Thermodynamic properties of caesium–cobalt phosphate CsCoPO4

Accepted Manuscript Thermodynamic properties of caesium–cobalt phosphate CsCoPO4 I.V. Korchemkin, V.I. Pet’kov, A.V. Markin, N.N. Smirnova, A.M. Kovalskii PII: DOI: Reference:

S0021-9614(15)00463-2 http://dx.doi.org/10.1016/j.jct.2015.12.017 YJCHT 4496

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J. Chem. Thermodynamics

Received Date: Revised Date: Accepted Date:

24 September 2015 15 December 2015 16 December 2015

Please cite this article as: I.V. Korchemkin, V.I. Pet’kov, A.V. Markin, N.N. Smirnova, A.M. Kovalskii, Thermodynamic properties of caesium–cobalt phosphate CsCoPO4, J. Chem. Thermodynamics (2015), doi: http:// dx.doi.org/10.1016/j.jct.2015.12.017

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Thermodynamic properties of caesium–cobalt phosphate CsCoPO4 I.V. Korchemkin a,∗, V.I. Pet’kov a, A.V. Markin a, N.N. Smirnova a, A.M. Kovalskii b a

Lobachevsky State University of Nizhni Novgorod, pr. Gagarina 23, Nizhni Novgorod 603950, Russia b National University of Science and Technology “MISIS”, Leninskii prospect 4, Moscow 119049, Russia

The heat capacity measurements of the crystalline phosphate CsCoPO4 with a β-tridymite structure were performed between T = (6 and 650) K. Phase transitions were found at (313.40, 486.9 and 514.4) K. They correspond to the polymorphic transformations between two monoclinic and two orthorhombic modifications of CsCoPO4, respectively. Thermodynamic functions С op,m /R, ∆ T0 H mo /RT, ∆ T0 S mo /R and Фmo /R were calculated over the range of T = (0 and 650) K from experimental values and the fractal dimension Dfr evaluated. Standard entropy of formation at T = 298.15 K was estimated to be (–386.40 ± 1.38) J · K−1 · mol−1 for crystalline phosphate CsCoPO4. Keywords: Caesium–cobalt phosphate; β-tridymite structure; Heat capacity; Phase transitions; Thermodynamic functions. 1. Introduction For few last decades compounds of the family AIBIIPO4 (AI − monovalent metal; BII − divalent metal with a tetrahedral coordination) are studied because of their ferroelectric, electrochemical and luminescent properties, catalytic activity [1−6]. These phosphates possess high chemical, thermal and radiation stability, opportunity to include cations a different size in crystal structure that can be used in design of hi-tech materials on their basis with demanded properties. Ability to contain large alkaline cations (especially, caesium) in high concentrations allows using ceramics, based on these phosphates, as materials for storage of nuclear wastes. These materials can provide their further commercial and medical applications, for example, as 137 Cs γ-radiation sources [7, 8]. One of the perspective candidates for matrix of caesium containing radioactive wastes storage can be caesium-cobalt phosphate CsCoPO4. It crystallizes in β-tridymite structure type with monoclinic symmetry [9]. Its structure is characterized by three-dimensional framework, which is formed by six-membered rings of tetrahedra CoO4 and PO4, linked by common vertices, and by large cavities that are occupied by Cs+ cations. In the literature, the information about thermodynamic properties of caesium containing β-tridymite type phosphates is reduced to several compounds: CsCoPO4, CsZnPO4, CsMgPO4, CsMnPO4 [9−12]. In earlier work [9] the temperature dependence of the CsCoPO4 heat capacity was measured over the range from ultra-low temperature to 573 K, but the standard thermochemical parameters of its formation at T = 298.15 K were not reported as well as its standard thermodynamic functions, because work was focused primarily on determination of influence of phosphate particle size on the phase transition enthalpy. Decreasing of phase transition enthalpy with decreasing the particle size around 0.1 mm was shown. Polymorph transitions (space groups: P21 → P21/a → Pna21 → Pnma) were observed and characterized too. However, knowledge of the CsCoPO4 compound thermodynamic functions over a wide temperature range is necessary as they are fundamental characteristics and needed for the different chemical process calculations in which this substance participates. ∗

Corresponding author. Tel.: +78314623234; fax: +78314623085. E-mail address: [email protected] (I.V. Korchemkin).

The purpose of the present work is to measure the heat capacity by adiabatic calorimetry and differential scanning calorimetry over the temperature range of T = (6 to 650) K of the crystalline caesium-cobalt phosphate CsCoPO4, to calculate the standard thermodynamic functions С op,m /R, ∆ T0 H mo /RT, ∆ T0 S mo /R and Фmo /R over the temperature range from (0 to 650) K and standard entropy of formation at 298.15 K, to determine the characteristic temperature and fractal dimensions Dfr. 2. Experimental 2.1. Synthesis and powder X-ray characterization The sample of phosphate CsCoPO4 was synthesized by crystallization from a solution of salts, containing the elements, forming the target product, using the procedure earlier applied for CsMgPO4 synthesis and described in [10]. The starting reagents for synthesis were CsCl, CoCl2·6H2O and NH4 H2PO4. The provenance and purity of the reagents used in this study are listed in table 1. The purity of the starting CoCl2·6H2O is explained by the uncertainty in the H2 O content in this chemical. That is why the cobalt concentration in the solution taken for synthesis was confirmed gravimetrically. The X-ray powder pattern of the sample was recorded on a Shimadzu XRD-6000 diffractometer using filtered CuKα radiation. The X-ray pattern only contained reflections characteristic of desired compound. A single phase of CsCoPO4 was observed having the monoclinic structure (sp.gr. P21/a, a = 184.11(8) nm, b = 54.76(3) nm, c = 93.01(5) nm, β = 90°, V = 9377(9) nm3) in agreement with the results [9]. According to quantitative phase analysis data (relative standard uncertainty of determination was 0.005 mass fraction), the sample contained less than 0.005 mass fraction of substantial impurities. 2.2 Electron microprobe analysis The results of investigation of chemical compositions were obtained using a JSM-7600F Schottky Field Emission Scanning Electron Microscope (JEOL) equipped with microanalysis system with energy-dispersive X-ray (EDX) detector OXFORD X-Max 80 (Premium). The acceleration voltage was 15 and 20 kV. The results from analyses monitored the homogeneity of the sample (table 2, figure 1) and corresponded to the formula Cs1.00(2)Co1.00(1)P1.00(1)O4. 2.3. Low-temperature heat capacity measurements (adiabatic calorimetry) The temperature dependence of the heat capacity of the sample was measured over the temperature range from (6 to 350) K on a BKT-3.07 thermophysical unit, which was a fully automated adiabatic vacuum calorimeter with discrete heating (table 3, Series 1−3). The design of the calorimeter and the procedure for measurements were similar to those described in [13]. The reliability of calorimeter operation was checked by measuring the heat capacity of specialpurity copper (OSCh-11-4 brand) and standard synthetic corundum and benzoic acid (K-2 brand). Calibration and test experiment results showed that the combined expanded relative uncertainty in heat capacity measurements was Uc, r( С op,m ) = 0.02 at temperatures from (5 to 15) K, Uc, r( С op,m ) = 0.005 at temperatures from (15 to 40) K and were Uc, r( С op,m ) = 0.003 over the temperature range between (40 and 350) K. The standard uncertainty in temperature measurements was u(T) = 0.01 K according to ITS-90. The calorimetric ampoule contained 1.3114 g of the investigated substance. The calorimetric ampoule was filled to a pressure of 4 kPa at room temperature with dry helium as a heat exchange gas. The heat capacity of the sample itself was between (40 and 75)% of the total heat capacity of (the calorimetric vessel + the sample) over the temperature interval between (6 and 350) K.

2.4. High-temperature heat capacity measurements (differential scanning calorimetry) Measurement of a heat capacity of the sample over the temperature range from (330 to 650) K carried out with use of differential scanning calorimeter DSC204F1 Phoenix of manufacture of firm Netzsch Geratebau, Germany. The design of calorimeter DSC204F1 Phoenix and a work technique are similar described in work [14]. Checking of reliability of work of a calorimeter carried out by means of standard calibration experiments on measurement of thermodynamic characteristics of fusion n-geptan, mercury, indium, tin, lead, bismuth and zinc. As a result of calibrations, it was found that the equipment and a measurement technique allow to measure temperatures of phase transformations with a standard uncertainty u(T) = 0.2 K, enthalpy of transitions u r(∆trH) = 0.02. A heat capacity defined by standard technique Netzsch Software, the combined expanded relative uncertainty of definition did not exceed Uc, r( С op,m ) = 0.025. Measurements spent at average speed of heating of an ampoule with substance of 5 K/min in argon atmosphere (table 3, Series 4). The calorimetric ampoule contained 0.0297 g of the investigated substance. 3. Results and discussion 3.1. Heat capacity and phase transitions Experimental points of and the smoothed curve C op ,m = f (T ) of crystalline CsCoPO4 (M = 286.8115 g · mol−1) over the range from T = (6 to 650) K are given in table 3 and illustrated in figure 2. The experimental points of in the temperature ranges, where there were no phase transitions, were smoothed as power polynomials: i

n T  C po, m = ∑ ai   . (1)  30  i =0 The relative deviations of experimental values from the smoothing functions are listed in figure 3. As figure 2 illustrates, the caesium-cobalt monophosphate undergoes three phase transitions within the temperature range studied. Observed endothermic transitions are reversible, they reproduced at repeated cooling and heating. The maximum of the heat capacity o of the sample in the transition range corresponds to phase transition temperature, which was Ttrs1

= (313.40 ± 0.01) K for the first transition (301−323) K. Enthalpy of transition ∆ trs1 H mo = (30.47 ± 0.57) J · mol−1 was calculated as the subtraction of integrals on the temperature curves of apparent and interpolated heat capacity of substance in the transition range (figure 2). Entropy of transition amounted to ∆ trs1 S mo = (0.094 ± 0.002) J · K−1 · mol−1. The second phase transition appears over the temperature interval from (472 to 499) K. The temperature of the phase o transition was Ttrs2 = (486.9 ± 0.2) К. Enthalpy and entropy of the second phase transition amounted to ∆ trs2 H mo = (344.7 ± 6.9) J · mol−1, ∆ trs2 S mo = (0.71 ± 0.02) J · mol−1 · К−1. The third phase transition appears over the temperature interval from (499 to 532) K. The temperature of o the phase transition was Ttrs3 = 514.4 ± 0.2 К. Enthalpy and entropy of the third phase transition amounted to ∆ trs3 H mo = (474.5 ± 9.5) J · mol−1, ∆ trs3 S mo = (0.92 ± 0.02) J · K−1 · mol−1. Parameters of phase transformations are listed in table 4. Otherwise the temperature dependences of heat capacity of compound under consideration hadn’t any features. The Debye theory was used to fit the experimental data in the range from T = (6 to 12) K and extrapolate it to 0 K [15]: (2) C op, m = n⋅D⋅(ΘD/T),

where D is the symbol of Debye's function, n and ΘD are specially selected parameters. Using this equation, we obtained ΘD = 79.08 K at n = 3 for CsCoPO4. Using the above parameters, Eq. (2) describes the C op, m values of the compound over the range from T = (6 to 12) K with relative standard uncertainty ur(ΘD) = 0.013. In subsequent calculations, we assumed that Eq. (2) described the heat capacity in the range from T = (0 to 12) K with the same uncertainty. According to powder diffraction high-temperature measurements [9, 16], the phase transitions corresponded to polymorphic transformations (P21 → P21/a → Pna21 → Pnma) between monoclinic and orthorhombic modifications of crystalline CsCoPO4, respectively. Considered modifications are structurally related and structural changes in the transitions between these modifications are negligible. Lowering the symmetry from orthorhombic to monoclinic is accompanied by a doubling of the parameter a cell, the deviation angle β between 90° and differentiation of the atom positions of the structure (and therefore the bond lengths and bond angles) [16]. Analogues phase transitions were discovered for CsZnPO4, CsMgPO4 and CsMnPO4 compounds [10−12].

3.2. Thermodynamic functions Standard thermodynamic functions of crystalline phosphate CsCoPO4 were calculated from the C op,m = f (T ) curve values in the range from (0 to 650) K (table 5). The procedure of calculating these functions was described in detail in [17]. The enthalpies and entropies were calculated by using the following equations: o Ttrs1

∫C

o m

T 0

∆ H =

o Ttrs 2

o p ,m

∫C

o m

( phaseI,T )dT + ∆ trs1 H +

∫

T

C op,m ( phaseIII, T )dT + ∆ trs3 H mo +

o Ttrs2

o m

∆ S =

∫C

o p ,m

( phaseIV, T )dT , (3)

o Ttrs3

o Ttrs1

T 0

( phaseII, T )dT + ∆ trs2 H mo +

o Ttrs1

0 o Ttrs 3

+

o p ,m

∫C

o Ttrs2

o p ,m

o trs1 m

( phaseI,T )d ln T + ∆ S +

∫C

o p ,m

( phaseII, T )d ln T + ∆ trs2 S mo +

o Ttrs1

0 o Ttrs 3

+

∫

o Ttrs2

T

C op,m ( phaseIII, T )d ln T + ∆ trs3S mo +

∫C

o p ,m

( phaseIV, T )d ln T ,

(4)

o Ttrs3

The functions Фmo (T) were found from the corresponding values of ∆ T0 H mo and ∆ T0 S mo and by the equation: Фmo = ∆ T0 S mo − ∆ T0 H mo / T (5)

The absolute entropies of the compound under the study S mo (CsCoPO4, cr, 298.15) = (180.21 ± 0.72) J · K−1 · mol−1 (table 5) and the corresponding simple substances { S o (Cs, cr, 298.15) = (85.23 ± 0.40), S o (Co, cr, 298.15) = 30.07, S o (P, cr, 298.15) = (41.09 ± 0.25), S o (O2, g, 298.15) = (205.152 ± 0.005)} J · K−1 · mol−1 taken from [18, 19] were used to calculate the standard entropy of formation of CsCoPO4, ∆ f S mo (CsCoPO4, cr, 298.15) = (–386.40 ± 1.38) J · K−1 · mol−1. This value corresponds to the following reaction: Cs(cr) + Co(cr) + P(cr, white) + 2О2(g) = CsCoPO4(cr) Reported uncertainties correspond to the combined expanded uncertainties for 0.95 level of confidence (k ≈ 2). 4. Conclusions

The general aim of these investigations was to report the results of a thermodynamic study of crystalline phosphate CsCoPO4 belonging to the β-tridymite structure type. The heat capacity of the phosphate was measured by adiabatic calorimetry and differential scanning calorimetry in the temperature range from (6 to 650) K. Phase transitions at 313.4, 486.9 and 514.4 K were confirmed. The standard thermodynamic functions for crystalline phosphate CsCoPO4 С op,m /R, ∆T0 H mo /RT, ∆T0 S mo /R and Фmo /R over the range from (0 to 650) K and the standard entropy of formation at T = 298.15 K were derived from experimental results. The lowtemperature (T < 50 K) dependence of the heat capacity was analysed on the basis of the heat capacity theory of Debye and the multifractal variant, and as a result, phosphate threedimensional structure was confirmed. Acknowledgments

This work was financially supported by the Russian Foundation for Basic Research (project No. 15-03-00716 а). References

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Figure captions FIGURE 1. Electron microscopic image of the caesium-cobalt phosphate CsCoPO4. FIGURE 2. Plot of heat capacity against temperature dependence for crystalline CsCoPO4: AB correspond to crI, DE − crII, point G − crIII and IJ − crIV, BCD, EFG, GHI − apparent heat capacities in the phase transition ranges. FIGURE 3. Plot of deviations of experimental heat capacity data from fitted against temperature for crystalline CsCoPO4.

TABLE 1 Provenance and purity of the samples used in this study Formula Provenance Mass fraction purity

CsCoPO4 CsCl CoCl2·6H2O NH4 H2PO4

Present work REACHEM REACHEM REACHEM

≥0.995 ≥0.9999 ≥0.99 ≥0.995

TABLE 2

Results of electron microprobe analysis of CsCoPO4 sample Point number

n(Cs)

n(Co)

n(P)

n(O)

1

0.98

0.99

1.02

4

2

1.02

1.00

1.00

4

3

1.00

0.98

1.02

4

4

0.98

1.01

1.00

4

5

1.02

0.99

1.00

4

6

0.99

1.02

0.99

4

1.01

1.01

0.98

4

1.00(2)

1.00(1)

1.00(1)

4

7 Average composition a

a

Standard uncertainty for element content u(n) = 0.01 molar fraction (with 0.68 level of confidence).

TABLE 3 Experimental molar heat capacities С op,m /R of CsCoPO4 (M = 286.8115 g · mol−1; R = 8.314472 J · K−1 · mol−1) po = 0.1 MPaa T/K T/K T/K С op,m /R С op,m /R С op,m /R

6.05 6.49 6.93 7.36 7.78 8.19 8.62 9.08 9.58 10.10 10.63 11.16 11.67 12.16 13.00 14.27 15.59 16.94

0.268 0.312 0.356 0.374 0.399 0.437 0.486 0.509 0.536 0.580 0.617 0.658 0.690 0.718 0.798 0.939 1.073 1.247

18.33 19.77 20.92 22.76 24.48 26.27 28.12 30.03 32.00 34.02 36.12 37.97 40.47 42.73 45.02 47.34 49.71 52.12

80.84 82.83 85.25 87.47 89.69 91.92 94.14 96.37 98.60 100.83 103.07 105.30 107.54 109.78 111.80 114.54 116.74 118.98 121.23 123.47 125.71 127.95 130.19 132.43 134.67 136.91

7.313 7.464 7.599 7.760 7.902 8.019 8.152 8.310 8.439 8.575 8.704 8.834 8.980 9.073 9.178 9.338 9.442 9.557 9.655 9.786 9.890 9.994 10.09 10.21 10.31 10.41

170.03 172.23 174.44 176.64 178.83 181.02 183.21 185.40 187.59 189.78 191.97 194.89 196.33 198.51 200.68 202.82 204.99 207.16 209.32 211.49 213.66 215.82 217.98 220.14 222.30 224.46

Series 1b 1.418 1.569 1.717 1.945 2.156 2.388 2.600 2.832 3.072 3.327 3.520 3.727 4.024 4.253 4.499 4.763 4.950 5.160 Series 2 11.98 12.05 12.13 12.22 12.31 12.40 12.50 12.57 12.64 12.70 12.77 12.85 12.90 12.98 13.07 13.15 13.22 13.29 13.37 13.43 13.50 13.57 13.65 13.72 13.79 13.84

54.56 57.05 59.55 62.07 64.59 67.13 69.70 72.02 74.09 76.18 78.27 80.36 82.45 84.54 86.65 89.36

5.388 5.593 5.773 5.978 6.170 6.374 6.543 6.747 6.904 7.047 7.168 7.302 7.446 7.557 7.718 7.887

265.17 267.30 269.42 271.51 273.63 276.36 278.40 280.51 282.62 284.72 286.82 288.92 291.02 293.09 295.18 297.25 299.32 301.38 303.43 305.47 307.51 309.32 311.46 313.44 315.42 317.39

15.16 15.24 15.31 15.36 15.41 15.49 15.54 15.61 15.67 15.71 15.77 15.83 15.90 15.95 16.00 16.06 16.12 16.20 16.28 16.38 16.55 16.73 17.12 17.36 17.33 17.22

139.14 10.51 Table 3 (continued) T/K С op,m /R

226.62

13.93

319.35

17.14

T/K

С op,m /R

T/K

С op,m /R

321.31 323.26 325.20 327.14 329.07 330.98 332.87 334.77 336.65 338.52 340.21 341.82 343.88 345.68 347.49 349.26

17.18 17.25 17.33 17.39 17.45 17.51 17.56 17.63 17.69 17.74 17.80 17.85 17.93 17.99 18.05 18.10

320.51 322.40 324.27 326.14 327.98

17.08 17.17 17.25 17.33 17.41

549.4 551.9 554.4 556.9 559.4 561.9 564.4 566.9 569.4 571.9 574.4 576.9 579.4 581.9 584.4 586.9 589.4 591.9 594.4 596.9 599.4 601.9 604.4 606.9

21.3 21.3 21.3 21.3 21.3 21.3 21.3 21.3 21.3 21.3 21.3 21.3 21.3 21.3 21.3 21.3 21.3 21.3 21.3 21.3 21.3 21.3 21.3 21.3

141.38 143.49 145.85 148.08 150.30 151.78 152.91 153.96 155.41 157.59 159.03 161.93 163.35 164.07 165.61 166.94 167.88

10.62 10.74 10.85 10.97 11.04 11.13 11.19 11.26 11.32 11.41 11.47 11.58 11.66 11.70 11.77 11.85 11.88

228.77 230.93 233.08 235.23 237.35 239.50 241.65 243.79 245.94 248.09 250.23 252.37 254.50 256.64 258.77 260.91 263.04

301.00 302.98 304.98 306.97 308.95

16.20 16.28 16.37 16.53 16.68

310.91 312.84 314.77 316.69 318.60

334.4 336.9 339.4 341.9 344.4 346.9 349.4 351.9 354.4 356.9 359.4 361.9 364.4 366.9 369.4 371.9 374.4 376.9 379.4 381.9 384.4 386.9 389.4 391.9

17.6 17.7 17.8 17.8 17.9 18.0 18.1 18.2 18.2 18.3 18.4 18.4 18.4 18.5 18.6 18.7 18.7 18.8 18.8 18.9 18.9 19.0 19.0 19.1

441.9 444.4 446.9 449.4 451.9 454.4 456.9 459.4 461.9 464.4 466.9 469.4 471.9 474.4 476.9 479.4 481.9 484.4 486.9 489.8 491.9 494.4 496.9 499.4

13.97 14.03 14.11 14.16 14.24 14.31 14.38 14.46 14.53 14.60 14.67 14.76 14.83 14.89 14.95 15.02 15.08 Series 3 17.13 17.37 17.30 17.14 17.04 Series 4 20.0 20.1 20.1 20.1 20.2 20.2 20.3 20.4 20.5 20.5 20.6 20.7 20.8 20.9 21.0 21.2 22.0 24.7 29.0 23.6 21.9 21.4 21.3 21.4

394.4 19.2 Table 3 (continued) T/K С op,m /R

501.9

21.5

609.4

21.3

T/K

С op,m /R

T/K

С op,m /R

396.9 19.2 504.4 21.8 611.9 21.4 399.4 19.3 506.9 22.3 614.4 21.4 401.9 19.3 509.4 23.1 616.9 21.4 404.4 19.4 511.6 25.9 619.4 21.4 406.9 19.4 514.4 30.5 621.9 21.4 409.4 19.4 517.3 23.9 624.4 21.4 411.9 19.5 518.6 22.7 626.9 21.4 414.4 19.5 520.2 22.2 629.4 21.4 416.9 19.6 523.1 21.8 631.9 21.4 419.4 19.6 526.9 21.5 634.4 21.4 421.9 19.6 529.4 21.4 636.9 21.4 424.4 19.7 531.9 21.3 639.4 21.4 426.9 19.7 534.4 21.3 641.9 21.4 429.4 19.8 536.9 21.3 644.4 21.4 431.9 19.8 539.4 21.3 646.9 21.4 434.4 19.9 541.9 21.3 649.4 21.4 436.9 19.9 544.4 21.3 439.4 20.0 546.9 21.3 a Standard uncertainty for temperature u(T) = 0.01 K and the combined expanded relative uncertainties for the heat capacities Uc, r( С op,m /R) = 0.02 in the temperature range from T = (5 to 15) K, Uc, r( С op,m /R) = 0.005 between T = (15 to 40) K, Uc, r( С op,m /R) = 0.003 in the temperature range from T = (40 to 340) K, u(T) = 0.2 K and Uc, r( С op,m /R) = 0.025 in the temperature range from T = (340 to 650) K for 0.95 level of confidence (k ≈ 2). b Series 1−3 include experimental results from adiabatic calorimetry and Series 4 − DSC.

TABLE 4 Thermodynamic characteristics of phase transformations for studied crystalline CsCoPO4 at pressure p = 0.1 MPaa Transitions crI ⇄ crII o /K Ttrs1

∆ trs1 H mo / J⋅mol-1

crII ⇄ crIII ∆ trs1 S mo / J⋅K-1⋅mol-1

o /K Ttrs2

∆ trs2 H mo / J⋅mol-1

crIII ⇄ crIV ∆ trs2 S mo / J⋅K-1⋅mol-1

o /K Ttrs3

∆ trs3 H mo / J⋅mol-1

∆ trs3 S mo / J⋅K-1⋅mol-1

313.40 ± 0.01 30.47 ± 0.57 0.094 ± 0.002 486.9 ± 0.2 344.7 ± 6.9 0.71 ± 0.02 514.4 ± 0.2 474.5 ± 9.5 0.92 ± 0.02 Standard uncertainty u is u(p) = 10 kPa; reported uncertainties correspond to the combined expanded uncertainties for 0.95 level of confidence (k ≈ 2)

a

TABLE 5 Thermodynamic functions of CsCoPO4 (M = 286.8115 g · mol−1); R = 8.314472 J · K−1 · mol−1; С op,m . standard molar heat capacity; ∆ T0 H mo /RT. standard molar enthalpy; ∆ T0 S mo /R. standard molar entropy; and Фmo = ∆ T0 S mo − ∆ T0 H mo / T (po = 0.1 MPa) a

T/K

С op,m /R

∆ T0 H mo /RT

5 6 7 8 9 10 15 20 25 30 35 40 45 50 60 70 80 90 100 110 120 130 140 150

0.163 0.280 0.348 0.420 0.492 0.564 0.997 1.617 2.233 2.825 3.403 3.970 4.500 4.981 5.820 6.585 7.284 7.908 8.535 9.091 9.597 10.09 10.58 11.06

0.0433 0.0702 0.105 0.140 0.175 0.210 0.394 0.6212 0.8765 1.153 1.433 1.715 1.995 2.270 2.794 3.281 3.739 4.168 4.573 4.959 5.325 5.672 6.005 6.326

∆ T0 S mo /R

Фmo /R

0.0585 0.0958 0.141 0.195 0.248 0.304 0.607 0.9762 1.398 1.859 2.338 2.830 3.328 3.828 4.812 5.767 6.693 7.587 8.453 9.293 10.11 10.89 11.66 12.41

0.0150 0.0252 0.0359 0.0550 0.0732 0.0938 0.213 0.3553 0.5216 0.7060 0.9048 1.115 1.333 1.557 2.018 2.486 2.954 3.420 3.880 4.334 4.781 5.221 5.654 6.079

Crystal I

160 170 180 190 200 210 220 230 240 250 260 270 273.15 280 290 298.15 300 310 313.40

11.52 11.95 12.35 12.72 13.06 13.38 13.69 14.01 14.34 14.67 15.00 15.31 15.40 15.59 15.85 16.08 16.13 16.47 16.58

6.636 6.937 7.226 7.506 7.775 8.035 8.285 8.527 8.762 8.992 9.216 9.436 9.505 9.651 9.861 10.03 10.06 10.27 10.33

13.13 13.85 14.54 15.22 15.88 16.52 17.15 17.77 18.37 18.96 19.55 20.12 20.30 20.68 21.23 21.67 21.77 22.31 22.47

6.498 6.909 7.314 7.712 8.104 8.489 8.869 9.243 9.611 9.973 10.33 10.68 10.79 11.03 11.37 11.65 11.71 12.04 12.14

∆ T0 H mo /RT

∆ T0 S mo /R

Фmo /R

10.34 10.48 10.69 10.89 11.10 11.29 11.49 11.68 11.87 12.05 12.23

22.48 22.86 23.39 23.91 24.43 24.95 25.46 25.95 26.45 26.93 27.41

12.14 12.37 12.70 13.02 13.34 13.65 13.97 14.27 14.58 14.88 15.18

Crystal II Table 5 (continued) T/K С op ,m /R 313.40 320 330 340 350 360 370 380 390 400 410

16.83 17.12 17.48 17.79 18.09 18.37 18.62 18.85 19.06 19.26 19.45

420 430 440 450 460 470 480 486.9

19.62 19.79 19.96 20.14 20.38 20.74 21.05 21.30

12.40 12.57 12.74 12.90 13.06 13.22 13.38 13.49

27.88 28.34 28.80 29.25 29.70 30.14 30.58 30.89

15.48 15.77 16.06 16.35 16.64 16.92 17.20 17.39

30.97 31.10 31.53 31.95 32.12

17.39 17.48 17.76 18.03 18.14

32.23 32.48 32.88 33.28 33.67 34.06 34.43 34.80 35.17 35.53 35.88 36.22 36.56 36.90 37.23

18.14 18.30 18.57 18.84 19.11 19.37 19.63 19.89 20.15 20.40 20.65 20.90 21.15 21.39 21.63

Crystal III 486.9 490 500 510 514.4

21.30 21.25 21.35 21.35 21.38

13.58 13.62 13.78 13.92 13.98

514.4 520 530 540 550 560 570 580 590 600 610 620 630 640 650

21.29 21.29 21.29 21.29 21.29 21.29 21.29 21.29 21.29 21.29 21.29 21.29 21.29 21.29 21.29

14.09 14.18 14.31 14.44 14.56 14.68 14.80 14.91 15.02 15.12 15.23 15.32 15.42 15.51 15.60

Crystal IV

a

Standard uncertainty of temperature u(T) = 0.01 K and combined expanded relative uncertainties for the heat capacities Uc,r( С op ,m /R) are 0.02, 0.005 and 0.003; and the combined expanded relative uncertainties Uc,r( ∆ T0 H mo /RT) are 0.022, 0.007 and 0.005;

Uc,r( ∆ T0 S mo /R) are 0.023, 0.008 and 0.006; Uc,r( Фmo /R) are 0.03, 0.01 and 0.009 in the ranges from T = (5 to 15) K, T = (15 to 40) K and T = (40 to 340) K, respectively. u(T) = 0.2 K, Uc,r( С op ,m /R) = 0.025, Uc,r( ∆ T0 H mo /RT) = 0.027, Uc,r( ∆ T0 S mo /R) = 0.030 and Uc,r( Фmo /R) = 0.032 in the temperature range from T = (340 to 650) K, respectively for 0.95 level of confidence (k ≈ 2).

The temperature dependence of the heat capacity of crystalline phosphate CsCoPO4. Ivan V. Korchemkin; Vladimir I. Pet'kov; Alexey V. Markin; Natalia N. Smirnova; Andrey M. Kovalskii.

Highlights •

The heat capacity of crystalline phosphate CsCoPO4 was performed between (6 and 650) K.

•

Phase transitions were found at 313.40, 486.9 and 514.4 K.

•

Thermodynamic functions were calculated over the range of T = (0 and 650) K.