Kinetics and mechanism of free-surface vaporization of groups IIA, IIIA and IVA nitrides analyzed thermogravimetrically by the third-law method

Article abstract of DOI:10.1016/j.tca.2005.07.007

The purpose of this work was to re-measure the enthalpy ΔrHT° of free-surface vaporization of hexagonal (h) Mg₃N₂, AlN, GaN, InN and Si₃N₄ and cubic (c) BN by the third-law method and by comparing them with the enthalpies calculated from thermodynamics to deduce the composition of primary products (bN and cN₂) for the generalized decomposition reaction: M_aN_b+2c ? aM + bN + cN₂. In addition to these nitrides, the literature data were used for the investigation of vaporization of h-Be₃N₂ and c-AlN and c-GaN. The relative standard deviation in determination of ΔrHT° values is ≤1% and in determination of b/(b + 2c) ratio is better than 2-4%. As a result of this study, some important features in the decomposition mechanism of different nitrides were revealed: the identity in composition of primary products for h-Be₃N₂ and h-Mg ₃N₂ (b/(b + 2c) = 0.75) and h-AlN and h-GaN (b/(b + 2c) = 0.42) and the release of only molecular nitrogen in cases of c-BN, c-AlN and c-GaN (b/(b + 2c) = 0). The last feature that was observed earlier for cubic metal oxides [B.V. L'vov, V.L. Ugolkov, F.F. Grekov, Kinetics and mechanism of free-surface vaporization of zinc, cadmium and mercury oxides analyzed thermogravimetrically by the third-law method, Thermochim. Acta 411 (2004) 187-193.] supports the effect of crystal symmetry on the decomposition mechanism. The distance between the closest atoms (NN) in a crystalline lattice has a secondary or no effect on the composition of primary products. These features might be useful for the development/improving of appropriate technologies (including nano-technologies) for production of solid materials by the chemical vapour deposition.

Full text of DOI:10.1016/j.tca.2005.07.007

Thermochimica Acta 438 (2005) 1–8
Kinetics and mechanism of free-surface vaporization of groups IIA, IIIA
and IVA nitrides analyzed thermogravimetrically by the third-law method
Boris V. L’vova,∗, Valery L. Ugolkovb
a
Department of Analytical Chemistry, St. Petersburg State Polytechnic University, St. Petersburg 195251, Russia
Laboratory of Thermodynamics and Kinetics, Institute of Silicate Chemistry, St. Petersburg 199155, Russia
b
Received 16 April 2005; received in revised form 30 June 2005; accepted 19 July 2005
Available online 31 August 2005
Abstract
The purpose of this work was to re-measure the enthalpy ꢀrHT◦ of free-surface vaporization of hexagonal (h) Mg3N2, AlN, GaN, InN and
Si3N4 and cubic (c) BN by the third-law method and by comparing them with the enthalpies calculated from thermodynamics to deduce the
composition of primary products (bN and cN2) for the generalized decomposition reaction: MaNb+2c ↔ aM + bN + cN2. In addition to these
nitrides, the literature data were used for the investigation of vaporization of h-Be3N2 and c-AlN and c-GaN. The relative standard deviation
in determination of ꢀrHT◦ values is ≤1% and in determination of b/(b + 2c) ratio is better than 2–4%. As a result of this study, some important
features in the decomposition mechanism of different nitrides were revealed: the identity in composition of primary products for h-Be3N2
and h-Mg3N2 (b/(b + 2c) = 0.75) and h-AlN and h-GaN (b/(b + 2c) = 0.42) and the release of only molecular nitrogen in cases of c-BN, c-AlN
and c-GaN (b/(b + 2c) = 0). The last feature that was observed earlier for cubic metal oxides [B.V. L’vov, V.L. Ugolkov, F.F. Grekov, Kinetics
and mechanism of free-surface vaporization of zinc, cadmium and mercury oxides analyzed thermogravimetrically by the third-law method,
Thermochim. Acta 411 (2004) 187–193.] supports the effect of crystal symmetry on the decomposition mechanism. The distance between
the closest atoms (N N) in a crystalline lattice has a secondary or no effect on the composition of primary products. These features might
be useful for the development/improving of appropriate technologies (including nano-technologies) for production of solid materials by the
chemical vapour deposition.
© 2005 Elsevier B.V. All rights reserved.
Keywords: Atomic nitrogen release; Effect of crystal symmetry; Free-surface vaporization of nitrides; Stoichiometry of reactions; Third-law method
1. Introduction
Besides, their decomposition mechanism is of con-
siderable scientific interest. For most of nitrides, the
evaporation coefficient is rather low in spite of their con-
gruent vaporization that yields (with the exception of BN)
only vapour species. Generally recognized explanation of
this phenomenon is based on the difference between the low
Over the past three decades, the development and com-
mercialization of light-emitting diodes and semiconductor
lasers operating in the infrared, red and green regions of the
optical spectrum have generated much interest in materials
capable of extending the operation of these devices into the
blue and ultraviolet regions. The hexagonal nitrides such as
AlN, GaN and InN are candidate materials for applications
at such energies. Knowledge of conditions and mechanism
of their decomposition is vital for film growth, processing of
devices and high-temperature operation.
˚
internuclear distance in the gaseous N2 molecule (1.07 A)
˚
and much larger distances (2.5–3.5 A) between closest
nitrogen atoms in a lattice of solid nitrides. As assumed, this
should cause the difficulty in accommodating on the surface
a gaseous molecule, which does not exist as a structural unit
in the condensed phase. However, this explanation is now
out of date. It has been shown that the so-called ‘difficulty’
in decomposition is actually related to the difference of
composition of primary products from the equilibrium one
∗
Corresponding author. Tel.: +7 812 552 7741; fax: +7 812 247 4384.
E-mail address: borislvov@rambler.ru (B.V. L’vov).
0040-6031/$ – see front matter © 2005 Elsevier B.V. All rights reserved.
doi:10.1016/j.tca.2005.07.007

2
B.V. L’vov, V.L. Ugolkov / Thermochimica Acta 438 (2005) 1–8
[1]. In case of gaseous products, atomic species (e.g., O,
S and N) are released in addition to equilibrium diatomic
molecules (O2, S2 and N2). From the recent analysis of crys-
tal structure for 12 different oxides, which evaporate with
releasing of molecular oxygen, and for 13 compounds, which
evaporate with releasing of atomic oxygen, it was revealed
that the first mechanism is observed for all oxides with the
cubic crystal structure [2]. The minimum O–O distance for
the maximum vapour flow J (in moles) in the absence of
any diffusion limitations can be evaluated with the use of
the Hertz–Langmuir equation that for simple vaporization of
solids (e.g., metals) is expressed as
P
J =
(2)
(2πMRT)1/2
Here P is the equilibrium vapour pressure of material with
the molar mass M at temperature T. To apply this equation to
reaction (1), it is necessary to take into account the condition
of congruent vaporization
˚
these oxides reaches 4 A, which is much higher than the
˚
internuclear distance in O2 molecule (1.21 A). For all other
compounds of different (from cubic) singony, the release of
oxygen occurs in the form of free O atoms. Therefore, the
distance between the closest atoms in a crystalline lattice
has a secondary or no effect on the composition of primary
products. A decisive role in this difference belongs to a local
symmetry in the position of atoms in a crystal. For those
oxides, where this symmetry is the highest and environment
is close to isotropic, there is the molecular mechanism of
dissociation. Oxygen atoms, which are in low-symmetrical
positions, leave their sites without recombination.
JA
JB
b
JC
c
=
=
(3)
a
or
PA
a(2πMART)1/2
PB
b(2πMBRT)1/2
PC
=
c(2πMCRT)1/2
=
(4)
The total maximum vapour flow Jꢁ (in kg m−2 s−1) in case
of reaction (1) is equal to
It is of interest to extend these investigations to decompo-
sition of other solid compounds, in particularly, of nitrides.
Such studies have been performed in some of our previ-
ous works [1,3–5]. However, analysis of stoichiometry of
decomposition reactions was based only on the literature data
relating to determination of evaporation coefficients by the
Knudsen (effusion) and Langmuir (free-surface) methods.
The reliability of these data, especially in case of Langmuir
measurements by the second-law method is rather low. As
a result, the composition of nitrogen species deduced from
these data varied in different publications. In particular, the
content of atomic N species in primary nitrogen products
reported in [1,4,5] were: 70, 75 and 50% for Be3N2; 60, 50
and 50% for h-AlN; 60, 50 and 50% for h-GaN.
MAPA
Jꢁ = MAJA + MBJB + MCJC =
(2πMART)1/2
MBPB
(2πMBRT)1/2
MCPC
(2πMCRT)1/2
+
+
(5)
On substitution PB and PC values for PA from Eq. (4), we
obtain
MRPA
a(2πMART)1/2
Jꢁ
=
(6)
or
a(2πMART)1/2
PA [bar] =
Jꢁ
(7)
γMR
The purpose of this work is to re-measure the enthalpy
of free-surface vaporization of some available to us nitrides
(Mg3N2, BN, AlN, GaN, InN and Si3N4) by the third-law
method and by comparing them with the enthalpies calcu-
lated from thermodynamics to deduce the stoichiometry of
appropriate vaporization reactions. In conclusion, a possible
correlation between the stoichiometry and crystal structure
of nitrides will be considered. It is expected that, as in many
other cases [4,5], application of the third-law method to these
measurements will significantly increase precision and accu-
racy of experimental results and, therefore, reliability of final
conclusions.
where MR is the molar mass of reactant. The coefficient
γ = 105 Pa bar−1 is the conversion factor from Pascal to bar
used in the further thermodynamic calculations with partici-
pation of PA.
The next step to determination of the molar enthalpy by
the third-law method is related to the evaluation of the equi-
librium constant of reaction (1) through the partial pressure
PA. Taking into account Eq. (4), we obtain
KP = PAa × PBb × PCc = δ × PAν
(8)
where
ꢀ ꢁ
ꢀ
ꢁ
ꢀ
ꢁ
b
b/2
c/2
ꢂ ꢃ
c
b
c
MB
MA
MC
MA
δ =
(9)
a
a
2. Theoretical
and
2.1. Determination of the molar enthalpy of free-surface
solid vaporization by the third-law method
ν = a + b + c
(10)
If we insert KP value from Eq. (8) into the fundamental equa-
tion of chemical thermodynamics
In case of a solid compound R vaporized in vacuum into
gaseous products A, B and C, that is
ꢀrHT◦ = T(ꢀrST◦ − R ln KP )
(11)
R (s) ↔ aA (g) + bB (g) + cC (g)
(1)

B.V. L’vov, V.L. Ugolkov / Thermochimica Acta 438 (2005) 1–8
3
where ꢀrHT◦ and ꢀrST◦ are the enthalpy and entropy of reac-
Table 1
Thermodynamic functions [7–10] used in the calculations
tion (1), we obtain
Species T (K)
State of
ꢀfHT◦ (kJ mol−1
)
ST◦ (J mol−1 K−1
)
ꢀrHT◦ = T(ꢀrST◦ − R ln δ − νR ln PA)
(12)
(13)
aggregation
c-AlN
Al
N2
N
h-AlN
Al
N2
N
h-AlN
Al
N2
N
c-BN
B
Be3N2
Be
N2
N
c-GaN
Ga
N2
h-GaN
Ga
N2
N
h-GaN
Ga
InN
In
N2
N
InN
In
N2
1300
1300
1300
1300
1700
1700
1700
1700
1800
1800
1800
1800
1800
1800
1600
1600
1600
1600
900
s
−274.2
350.7
31.5
493.5
−254.1
359.0
45.5
501.8
−248.9
361.1
48.9
503.9
−187.5a
596.3
−436.5
357.3
41.9
499.7
−128.7b
287.6
18.2
−112.7b
294.6
28.1
491.4
−107.1b
296.8
−90.6a
257.0
21.5
487.3
−84.5a
259.7
24.8
83.2
195.3
236.8
183.8
96.7
200.9
246.2
189.4
99.6
202.1
248.2
190.6
82.7
190.7
215.4
171.1
244.0
188.1
86.5b
197.8
224.6
101.9b
204.5
234.1
182.1
106.2b
206.3
106.0a
201.5
228.1
178.3
111.6a
204.1
231.2
180.3
246.0
177.5
256.3
179.1
308.1
204.9
The molar value of enthalpy is equal to
g
g
g
s
g
g
g
s
g
g
g
s
g
s
g
g
g
s
g
g
s
g
g
g
s
g
s
g
g
g
s
g
g
g
s
g
s
g
s
ꢀ
ꢁ
ꢀrHT◦
ν
ꢀrST◦
ν
R ln δ
= T
−
− R ln PA
ν
2.2. Thermodynamic calculation of the reaction
enthalpy and entropy
The ꢀrHT◦ and ꢀrST◦ values for the reactions with known
stoichiometry are calculated by the obvious equations:
ꢀrHT◦ = aꢀfHT◦ (A) + bꢀfHT◦ (B)
+cꢀfHT◦ (C) − ꢀHT◦ (R)
(14)
(15)
and
900
900
ꢀrST◦ = aST◦ (A) + bST◦ (B) + cST◦ (C) − ST◦ (R)
1200
1200
1200
1200
1300
1300
1000
1000
1000
1000
1100
1100
1100
1100
The magnitudes of thermodynamic functions (the standard
enthalpies of formation ꢀfHT◦ and absolute values of entropy
ST◦) for the components of decomposition reactions of nitrides
at different temperatures are listed in Table 1.
3. Experimental
The experiments were carried out with a Netzsch STA 429
instrument on the TG and DSC measuring head. The actual
measured quantities were the mass change of the sample per
time unit, ꢀm/ꢀt, and the absolute crucible temperature. An
open alumina crucible 5.7 mm inner diameter and 4.0 mm
high was used as a sample container. The reacting materials
were commercial high purity powders of Mg3N2 (99.5%),
GaN (99.99%) and InN (99.99%) from Aldrich, Si3N4 (H-1)
from Stark and AlN and BN of undefined origin. To pre-
vent the ejection of powder from a crucible under violent
evaporation, 1:1 mixtures of some nitrides (Mg3N2, GaN and
InN) with high purity Al2O3 powder were used. A powder
sample (5–30 mg) introduced into a crucible was leveled and
pressed manually (about 1 kg mm−2) into a flat pellet. The
total (outer) surface area of pellet was calculated taking into
account the crucible diameter and the thickness of pellet.
The sample chamber was evacuated to a residual pressures
about 5 × 10−8 bar with the use of rotation and oil-diffusion
pumps. All measurements have been conducted at continuous
pumping under isothermal conditions. The heating rate of the
sample from the room temperature to intermediate one (20 K
lower than the desired temperature) was 20 K min−1 and from
intermediatetothedesiredtemperaturewas2 K min−1. Atthe
beginning of each measuring cycle, the system was heated at
the temperature chosen, usually for 10 min, to reach a con-
stant rate of the decomposition.
N
489.3
−353.8
165.7
−340.8
167.8
−576.6
479.7
Mg3N2 1200
Mg 1200
Mg3N2 1300
Mg
Si3N4
Si
1300
1700
1700
g
a
From [7].
From [10].
b
The absolute value of the decomposition rate, Jꢁ, for
powder samples was estimated using the method proposed
in our previous work [6]. It consists in the evaluation of the
absolute decomposition rate of a powder sample (reduced
to the unit of the outer surface area of a pellet formed by the
powder sample in a cylindrical crucible). The value received
is lowered by the correction (empirical) factor and then
used for the calculation of molar enthalpy by the third-law
method. The value of this factor (2.8 0.4), as was shown
in [6], does not depend on the temperature, residual pressure
of gas in the reactor, grain size and mass of a powder
sample.
The changes of the mass and surface area of powders dur-
ing measuring cycle were also taken into account. A decrease

4
B.V. L’vov, V.L. Ugolkov / Thermochimica Acta 438 (2005) 1–8
of the surface area, as was checked experimentally, was
proportional to (1 − αm)2/3 where αm is the decomposition
degree by the time of measurement. (This dependence can
be interpreted as a combined result of the reduction of num-
ber and size of particles in the process of decomposition.)
Temperature was measured with Pt–Pt10% Rh thermocouple
placedwithitsjunctionimmediatelybelowthecrucible. Tem-
perature variations in the process of mass-change measure-
ments (usually, during 20–30 min) did not exceed 0.2 K. A
single measurement of the decomposition rate took entirely
about 2–3 h.
BN deserves special consideration. This is the only nitride
under investigation that decomposes with formation of a solid
product (boron). Its decomposition can be described by the
reaction,
c-BN (s) ↔ B (g) + 0.5N2 → B (s) + 0.5N2
(16)
However, kinetics of c-BN decomposition is determined only
by the first stage of reaction. The partial returning of the
condensation energy to reactant can be neglected [5] because
the equivalent pressure of B for reaction (16) at 1800 K is only
one order of magnitude higher than the saturated pressure of
metal. Nevertheless, the 2% difference in experimental and
theoretical ꢀrHT◦/ν values for BN in Table 2 may be related
to this approximation.
4. Results and discussion
Table 5 summarizes both the averaged data obtained in
this work (Table 2) and the results obtained from analysis
of the literature (Table 4). Besides, Table 5 contains the
data, which describe the crystal structure of nitrides: the
system (singony), space group and N–N minimum distance
[19,20]. There are some controversies in definition of the
system for Mg3N2. In some reference books it is defined
as cubic one. At the same time, Mitchell [21] observed
for Mg3N2 two polymorphous transitions at 823 3 and
1061 5 K. The enthalpies of both transitions were very low.
Our attempts to repeat these experiments allowed observ-
ing with some degree of certainty only the first transition
at 823 K. Nevertheless, taking into account that Be3N2 and
Ca3N2 possess the hexagonal system at high temperatures,
we assigned to decomposing Mg3N2 the hexagonal system
as well.
The experimental conditions and results of determination
of the molar enthalpy for vaporization of Mg3N2, BN, AlN,
GaN, InN and Si3N4 by the third-law method are presented
in Table 2. The stoichiometry of reaction indicated in the
first column was deduced on a basis of the best correlation
between the ꢀrHT◦/ν value measured experimentally and that
calculated for a given temperature from the thermodynamic
data listed in Table 1. For illustration of the effect of stoi-
chiometry on the experimental and theoretical ꢀrHT◦ values,
wereportinTable3thecorrespondingdataforAlN. Ascanbe
seen, an increase of N species in primary products from 40 to
44% reduces the experimental value by 0.06% and increases
the theoretical value by 1.1%. In case of Mg3N2, an increase
of N species in primary products from 70 to 75% reduces the
experimental value by 0.06% and increases the theoretical
ꢀrHT◦/ν value by 2%. Therefore, taking into account that the
relative standard deviation in determination of ꢀrHT◦/ν in all
cases is ≤1%, the uncertainty in the deduced stoichiometry of
reactions (reduced to the content of N species) cannot exceed
2–4%.
The experimental conditions and the results of our cal-
culation by the third-law method of the molar enthalpy for
vaporization of hexagonal Be3N2, Mg3N2, AlN, GaN, InN
and Si3N4 and cubic BN, AlN and GaN based on the lit-
erature data [11–17] are presented in Table 4. It should be
noted that all calculations of ꢀrHT◦/ν values in Tables 2 and 4
have been performed with Eq. (13), which in contrast with
appropriate equations in our earlier works (with the excep-
tion of [18]) takes into account the congruent condition of
decomposition in the form of additional term (R ln δ)/ν. Its
values for different nitrides are listed in Table 4. Use of this
improved calculation scheme increases the ꢀrHT◦/ν values
for some nitrides by 7–8 kJ mol−1. This table contains also
the ꢀrHT◦/ν values measured in original publications by the
second-lawmethod. Thededuced ꢀrHT◦/ν valuesforMg3N2,
BN, AlN, GaN, InN and Si3N4 were taken from Table 2. For
Be3N2, ꢀrHT◦/ν value was deduced from a comparison with
the experimental value calculated by the third-law method
from the literature data. The values of ꢀrHT◦/ν for cubic BN,
AlN and GaN correspond to the equilibrium reactions with
a release of only molecular nitrogen. Decomposition of c-
From analysis of the data listed in Tables 2–5, the follow-
ing conclusions can be deduced.
1. Special attention must be given to the distinct difference
in the decomposition of the cubic and hexagonal nitrides.
All cubic nitrides decompose with a release of only molec-
ular nitrogen and all hexagonal nitrides decompose with
a release from 32 to 75% atomic nitrogen. The first part
of this regularity is in a full agreement with the decom-
position mechanism of oxides [2]. This is not the case for
hexagonal nitrides. For all oxides and some double oxides
(MgSO4 and BaSO4) with the different from cubic system
(II, III, IIIa, IV and V), the release of oxygen occurs in
the form of free atoms only but not as a mixture of O and
O2 [2].
2. The identical stoichiometry of decomposition reactions is
observed for two pairs of nitrides of identical composition
(Be3N2/Mg3N2 and AlN/GaN) in spite of great differ-
ence in their decomposition temperatures: 1600/1200 and
1800/1300 K. Apparently, the stoichiometry of decom-
position is not dependent on the temperature. However,
the stoichiometry of InN decomposition unexpectedly
differs from that of AlN and GaN. The reason remains
unclear.
3. No correlation between the stoichiometry and minimum
N–N distance in crystals are observed. What is more, the

Table 2
Experimental conditions for nitride decomposition in vacuum (n × 10−8 bar) and the results of determination of the molar enthalpy by the third-law method (this work)
(ꢀST◦/ν)
(∆rHT◦/ν) (kJ mol−1
)
a
b
Deduced reaction
T (K)
m0 (mg)
S0
(mm2)
αm
Sm
(mm2)
(ꢀm/ꢀt)
(␮g s−1
JΣ
PA
ν
)
(kg m−2 s−1
)
(bar)
(J mol−1 K−1
)
Third law
Deduced
Mg3N2 ↔ 3Mg (g) + 1.5N + 0.25N2
1261
1232
1201
10.2c
10.2c
9.8c
47.4
47.4
47.4
0.369
0.206
0.143
34.9
40.6
42.8
0.987
0.540
0.234
1.01 × 10−5
4.75 × 10−6
1.95 × 10−6
1.17 × 10−7
7.75 × 10−8
3.14 × 10−8
4.75
4.75
4.75
129.8
130.0
130.1
335.6
332.3
333.1
335.5
335.6
335.8
BN ↔ B (g) + 0.5N2
1800
1799
30.0
30.0
60.0
60.0
0.016
0.013
59.3
59.5
0.51
0.43
3.07 × 10−6
5.63 × 10−8d
1.5
1.5
154.7
154.7
526.1
528.7
538.8
538.8
↓
2.59 × 10−6
3.30 × 10−5
4.17 × 10−5
4.74 × 10−8d
4.06 × 10−7
5.13 × 10−7
AlN ↔ Al (g) + 0.42N + 0.29N2
GaN ↔ Ga (g) + 0.42N + 0.29N2
1784
1785
30.0
30.0
61.8
61.8
0.046
0.066
59.9
59.0
5.53
6.90
1.71
1.71
149.4
149.4
492.0
488.8
488.9
488.9
1268
1256
1277
1257
1256
1266
1267
10.0
5.0c
50.6
45.7
50.5
50.5
50.5
45.7
45.7
0.070
0.042
0.20
0.030
0.037
0.046
0.046
48.2
44.4
43.6
49.5
49.2
44.2
44.2
1.49
0.53
2.09
1.33
1.35
1.41
1.20
1.10 × 10−5
4.27 × 10−6
1.71 × 10−5
9.60 × 10−6
9.80 × 10−6
1.14 × 10−5
9.69 × 10−6
9.04 × 10−8
3.51 × 10−8
1.41 × 10−7
6.52 × 10−8
8.06 × 10−8
9.37 × 10−8
7.97 × 10−8
1.71
1.71
1.71
1.71
1.71
1.71
1.71
144.4
144.5
144.4
144.5
144.5
144.4
144.4
361.4
368.0
359.3
361.9
359.4
360.5
362.5
363.1
363.2
363.0
363.2
363.2
363.1
363.1
10.0c
10.1c
10.0c
5.0c
4.5c
InN ↔ In (g) + 0.32N + 0.34N2
1028
1008
1009
10.0c
10.0c
10.0c
54.6
54.6
54.6
0.070
0.040
0.035
52.1
53.2
53.3
0.137
0.131
0.126
9.40 × 10−7
8.79 × 10−7
8.44 × 10−7
5.93 × 10−9
5.55 × 10−9
5.33 × 10−9
1.66
1.66
1.66
138.6
138.7
138.7
311.2
305.8
306.4
307.5
307.7
307.7
␣,␤-Si3N4 ↔ 3Si (g) + 1.8N + 1.1N2
1700
1699
30.0
30.0
61.8
61.8
0.020
0.019
60.9
61.0
1.34
1.29
7.86 × 10−6
8.41 × 10−8
5.9
5.9
155.3
155.3
501.6
501.8
503.2
503.2
7.57 × 10−6
8.10 × 10−8
a
The surface area by the time of measurement calculated by the equation Sm = S0(1 − αm)2/3
.
b
c
d
JΣ = (ꢀm/ꢀt)/(2.8Sm).
Diluted with Al2O3 in 1:1 ratio.
Corresponds to the nitrogen pressure and calculated by the equation PN = J(2πMN2 RT)1/2(γMN
−1
)
2
.
2

6
B.V. L’vov, V.L. Ugolkov / Thermochimica Acta 438 (2005) 1–8
Table 3
Effect of reaction stoichiometry on the experimental and calculated values of molar enthalpy
Deduced reaction
ν
(ꢀST◦/ν)
(R ln δ/ν)
(J mol−1 K−1
)
(ꢀHT◦/ν) (kJ mol−1
)
(J mol−1 K−1
)
Third lawa
Deduced
AlN ↔ Al (g) + 0.5N2
1.5
151.2
149.5
149.4
149.3
146.7
−1.87
−4.02
−4.04
−4.05
−1.36
488.3
489.1
488.9
488.8
479.3
423.1
486.1
488.9
491.6
557.1
AlN ↔ Al (g) + 0.40N + 0.30N2
AlN ↔ Al (g) + 0.42N + 0.29N2
AlN ↔ Al (g) + 0.44N + 0.28N2
AlN ↔ Al (g) + N
1.70
1.71
1.72
2.0
At PA = 5.1 × 10−7 bar and T = 1785 K.
a
surface of BN and reduction of the effective value of emit-
tance factor ε [5]. Even if we exclude this discrepancy (for
BN) from consideration, the mean relative standard devi-
ation between ꢀrHT◦/ν measured by the second-law and
the deduced values will be equal to 13%. It is clear that
the interpretation of stoichiometry on the basis of ꢀrHT◦
measured by the second-law method would be very unre-
liable. The correlation between ꢀrHT◦/ν measured by the
third-law method and the deduced values for AlN, GaN,
InN, Si3N4 and BN taken from Table 2 is much better.
The relative standard deviation is only 2.6%. The value
ꢀrHT◦/ν = 296 kJ mol−1 for Mg3N2 calculated from the
data in [12] is obviously underestimated. It follows from
a comparison of this value with ꢀrHT◦/ν = 305 kJ mol−1
measured in [12] for the Knudsen vaporization of Mg3N2.
The value ꢀrHT◦/ν for the free-surface (Langmuir) vapor-
ization cannot be less than the value measured under
conditions close to the equilibrium.
˚
minimum N–N distance for InN (3.5 A) is higher than
˚
that for AlN and GaN (3.1 A) despite the lower content
of free N atoms in the primary products of decompo-
sition (32 and 42%, respectively). A generally recog-
nized explanation of a low evaporation coefficients for
nitrides [13], which is based on the difference between
the low internuclear distance in the gaseous N2 molecule
(1.07 A) and much larger distances (2.5–3.5 A) between
closest nitrogen atoms in a lattice of solid nitrides, is
untrue.
˚
˚
4. From the data listed in Table 4 it can be seen that the val-
ues of ꢀrHT◦/ν obtained by the third-law method are more
reliable than those obtained by the second-law method. In
seven from ten instances, the data obtained by the second-
law method are lower. The difference in ꢀrHT◦/ν for BN
reaches 60%. We explain this systematic underestimation
by the effect of self-cooling, which was especially signif-
icant for BN because of formation of a boron layer on the
Table 4
Experimental conditions for nitride decomposition and the results of our calculation of the molar enthalpy by the third-law method (based on the literature data)
Deduced reaction
Sample
T (K) PA (bar)
ν
(R ln δ/ν)
(J mol−1 K−1
(ꢀST◦/ν)
(ꢀHT◦/ν) (kJ mol−1
)
Reference
)
(J mol−1 K−1
)
Second Third Deduced
law
law
Be3N2 ↔ 3Be (g) + 1.5N + 0.25N2
Pressed
pellet
1600
1200
1800
1300
1300
1.5 × 10−9a 4.75 −2.53
129.4
130.1
149.3
143.9
143.9
137.9
428
481
480.2
335.8
488.8
362.8
362.8
306.8
[11]
[12]
[13]
[14]
[15]
[14]
Mg3N2 ↔ 3Mg (g) + 1.5N + 0.25N2 Pressed
1.3 × 10−6
1.7 × 10−7
1.0 × 10−7
2.8 × 10−7
5.4 × 10−8
2.9 × 10−7
4.75 −3.60
1.71 −4.04
1.71 −5.80
1.71 −5.80
1.66 −6.59
5.9 −4.29
238b
494b
379
296
509
369
358
312
pellet
Pressed
pellet
MOCVD
film
Pressed
pellet
h-AlN ↔ Al (g) + 0.42N + 0.29N2
h-GaN ↔ Ga (g) + 0.42N + 0.29N2
h-GaN ↔ Ga (g) + 0.42N + 0.29N2
InN ↔ In (g) + 0.32N + 0.34N2
305
Polycrystal 1100
film
336
␣,␤-Si3N4 ↔ 3Si (g) + 1.8N + 1.1N2 Powder
1713
1800
155.2
154.7
480b
329b
488
539
503.1
538.8
[16]
[13]
c-BN ↔ B (g) + 0.5N2
Pressed
pellet
MOCVD
film
2.4 × 10−8c 1.5
1.20d
↓
c-AlN ↔ Al (g) + 0.5N2
c-GaN ↔ Ga (g) + 0.5N2
1300
900
1.2 × 10−8
1.5 −1.87
153.7
149.1
414
261
399
308
427.1
283.6
[14]
[17]
MBE film
1.2 × 10−10 1.5 −3.18
MOCVD: metal organic chemical vapour deposition; MBE: molecular beam epitaxy.
a
PA is reduced by a factor 2.8 to correct the porosity (18%) of pressed pellet.
Calculated in this work on the basis of experimental data reported in original publications.
b
c
Corresponds to the nitrogen pressure.
d
Taking into account that δ = (a/b)a(MA/MB)a/2
.

B.V. L’vov, V.L. Ugolkov / Thermochimica Acta 438 (2005) 1–8
7
Table 5
Decomposition mechanism of nitrides in vacuum versus their crystal structure (overall data)
Deduced reaction
b/(b + 2c)a
(%)
Sample
System Space
group
N–N minimum
T (K) (ꢀrHT◦/ν) (kJ mol−1
)
Reference
˚
distance (A)
Second Third Deduced
law
law
481
Be3N2 ↔ 3Be (g) + 1.5N + 0.25N2
75
Pressed
pellet
Pressed
pellet
III
194
194
2.84
3.29
1600 428
480
336
[11]
[12]
Mg3N2 ↔ 3Mg (g) + 1.5N + 0.25N2 75
IIIb
1200 238
296
Pellet
1231 350
1800 494c
334
509
336
489
This work
[13]
h-AlN ↔ Al (g) + 0.42N + 0.29N2
h-GaN ↔ Ga (g) + 0.42N + 0.29N2
42
42
Pressed
pellet
Pellet
III
III
186
186
3.07
3.17
1785
–
490
369
489
363
This work
[14]
MOCVD
film
Pressed
pellet
1300 379
1300 305
358
363
[15]
Pellet
1264
–
362
312
363
307
This work
[14]
InN ↔ In (g) + 0.32N + 0.34N2
32
Polycrystal III
film
186
3.51
1100 336
Pellet
1015
1713 480c
1700
1800 329c
–
308
308
This work
␣,␤-Si3N4 ↔ 3Si (g) + 1.8N + 1.1N2 45
Powder
Pellet
III
I
159, 176 2.82, 2.79
488
502
503
503
[16]
This work
–
c-BN ↔ B (g) + 0.5N2
0
Pressed
pellet
216
2.56
539
539
[13]
↓
Pellet
1800
–
527
399
539
427
This work
[14]
c-AlN ↔ Al (g) + 0.5N2
c-GaN ↔ Ga (g) + 0.5N2
0
0
MOCVD
film
MBE film
I
I
216
216
3.09
3.09
1300 414
900 261
308
284
[17]
MOCVD: metal organic chemical vapour deposition; MBE: molecular beam epitaxy.
a
Content of atomic nitrogen species in the reaction MaNb+2c ↔ aM (g) + bN + cN2.
b
Polymorphous transition from the cubic (␣) to hexagonal (␤) structure for Mg3N2 at 823 K has been observed in [21] and supported in this work.
c
Calculated in this work on the basis of experimental data reported in original publications.
5. Conclusions
appropriate technologies (including nano-technologies) for
production of solid materials by the chemical vapour depo-
sition.
The application of the third-law method to investigation of
kinetics of the congruent dissociative vaporization of metal
nitrides has made it possible to interpret the composition of
primary nitrogen products (bN and cN2) with a precision,
which is inaccessible for the second-law method. The rela-
tive standard deviation in determination of ꢀrHT◦/ν values
is lower than 1% and in determination of b/(b + 2c) ratios
is better than 2–4%. As a result, some important features
in the decomposition mechanism of different nitrides were
revealed: the identity in composition of products for hexago-
nal Be3N2 and Mg3N2 (b/(b + 2c) = 0.75) and AlN and GaN
(b/(b + 2c) = 0.42) and the release of only molecular nitrogen
in cases of cubic BN, AlN and GaN (b/(b + 2c) = 0). The last
feature was observed earlier [2] for cubic metal oxides and
deserves further study in relation to the obvious effect of crys-
tal symmetry on the decomposition mechanism. At the same
time, the distance between the closest atoms (N–N) in a crys-
talline lattice has a secondary or no effect on the composition
of primary products. These features might be important not
only for fundamental studies of the effect of crystal structure
on thermal stability of solids but also for the development of
Acknowledgement
The authors thank Professor F.F. Grekov (Department of
Electronics Materials Technology, St. Petersburg State Poly-
technic University) for providing c-BN and h-AlN powders
for our experiments.
References
[1] B.V. L’vov, A.V. Novichikhin, Quantitative interpretation of the evap-
oration coefficients for the decomposition or sublimation of some
substances in vacuo, Thermochim. Acta 290 (1997) 239–251.
[2] B.V. L’vov, V.L. Ugolkov, F.F. Grekov, Kinetics and mechanism of
free-surface vaporization of zinc, cadmium and mercury oxides ana-
lyzed thermogravimetrically by the third-law method, Thermochim.
Acta 411 (2004) 187–193.
[3] B.V. L’vov, Kinetics and mechanism of thermal decomposition of
GaN, Thermochim. Acta 360 (2000) 85–91.

8
B.V. L’vov, V.L. Ugolkov / Thermochimica Acta 438 (2005) 1–8
[4] B.V. L’vov, The interrelation between the temperature of solid and in argon and nitrogen gases, J. Phys. Chem. 72 (1968) 2241–
decompositions and the E parameter of the Arrhenius equation, Ther-
mochim. Acta 389 (2002) 199–211.
[5] B.V. L’vov, Application of the third-law methodology to investiga-
tion of decomposition kinetics, Thermochim. Acta 424 (2004) 183–
199.
[6] B.V. L’vov, V.L. Ugolkov, Kinetics of free-surface decomposition
of dolomite single crystals and powders analyzed thermogravimetri-
cally by the third-law method, Thermochim. Acta 401 (2003) 139–
147.
[7] J.H. Edgar (Ed.), Properties of Group III Nitrides, INSPEC, London,
1994.
[8] L.V. Gurvich, I.V. Veits, V.A. Medvedev, et al., Thermodynamic
Properties of Individual Substances, Nauka, Moscow, 1978–1982 (in
Russian).
[9] V.A. Kireev, Methods of Practical Calculations in Thermodynamics
of Chemical Reactions, Khimiya, Moscow, 1975 (in Russian).
[10] J. Leitner, A. Strejc, D. Sedmidubsky, K. Ru˚zˇicˇka, High temperature
enthalpy and heat capacity of GaN, Thermochim. Acta 401 (2003)
169–173.
[11] C.L. Hoenig, A.W. Searcy, Vapour pressure, enthalpy, evapora-
tion coefficient, and enthalpy of activation of the beryllium nitride
(Be3N2) decomposition reaction, J. Am. Ceram. Soc. 50 (1967)
460–466.
2243.
[13] L.H. Dreger, V.V. Dadape, J.L. Margrave, Sublimation and decompo-
sition studies of boron nitride and aluminium nitride, J. Phys. Chem.
66 (1962) 1556–1559.
[14] O. Ambacher, M.S. Brandt, R. Dimitrov, T. Metzger, M. Stutzmann,
R.A. Fisher, A. Miehr, A. Bergmaier, G. Dollinger, Thermal stability
and desorption of group III nitrides prepared by metal organic chem-
ical vapour deposition, J. Vac. Sci. Technol. B 14 (1996) 3532–3542.
[15] Z.A. Munir, A.W. Searcy, Activation energy for the sublimation of
gallium nitride, J. Chem. Phys. 42 (1965) 4223–4228.
[16] E.A. Ryklis, A.S. Bolgar, V.V. Fesenko, Investigation of evapora-
tion and thermodynamic properties of silicon nitride, Poroshkovaya
Metallurgia 73 (1969) 92–96 (in Russian).
[17] O. Brandt, Hui Yang, K.H. Ploog, Surface kinetics of zinc-blende
(0 0 1) GaN, Phys. Rev. B 54 (1996) 4432–4435.
[18] B.V. L’vov, V.L. Ugolkov, The self-cooling effect in the process
of dehydration of Li2SO4·H2O, CaSO4·2H2O and CuSO4·5H2O in
vacuum, J. Therm. Anal. Calorim. 74 (2003) 697–708.
[19] W. Kraus, G. Nolze, Powder cell—a program for the representation
and manipulation of crystal structures and calculation of the resulting
X-ray powder, J. Appl. Cryst. 29 (1996) 301–303.
[20] International Crystal Structure Data, Gmelin Institute, Karlsruhe,
1996.
[12] B.A.H. Blank, A.W. Searcy, The rate of sublimation of magne-
sium nitride from effusion cells and from free surfaces in vacuo
[21] D.W. Mitchell, Heat content and heat of formation of magnesium
nitride, Ind. Eng. Chem. 41 (1949) 2027–2031.