Enthalpy of formation and lattice energy of bismuth perrhenate doped by neodymium and indium oxides

Enthalpy of formation and lattice energy of bismuth perrhenate doped by neodymium and indium oxides

Accepted Manuscript Title: Enthalpy of formation and lattice energy of bismuth perrhenate doped by neodymium and indium oxides Authors: N.I. Matskevic...

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Accepted Manuscript Title: Enthalpy of formation and lattice energy of bismuth perrhenate doped by neodymium and indium oxides Authors: N.I. Matskevich, Th. Wolf, P. Adelmann, A.N. Semerikova, N.V. Gelfond, E.S. Zolotova, M.Yu. Matskevich PII: DOI: Reference:

S0040-6031(17)30265-4 https://doi.org/10.1016/j.tca.2017.10.010 TCA 77852

To appear in:

Thermochimica Acta

Received date: Revised date: Accepted date:

4-5-2017 8-10-2017 12-10-2017

Please cite this article as: N.I.Matskevich, Th.Wolf, P.Adelmann, A.N.Semerikova, N.V.Gelfond, E.S.Zolotova, M.Yu.Matskevich, Enthalpy of formation and lattice energy of bismuth perrhenate doped by neodymium and indium oxides, Thermochimica Acta https://doi.org/10.1016/j.tca.2017.10.010 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Enthalpy of formation and lattice energy of bismuth perrhenate doped by neodymium and indium oxides N.I. Matskevicha,b,c*, Th. Wolfa*, P. Adelmanna, A.N. Semerikovab, N.V. Gelfondb, E.S. Zolotovab, M.Yu. Matskevichb a

Karlsruhe Institute of Technology, Institute of Solid State Physics, Karlsruhe, D-76344, Germany

b

Nikolaev Institute of Inorganic Chemistry, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, 630090, Russia

c

Physical Department, Novosibirsk State University, Novosibirsk, 630090, Russia

Highlights    

We measured formation enthalpy of Bi12.5Nd1.4In0.1ReO24.5.   We calculated lattice energy for Bi12.5Nd1.4In0.1ReO24.5.  Lattice energy has linear character from lanthanides radius. 

Abstract For the first time the standard formation enthalpy of Bi12.5Nd1.4In0.1ReO24.5 has been determined by solution calorimetry by combining the solution enthalpies of Bi12.5Nd1.4In0.1ReO24.5, 1.4NdCl3 + 0.1InCl3 mixture in 2 M HCl and literature data. The lattice energy for Bi12.5Nd1.4In0.1ReO24.5 has been calculated using Born-Haber cycle. The dependence of lattice energy for Bi12.5R1.5ReO24.5 (R – rare earth element) from radius of rare earth metal was constructed. It was established that dependence was linear and had form: Ulat = -129450 + 45070 rR. Linear character of experimentally obtained dependence was explained using modified variant of Kapustinskii formula obtained by us as following: U = A + BrR. Keywords: doped bismuth oxide; formation enthalpy; lattice energy 1. Introduction Compounds on the bismuth oxide basis are multifunctional materials which are perspective to be used as inorganic ecological pigments, ceramic oxygen generators, scintillators, etc. [1-10]. One of their most important functional characteristics is a high ionic conductivity. -Bi2O3 has the highest ionic conductivity among solid-state ionic conductors [11-14]. But the problem of applying - bismuth oxide is its existence in a narrow temperature range (1000-1100 K). Below 1000 K the -modification of bismuth oxide transfers to another oxide modification which has a lower ionic conductivity than -Bi2O3. _________________________________ 1   

*Corresponding author. E-mail: [email protected] There were a lot of attempts to stabilize -Bi2O3 by a variety of elements at room temperature. It was performed substituting by isovalent or nonisovalent elements such as rareearth metals, niobium, tungsten, etc. About 10 years ago new oxide compounds where bismuth was substituted by rare-earth elements and rhenium (bismuth perrhenates) were synthesized [1518]. The structure of these compounds is related to cubic -Bi2O3 (fluorite, space group Fm-3m). The compounds possess a high ionic conductivity in the temperature range of 500-900 K. The general formula of these compounds is Bi12.5R1.5ReO24.5 (R – a rare-earth element). Authors [19-20] found that small excess of tungsten oxide (in the range from 0.2 wt% to 0.5 wt%) to ZnMoO4 can improve physico-chemical properties. In papers [21-22] the effect of rare earth elements replacing by indium in doped barium cerates was studied. It was shown that thermodynamic stability of barium cerates was increased by indium adding. Our research is devoted to thermodynamic investigation of bismuth perrhenate doped by indium and neodymium oxides. Solution calorimetry will be used to measure standard formation enthalpy (fHo), and then lattice energy will be calculated on the basis of fHo. The lattice energy will be calculated using Born–Haber cycle. Earlier we measured the formation enthalpies for Bi12.5R1.5ReO24.5 (R = La, Nd, etc.). Based on experimental data of this paper and our earlier thermochemical data we constructed the dependence of lattice energy for Bi12.5R1.5ReO24.5 from radius of rare earth elements. 2. Material and methods A compound Bi12.5Nd1.4In0.1ReO24.5 was synthesized from bismuth oxide, neodymium oxide, indium oxide and ammonium perrhenate. The following compounds were used: Bi2O3 (99.999%, ABCR), NH4ReO4 (>99%, Alfa Aesar, Johnson Matthey Company), Nd2O3 (99.9%, Reacton, Rare Earth Products, Division of Johnson Mattey Chemical LTD), and In2O3 (99.99%, Reacton, A Johnson Matthey Company). Nd2O3 and In2O3 were treated at 900 K up to a constant weight before the synthesis. Initial compounds were mixed and ground in a planetary ball mill. Then the mixture was pressed in a pallet, placed into a furnace and heat treated in air at 1100 K. Grinding, pelletizing, and sintering procedures were repeated on the sample to ensure complete reaction. Phase identification was carried out by powder X-ray diffraction (XRD) using a STADIP, Stoe diffractometer (Germany) with Mo_radiation. Sample Bi12.5Nd1.4In0.1ReO24.5 was confirmed to be single phase. We have done a refinement of lattice parameters with a program called “Index & Refine” from the Stoe software package. Bi12.5Nd1.4In0.1ReO24.5 is cubic (fluorite) at room temperature. Space group is Fm3m. The refined cell parameters for Bi12.5Nd1.4In0.1ReO24.5 2   

are: a = 0.56116 ± 16 nm, a cell volume – 0.1767 nm3. Here the standard uncertainty is presented (for standard uncertainties the default level of confidence is 0.68) for cell parameter “a”. Figure for X-ray diffraction is presented in paper [22]. We also characterized the Bi12.5Nd1.4In0.1ReO24.5 phase by infra-red spectroscopy. Infra-red spectroscopy showed the rhenium had valence +7. The same valence of rhenium (+7) was noted in papers [11, 15, 18] for bismuth perrhenates doped by rare-earth elements. We performed analysis of phase Bi12.5Nd1.4In0.1ReO24.5 using differential dissolution method [23] as well. The differential dissolution method is more efficient in solving problem when it is necessary to determine minor phases within complex substances. It is one or two orders of magnitude more sensitive than power X-ray diffraction. According to differential dissolution method the compound Bi12.5Nd1.4In0.1ReO24.5 was confirmed to be monophasic. Sample Bi12.5Nd1.4In0.1ReO24.5 was also characterized by chemical analysis. For the analysis of Bi, Nd, In a spectrophotometric method (spectrophotometer SF-46) was used. The ARL ADVANT’XP sequential X-ray Fluorescence Spectrometer was used to analyze Re content. The oxygen content was determined by reducing melting method. According to results of analysis the investigated compound (Bi12.5Nd1.4In0.1ReO24.5) corresponds to above-mentioned formula. Found content of In was 0.31 ± 0.03 wt.% (calculated 0.33 wt.%). Found content of oxygen was 11.47 wt.% (calculated 11.52 wt.%). Characterization of chemical samples used in this study is presented in Table 1. NdCl3 and InCl3 were prepared as described in paper [21]. NdCl3 was prepared from Nd2O3. Nd2O3 was dissolved in an excess of hydrochloric acid. Purified chlorine gas was bubbled through the solutions. Solution was then evaporated. Further drying was accomplished by evaporating under vacuum at about 350 K until the remaining chloride crystals appeared in composition. Final drying was accomplished by heating slowly in a hydrogen chloride atmosphere to a final temperature of 600 to 700 K. InCl3 was synthesized from Cl2 and In. Chlorine gas was passed over indium at temperature about 450 K. All manipulations with NdCl3 and InCl3 were performed in a dry box (pure Ar gas). NdCl3 and InCl3 mixture was prepared in ratio 1.4:0.1. Solution calorimetry was used to determine thermochemical characteristics. The solution calorimetric experiments were carried out in an automatic calorimeter with an isothermal jacket. The calorimeter consists of a Dewar vessel with a brass cover (V = 250 ml). The thermometer, calibration heater, cooler, mixer, and device to break ampoules were mounted on the lid closing the Dewar vessel. The construction of solution calorimeter together with the calorimetric procedure was described elsewhere [24-26]. The resistance of thermometer was measured by high precision voltmeter Solartron 7061. An interface, designed according to IEEE 3   

488 standard, was created to connect the calorimeter heater and thermistor to the computer. The program allows one to measure and record the vessel temperature and calibration parameters. The program was written in Matlab in our laboratory. Automatic calibration of the calorimeter was used. The calorimetric vessel was maintained at 298.15 K. The dissolution of potassium chloride in water was performed to calibrate the calorimeter. We dissolved KCl and measured dissolution heat (T = 298.15 K). The final solution molarity was 0.028 mol kg1 (it corresponds to about 0.5 g KCl dissolved in calorimetric vessel with volume 250 ml). The experiments were performed as following. We dissolved potassium chloride and measured the temperature rise of reaction (Tex). Next we carried out the calibration experiment with using heater, i.e. introduced exact quantity of heat (Hcal) and measured the temperature rise of calibration experiment (Tcal). The energy equivalent of calorimeter was calculated as following: H = Hcal/ Tcal. The heat of reaction was calculated as Hex = H x Tex. The dissolution heat of KCl obtained by us was 17.41  0.08 kJ mol1. The standard uncertainty is reported. The literature data are: 17.47  0.07 kJ mol1 [27]. As it is possible to see, our data are in a good agreement with literature values. It means that calorimeter is working correctly. To determine the standard formation enthalpy of bismuth perrhenate doped by neodymium and indium oxides the thermochemical cycle was constructed in such a way that bismuth oxide was solved in 2 M HCl (solution 1) to form solution 2. Then rhenium oxide (Re2O7) was solved in solution 2 forming solution 3. Then neodymium chloride and indium chloride (1.4 NdCl3 + 0.1InCl3) mixture was solved in solution 3 to form solution 4. Bi12.5Nd1.4In0.1ReO24.5 was also solved in 2 М hydrochloric acid. The scheme of thermochemical reactions is presented below. 6.25 Bi2O3(s) + solution 1 = solution 2 + 6.25solHo1

(1)

0.5 Re2O7(s) + solution 2 = solution 3 + 0.5solHo2

(2)

[1.4 NdCl3(s) + 0.1InCl3(s)] + solution 3 = solution 4 + solHo3

(3)

Bi12.5Nd1.4In0.1ReO24.5 + solution 1 = solution 4 + 2.25 H2O (sol) - 4.5 HCl (sol) + solHo4 (4) Using Gess law the following reaction can be obtained: 6.25Bi2O3(s) + 0.5Re2O7(s) + 1.4NdCl3(s) + 0.1InCl3(s) + 2.25H2O(sol) = Bi12.5Nd1.4In0.1ReO24.5(s) + 4.5HCl(sol) + rHo5

(5)

The weight of compound (Bi12.5Nd1.4In0.1ReO24.5) to perform the calorimetric experiment was about 0.2 g. The calorimetric experiments were performed at 298.15 K. 3. Results and discussion Earlier we measured [21] the formation enthalpy of barium cerate doped by Gd and In. We 4   

established that In adding increased the thermodynamic stability. As the ion radius of Nd3+ (r(Nd3+) = 0.0983 nm) is larger than that of In3+ (r(In3+) = 0.0800 nm) [28], the standard formation enthalpy and lattice energy of Bi12.5Nd1.4In0.1ReO24.5 can be supposed to be larger than the same values for Bi12.5Nd1.5ReO24.5. The solution enthalpy of neodymium and indium chloride mixture (1.4NdCl3 + 0.1InCl3) and that of Bi12.5Nd1.4In0.1ReO24.5 were measured. The values are: solHo3 = 202.90 ± 0.71 kJ mol-1, solHo4 = 873.66 ± 2.02 kJ mol-1. Six parallel calorimetric experiments were performed. The standard uncertainty was determined. The detailed results are presented in Table 2,3. Earlier [29] we measured solution enthalpies for bismuth and rhenium oxide as following values: solHo1(Bi2O3, 298.15 K) = 114.4 ± 1.1 kJ mol-1; solHo2(Re2O7, 298.15 K) = 27.2 ± 0.1 kJ mol-1. Here the uncertainties for 95% confidential interval were presented. We have checked for our thermochemical cycle that within the uncertainties the changing in the dissolution sequence of compounds does not influence on enthalpy of dissolution. So, we used the value for dissolution enthalpy of Re2O7 taken from [29]. On the basis of solution enthalpies measured (solHo3 and solHo4) as well as solution enthalpies for bismuth oxide and rhenium oxide measured by earlier [29] the enthalpy was calculated for the following reaction: 6.25Bi2O3(s) + 0.5Re2O7(s) + 1.4NdCl3(s) + 0.1InCl3(s) + 2.25H2O(sol) = Bi12.5Nd1.4In0.1ReO24.5(s) + 4.5HCl(sol) + rHo5

(5)

Here: rHo5 = 6.25solHo1 + 0.5solHo2 + solHo3 - solHo4 = 57.84 ± 3.44 kJ mol-1 The standard uncertainty was determined for reaction (5). Then using standard formation enthalpies of bismuth oxide, rhenium oxide, neodymium chloride, indium chloride taken from book reference [27] and standard formation enthalpies of water and hydrochloric acid presented in paper [30] the standard formation enthalpy of Bi12.5Nd1.4In0.1ReO24.5 was calculated as follows: fH(Bi12.5Nd1.4In0.1ReO24.5, s, 298.15 K) = rHo5 – 4.5 fH(HCl, sol, 298.15 K) + 2.25 fH(H2O, sol, 298.15 K) + 0.1 fH(InCl3, s, 298.15 K) + 1.4fH(NdCl3, s, 298.15 K) + 0.5fH(Re2O7, s, 298.15 K) + 6.25fH(Bi2O3, s, 298.15 K) = 5727.2 ± 7.5 kJ mol-1 Here the standard uncertainty was determined for standard formation enthalpy of Bi12.5Nd1.4In0.1ReO24.5. As it is possible to see, the standard formation enthalpy of Bi12.5Nd1.4In0.1ReO24.5 investigated in our paper (fH(Bi12.5Nd1.4In0.1ReO24.5, s, 298.15 K)) which equals to 5727.2 ± 7.5 kJ mol-1 is larger than that of Bi12.5Nd1.5ReO24.5 (5702.6 ± 9.0 kJ mol-1, the uncertainty for 95% confidential 5   

interval is reported) obtained in [29]. It confirmed our suggestion that adding indium increased the standard formation enthalpy. Using Born-Haber cycle the lattice energy for Bi12.5Nd1.4In0.1ReO24.5 was calculated as follows: 12.5Bi(s) + 1.4Nd(s) + 0.1In(s) + Re(s) + 12.25O2(g) = Bi12.5Nd1.4In0.1ReO24.5(s)

(6)

12.5 Bi3+(g) = 12.5Bi(s) 1.4Nd3+(g) = 1.4Nd(s)

(7) (8)

0.1In3+(g) = 0.1In(s) 7+

(9)

Re (g) = Re(s)

(10)

24.5O2-(g) = 12.25O2(g)

(11)

____________________________________________________ 12.5 Bi3+(g) + 1.4Nd3+(g) + 0.1In3+(g) + Re7+(g) +24.5O2-(g) = Bi12.5Nd1.4In0.1ReO24.5

(12)

Here: latHo12 = fHo6 + 12.5rHo7 +1.4rHo8 + 0.1rHo9 + rHo10 + 24.5rHo11, where fHo6 – standard formation enthalpy for Bi12.5Nd1.4In0.1ReO24.5, rHon (n = 7-11) – enthalpy for reactions (7)-(11). latHo12 = 124 600 ± 39 kJ mol-1 is a lattice energy for Bi12.5Nd1.4In0.1ReO24.5. The standard uncertainty is reported. Data for formation enthalpies of Bi3+(g), Nd3+(g), In3+(g), Re7+(g), O2-(g) were taken from reference book [27]. The comparison of lattice energies for Bi12.5Nd1.4In0.1ReO24.5 and Bi12.5Nd1.5ReO24.5 (124 446 ± 40 kJ mol-1[31], the standard uncertainty is reported) allows one to see that the lattice energy for Bi12.5Nd1.4In0.1ReO24.5 is larger than the lattice energy for Bi12.5Nd1.5ReO24.5. Increasing of lattice energy for Bi12.5Nd1.4In0.1ReO24.5 correlates with decreasing of ion radius for In3+ in comparison with that of Nd3+. Earlier we measured the formation enthalpies and calculated lattice energies for compounds with general formula Bi12.5R1.5ReO24.5 (R = La, Nd, Sm, Gd, Dy, Ho, Yb, Lu) [13, 16, 17, 29, 31]. The structure for all the compounds is cubic (Fm3m). Only rare earth elements are changed in compounds. So, we think that it is useful to construct dependence of lattice energies from radius of rare earth elements for Bi12.5R1.5ReO24.5 adding data of this paper for lattice energy of Bi12.5Nd1.4In0.1ReO24.5. The values of lattice energy and ionic radius of rare earth elements are presented in Table 4. The radius was taken from paper [28]. The dependence of lattice energy from ionic radius of rare earth elements is presented in Figure 1. As it is possible to see, the dependence

6   

is linier. Using least square method we find the following equation for dependence Ulat from r: Ulat = -129450 + 45070 rR. To explain the linear character of obtained dependence we considered the Kapustinskii rule. According to Kapustinskii rule the lattice energy can be calculated as following: 1070.9







(25)

Here: U – lattice energy; Zk – the numbers of elementary charge of cation; Za - the numbers of elementary charge of anion; rk and ra are the radii of the cation and anion, m – number of ions in the empirical formula. After some mathematic transformations for compounds with general formula Bi12.5R1.5ReO24.5 the expression for lattice energy is possible to present as following: (12) Here: rR - radius of rare earth elements. So, experimentally obtained linear dependence of lattice energy for compounds with general formula Bi12.5R1.5ReO24.5 from radius of rare earth element can be explained using modified variant of Kapustinskii rule.

4. Conclusions The standard formation enthalpy of Bi12.5Nd1.4In0.1ReO24.5 has been measured by solution calorimetry in 2 M HCl for the first time. Born–Haber cycle has been used to calculate the lattice energy for Bi12.5Nd1.4In0.1ReO24.5 based on the standard formation enthalpy obtained experimentally. The comparison of energetic characteristics for Bi12.5Nd1.4In0.1ReO24.5 and Bi12.5Nd1.5ReO24.5 has shown that adding indium increases the standard formation enthalpy and lattice energy. The dependence of lattice energy for Bi12.5R1.5ReO24.5 from rare earth radius was constructed. It was noted that dependence is linear. We explained the linear character of dependence using modified variant of Kapustinskii rule. Acknowledgments This work was supported by Karlsruhe Institute of Technology, RFBR (Project 13-0800169 and Project 16-08-00226), Government Task for Nikolaev Institute of Inorganic Chemistry SB RAS and Physical Department of Novosibirsk State University.

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23. V.V. Malakhov, A.A. Vlasov, L.S. Dovlitova, J. Anal. Chem. 59 (2004) 1014-1024. 24. N.I. Matskevich, Th. Wolf, J. Chem. Thermodyn. 42 (2010) 225-228. 25. N.I. Matskevich, Th. Wolf, Thermochim. Acta 421 (2004) 231-233. 26. N.I. Matskevich, Th. Wolf, I.V. Vyazovkin, P. Adelmann, J. Alloys Compd. 628 (2015)126129. 27. V.P. Glushko, Termicheskie Konstanty Veshchestv (Thermal Constants of Substances), VINITI, Moscow, 1965–1982, 1–10. 28. R.D. Shannon, Acta Cryst. A32 (1976) 751-767. 29. A.N. Bryzgalova, N.I. Matskevich, C. Greaves, C.H. Hervoches, Thermochim. Acta 513 (2011) 124-127. 30. L.R. Morss, Chem. Rev. 76 (1976) 827-841. 31. N.I. Matskevich, Th. Wolf, C. Greaves, P. Adelmann, I.V. Vyazovkin, M.Yu. Matskevich, J. Chem. Thermodyn. 91 (2015) 234-239. TABLE 1 Characterization of chemical samples used in this study Methods of analysis Mass fraction purity >0.99999 Spectrophotometric method

Chemical name

Chemical formula

Source

State

Bismuth oxide

Bi2O3

ABCR

Solid

Reacton, Rare Earth Products, Johnson Mattey Company

Solid

>0.999

Spectrophotometric method

Neodymium Nd2O3 oxide

Indium oxide

In2O3

Reacton, Johnson Mattey Company

Solid

>0.9999

Spectrophotometric method

Ammonium perrhenate

NH4ReO4

Alfa Aesar, Johnson Mattey Company

Solid

>0.99

X-ray Fluorescence method

Bismuth perrhenate doped

Bi12.5Nd1.4In0.1ReO24.5

Synthesis

Solid

>0.99

Differential solution method, X-ray diffraction, Spectrophotometric 9 

 

by neodymium and indium oxides Neodymium NdCl3 chloride Indium chloride

InCl3

Synthesis

Solid

>0.99

Synthesis

Solid

>0.99

method, X-ray Fluorescence method, Reducing melting method X-ray diffraction, Spectrophotometric method X-ray diffraction, Spectrophotometric method

The standard uncertainties for methods are 0.1-1.0%.

TABLE 2 The molar solution enthalpies (solHo) of mass (m) of Bi12.5Nd1.4In0.1ReO24.5 (molar mass: 3217.6583 g mol-1) in 250 cm3 of 2 mol dm-3 HCl at the temperature 298.15 K and pressure p = 0.1 MPaa. m/ g

He/J -1

H/ J

solHo/ kJ mol-1

0.199967

1.8645

-54.488

-876.76

0.200015 

1.8850

-54.666

-879.41

0.199885

1.8555

-53.728

-864.89

0.199983

1.8681

-54.360

-874.63

0.200013

1.8549

-54.220

-872.26

0.200128

1.8429

-54.361

-874.02

Here: He is heat equivalent, H is enthalpy, the standard uncertainty is provided. aStandard uncertainties u are u(T) = 0.01 K, u(p) = 0.05p, u(m) = 0.000005 g, u(cHCl) = 0.003 mol dm-3, u(He) = 0.0001 J -1, u(V) = 0.003 dm-3, u(solHo) = 2.0 kJ mol-1 TABLE 3 The molar solution enthalpies (solHo) of mass (m) of (1.4NdCl3 +0.1InCl3) (molar mass: 372.9565 g mol-1) in 250 cm3 of 2 mol dm-3 HCl at the temperature 298.15 K and pressure p = 0.1 MPaa. m(NdCl3) / g

m(InCl3)/g

He/J -1

H/ J

solHo/ kJ mol-1

0.043564

0.002688

1.8375

-25.361

-204.50

0.043562 

0.002693

1.8580

-24.951

-201.18

0.043738

0.002712

1.8419

-25.453

-204.37

0.043583

0.002680

1.8537

-25.374

-204.56

0.043528

0.002750

1.8613

-25.000

-201.48 10 

 

0.043623

0.002714

1.8429

-201.29

-25.009

Here: He is heat equivalent, H is enthalpy, the standard uncertainty is provided. aStandard uncertainties u are u(T) = 0.01 K, u(p) = 0.05p, u(m) = 0.000005 g, u(cHCl) = 0.003 mol dm-3, u(He) = 0.0001 J -1, u(V) = 0.003 dm-3, u(solHo) = 0.7 kJ mol-1 Table 4. Lattice energy and ionic radius of rare earth elements for Bi12.5R1.5ReO24.5 ______________________________________________________________________ Compound

Elat, kJ/mol

r, nm

_______________________________________________________________________ Bi12.5La1.5ReO24.5

124 189

Bi12.5Nd1.5ReO24.5

124 446

0.1109

Bi12.5Nd1.4In0.1ReO24.5

124 600

0.1096

Bi12.5Sm1.5ReO24.5

124 579

0.1079

Bi12.5Gd1.5ReO24.5

124 693

0.1053

Bi12.5Dy1.5ReO24.5

124 779

0.1027

Bi12.5Ho1.5ReO24.5

124 853

0.1015

Bi12.5Yb1.5ReO24.5

125 063

0.0985

Bi12.5Lu1.5ReO24.5

125 023

0.0977

0.1160

_______________________________________________________________________________________________________________

11   

Fig. 1. Dependence of lattice energies for Bi12.5(R, In)1.5ReO24.5 as the function of r (r – an ion radius of a rare-earth element).

 

12