Thermodynamic properties of dysprosium polyselenides

J. Chem. Thermodynamics 102 (2016) 89–94

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Thermodynamic properties of dysprosium polyselenides L.N. Zelenina a,b,⇑, T.P. Chusova a, A.V. Isakov a a b

Nikolaev Institute of Inorganic Chemistry, Siberian Branch of Russian Academy of Sciences, Ac. Lavrentyev Ave. 3, 630090 Novosibirsk, Russia Novosibirsk State University, Pirogova Street 2, 630090 Novosibirsk, Russia

a r t i c l e

i n f o

Article history: Received 7 April 2016 Received in revised form 9 June 2016 Accepted 2 July 2016 Available online 4 July 2016 Keywords: Rare-earth polyselenides Vapor pressure measurement Phase diagram Enthalpy of formation Absolute entropy Thermodynamic simulation

a b s t r a c t A detailed thermodynamic study of the DySe1.875–DySe1.50 system has been performed using a static method within the temperature range 595–1330 K. Single crystals of DySe1.875 composition grown by chemical transport reactions were investigated as an initial compound. The p–T–x dependences obtained in this study show that the regions between the boundary compositions DySe1.875 and DySe1.50 consist of discrete stoichiometric phases whose compositions submit to the same dependence (LnnSe2n
1) which was found earlier for the other similar systems. A set of standard thermodynamic functions (DfH°298, S°298) were determined for each polyselenide using the enthalpy and entropy of stepwise dissociation processes calculated from experimental data. The information obtained was used for thermodynamic simulation of crystal growth processes in the system studied. Ó 2016 Elsevier Ltd.

1. Introduction Rare-earth polyselenides are promising for the creation of functional materials with effective optical, magnetic and thermoelectric properties. A characteristic feature of these compounds with LnSex composition (1.5 < x < 2.0) is the ability of selenium atoms to create a low-dimensional structure in anion sublattice [1,2]. This ability appears in a rich variety of superstructures whose period grows with decrease of x [3,4]. The displacement of the selenium atoms in new positions of superstructures leads to charge density wave formation and to the emergence of electronicstructural transitions [5,6]. For experimental investigation of their properties the high-quality crystals of rare-earth polyselenides are needed. These crystals are difficult to obtain without knowledge of the thermodynamic parameters (pSe–T–x) which define the conditions of their growth. Previously, we have studied the polyselenides of cerium group in the systems LnSe2-d–LnSe1.5 (Ln = La, Ce, Nd, Pr, Gd, Sm) [7–10] and revealed the regularity (LnnSe2n
1) in the composition change of solid phases under stepwise removing the selenium atoms from anionic lattice. This work is devoted to the polyselenides of yttrium group, namely DySex (1.5 < x < 1.875). In the literature, there is generally information only on the boundary compounds of this system. For DySe1.5 (Dy2Se3) there are information on synthesis [11] and ⇑ Corresponding author at: Nikolaev Institute of Inorganic Chemistry, Siberian Branch of Russian Academy of Sciences, Ac. Lavrentyev Ave. 3, 630090 Novosibirsk, Russia. E-mail address: [email protected] (L.N. Zelenina). http://dx.doi.org/10.1016/j.jct.2016.07.004 0021-9614/Ó 2016 Elsevier Ltd.

structure [12,13] and thermodynamic characteristics of the formation reaction (DfH°298, DfG°298, DfS°298) [14] obtained by calorimetrical method. The synthesis and structure of DySe1.875 (Dy8Se15) are described in [15]. The only intermediate phase with composition DySe1.84 is presented in [16] (synthesis) and in [6] (structure). As concerns the other intermediate polyselenides with the selenium content from 1.875 to 1.5 the literature data have sketchy information about the number of phases and their real composition while their thermodynamic properties aren’t presented at all. The aim of this work is to clarify the compositions and homogeneity regions of intermediate phases in the system DySe1.875–DySe1.5, to obtain a set of standard thermodynamic functions of these phases and to calculate the optimal growth conditions for intermediate phases by thermodynamic simulation. 2. Experimental The samples investigated in this work were synthesized from the elements of mass fraction purity as follows (Dy: 0.9999, powder Strem; Se: 0.9999, powder, Fluka) in the Institute of Inorganic Chemistry of the Technical University of Dresden, Germany by the way described in detail in [15]. Obtained product was single crystals which have been characterized by X-ray powder diffraction (STOE IPDS-II, MoKa radiation, graphite monochromator), single crystal X-ray diffraction (IPDS-1 Stoe & Cie., MoKa-Radiation, Graphite-Monochromator) and by EDXA (Zeiss scanning electron microscope 982 Gemini with Noram Voyager analytic unit). According to the analysis results the samples were pure single crystals with composition DySe1.875 (see Appendices, Table A.1).

L.N. Zelenina et al. / J. Chem. Thermodynamics 102 (2016) 89–94

The selenium vapor pressure has been measured by the static method with quartz membrane-gauge manometers [17] using an anisothermic [18,19] procedure. The schematic diagram of the experimental setup, the main characteristics of the experimental unit and the procedure of operation were described in more detail in our previous works [9,10,20]. The temperature of manometer inner chamber where the investigated sample was placed is measured by a platinum-(platinum + 0.1 mass fraction of rhodium) thermocouple (type S), preliminarily calibrated with the use of standard substances, with accuracy ±0.3 K. A radial and linear gradient of the temperature in the furnace does not exceed 0.5 K throughout the volume occupied by the inner chamber. The sensitivity of the membrane gauge-manometers used in the present study varied from 7 to 13 Pa. The compensating pressure is measured by use of mercury manometer (inner diameter 25 mm) and cathetometer, with an error of less than 5 Pa. The other instrumental errors were no more than 133 Pa. The accuracy in the determination of the sample mass was ±0.01 mg. The volume of the membrane-gauge manometer was defined as a difference between the weight of the manometer filled with water and an empty one, with the accuracy of 10
4 dm3. The uncertainty in values of composition (x) obtained from uncertainties of pressure (133 Pa), temperature (0.5 K), volume (10
4 dm3) and mass (0.01 mg) was 0.01 formula units. Thus, the standard uncertainties (u) in values of pressure, temperature and solid phase composition were 133 Pa, 0.5 K and 0.01 f. u., accordingly. The investigated sample was loaded into the inner chamber of membrane-gauge manometer and it was heated at 373 K under dynamic vacuum for one hour; then it was sealed. Pressure measurements were recorded after reaching the equilibrium at a given temperature. The measurements have been realized in wide intervals of temperature (595 6 T/K 6 1330), pressure (0.06 6 p/kPa 6 58.0) and composition (1.5 6 x/f. u. 6 1.875). The pressures measured from low to high temperatures and backwards were identical at the same temperature. This procedure guaranteed the achievement of equilibrium. The time of the three-phase equilibrium establishment in our experiments varied from 100 h at low temperatures to one hour at high temperatures.

mj is the initial sample mass and M is its molecular mass; R is the gas constant. Four experiments with different values of crystal mass and manometer volume (2.38 6 m/V, g/dm3 6 14.77) were carried out to scan the whole compositional range from DySe1.875 to DySe1.5. Total pressure was recalculated on partial pressure of Se2(g) as this species is predominant in the gas phase under experimental conditions. The obtained p(Se2)–T–x dependencies plotted as two-dimensional lg p
1/T and x
1/T diagrams are presented in Fig. 1a, b. As well as in earlier studied systems [7–10] the experimental data have a step-like form (Fig. 1a). It means that in the system studied there are intermediate phases of constant composition. The compositions of these solid phases were established from the x
1/T diagram (Fig. 1b). After transforming to stoichiometry these compositions submit to earlier found regularity LnnSe2n
1 with n = 3 (DySe1.67), 4 (DySe1.75), 5 (DySe1.80) and 7 (DySe1.85). The points from different experiments (Fig. 1a), lying on one straight line (I–V), belong to monovariant three-phase equilibrium between two adjacent solid polyselenides and the selenium vapor phase. The monovariant three-phase equilibria in this system can be represented by following formal reactions:

(a) 4.5

V

x ¼ ðNSe =N Dy Þij ¼

8 pSeðnÞ V  X n RT ij j n¼1

mj =M

I

3.5 3.0 exp. 1 m/V = 7.86 exp. 2 m/V = 2.38 exp. 3 m/V = 14.77 exp. 4 m/V = 3.90

2.5 2.0

0.9

1.0

1.1

1.2

1.3

1.4

3

10 K/T

(b) 1.90

I

1.85

II

1.80

III

1.75

x in DySex

The total pressure over DySe1.875 samples was measured as a function of temperature at fixed volume in four experiments. These experimental data are presented in Appendices (Fig. A.1). As can be seen from this figure all samples along with DySe1.875 monocrystals contained free selenium, which is X-ray amorphous substance. Thanks to the static method, we could accurately determine the amount of free selenium in each experiment. This amount was calculated at the points of exit in unsaturated vapor from monovariant equilibrium line Se(l) = Se(g) [21]. The initial Se/Dy ratio is presented in the legend of the Fig. A.1 for each experiment. The composition of the condensed phases (x in DySex) was calculated according to the equation:

NSe;j


III II

0.8

3. Results and discussion

IV

4.0

lgp(Se2)/Pa

90

IV

1.70 1.65 exp. 1 m/V = 7.86 exp. 2 m/V = 2.38 exp. 3 m/V = 14.77 exp. 4 m/V = 3.90

1.60 1.55

V

1.50

ij

;

ð1Þ

where x = (NSe/NDy)ij is the atomic ratio in the condensed phase at a temperature Tij for any data point i of experiment j; NSe,j is the initial amount of selenium g-atom in the sample; pSe(n)ij is partial pressure of Sen calculated from the experimental total pressure using equilibrium constants for the reaction Sen = nSe taken from [21]; n is number of atoms in Sen molecule and Vj is manometer volume;

1.45

0.8

0.9

1.0

1.1

1.2

1.3

1.4

3

10 K/T Fig. 1. Temperature dependence of Se2 pressure (a) and solid phase composition (b) for DySex dissociation plotted as lg p = f(1/T) and x = f(1/T). The lines I–V (a) and regions I–V (b) correspond to monovariant three-phase equilibrium between two adjacent solid polyselenides and the selenium vapor phase. Sample mass and manometer volume (m/V, g/dm3) are presented in the legend of this figure for each experiment.

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L.N. Zelenina et al. / J. Chem. Thermodynamics 102 (2016) 89–94 Table 1 Absolute entropies (S°298) and heat capacities (C°p,298) of compounds at T = 298 K, which were used for calculation. Compound

S°298/J K
1 mol
1

C°p,298/J K
1 mol
1

Reference

Se2(g) Se(s) DySe1.50(s) DySe1.67(s) DySe1.75(s) DySe1.80(s) DySe1.85(s) DySe1.875(s)

247.28 ± 0.30 42.27 ± 0.25 120.3 ± 10 127 131 133 135 136

41.742 ± 0.05 25.05 ± 0.05 64.7 ± 7 69.0 71.0 72.2 73.5 74.1

[21] [21] [24]



I: 80DySe1:875 ðsÞ ¼ 80DySe1:85 ðsÞ þ Se2 ðgÞ

lnðp=p Þ  2r ¼ A
B=T
C  lnðTÞ;

II: 40DySe1:85 ðsÞ ¼ 40DySe1:80 ðsÞ þ Se2 ðgÞ

IV: 25DySe1:75 ðsÞ ¼ 25DySe1:67 ðsÞ þ Se2 ðgÞ V: 11:76DySe1:67 ðsÞ ¼ 11:76DySe1:50 ðsÞ þ Se2 ðgÞ: The experimental pressures belonging to I–V processes in the systems studied are collected in the section Appendices (Table A.2). For the processes I–V the partial pressure of Se2 is expressed by equation: 





p ¼ p exp½
Dr H298 =RT þ Dr S298 =R þ uðDr C p; TÞ;

ð2Þ

where p° is the standard pressure of 101.325 kPa, DrH°298 and DrS°298 are the enthalpy and the entropy of the process, respectively, at T = 298 K and u(DrC°p,T) is some function of temperature which is determined by difference in heat capacities of reaction ingredients. The processing of the experimental data was carried out by least-squares method with criterion function based on the principle of maximal likelihood [22,23]:

W¼

X

2

ðpe ðSe2 Þ
pc ðSe2 ÞÞ2 =ððDpÞ2 þ ðdp=dTÞ  ðDTÞ2 Þ;

ð3Þ

where pe(Se2) is the pressure of Se2 obtained from experimental pressure using the equilibrium constants for the process Sen(g) = nSe(g) [21], pc(Se2) is the pressure calculated by equation (2), Dp and DT are the uncertainties in the measurements of the pressure and temperature, respectively. The procedure of data processing included the calculation both required parameters (DrH°298 and DrS°298) and their expanded uncertainties U (0.95 level of confidence). The calculation was performed on the basis of the second and third law of thermodynamics. It means that in the case of the second law, enthalpy and entropy were the sought values while heat capacities were considered to be known. When carrying out the treatment according to the third law, the entropy of the reaction was also considered to be known. For performing these calculations the values of the heat capacities of the compounds participating in the I–V equilibria are required. For treatment according to the third law absolute entropies of these compounds are also necessary. In the case of gaseous selenium these values are taken from IVTANTERMO Database [21]. Absolute entropies and heat capacities of the intermediate polyselenides were estimated by Neumann-Kopp’s additive rule. Calculation was carried out on the basis of the equation:

LnSex ðsÞ ¼ LnSe1:5 ðsÞ þ ðx
1:5ÞSeðsÞ:

ð5Þ

r2 ¼ a=T 2
b=T þ c;

III: 40DySe1:80 ðsÞ ¼ 40DySe1:75 ðsÞ þ Se2 ðgÞ



Our estimation on the equation: DySex(s) = DySe1.5(s) + (x
1.5) Se(s)

ð4Þ

For solid selenium these values were also taken from IVTANTERMO Database [21]. Unfortunately the experimental values of low-temperature DySe1.5(s) heat capacity are not obtained yet therefore we used the values of C°p,298(DySe1.5, s) and S°298(DySe1.5, s) [24] estimated by comparative method. All these values are presented in Table 1. The results of the processing of all our experimental data are presented in Tables 2 and 3. The Se2 pressure in the monovariant equilibria I–V was approximated by the following expression:

where r2 is the temperature dependence of dispersion of pressure calculated by expression (5). The uncertainties in the thermodynamic values (DrH°298 and DrS°298) refer to 95 per cent confidence limit. The deviations of experimental pressure values from those calculated by the equations given in Table 2 were random and did not exceed standard uncertainties in temperature u(T) and pressure u(p) measurements. As an example such deviations are shown in Appendices (Fig. A.2) for the reaction I. 80DySe1.875(s) = 80DySe1.85(s) + Se2(g). The results obtained by using the second-law approach are in good agreement with the same values calculated on the thirdlaw method (Table 3). This fact confirms the absence of systematic errors in our experiments. The thermodynamic characteristics of the dissociation processes (DrH°298, DrS°298) from Table 3 obtained by second-law treatment were used to calculate the standard thermodynamic functions of polyselenides (DfH°298, S°298). Standard enthalpy of Se2(g) formation (DfH°298 (Se2, g) = 144.144 kJ mol
1) which was necessary for calculation was taken from IVTANTERMO Database [21]. The values obtained are presented in Table 4 together with the experimental value of standard enthalpy of formation [14] and the estimated value of absolute entropy [24] of DySe1.5(s) used at calculations. The information obtained was used to calculate the phase equilibria with participation of compounds studied. To select the optimal conditions for growing crystals of DySe1.67, DySe1.75 and Table 2 Temperature dependences of Se2 pressure ln(p/p°) ± 2r = A
B/T
Cln(T) for I–V reactions of DySe1.875–DySe1.5 system, where p° is the standard pressure of 101.325 kPa, r2 = a/T2
b/T + c. Number of reaction

A

B

C

a

b

c

I II III IV V

26.253 25.962 26.150 26.128 25.348

19435.8 19501.1 21833.1 24067.1 24692.2

1.01250 1.00294 1.00294 1.00847 1.00546

27,306 17,847 10,740 12,142 8443.1

65.639 42.606 21.237 21.232 14.450

0.03947 0.02546 0.01051 0.00930 0.00619

Table 3 Thermodynamic characteristics (DrH°298, DrS°298) for the stepwise dissociation processes of dysprosium polyselenides.* Number of reaction

I II III IV V

DrH°298/kJ mol
1

DrS°298/J K
1 mol
1

Second law

Third law

Second law

Third law

159.1 ± 2.7 159.6 ± 2.2 179.0 ± 1.7 197.6 ± 1.8 202.8±1.5

160 ± 2.7 162 ± 2.2 180 ± 1.7 199 ± 1.8 202±1.5

161.9 ± 3.3 160.0 ± 2.6 161.6 ± 1.6 161.1 ± 1.6 163.1±1.3

163 ± 10 163 ± 10 163 ± 10 163 ± 10 163 ± 10

* Combined expanded uncertainties Uc (0.95 level of confidence) are presented in the table for DrH°298 and DrS°298.

L.N. Zelenina et al. / J. Chem. Thermodynamics 102 (2016) 89–94

Table 4 Standard enthalpies of formation (DfH°298) and absolute entropies (S°298) of dysprosium polyselenides at T = 298 K.* Solid phase


DfH°298/kJ mol–1

S°298/J K
1 mol
1

DySe1.875 DySe1.85 DySe1.80 DySe1.75 DySe1.67 DySe1.50

490.5 ± 16.0 490.4 ± 15.9 489.9 ± 15.9 489.1 ± 15.8 486.9 ± 15.8 482.0 ± 15.7 [14]

136.3 ± 11 135.2 ± 11 133.0 ± 11 130.9 ± 11 127.5 ± 10 120.3 ± 10 [24]

* Combined expanded uncertainties Uc (0.95 level of confidence) are presented in the table for DfH°298 and S°298.

Table 5 List of the chemical compounds used for thermodynamic simulation. Phase state

Chemical compounds

Solid

Dy, DySe1.50, DySe1.67, DySe1.75, DySe1.80, DySe1.85, DySe1.875, Se (4 modifications), Dy2O3, DyI3, SeO2, SiO2 (9 modifications), I2 SeO2, I2 Si3, Si2, Se8, Se7, Se6, Se5, Se4, Se3, Se2, Se, Dy, DyO, SiO2, SiO, SeO2, SeO, O2, O3, DyI, DyI3, SiI, SiI2, SiI3, SiI4, IO, I2, I, Ar, O, Si

Liquid Gas

Table 6 Results of the simulation of the crystals growth process of DySe1.67, DySe1.75 and DySe1.80 by the vapor transport technique using iodine as the transport reagent. Atomic concentrations of elements n, g/atom I

0.05 0.2 0.5 0.05 0.2 0.5 0.05 0.1 0.5

Se

1.80 1.80 1.80 1.875 1.75 1.75 1.75 1.875 1.67 1.67 1.875

Total pressure p = 101.325 kPa

Dy

1 1 1 1 1 1 1 1 1

depending on the atomic concentrations of iodine, selenium, and dysprosium. It should be noted that none of the variants of equilibrium calculation did not reveal the existence of products of interaction of quartz with the initial components. The main results of simulation are presented in Table 6. The obtained dependence of a yield of phases on the temperature of synthesis and the concentration of iodine for the initial chemical composition of DySex has allowed us to determine the optimum conditions of carrying out equilibrium processes. 4. Conclusion The pressure of selenium in the process of DySe1.875 dissociation has been measured by static method for the first time. The p–T–x dependences obtained have revealed the existence of dysprosium polyselenide phases whose composition submits to the same general formula LnnSe2n
1 found earlier for other rare-earth polyselenides. On the base of thermodynamic characteristics of dissociation processes calculated from experimental data a set of standard thermodynamic functions (DfH°298, S°298) was obtained. This set was used for thermodynamic simulation of chemical transport reactions with iodine as a transport agent. As a result of the simulation the optimal conditions for growing crystals of DySe1.67, DySe1.75 and DySe1.80 were obtained. Acknowledgments

Condensed phases formed T/K

Composition (x in DySex)

Yield (mol% DySex)

847–970 890–1000 914–1018 1000–1028 936–1032 1000–1096 1018–1137 1033–1155 1031–1044 1062–1076 1163–1178

1.80 1.80 1.80 1.80 1.75 1.75 1.75 1.75 1.67 1.67 1.67

95.0 80.0 50.0–83.3 83.6–83.3 95.0–98.3 93.3 83.3 83.3 98.3 96.7 83.3

Appendix Table A.1 Characterization of the samples. Element

Provenance

Dy Se

Powder, Strem 0.9999 Powder, Fluka 0.9999 Single crystals of dysprosium polyselenide Composition Mass fraction purity DySe1.875±0.013 0.999

Mass fraction purity

5.0 4.5 = (l) Se

4.0

Se ) (g

DySe1.80 the thermodynamic simulation of chemical transport reactions with iodine as a transport agent has been carried out in a wide interval of temperatures and initial concentration of iodine and selenium. The list of the condensed phases and the gaseous species included in the calculations is presented in Table 5. The calculation of equilibria is based on the minimization of the total Gibbs energy of the system studied and carried out an iterative Newton’s method for nonlinear systems [25,26]. The standard thermodynamic functions of dysprosium polyselenides are presented in this work. Thermodynamic data of dysprosium iodides are taken from [27–29] for other compounds from [21]. The calculations were performed for the total pressure of 101.325 kPa, therefore, inert gas (Ar) was added to the system. Oxygen and silicon in the ratio 2:1 have been included in the calculations because the synthesis of crystals is usually carried out in quartz reactors. The presence of gaseous Dy, Si and O atoms in the list (Table 5) is connected with the feature of equilibrium calculation program: the formation functions of compounds are calculated by the formation reactions from monatomic gases. Possible condensed phases in the equilibrium with the gas phase were calculated for a wide range of ratios of atomic concentrations of the elements (Ar:Dy: Se:I:O:Si) and temperatures (873–1223 K). The calculation gave the temperature ranges of the existence of the DySe1.67, DySe1.75 and DySe1.80 phases without admixture of other condensed phases

The authors thank Prof. Dr. Th. Doert, Institute of Inorganic Chemistry of the Technical University of Dresden, Germany for synthesis and analysis of DySe1.875. This work was financially supported by the Russian Foundation for Basic Research, Russia (project No. 14-03-00619-a).

lgpexp/Pa

92

3.5 3.0 2.5

[21] exp. 1 NSe/NDy = 1.932

2.0

exp. 3 NSe/NDy = 1.900

0.7

exp. 2 NSe/NDy = 1.932 exp. 4 NSe/NDy = 1.900

0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

3

10 K/T Fig. A.1. Temperature dependence of total experimental pressure for DySe1.875– DySe1.5 system. The initial Se/Dy ratio is presented in the legend of the figure for each experiment.

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L.N. Zelenina et al. / J. Chem. Thermodynamics 102 (2016) 89–94

Table A.2 Experimental values of pressure pexp measured at temperature T for solid phase composition x in DySex in experiment Nexp. The values of pSe2, which used further for thermodynamic computations, are calculated from experimental pressure pexp.* pSe2 /Pa

x/f. u.

Nexp: m/V/(g/dm3)

I. 80DySe1.875(s) = 80DySe1.85(s) + Se2(g) 827.7 3700 836.0 4330 846.0 5440

1910 2280 2870

1.861 1.851 1.851

1: 7.86

789.6 798.4 803.2 803.1 802.9

1170 1250 1590 1550 1540

650 750 910 890 890

1.871 1.869 1.852 1.856 1.857

2: 2.38

844.0 849.0 848.8 846.3 844.2 842.1 840.3

5400 5960 5580 5460 5320 5160 5000

2890 3150 3040 2880 2780 2670 2580

1.853 1.851 1.853 1.853 1.854 1.856 1.857

3: 14.77

784.25

930

540

1.851

4: 3.90

II. 40DySe1.85(s) = 40DySe1.80(s) + Se2(g) 865.7 5540 863.1 4960

3470 3190

1.821 1.822

1: 7.86

819.2 817.6 823.8

1540 1530 1840

1040 1020 1210

1.819 1.819 1.801

2: 2.38

868.8 873.9 872.4 870.0 866.2 868.1

6840 7070 6580 6460 6340 6430

4050 4320 4080 3950 3780 3880

1.848 1.844 1.845 1.847 1.849 1.850

3: 14.77

797.5 803.6 801.7 799.9 805.8 813.9 818.6

900 1000 980 960 1030 1230 1440

600 680 670 640 710 860 990

1.842 1.839 1.839 1.840 1.838 1.832 1.824

4: 3.90

III. 40DySe1.80(s) = DySmSe1.75(s) + Se2(g) 1019.9 11,780 1025.1 13,010

11,120 12,310

1.799 1.770

1: 7.86

955.7

2950

2840

1.799

2: 2.38

1028.5 1037.6 1035.7 1035.6

14,090 16,730 16,400 16,330

13,260 15,700 15,380 15,320

1.799 1.777 1.778 1.778

3: 14.77

968.7 970.4 971.4 963.4 976.0 973.8

3980 4010 3980 3620 4520 4500

3820 3850 3830 3480 4340 4310

1.791 1.792 1.792 1.799 1.749 1.750

4: 3.90

IV. 25DySe1.75(s) = DySmSe1.67(s) + Se2(g) 1164.1 19,360 1164.6 19,470 1165.0 19,480 1184.4 27,290

19,020 19,120 19,130 26,750

1.749 1.749 1.748 1.745

1: 7.86

1083.8

4410

4370

1.700

2: 2.38

1173.3 1187.7

22,420 29,160

22,010 28,560

1.749 1.680

3: 14.77

1093.2 1103.0 1108.1

5480 6590 7330

5420 6500 7230

1.746 1.728 1.713

4: 3.90

28,040 37,930

1.670 1.609

1: 7.86

T/K

pexp/Pa

V. 11.76DySe1.67(s) = 11.76DySe1.50(s) + Se2(g) 1203.2 28,550 1222.8 38,700

(continued on next page)

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L.N. Zelenina et al. / J. Chem. Thermodynamics 102 (2016) 89–94

Table A.2 (continued)

*

Nexp: m/V/(g/dm3)

T/K

pexp/Pa

pSe2 /Pa

x/f. u.

1235.3 1243.00

46,530 51,310

45,550 50,200

1.552 1.517

1126.8 1135.5 1136.1 1136.3 1156.3 1117.6 1145.8 1148.4

7540 8640 8740 8820 12,460 6770 10,540 11,540

7450 8540 8640 8710 12,290 6690 10,410 11,380

1.618 1.590 1.587 1.585 1.510 1.638 1.540 1.523

1232.8

45,300

44,350

1.608

3: 14.77

1127.8 1147.9 1157.7 1167.8 1177.6

7500 10,560 12,870 15,520 17,750

7410 10,480 12,700 15,300 17,480

1.670 1.630 1.594 1.553 1.519

4: 3.90

2: 2.38

Standard uncertainties u are u(T) = 0.5 K, u(p) = 133 Pa and u(x) = 0.01 f. u.

120 100

pexp(Se2) - pcalc(Se2)/Pa

80 60 40 20 0 -20 -40 -60 -80 -100 -120

exp. 1 exp. 2 exp. 3 exp. 4

780 785 790 795 800 805 810 815 820 825 830 835 840 845 850 855

T/K Fig. A.2. Difference between the values of experimental pressure (pexp) and calculated one (pcalc) by the corresponding equation in Table 2 for the reaction I. 80DySe1.875(s) = 80DySe1.85(s) + Se2(g) in four series of experiments.

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JCT 16-268