Thermodynamic Properties of FeNb2O6 and FeTa2O6

Article abstract of DOI:10.1134/S0020168518070087

Empirical calculational approaches have been used to evaluate the enthalpy, entropy, heat capacity, and melting point of iron(II) niobate and iron(II) tantalate and the coefficients A, B, and C in an equation for the temperature dependence of their heat c

Full text of DOI:10.1134/S0020168518070087

ISSN 0020-1685, Inorganic Materials, 2018, Vol. 54, No. 7, pp. 700–705. © Pleiades Publishing, Ltd., 2018.
Original Russian Text © A.N. Mansurova, V.M. Chumarev, R.I. Gulyaeva, 2018, published in Neorganicheskie Materialy, 2018, Vol. 54, No. 7, pp. 738–743.
Thermodynamic Properties of FeNb2O6 and FeTa2O6
A. N. Mansurovaa, V. M. Chumareva, *, and R. I. Gulyaevaa
aInstitute of Metallurgy, Ural Branch, Russian Academy of Sciences, ul. Amundsena 101, Yekaterinburg, 620016 Russia
*e-mail: pcmlab@mail.ru
Received October 18, 2017; in final form, January 18, 2018
Abstract—Empirical calculational approaches have been used to evaluate the enthalpy, entropy, heat capac-
ity, and melting point of iron(II) niobate and iron(II) tantalate and the coefficients A, B, and C in an equation
for the temperature dependence of their heat capacity. The melting point of FeTa2O6 has been experimentally
°
determined to be 1891 5 K. The calculated heat capacity ( (298.15 K)) of iron tantalate and the Gibbs
Cp
energies of formation of FeN2O6 and FeTa2O6 have been compared to previously reported data.
Keywords: iron niobate, iron tantalate, thermodynamic properties, entropy, enthalpy, heat capacity, melting
point
DOI: 10.1134/S0020168518070087
INTRODUCTION
CALCULATIONAL APPROACH
The standard enthalpies of formation of FeNb2O6
and FeTa2O6 were evaluated using methods proposed
by Kasenov [12, 18] and Tsagareishvili et al. [19]. The
standard enthalpy of formation (ΔfH°(298.15 K)) of
the mixed oxides was calculated by the ion increment
method [12, 18], which relies on the additive summa-
tion of thermodynamic constants of ions: standard
There is not much information available about the
thermochemical properties of metal niobates and tan-
talates: Ca [1], Mg [2], Sr [3], Be [4], Ba [5], and Mn
[6]. Poorly studied compounds include iron niobate
(FeNb2O6) and iron tantalate (FeTa2O6). Data on their
thermochemical properties available in the literature
and known thermodynamic databases are limited to
results of experimental determinations of the standard
enthalpies of formation of FeNb2O6 and FeTa2O6 [7,
8], heat capacity of FeTa2O6 in the temperature range
from 30 to 313 K [9], and the phase transition tem-
peratures of FeNb2O6 [10, 11]. Available data are
insufficient, for example, for adequately calculating
equilibrium states of practically important systems
containing these oxides. Moreover, the thermody-
namic properties of FeNb2O6 and FeTa2O6 are of the-
oretical and practical interest for inorganic materials
research.
enthalpy of the M2+ cation in aqueous solution and
n−
standard enthalpy of the
diluted aqueous solution:
anion in an infinitely
XαOβ
Δf H°(M(XαOβ)n, cr., 298.15K)
= mΔf H°(Mn+(H2O,sol-n), 298.15K)K
+ nΔf H°((XαOβ)m−, 298.15K),
(1)
where M denotes the metal; X denotes the salt-forming
element; O denotes oxygen; ΔfH°(XαOβ)m–, 298.15 K) is
the enthalpy increment of the anion; ΔfH°(Mn+(H2O,
sol-n), 298.15 K) is the standard enthalpy of formation
of a metal ion in an aqueous solution; K is a propor-
tionality coefficient; n and m are the charges on the
cation and anion, respectively; and α and β are the
amounts of the salt-forming element and oxygen,
respectively. In addition, the heats of formation of the
double oxides were evaluated by the additive summa-
tion of the standard enthalpies of formation of their
constituent binary oxides with allowance for an empir-
ical correction coefficient, using the following equa-
tions [19]:
Data on the properties of refractory mixed oxides,
including metal niobates and tantalates, are limited
because they are difficult to study experimentally.
Because of this, wide use is made of calculational
methods for assessing thermodynamic characteristics
of mixed oxides [10, 12–17].
In this paper, we report calculations of the standard
enthalpy, entropy, and heat capacity of FeNb2O6 and
FeTa2O6 and determination of the melting point of
FeTa2O6 by thermal analysis.
700

THERMODYNAMIC PROPERTIES OF FeNb2O6 AND FeTa2O6
701
The heat capacity and entropy of the mixed oxides
were evaluated by the additive summation of the stan-
dard heat capacities of their constituent binary oxides
[13, 14, 20]:
'
Δf H°(MM2O6, 298.15K)
'
(2)
(3)
= Δ H° MO, 298.15K + Δ H°(M O ,298.15K)
(
)
f
f
2
5
'
+Δf,ox MM2O6, 298.15K ,
(
)
°
'
Cp (MM2O6, 298.15K)
(4)
(5)
°
°
'
= Cp (MO, 298.15K) + Cp (M2O5, 298.15K),
'
Δ
f,oxH°(MM2O6, 298.15K) = –29.274mО,
'
S°(MM2O6, 298.15K)
'
where ∆ H°(MO, 298.15 K), ∆ H°( O5, 298.15 K),
M2
f
f
'
= S°(MO, 298.15K) + S°(M2O5, 298.15K).
'
and ∆f,oxH°(M O6, 298.15 K) are the enthalpies of
M2
The coefficients A, B, and C in the normalized
equation for the temperature dependence of heat
the binary oxides and a correction term for the mixed
oxide, and mO is the number of oxygen atoms per mol-
ecule of the mixed oxide. Equations (2) and (3) are
recommended by Tsagareishvili et al. [19] for evaluat-
ing the heat of formation of mixed oxides if (Pauling’s)
electronegativity of their central cation (M') is ≥1.9.
'
capacity of an M O6 oxide
M2
−3
5
−2
°
(6)
(7)
Cp = A + B ×10 T + C ×10 T ,
were found using the formulas [21]
−3
5
−2
°
Tm ×10 (Cp (298.15K) + 4.7n) −1.25n ×10 Tm − 9.05n
Tm ×10−3 − 0.298
A =
,
perature dependence of its molar heat capacity using
the following equation [24]:
25.6n + 4.2n ×105Tm−2 − Cp(298.15K)
ꢀ
(8)
(9)
B =
,
Tm ×10−3 − 0.298
C = –4.2n,
'
S°(MM2O6, 298.15K)
298.15
(12)
where n is the number of atoms per molecule, Tm (K)
ꢀ
dT
T
= S°(0 K) +
Cp (298.15K)
.
∫
0
ꢀ
is the melting point of the mixed oxide, and (298.15 K)
Cp
The standard Gibbs free energy ΔG°(298.15 K) was
(J/(mol K)) is the heat capacity of the mixed oxide
evaluated additively from the heat capacities of its con-
stituent binary oxides.
calculated by the Nernst equation [13, 14]:
'
ΔG°(MM2O6, 298.15K)
The enthalpy increment H°(298.15 K) – H°(0 K)
was determined using the following equation [22]:
'
(13)
= Δf H°(MM2O6, 298.15K)
H°(298.15K) − H°(0 K)
'
(10)
− T Δf S°(MM2O6, 298.15K),
ꢀ
≈ 0.5Cp (298.15K) × 298.15,
'
'
where ΔG°(M O , 298.15 K) and ΔS°(M O6,
M2
M2
with the heat capacity taken to vary linearly in the
range from 0 to 298 K.
6
298.15 K) are the standard Gibbs energy and standard
To evaluate the entropy, we used the Kumok incre-
ment method [23], which involves the summation of
the entropy increments of the cation, S°(M2+, 298.15 K),
'
entropy of formation of the M O6 oxide.
M2
'
The melting point of the M O6 oxide was calcu-
M2
lated using the following relation [25]:
and anion, S°(M' −, 298.15 K), with allowance for the
O3
coefficients for the cation (nc) and anion (na), accord-
(14)
Тm ≈ k x(i) Tm(i),
∑
ing to the following equation:
where x(i) is the mole fraction of the ith binary oxide
in the mixed oxide, Tm(i) is the melting point of the
binary oxide, and k is an empirical correlation coeffi-
cient for similar compounds. The coefficient k was
2+
'
S°(MM2O6, 298.15K) = ncS°(M ,298.15K)
(11)
+n S° M'O−, 298.15K .
(
)
a
3
In addition, the entropy of each mixed oxide was evaluated using experimentally determined melting
determined from the experimentally determined tem- points of metal niobates and tantalates.
INORGANIC MATERIALS Vol. 54 No. 7 2018

702
MANSUROVA et al.
RESULTS AND DISCUSSION
Equation (1) for calculating the standard enthalp-
ies of formation of FeNb2O6 and FeTa2O6 from the ion
V5+
–900
increments ∆
2+(H2O, sol-n, 298.15 K)),
fH°(Fe
∆fH°((NbΟ3)–, 298.15 Κ), and ∆fH°((TaΟ3)–, 298.15 Κ)
–1000
was written in the form
Nb5+
Δf H°(FeNb2O6, cr.,298.15K)
–1100
–1200
Ta5+
= Δf H°(Fe2+(H2O, sol-n, 298.15K))K
(15)
+ Δf H°((NbO3)−, 298.15K),
0.04
0.05
0.06
Δf H°(FeTa2O6, cr.,298.15K)
Orbital radius of M5+, nm
= Δf H°(Fe2+(H2O, sol-n, 298.15K))K
(16)
+ 2Δf H°((TaO3)−, 298.15K).
5+
Fig. 1. Correlation between the ionic radius of M and
The ΔfH°(M2+(H2O, sol-n, 298.15 K)) of Fe2+ was
the enthalpy increment ∆ H°(
radii are borrowed from Ref. [28].
−, 298.15 K). The ionic
MO3
f
taken to be –87.110
0.836 kJ/mol [10] and the
enthalpy increments of the anions were taken to be
Δ H°((Nb −), 298.15 K) = –1084.0
20.3 kJ/mol
O3
f
EXPERIMENTAL
The melting points of FeTa2O6 and MnTa2O6 were
and Δ H°((V −), 298.15 K) = –905.0 21.3 kJ/mol
O3
f
−
[12]. The enthalpy increment of Ta
(–1132.5
O3
determined experimentally. Samples for this investiga-
tion were prepared by solid-state reactions: an appro-
priate stoichiometric mixture of the FeO, MnO (pure
grade), and Ta2O5 oxides was reacted at 1473 K for 10 h
under flowing helium. The iron(II) oxide was pre-
pared by heat-treating a pressed mixture of pure-grade
Fe2O3 and carbonyl Fe for six days at 973 K in hermet-
ically sealed silica ampules, and the Ta2O5 oxide was
prepared by oxidizing a metallurgical grade B tanta-
lum powder (99.5% Ta, 0.3% O, and 0.2% N) in air for
4 h at 1373 K (in two heating steps). The only phases
identified in the synthesis products by X-ray diffraction
(XRD7000C diffractometer) were FeO and β-Ta2O5,
respectively. According to X-ray diffraction results,
the synthesized FeTa2O6 and MnTa2O6 samples were
single-phase. Their unit-cell parameters were calcu-
lated using the Celref program [26]. The FeTa2O6
sample had a tetragonal crystal lattice with unit-cell
parameters a = 0.47450 nm, c = 0.91848 nm, and V =
206.79 nm3 (the unit-cell parameters were calculated
using the ICDD card no. 85-72 (release 2012) [27]).
The MnTa2O6 sample had an orthorhombic crystal
lattice with unit-cell parameters a = 1.4429 nm, b =
0.5763 nm, c = 0.5087 nm, and V = 0.4230 nm3
(ICDD card no. 00-072-485, release 2012).
20.8 kJ/mol) was found under the assumption that the
enthalpy increments of the V5+, Nb5+, and Ta5+ anions
were a linear function of their ionic radii (Fig. 1),
which were borrowed from Ref. [28]. The coefficients K in
Eqs. (15) and (16) were taken to be 1.015 0.019 [12]
and 1.014 0.019, respectively; the charge of the cat-
ion was taken to be n = 2; and the charge of the anion,
m = 1. As a result of our calculations, we obtained
ꢀ
∆
298.15 K)= –2256.4 41.4 kJ/mol and
fH (FeNb2O6,
∆fH°(FeTa2O6, 298.15 K) = –2353.3 42.4 kJ/mol.
The standard enthalpies of formation of FeNb2O6
and FeTa2O6 according to Eqs. (2) and (3) were found
by adding up the enthalpies of formation of the binary
oxides FeO, Nb2O5, and Ta2O5 with allowance for the
'
correction term Δf.охH°(M O6, 298.15 K) [19]:
M2
Δ H° FeNb O , 298.15K
= Δf H°(FeO, 298.15K)
(
)
f
2
6
(17)
(18)
+ Δf H°(Nb2O5, 298.15K)
+ Δf,oxH°(FeNb2O6, 298.15K),
Δ H° FeTa O , 298.15K
= Δf H°(FeO, 298.15K)
(
)
f
2
6
+ Δf H°(Ta2O5, 298.15K)
The melting points were measured using a Netzsch
STA 449 C thermoanalytical system. The FeTa2O6 and
MnTa2O6 oxides were characterized by differential scan-
ning calorimetry (DSC) during heating to 1913 K at a rate
of 20 K/min in flowing argon (30 mL/min). The oxides
under investigation were heated in platinum-alloy cru-
cibles using alundum substrates and lids.
+ Δf,oxH°(FeTa2O6, 298.15K).
The values of ∆fH°(FeO, 298.15 K), ∆fH°(Nb2O5,
298.15 K), and ∆fH°(Ta2O5, 298.15 K) were taken,
according to Ref. [10], to be –264.85 4.18, –1897.86
1.67, and –2047.23 1.67 kJ/mol, respectively, with
'
Δf,охH°(M O6, 298.15 K) = –175.88 kJ/mol for six
M2
INORGANIC MATERIALS
Vol. 54
No. 7
2018

THERMODYNAMIC PROPERTIES OF FeNb2O6 AND FeTa2O6
703
Table 1. Experimental and calculated standard enthalpies of formation of the oxides
∆fH°(298.15 Κ), kJ/mol
'
'
∆ H°(M O6, 298.15 K), kJ/mol
∆ H°(M O6, 298.15 K), kJ/mol
M2
M2
f
f
Oxide
calculation by Eq. (1), method from
Ref. [12]
calculation by Eqs. (2) and (3),
method from Ref. [19]
experiment
FeNb2O6
FeTa2O6
–2271.8 24.0 [7]
–2365.5 24.0 [8]
–2256.4 41.4
–2353.3 42.4
–2338.59 5.85
–2487.96 5.85
Table 2. Thermodynamic properties of the FeNb2O6 and FeTa2O6 oxides
–3
°
S°(298.15 K),
= A + B × 10 T +
C × 105 T–2
Cp
°
H°(298.15 K) –
(298.15 K),
Cp
ΔG°(298.15 K), kJ/mol
calc., Eq.(13) literature
J/(mol K)
Oxide
H°(0 K),
J/(mol K)
Eq. (4)
kJ/mol
Eq. (5)
Eq. (11)
A
B
C
FeNb2O6 198.0 1.2 197.9 6.1 182.0 0.8 213.38 34.88 –37.8 27.13 0.12 –2197.4 42.6 –2172 24 [7]
FeTa2O6 200.7 2.1 192.1 9.5 184.7 0.9 217.97 29.44 –37.8 27.53 0.13 –2233.7 42.6 –2219 24 [8]
oxygen atoms in the oxides. Even though in our calcu- (Eq. (11)) yielded similar values: 197.9
lations we neglected the condition formulated by 192.7 9.5 J/(mol K), respectively. The standard
Tsagareishvili et al. [19] that the electronegativity of the entropy of FeTa2O6 calculated by Eq. (12) from the tem-
6.1 and
central cation should be ≥1.9, whereas the electronegativ-
perature dependence of its heat capacity (19) is
ities of the Nb5+ and Ta5+ cations are 1.6 and 1.5, respec- 176.2 J/(mol K). The enthalpy increments H°(298.15 K) –
tively [29], the values obtained by us, ∆fH°(FeNb2O6, H°(0 K) of FeNb2O6 and FeTa2O6 presented in Table 2
298.15 K) = –2338.59 5.85 kJ/mol and ∆fH°(FeTa2O6,
298.15 K) = –2487.96 5.85 kJ/mol (Table 1), slightly
exceed experimental data [7, 8].
°
were determined using Eq. (10) and
(298.15 K)
Cp
data.
The melting points of iron niobate and iron tanta-
late were calculated by formula (14) using the follow-
ing Tm values: 1650 (FeO), 2115 (MnO), 1785
(Nb2O5), and 2058 K (Ta2O5) (borrowed from Ref.
[15]). From the measured melting points of MnNb2O6
(1767 3 K [6]) and MnTa2O6 (1883 5 K), the coef-
ficient k was determined to be ≈0.9. The use of this
value of k in formula (14) leads to an underestimated
melting point of FeNb2O6 in comparison with experi-
mental data [10, 11]. Because of this, the k values
obtained for manganese niobate and manganese tan-
The experimental heat capacity data reported by
White and Neshad [9] for FeTa2O6 were fitted to the
following equation:
–3
°
Cp(FeTa2O6) = −27.02 + 1129.02 ×10 T
(19)
– 0.065 ×105T –2 + 1405.48 ×10–6T 2,
°
from which we obtain
184.58 3.70 J/(mol K).
(FeTa2O6, 298.15 K) =
Cp
°
In addition, the (298.15 K) and S°(298.15 K) of talate cannot be used in calculating the Tm of
Cp
iron niobate and iron tantalate were evaluated using FeNb2O6.
the Neumann–Kopp rule. The S°(298.15 K) and
It follows from previously reported data [10] on the
Cpꢀ
melting point of FeNb2O6 (1733 20 K) that the coef-
ficient k is 1.009. Substituting this value in formula
(14), we obtain for FeTa2O6 Tm = 1874 K. According to
previously reported experimental data [11], the Tm of
FeNb2O6 is 1693 3 K, with k = 0.995. Using this
value of k in Eq. (14), we obtain for FeTa2O6 Tm = 1844 K.
According to the present thermal analysis data for
FeTa2O6, the melting onset temperature is 1891 5 K
and the coefficient k calculated using data from Ref.
[15] is 1.02. Using the melting point of Ta2O5 (2145 K)
[10] as the Tm of the FeTa2O6 compound, we obtain
k = 0.997. Given that even similar compounds may
differ in the value of the coefficient k, Eq. (14) can only
(298.15 K) of the binary oxides FeO, Nb2O5, and
Ta2O5 were borrowed from Refs. [1, 10]. The calcu-
°
lated S°(298.15 K) and (298.15 K) of FeNb2O6 are
Cp
198.0 1.2 and 182.0 0.8 J/(mol K), and those of
FeTa2O6 are 200.7 2.1 and 184.7 0.9 J/(mol K),
respectively (Table 2). It is worth noting that the molar
heat capacity obtained for FeTa2O6 agrees with exper-
°
imental data [9], whereas the
(298.15 K) of
Cp
FeNb2O6 exceeds the value obtained previously for
this compound [11]. In comparison with calculation
1
by Eq. (5), the estimate of the S°(298.15 K) of
FeNb2O6 and FeTa2O6 by an increment method [23]
INORGANIC MATERIALS Vol. 54 No. 7 2018

704
MANSUROVA et al.
be used for approximate calculations of the melting sian Academy of Sciences; project no. 0396-2015-
points of niobates and tantalates of particular metals.
0082) and carried out using equipment at the Ural-M
Shared Research Facilities Center.
The coefficients A, B, and C in Eq. (6) were calcu-
lated using formulas (7)–(9), the experimental data
reported for FeTa2O6 by White and Neshad [9], and
REFERENCES
°
1. Knacke, O., Kubaschewski, O., and Hesselman, K.,
Thermochemical Properties of Inorganic Substances,
Berlin: Springer, 1991, pp. 1–2412.
2. Abbattista, F., Rolando, P., and Borrqni, G., Magne-
sium oxide–niobium pentoxide system, Ann. Chim.,
1970, vol. 60, pp. 426–435.
3. Carruthers, J.R. and Grasso, M., Phase equilibria rela-
tions in the ternary system BaO–SrO–Nb2O5, J. Elec-
trochem. Soc., 1970, vol. 117, pp. 1426–1430.
the calculated (298.15 K) of FeNb2O6. With the A,
Cp
B, and C values thus obtained (Table 2), the tempera-
ture dependences of the heat capacities can be repre-
sented by the following equations:
ꢀ
Cp (FeNb2O6)
(20)
= 213.86 + 0.03460T – 37.8 ×105T –2,
4. Yyangman, V.S., Glusko, V.P., Medvedev, V.A., and
Gurvich, L.V., Thermal Constant of Substance, New
York: Wiley, 1999, vols. 1–8.
5. Ilhan, M., Mergen, A., Sarıoğlu, C., and Yaman, C.,
Heat capacity measurements on BaTa2O6 and deriva-
tion of its thermodynamic properties, J. Therm. Anal.
Calorim., 2017, vol. 128, pp. 707–711.
6. Mansurova, A.N., Gulyaeva, R.I., Chumarev, V.M.,
and Mar’evich, V.P., Thermochemical properties of
MnNb2O6, J. Therm. Anal. Calorim., 2010, vol. 101,
no. 1, pp. 45–47.
ꢀ
Cp(FeTa2O6)
(21)
= 217.97 + 0.02944Т – 37.8 ×105Т –2.
°
It follows from these equations that
(FeNb2O6,
Cp
°
298.15 K) = 181.65 J/(mol K) and (FeTa2O6, 298.15 K) =
Cp
°
184.22 J/(mol K). These values (Table 2) are in sat-
isfactory agreement with those calculated by Eq. (4).
Cp
Using the enthalpy and entropy values calculated
according to Eqs. (1) and (5) (Tables 1, 2), we deter-
mined the standard Gibbs energy (Table 2). The
ΔG°(298.15 K) values thus obtained are in satisfactory
agreement (to within experimental uncertainty) with
data in the literature [7, 8].
Thus, the enthalpies of formation of the FeNb2O6
and FeTa2O6 oxides calculated by the increment and
additive methods [12, 18, 19] are in satisfactory agree-
ment with known data in the literature. However, the
best result is provided by calculation of the standard
enthalpy of formation of the oxides by the increment
method. It seems likely that the “additive” method is
only applicable when the electronegativity of the cen-
tral anion in the oxide is ≥1.9.
The additive and increment methods can be used
with a high degree of reliability for calculating the entro-
pies of iron niobate and iron tantalate. The standard heat
capacities of the FeNb2O6 and FeTa2O6 calculated by the
additive method are in satisfactory agreement with
experimental data available in the literature.
The measured melting points of FeTa2O6 (1891 5 K)
and MnTa2O6 (1883 5 K) indicate that there are sig-
nificant differences between the correction coeffi-
cients in formula (14) for calculation of Tm for iron and
manganese tantalate niobates, suggesting that it has a
limited application area.
7. Zabeivorota, N.S., Lykasov, A.A., and Mikhailov, G.G.,
Phase equilibria in the system Fe–FeNb2O6–Nb2O5–
Nb, Izv. Akad. Nauk SSSR, Neorg. Mater., 1988, vol. 24,
no. 8, pp. 1364–1367.
8. Zabeivorota, N.S., Lykasov, A.A., and Mikhailov, G.G.,
Free energy of formation of FeTa2O6 between 1470 and
1750 K, Izv. Akad. Nauk SSSR, Neorg. Mater., 1981,
vol. 17, no. 9, pp. 1725–1726.
9. White, M.A. and Neshad, G., The heat capacities of the
tantalates MTa2O6, M = Mg, Fe, Co, Ni, J. Chem.
Thermodyn., 1991, vol. 23, pp. 455–460.
10. Thermal Constants of Substances Database. Working
Version 2. http://www.chem.msu.ru/cgi-bin/tkv.pl?
show=welcome.html.
11. Mansurova, A.N., Gulyaeva, R.I., Chumarev, V.M.,
and Petrova, S.A., High-temperature heat capacity and
temperatures of phase transformations of the FeNb2O6,
J. Alloys Compd., 2017, vol. 695, pp. 2483–2487.
12. Kasenov, B.K., Termodinamicheskie raschety v khimii i
metallurgii (Thermodynamic Calculations in Chemis-
try and Metallurgy), Almaty: Ruan, 1994.
13. Moiseev, G.K. and Vatolin, N.A., Nekotorye zakono-
mernosti izmeneniya i metody rascheta termokhimich-
eskikh svoistv neorganicheskikh soedinenii (Thermo-
chemical Properties of Inorganic Compounds: Some
General Trends and Calculational Approaches), Yekat-
erinburg: Ural. Otd. Ross. Akad. Nauk, 2001.
14. Moiseev, G.K., Vatolin, N.A., Marshuk, L.A., et al.,
Temperaturnye zavisimosti privedennoi energii Gibbsa
nekotorykh neorganicheskikh veshchestv (al’ternativnyi
bank dannykh ASTRA) (Temperature Dependences of
the Reduced Gibbs Energy for Some Inorganic Sub-
stances (ASTRA Alternative Database)), Yekaterin-
burg: Ural. Otd. Ross. Akad. Nauk, 1997.
ACKNOWLEDGMENTS
This work was supported by the Russian Federation
Ministry of Education and Science (state research tar-
get for the Institute of Metallurgy, Ural Branch, Rus-
15. Outokumpu HSC Chemistry for Windows. Chemical
Reactions and Equilibrium Software with Extensive Ther-
INORGANIC MATERIALS
Vol. 54
No. 7
2018

THERMODYNAMIC PROPERTIES OF FeNb2O6 AND FeTa2O6
705
mochemical Database HSC. Version 6.2.8. http://hsc-
micheskoi termodinamiki (Direct and Inverse Problems
in Chemical Thermodynamics), Novosibirsk, 1987,
pp. 108–128.
chemistry.net/index.html.
16. MSI Eureka Data Bases. The Materials Properties &
Phase Diagrams Center. www. msi-eureka.com.
24. Vatolin, N.A. and Moiseev, G.K., Opredelenie tempera-
tur i teplot fazovykh perekhodov I roda nekotorykh neor-
ganicheskikh veshchestv (Determination of the tem-
peratures and heats of first-order phase transitions of
some inorganic substances), Available from VINITI,
1976, no. 4435-76.
25. Tsagareishvili, D.Sh., Equations for calculating melt-
ing-induced changes in some thermal and elastic prop-
erties of crystals, Teplofiz. Vys. Temp., 1981, vol. 19,
no. 1, pp. 75–79.
17. NIST: National Institute of Standards and Technology.
www.nist.gov.
18. Kasenov, B.K., Calculation of the enthalpy of forma-
tion of crystalline nonferrous metal salts, Tsvetn. Met.,
1990, no. 3, pp. 44–46.
19. Tsagareishvili, D.Sh., Gvelesiani, G.G., Baratashvili, I.B.,
Moiseev, G.K., and Vatolin, N.A., Thermodynamic
functions of YBa2Cu3O7, YBa2Cu3O6, Y2BaCuO5, and
BaCuO2, Zh. Fiz. Khim., 1990, vol. 64, no. 10,
pp. 2606–2610.
20. Yokokawa, H., Tables thermodynamic properties of
inorganic components, Spec. Issue J. Nat. Chem. Lab.
Ind., 1988, vol. 83, pp. 27–121.
21. Kubaschewski, O. and Ünal, H., An empirical estima-
tion of the heat capacities of inorganic compounds,
High Temp.–High Pressures, 1977, vol. 9, pp. 361–365.
26. Laugier, J. and Bochu, B., LMGP-Suite of Programs for
the Interpretation of X-ray Experiments. ENSP. Greno-
ble: Lab. Materiaux Genie Phys., 2003.
27. Powder Diffraction File PDF2, Release 2012. Interna-
tional Centre for Diffraction Data (ICDD), 2012.
28. Svoistva neorganicheskikh soedinenii. Spravochnik (Proper-
ties of Inorganic Compounds: A Handbook), Efimov, A.I.,
Eds., Leningrad: Khimiya, 1983, pp. 15–16.
22. Morachevskii, A.G. and Sladkov, I.B., Termodinamich-
eskie raschety v metallurgii (Thermodynamic Calcula-
tions in Metallurgy), Moscow: Metallurgiya, 1993.
29. CRS Handbook of Chemistry and Physics, Lide, D.R.,
Ed., Boca Raton: CRC, 2007, 87th ed., p. 9.77.
23. Kumok, V.N., Problem of matching thermodynamic
Translated by O. Tsarev
evaluation methods, in Pryamye i obratnye zadachi khi-
INORGANIC MATERIALS Vol. 54 No. 7 2018