Equilibrium vapor composition in the Pb-I2 system

Article abstract of DOI:10.1023/A:1016256828740

The equilibrium vapor composition in the Pb-I₂ system at temperatures from 400 to 2000 K and total pressures from 10² to 10⁵ Pa was assessed by thermodynamic analysis. The results show that the dominant vapor species is Pb

Full text of DOI:10.1023/A:1016256828740

Inorganic Materials, Vol. 38, No. 7, 2002, pp. 735–737. Translated from Neorganicheskie Materialy, Vol. 38, No. 7, 2002, pp. 880–882.
Original Russian Text Copyright © 2002 by Rybak, Kurilo.
Equilibrium Vapor Composition in the Pb–I2 System
O. V. Rybak and I. V. Kurilo
Lviv State Polytechnic University, ul. St. Bandery 12, Lviv, 79013 Ukraine
e-mail: kuriloiv@org.lviv.net
Received July 17, 2001; in final form, January 31, 2002
Abstract—The equilibrium vapor composition in the Pb–I2 system at temperatures from 400 to 2000 K and
total pressures from 102 to 105 Pa was assessed by thermodynamic analysis. The results show that the dominant
vapor species is PbI2. PbI2 dissociation is significant starting at 1000–1300 K, depending on the total pressure
in the system.
INTRODUCTION
acteristics of the reactions involved makes it possible to
draw a number of conclusions about the key features of
the process as a whole, such as the reaction path, devi-
ations from equilibrium, and the influence of individual
reactions on the overall process.
PbI2 crystals are potentially attractive as materials
for optical information recording systems, nonlinear
optical devices, and x-ray and gamma detectors [1, 2].
The known techniques for melt growth of large PbI2
crystals are incapable of ensuring the desired structural
perfection of the crystals, which reflects on the engi-
neering performance of PbI2-based devices. Large, sto-
ichiometric PbI2 single crystals with a low dislocation
density can be grown from the vapor phase in the pres-
ence of excess iodine [3]. This process, however, has
not yet been studied in sufficient detail.
To assess the vapor composition over PbI2 in the
temperature range 400–2000 K at total pressures of 102,
103, 104, and 105 Pa, we carried out thermodynamic
analysis of the Pb–I2 system. The vapor species
included in our analysis were I, I2, Pb, PbI, and PbI2.
The corresponding vapor-phase equilibria are
I2(g)
PbI2(g)
PbI2(g)
2I(g),
(1)
(2)
(3)
In this context, it is of interest to analyze the equilib-
rium vapor composition in a closed system. Informa-
tion about the temperature-dependent compositions of
the vapor and condensed phases helps to clarify the
mechanism of mass transport in the growth system and
optimize the growth procedure. By varying the process
parameters, one can control the quality of the growing
crystal.
PbI(g) + I(g),
Pb(g) + I2(g).
Depending on their melting and boiling points, the
reactants may be in different states of aggregation, pro-
ducing different vapor pressures. The equilibrium con-
stants of independent reactions in the range 300–2000 K
were calculated using the reported thermodynamic
functions of the substances involved [4, 5] (table).
EXPERIMENTAL
The equilibrium pressures of vapor species can be
determined either experimentally or by thermodynamic
calculations.
We used Knudsen cell mass spectrometric measure-
ments to study the sublimation and thermal dissociation
of PbI2 in the temperature range 300–873 K. The mass
spectra of saturated vapor over PbI2 crystals showed the
presence of PbI2 molecules and minor amounts of
iodine and lead.
In terms of the partial pressures p1 = p(I), p2 = p(I2),
p3 = p(Pb), p4 = p(PbI), and p5 = p(PbI2), the equilib-
rium constants for reactions (1)–(3) have the form
K1 = p21/p2,
K2 = p1 p4/p5,
K3 = p2 p3/p5.
(4)
(5)
(6)
CALCULATIONAL APPROACH
In addition,
p1 + 2p2 + p4 + 2p5 = 2(p3 + p4 + p5)
Although crystal growth from the vapor phase is a
nonequilibrium process, it can be analyzed, to a reason-
able approximation, with the use of equilibrium ther-
(7)
modynamics since knowledge of the equilibrium char- (the amount of iodine atoms per unit volume is twice as
0020-1685/02/3807-0735$27.00 © 2002 MAIK “Nauka/Interperiodica”

736
RYBAK, KURILO
p, Pa
105
(a)
(b)
103
101
10–1
10–3
10–5
10–7
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
(c)
(d)
105
103
101
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
10–1
10–3
10–5
10–7
p1
p2
p3
p4
p5
*
300 500 700 900 1100 1300 1500 1700 1900 300 500 700 900 1100 1300 1500 1700 1900
T, K
2
3
4
Fig. 1. Calculated temperature-dependent partial pressures in the Pb–I system at total pressures of (a) 10 , (b) 10 , (c) 10 , and
2
5
(d) 10 Pa; p –p have the same meaning as in text.
1
5
The system of nonlinear algebraic equations (4)–(8)
large as that of lead atoms),
p = p1 + p2 + p4 + p4 + p5
(Dalton Law).
can be reduced to an equation of the fourth degree in p1:
(8)
2p41 + (K1 + 3K2 )p31 + (2K1K2 + 4K1K3 )p21
(9)
+ (3K3K21 – pK1K2 )p1 – 2K3K21 p = 0.
Equilibrium constants of independent reactions in the Pb–I2
system
This equation was solved numerically. Next, using
appropriate substitutions, we found p2, p3, p4, and p5.
The calculated partial pressures of vapor species in the
Pb–I2 system at temperatures in the range 300–1700 K
and different total pressures are displayed in Fig. 1.
T, K
K1
K2
K3
300
400
500
4.2 × 10–25 4.10 × 10–58 1.20 × 10–31
1.45 × 10–14 4.10 × 10–40 7.50 × 10–23
2.8 × 10–11 2.20 × 10–29 7.20 × 10–18
600
700
800
900
1.2 × 10–8
1.02 × 10–6
2.70 × 10–5
3.60 × 10–4
4.20 × 10–3
1.50 × 10–2
6.20 × 10–2
0.20
2.86 × 10–22 8.20 × 10–14
4.00 × 10–17 6.50 × 10–11
1.40 × 10–13 5.00 × 10–9
7.00 × 10–11 1.70 × 10–7
DISCUSSION
The above results lead us to the following conclu-
sions:
1. At total pressures from 102 to 105 Pa and temper-
atures from 300 to 1000 K, the dominant vapor species
is PbI2. Its pressure exceeds those of other vapor spe-
cies by one to five orders of magnitude.
2. PbI2 dissociation into I, I2, Pb, and PbI is signifi-
cant starting at 1000–1300 K, depending on the total
pressure. The main dissociation products are I and Pb.
The PbI vapor pressure rises with increasing tempera-
ture and total pressure but, in the range 300–1300 K,
remains three to five orders of magnitude lower than the
PbI2 pressure. Only above 1500 K is the pressure of PbI
vapor comparable to that of PbI2, but the net iodide
pressure (PbI + PbI2) remains three to four orders of
1000
1100
1200
1300
1400
1500
1600
1700
1800
1900
2000
9.00 × 10–9
4.60 × 10–7
4.60 × 10–6
3.06 × 10–5
1.60 × 10–4
6.50 × 10–4
2.20 × 10–3
6.70 × 10–3
1.80 × 10–2
4.20 × 10–2
9.20 × 10–2
2.40 × 10–6
1.90 × 10–5
6.20 × 10–5
1.15 × 10–4
2.00 × 10–4
3.30 × 10–4
5.03 × 10–6
7.40 × 10–4
1.04 × 10–3
1.42 × 10–3
1.90 × 10–3
0.57
1.39
3.05
6.09
11.30
19.70
32.40
INORGANIC MATERIALS Vol. 38 No. 7 2002

EQUILIBRIUM VAPOR COMPOSITION IN THE Pb–I2 SYSTEM
737
magnitude lower than the pressure of the dissociation interest. At the same time, the growth duration is too
products (Pb, I, and I2).
long for practical applications. In this context, there is
a need for theoretical analysis and experimental studies
of the effects that the growth conditions and iodine
overpressure have on the rate of PbI2 transport and the
morphology of the resulting crystals. Such information
is crucial for optimizing the conditions of PbI2 crystal
growth. These issues will be addressed in subsequent
communications.
3. To a first approximation, the vapor-phase equilib-
rium in the Pb–I2 system between 300 and 1000 K can
be described by scheme (3).
Our experimental and calculation results on the
equilibrium vapor composition in the Pb–I2 system pro-
vide guidelines for choosing the conditions of PbI2
growth from the vapor phase. Since the temperature of
the growth zone should not exceed 685 K (melting point
of PbI2), and a temperature gradient of 100–400 K is typ-
ically sufficient for vapor transport growth, the highest
temperature of the source zone is 1000–1100 K. At
temperatures from 700 to 1100 K and total pressures
from 103 to 105 Pa, the dominant vapor species in the
Pb–I2 system is PbI2. The proportion of the dissociation
products under these conditions does not exceed 1%.
As PbI2 slightly dissociates in the temperature range in
question, which may lead to deposition of nonstoichio-
metric material, the process should be run at an iodine
overpressure no lower than the dissociation pressure
(103 Pa). The mechanism of mass transport in the
growth system depends on the relationship between the
total pressure and the difference in the vapor pressures
in the source and growth zones.
REFERENCES
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Note that, in the growth procedure described in [3],
the iodine overpressure is substantially higher than the
pressure of PbI2 dissociation at the temperatures of
5. Rolsten, R.F., Iodide Metals and Metal Iodides, New
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metally i iodidy metallov, Moscow: Metallurgiya, 1968.
INORGANIC MATERIALS Vol. 38 No. 7 2002