefficient, the vapor pressure of water over salt solutions, or ͑less com-monly͒ mineral solubilities.
The model requires only two-ion (␤ MX once their values have been determined for a particular system, the same values may be used for all other relevant systems. 9 The high-temperature Pitzer model 8 employed in the present study uses the following equation to represent the temperature dependence of each of these ion interaction parameters: where represents any of the above-noted practical interaction parameters, 13 T r is the reference temperature ͑298.15 K͒, and a 1 , a 2 , a 3 , and a 4 are fitted coefficients. A variety of other forms are extant in the literature ͑e.g., Refs. 10, 14͒. For the model used here, 8 data taken from other models ͑see the following͒ were refit as necessary for consistency with the above temperature function. The differences associated with refitting from a different temperature function are negligible within the temperature ranges of the original fits. Although the high-temperature Pitzer model used in the present study is a fairly comprehensive one accounting for the nonideal behavior of highly concentrated electrolytes over a wide range of temperature ͑nominally 0-200°C͒, there are still significant data needs for common ions. The present model was founded on earlier high-temperature Pitzer models ͑Refs. 10, 14, and references cited by them͒, supplemented by parameter data from several other sources. 11,[15][16][17][18][19][20][21][22][23][24] It is also partly based on refitting of parametrizations from the published literature to the most widely used ͑standard͒ form of the Pitzer equations. 25 The Yucca Mountain Project high-temperature Pitzer model contains robust thermodynamic submodels for the Na-NO 3 , Na-Cl, K-Cl, Na-K, and K-Na-Cl ion interactions. The Na-NO 3 model is based on data from Ϫ37 to 152°C 11 that was refit for consistency with the standard Pitzer form. Some degradation in fit quality results from this refitting, increasing the deviation in the osmotic coefficient from about 0.01 to about 0.02. 25 Similarly, two-ion and three-ion models in the K-Na-Cl system are based on data from 0 to 300°C 10 fit using the standard Pitzer form. In contrast, the K-NO 3 and Cl-NO 3 models are based on only 25°C data 9 and there are no parameters for the Na-K-NO 3 , Na-Cl-NO 3 , or K-Cl-NO 3 ion interactions. Our experimental data in the NaCl-NaNO 3 -H 2 O system indicate that temperature dependent parameters for Cl-NO 3 and/or Na-Cl-NO 3 ion interactions are needed to describe the relative humidity and the solution composition near the eutonic where maximum solubilities are approached. The absence of temperature dependent parameters for K-NO 3 ion interactions in the Yucca Mountain Project high-temperature Pitzer model is the primary cause of the poor prediction of the deliquescence of salt mixtures containing KNO 3 at elevated temperatures ͑Figs. 3-5͒ as well as the measured % relative humidity and solubility of KNO 3 at elevated temperature ͑Fig. 7͒. Additionally, some of the mismatch in the NaCl-KNO 3 -H 2 O system may also be due to the absence of temperature dependent paramaters for Cl-NO 3 , Na-Cl-NO 3 , and/or K-Cl-NO 3 ion interactions, in addition to the absence of temperature dependent K-NO 3 ion interaction parameters.

B. Implications for radioactive waste disposal
It is important that geochemical calculations of the chemical environment at the waste package surfaces use a robust high-temperature Pitzer ion interaction model for common ions, because the deliquescence of aerosol salts and dust is likely to be a primary source of brines that contact the waste containers and drip shields. In addition to the discrepancy identified for relative humidity and solution composition for salt mixtures containing KNO 3 stemming from the use of a constant temperature model for K-NO 3 interactions, discrepancies for magnesium and ammonium salt mixtures at elevated temperatures are likely because the model includes constant temperature models for many of their respective ion interactions. 8 Osmotic and activity coefficients must be experimentally determined as a function of temperature to derive the ion interaction parameters needed to describe the nonideal behavior of these concentrated solutions, because the Pitzer model is empirically based. Of the salt systems listed above, robust models for potassium salts are probably the most important at high temperature, because magnesium FIG. 7. Comparison of predicted and measured niter (KNO 3 ) ͑a͒ % relative humidity and ͑b͒ solubility as a function of temperature. Measured data are from Kracek 12 and Linke, 13 respectively. Predictions were made using EQ3/6 version 8 geochemical code and the Yucca Mountain high temperatured Pitzer ion interaction thermodynamic database ͑Refs. 6 and 8͒.
concentrations are likely to be limited by insoluble silicate minerals 26 and ammonium concentrations are likely to be limited by gas volatility.
Recent modeling efforts by the Yucca Mountain Project predict that mixtures of NaCl, KNO 3 and/or NaNO 3 are the most prevalent mineral assemblages that may deliquesce in repository environments using the current high-temperature Pitzer model. 8 As the temperature increases, the deliquescence relative humidity and the NO 3 concentrations increase ͑Fig. 7͒. We expect only small differences between predicted and actual deliquescence relative humidity and brine composition at temperatures below 60°C, because the model adequately predicts niter solubility at these temperatures. However, at higher temperatures, much larger differences between predicted and actual environment are expected, because the model underpredicts niter solubility by about 200% at 135°C ͓Fig. 7͑b͔͒. At these temperatures the current Pitzer model will significantly underpredict brine NO 3 brine composition because the K-NO 3 interactions will be more important. This is clearly illustrated in our KNO 3 -NaNO 3 and NaCl-KNO 3 deliquescence experiments, where NO 3 concentrations can be twice the predicted concentrations. Additionally, it is likely that calculated deliquescence relative humidities for the three salt system are of limited accuracy, because the current model for KNO 3 is of limited accuracy at high temperature ͑Fig. 8͒. Therefore calculated dry-out or deliquescence temperatures are uncertain. Dry-out or deliquescence temperatures made assuming a total pressure similar to current atmospheric pressure ͑0.90 bar͒ predict that a brine saturated with NaCl, NaNO 3 , and KNO 3 would boil just above 135°C. 6

VI. CONCLUSIONS
Adsorption of water by deliquescent salt minerals found in aerosols and dusts that may be deposited on waste package surfaces during the construction and ventilation stages of a high-level radioactive waste repository at Yucca Mountain, NV, will be a primary source of brines that might lead to corrosion of the waste package surfaces. Although the deliquescence relative humidity of most pure salt minerals is known over a range of temperature, the behavior of salt mixtures at elevated temperatures is unknown. Our reversed deliquescent experimental results in saturated NaCl-NaNO 3 -H 2 O, KNO 3 -NaNO 3 -H 2 O, and NaCl-KNO 3 -H 2 O systems from 90 to 120°C show that use of 25°C parameter values for K-NO 3 and Cl-NO 3 ͑and possibly for three-ion parameters in the Na-K-Cl-NO 3 sys-tem͒ in the Yucca Mountain Project high-temperature Pitzer model do not accurately predict the equilibrium solubility and corresponding relative humidity of KNO 3 salt mixtures and of NaCl-NaNO 3 mixtures near the eutonic composition.
FIG. 8. Model predictions of brine ͑a͒ % relative humidity and ͑b͒ solution composition as a function of temperature at the deliquescence point for a NaCl-NaNO 3 -KNO 3 mineral assemblage ͑Ref. 8͒. Predictions were made with EQ3/6 geochemical code and the high temperature Pitzer ion interaction thermodynamic data base. Triangles, circles, squares, and diamonds represent NO 3 , Na, K, and Cl concentrations.