Thermodynamic study of Cs3Na(MoO4)2: Determination of the standard enthalpy of formation and standard entropy at 298.15 K

Abstract The enthalpy of formation at 298.15 K and low temperature heat capacity of Cs3Na(MoO4)2 have been measured for the first time in this work using solution calorimetry and thermal-relaxation calorimetry in the temperature range T = (1.9–299.6) K, respectively. The solution calorimetry measurements, performed in 2 M HNO3 solution, have yielded an enthalpy equal to Δ r H m (298.15 K) = (6.79  ±  1.72)  kJ · mol−1 for the reaction: 3 / 2 Cs 2 MoO 4 ( cr ) + 1 / 2 Na 2 MoO 4 ( cr ) = Cs 3 Na ( MoO 4 ) 2 ( cr ) Combining with the enthalpies of formation of Cs2MoO4(cr) and Na2MoO4(cr), also determined in this work in 0.1 M CsOH and 0.1 M NaOH solutions, respectively, the standard enthalpy of formation of Cs3Na(MoO4)2 at 298.15 K has been determined as Δ f H m o (Cs3Na(MoO4)2, cr, 298.15 K) = −(2998.5  ±  3.0) kJ · mol−1. The heat capacity and entropy values of Cs3Na(MoO4)2 at 298.15 K have been derived as C p , m o ( Cs 3 Na ( MoO 4 ) 2 , cr , 298.15 K ) = ( 296.3 ± 3.3 )  J · K−1 · mol−1 and S m o ( Cs 3 Na ( MoO 4 ) 2 , cr , 298.15 K ) = ( 467.2 ± 6.8 )  J · K−1 · mol−1. Combining the newly determined thermodynamic functions, the Gibbs energy of formation of Cs3Na(MoO4)2 at 298.15 K has been derived as Δ f G m o ( Cs 3 Na ( MoO 4 ) 2 , cr , 298.15 K ) = - ( 2784.6 ± 3.4 )  kJ · mol−1. Finally, the enthalpies, entropies and Gibbs energies of formation of Cs3Na(MoO4)2 from its constituting binary and ternary oxides have been calculated.


Introduction
A recent re-investigation of the Na 2 MoO 4 -Cs 2 MoO 4 system has revealed the existence of the double molybdate phase Cs 3 Na (MoO 4 ) 2 [1]. Although the Na 2 MoO 4 -Cs 2 MoO 4 pseudo-binary phase diagram has been investigated as early as 1964 [2] by thermal analysis and X-ray diffraction, the presence of this intermediate compound had not been identified to this date. The newly synthesized compound belongs to the class of double molybdate materials A n R m (MoO 4 ) 2 (A = alkalis, alkaline-earths, Cu, Tl; R = rare earth elements, Bi, Pb, Zn), which have attracted much interest in recent years because of their interesting properties as phosphor luminescent materials [3,4], solid state lasers [5,6], ferroelastics and ferroelectrics [7][8][9]. The existence of the Cs 3 Na(MoO 4 ) 2 phase is also of relevance for the safety assessment of next generation Sodium cooled Fast Reactors [10]. During irradiation of the (U 1Ày Pu y )O 2Àx nuclear fuel in such reactors, cesium and molybdenum are gener-ated with a high fission yield [11], and subsequently migrate from the centre of the fuel pin towards the pellet rim due to the strong axial temperature gradient ($450 KÁmm À1 ). They accumulate in the space between the fuel and cladding in the form of a 150-300 lm layer of cesium orthomolybdate Cs 2 MoO 4 [11]. In case of a breach of the stainless steel cladding, although extremely rare under normal operating conditions, the liquid sodium coolant in these reactors would come into contact with the cesium orthomolybdate layer. The aftermath of this reaction is still subject of controversy. Past studies have suggested a substitution of the cesium by sodium to form sodium molybdate and cesium metal which would dissolve in the liquid sodium [12,13]. But the later work by [14] has contradicted this hypothesis, and rather suggested the formation of cesium, sodium and molybdenum oxides. In light of the evidence for the possible formation of the Cs 3 Na (MoO 4 ) 2 quaternary phase [1], the mechanism of the interaction between liquid sodium and cesium orthomolybdate needs to be re-visited [10]. To this end, the determination of the thermodynamic properties of Cs 3 Na(MoO 4 ) 2 is a necessity. In this work we report for the first time the determination of the standard enthalpy of formation and standard entropy of Cs 3 Na (MoO 4 ) 2 at 298.15 K using solution calorimetry and low temperature thermal-relaxation calorimetry. The standard enthalpies of formation of Cs 2 MoO 4 and Na 2 MoO 4 were moreover measured with the same solution calorimeter, and compared to literature data to serve as a benchmark for the present studies. Combining the newly determined thermodynamic functions, the Gibbs energy of formation of Cs 3 Na(MoO 4 ) 2 at 298.15 K was derived, as well as the Gibbs energies of formation from the constituting oxides (Table 10).

Sample preparation
Cs 3 Na(MoO 4 ) 2 was synthesized by reaction between accurately weighted quantities of cesium orthomolybdate Cs 2 MoO 4 and sodium orthomolybdate (Na 2 MoO 4 anhydrous, 99.9% trace metal basis, Sigma-Aldrich). The cesium orthomolybdate starting material was synthesized as described in [15]. The stoichiometric mixture was heated under argon inside a tightly closed stainless steel container at 723 K for 200 h, with intermediate regrinding steps. Because of the molybdates' hygroscopic nature, handling was done exclusively inside the dry atmosphere of an argon-filled glove box. The purity of the sample was examined by X-ray and neutron diffraction [10] at room temperature, Differential Scanning Calorimetry [10], and ICP-MS analysis. No secondary phases were detected by XRD and neutron diffraction. The ICP-MS analysis yielded a cesium to molybdenum ratio of (1.44 AE 0.07 1 ) at/at and a sodium to molybdenum ratio of (0.51 AE 0.03 2 ), which corresponds to the global composition Cs 2:88ðAE0:14Þ Na 1:02ðAE0:06Þ (MoO 4 ) 2 , hence within uncertainties, in good agreement with the stoichiometric formula. In addition, the Differential Scanning Calorimetry measurements performed on this compound, and reported in detail in [10], showed a single peak in the heat flow signal as a function of temperature, corresponding to the melting event. No additional peaks could be assigned to impurities, in good agreement with the X-ray and neutron diffraction data. The sample purity is expected to be better than 99 wt% (Table 1).

Powder X-ray and neutron diffraction
The X-ray diffraction measurements were carried out at room temperature (295 AE 3 3 K) using a PANalytical X'Pert PRO X-ray diffractometer mounted in the Bragg-Brentano configuration with a Cu anode (0.4 mm Â 12 mm line focus, 45 kV, 40 mA). The X-ray scattered intensities were measured with a real time multi strip (RTMS) detector (X'Celerator). The data were collected by step scanning in the angle range 10°6 2h 6 120°with a step size of 0.008°( 2h); total measuring time was about 8 h.
Neutron diffraction data were recorded on the beamline PEARL at the Hoger Onderwijs Reactor at TU Delft [16]. The sample was encapsulated in a vanadium container hermetically closed with a rubber o-ring. The data were collected at room temperature (295 AE 3 4 K), at a fixed wavelength (k = 0.1667 nm) for 43 h over the range 11°6 2h 6 158°. Structural analysis was performed by the Rietveld method with the Fullprof2k suite [17]. Cs 3 Na(MoO 4 ) 2 crystallizes with a hexagonal structure, in space group P3m1 (Z = 1), belonging to the glaserite type. The refined cell parameters by XRD (a = 0.634381 5 and c = 0.821888 6 nm (note that the statistically derived s.u.´s are underestimated by about one order of magnitude); q = 4.2991 7 gÁcm À3 ) and neutron diffraction (a = 0.63352 8 and c = 0.82068 9 nm (note that the statistically derived s.u.´s are underestimated by about one order of magnitude); q = 4.317 10 gÁcm À3 ) were found in good agreement with the single crystal data of Zolotova et al. (a = 0.63461 11 and c = 0.82209 12 nm) [1]. The refined lattice parameters using XRD are considered more precise than those derived from the neutron diffraction data. A detailed structural study of this compound can be found in [10] ( Fig. 1).

Solution calorimetry
The enthalpy of dissolution of Cs 3 Na(MoO 4 ) 2 , Cs 2 MoO 4 and Na 2 -MoO 4 materials were measured using a TA Instruments Precision Solution Calorimeter (semi-adiabatic or isoperibolic calorimeter) and TAM IV thermostat. The calorimetric unit consists of a reaction vessel and stirrer system (motor and gold stirrer holding a glass ampoule). The experiments were performed in a thin-walled 25 mL Pyrex-glass reaction vessel equipped with a thermistor for measuring the temperature rise and a heater for calibration during the measurement and equilibration of the initial baseline in the optimal operating range of the calorimeter before starting the experiment. The samples to be studied were placed inside a 1 mL glass ampoule, which was subsequently sealed using bee wax. The latter operation was performed in the dry atmosphere of the glove box because of the sensitivity of the samples to air and moisture. The solid samples were dissolved into solution (cesium hydroxyde CsOH, sodium hydroxyde NaOH, or nitric acide HNO 3 solutions) by breaking the bottom of the glass ampoule on the sapphire breaking tip mounted at the bottom of the reaction vessel. The heat of breaking is exothermic, with a value below 10 mJ, and can thus be neglected. The temperature during the measurements was maintained in the oil bath with an accuracy of AE1Á10 À4 K. Electrical calibrations were performed immediately before and after each enthalpy of reaction measurement so as to determine the energy equivalent of the system. and Na 2 MoO 4 were determined with this instrument in cesium hydroxyde CsOH and sodium hydroxide NaOH solutions as described below, and found in excellent agreement with the literature data [22][23][24][25][26].

Low temperature heat capacity
Low temperature heat capacity measurements were performed on m = 13.04 14 mg of Cs 3 Na(MoO 4 ) 2 in the temperature range T = (1.9-299.6) K using a PPMS (Physical Property Measurement System, Quantum Design) instrument at applied magnetic fields B = 0 and 9 T. This technique is based on a relaxation method, which was critically assessed by Lashley et al. [27]. The contributions of the sample platform, wires, and grease were deduced by a separate measurement of an addenda curve. Based on the experience acquired on this instrument with standard materials and other compounds [28], the uncertainty was estimated at about 1% from 100 to 300 K, and reaching about 3% at the lowest temperatures [27,28].

Enthalpy of formation of Cs 2 MoO 4
To assess the performance of our instrument, the enthalpy of formation of Cs 2 MoO 4 was firstly determined in CsOH solution, with a thermochemical cycle very similar to that of O'Hare and Hoekstra [22]. The detail of the reaction scheme used to derive these data is listed in Table 2. Cesium orthomolybdate and molybdenum oxide (MoO 3 , 99.5%, Alfa Aesar) were dissolved in 0.1 M and 0.148 M CsOH solutions, respectively. The details of the calorimetric results for the dissolution of both compounds are listed in Table 3. The dissolutions in both cases were instantaneous. Supposing the solutions formed by reactions (1a) and (2a) in Table 2 are identical, one obtains the following enthalpy of reaction D r H o m ¼ D r H 2 À D r H 1 ¼ Àð79:30 AE 1:17Þ kJÁmol À1 for the reaction: The enthalpy of reaction (4a) in Table 2 was derived from the enthalpy of formation of CsOH(aq) reported by Gunn [29], i.e.,   of formation of MoO 3 (cr) was taken from the review work by Cordfunke and Konings [23]. Finally, the correction for the relative partial molar enthalpy of water in 0.1 M CsOH solution was considered negligible ( Table 2). The summation of reactions (1a)-(6a) such that D r H 7a ¼ D r H 1a À D r H 2a þ D r H 3a þ D r H 4a þ D r H 5a À D r H 6a yields the standard enthalpy of formation of Cs 2 MoO 4 as D f H o m (Cs 2 MoO 4 , cr, 298.15 K) = À(1514.7 AE 1.5) kJÁmol À1 . The latter value is in excellent agreement with that measured by O'Hare and Hoekstra in 0.2 M CsOH solution (99.41 mL) using a LKB-8700 Precision Calorimeter System [22], and the recommended value in the review work of Cordfunke and Konings [23], i.e., D f H o m (Cs 2 MoO 4 , cr, 298.15 K) = À(1514.5 AE 1.0) kJÁmol À1 .

Enthalpy of formation of Na 2 MoO 4
Next, the enthalpy of formation of Na 2 MoO 4 was measured in NaOH solution. Using a similar procedure as previously, Na 2 MoO 4 and MoO 3 were dissolved in 0.1 M and 0.164 M NaOH solutions, respectively. The dissolutions were again instantaneous. The corresponding reaction scheme is shown in Table 4, and the detail of the calorimetric results are listed in Table 5. The enthalpy of reaction The enthalpy of reaction (4b) in Table 2 was derived from the enthalpy of formation of NaOH(aq) reported by Gunn [29], i.e. Table 3 Calorimetric results for the dissolution of

Enthalpy of formation of Cs 3 Na(MoO 4 ) 2
The enthalpy of formation of Cs 3 Na(MoO 4 ) 2 was determined in 2 M HNO 3 solution. Surprisingly, this quaternary compound could not be dissolved in a basic solution such as {NaOH + CsOH}. However, the dissolutions of Cs 3 Na(MoO 4 ) 2 and the constituting ternary oxides Na 2 MoO 4 and Cs 2 MoO 4 were complete in nitric acid solution. The thermochemical cycle used in this case is detailed in Table 6 and the calorimetric results in Table 7. The reaction scheme is as follows: The amount of sample dissolved was adjusted such that sol:1 and sol:3 had the same composition. The enthalpy of the reaction of formation from the constituting ternary oxides (6)  Combining with the newly determined standard enthalpies of formation of Cs 2 MoO 4 (cr) and Na 2 MoO 4 (cr), the standard enthalpy of formation of Cs 3 Na(MoO 4 ) 2 (cr) is finally derived as D f H o m (Cs 3 Na (MoO 4 ) 2 , cr, 298.15 K) = À(2998.5 AE 3.0) kJÁmol À1 .

Low temperature heat capacity of Cs 3 Na(MoO 4 ) 2
The low temperature heat capacity data of Cs 3 Na(MoO 4 ) 2 measured in the absence of magnetic field in the temperature range T = (1.9-299.6) K are shown in Fig. 2a and listed in Table A. 1. The heat capacity of Cs 3 Na(MoO 4 ) 2 increases smoothly with temperature, and reaches values that are about 60 JÁK À1 Ámol À1 below the classical Dulong-Petit limit (C lat ¼ 3nR $349 JÁK À1 Ámol À1 for the fourteen atoms in the formula unit) as the temperature approaches 298.15 K. The collected data do not exhibit any anomaly, and the applica-    tion of a 9 T magnetic field (not shown) does not affect the results, as expected for such insulating material.
The thermodynamic functions of Cs 3 Na(MoO 4 ) 2 were derived at 298.15 K by fitting the experimental data using the OriginPro 2015 software to theoretical functions below T = 10.0 K [34], and a combination of Debye and Einstein heat capacity functions [35][36][37] from T = (10.0 to 299.6) K. The fitting was done with the Levenbergh Marquardt iteration algorithm, using Origin C type fitting   At very low temperatures (T < 10.0 K), the phonon contribution is well-represented using an harmonic-lattice model [34], as expressed by Eq. (7), where the number of required terms augments with the high temperature limit of the fit: Four terms were used over the temperature range T = (1.9-10.0) K. The corresponding coefficients are listed in Table 8. The electronic contribution of the conduction electrons at the Fermi surface are represented with a linear term cT [38]. In this case, Cs 3 -Na(MoO 4 ) 2 being an insulating material, the electronic specific heat is zero.
Above T = 10.0 K, the lattice contribution dominates and can be modelled using a combination of Debye and Einstein functions [39], as written in Eq. (8). Such method has been applied successfully in the literature to different classes of inorganic compounds: iron phosphates [40][41][42], zirconolite [35], calcium titanate [36], dicesium molybdate [43], sodium uranate and neptunate [44]. Three Einstein functions were used in this work to fit the data. Fitting with a single or two Einstein functions was attempted, but could not reproduce accurately the high temperature region. The fitted parameters are listed in Table 8. The sum (n D þ n E1 þ n E2 þ n E3 ) is slightly smaller than 14. The deviation of the fitted data from the experimental results remains below about 1.5% over the temperature range T = (10-299.6) K, as shown in Fig. 3.
where Dðh D Þ; Eðh E1 Þ; Eðh E2 Þ and Eðh E3 Þ are the Debye and Einstein functions, respectively, as written in Eqs. (9) and (10). h D ; h E1 ; h E2 and h E3 are the characteristic Debye and Einstein temperatures. n D ; n E1 ; n E2 and n E3 are adjustable parameters, whose sum (n D þ n E1 þ n E2 þ n E3 ) should be approximately equal to the number of atoms in the formula unit (i.e., 14 in this case).
The entropy, enthalpy and Gibbs energy of formation of Cs 3 Na (MoO 4 ) 2 from its constituting oxides were finally derived as listed in Table 10. These data were calculated using the following values for the enthalpies of formation of Cs 2 O(cr), Na 2 O(cr), MoO 3 (cr), Cs 2 MoO 4 (cr) and Na 2 MoO 4 (cr), respectively: À(345.98 AE 1.17) [23], À(417.98 AE 4.20) [47], À(745.0 AE 1.0) [23], À(1514.7 AE 1.5) (this work), À(1466. 5 2 is not stable with respect to Cs 2 MoO 4 (cr) and Na 2 MoO 4 (cr) at room temperature. However, the calculation of the Gibbs energy for this reaction in the temperature range T = (298.15-778) K yields 19 D f G o m;ter:ox: ðT=KÞ = (7.141-0.0162 T) kJÁmol À1 , which becomes negative above T = 440 K. This result is in accordance with the observations of Zolotova et al. [1], who reported that ''according to XRD data, a noticeable interaction between Na 2 MoO 4 and Cs 2 MoO 4 begins at 250°C" (523 K). It also explains the need for a very long thermal treatment (150 h at 693 K in the work of [1] and 200 h at 723 K in this work) to obtain a complete reaction between the sodium and cesium molybdates.

Conclusions
The enthalpies of formation of Cs 2 MoO 4 , Na 2 MoO 4 and Cs 3 Na (MoO 4 ) 2 have been measured in this work using solution calorimetry in 0.1 M CsOH, 0.1 M NaOH, and 2 M HNO 3  3) kJÁmol À1 , were found in very good agreement with the literature, which gave us good confidence in the accuracy of our measurements. The measurements on a well-characterized sample of the double molybdate Cs 3 Na(MoO 4 ) 2 have yielded: D f H o m (Cs 3 Na(MoO 4 ) 2 , cr, 298.15 K) = À(2998.5 AE 3.0) kJÁmol À1 . The experimental low temperature heat capacity data of Cs 3 Na(MoO 4 ) 2 have been fitted to theoretical functions below 10 K and to a combination of Debye and Einstein functions above this temperature. The derived standard entropy is S o m ðCs 3 NaðMoO 4 Þ 2 ; cr; 298:15KÞ ¼ ð467:2 AE 6:8Þ JÁK À1 Ámol À1 . Finally, the Gibbs energy of formation of Cs 3 Na(MoO 4 ) 2 from its constituting elements and oxides have been derived. The compounds appears to be metastable with respect to Cs 2 MoO 4 and Na 2 MoO 4 at room temperature. However, the Gibbs energy of the reaction of formation from the constituting ternary oxides becomes negative above T = 440 K. These results concur with the observations of Zolotova et al. [1] and ours regarding the ease of the synthesis reaction.