Molecular and ionic sublimation of neodymium tribromide polycrystals and single crystals

Article abstract of DOI:10.1134/S0036023609080038

The molecular and ionic sublimation of polycrystals and single crystals under Knudsen effusion and Langmuir evaporation conditions is reported. In both sublimation regimes, the sublimation product at 780-1050 K contains neodymium tribromide monomer and dimer molecules, as well as the negative ions NdBr ₄ ^-, Nd₂Br ₇ ^-, and Br^-. The dimer-to-monomer flux ratio j(Nd₂Br ₆)/j(NdBr₃)is larger in the molecular beam coming out of the effusion hole, while the ratio of the sublimation fluxes of the negative ions, j(Nd₂Br ₇ ^- )/j(NdBr ₄ ^- ), is independent of the sublimation conditions. The partial pressures of the neutral components of the vapor have been determined, and the enthalpies and activation energies of sublimation of neodymium tribromide as monomer and dimer molecules and NdBr ₄ ^- and Nd ₂Br ₇ ^- ions have been calculated. The equilibrium constants of ion-molecule reactions have been measured, and the enthalpies of these reactions have been determined. Based on these data, values of the thermodynamic properties Δ _s H ⁰(298.15) and Δ _f H ⁰(298.15) are recommended for the monomer and dimer molecules and the NdBr ₄ ^- and Nd₂Br ₇ ^- ions.

Full text of DOI:10.1134/S0036023609080038

ISSN 0036-0236, Russian Journal of Inorganic Chemistry, 2009, Vol. 54, No. 8, pp. 1181–1188. © Pleiades Publishing, Inc., 2009.
Original Russian Text © L.S. Kudin, M.F. Butman, V.B. Motalov, S.N. Nakonechnyi, K.W. Krämer, 2009, published in Zhurnal Neorganicheskoi Khimii, 2009, Vol. 54, No. 8,
pp. 1245–1252.
SYNTHESIS AND PROPERTIES
OF INORGANIC COMPOUNDS
Molecular and Ionic Sublimation of Neodymium Tribromide
Polycrystals and Single Crystals
L. S. Kudina, M. F. Butmana, V. B. Motalova, S. N. Nakonechnyi, and K. W. Krämerb
a Ivanovo State University of Chemistry and Technology, pr. Engelsa 7, Ivanovo, 153460 Russia
b University of Bern, Bern, Switzerland
E-mail: kudin@isuct.ru
Received April 9, 2008
Abstract—The molecular and ionic sublimation of polycrystals and single crystals under Knudsen effusion
and Langmuir evaporation conditions is reported. In both sublimation regimes, the sublimation product at 780–
1050 K contains neodymium tribromide monomer and dimer molecules, as well as the negative ions NdBr–4,
Nd Br– , and Br–. The dimer-to-monomer flux ratio j(Nd2Br6)/j(NdBr3) is larger in the molecular beam coming
2
7
out of the effusion hole, while the ratio of the sublimation fluxes of the negative ions, j(Nd2Br– )/j(NdBr– ), is
7
4
independent of the sublimation conditions. The partial pressures of the neutral components of the vapor have
been determined, and the enthalpies and activation energies of sublimation of neodymium tribromide as mono-
mer and dimer molecules and NdBr– and Nd2Br– ions have been calculated. The equilibrium constants of ion–
4
7
molecule reactions have been measured, and the enthalpies of these reactions have been determined. Based on
these data, values of the thermodynamic properties ∆sH0(298.15) and ∆fH0(298.15) are recommended for the
monomer and dimer molecules and the NdBr– and Nd2Br– ions.
4
7
DOI: 10.1134/S0036023609080038
This study of neodymium tribromide sublimation time and, from the temperature dependences of ion cur-
continues our systematic investigation of the molecular rents, derived the activation energies of sublimation of
and ionic sublimation of lanthanide tribromide poly- NdBr3 as monomers and dimers.
crystals under equilibrium conditions (Knudsen effu-
The ionic sublimation of neodymium tribromide
sion) and lanthanide tribromide single crystals under
was studied under both Knudsen effusion and Lang-
conditions of free evaporation from an open surface
muir evaporation conditions. This study allowed the
(Langmuir evaporation) [1–5].
enthalpies of formation of the negatively charged ions
NdBr–4 and Nd2Br–7 to be determined for the first time.
The saturation vapor pressure over NdBr3 was mea-
sured earlier by the Knudsen effusion method [6, 7],
boiling point method [8–10], torsion method [11], and
mass spectrometry [12]. Gietmann et al. [12] detected
dimers in the vapor phase, while the other authors [6–
EXPERIMENTAL
Mass spectrometric experiments were carried out on
an MI 1201 commercial magnetic sector mass spec-
trometer (∠90°, curvature radius of 200 mm) modified
for high-temperature studies. The experimental setup
and procedure are detailed elsewhere [1].
Neodymium tribromide (99.99%) was synthesized
using the NH4Br-based procedure [13, 14]. An NdBr3
single crystal was grown by the vertical Bridgman tech-
nique using a neodymium tribromide powder sealed in
a glass tube.
11] measured the total vapor pressure and processed the
data under the assumption that the vapor consists only
of monomers.
In this study, we calculate the second- and third-law
enthalpies of sublimation of neodymium tribromide as
monomers and dimers, using new experimental vapor
pressure data, relevant data available from the litera-
ture, and an updated set of thermodynamic functions.
Based on the results obtained, we recommend thermo-
dynamic parameters of the monomer and dimer mole-
cules.
In the Knudsen measurements of sublimation, an
In addition to performing thermodynamic experi- NdBr3 powder was evaporated from a molybdenum
ments under Langmuir conditions, we studied the sub-
limation kinetics of an NdBr3 single crystal for the first
effusion cell. The ratio of the cross-sectional area of the
cell to the effusion aperture area was about 400. In
1181

1182
KUDIN et al.
Table 1. Electron impact ionization mass spectra of neodymium tribromide recorded using the effusion cell (EC) technique
and sublimation from the open surface (OS) of a single crystal and the appearance energies (AE) of ions
Technique T, K Ee, eV Nd+ NdBr+ NdBr+2 NdBr+3 Nd2+
NdBr2+ NdBr22+ Nd2Br+
5
Refe-
rence
Relative ion
current, %
EC
OS
858
858
70
21
23.9
19.1
12.3
28.1
100
100
11.8
13.5
4.3
2.0
0.1
1.1
0.6
Not
Not
Not
[12]
measured measured measured
858
70
14.8
7.7
100
12.3 The same The same The same 0.7
AE, eV
18.1
18.4
13.5
14.6
10.3
10.7
10.2
10.1
31.6
27.0
Not
10.4
[12]
Not
Not measured 11.3
measured measured The same
Note: The relative ion currents take into account the variety of isotopic species of the ions. The scale of ionizing electron energies is cali-
brated against the ionization energies of the silver atom and water molecule as standards. The error in the appearance energy of the
ions is estimated at 0.5 eV.
Table 2. Coefficients of the equation logI = –A × 103/T + B
A
B
∆T, K
N
A
B
∆T, K
N
Ion
effusion cell
open surface
Nd+
NdBr+
14.37 0.79 20.79 0.91 803–924
14.85 0.87 21.06 1.01 802–924
13
12
15.15 0.17 23.01 0.21 790–835
15.11 0.44 22.69 0.55 802–825
18
9
NdBr+2
13.99 0.60 20.98 0.71 780–912
14.87 0.87 21.06 0.99 803–924
19
12
14.82 0.34 23.00 0.51 799–831
15.12 0.13 22.90 0.16 799–879
10
17
NdBr+3
Nd2+
NdBr2+
13.82 0.90 19.42 1.03 825–930
13.64 0.93 19.08 1.05 861–910
16
7
NdBr22+
13.80 1.35 17.83 1.53 861–910
19.43 2.06 25.36 2.33 851–930
8
Nd2Br+
19
20.04 0.12 27.38 0.14 814–880
15
5
Note: N is the number of measurements. The numbers after the sign are standard deviations.
Langmuir measurements, an NdBr3 single crystal was the range 780−930 K were similar to the spectra of other
LnBr3 compounds [1–5] and indicated the presence of the
secured in a molybdenum holder. The (001) face of the
crystal (3 × 3 mm) was sublimed, which was obtained
by cleavage immediately before mounting the evapora-
tor in the mass spectrometer.
Nd+, NdBr+, NdBr2+, NdBr3+, Nd2Br+5 , Nd2+, NdBr2+, and
NdBr22+ ions both in effusion measurements and in subli-
Molecular components of the vapor were identified
while operating the ion source in the electron impact
ionization mode. Mass spectra were recorded at an
electron energy of Ee = 70 eV and a cathode emission
current of Iemis = 1 mA. In ionic sublimation experi-
ments, the thermal ions generated inside the effusion
cell or on the crystal surface were extracted by a weak
electric field of 104–105 V m–1 produced between the
cell and the collimator electrode.
mation from an open single-crystal surface.
The standard procedure of assigning the observed
ions to their molecular precursors, including an analy-
sis of the shapes of the ionizations efficiency (IE)
curves for various ions, measurement of the appearance
energy (AE) of ions by linear extrapolation of the near-
threshold portions of the IE curves (Table 1), and deter-
mination of the coefficients of the temperature depen-
dences of ion currents (logIi = –A × 103/T + B, Table 2),
led us to the following conclusion: the ions containing
one neodymium atoms result mainly from the ioniza-
tion of the monomer molecule NdBr3, and the Nd2Br5+
RESULTS AND DISCUSSION
Molecular Sublimation
ion is a product of the dissociative ionization of the
Nd2Br6 dimer.
Mass spectra. The mass spectra obtained by elec-
tron impact ionization of a molecular beam (Table 1) in
RUSSIAN JOURNAL OF INORGANIC CHEMISTRY Vol. 54 No. 8 2009

MOLECULAR AND IONIC SUBLIMATION OF NEODYMIUM TRIBROMIDE POLYCRYSTALS
1183
Φ
Although the mass spectra obtained using the Knud-
sen and Langmuir sublimation techniques are qualita-
tively similar, they differ in their relative ion intensities.
Figure 1 plots the temperature dependences of the rela-
tive partial ionization cross section Φ (ratio of the cur-
rent due to a given ion to the total current due to all ions
formed from a given molecule) for singly charged ions.
Clearly, the Φ data obtained for various ions using the
two sublimation techniques differ in magnitude and
show somewhat different temperature dependences.
This result once again demonstrates the distinctive fea-
tures of electron impact fragmentation in the two subli-
mation techniques, confirming earlier observations for
LuBr3 [2] and HoBr3 [4]. We explain these distinctive
features at the qualitative level in terms of the “super-
thermal” vibrational–rotational excitation of the mole-
cules being sublimed from the open surface of an ionic
crystal. Specifically, we consider these features to arise
from the conversion of the Stark energy of admolecules
in the electric field of the excess surface charge of
defect and impurity origins (see, e.g., [15–17]) into the
vibrational–rotational excitation energy.
0.8
0.8
+
Nd
0.7
0.6
0.7
0.6
+
NdBr
NdBr
NdBr
+
2
+
0.16
0.12
0.16
0.12
3
+
Nd Br
2
5
0.08
0.04
0
0.08
0.04
0
760 800 840 880 920 760 800 840 880 920
T, K
Fig. 1. Temperature dependences of the relative partial ion-
ization cross sections (Φ) of the NdBr molecule under
electron impact in the Knudsen and Langmuir sublimation
techniques.
3
mide according to our data, mass spectrometric data
reported by Gietmann et al. [12], and total vapor pres-
sure data [6–11]. Clearly, the scatter in the vapor pres-
sure data for NdBr3 is greater than one order of magni-
tude. Our data fall in the middle of the range of the pres-
sures determined by total vapor pressure measurements
[6, 7, 11] by the effusion method [6, 7] and the torsion
method [11] and exceed the mass spectrometric pres-
sure values reported in [12] by a factor of about 4. The
proportion of dimer molecules in the temperature range
examined is at most 1%, being 0.07% at 700 K, 0.3% at
800 K, and 0.9% at 900 K.
The partial pressures of molecules (pi) in the vapor
phase were calculated using the following standard
relationship of electron impact ionization mass spec-
trometry:
pi = kIiT/σmi ol
,
(1)
where k is the sensitivity constant of the instrument
(determined by evaporation of silver metal in a separate
experiment), T is the cell temperature, Ii =
Iij/(ajγ j)
∑
j
is the total current due to all types of ions forming from
molecule i, a is the coefficient accounting for the natu-
ral abundances of the isotopes of ion j, γ is the ion-to-
electron conversion efficiency (accepted to be γ ~ M–1/2
[18], where å is the molecular weight of the ion), and
The enthalpy of sublimation of NdBr3 as monomer
and dimer molecules were derived from the tempera-
ture dependences of the partial pressures of the compo-
nents of the saturated vapor (Table 3) using the second-
and third-law data processing techniques. The neces-
sary thermodynamic functions of NdBr3 in the con-
densed state were calculated by G.A. Bergman (Joint
Institute for High Temperatures, Russian Academy of
Sciences) [21]. The thermodynamic functions of gas-
eous NdBr3 were calculated by us in the rigid rotor–har-
monic oscillator (RRHO) approximation. In these cal-
culations, we used the molecular constants recom-
mended based on an analysis of available experimental
and theoretical data [22]. The thermodynamic functions
of the dimer Nd2Br6 were estimated by a comparative
method, as in the case of Lu2Br6 [2], under the assump-
tion that the ratio of a thermodynamic function of the
monomer to the same function of the dimer (derived
from molecular parameters taken from [23, 24]) is
invariable throughout the lanthanide series and is equal
to the same ratio averaged between lanthanum and dys-
prosium.
σmi ol is the total ionization cross section of the ith mol-
ecule at the working energy of the ionizing electrons
(calculated from the ionization cross sections of atoms
(σat) [19] using the relationship σmol = 0.75 σaj t [20]).
∑
j
The temperature dependences of the saturation
vapor pressures (p, Pa) of monomer and dimer mole-
cules were approximated by the equations
log p(NdBr3) = (–14.61 0.60)103/T
(2)
+ (15.39 0.71), T = 780–924 K;
log p(Nd2Br ) = (–19.81 2.06)103/T
6
(3)
+ (18.75 2.33), T = 851–930 K.
Here, the numbers after the sign are standard devia-
tions.
Figure 2 plots the partial pressures of the compo-
The results of the processing of the totality of exper-
nents of the saturated vapor over neodymium tribro- imental data using a single set of thermodynamic func-
RUSSIAN JOURNAL OF INORGANIC CHEMISTRY Vol. 54 No. 8 2009

1184
KUDIN et al.
p, Pa
4
10
f
2
10
0
10
e
c
–2
10
d
a
b
T = 955 K
m
–4
10
a'
b'
0.7
0.8 1.0
10 /T, K
1.1
1.2
1.3
3
–1
Fig. 2. Temperature dependences of the vapor pressure over neodymium tribromide: (a) monomer, this work; (a') dimer, this work;
(b) monomer [12]; (b') dimer [12]; (c) [7]; (d) [11]; (e) [6]; (f) [8−10].
∆sH°(298.15)III is the third-law enthalpy of sublimation,
tions (Table 4) are presented in Table 5. In the calcula-
∆sS°(T)II is the second-law entropy of sublimation, and
tion of the enthalpy of sublimation as monomers, the
total pressure data [7–11] were corrected for the vapor
∆sS°(T)III is the third-law entropy of sublimation.
composition derived from mass spectrometric data. It
The second- and third-law enthalpies of sublimation
of neodymium tribromide as dimer molecules (Table 5)
are in good agreement with one another and with the
enthalpy data reported in [12]. The value of
∆sH°(298.15) = 398 20 kJ mol–1 was accepted as the
recommended value.
can be seen from Table 5 that the enthalpies of sublima-
tion/evaporation as monomer molecules calculated by
two independent methods from data of different authors
fall between 262.1 and 317.2 kJ mol–1 (second law) or
between 274.7 and 305.9 kJ mol–1 (third law). A more
detailed data analysis based on examination of the tem-
perature variation of the third-law enthalpy of sublima-
tion (∆sH°(298.15)) and on a comparison between
experimental (second-law) and theoretically calculated
(third-law) entropies of sublimation (∆sSo(T)) did not
indicate that the data of some particular study are pref-
erable. For this reason, we accepted the weighted aver-
age value of ∆sHo(298.15) = 298 5 kJ mol–1 as the rec-
ommended enthalpy of sublimation. This value was
calculated using the formula
°
The enthalpies of formation (∆fH (298.15)) of
the monomer (–566 6 kJ mol–1) and dimer (–1333
20 kJ mol–1) were obtained by combining the accepted
values of the enthalpies of sublimation and the enthalpy
of formation of crystalline neodymium tribromide [25]:
∆fH°(NdBr3, cr, 298.15) = –864.0 3.0 kJ mol–1. The
value that we obtained for the NdBr3 molecule (–566
6 kJ mol–1) differs markedly from the enthalpy esti-
mated within the valence state atoms in molecules
model [26].
°
∆sH°(298.15) =
ki∆sHi (298.15),
(4)
∑
The activation energies of sublimation (Es) of
crystalline neodymium tribromide as monomer and
dimer molecules were derived from the regression
i
where ki = 0.5/(ai / ai) + 0.5/(bi / bi) ,
∑
∑
coefficients
of
the
relationships
between
i
i
log( IjT/(ajγ j) ) and 1/T (j: Nd+, NdBr+, NdBr2+,
∑
2
d
III
j
⎛
⎝
⎞
°
------
dT
ai =
∆sHi (298.15)
,
∑
NdBr+3 , Nd2+, NdBr2+, NdBr22+ ) and between
logINd Br+T and 1/T observed under free sublimation
⎠
i
2
II
III
°
°
2
5
bi =
(∆sSi (T) – ∆sSi (T) ) ,
∑
conditions: Es(NdBr3, 820 K) = 292.1 3.3 kJ mol–1 and
i
RUSSIAN JOURNAL OF INORGANIC CHEMISTRY Vol. 54 No. 8 2009

MOLECULAR AND IONIC SUBLIMATION OF NEODYMIUM TRIBROMIDE POLYCRYSTALS
1185
Table 3. Experimental equilibrium constants of the sublimation reactions of the neodymium tribromide monomer (K0 = pmon/p0,
p0 = 101325 Pa) and dimer (K0 = pdim/p0) and the enthalpies of ion–molecule reactions
T, K; lnK0
NdBr3, cr = NdBr3, g
886, –14.044;
780, –19.492;
866, –14.652;
832, –15.527.
874, –14.855;
876, –14.821;
839, –15.866;
859, –15.542;
861, –14.845;
824, –16.454;
851, –15.844;
877, –14.217;
803, –17.478;
827, –16.878;
912, –13.183;
904, –13.141;
803, –18.304;
883, –14.074;
876, –14.305;
2NdBr3, cr = Nd2Br6, g
868, –20.529;
873, –20.071;
859, –21.330;
884, –20.018.
889, –19.709;
875, –20.164;
851, –21.810;
906, –19.087;
903, –18.929;
865, –20.301;
930, –16.492;
904, –18.599;
875, –20.647;
906, –18.487;
886, –19.748;
861, –20.738;
923, –16.923;
876, –20.513;
877, –20.149;
NdBr3 + LuBr– = LuBr3 + NdBr–
4
4
912, –1.339;
935, –1.923;
947, –1.245;
899, –1.862;
940, –1.515;
971, –1.802;
887, –1.313;
907, –2.237.
969, –1.880;
911, –1.376;
881, –1.606.
913, –1.777;
852, –2.450;
881, –1.554;
905, –1.803;
Nd2Br– = NdBr3, cr + NdBr–
7
4
953, –3.428;
923, –2.281;
1028, –3.450;
896, –2.078;
1043, –3.260;
870, –2.224;
1053, –3.750;
889 –2.119;
1053, –4.049;
920, –2.204;
896, –2.014;
950, –2.669.
Table 4. Thermodynamic functions (I) Φ0(T) (J mol–1 K–1) and (II) H0(T) – H0(0) (J mol–1) used in the calculations
NdBr3, cr NdBr3 Nd2Br6
NdBr–4
Nd2Br–
7
T, K
I
II
I
II
I
II
I
II
I
II
298.15
700
108.74
184.19
196.88
208.34
220.99
25.30
65.77
76.97
88.50
147.55
341.37
403.78
414.05
423.19
431.42
20.57
53.54
61.81
70.09
78.38
525.91
663.38
686.03
706.20
724.36
44.81
117.46
135.67
153.90
172.14
372.32
453.60
466.97
478.87
489.59
26.77
69.73
80.49
91.27
102.05
549.75
704.30
729.87
752.65
773.20
51.57
135.22
156.17
177.14
198.13
for LnBr
800
900
1000
–1 –1
Note: The errors in the Gibbs energy functions were estimated as was suggested in [20] and were taken to be 12 J mol
K
3
–1 –1
and 40 J mol
K
for Ln Br (T = 1000 K).
2 6
RUSSIAN JOURNAL OF INORGANIC CHEMISTRY Vol. 54 No. 8 2009

1186
KUDIN et al.
Table 5. Enthalpies (kJ mol–1) and entropies (J mol–1 K–1) of sublimation of NdBr3 as monomer and dimer molecules (N is
the number of measurements, and Thm is the harmonic mean temperature)
Second law
Third law
Reference
∆T, K
N
Thm
∆sHo(Thm)
∆sSo(Thm) ∆sHo(298.15) ∆sHo(298.15) ∆sSo(Thm)
NdBr3, cr = NdBr3, g
780–912
812–954
849–975
889–948
866–954
956–1019
1258–1559
19
65
853
884
912
918
910
987
1409
279.6 11.5 198.9 13.5 291.7 11.9 289.4 12.0 196.1 12.0 This work
287.4 3.8 200.7 4.0 300.5 3.8 295.5 12.0 195.1 12.0 [12]
251.3 3.8 183.4 3.9 274.7 3.8 274.7 12.0 194.2 12.0 [8]
247.7 3.8 146.3 3.9 262.1 3.8 305.9 12.0 193.7 12.0 [7]
289.4 2.9 193.0 3.8 303.5 2.9 304.5 12.0 194.1 12.0 [11]
253.6 5.7 154.2 5.7 317.2 5.7 305.6 12.0 142.2 12.0 [11]
6
199.0
107.3
292.9
303.6 12.0 116.7 12.0 [8–10]
2NdBr3, cr = Nd2Br6, g
851–930
817–951
19
65
884
884
379.3 39.4 263.1 39.6 395.8 39.6 397.2 30.0 264.7 30.0 This work
379.5 8.1 261.7 7.7 396.0 8.1 398.6 30.0 264.8 30.0 [12]
Note: For the second-law values, the numbers after the sign are standard deviations. For the third-law values, these numbers are the lim-
iting errors taking into account the statistical error and the systematic errors in the temperature and pressure measurements and in
the reduced Gibbs energy function.
Es(Nd2Br6, 838 K) = 383.6 7.0 kJ mol–1). These val-
ues are equal to the enthalpies of sublimation of the
monomer and dimer molecules within the indicated
errors. At the same time, the dimer-to-monomer flux
ratio is much larger in the beam coming out of the effu-
sion hole. For example, at 850 K, the flux ratio
j(Nd2Br6)/j(NdBr3) for the NdBr3 surface under the
Knudsen and Langmuir conditions is 1.71 × 10–3 and
5.31 × 10–6, respectively; that is, the fraction of sub-
limed dimers decreases by more than 2 orders of mag-
nitude on passing from the dynamic equilibrium subli-
mation conditions to sublimation from an open surface.
This factor provides an estimate for the ratio of the sub-
limation coefficients of the dimer αs(Nd2Br6) and mono-
mer αs(NdBr3) under the Langmuir conditions.
Ionic Sublimation
Mass spectra. Here, we present the first study of ion
sublimation from the NdBr3 surface between 800 and
1050 K. Both in equilibrium sublimation and in free
sublimation, we observed the thermal emission of the
negative ions NdBr4– and Nd2Br–7 *. In the free sublima-
tion of an NdBr3 single crystal, we observed a weak sig-
nal from the bromide ion. The ion current ratio
I(NdBr–4 )/I(Nd2Br–7 ) in the temperature range exam-
ined varied within 1–2 orders of magnitude and was
independent of the sublimation conditions. A similar
result was obtained in earlier studies [1, 2, 4]. This corrob-
*The positive ion mass spectra always indicated intensive emission
of ions of alkali metals, which were present in the sample as an
impurity.
RUSSIAN JOURNAL OF INORGANIC CHEMISTRY Vol. 54 No. 8 2009

MOLECULAR AND IONIC SUBLIMATION OF NEODYMIUM TRIBROMIDE POLYCRYSTALS
1187
orates the hypothesis that the sublimation of ionic clusters lanthanide series are linearly independent. The thermo-
dynamic functions of Nd2Br–7 were estimated by an
takes place via a “diffusionless” mechanism [2].
The enthalpy and activation energy of sublima-
additivity method using an empirical correction, as was
tion of the NdBr–4 ion were derived from the slope of done in [29]. The thermodynamic functions of the
LuBr3 molecule and the LuBr–4 ion were taken from [2];
those of crystalline NdBr3, from [21]. The following
enthalpies of formation (∆fH0(298.15 K), kJ mol–1) were
the log logIT1/2 = f(1/í) curve. At the mean experimental
temperature, ∆sH°(NdBr–4 , 879 K) = 290.0 13.6 kJ mol–1
and Es(NdBr–4 , 848 K) = 286.5 13.5 kJ mol–1. Within
the indicated errors, these values are equal to the
enthalpy of sublimation (279.6 kJ mol–1) and the activa-
tion energy of sublimation (292.1 kJ mol–1) of the
NdBr3 monomer.
also used: LuBr3, –538 15 [2]; LuBr–4 , –1085 23 [2];
NdBr3, cr, –864.0 3.0 [25].
ACKNOWLEDGMENTS
The enthalpies of formation of ions. The enthalpy
This study was supported by the Russian Founda-
tion for Basic Research, project no. 06-03-32496.
of formation of the NdBr–4 ion was determined by a
procedure based on investigation of gas-phase ion–
molecule exchange reactions in binary or more com-
plex systems [27]. To make use of this procedure, we stud-
ied the LuBr3–NdBr3 system and measured the equilib-
rium constant of the following reaction (Table 3):
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