Chemical Geology 401 (2015) 83–95
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The solubility of xenotime-(Y) and other HREE phosphates (DyPO4, ErPO4 and YbPO4) in aqueous solutions from 100 to 250 °C and psat Alexander P. Gysi a,⁎,1, Anthony E. Williams-Jones a, Daniel Harlov b,c a b c
Department of Earth and Planetary Sciences, McGill University, 3450 University Street, Montreal, Quebec H3A 0E8, Canada GeoforschungsZentrum, Telegrafenberg, D-14473 Potsdam, Germany Department of Geology, University of Johannesburg, P.O. Box 524, Auckland Park 2006, South Africa
a r t i c l e
i n f o
Article history: Received 1 December 2014 Received in revised form 16 February 2015 Accepted 18 February 2015 Available online 26 February 2015 Editor: Carla M Koretsky Keywords: Xenotime-(Y) Solubility product Thermodynamic properties Rare earth elements Experiments
a b s t r a c t Xenotime (YPO4) is a heavy rare earth element (HREE) phosphate, the principal host to economic HREE mineralization and a common accessory mineral in igneous, metamorphic and sedimentary rocks. Many occurrences of xenotime-(Y) are of hydrothermal origin, and therefore, determination of its solubility in aqueous fluids may help to evaluate the mobility of HREE in crustal fluids. We have measured the solubility of the HREE phosphate end-members YPO4, ErPO4, DyPO4 and YbPO4 in aqueous HClO4–H3PO4 solutions at temperatures from 100 to 250 °C and saturated water vapor pressure (psat) corresponding to the reaction: HREEPO4 = REE3+ + PO3− 4 (Ks0). The logarithm of the solubility products (logKs0) determined for these end-members, can be evaluated as a function of temperature (in K) using the equation logKs0 = A + BT + C / T + Dlog(T). Reliable fits to our data yields the following coefficients: YPO4, A = − 876.93, B = − 0.25127, C = 2.327e+4, D = 342.82; DyPO4, A = −1150.2, B = −0.31778, C = 3.132e+4, D = 450.32; ErPO4, A = −555.90, B = −0.17933, C = 1.373e+4, D = 217.42; and YbPO4, A = −419.76, B = −0.15215, C = 8.941e+3, D = 165.27. A comparison of our solubility products to those calculated with the available enthalpy, entropy and heat capacity values from calorimetric determinations, and the corresponding properties of the aqueous species (Y3+, Dy3+, Er3+, Yb3+, PO3− 4 ), shows that our solubility products for YPO4 and ErPO4 are orders of magnitude different from the calculated solubility products. By contrast, the calculated solubility products for YbPO4 are in good agreement with the measured values for the range of temperature considered in our experiments. There are no data available for the heat capacity of DyPO4, and consequently our experimental results provide the first data that permit the solubility of this HREE phosphate to be calculated for elevated temperature. We have developed a method that allows our data to be extrapolated to 25 °C and have reconciled the measured calorimetric and solubility data. The results are used to recommend standard thermodynamic properties for the HREE phosphates at 25 °C and 1 bar. © 2015 Elsevier B.V. All rights reserved.
1. Introduction Xenotime-(Y) is the most commonly occurring accessory HREE mineral in nature. In some HREE-rich mineral deposits, for example, Browns Range, Australia (Cook et al., 2013), and Lofdal, Namibia (Wall et al., 2008), it is the principal ore mineral. It is also commonly hydrothermal in origin (e.g., England et al., 2001; Schaltegger et al., 2005; Cook et al., 2013). In addition to being an important ore mineral, xenotime-(Y) is an important accessory mineral in igneous, metamorphic and sedimentary rocks, being frequently used for dating purposes or as a
⁎ Corresponding author. Tel.: +1 303 273 3828. E-mail address:
[email protected] (A.P. Gysi). 1 Present address: Department of Geology and Geological Engineering, Colorado School of Mines, 1516 Illinois Street, Golden, CO 80401, United States.
http://dx.doi.org/10.1016/j.chemgeo.2015.02.023 0009-2541/© 2015 Elsevier B.V. All rights reserved.
geothermometer (e.g., Gratz and Heinrich, 1997; Heinrich et al., 1997; Rasmussen et al., 2011). Studies of the solubility of xenotime-(Y) in aqueous fluids have been restricted mainly to the high temperatures and pressures relevant to understanding metamorphic processes (Tropper et al., 2011, 2013). Indeed, with the exception of the study of Cetiner et al. (2005), there have been no experimental studies reporting the solubility of xenotime(Y) at hydrothermal conditions. In contrast, there have been several low temperature solubility studies of synthetic hydrated HREE phosphate phases (Byrne and Kim, 1993; Firsching and Brune, 1991; Jonasson et al., 1985; Liu and Byrne, 1997). There have been, calorimetric studies of the HREE phosphates by Ushakov et al. (2001), who measured the enthalpy of YPO4, DyPO4, ErPO4 and YbPO4, and by Gavrichev et al. (2010, 2012, 2013), who measured the entropy and heat capacity of YPO4, ErPO4 and YbPO4. In principle, the results from these studies can be used in conjunction with the thermodynamic data for the
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2. Methods
diluted (1/15) in a 2% HNO3 (Fisher Scientific, trace metal grade) blank matrix solution for inductively coupled plasma mass spectrometry (ICP-MS) analysis to determine P and REE concentrations. After this, the sample holders were extracted and the walls of the reactors were washed with a concentrated sulfuric acid solution (Fisher Scientific, trace metal grade), which was then diluted (1/15) and analyzed using ICP-MS to detect formation of solids. The presence of the REE was not detected in these washing solutions (b0.2 ppt), indicating that there was no significant precipitation of a REE phase on the reactor walls during quenching. To determine if equilibration was reached during the experiments, we conducted a series of kinetic experiments for durations between 1 to 25 days. These preliminary experiments were conducted at the lower of the temperatures investigated (i.e., 100 and 150 °C) as kinetic inhibition of equilibration increases with decreasing temperature. Duplicate/triplicate experiments were conducted to determine the reproducibility of the measured solubility for conditions in which equilibrium was deemed to have been attained (see Section 4).
2.1. Materials
2.3. Analytical
Pure synthetic, euhedral HREEPO4 crystals (YPO4, ErPO4, DyPO4 and YbPO4) were grown utilizing the synthesis techniques outlined in Cherniak et al. (2004). A HREEPO4 powder (submicron grain size) was precipitated by mixing a HREE nitrate solution with an ammonium dihydrogen phosphate solution (1:1 molar amounts). After the precipitate settled, the excess fluid was poured off and the precipitate allowed to dry. The ground powders were dry mixed with a Pb-free NaCO3– MoO3 flux (75NaCO3:25MoO3:2REEPO4 molar ratio), placed in a Pt crucible with a cover and gradually heated in open air to 1375 °C over a period of 4 h. The crucible was left at 1375 °C for 15 h, and then slowly cooled to 870 °C at 3 °C/h over 6–7 days. The flux and embedded HREEPO4 crystals were then boiled in successive beakers of distilled H2O until the crystals were totally freed from the flux such that the flux could be poured off, leaving the crystals behind. The composition and purity of the crystals was verified by electron microprobe analysis, which showed that concentrations of HREE, other than the REE from which the crystals were synthesized, were below the detection limit (b0.08 wt.%). The typical habit and morphology of unreacted and reacted synthetic YPO4 and YbPO4 crystals used in the hydrothermal experiments are shown in Fig. 1. The unreacted crystals display welldeveloped growth steps, which in the reacted crystals, have been etched preferentially along edges. The starting experimental aqueous solutions contained perchloric (HClO4) and phosphoric (H3PO4) acid. Perchloric acid (Fisher Scientific, trace metal grade HClO4) was added to 400 ml Milli-Q water (18 MΩ-cm) to ensure a measured pH of 2 at room temperature. This made it possible to control the initial chloride concentration. The phosphate concentration was ~2700 ppb, which was achieved by adding an aliquot of ~0.8 ml from a phosphoric acid stock solution (Fisher Scientific, trace metal grade H3PO4) to the 400 ml perchloric acid solution.
The pH of the starting experimental solutions (Appendix A) was measured at room temperature using a combination electrode (Cole Parmer) and a Fisher Scientific (Accumet® model 25) pH meter. The electrode was calibrated using commercial buffer solutions (Fisher Scientific; pH 1, 2 and 3 buffer solutions), which enabled measurements to be made to a precision of 0.02 pH units. The quenched experimental solutions were analyzed using a Thermo Finnigan iCapQ quadrupole ICP-MS. Standards and samples were all diluted using 2% HNO3 (Fisher Scientific, trace metal grade) blank solutions. The calibration was carried out using a multi-element REE standard, a P standard (SCP Science, NIST traceable certified standards) and single REE (La, Ce and Nd) standards (VHG Labs, NIST traceable certified standards), with the latter being used for interference corrections due to oxide (18O and 16O) formation, which varied between 1 and 3%. Analyzed samples were blank-subtracted and a drift correction was applied using In (VHG Labs, NIST traceable certified standards) as an internal standard. Phosphorous is difficult to analyze in the ppb range due to an interference with nitrogen (14N16OH and 15N16O) from the HNO3 in the blank matrix, which results in high background counts. To avoid this problem, standard curves were constructed with concentrations in the range of N 40 to 400 ppb, which corresponds to the concentration ranges of the diluted experimental solutions. In this concentration range, the linear regression coefficients were 0.9999. The analytical precision of triplicate ICP-MS runs based on a 95% confidence level, was 2% for P and b1% for Y, Dy, Er and Yb. The limit of detection (LOD) was determined from the 3σ (standard deviation) value of the blank, which was established by multiple measurements of the total procedural blank analyzed during the period of this study. The LODs were 34 ppb for P and 0.2 ppt for REE.
aqueous species to determine the solubility product of xenotime-(Y). However, direct measurement of the solubility provides a more reliable means of quantitatively evaluating the controls of hydrothermal xenotime-(Y) mineralization. In this study, we report the results from experiments designed to determine the solubility of HREE phosphates (YPO4, DyPO4, ErPO4 and YbPO4) in aqueous HClO4–H3PO4 solutions at temperatures up to 250 °C and saturated water vapor pressure. These results are used to evaluate solubility products for these phases. We then compare our solubility data to results from previous experimental studies and critically assess the thermodynamic properties of the HREE phosphates. Based on this assessment, we recommend a new set of thermodynamic data for the HREE phosphates, and use these data in a fluid–rock reaction path model to illustrate how the mobility of the HREE in hydrothermal fluids is affected by fluid composition, temperature, pH and fluid/rock ratio.
3. Aqueous speciation and theoretical considerations 2.2. Experiments The experiments were carried out for up to 25 days using 50 ml Ti grade 2 batch reactors at 100, 150, 200 and 250 °C under a saturated water vapor pressure (psat). Each reactor was loaded with a handmade sample holder (Ti foil, Alfa Aesar, 99.7%) containing a synthetic HREE phosphate crystal and 20 ml of the starting aqueous HClO4– H3PO4 solution. Before the experiments, the autoclaves were purged of air with a stream of dry nitrogen. The autoclaves were then sealed using graphite gaskets and heated in a Barnstead Thermolyne™ muffle furnace (model 30400). Temperature was recorded with an Omega® temperature logger using a K-type thermocouple located at the center of the furnace. The experimental temperature was maintained to within 0.5 °C. After the experiments, the autoclaves were quenched in cold water for 20 min. The experimental solution was pipetted out and
The ionization of orthophosphoric acid as a function of proton (H+) activity can be described by the reactions, 0
−
þ
H3 PO4 ¼ H þ H2 PO4 ðK1 Þ H2 PO4 HPO4
−
2−
þ
¼ H þ HPO4 þ
¼ H þ PO4
2−
3−
ð1Þ
ðK2 Þ
ð2Þ
ðK3 Þ
ð3Þ
and the dissolution of the HREE phosphates by the reactions, 3þ
REEPO4 ðsÞ ¼ REE
þ PO4
3−
ðKS0 Þ
ð4Þ
A.P. Gysi et al. / Chemical Geology 401 (2015) 83–95
a) YPO4 unreacted
85
e) YPO4 unreacted
growth steps
250 µm
b) YPO4 reacted at 100 to 250 °C
10 µm
f ) YPO4 reacted at 100 to 250 °C
leached steps 500 µm
c) YbPO4 unreacted
200 µm
d) YbPO4 reacted at 100 to 250 °C
5 µm
g) YbPO4 unreacted
10 µm
h) YbPO4 reacted at 100 to 250 °C
leached surface
200 µm
10 µm
Fig. 1. Scanning electron microscope (SEM) photomicrographs of unreacted synthetic YPO4 and YbPO4 crystals and the corresponding crystals after reaction at 100 to 250 °C. The surfaces of the unreacted crystals (e and g) display growth steps, which after reaction (f and h) display evidence of leaching.
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A.P. Gysi et al. / Chemical Geology 401 (2015) 83–95 þ
3þ
REEPO4 ðsÞ þ H ¼ REE
þ HPO4
2−
ðKS1 Þ
ð5Þ
−
ð6Þ
Table 1 Aqueous species considered in the calculations and sources of thermodynamic data. Species
þ
3þ
þ
3þ
REEPO4 ðsÞ þ 2H ¼ REE REEPO4 ðsÞ þ 3H ¼ REE
þ H2 PO4 ðKS2 Þ 0
þ H3 PO4 ðKS3 Þ:
Yb species Yb3+ +2 Yb(OH)03, Yb(OH)+ , Yb(OH)− 2 , Yb(OH) 4
ð7Þ
Dy species Dy3+ Dy(OH)03 +2 Dy(OH)+ , Dy(OH)− 2 , Dy(OH) 4
The acidic (pH ~2) experimental solutions used in our study allowed us to increase the solubility of HREE phosphates and avoid complexation and hydrolysis of REE, thereby ensuring that the latter occurred dominantly as free REE3 + species. The main phosphate species were 0 H3PO04 and H2PO− 4 ; at N100 °C the dominant species was H3PO4. This enabled us to determine the equilibrium constant, KS3, using activities of the principal aqueous species in our experiments: a
K S3
3þa
H3 PO04 3
REE ¼ ða HþÞ
:
Er species Er3+ Er(OH)03 +2 Er(OH)+ , Er(OH)− 2 , Er(OH) 4 Y species Y3+ +2 Y(OH)03, Y(OH)+ , Y(OH)− 2 , Y(OH) 4
ð8Þ
Major P species H3PO04 H2PO4−, HPO42−, PO43−
The solubility product KS0 was retrieved using published values for the first, second and third ionization constants of orthophosphoric acid (K1, K2 and K3; Appendix B) and the relationship: KS0 ¼ KS3 K1 K2 K3 :
pffiffi Az2i I pffiffi þ Γ γ þ bγ I 1 þ a B I
ð10Þ
where I, the effective ionic strength, is given by I¼
1X 2 mz i i i 2
Other species OH−, H+ H02, O02 ClO− 4
ð9Þ
Aqueous speciation calculations were carried out using GEMSelektor v.3 (Karpov et al., 1997, 2001; Wagner et al., 2012; Kulik et al., 2013). The ClO− 4 concentration of the starting aqueous HClO4– H3PO4 solution was determined from the measured pH at room temper2− 3− ature. The activity of REE3+, H+, H3PO04, H2PO− 4 , HPO4 and PO4 at the experimental conditions was determined from the concentrations of REE and P in the quenched experimental solutions (Appendix A), values of K1–K3 (H+ and phosphate species) and estimates of the corresponding activity coefficients (see below). Thermodynamic properties for the aqueous species were calculated at the temperature of interest and psat using the revised HKF equation-of-state (Helgeson et al., 1981; Shock and Helgeson, 1988; Shock et al., 1992; Tanger and Helgeson, 1988). The properties of H2O were calculated from the IAPS-84 equation-ofstate (Kestin et al., 1984). A standard state of unit activity was adopted for pure H2O and for aqueous species in a hypothetical 1 molal solution referenced to infinite dilution at any temperature and pressure. Thermodynamic data for aqueous species considered in the speciation calculations (Table 1) were taken from Shock and Helgeson (1988), Shock et al. (1989), Haas et al. (1995), and Shock et al. (1997). The activity coefficients (γi) of charged aqueous species were calculated using the extended Debye–Hückel equation (Robinson and Stokes, 1968), logγi ¼
Minor P species − 0 −3 −4 H2P2O−2 7 , H3P2O7 , H4P2O7, HP2O7 , P2O7
ð11Þ
A and B are the Debye–Hückel parameters (Helgeson and Kirkham, 1974; Helgeson et al., 1981), Γγ is a mole fraction to molality conversion factor, bγ is the extended term parameter, ai is the ion size parameter, mi is the molal concentration and zi is the charge of the ith aqueous species. The value bγ is an empirical parameter that depends on the background electrolyte and was set to 0.21, the value determined by Migdisov and Williams-Jones (2007) for perchloric solutions (HClO4/NaClO4) based on the results of hydrothermal solubility experiments at temperatures up to 250 °C. The ion size parameters of individual ions were taken from Kielland (1937) except for ClO− 4 (4.5 Å), which was taken from
References 1,2 3,5
1,2 3 3,5
1,2 3 3,5
1,2 1
4 1,2
1
1,2 4 1,2
1
(Shock et al., 1997). (Shock and Helgeson, 1988). 3 (Haas et al., 1995). 4 (Shock et al., 1989). 5 Revised data from SUPCRT92 (Johnson et al., 1992), slop98.dat database. 2
Migdisov and Williams-Jones (2007). Activity coefficients for neutral species were assumed to be unity. 4. Solubility of HREE phosphates The compositions of the quenched experimental solutions are given in Appendix A. The time required for equilibrium between HREE phosphate crystals and the starting aqueous HClO4–H3PO4 solutions at the experimental temperature and psat was evaluated for YPO4, and YbPO4 at 100 °C and YbPO4 at 150 °C. The results of the kinetic experiments are shown in Fig. 2. The data indicate that at 100 °C, the Y concentration reached saturation with YPO4 crystals in contact with the experimental solutions after ~10 days. This corresponds to the time required for the measured Y concentration to reach a steady state value. Additional evidence that equilibrium was reached in ~10 days is provided by the good agreement in the results obtained from repeated experiments carried out at the same conditions (experiments in duplicate and triplicate) with YPO4 and DyPO4 crystals (Appendix A). Experiments with YbPO4 were more sluggish. After 15 days of reaction at 100 °C, the concentration of Yb in solution continued to increase (compare experiments after 15 days and 25 days, Appendix A). Duplicate experiments with ErPO4 crystals showed similar uncertainties in the calculated solubility after 25 days of reaction to those for YPO4 and DyPO4, whereas duplicate experiments with YbPO4 crystals showed much larger uncertainties at this temperature. Experiments longer than 25 days were not attempted because of the higher risk of leakage and possible reaction of the aqueous HClO4–H3PO4 solutions with the titanium autoclaves. Therefore, kinetic experiments had to be conducted at 150 °C to assess the solubility of YbPO4. As shown in Fig. 2, the Yb concentrations in the experimental solutions reached a steady state concentration, i.e., saturation with the YbPO4 crystals after ~5 days. It should be noted that the variations in Yb concentration over time were higher than in the solubility experiments with the YPO4 crystals, and that this is reflected in slightly larger uncertainties in their calculated solubility products. The reason for the
A.P. Gysi et al. / Chemical Geology 401 (2015) 83–95
5.5
100 and 250 °C. Duplicate and triplicate experiments display excellent reproducibility with uncertainties in logKs0 generally being b 0.2. Values of logKs0 do not vary linearly with 1/T indicating that the enthalpy of reaction varies with temperature (Fig. 3). The experimental data were fitted to an equation with the form,
a) T = 100 °C
log mY
6.0
logK ¼ A þ BT þ
7.0
in which T is the temperature in Kelvin. Details of the fitting procedure and the significance of the coefficients A, B, C, D and E are given in Appendix C. As is evident from Table 3, only the first three coefficients were needed for the initial fit of our experimental data for temperatures between 100 and 250 °C, yielding regression coefficients (R2) between 0.992 and 0.998. However, extrapolation of the experimental fit to 25 °C leads to large uncertainties at the 95% confidence level (Fig. 3). To better constrain the logKs0 extrapolated to 25 °C, our data therefore needed to be compared to results from previous studies of the solubility of HREE phosphates at lower temperature.
0
10
6.8
20
30
b) T = 150 °C
7.0
log mYb
7.2
ð12Þ
5. Discussion
7.4
5.1. Comparison to previous studies
7.6 7.8 8.0 0
5
10
15
20
Time (days) Fig. 2. Results from kinetic experiments showing the time required for YPO4 and YbPO4 to reach equilibrium with the aqueous HClO4–H3PO4 solutions. This is displayed as the logarithm of dissolved molality (m) in mol/kg of REE as a function of time (days). The error bars represent the standard deviation of duplicate experiments and the gray lines the steady state concentration used in determining solubility products. The concentrations reached the steady value after ~10 days at 100 °C and after ~5 days at 150 °C.
slower dissolution kinetics of YbPO4 is unclear but may be related to the smaller size of the YbPO4 crystals compared to the YPO4 crystals, which would result in a smaller reactive surface area (Fig. 1). The solubility products of the HREE phosphates were calculated from the measured concentrations of REE and P in the quenched experimental solutions (Appendix A) and the activities of the related aqueous species. The resulting values of the logarithm of Ks0 for YPO4, DyPO4, ErPO4 and YbPO4 are listed in Table 2. The solubility of the HREE phosphates is retrograde between 100 and 250 °C, with logKs0 varying ~ 5 orders of magnitude. In this temperature range, the solubility of the HREE phosphates increases with the ionic radii of the respective REE (Shannon, 1976). The solubility increases in the following order: DyPO4 (1.027 Å) N ErPO4 (1.004 Å) N YbPO4 (0.985 Å). However, YPO4 (1.019 Å) has a higher solubility than DyPO4 at temperatures between Table 2 Values of the logarithm of the solubility product (logKs0) of HREE phosphates determined experimentally at temperature (T) and saturated water vapor (psat). Aqueous speciation calculations were carried out using the aqueous species listed in Table 1 and Ks0 was calculated using Eqs. (8) and (9). The uncertainty is based on the results of duplicate/triplicate experiments. T (°C)
logKs0 (YPO4)
1σ
logKs0 (DyPO4)
1σ
logKs0 (ErPO4)
1σ
logKs0 (YbPO4)
1σ
100 150 200 250
−26.74 −27.67 −29.77 −31.83
±0.15 ±0.03 ±0.03 ±0.07
−26.75 −27.70 −29.98 −32.29
±0.04 ±0.04 ±0.16 ±0.07
−26.87 −28.26 −30.19 −32.38
±0.13 ±0.16 ±0.03 ±0.01
−27.57a −28.81 −30.85 −32.90
±0.39b ±0.17 ±0.12 ±0.02
Value based only on experiments quenched after 25 days. Uncertainty based on differences between logKs0 values calculated for experiments quenched after 15 and 25 days. b
C E þ DlogðTÞ þ 3 T T
6.5
7.5
a
87
Previous investigations of the thermodynamic properties of HREE phosphates have been carried out using solubility experiments (Jonasson et al., 1985; Firsching and Brune, 1991; Byrne and Kim, 1993; Liu and Byrne, 1997; Cetiner et al., 2005), mainly at low temperature, and calorimetric methods (Ushakov et al., 2001; Gavrichev et al., 2010, 2012, 2013). These data are compared to our extrapolated values in Fig. 3. Our values of logKs0 for YPO4 extrapolated to 25 °C (Fig. 3a) are similar to, but slightly higher than the values reported by Cetiner et al. (2005) and an order of magnitude higher than the values calculated from Gavrichev et al. (2010). However, for the estimated uncertainty at the 95% confidence level, our value at 25 °C is indistinguishable from the other two values. Cetiner et al. (2005) concluded that their YPO4 experiments did not reach equilibrium, and that they may therefore have underestimated the logKs0 value, possibly explaining why our extrapolated value for 25 °C is slightly higher than their value. In contrast to the studies of Cetiner et al. (2005) and Gavrichev et al. (2010), the solubility experiments of Firsching and Brune (1991) and Liu and Byrne (1997) yielded values of logKs0 for YPO4 at 25 °C that are several orders of magnitude higher than our extrapolated value. These studies used very fine-grained HREE phosphate powders that were synthetized in aqueous solutions at low temperature, and this may have led to colloid formation (Firsching and Brune, 1991) and/or poor crystallinity depending on the method employed (Liu and Byrne, 1997). The very high reactive surface area and problems of dissolution/re-precipitation kinetics may have resulted in higher than equilibrium concentrations of the HREE, which could explain why their calculated 25 °C logKs0 value for YPO4 is so much higher than our value. In addition, it is possible that their synthesized powders comprised hydrated HREE phosphates. In light of the absence of information on the nature of the solids, it is not possible to satisfactorily explain the high solubility of YPO4 reported by Firsching and Brune (1991) and Liu and Byrne (1997). The only published values of logKs0 for DyPO4 at 25 °C are those of Firsching and Brune (1991) and Liu and Byrne (1997). These values are orders of magnitude higher than the values determined in our study (Fig. 3b). As suggested above for experiments on YPO4, the studies by these authors were likely compromised by problems associated with the nature of the solid (colloidal solid formation, poor crystallinity and/ or hydration). Therefore, the values of logKs0 reported by them are considered unreliable. More experimental data are available for ErPO4 and YbPO4 than for DyPO4, but the values for logKs0 vary by several orders of magnitude
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A.P. Gysi et al. / Chemical Geology 401 (2015) 83–95
T (°C) 250
200
150
T (°C)
100
25
250
24 2 3
25
100
25 5
5
logK s0 ErPO 4
logKs0 YPO4
150
24
26 27 1
1
28
4
29 30 31
3 2
2
26 28
6
30 32
32
(c)
(a)
33
34 1.8
2.0 250
2.2 200
2.4
2.6
150
2.8
3.0
3.2
100
3.4
1.8
25
24 3 2
2
24
logK s0 YbPO 4
26 27 28 29 30
26 28
2.0 250
22
25
logKs0 DyPO4
200
2.2 200
2.4
2.6
150
2.8
3.0
3.2
100
3.4 25
(1) Cetiner et al. (2005) (2) Firsching and Brune (1991) (3) Liu and Byrne (1997) (4) Gavrichev et al. (2010) (5) Jonasson et al. (1985) (6) Gavrichev et al. (2012) (7) Gavrichev et al. (2013) (8) Byrne and Kim (1993)
8 3 2 7
2
30
31 32
32
(b)
33
(d)
34 1.8
2.0
2.2
2.4
2.6 2.8 103/ T (K)
3.0
3.2
1.8
3.4
2.0
2.2
2.4
2.6
2.8
3.0
3.2
3.4
103/ T (K)
Fig. 3. Plots showing the logarithm of the solubility products of HREE phosphates (logKs0) vs. 1/T calculated from the experimental data collected in this study for temperatures between 100 and 250 °C together with non-linear fits (Eq. (12)) extrapolated to 25 °C at the 95% confidence interval. The experimental data and coefficients from the regressions (fit 1) are reported in Tables 2 and 3. Also shown are experimentally determined values of logKs0 (numbered symbols) from other studies and logKs0 values calculated from thermodynamic data reported in calorimetric studies. Note that the calorimetric data of Gavrichev et al. (2010, 2012, 2013) include measurements of enthalpy by Ushakov et al. (2001); log Ks0 values were calculated using ΔfG0 for PO3− and REE3+ from Shock et al. (1997) and Shock and Helgeson (1988) (Appendix B). The error bars or symbol sizes represent the 1σ values from duplicate/triplicate 4 experiments.
that calculated from Gavrichev et al. (2013). However, for the reasons discussed earlier, little confidence can be placed on the values reported by Firsching and Brune (1991), and it may simply be coincidence that
at 25 °C (Fig. 3c–d). The logKs0 value for ErPO4 at 25 °C, which is most similar to our extrapolated value, is that of Firsching and Brune (1991). For YbPO4, it is the value of Firsching and Brune (1991) and
Table 3 Coefficients for the temperature (in K) dependence of the solubility products (logKs0) of HREE phosphates at saturated water vapor (psat) determined from regression of the experimental values listed in Table 2 fitted to Eq. (12). R2
logK = A + BT + C/T + Dlog(T) A Fit 1 logKs0 (YPO4) logKs0 (DyPO4) logKs0 (ErPO4) logKs0 (YbPO4)
32.69 43.83 19.60 19.43
logKs0
c
Δf H0Tr,Pr
S°298.15 K
(298.15 K)
(kJ/mol)
(J/mol/K)
B
C
D
−0.0866 −0.1006 −0.0733 −0.0735
−1.009e+4 −1.231e+4 −7.126e+3 −7.290e+3
– – – –
0.994 0.996 0.998 0.992
−26.98 −27.48 −26.17 –26.93
−2038.7 −2039.1 −1994.7 –1963.0
– – – –
Fit 2 optimized for ΔH logKs0 (YPO4) logKs0 (DyPO4) logKs0 (ErPO4) logKs0 (YbPO4)
−612.64 −897.40 −225.00 −396.90
−0.20280 −0.27095 −0.11812 −0.14775
1.374e+4 2.220e+4 1.775e+3 8.141e+3
242.88 354.73 92.332 156.58
0.993 0.996 0.998 0.991
−25.88 −25.98 −25.80 −26.20
−1987.7 ± 1.7a −1967.9 ± 2.6a −1976.9 ± 2.1a −1929.4 ± 4.9a
40.0 67.5 48.7 105.9
Fit 3 optimized for ΔS logKs0 (YPO4) logKs0 (DyPO4) logKs0 (ErPO4) logKs0 (YbPO4)
−876.93 −1150.2 −555.90 −419.76
−0.25127 −0.31778 −0.17933 −0.15215
2.327e+4 3.132e+4 1.373e+4 8.941e+3
342.82 450.32 217.42 165.27
0.993 0.995 0.998 0.991
−25.52 −25.63 −25.34 −26.18
−1969.7 −1950.6 −1954.1 −1928.1
93.9b 119.0d 116.6b 109.7b
a
Ushakov et al. (2001), oxide melt calorimetry. Gavrichev et al. (2010, 2012), adiabatic calorimetry. 0 Enthalpy of formation recalculated from ΔrHTr,Pr using Eq. (4) and thermodynamic data for REE3+ and PO3− listed in Appendix B. 4 d Entropy retrieved from linear interpolation of the entropy vs. ionic radii data for GdPO4, ErPO4, YbPO4, LuPO4. The entropy data were taken from Thiriet et al. (2005) and Gavrichev et al. (2006, 2012, 2013). b c
A.P. Gysi et al. / Chemical Geology 401 (2015) 83–95
the values reported by them for ErPO4 and YbPO4 are similar to those predicted by our study. The values of logKs0 at 25 °C reported by Byrne and Kim (1993), Liu and Byrne (1997) and Jonasson et al. (1985), for hydrated HREE phosphates are consistently higher than those reported by us. This supports the observation made earlier that the high values of logKs0 at 25 °C reported by Firsching and Brune (1991) may reflect the presence of hydrated HREE phosphates in the solids used in their experiments. The method of HREE phosphate synthesis could also have affected the results of the calorimetric studies. The values of logKs0 at 25 °C calculated from Gavrichev et al. (2010, 2012, 2013) differ to varying degrees from those determined in our study depending on the particular HREE phosphate considered (Fig. 3). A further reason for the differences may be that, whereas the entropy and heat capacity reported by Gavrichev et al. (2010, 2012, 2013) are based on their own calorimetric measurements, their enthalpy values for the HREE phosphates are based on the calorimetric measurements of Ushakov et al. (2001). 5.2. Constraining experimental fits and extrapolation to 25 °C As mentioned above, the extrapolation of logKs0 to 25 °C resulted in relatively large uncertainties at the 95% confidence interval (Fig. 3). To better constrain the extrapolated values, we used the Van't Hoff relation and the coefficients of the fitted logKs0 function to retrieve either the enthalpy or entropy values (Appendix C). As a first step, we retrieved the standard enthalpy of reaction (ΔrH0Tr,Pr) of the HREE phosphates by using coefficients A–C fitted to our experimental values (see Fit 1 in 0 Table 3). The standard enthalpy of formation (Δf HTr,Pr ) values obtained are generally more negative by ~ 20–70 kJ/mol than the calorimetric
89
values of Ushakov et al. (2001). In a second step, we used the values of Ushakov et al. (2001) for enthalpy at 298.15 K to constrain parameter D in Eq. (12). This allowed us to refit our experimental data using four coefficients (Fit 2 in Table 3). In a third step, we used the data of Gavrichev et al. (2010, 2012, 2013) for entropy at 298.15 K to constrain parameter A (Fit 3 in Table 3). The optimized fits (Fit 2 optimized for enthalpy; Fit 3 optimized for entropy) are compared in Fig. 4. This optimization made the slopes of the logKs0 vs. 1/T curves based on our experiments more consistent with those based on the calorimetric data for temperatures between 25 and 100 °C. The slopes resulting from Fit 2 and Fit 3 are very similar. However, the high temperature (100 to 250 °C) logKs0 values for YPO4 and ErPO4 were underestimated by several orders of magnitude using calorimetric data relative to our experimentally determined values. In contrast, the corresponding logKs0 values for YbPO4 are in excellent agreement with our values. This suggests that the thermodynamic data for the aqueous species (REE3 + and PO34 −), more specifically the standard Gibbs energy, is not the source of the disagreement over the values of logKs0 determined using our solubility experiments and those calculated from the calorimetric data. To identify the source of the discrepancy, we therefore recalculated the standard thermodynamic properties of the HREE phosphates at 25 °C and 1 bar using our extrapolated logKs0 values (Table 3) and the relation: logK ¼
−Δr G0Tr;Pr RTlnð10Þ
ð13Þ
where ΔrG0Tr,Pr is the standard Gibbs energy of reaction for the dissolution of HREE phosphates (Eq. (4)). Using the ΔrG0Tr,Pr values from our solubility measurements and the data in Appendix B for the aqueous species, we
T (°C) 250 25 26
200
150
T (°C)
100
25 24
a)
250
200
150
100
25
c)
26
logKs0 ErPO4
logKs0 YPO4
27 28 29 30 31
28 30 32
32 34 33 34
36 1.8
25 26
2.0
250
2.2
200
2.4
2.6
150
2.8
3.0
3.2
100
3.4
25
26
logKs0 YbPO4
28 29 30
2.0
250
25
b)
27
logKs0 DyPO4
1.8
2.2
200
2.4
150
2.6
2.8
3.0
3.2
100
3.4
25
d)
27 28 29 30
31
31
32
32
33
33
This study Fit 1 Fit 2 optimized ΔH Fit 3 optimized ΔS Calorimetric data Calc. using Table 4
34
34 1.8
2.0
2.2
2.4
2.6
103/T (K)
2.8
3.0
3.2
3.4
1.8
2.0
2.2
2.4
2.6
2.8
3.0
3.2
3.4
103/T (K)
Fig. 4. Plots showing optimized fits of the logarithm of the solubility products for HREE phosphates (logKs0) vs. 1/T. For comparison, our experimentally determined logKs0 values for temperatures between 100 and 250 °C are also shown. The fits made use of entropy and enthalpy values for HREE phosphates from Gavrichev et al. (2010, 2012, 2013) and Ushakov et al. (2001), respectively (Table 3). See text for details on the optimization method.
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A.P. Gysi et al. / Chemical Geology 401 (2015) 83–95
0 determined the standard Gibbs energy of formation (Δf GTr,Pr ) of the HREE phosphates. Using,
0
0
0
Δ f GTr;Pr ¼ Δ f H Tr;Pr þ T r Δ f STr
5.4. Application of the data to the coupled dissolution of zircon and precipitation of hydrothermal xenotime-(Y)
ð14Þ
Here we describe an application of our data to xenotime-bearing REE deposits in which the solubility of xenotime-(Y) in a hydrothermal fluid was evaluated using the data in Table 4 and the geochemical software package GEM-Selektor v.3 (http://gems.web.psi.ch; Wagner et al., 2012; Kulik et al., 2013). In these deposits, zircon commonly shows textural evidence of having been replaced by xenotime-(Y), as is the case in HREE-rich carbonate-bearing rocks at Lofdal, Namibia (Wall et al., 2008). Similar textures are observed in metamorphic rocks. For example at Jack Hills, Australia, detrital zircon was altered to xenotime-(Y) (Rasmussen et al., 2011). The latter locality contains rocks that have been dated at N 4 Ga, and is thus important for interpreting the nature of the Hadean Earth (Rasmussen et al., 2011). To understand this apparently common coupled dissolution of zircon and precipitation of xenotime-(Y), we use a hydrothermal fluid-rock reaction path model. In this model, we assess the role of mineral solubility, pH, temperature and the complexation of REE and Zr with major ligands on the overall mobility of REE and Zr. The reaction path model involves titration of an acidic (1 m acid) fluid with 0 to 100 g of an HREE-rich carbonate-bearing rock. The rock composition (sample VNP130) was selected from Wall et al. (2008), and is for a rock in which an albite-bearing mineral assemblage was replaced by carbonates ± quartz ± apatite ± Fe oxides. Altered zircon crystals and hydrothermal xenotime-(Y) are present in the sample. In the model, it was assumed that the acidic fluid is progressively buffered by the carbonate-rich rock at the hydrothermal stage (i.e., at conditions for which albite was unstable). This model explains why the bulk rock composition reflects Na depletion (Wall et al., 2008). Two models were considered, both involving titration of the carbonate-rich rock at temperatures from 400 to 150 °C and 1 kbar. Model 1 employed an H3PO4-fluid (1 m H3PO4; Fig. 5) and Model 2 an H3PO4–HCl–HF-fluid (0.2 m H3PO4, 0.4 m HF and 0.4 m HCl; Fig. 6). Gysi and WilliamsJones (2013) evaluated the role of hydrothermal processes in mobilizing Zr and REE in a peralkaline granitic-hosted REE–Zr–Nb deposit at
0 we then retrieved either their standard enthalpy (Δf HTr,Pr ) or their standard entropy (ΔfS0Tr) of formation. The latter was used to determine the third law entropy (S0Tr). The use of Fit 3 optimized for the entropy values 0 measured by Gavrichev et al. (2010, 2012, 2013) yields values of Δf HTr,Pr , which are ~1 to 23 kJ/mol less negative than those measured by Ushakov et al. (2001) (Table 3). We consider this to be acceptable given the large 0 variations in the values of Δf HTr,Pr obtained by different experimental methods (Table 4). By contrast, the use of Fit 2 optimized to the values 0 of Δf HTr,Pr reported by Ushakov et al. (2001) yields very low S0Tr values compared to those measured by Gavrichev et al. (2010, 2012, 2013) (Table 3). We therefore conclude that Fit 3 is the most reliable fit to our data.
5.3. Recommended thermodynamic data for HREE phosphates In Table 4, we report the thermodynamic data retrieved from our experimental data using Fit 3 and Eqs. (13) and (14). These data can be used to calculate the stability of HREE phosphates at conditions of temperature and pressure different from those considered in this study. For DyPO4, we used the Cp° data for ErPO4 (Gavrichev et al., 2012) as no other data are available. However, the calculated and experimentally determined values of logKs0 for DyPO4 at temperatures between 100 and 200 °C differ more than for the other HREE phosphates. For temperatures between 100 and 250 °C, we therefore recommend the use of our experimentally determined logKs0 data for DyPO4 over the values that can be calculated using the recommended thermodynamic properties listed in Table 4. The logKs0 values calculated using the recommended values for YPO4, ErPO4 and YbPO4, are very similar to our experimentally determined values and provide confidence that they will reliably predict the solubility of these HREE phosphates at hydrothermal conditions (Fig. 4).
Table 4 Thermodynamic properties of HREE phosphates at standard conditions of 25 °C and 1 bar derived in this study and those of other studies. The values shown in bold are those recommended in this study unless otherwise noted. Cp° = a + bT + c/T2 + d/T0.5 + eT2 J/K/mol
Δf G0Tr,Pr kJ/mol
Δf H0Tr,Pr kJ/mol
S°298.15 K J/mol/K
Vm cm3/mol
−1849.8 −1867.9 ± 1.7a,b – – −1863.4d −1829.1 – −1832.5 −1855.4 ± 2.1a,b −1825.2e −1834.9f −1830.9g −1808.4 −1809.8 ± 4.9a,b
−1969.7 −1987.7 ± 1.7 a −1955 ± 1.7 c −1966 ± 1.7 c −2008d −1950.6 −1967.9 ± 2.6 a −1954.1 −1976.9 ± 2.1 a – – – −1928.1 −1929.4 ± 4.9 a
93.9 93.86 ± 0.08b – – – 119.0 – 116.6 116.63 ± 0.06b – – – 109.7 109.7 ± 0.1b
43.14h
161.0i
43.35h
264.2i,j
a YPO4
DyPO4 ErPO4
YbPO4 a b c d e f g h i j
42.37
h
41.64h
264.2
b
i
247.6i
T range (K)
c 0.00421i
−0.03543i,j i
d
−2.655e+6i
4.92e+5i,j i
−0.03543
4.92e+5
−0.02291i
2.56e+5i
e
−594.3i
−2753i,j
3.915e-6i
298–1600
9.42e-6i,j
298–1600
i
9.42e−6
i
298–1600
−2463i
6.867e-6i
298–1800
−2753
Ushakov et al. (2001), oxide melt calorimetry. Gavrichev et al. (2010, 2012, 2013), adiabatic calorimetry. Marinova et al. (1973), reported in a (in Russian). Cetiner et al. (2005), solubility experiments. Jonasson et al. (1985), solubility experiments. Firsching and Brune (1991), solubility experiments. Liu and Byrne (1997), solubility experiments. Ni and Hughes (1995). Refitted (within 1%) using data reported in Gavrichev et al. (2010, 2012, 2013). Cp0 assumed to be the same as that for ErPO4 due to the lack of thermodynamic data. We therefore recommend logKs0 fits for the temperature function given in Table 3.
A.P. Gysi et al. / Chemical Geology 401 (2015) 83–95
(a) Mineralogy H3PO4-fluid
91
(a) Mineralogy H3PO4-HCI-HF-fluid
Carbonates
Carbonates
Quartz
Quartz
Feldspar
Feldspar
Fe-phyllosilicates
Fe-phyllosilicates
Al-phyllosilicates Fe oxides Zircon Xenotime-(Y)
Al-phyllosilicates Fe oxides Zircon Xenotime-(Y)
Monazite-(Ce) pH
