- Email: [email protected]
Thermodynamic reassessment of the AlN-Al2O3 system
Cafphod.Vol. 22, No. 2, pp. 1B-201, 1999 cb 1999 Elsevier Science Ltd, All rights reserved. 0364~5916/98/ $-see front matter PII: SO364-5916(98)00023-6
> Pergamon
THERMODYNAMIC REASSESSMENT AlN-A1203 SYSTEM
P.Tabary’p”,
OF THE
C. Servant’
* Laboratoire de MCtallurgie Structurale, URA CNRS 1107, UniversitC de Paris-Sud, 0rsa.y Cedex, France. *+ SociCte Pechiney-ElectromCtallurgie, Usine de Chedde, 74000 Le Fayet, France.
ABSTRACT.
91405
The AlN-AlrOs system has been reassessed due to new experimental data published in particular near the AlrOs rich part and relative to the # and 6 phases. The Gibbs energy of formation of the solution and compound phases in the AlN-AlrOs binary section were derived from an optimisation procedure using all the available experimental thermodynamic and phase diagram data. The thermodynamic description of the ordered compounds was made using the sub-lattice model, while a Redlich-Kister polynomial was used for the solution phases.
1 - Introduction
Aluminium oxynitrides, produced by the Pechiney Electrometallurgie Society, with an amount of AlN (% mole) ranging from 43.3 f2.2 to 3.5 f0.2 were studied especially at high temperature
[ 11. These
alloys
Several phase
previous
phases
have
were taken
of the composition
phase 7-AION present
?&inal
into
of 1201, two structure)
(with
a c$’ spine1
spine1 work,
having
and
system,
and
quaternary
devoted
a-AlrOs
or quaternary
AI-0-N-Si
to the
phases
structure
Al-0-N-Si
systems
AlN-AlrOs
a corundum
Al, AlsOsNr
the composition
spine1
AlsOsNd
6 phases
(with
in addition
a composition
the 4’ and
Al-O-N
and
of the other
and
Al-O-N
binary
AlN, the spine1 (AIN(s rrs~-AlrOs(s,ss2))
account
range
to the ternary
by [2-141.
assessments
Liquid,
AI-O-N
materials.
devoted
ternary first
compound
[ 181 of the ternary
polytype
data published
of the In the
were considered:
assessment
as abrasive
been
assessments by (15,201.
as a stoichiomctric ture),
used
experimental
diagrams
Several made
are mainly
were (with
was
In the assessment
was AlrsOr,N~.
of temperature
taken
into
account:
A1703Ns
AIN
polytype
structure).
not
taken The
were considered
into
account),
6 phase
it was
was not taken
due to new available
(with The
a 21R
AIN
A122033N2
account.
experimental
width In the
regrouped into
version received on 26 !%ptember 1997, Revised version on 5 May 1998
179
struc-
The
was optimized.
a 12H
range.
four (16, 171
a 27R AlN polytype
of the spine1
as a function
been
1151, A!rOaNL
structure). (with
have section,
with
thr
In the data
(11.
180
I’. TABARY AND C. SERVANT
The 4’ phase was found by [4], then successively studied by [21] and denoted Y phase, [22] and denoted & phase, [23] and denoted e phase, and finally by [lo, 241 and denoted # phase. Two forms were identified The 6 phase was found by Long [25], th en studied by [2,5,21_23,26-301. by Lefebvre [28, 291, denoted: 61 and 62. In the present work, we have not distinguished these two forms in the calculated assessment. 2 - Thermodynamic
modelling
2-l - Brief outline a) Pure solid elements: The pure elements in their stable structure at 25°C (298.15K) were chosen as the reference state for the system. The thermodynamic functions for the stable and metastable states are taken from the Scientific Group Thermodata Europe (SGTE) [31]. b) Substitutional solutions: For the liquid phase (denoted by ‘p) the Redlich-Kister the excess Gibbs energy ‘=Gp :
polynomial
[32] was used to describe
where x; and xj are the mole fractions of components i and j in the phase ‘p. The interaction terms Lzj can be composition and temperature dependent as follows:
pj
= c,
“LKj
( x’
-xi’
)’
(2)
where v is the power in the Redlich-Kister expansion. c) Compounds: The polytypes 27R, 21R, 12H and the 6 phase were modelled as stoichiometric compounds. The compounds which exhibit a range of non-stoichiometry (r-AlON spinel, d’-AlON) were modelled using the sub-lattice model . They can be described schematically as follows: (A;;B:;,
.. .. .. )JA;;B;;
.. .. . . ), .. . . .
where the species A’, B’..., and A”,B”... can be atoms, ions or vacancies. p and q are the number of sites, yi and Y”B the respective site fractions of the elements A and B in their respective subthe thermodynamic quantities are referred to one lattices designated by ’ and “. If p+q+...=l, mole of sites. For each sub-lattice s, the site fraction of the species is equal to
yf = n:/(n;,
+ Cj 72;) = nf/n’
with: CL& = 1 and ‘& n’ = n
(3) (4)
where nl is the number of species j in sub-lattice s, R’ is the number of sites in sub-lattice s, and n the total number of sites. n’ is related to n by n’=p.n/(p+q+...). The molar Gibbs energy, as formulated by Hillert and Staffansson [33] and generalised by Sundman and Agren [34], is defined as follows:
AIN-AI,O,-THERMODYNAMIC
cf;‘,
which defines a hyper-surface
G A,B,, represent
The terms Ai,Bi
(5)
+G” m +G’” m
G m =G’fm The term
which may ie’stable
The term
the Gibbs energy
Li,j:i and Li;i,j represent
for a given occupancy
polynomial
as follows: Y;
[(QO+ &!I’) +
yj
is equal to:
of formation
to the molar configurational
sub-lattice
Li,j:i =
of reference,
of the stoichiometric
compounds
or me&table.
Gz is related
The terms
181
REASSESSMENT
The number of sub-lattices
entropy
the interaction
of the other,
and is equal to:
parameters
between
and are also described
the atoms,
ions on one
by a Redlich-Kister
(a~t hT)(Yi - Yj) + ... + (an + bn’)(Y*- Yj)" I
and the species occupying
them is generally
[32]
(9J
obtained
from structural
information. 2-2 .
l
on phase
- Details
Gas phase.
Eighteen
modynamic
properties
modelling
gaseous
species were used which are listed in Appendix
are found in the JANAF
Liquid phase.
Different
two-sublattice
model for ionic liquid:
was used where Q-3 -P is the average (with
the charge
the quaternary
descriptions
and P varies with composition
valency -3)
on the second
allows
system
SiOz and SiN.13.
the liquid of the AlzOs-CaO-SiOz et al. [36].
atoms because
may be justified
with an Al atom each 0 is shared
to be extended
system
of two species:
by the hypothesis in the middle should between
AlN,
Al203
Al203
ther
of [18], a
electroneutrality,
of hypothetical
all the way to liquid
species
this model with the species
ie
vacancies Al.
For
and in addition
could not he used to
and the species AlOl 5 was then considered
For the reason of compatibility,
[20], the liquid consisted
of A1203
The presence
[19] used the same
SiO, -‘,
al.
However,
1. Their
[35].
in order to maintain
sub-lat.tice.
the description
Al-0-N-Si,
Tables
have been used by [18, 201. In the description
describe
by HaUstedt
Thermodynamic
in the description
of Dumitrescu
et
AlN and AlOl s. The choice
of AIO1,s instead
made
of triangles
by [37] that
a network
form in the liquid.
two Al. So for the same reasons
The basic
of 0
unit is AIOl 6
of compatibility,
the two
species AlN and AICI1.s were used in the present work. It was found that it was necessary to introduce an excess term of degree 0. In the work of 1201 no excess term was considered for the optimization
of the liquid phase of the AIN-AI,03
system.
P. TABARY AND C. SERVANT
182
s Polytypes. The polytypes denoted 3(m+2)P with a m(m+l) AlN molar fraction were described using three sub-lattices: (Al)(,+r) (N), (0)s. The crystalline structures of the polytypes is either rhombohedral or hexagonal, [7]. Along the c-dimension, the structure consists of “n” layers where “n” is the numeral of the Ramsdell symbol, [7]. The nR polytypes consist of three rhombohedrally related blocks each of n/3 layers, while the hexagonal nH consist of two blocks related by a c-glide plane and each containing n/2 layers. The number of layers per symmetry-related blocks in the polytypes 12H, 21R and 27R found in the AIN-ALrOs system is respectively 6, 7 and 9. Th us, m=(n-2) is respectively equal to 2 (12H), 5 (21R) and 7 (27R). The Gibbs energy OGs(,+r) of the 3(n+2) polytype was modelled as:
with the thermodynamic
parameters a and b to optimize.
s r,AlON spine1 phase. The spine1 phase was described as that of the pseudo-binary AlrOsMgO system (381 baaed upon r-AlrOs using three sub-lattices: the tetrahedral, the octahedral and the anionic sub-lattices as follows: (A1+3)r (Al+‘,Va’)r (N-3,0-2),, where Va” represent real vacancies with no charge. Controversies exist on the occupation by vacancies of the tetrahedral or octahedral sites. In fact, Hallsted [38] proposed a distribution of vacancies on the octahedral interstitial sites for the r-AlON spine1 for reasons of compatibility with the magnetite of the Fe-O system (391. Nuclear Magnetic Resonance (NMR) measurements made by Dupree et al [40] are in agreement with this hypothesis, but some doubt exists on their conclusions because these authors have assumed a completely normal distribution of cations. On the contrary, from electron diffraction measurements of the scattered intensities of r-AlON spinel, r-Al203 and &AlrOs, Jayaram et al 1411 concluded that vacancies prefentially form on the tetrahedral sites. Previously, by high resolution, solid state aluminium NMR, John et al [42] have found that an amount of 75 f 4 % of octahedral sites are occupied by cations, which correspouds to a total occupation of the octahedral sites in r-A&03. The general formula of the +y-AION spine1 used corresponds to a linear electrically neutral combination of four hypothetical charged compounds: (Alt3)r (Alt3)r (Nm3),, (Alt3)r (Alt3)r (O-*),, (Al+3)1 (Va’)r (Ne3)d and (Al+3)r (Va’)r (O-‘)J. The domain of stability of the T-AlON spine1 is therefore a line running from : (5/6*[(A1+3)r
(Alt3)r (O-‘),I
+ 1/6*[(A1+3)r (Va’)r (O-‘),I)
to (3/4*[(Al+3)1
(A1+3)r (O-*),1 + l/4*
[(A1+3), (A1+3)2 (N-3),]).
The compound (A1+3)r (Al+‘)2 (O-‘) 4 is taken as the reference for the Gibbs enthapies of formation as follows:
oG[(Al+3)1 (AlC3)r (O-2),]
= 3*OG(Al) + 4*‘G( l/20*)
= HSER.
AIN-A&O,-THERMODYNAMIC
REASSESSMENT
183
It can be easily shown that:
a) oG-,-~,~3 = 3/4*(5/6*“G[(Al*3)i 2*RT+(1/6*Ln1/6+5/6*Ln5/6)), oG[(Al+3)1
(Va’)s
(O-‘)a]
b) oG~~+"Ga-~,20s 1/4*(a
+ b*T),
oWA1+3)~
(Al+3)z
(O-‘)a]
i-
1/6*OG[(AP)i
(Va”)r
(C-2)4]
+
and:
+ 5*H SEn[(Al+s)r
= 2/4*OG[(Alf3)r
(A1+3)z
(A1+3)r
(O-“),]
(0-‘)4]
+
= 6*‘G,_alao,
1/4*OG[
+ 44.954*T.
(A1+3)1
(Al+3)2
(N-3)4
_
and:
(A1+3)2
(N-%1
+
3*HSER[(A1+3)1
(A1+3)2
(O-2)r]
= 4e”GaIN
+ 4*“G=_A~30s
+
a + b*T.
c) oG~~~+“Ga-~~,oJ = 1/4*(a’ + b’*T), and:
FJy3)1
(Va’)s
In the present
l
(N-%]+9*H
work,
optimize
the domain
#-AiON
phase.
It is first necessary ture refinement Compared
to summarize
due to these antiphase electron
The +‘-AiON
parameters
the #-AlON
deviation
of 7
Vacancies
domains.
=
[-l/4,
The structural
a composition
become
spine1 lattice,
with a mutual
struc-
0, l/4]
model
distorsion to a spine1
one versus the other.
proposed,
on the diffraction was confirmed
Inside a patterns
by high res-
range from about
of the modulation
anions do not occupy
substitution
10 to 20 mole % of AlN.
vector are function content
and vacancy
their ideal position_
in the y-AlON
spinel.
The
of the composition They
fraction. present
a
The anionic sub-lattice
of 0 and N atoms.
on the octahedral
sites in the antiphase
interface
planes,
when they
ordered.
This order corresponds
to a splitting
spine1 into two distinctive amount
the crystalline
experiments.
and the direction
are situated
to
as in the work of [29].
of the ions correspond
Intense satellites appeared
to ideality very close to that observed
is disordered,
-
+ a’ +
lattice presents a monoclinic
of the phase which is related to the increase in the nitrogen As in the 7-AlON
(N-3)4]
a, a’, b and b’ were sufficient
by [l] concerning
The mean positions
translated
phase presents
lattice parameters
(Va”)s
4*“G~~~+12*oG,_4~,o,
(Ow2)4]=
the results obtained
spine1 lattice,
microscopy
1/4*“G[(A1+3)1
phase.
variant, the lattice remains monoclinic. olution
+
No excess term was necessary
in composition.
two variants
(OP2)q]
(A1+3)2
the four thermodynamic of the spinel.
to the r-AlON
having
(Al+3)z
‘zR[(Al+“)i
of the #-AlON
due to a modulation lattice
9/4*“G[(Al*3)r
sub-lattices
of vacancies on the octahedral
cies on the antiphase
interfaces
of the sub-lattice as follows: sub-lattice.
number
(A1+3)r_2,
2, (AF3,Vao), and (Va”)z2,
2x is proportional
[l], and so is a function
of the -y-AlON where 2x is the
to the density of vacan-
of the composition
of the @-AlON
on a sub-lattice,
several solutions
phase. In order to use a variable amount of atoms or vacancies have been investigated which are summarized below:
P. TABARY
104
AND C. SERVANT
1. The optimization of the stoichiometric the compound with the formula:
#‘-AlON phase with 15 mole % of AlN, that is
The Gibbs energy of the two compounds involved is as follows: G(AI:Al:Va:N)
= G(Al:Al:Va:O)
= 0.233*‘G~l~
+ 1.259*OG,_Ar,o, + a + b*T,
where a and b are thermodynamic parameters to optimize. Unfortunately, this optimization has not given any information on the junction of the 4’ and -/-AlON spine1 phase domains and, as a consequence, on the precipitation mechanism from the liquid state. 2. In order to take into account the composition range of the #‘-AlON phase, substitutions can be introduced in the sub-lattices number 2 and 3, as follows:
so eight charged compounds are defined. In order to simplify the optimization, it is possible to identify the compounds containing oxygen with the corresponding compounds containing nitrogen (we defined the variable X which indifferently represents the 0 and N atoms), so only four compounds were considered: oG(Al:Al:Al:X),
‘G(Al:Al:Va:X),
‘G(Al:Va:Va:X)
and ‘G(Al:Va:Al:X).
This last term was assumed to be very unstable. Consequently three compounds and only six thermodynamic parameters a and b have been optimized. The nitrogen enriched part of the composition range of the b’-AlON phase is modelled with the terms OG(Al:Al:Va:X) and ‘G(Al:Al:Al:X), while the nitrogen depleted part is modelled with the terms ‘G(AI:Al:Va:X) and ‘G(Al:Va:Va:X). With this way of modelling, first the optimization works with difficulty due to the possibility of having vacancies in two sublattices and secondly terms of entropy of mixing are introduced which have a priori no physical meaning when taking into account the structural results obtained by [l]. 3. To optimize the +‘-AlON phase by using the three sub-lattice model as follows: ( Al+3)1 ( AP3,VaU)r (Nm3,0m2)d and by introducing a term of entropy equal to that of the r-AlON spine1 diminished of the term of mixing:
We calculated this correction to be equal to AS = 44*T for the term ‘G(AI:Va:O) and AS = 151*T for the term ‘G(Al:Va:N). The optimization of the terms of enthalpy H(Al:Va:O) and H(Al:Va:N) did not allow a correct description of the d’-AlON phase which became too much stable at low temperature. 4. Finally, the 4’-AlON phase was modelled with three sub-lattices and the two terms OG(Al:AI:N) and ‘G(Al:Va:N) (4 thermodynamic parameters a,b, a’ and b’) have been optimized. The term ‘G(Al:Va:O)-y w hi c h corresponds to a hypothetical d’-Al203 phase (instead of T-AlsO3) was kept. As mentioned above, the term of entropy of mixing of the sub-lattice (:AI,Va:) has no special physical meaning when considering the structural results [ 11. s 6-AlON phase The composition range of the 6-AlON phase, comprised between about 5 to 10 mole % AlN [l], is narrower than that of the @-AlON phase. between about 5 to 10 mole
AIN-AI,O,-THERMODYNAMIC
REASSESSMENT
185
$ZoAlN (I]. No data on the evolution of the phase boundaries of 6-AION as a function of temperature being available, this phase has been optimized as a stoichiometric phase having a chosen composition of 7 mole % of AlN and the sub-lattices:
The stability of this 6-AlON phase was optimized versus temperature with two terms of Gibbs energy “G(Al:Al:Va:O) and ‘G(Al:Al:Va:N) that is four parameters a, a’,b and b’. In fact, two parameters (a and b) are sufficient if it is assumed that: OG(Al:Al:Va:O)
- HSER =OG(Al:Al:Va:N)
- H ‘SER = O.l*‘Gai~
+ 1.3*‘Gcl-AlaoJ + a + b*T.
3 - Optimization 3-l
- Optimisation
procedure
The evaluation of the thermodynamic properties of the solution and compound phases were derived from an optimisation procedure using the available experimental phase diagram and thermodynamic data, and using the module PARROT developed by Jansson [43] and contained in the Thermo-Calc databank system [44]. The optimization is carried out by minimizing an error sum by varying selected model parameters. This sum of errors is calculated from the experimental data. Each experiment is characterized by a weight according to its estimated accuracy. l
Components used: As all the equilibria studied experimentally concerned the pseudo-binary section AlN-Ai20s, we first used the components x(Al~Os), x(AlN) and x(N) with x(N)=O, then the components of the ternary system: x(Al), x(0) and x(N).
3-2 - Available l
data
The thermodynamic
parameters of AlNliquid vary very slightly according to [45]: o
liquid
G ALN
o
Gzy
= 70679 - 23*T J/mole of AlN
oG~~-“G>~:r;”
= 70541 - 23*T J/mole of AlN
-
or (191:
The second expression was considered in the work of (201 as well as in the present work. In fact, these two different expressions lead to a very small variation in the temperature of melting of AlN (6°C). . The specific heat at constant pressure of the r-AlON temperature by [46, 11, 471.
spine1 has been determined at low
. The enthalpy of melting of some phases was measured [l] using the thermal differential analysis. For each measurement, a standard measurement of the enthalpy of melting of corundum was made. It was calibrated to a value of 111136 f 3976 J/mole [35j. For the yAlON spinel, 4’ and 6 phases, the enthalpy of melting was found respectively equal to 38290, 60675 and 63597 J/mole. For the 4’ phase, the measured enthalpy does not correspond to
186
P. TABARY AND C. SERVANT
Table
1:
Comparison
of the experimental
and optimized’
binary
equilibria
(“C,
mole
% AlN,
J/mole)
Phase
Supplementary condition
Experiment
equilibria
AlN - 7
1750
c(7)=31.99 31.45’
f 3.3
]I31
AIN - 7
1850
;~j,“““”
f 3.2
1131
-y - a-Al~Os
1750
c(r)=22.01 23.97’
+ 3.?
[I31
-y - a-AlzOs
1850
f 3.9
[131
7 - Liq.
x(y)=c(Liq.)
c(7)=19.00 19.03’ 2082 l 30 2085’
4’ - Liq.
x(#)=c(Liq.)
2060 f 2065’
6 - Liq.
1
Experiment
2
Experiment
3
Ref.
Ii,=36853 36936’
f 2454
x($=32.90 33.67’
10
Ii,=48967 46563’
YIZ2670
x(&)=21.2 21.48’
x(+c(Liq.)
2050 f 50 2042’
II,=63499 63206’
zt 5098
111
7-d
2000
x(+21.36 20.90’
x(+18.25 18.07’
+ 2.1
]ll
4’ - 6
2000
x(+10.75 11.14’
a congruent
melting
to the nitrogen
f
2.2
0.5*(Tb+T,)
[l]
[II
[ll [ll
of which
part of the composition
within less than 5”C, it was considered to:
10
* 2.2
of this phase the composition
depleted
f
range.
to be congruent
where Tb and T, respectively
(11 mole % AlN)
However,
and occurring
correspond
corresponds
as the melting
occurs
at a temperature
to the beginning
equal
and end of the
melting.
3-3 - Results The optimized optimized
thermodynamic
equilibria
For a ternary
system,
each three-phase Sex(N)=0
are compared according
equilibrium,
parameters
to the law of variance,
two conditions
(which gives the composition
For a two-phase the reaction
equilibrium,
1. 7-AlON
- a-Al203
determined (prolongation
condition
The experimental
and
taken into account: section
For
3*x(Al)-2*x(O)-
AlN-AlrOs),
and p=lO’
must be added such as the temperature
Pa. of
of the phase ‘p in % mole of AlN: x(p).
of melting of the phases is given in J/mole. equilibrium.
both by the entectoid of the domain
The composition reaction
of the 7-AION
depleted
of -/-AION
(T=1637”C)
in equilibrium
and the equilibrium
spinel) and a-AlrOa
these two points are fixed, it is difficult to modify on the nitrogen
1.
below.
there are five degrees of freedom.
are therefore
on the pseudobinary
a supplementary
or the composition
In Table 1, the enthalpy
are listed in Appendix
in Tables 1 and 2 and discussed
part even by introducing
(T=2154”C).
the phase boundaries interaction
with a-AlsOz
is
between 7-AlrOa In fact, when
of the -y-AION spine1
parameters
on the sub-lattices
AIN-A&O,-THERMODYNAMIC of the 7-AlON
spinel.
This temperature
of stability
of AlrOs(l;s)
of 7-AlsOs
(-23.42
at 298.15
K, evaluated
at 700°C
from 7-AlzOs
By modifying of 2J/mole.K expression of ‘G7-AlzOs
= -26.78
f
0.41 kJ/mole
2727°C
at 1197°C.
can give a non negligible
(1110.41976)
temperature
in the thermodynamic
range, we calculated
compared
of the transition a-AlzOs
-+7-AlzOs
that
to the value used by was calculated equal to
This variation has been considered as negligible and we used for
the expression given in the work of [20]. reaction:
12H - Liquid - 7-AlON.
the congruent melting of the 7-AlON parameters of the 7-AION
The temperatures
spine1 are very near.
of the eutectic
The optimized
spine1 or 12H phases have a poor influence
difference, The consequence of this low difference in temperature the compositions observations:
of the liquid and the 7-AlON
low amount
sample containing 43.3 f
of the polytype 2.2 mole % AlN.
was found equal to 39.8 mole % AlN. excess term oL~~~~,,AIN) 3. 7-AlON
of dissolution
+7-AlzOs.
was equal to +0.15J/mole.K
[26]. The resulting temperature
Z!. Eutectic
of transition a-AlrOs
in the 1227°C
213O”C, instead of 2154°C.
situated in the domain
AS(7-AlzOs)
the prefactor of temperature
the variation of S(7-AlsOs)
‘G7-AlrOs
to a-AlsOs
on these values and in particular
uncertainty on the temperature
(T=2154”C),
by [48] using both the enthalpy
1491) and the standard entropy (52.3 f 2 J/(mole.K) R ecently, Chen et al. [51] proposed analysis [50]).
by statistics
the heat of transformation The uncertainties
of transition
has been evaluated
kJ/mole,
187
REASSESSMENT
spine1 stability:
to 7-AlrOs
spinel;
OIL
this low temperature
is a low difference between
this fact is in agreement
I2H melting
at the eutectic
The optimized
composition
The optimization
with our
temperature
in the
of the eutectic liquid
was easilyperformed
= a + b*T for the liquid phase as mentioned According
reaction and
thermodynamic
by using an
above.
to [3], the stability of the 7-AlON
spine1 phase compared
is due to a decrease in the amount of the vacancies on the cationic sub-lattice
This hypothesis is not in satisfactory
agreement with the instability
.
of the spine1 having 56
mole % AlN and which does not contain vacancies. Mac Cauley [9] proposed that the addition of nitrogen anion to a-AlzOs
would induce a local
charge which is relaxed when an aluminium cation moves from an octahedral to a tetrahedral site. Nitrogen would therefore stabilize cations on the tetrahedral In the present work, the two optimized temperature
terms (a+b*T)
sites at low temperatures.
and (a’+b’*T)
are positive in the
range studied.
In Figure 1 are shown the terms of mixing energy in the anionic and cationic sub-lattices 2660°C x=35
as a function of the composition
in AlN.
If the mixing x*AlN+(l-x)*7-AlzOs
mole % AlN is taken as a reference for the 7-AlON
mixing is calculated
equal to about
- 11.2 kJ/mole.
between the respective energies of mixing of 7-AlON of the 7-AlON
spine1 at low temperature
spinel, the additional
This
energy of
value represents the difference
spine1 and 7-AlrOs.
would be due to the entropy
both by the presence of nitrogen in the anionic sub-lattice
at
with
So the stabilization of mixing
created
and of vacancies on the cationic
sub-lattice. 4. Peritectic
reaction:
7-AlON
example when T=2063oC, liquidus of 7-AlON
spinel++‘+Liquid:
In the temperature
the difference in composition
is about
4.4 mole % AlN,
between the less enriched nitrogen composition most enriched nitrogen composition
range studied
between the optimized
and for
solidus and
which is slightly higher than the difference of 7-AlON
(23.5 f
of 4’ (20 mole % AlN).
0.25 mole % AlN)
and the
This fact is in agreement with a
peritectic reaction. !i. Comparative
stability
energies of the 7-AlON
of 7-AlON
and 4’:
In Figure 2 are shown the curves of the Gibbs
and 6’ phases at 2000°C.
Despite
of the lack of knowledge of the
P. TABARY AND C. SERVANT
188 exact composition in nitrogen
in AIN of the 4’ phase
(20 mole
% AlN)
the liquid,
that
phase
agreement
with the hypothesis
are more stable 6. Solid-gas mole
is more
equilibria:
temperature observed
stable
of Lejus
equal
agreement
suppose
7-AlON
was used.
was found
at 1925”C, its composition to indicate
[3] which
than
No equilibrium
is in better
seems
that,
at high temperature
at low temperature
% AlN)+Liquid
forming
at 2060°C
with
than
-/-AlON.
that
the ordered composition.
against
the rapidity
given
of vaporisation
of
fact is not in
phases
of the reaction:
2364°C
enough
of stability
This
for a given
The temperature
to 2307°C
enriched
in the region
(in fact 6)
27R+gas(85
by (181. This
of the material
lower
that
we
at 2350°C.
4 - Discussion From the comparison good agreement
s the temperature much
shown
the temperatures
of the invariant
in Tables
of reaction
reaction:
1 and 2, it will be noted that there is a fairly obtained
by the different
AlN - 7 - a-AlsOs
optimized
authors,
except
for:
by [18] which is too
low.
s the temperatures in the present The
of the results
between
phase
without
of the reactions:
27R-21R-Liq.
diagram
including
that
lower temperature compositions
AlN-AlsOs the limit
calculated
is reported
of 1637°C)
by [13, 141 are slightly
diagram
by Dumitrescu
optimized
by (201 and
does
not
spine1 domain
studied
than in the present enriched
it will be noted
melt
to the present
3. Magnification
optimization
is shown
in Figure
by (3) is situated
work and that
4. at
the phase
in AlN.
et al 1201 is reported
the present work. On the AlN rich side of the diagram, 27R polytype
according
in Figure
of the 7-AION
(ISOO’C, instead
determined
The calculated
at 1 bar,
the gas phase,
It will be noted
1. the
and AlN-27R-Liq.
work.
in Figure
4 for comparison
with
that:
congruently.
Its stability
domain
according
to our experimental
with
-/-AlON
is
[l] instead
of
narrower; 2. the 21R polytype
melts
at 2303°C
results
2709°C; 3. the eutectic atures near.
composition
of the eutectic The optimized
agreement On the AlsOs phases
with
- 7-AlON)
and the congruent
thermodynamic
have a poor influence 4. the composition
(12H - Liquid
reaction
parameters
on this low temperature
is depleted melting
is nitrogen.
of the T-AlON
of the y-AlON
The temperspine1 are very
spine1 and 12H phases
difference.
of the _I-AION spine1 at low temperature
is enriched
in nitrogen
rich side of the phase
diagram,
our diagram
has taken
into account
the two
@ and 6.
The calculated
in
the literature.
diagram
reported
in Figure
5a and b takes into account
the gas phase.
AIN-AI,O,-THERMODYNAMIC REASSESSMENT
Table 2: Comparison
of the temperatures
(“C) of the equilibria and composition
189
of phases involved
F’hase equilibria
Present work
Present work
Ref. [20]
(cd.)
(ew)
2111 2080 x( Liq. ) = 39.80 2048 1908 1891
2115 2079 38.50 2045 1910 1890
1539
1640 + 20
1612
2303 x( Liq. ) = 43.75 2428 1925 x( 4’ ) = 14.02 1985 2041 2036 2064
2300 44.92 2427 1925 13.97 1960
2709
Ref. [18]
Ref. [17]
1Ref. 1151
ZlR-lZH-Liq. IIH-Liq.-y 2 lR-12H-y X’R-21Ry AlN-27R-y AlNy-a-Al20s ;!7R-Liq.7 ;!7R-21R-Liq. MN-27R-Liq. -,-c#J’-Q-Al~o~ tb’-6-a-A1203 cb’-Liq.-6 ii-Liq.-a-All03 y+‘-Liq. wA12Os-Liq.--y .AlN-yLiq. (Congruent melting of 7 Congruent melting of 27R AlN-27R-gas(l35 % mole AlN) 27R-gas(85 % mole AlN)-Liq.
f 10 f 30 f 5.9 xt 10 f 20 * 30
& f f f f
50 22 200 50 2.1
2198 2064 2032 2000 1877
2664
1879 1354 2061
2594
2042 2085 2307.3 2306.8
2768 2365.9 2364.7
1603
1987 2000 2163 2725 2350
1917 1927 1934
190
P. TABARY AND C. SERVANT
5 - Conclusion
We optimized a consistent set of thermodynamic parameters to assess by calculation the AlN-AlrOs pseudo-binary system in which the fl-AlON and &AlON phases were taken into account. Our results were compared with those from previous optimizations.
References PI
P. Tabary, Ph. D. Thesis, UniversitC de Paris-Sud, Centre d’orsay, France, (1997).
PI
Adams, T.R. AuCoin, G.A. Wolf, J. Electr. Sot., 109, 1050-1054 (1962).
131
A.M. Lejus, Rev. ht. Haute3
[41
R. Collongues, F. Cohn, J. Thery, D. Michel, M. Perez y Jorba, Bull. Sot. Fr. Ceram. 77, 51 (1967).
i51
R. Collongues, .C. Gilles, A.M. Lejus, M. Perez y Jorba, D. Michel, Mat. Bul.,
Temp.
tl, 53-95 (1964).
et R&act.,
Res.
2, 837-848 (1967).
161
L.J. Gauckler, H.L. Lukas, G. Petzow, J. Am. Ceram. Sot., 58, 7-8, 377 (1975).
[71
K.H. Jack, J. Mat. Sci., 11, 1135-1158(1976).
181
T. Saks& Yogyo Kyokai Shi, 86, 125-130 (1978).
[91
J.W. MacCauley, N.D. Corbin, J. Am.
PO1
J.W. MacCauley, N.D. Corbin, Progress Publishers, ill-118 (1983).
WI
G.D. Quinn, N.D. Corbin, J.W. MacCauley, Am. (1984).
P21
D.Goeuriot-Launay, P. Goeuriot, F. Thevenot, J. Mat. Sci., 27, 358-364,
(1992).
1131
H.X. Wiiems, M.M.R.M. Hendrix, G. De With, R. Metselaar, J. Eur. Sot., 10, 327-338 (1992).
Ceram.
1141
H.X. Wiiems, M.M.R.M. Hendrix, G. De With, R. Metselaar, J. Eur. Sot., 10, 339-346(1992).
Ceram.
1151
L. Kaufman, Calphad,
[I61
Ceram.
Sot.,
in Nitrogen
62, 9-10, 476-479 (1979).
Ceramics, Martinus Nijhoff
Ceram.
Sot.
Bull.,
63,
5, 723
3, 4, 275-291 (1979).
P. Diirner, L.J. Gauckler, H. Krieg, H.L. Lukas, G. Petzow, J. Weiss, Calphad, (1979).
4, 241-257
1171
P. Diirner, L.J. Gauckler, H. Krieg, H.L. Lukas, G. Petzow, J. Weiss, J. Materials Science, 16, 935-943(1981).
1181
M. Hillert, S. Jonsson, 2. Metallkd.,
83,
714-719 (1992).
3,
AIN-A&O,-THERMODYNAMIC
P91
M. Hiiert,
PO1
L. Dumitrescu,
WI
F. CoIin, Rev. Int. Hautes
Temp. et R$mct.,
WI
D. Michel, M. Huber, Rev.
Int. Hautes
P31
P. Bassoul,
1241
N.D.
P51
G. Long, L.M. Foster, .7. Am.
PI
A.M.
P71
D. Michel, Rev.
b-4
A. Lefebvre, J.C. GiIIes, R. CoIIongues, Mater.
PI
S. Jonsson, 2. Metallkd., B. Sundman,
Corbin, J. Europ.
J. Eur.
Cemm.
Ceram.
15, 239-245
Sot.,
Temp. et RLfmct., Chem.,
Masson,
Acad. SC., 254,
Temp. et RQmct.,
5, 225-242
de Phases
A.T.
1321
0. Redlich, and A. Kister, Ind. Eng.
Chem., 40, 345-348
[331
M. HiIlert, and L.I. Staffanson,
Chem. Stand.,
I341
B. Sundman
[351
M.W. A.N.
8, 235-242
15, 4, 327-328,
Acta
and J. Agren, J. Phys.
Jr. Chase, Syverud,
Ref. Data,
CA.
Davies,
JANAF
et Stoechiome’trie,
J.R.
(1975).
351-353,
374-375
(1991). (1948).
24, 3618-3626 (1970).
Chem. Solids,
42, 297-301
Jr. Downey,
D.J.
Thermodynamic
(1981).
Frurip, R.A.
McDonald,
Tables, Third Edition, J. Phys. Chem.
14 Suppl. 1, (1985).
[361
B. Hallstedt,
[371
F.D.
[381
Calphad,
(1972).
(1973).
[311
Dinsdale,
(1970).
Res. BUN., 7, 557-566
A. Lefebvre,
Cryst.,
(1974).
2780 (1962).
t301
J. Appl.
10,56-65
Sot., 44, 255 (1961).
Cemm.
Paris, 109-120
(1972).
7, 145-150
5, 143-154,(1989).
Sot.,
A. Lefebvre, J.C. GiIles, R. CoIIongues, Diugrammes iditeur
(1995).
(1968).
5, 267-283
J. Solid State
Lejus and R. CoIIongues, C.R.
Int. Hautes
(1992).
83, 720-728
A. Lefebvre, J.C. Giies,
191
REASSESSMENT
M. HiIIert, M. SeIIby, B. Sundman,
Richardson,
Press, London,
Fhysical
Chemistry
of Melts
Calphad,
18, 31-37 (1994).
in Metallurgy,
vol. 1, Academic
284 (1974).
B. HalIsted, Report
Trita-Mac-399,
The Royal Institute of Technology, Stockholm,
Sweden, (1991).
(391
B. Sundman,
J. Phase
PO1
R. Dupree,
1411
V. Jayaram,
I421
C.S. John, N.C.M.
[431
B. Jansson, Ph. D. Thesis,
I441
B. Sundman,
M.H. C.G.
E&l,
12, 127-140,
Lewis, M.E.
Smith,
Levi, Acta Metall., Alma,
G.R.
(1991).
Phil. Mag. A, 53, L17-20 37, 559-578
Hays, Appl.
(1989).
Catalysis,
6, 341-346
Royal Inst. Techn., Stockholm,
B. Jansson, and J.-O.
Anderson,
(1986).
(1983).
Sweden, (1983).
Gulphad, 2, 9 1533190 (1985).
192
P. TABARY AND C. SERVANT
1451
M. Hihert, S. Jonsson, Met. Bans. A, 23, 3141-3149 (1992).
1461
T.M. Harnett, R.L. GentiIman, “Optical and mechanicalproperties of highly transparent spine1 and AlON domes”, SPIE-Ad vances in Optical Mater&Is, 505, edited by S. Us&ant, Society of Photo-optical Instrumentation Engineers, BeRingham, WA, 15 (1984).
1471
P. Lefort, G. Ado, M. Billy, J. de Phys. Cl, 47 (Supplement to 2 February), 521 (1986).
[481
A. Dinsdale, private communication.
1491
A. Navrotsky, B.A. WeschIer, K. Geisinger, F. Seifert, J. Am. Ceram. Sot., 69, 5, 418422 (1986).
1561
M.W. Chase Jr., R.A. Curnutt, R.A. McDonald, A.N. Syverud, J. Phys. Chem. Ref. Data, 7, 838 (1978).
1511
Q. Chen W. Zeng, X. Chen, S. Gu, G. Yang, H. Zhou, Z. Yin, Thermochemica Acta, 253,33-39 (1995).
Appendix
1: Thermodynamic
Description
of the AlN-AlsO3
pseudo-binary
system
AII parameters values are given in SI units (joules, moles, kelvin) and R=8.31451 .I/(mol.K). The thermodynamic functions, available in the Thermo-CaIc databank [39], are listed below. Gas Model: (A1,A1N,A10,A10s,A1rO,AlrOr,N,NO,NOr,NOs,Nz, GqgS(T)
- ‘%;ff:$
=
F5lT
NrO,N 2 0
3,
N2 0
4,
N3, 0 , 0
+ RTLNP
FUNCTION F51T : (298.15
FUNCTION F274T : (298.15
G:,:;,(T)
_
0H’8B~15K fee-“,.A,
FUNCTION F279T : (298.15
-
Ops.‘6K l/ad4ok-oa(G)
=
F279T + RTLNP
2,
0 3)
AIN-AI,O,-THERMODYNAMIC REASSESSMENT
+5%464.7364+42%04.828T-‘-29.5986666T -27.3771672TLN(T)-.008706%04T’+1.5475%667~10-V I800
l?UPCTION P301T : 1298.15
-
G;&(T)
2*“H;:‘;f,A,
- oH$$&,,(,j
=
F429T
+ RTLNP
:?‘UNCTION F42OT : I 298.15
:?UNCTION F440T : 1.298.15
G$fS(T)
-
oH$&ye_,,(,J
=
F7202T
+ RTLNP
:?UNCTION F7202T : +?96.15
:?UNCTION F7215T : l’298.15
193
194
P. TABARY AND C. SERVANT
FUNCTION F7225T : (298.15
FUNCTION F7239T : (298.15
G%<‘(T)
- 2*“H:9:&$&o)
=
F7307T + RTLNP
FUNCTION F7307T : (298.15
FUNCTION F7330T : (298.15
FUNCTION F7345T : (298.15
FUNCTION F7352T : (298.15
AIN-AI,O,-THERMODYNAMIC
REASSESSMENT
(a00
G$fs(T)
- 3*“H;~$$_Nl(oj
=
F7363T +
RTLNP
I’UNCTION F7363T : (298.15
GgfS(T)
- %;~~~,X,_,,~,~
=
F7397T +
RTLNP
FUNCTION F7397T : (298.15
G$jf(T)
- 2*“H;~~~~_ol~G,
=
F7531T + RTLNP
FUNCTION F7531T : (298.15
Ggis(T)
- 3*“H;;:$~_olco,
=
F7683T +
RTLNP
FUNCTION F7683T : 1:298.15
h&-Liquid Model: (AlN)
(Al0l.s)
OGlonlc-trqurd T _OH’B8.‘6K _oHm8.‘6x l,IMdr-NIcGj ( ) AIN fsc-.&Al FUNCTION GALNLIQ (298.15
:
=
+l*GALNLIQ
195
196
P. TABARY AND C. SERVANT
-345837.2+359.86191T-54.308659TLN(T)
OG:~~c;Li~id(T)_OH~l~~~,
+8.55504041t10-~T’+2326379.8T-‘-1.25565031~10~-‘+7O54l-23T
_ 1.5*0H’%3.‘6K l/ZMdr-01(G)
=
+
0.5eGAL203LQ
FUNC;ION GAL203LQ : (298.15
OLloniC4
‘Wd = -113633.32
+ 55.887*T
AIN,AIO,.s
27R Model:
(Al+‘)0
(N-*)7
(O-l),
O@R
A,+s:p,-s:&T) - 9*‘H;;::& + GCORUND + 87047 - 42.95+T
FUNCTION GALN : (298.15
- 7*“H;~f$~_N1cc)
- 3*“H;;f~~e_,,c,j
= +7*GALN
+8.55504041t10-%CT’+2326379.8T-‘-:.25565O3l~lO~-~
FUNCTION GCORUND : (298.15
21R Model:
(AI+S)7 (N-S)5
(O-*)3
oG”R A,+s:N-,:O-a(T) - 7*‘H;zL’&, + GCORUND + 84986 - 41.96eT
- 5*“H:~&~e_NlcoJ
- 3*“H;~;~~e_olcCj
= +5*GALN
-3*'Hf~~~_,~(q
=
121i Model:
(A1+3)e (N-‘),
0(-p" AI+s:N-a:pa(T)+
GCORUND
y-AlON
(0-‘)a ~*'H:~'~~,AI-~*'H:~~~_N~(c)
+ 83041-
40.87eT
spine1
Model: (Al+‘)1
(AI+‘,Va’)r
(N-‘$-‘)I
+4*GALN
AIN-A&O,-THERMODYNAMIC
“G;;;;;;:?;::(T) - 3*‘H;$‘& + 255386 - k5.28eT “G;;+?f”,C’,“-‘(T)
- 4+0H:$z_Ns(Cj
REASSESSMENT
= +4*GALN
+ 4*GCORUND
- oH;tf:;T,,,
- 4*“Hf~;$&,,1(o)
= +I*GALN
+ 12eGCORUND
- OH;FfL’;fAr
- 4*“H;;;$‘_o,(cj
= +LI*GGAMMA
+ 442813 - 49.25*T
“G’,;+?f;~.$“(T)
FUNCTION GGAMMA : (2198.15
+ 44.954*T + 1.2+T
-.070794Tz+1.4913451*10-9’+981165T-’
(600
&‘-AlON
spine1
Model: (A1+J)l (AI+S,Va0)2 (N-*,O-‘)4 “G$;e;>.$f(T) - 3t”H;~;‘& t 71508.778 - 49.9663eT
- 4*“H;~:$&1(CI
“G$;+::~‘$$*‘(T) - ‘H;z:‘;fA, t 2570309.7 - 1094.0672tT
hAlON
- 4t”H;;f$&NI(Cj
= +4*GALN
= +4+GALN
+ 4*GCORUND
+ lP*GCORUND
spine1
Model: (A1+3)1 (Al+‘)u
(Va’)o.s
(N-SP-‘)~
oG;;$:~~;;z;_,(T) - 2.7*‘H;::‘:TA, t 51323.87 - 20_116+T
- 4*“H;;:$~_Nlco,
= +O.l*GALN
+ l.J*GCORUND
“~~“;;+‘~~~~;~~;_,(T) - 2.7*0H3Tf2;f,A, $ 51323.87 - 20.116+T
- 4t”H:~f$“_ol(cj
= +O.l*GALN
+ l.S*GCORUND
LX-AI
Model: (Al)1 (Va), O’G:;;;;,A’(T)
- OH;::‘&
=
GHSERAL
GHSERAL : (298.15
197
198
P. TABARY AND C. SERVANT
5 2. -
-_
-_ --__
-25
50
_ _ AG . (cation) - _nux. ____
/
I
I
I
I
40
30
20
10
0
mole % AIN Figure 1: Energy of mixing in the anionic (- -) and cationic (- - - -) sub-lattices at 2000°C function of composition of r-AlON spine1 and total energy of mixing (-).
x(A1203)
Figure 2: Gibbs energy of the -y-AlON and qS’-AlON spine1 phases at 2000°C as a function of position.
AIN-A&O,-THERMODYNAMIC
3000
I
I
I
199
REASSESSMENT
I
McCauley and Co&in (1979)
AL XALON [rL+12H VL+ALON cALON+p~lyk
LS
McCauley and C&in
(1983)
_ TALON ~L+ALON
j 2303
“:.,,
‘fL+iZH
I
*L+PlR +L+Y +27R+21R A2621R+ALON Quinn et aL(t994) _ )(ALON Cannard (1988) AAIN QAIN+ALON *AlN+27R
1639
_.. _.... .......__ __.... .. .
012
Willems et aL(1992)
.
. ._.
014
AIN
Figure
3 : Calculated
present
optimization
.
._.. .._.._._........ .._.._....__ Y..
016
018
phase
diagram without
of the pseudo-binary including
1 I
A’2o3
‘Al,O,
(--)
_____ ____
system
the gas phase compared
AIN-A1203
according
to the
with the work of [20] (.....).
200
P. TABARY AND C. SERVANT
2300 McCauley and Corbin (1979)
2200
AL XALON
qL+lZH
G
2100
VL+ALON @LON+polyA and Chin !i LO36McCauley
0
g
WLON
2000
5-
~L+ALON ‘y’L+lPH
z is
)J(L+21 R i-L+*’ +27R+21
E lgoo a> I1800
R
*2lR+ALON Quinn et at.(rsaq #ALON Catward (1988) AAIN @N+ALON
1700
#,UN+27R
1639
Willems et aL(lss2) @ON
1600 0.2
k& AIN
Figure 4 : Detail of Figure 3.
0.4
0.6 ‘Al,O,
0.8
1 .O A’,%
(1983)
AIN-A&O,-THERMODYNAMIC REASSESSMENT
Gas+Liquid
I_ :
2400 -
_/r_
II
2200 0
0.2
I 0.4
\ 0.6
/’
/I
Liquid
I 0.8
: :
1Ya6.‘
li
d w 2300-
: /
2320 5 AIN+ iZ 2315Gas d q 231011ol.s ,E 2 2306-
201
-
!.+ e 22Q5-
-
22QO-
1.0
2286
P” nFi
0
I 0.1
I 0.2
I 0.3
I 0.4
, 0.6
I 0.8
I 0.7
0.
xW203) (b)
Figure 5: a) Calculated phase diagram of the pseudo-binary system AlN-AlsO3 according to t present optimization including the gas phase; b) Detail of Figure 5a.
> Pergamon
THERMODYNAMIC REASSESSMENT AlN-A1203 SYSTEM
P.Tabary’p”,
OF THE
C. Servant’
* Laboratoire de MCtallurgie Structurale, URA CNRS 1107, UniversitC de Paris-Sud, 0rsa.y Cedex, France. *+ SociCte Pechiney-ElectromCtallurgie, Usine de Chedde, 74000 Le Fayet, France.
ABSTRACT.
91405
The AlN-AlrOs system has been reassessed due to new experimental data published in particular near the AlrOs rich part and relative to the # and 6 phases. The Gibbs energy of formation of the solution and compound phases in the AlN-AlrOs binary section were derived from an optimisation procedure using all the available experimental thermodynamic and phase diagram data. The thermodynamic description of the ordered compounds was made using the sub-lattice model, while a Redlich-Kister polynomial was used for the solution phases.
1 - Introduction
Aluminium oxynitrides, produced by the Pechiney Electrometallurgie Society, with an amount of AlN (% mole) ranging from 43.3 f2.2 to 3.5 f0.2 were studied especially at high temperature
[ 11. These
alloys
Several phase
previous
phases
have
were taken
of the composition
phase 7-AION present
?&inal
into
of 1201, two structure)
(with
a c$’ spine1
spine1 work,
having
and
system,
and
quaternary
devoted
a-AlrOs
or quaternary
AI-0-N-Si
to the
phases
structure
Al-0-N-Si
systems
AlN-AlrOs
a corundum
Al, AlsOsNr
the composition
spine1
AlsOsNd
6 phases
(with
in addition
a composition
the 4’ and
Al-O-N
and
of the other
and
Al-O-N
binary
AlN, the spine1 (AIN(s rrs~-AlrOs(s,ss2))
account
range
to the ternary
by [2-141.
assessments
Liquid,
AI-O-N
materials.
devoted
ternary first
compound
[ 181 of the ternary
polytype
data published
of the In the
were considered:
assessment
as abrasive
been
assessments by (15,201.
as a stoichiomctric ture),
used
experimental
diagrams
Several made
are mainly
were (with
was
In the assessment
was AlrsOr,N~.
of temperature
taken
into
account:
A1703Ns
AIN
polytype
structure).
not
taken The
were considered
into
account),
6 phase
it was
was not taken
due to new available
(with The
a 21R
AIN
A122033N2
account.
experimental
width In the
regrouped into
version received on 26 !%ptember 1997, Revised version on 5 May 1998
179
struc-
The
was optimized.
a 12H
range.
four (16, 171
a 27R AlN polytype
of the spine1
as a function
been
1151, A!rOaNL
structure). (with
have section,
with
thr
In the data
(11.
180
I’. TABARY AND C. SERVANT
The 4’ phase was found by [4], then successively studied by [21] and denoted Y phase, [22] and denoted & phase, [23] and denoted e phase, and finally by [lo, 241 and denoted # phase. Two forms were identified The 6 phase was found by Long [25], th en studied by [2,5,21_23,26-301. by Lefebvre [28, 291, denoted: 61 and 62. In the present work, we have not distinguished these two forms in the calculated assessment. 2 - Thermodynamic
modelling
2-l - Brief outline a) Pure solid elements: The pure elements in their stable structure at 25°C (298.15K) were chosen as the reference state for the system. The thermodynamic functions for the stable and metastable states are taken from the Scientific Group Thermodata Europe (SGTE) [31]. b) Substitutional solutions: For the liquid phase (denoted by ‘p) the Redlich-Kister the excess Gibbs energy ‘=Gp :
polynomial
[32] was used to describe
where x; and xj are the mole fractions of components i and j in the phase ‘p. The interaction terms Lzj can be composition and temperature dependent as follows:
pj
= c,
“LKj
( x’
-xi’
)’
(2)
where v is the power in the Redlich-Kister expansion. c) Compounds: The polytypes 27R, 21R, 12H and the 6 phase were modelled as stoichiometric compounds. The compounds which exhibit a range of non-stoichiometry (r-AlON spinel, d’-AlON) were modelled using the sub-lattice model . They can be described schematically as follows: (A;;B:;,
.. .. .. )JA;;B;;
.. .. . . ), .. . . .
where the species A’, B’..., and A”,B”... can be atoms, ions or vacancies. p and q are the number of sites, yi and Y”B the respective site fractions of the elements A and B in their respective subthe thermodynamic quantities are referred to one lattices designated by ’ and “. If p+q+...=l, mole of sites. For each sub-lattice s, the site fraction of the species is equal to
yf = n:/(n;,
+ Cj 72;) = nf/n’
with: CL& = 1 and ‘& n’ = n
(3) (4)
where nl is the number of species j in sub-lattice s, R’ is the number of sites in sub-lattice s, and n the total number of sites. n’ is related to n by n’=p.n/(p+q+...). The molar Gibbs energy, as formulated by Hillert and Staffansson [33] and generalised by Sundman and Agren [34], is defined as follows:
AIN-AI,O,-THERMODYNAMIC
cf;‘,
which defines a hyper-surface
G A,B,, represent
The terms Ai,Bi
(5)
+G” m +G’” m
G m =G’fm The term
which may ie’stable
The term
the Gibbs energy
Li,j:i and Li;i,j represent
for a given occupancy
polynomial
as follows: Y;
[(QO+ &!I’) +
yj
is equal to:
of formation
to the molar configurational
sub-lattice
Li,j:i =
of reference,
of the stoichiometric
compounds
or me&table.
Gz is related
The terms
181
REASSESSMENT
The number of sub-lattices
entropy
the interaction
of the other,
and is equal to:
parameters
between
and are also described
the atoms,
ions on one
by a Redlich-Kister
(a~t hT)(Yi - Yj) + ... + (an + bn’)(Y*- Yj)" I
and the species occupying
them is generally
[32]
(9J
obtained
from structural
information. 2-2 .
l
on phase
- Details
Gas phase.
Eighteen
modynamic
properties
modelling
gaseous
species were used which are listed in Appendix
are found in the JANAF
Liquid phase.
Different
two-sublattice
model for ionic liquid:
was used where Q-3 -P is the average (with
the charge
the quaternary
descriptions
and P varies with composition
valency -3)
on the second
allows
system
SiOz and SiN.13.
the liquid of the AlzOs-CaO-SiOz et al. [36].
atoms because
may be justified
with an Al atom each 0 is shared
to be extended
system
of two species:
by the hypothesis in the middle should between
AlN,
Al203
Al203
ther
of [18], a
electroneutrality,
of hypothetical
all the way to liquid
species
this model with the species
ie
vacancies Al.
For
and in addition
could not he used to
and the species AlOl 5 was then considered
For the reason of compatibility,
[20], the liquid consisted
of A1203
The presence
[19] used the same
SiO, -‘,
al.
However,
1. Their
[35].
in order to maintain
sub-lat.tice.
the description
Al-0-N-Si,
Tables
have been used by [18, 201. In the description
describe
by HaUstedt
Thermodynamic
in the description
of Dumitrescu
et
AlN and AlOl s. The choice
of AIO1,s instead
made
of triangles
by [37] that
a network
form in the liquid.
two Al. So for the same reasons
The basic
of 0
unit is AIOl 6
of compatibility,
the two
species AlN and AICI1.s were used in the present work. It was found that it was necessary to introduce an excess term of degree 0. In the work of 1201 no excess term was considered for the optimization
of the liquid phase of the AIN-AI,03
system.
P. TABARY AND C. SERVANT
182
s Polytypes. The polytypes denoted 3(m+2)P with a m(m+l) AlN molar fraction were described using three sub-lattices: (Al)(,+r) (N), (0)s. The crystalline structures of the polytypes is either rhombohedral or hexagonal, [7]. Along the c-dimension, the structure consists of “n” layers where “n” is the numeral of the Ramsdell symbol, [7]. The nR polytypes consist of three rhombohedrally related blocks each of n/3 layers, while the hexagonal nH consist of two blocks related by a c-glide plane and each containing n/2 layers. The number of layers per symmetry-related blocks in the polytypes 12H, 21R and 27R found in the AIN-ALrOs system is respectively 6, 7 and 9. Th us, m=(n-2) is respectively equal to 2 (12H), 5 (21R) and 7 (27R). The Gibbs energy OGs(,+r) of the 3(n+2) polytype was modelled as:
with the thermodynamic
parameters a and b to optimize.
s r,AlON spine1 phase. The spine1 phase was described as that of the pseudo-binary AlrOsMgO system (381 baaed upon r-AlrOs using three sub-lattices: the tetrahedral, the octahedral and the anionic sub-lattices as follows: (A1+3)r (Al+‘,Va’)r (N-3,0-2),, where Va” represent real vacancies with no charge. Controversies exist on the occupation by vacancies of the tetrahedral or octahedral sites. In fact, Hallsted [38] proposed a distribution of vacancies on the octahedral interstitial sites for the r-AlON spine1 for reasons of compatibility with the magnetite of the Fe-O system (391. Nuclear Magnetic Resonance (NMR) measurements made by Dupree et al [40] are in agreement with this hypothesis, but some doubt exists on their conclusions because these authors have assumed a completely normal distribution of cations. On the contrary, from electron diffraction measurements of the scattered intensities of r-AlON spinel, r-Al203 and &AlrOs, Jayaram et al 1411 concluded that vacancies prefentially form on the tetrahedral sites. Previously, by high resolution, solid state aluminium NMR, John et al [42] have found that an amount of 75 f 4 % of octahedral sites are occupied by cations, which correspouds to a total occupation of the octahedral sites in r-A&03. The general formula of the +y-AION spine1 used corresponds to a linear electrically neutral combination of four hypothetical charged compounds: (Alt3)r (Alt3)r (Nm3),, (Alt3)r (Alt3)r (O-*),, (Al+3)1 (Va’)r (Ne3)d and (Al+3)r (Va’)r (O-‘)J. The domain of stability of the T-AlON spine1 is therefore a line running from : (5/6*[(A1+3)r
(Alt3)r (O-‘),I
+ 1/6*[(A1+3)r (Va’)r (O-‘),I)
to (3/4*[(Al+3)1
(A1+3)r (O-*),1 + l/4*
[(A1+3), (A1+3)2 (N-3),]).
The compound (A1+3)r (Al+‘)2 (O-‘) 4 is taken as the reference for the Gibbs enthapies of formation as follows:
oG[(Al+3)1 (AlC3)r (O-2),]
= 3*OG(Al) + 4*‘G( l/20*)
= HSER.
AIN-A&O,-THERMODYNAMIC
REASSESSMENT
183
It can be easily shown that:
a) oG-,-~,~3 = 3/4*(5/6*“G[(Al*3)i 2*RT+(1/6*Ln1/6+5/6*Ln5/6)), oG[(Al+3)1
(Va’)s
(O-‘)a]
b) oG~~+"Ga-~,20s 1/4*(a
+ b*T),
oWA1+3)~
(Al+3)z
(O-‘)a]
i-
1/6*OG[(AP)i
(Va”)r
(C-2)4]
+
and:
+ 5*H SEn[(Al+s)r
= 2/4*OG[(Alf3)r
(A1+3)z
(A1+3)r
(O-“),]
(0-‘)4]
+
= 6*‘G,_alao,
1/4*OG[
+ 44.954*T.
(A1+3)1
(Al+3)2
(N-3)4
_
and:
(A1+3)2
(N-%1
+
3*HSER[(A1+3)1
(A1+3)2
(O-2)r]
= 4e”GaIN
+ 4*“G=_A~30s
+
a + b*T.
c) oG~~~+“Ga-~~,oJ = 1/4*(a’ + b’*T), and:
FJy3)1
(Va’)s
In the present
l
(N-%]+9*H
work,
optimize
the domain
#-AiON
phase.
It is first necessary ture refinement Compared
to summarize
due to these antiphase electron
The +‘-AiON
parameters
the #-AlON
deviation
of 7
Vacancies
domains.
=
[-l/4,
The structural
a composition
become
spine1 lattice,
with a mutual
struc-
0, l/4]
model
distorsion to a spine1
one versus the other.
proposed,
on the diffraction was confirmed
Inside a patterns
by high res-
range from about
of the modulation
anions do not occupy
substitution
10 to 20 mole % of AlN.
vector are function content
and vacancy
their ideal position_
in the y-AlON
spinel.
The
of the composition They
fraction. present
a
The anionic sub-lattice
of 0 and N atoms.
on the octahedral
sites in the antiphase
interface
planes,
when they
ordered.
This order corresponds
to a splitting
spine1 into two distinctive amount
the crystalline
experiments.
and the direction
are situated
to
as in the work of [29].
of the ions correspond
Intense satellites appeared
to ideality very close to that observed
is disordered,
-
+ a’ +
lattice presents a monoclinic
of the phase which is related to the increase in the nitrogen As in the 7-AlON
(N-3)4]
a, a’, b and b’ were sufficient
by [l] concerning
The mean positions
translated
phase presents
lattice parameters
(Va”)s
4*“G~~~+12*oG,_4~,o,
(Ow2)4]=
the results obtained
spine1 lattice,
microscopy
1/4*“G[(A1+3)1
phase.
variant, the lattice remains monoclinic. olution
+
No excess term was necessary
in composition.
two variants
(OP2)q]
(A1+3)2
the four thermodynamic of the spinel.
to the r-AlON
having
(Al+3)z
‘zR[(Al+“)i
of the #-AlON
due to a modulation lattice
9/4*“G[(Al*3)r
sub-lattices
of vacancies on the octahedral
cies on the antiphase
interfaces
of the sub-lattice as follows: sub-lattice.
number
(A1+3)r_2,
2, (AF3,Vao), and (Va”)z2,
2x is proportional
[l], and so is a function
of the -y-AlON where 2x is the
to the density of vacan-
of the composition
of the @-AlON
on a sub-lattice,
several solutions
phase. In order to use a variable amount of atoms or vacancies have been investigated which are summarized below:
P. TABARY
104
AND C. SERVANT
1. The optimization of the stoichiometric the compound with the formula:
#‘-AlON phase with 15 mole % of AlN, that is
The Gibbs energy of the two compounds involved is as follows: G(AI:Al:Va:N)
= G(Al:Al:Va:O)
= 0.233*‘G~l~
+ 1.259*OG,_Ar,o, + a + b*T,
where a and b are thermodynamic parameters to optimize. Unfortunately, this optimization has not given any information on the junction of the 4’ and -/-AlON spine1 phase domains and, as a consequence, on the precipitation mechanism from the liquid state. 2. In order to take into account the composition range of the #‘-AlON phase, substitutions can be introduced in the sub-lattices number 2 and 3, as follows:
so eight charged compounds are defined. In order to simplify the optimization, it is possible to identify the compounds containing oxygen with the corresponding compounds containing nitrogen (we defined the variable X which indifferently represents the 0 and N atoms), so only four compounds were considered: oG(Al:Al:Al:X),
‘G(Al:Al:Va:X),
‘G(Al:Va:Va:X)
and ‘G(Al:Va:Al:X).
This last term was assumed to be very unstable. Consequently three compounds and only six thermodynamic parameters a and b have been optimized. The nitrogen enriched part of the composition range of the b’-AlON phase is modelled with the terms OG(Al:Al:Va:X) and ‘G(Al:Al:Al:X), while the nitrogen depleted part is modelled with the terms ‘G(AI:Al:Va:X) and ‘G(Al:Va:Va:X). With this way of modelling, first the optimization works with difficulty due to the possibility of having vacancies in two sublattices and secondly terms of entropy of mixing are introduced which have a priori no physical meaning when taking into account the structural results obtained by [l]. 3. To optimize the +‘-AlON phase by using the three sub-lattice model as follows: ( Al+3)1 ( AP3,VaU)r (Nm3,0m2)d and by introducing a term of entropy equal to that of the r-AlON spine1 diminished of the term of mixing:
We calculated this correction to be equal to AS = 44*T for the term ‘G(AI:Va:O) and AS = 151*T for the term ‘G(Al:Va:N). The optimization of the terms of enthalpy H(Al:Va:O) and H(Al:Va:N) did not allow a correct description of the d’-AlON phase which became too much stable at low temperature. 4. Finally, the 4’-AlON phase was modelled with three sub-lattices and the two terms OG(Al:AI:N) and ‘G(Al:Va:N) (4 thermodynamic parameters a,b, a’ and b’) have been optimized. The term ‘G(Al:Va:O)-y w hi c h corresponds to a hypothetical d’-Al203 phase (instead of T-AlsO3) was kept. As mentioned above, the term of entropy of mixing of the sub-lattice (:AI,Va:) has no special physical meaning when considering the structural results [ 11. s 6-AlON phase The composition range of the 6-AlON phase, comprised between about 5 to 10 mole % AlN [l], is narrower than that of the @-AlON phase. between about 5 to 10 mole
AIN-AI,O,-THERMODYNAMIC
REASSESSMENT
185
$ZoAlN (I]. No data on the evolution of the phase boundaries of 6-AION as a function of temperature being available, this phase has been optimized as a stoichiometric phase having a chosen composition of 7 mole % of AlN and the sub-lattices:
The stability of this 6-AlON phase was optimized versus temperature with two terms of Gibbs energy “G(Al:Al:Va:O) and ‘G(Al:Al:Va:N) that is four parameters a, a’,b and b’. In fact, two parameters (a and b) are sufficient if it is assumed that: OG(Al:Al:Va:O)
- HSER =OG(Al:Al:Va:N)
- H ‘SER = O.l*‘Gai~
+ 1.3*‘Gcl-AlaoJ + a + b*T.
3 - Optimization 3-l
- Optimisation
procedure
The evaluation of the thermodynamic properties of the solution and compound phases were derived from an optimisation procedure using the available experimental phase diagram and thermodynamic data, and using the module PARROT developed by Jansson [43] and contained in the Thermo-Calc databank system [44]. The optimization is carried out by minimizing an error sum by varying selected model parameters. This sum of errors is calculated from the experimental data. Each experiment is characterized by a weight according to its estimated accuracy. l
Components used: As all the equilibria studied experimentally concerned the pseudo-binary section AlN-Ai20s, we first used the components x(Al~Os), x(AlN) and x(N) with x(N)=O, then the components of the ternary system: x(Al), x(0) and x(N).
3-2 - Available l
data
The thermodynamic
parameters of AlNliquid vary very slightly according to [45]: o
liquid
G ALN
o
Gzy
= 70679 - 23*T J/mole of AlN
oG~~-“G>~:r;”
= 70541 - 23*T J/mole of AlN
-
or (191:
The second expression was considered in the work of (201 as well as in the present work. In fact, these two different expressions lead to a very small variation in the temperature of melting of AlN (6°C). . The specific heat at constant pressure of the r-AlON temperature by [46, 11, 471.
spine1 has been determined at low
. The enthalpy of melting of some phases was measured [l] using the thermal differential analysis. For each measurement, a standard measurement of the enthalpy of melting of corundum was made. It was calibrated to a value of 111136 f 3976 J/mole [35j. For the yAlON spinel, 4’ and 6 phases, the enthalpy of melting was found respectively equal to 38290, 60675 and 63597 J/mole. For the 4’ phase, the measured enthalpy does not correspond to
186
P. TABARY AND C. SERVANT
Table
1:
Comparison
of the experimental
and optimized’
binary
equilibria
(“C,
mole
% AlN,
J/mole)
Phase
Supplementary condition
Experiment
equilibria
AlN - 7
1750
c(7)=31.99 31.45’
f 3.3
]I31
AIN - 7
1850
;~j,“““”
f 3.2
1131
-y - a-Al~Os
1750
c(r)=22.01 23.97’
+ 3.?
[I31
-y - a-AlzOs
1850
f 3.9
[131
7 - Liq.
x(y)=c(Liq.)
c(7)=19.00 19.03’ 2082 l 30 2085’
4’ - Liq.
x(#)=c(Liq.)
2060 f 2065’
6 - Liq.
1
Experiment
2
Experiment
3
Ref.
Ii,=36853 36936’
f 2454
x($=32.90 33.67’
10
Ii,=48967 46563’
YIZ2670
x(&)=21.2 21.48’
x(+c(Liq.)
2050 f 50 2042’
II,=63499 63206’
zt 5098
111
7-d
2000
x(+21.36 20.90’
x(+18.25 18.07’
+ 2.1
]ll
4’ - 6
2000
x(+10.75 11.14’
a congruent
melting
to the nitrogen
f
2.2
0.5*(Tb+T,)
[l]
[II
[ll [ll
of which
part of the composition
within less than 5”C, it was considered to:
10
* 2.2
of this phase the composition
depleted
f
range.
to be congruent
where Tb and T, respectively
(11 mole % AlN)
However,
and occurring
correspond
corresponds
as the melting
occurs
at a temperature
to the beginning
equal
and end of the
melting.
3-3 - Results The optimized optimized
thermodynamic
equilibria
For a ternary
system,
each three-phase Sex(N)=0
are compared according
equilibrium,
parameters
to the law of variance,
two conditions
(which gives the composition
For a two-phase the reaction
equilibrium,
1. 7-AlON
- a-Al203
determined (prolongation
condition
The experimental
and
taken into account: section
For
3*x(Al)-2*x(O)-
AlN-AlrOs),
and p=lO’
must be added such as the temperature
Pa. of
of the phase ‘p in % mole of AlN: x(p).
of melting of the phases is given in J/mole. equilibrium.
both by the entectoid of the domain
The composition reaction
of the 7-AION
depleted
of -/-AION
(T=1637”C)
in equilibrium
and the equilibrium
spinel) and a-AlrOa
these two points are fixed, it is difficult to modify on the nitrogen
1.
below.
there are five degrees of freedom.
are therefore
on the pseudobinary
a supplementary
or the composition
In Table 1, the enthalpy
are listed in Appendix
in Tables 1 and 2 and discussed
part even by introducing
(T=2154”C).
the phase boundaries interaction
with a-AlsOz
is
between 7-AlrOa In fact, when
of the -y-AION spine1
parameters
on the sub-lattices
AIN-A&O,-THERMODYNAMIC of the 7-AlON
spinel.
This temperature
of stability
of AlrOs(l;s)
of 7-AlsOs
(-23.42
at 298.15
K, evaluated
at 700°C
from 7-AlzOs
By modifying of 2J/mole.K expression of ‘G7-AlzOs
= -26.78
f
0.41 kJ/mole
2727°C
at 1197°C.
can give a non negligible
(1110.41976)
temperature
in the thermodynamic
range, we calculated
compared
of the transition a-AlzOs
-+7-AlzOs
that
to the value used by was calculated equal to
This variation has been considered as negligible and we used for
the expression given in the work of [20]. reaction:
12H - Liquid - 7-AlON.
the congruent melting of the 7-AlON parameters of the 7-AION
The temperatures
spine1 are very near.
of the eutectic
The optimized
spine1 or 12H phases have a poor influence
difference, The consequence of this low difference in temperature the compositions observations:
of the liquid and the 7-AlON
low amount
sample containing 43.3 f
of the polytype 2.2 mole % AlN.
was found equal to 39.8 mole % AlN. excess term oL~~~~,,AIN) 3. 7-AlON
of dissolution
+7-AlzOs.
was equal to +0.15J/mole.K
[26]. The resulting temperature
Z!. Eutectic
of transition a-AlrOs
in the 1227°C
213O”C, instead of 2154°C.
situated in the domain
AS(7-AlzOs)
the prefactor of temperature
the variation of S(7-AlsOs)
‘G7-AlrOs
to a-AlsOs
on these values and in particular
uncertainty on the temperature
(T=2154”C),
by [48] using both the enthalpy
1491) and the standard entropy (52.3 f 2 J/(mole.K) R ecently, Chen et al. [51] proposed analysis [50]).
by statistics
the heat of transformation The uncertainties
of transition
has been evaluated
kJ/mole,
187
REASSESSMENT
spine1 stability:
to 7-AlrOs
spinel;
OIL
this low temperature
is a low difference between
this fact is in agreement
I2H melting
at the eutectic
The optimized
composition
The optimization
with our
temperature
in the
of the eutectic liquid
was easilyperformed
= a + b*T for the liquid phase as mentioned According
reaction and
thermodynamic
by using an
above.
to [3], the stability of the 7-AlON
spine1 phase compared
is due to a decrease in the amount of the vacancies on the cationic sub-lattice
This hypothesis is not in satisfactory
agreement with the instability
.
of the spine1 having 56
mole % AlN and which does not contain vacancies. Mac Cauley [9] proposed that the addition of nitrogen anion to a-AlzOs
would induce a local
charge which is relaxed when an aluminium cation moves from an octahedral to a tetrahedral site. Nitrogen would therefore stabilize cations on the tetrahedral In the present work, the two optimized temperature
terms (a+b*T)
sites at low temperatures.
and (a’+b’*T)
are positive in the
range studied.
In Figure 1 are shown the terms of mixing energy in the anionic and cationic sub-lattices 2660°C x=35
as a function of the composition
in AlN.
If the mixing x*AlN+(l-x)*7-AlzOs
mole % AlN is taken as a reference for the 7-AlON
mixing is calculated
equal to about
- 11.2 kJ/mole.
between the respective energies of mixing of 7-AlON of the 7-AlON
spine1 at low temperature
spinel, the additional
This
energy of
value represents the difference
spine1 and 7-AlrOs.
would be due to the entropy
both by the presence of nitrogen in the anionic sub-lattice
at
with
So the stabilization of mixing
created
and of vacancies on the cationic
sub-lattice. 4. Peritectic
reaction:
7-AlON
example when T=2063oC, liquidus of 7-AlON
spinel++‘+Liquid:
In the temperature
the difference in composition
is about
4.4 mole % AlN,
between the less enriched nitrogen composition most enriched nitrogen composition
range studied
between the optimized
and for
solidus and
which is slightly higher than the difference of 7-AlON
(23.5 f
of 4’ (20 mole % AlN).
0.25 mole % AlN)
and the
This fact is in agreement with a
peritectic reaction. !i. Comparative
stability
energies of the 7-AlON
of 7-AlON
and 4’:
In Figure 2 are shown the curves of the Gibbs
and 6’ phases at 2000°C.
Despite
of the lack of knowledge of the
P. TABARY AND C. SERVANT
188 exact composition in nitrogen
in AIN of the 4’ phase
(20 mole
% AlN)
the liquid,
that
phase
agreement
with the hypothesis
are more stable 6. Solid-gas mole
is more
equilibria:
temperature observed
stable
of Lejus
equal
agreement
suppose
7-AlON
was used.
was found
at 1925”C, its composition to indicate
[3] which
than
No equilibrium
is in better
seems
that,
at high temperature
at low temperature
% AlN)+Liquid
forming
at 2060°C
with
than
-/-AlON.
that
the ordered composition.
against
the rapidity
given
of vaporisation
of
fact is not in
phases
of the reaction:
2364°C
enough
of stability
This
for a given
The temperature
to 2307°C
enriched
in the region
(in fact 6)
27R+gas(85
by (181. This
of the material
lower
that
we
at 2350°C.
4 - Discussion From the comparison good agreement
s the temperature much
shown
the temperatures
of the invariant
in Tables
of reaction
reaction:
1 and 2, it will be noted that there is a fairly obtained
by the different
AlN - 7 - a-AlsOs
optimized
authors,
except
for:
by [18] which is too
low.
s the temperatures in the present The
of the results
between
phase
without
of the reactions:
27R-21R-Liq.
diagram
including
that
lower temperature compositions
AlN-AlsOs the limit
calculated
is reported
of 1637°C)
by [13, 141 are slightly
diagram
by Dumitrescu
optimized
by (201 and
does
not
spine1 domain
studied
than in the present enriched
it will be noted
melt
to the present
3. Magnification
optimization
is shown
in Figure
by (3) is situated
work and that
4. at
the phase
in AlN.
et al 1201 is reported
the present work. On the AlN rich side of the diagram, 27R polytype
according
in Figure
of the 7-AION
(ISOO’C, instead
determined
The calculated
at 1 bar,
the gas phase,
It will be noted
1. the
and AlN-27R-Liq.
work.
in Figure
4 for comparison
with
that:
congruently.
Its stability
domain
according
to our experimental
with
-/-AlON
is
[l] instead
of
narrower; 2. the 21R polytype
melts
at 2303°C
results
2709°C; 3. the eutectic atures near.
composition
of the eutectic The optimized
agreement On the AlsOs phases
with
- 7-AlON)
and the congruent
thermodynamic
have a poor influence 4. the composition
(12H - Liquid
reaction
parameters
on this low temperature
is depleted melting
is nitrogen.
of the T-AlON
of the y-AlON
The temperspine1 are very
spine1 and 12H phases
difference.
of the _I-AION spine1 at low temperature
is enriched
in nitrogen
rich side of the phase
diagram,
our diagram
has taken
into account
the two
@ and 6.
The calculated
in
the literature.
diagram
reported
in Figure
5a and b takes into account
the gas phase.
AIN-AI,O,-THERMODYNAMIC REASSESSMENT
Table 2: Comparison
of the temperatures
(“C) of the equilibria and composition
189
of phases involved
F’hase equilibria
Present work
Present work
Ref. [20]
(cd.)
(ew)
2111 2080 x( Liq. ) = 39.80 2048 1908 1891
2115 2079 38.50 2045 1910 1890
1539
1640 + 20
1612
2303 x( Liq. ) = 43.75 2428 1925 x( 4’ ) = 14.02 1985 2041 2036 2064
2300 44.92 2427 1925 13.97 1960
2709
Ref. [18]
Ref. [17]
1Ref. 1151
ZlR-lZH-Liq. IIH-Liq.-y 2 lR-12H-y X’R-21Ry AlN-27R-y AlNy-a-Al20s ;!7R-Liq.7 ;!7R-21R-Liq. MN-27R-Liq. -,-c#J’-Q-Al~o~ tb’-6-a-A1203 cb’-Liq.-6 ii-Liq.-a-All03 y+‘-Liq. wA12Os-Liq.--y .AlN-yLiq. (Congruent melting of 7 Congruent melting of 27R AlN-27R-gas(l35 % mole AlN) 27R-gas(85 % mole AlN)-Liq.
f 10 f 30 f 5.9 xt 10 f 20 * 30
& f f f f
50 22 200 50 2.1
2198 2064 2032 2000 1877
2664
1879 1354 2061
2594
2042 2085 2307.3 2306.8
2768 2365.9 2364.7
1603
1987 2000 2163 2725 2350
1917 1927 1934
190
P. TABARY AND C. SERVANT
5 - Conclusion
We optimized a consistent set of thermodynamic parameters to assess by calculation the AlN-AlrOs pseudo-binary system in which the fl-AlON and &AlON phases were taken into account. Our results were compared with those from previous optimizations.
References PI
P. Tabary, Ph. D. Thesis, UniversitC de Paris-Sud, Centre d’orsay, France, (1997).
PI
Adams, T.R. AuCoin, G.A. Wolf, J. Electr. Sot., 109, 1050-1054 (1962).
131
A.M. Lejus, Rev. ht. Haute3
[41
R. Collongues, F. Cohn, J. Thery, D. Michel, M. Perez y Jorba, Bull. Sot. Fr. Ceram. 77, 51 (1967).
i51
R. Collongues, .C. Gilles, A.M. Lejus, M. Perez y Jorba, D. Michel, Mat. Bul.,
Temp.
tl, 53-95 (1964).
et R&act.,
Res.
2, 837-848 (1967).
161
L.J. Gauckler, H.L. Lukas, G. Petzow, J. Am. Ceram. Sot., 58, 7-8, 377 (1975).
[71
K.H. Jack, J. Mat. Sci., 11, 1135-1158(1976).
181
T. Saks& Yogyo Kyokai Shi, 86, 125-130 (1978).
[91
J.W. MacCauley, N.D. Corbin, J. Am.
PO1
J.W. MacCauley, N.D. Corbin, Progress Publishers, ill-118 (1983).
WI
G.D. Quinn, N.D. Corbin, J.W. MacCauley, Am. (1984).
P21
D.Goeuriot-Launay, P. Goeuriot, F. Thevenot, J. Mat. Sci., 27, 358-364,
(1992).
1131
H.X. Wiiems, M.M.R.M. Hendrix, G. De With, R. Metselaar, J. Eur. Sot., 10, 327-338 (1992).
Ceram.
1141
H.X. Wiiems, M.M.R.M. Hendrix, G. De With, R. Metselaar, J. Eur. Sot., 10, 339-346(1992).
Ceram.
1151
L. Kaufman, Calphad,
[I61
Ceram.
Sot.,
in Nitrogen
62, 9-10, 476-479 (1979).
Ceramics, Martinus Nijhoff
Ceram.
Sot.
Bull.,
63,
5, 723
3, 4, 275-291 (1979).
P. Diirner, L.J. Gauckler, H. Krieg, H.L. Lukas, G. Petzow, J. Weiss, Calphad, (1979).
4, 241-257
1171
P. Diirner, L.J. Gauckler, H. Krieg, H.L. Lukas, G. Petzow, J. Weiss, J. Materials Science, 16, 935-943(1981).
1181
M. Hillert, S. Jonsson, 2. Metallkd.,
83,
714-719 (1992).
3,
AIN-A&O,-THERMODYNAMIC
P91
M. Hiiert,
PO1
L. Dumitrescu,
WI
F. CoIin, Rev. Int. Hautes
Temp. et R$mct.,
WI
D. Michel, M. Huber, Rev.
Int. Hautes
P31
P. Bassoul,
1241
N.D.
P51
G. Long, L.M. Foster, .7. Am.
PI
A.M.
P71
D. Michel, Rev.
b-4
A. Lefebvre, J.C. GiIIes, R. CoIIongues, Mater.
PI
S. Jonsson, 2. Metallkd., B. Sundman,
Corbin, J. Europ.
J. Eur.
Cemm.
Ceram.
15, 239-245
Sot.,
Temp. et RLfmct., Chem.,
Masson,
Acad. SC., 254,
Temp. et RQmct.,
5, 225-242
de Phases
A.T.
1321
0. Redlich, and A. Kister, Ind. Eng.
Chem., 40, 345-348
[331
M. HiIlert, and L.I. Staffanson,
Chem. Stand.,
I341
B. Sundman
[351
M.W. A.N.
8, 235-242
15, 4, 327-328,
Acta
and J. Agren, J. Phys.
Jr. Chase, Syverud,
Ref. Data,
CA.
Davies,
JANAF
et Stoechiome’trie,
J.R.
(1975).
351-353,
374-375
(1991). (1948).
24, 3618-3626 (1970).
Chem. Solids,
42, 297-301
Jr. Downey,
D.J.
Thermodynamic
(1981).
Frurip, R.A.
McDonald,
Tables, Third Edition, J. Phys. Chem.
14 Suppl. 1, (1985).
[361
B. Hallstedt,
[371
F.D.
[381
Calphad,
(1972).
(1973).
[311
Dinsdale,
(1970).
Res. BUN., 7, 557-566
A. Lefebvre,
Cryst.,
(1974).
2780 (1962).
t301
J. Appl.
10,56-65
Sot., 44, 255 (1961).
Cemm.
Paris, 109-120
(1972).
7, 145-150
5, 143-154,(1989).
Sot.,
A. Lefebvre, J.C. GiIles, R. CoIIongues, Diugrammes iditeur
(1995).
(1968).
5, 267-283
J. Solid State
Lejus and R. CoIIongues, C.R.
Int. Hautes
(1992).
83, 720-728
A. Lefebvre, J.C. Giies,
191
REASSESSMENT
M. HiIIert, M. SeIIby, B. Sundman,
Richardson,
Press, London,
Fhysical
Chemistry
of Melts
Calphad,
18, 31-37 (1994).
in Metallurgy,
vol. 1, Academic
284 (1974).
B. HalIsted, Report
Trita-Mac-399,
The Royal Institute of Technology, Stockholm,
Sweden, (1991).
(391
B. Sundman,
J. Phase
PO1
R. Dupree,
1411
V. Jayaram,
I421
C.S. John, N.C.M.
[431
B. Jansson, Ph. D. Thesis,
I441
B. Sundman,
M.H. C.G.
E&l,
12, 127-140,
Lewis, M.E.
Smith,
Levi, Acta Metall., Alma,
G.R.
(1991).
Phil. Mag. A, 53, L17-20 37, 559-578
Hays, Appl.
(1989).
Catalysis,
6, 341-346
Royal Inst. Techn., Stockholm,
B. Jansson, and J.-O.
Anderson,
(1986).
(1983).
Sweden, (1983).
Gulphad, 2, 9 1533190 (1985).
192
P. TABARY AND C. SERVANT
1451
M. Hihert, S. Jonsson, Met. Bans. A, 23, 3141-3149 (1992).
1461
T.M. Harnett, R.L. GentiIman, “Optical and mechanicalproperties of highly transparent spine1 and AlON domes”, SPIE-Ad vances in Optical Mater&Is, 505, edited by S. Us&ant, Society of Photo-optical Instrumentation Engineers, BeRingham, WA, 15 (1984).
1471
P. Lefort, G. Ado, M. Billy, J. de Phys. Cl, 47 (Supplement to 2 February), 521 (1986).
[481
A. Dinsdale, private communication.
1491
A. Navrotsky, B.A. WeschIer, K. Geisinger, F. Seifert, J. Am. Ceram. Sot., 69, 5, 418422 (1986).
1561
M.W. Chase Jr., R.A. Curnutt, R.A. McDonald, A.N. Syverud, J. Phys. Chem. Ref. Data, 7, 838 (1978).
1511
Q. Chen W. Zeng, X. Chen, S. Gu, G. Yang, H. Zhou, Z. Yin, Thermochemica Acta, 253,33-39 (1995).
Appendix
1: Thermodynamic
Description
of the AlN-AlsO3
pseudo-binary
system
AII parameters values are given in SI units (joules, moles, kelvin) and R=8.31451 .I/(mol.K). The thermodynamic functions, available in the Thermo-CaIc databank [39], are listed below. Gas Model: (A1,A1N,A10,A10s,A1rO,AlrOr,N,NO,NOr,NOs,Nz, GqgS(T)
- ‘%;ff:$
=
F5lT
NrO,N 2 0
3,
N2 0
4,
N3, 0 , 0
+ RTLNP
FUNCTION F51T : (298.15
FUNCTION F274T : (298.15
G:,:;,(T)
_
0H’8B~15K fee-“,.A,
FUNCTION F279T : (298.15
-
Ops.‘6K l/ad4ok-oa(G)
=
F279T + RTLNP
2,
0 3)
AIN-AI,O,-THERMODYNAMIC REASSESSMENT
+5%464.7364+42%04.828T-‘-29.5986666T -27.3771672TLN(T)-.008706%04T’+1.5475%667~10-V I800
l?UPCTION P301T : 1298.15
-
G;&(T)
2*“H;:‘;f,A,
- oH$$&,,(,j
=
F429T
+ RTLNP
:?‘UNCTION F42OT : I 298.15
:?UNCTION F440T : 1.298.15
G$fS(T)
-
oH$&ye_,,(,J
=
F7202T
+ RTLNP
:?UNCTION F7202T : +?96.15
:?UNCTION F7215T : l’298.15
193
194
P. TABARY AND C. SERVANT
FUNCTION F7225T : (298.15
FUNCTION F7239T : (298.15
G%<‘(T)
- 2*“H:9:&$&o)
=
F7307T + RTLNP
FUNCTION F7307T : (298.15
FUNCTION F7330T : (298.15
FUNCTION F7345T : (298.15
FUNCTION F7352T : (298.15
AIN-AI,O,-THERMODYNAMIC
REASSESSMENT
(a00
G$fs(T)
- 3*“H;~$$_Nl(oj
=
F7363T +
RTLNP
I’UNCTION F7363T : (298.15
GgfS(T)
- %;~~~,X,_,,~,~
=
F7397T +
RTLNP
FUNCTION F7397T : (298.15
G$jf(T)
- 2*“H;~~~~_ol~G,
=
F7531T + RTLNP
FUNCTION F7531T : (298.15
Ggis(T)
- 3*“H;;:$~_olco,
=
F7683T +
RTLNP
FUNCTION F7683T : 1:298.15
h&-Liquid Model: (AlN)
(Al0l.s)
OGlonlc-trqurd T _OH’B8.‘6K _oHm8.‘6x l,IMdr-NIcGj ( ) AIN fsc-.&Al FUNCTION GALNLIQ (298.15
:
=
+l*GALNLIQ
195
196
P. TABARY AND C. SERVANT
-345837.2+359.86191T-54.308659TLN(T)
OG:~~c;Li~id(T)_OH~l~~~,
+8.55504041t10-~T’+2326379.8T-‘-1.25565031~10~-‘+7O54l-23T
_ 1.5*0H’%3.‘6K l/ZMdr-01(G)
=
+
0.5eGAL203LQ
FUNC;ION GAL203LQ : (298.15
OLloniC4
‘Wd = -113633.32
+ 55.887*T
AIN,AIO,.s
27R Model:
(Al+‘)0
(N-*)7
(O-l),
O@R
A,+s:p,-s:&T) - 9*‘H;;::& + GCORUND + 87047 - 42.95+T
FUNCTION GALN : (298.15
- 7*“H;~f$~_N1cc)
- 3*“H;;f~~e_,,c,j
= +7*GALN
+8.55504041t10-%CT’+2326379.8T-‘-:.25565O3l~lO~-~
FUNCTION GCORUND : (298.15
21R Model:
(AI+S)7 (N-S)5
(O-*)3
oG”R A,+s:N-,:O-a(T) - 7*‘H;zL’&, + GCORUND + 84986 - 41.96eT
- 5*“H:~&~e_NlcoJ
- 3*“H;~;~~e_olcCj
= +5*GALN
-3*'Hf~~~_,~(q
=
121i Model:
(A1+3)e (N-‘),
0(-p" AI+s:N-a:pa(T)+
GCORUND
y-AlON
(0-‘)a ~*'H:~'~~,AI-~*'H:~~~_N~(c)
+ 83041-
40.87eT
spine1
Model: (Al+‘)1
(AI+‘,Va’)r
(N-‘$-‘)I
+4*GALN
AIN-A&O,-THERMODYNAMIC
“G;;;;;;:?;::(T) - 3*‘H;$‘& + 255386 - k5.28eT “G;;+?f”,C’,“-‘(T)
- 4+0H:$z_Ns(Cj
REASSESSMENT
= +4*GALN
+ 4*GCORUND
- oH;tf:;T,,,
- 4*“Hf~;$&,,1(o)
= +I*GALN
+ 12eGCORUND
- OH;FfL’;fAr
- 4*“H;;;$‘_o,(cj
= +LI*GGAMMA
+ 442813 - 49.25*T
“G’,;+?f;~.$“(T)
FUNCTION GGAMMA : (2198.15
+ 44.954*T + 1.2+T
-.070794Tz+1.4913451*10-9’+981165T-’
(600
&‘-AlON
spine1
Model: (A1+J)l (AI+S,Va0)2 (N-*,O-‘)4 “G$;e;>.$f(T) - 3t”H;~;‘& t 71508.778 - 49.9663eT
- 4*“H;~:$&1(CI
“G$;+::~‘$$*‘(T) - ‘H;z:‘;fA, t 2570309.7 - 1094.0672tT
hAlON
- 4t”H;;f$&NI(Cj
= +4*GALN
= +4+GALN
+ 4*GCORUND
+ lP*GCORUND
spine1
Model: (A1+3)1 (Al+‘)u
(Va’)o.s
(N-SP-‘)~
oG;;$:~~;;z;_,(T) - 2.7*‘H;::‘:TA, t 51323.87 - 20_116+T
- 4*“H;;:$~_Nlco,
= +O.l*GALN
+ l.J*GCORUND
“~~“;;+‘~~~~;~~;_,(T) - 2.7*0H3Tf2;f,A, $ 51323.87 - 20.116+T
- 4t”H:~f$“_ol(cj
= +O.l*GALN
+ l.S*GCORUND
LX-AI
Model: (Al)1 (Va), O’G:;;;;,A’(T)
- OH;::‘&
=
GHSERAL
GHSERAL : (298.15
197
198
P. TABARY AND C. SERVANT
5 2. -
-_
-_ --__
-25
50
_ _ AG . (cation) - _nux. ____
/
I
I
I
I
40
30
20
10
0
mole % AIN Figure 1: Energy of mixing in the anionic (- -) and cationic (- - - -) sub-lattices at 2000°C function of composition of r-AlON spine1 and total energy of mixing (-).
x(A1203)
Figure 2: Gibbs energy of the -y-AlON and qS’-AlON spine1 phases at 2000°C as a function of position.
AIN-A&O,-THERMODYNAMIC
3000
I
I
I
199
REASSESSMENT
I
McCauley and Co&in (1979)
AL XALON [rL+12H VL+ALON cALON+p~lyk
LS
McCauley and C&in
(1983)
_ TALON ~L+ALON
j 2303
“:.,,
‘fL+iZH
I
*L+PlR +L+Y +27R+21R A2621R+ALON Quinn et aL(t994) _ )(ALON Cannard (1988) AAIN QAIN+ALON *AlN+27R
1639
_.. _.... .......__ __.... .. .
012
Willems et aL(1992)
.
. ._.
014
AIN
Figure
3 : Calculated
present
optimization
.
._.. .._.._._........ .._.._....__ Y..
016
018
phase
diagram without
of the pseudo-binary including
1 I
A’2o3
‘Al,O,
(--)
_____ ____
system
the gas phase compared
AIN-A1203
according
to the
with the work of [20] (.....).
200
P. TABARY AND C. SERVANT
2300 McCauley and Corbin (1979)
2200
AL XALON
qL+lZH
G
2100
VL+ALON @LON+polyA and Chin !i LO36McCauley
0
g
WLON
2000
5-
~L+ALON ‘y’L+lPH
z is
)J(L+21 R i-L+*’ +27R+21
E lgoo a> I1800
R
*2lR+ALON Quinn et at.(rsaq #ALON Catward (1988) AAIN @N+ALON
1700
#,UN+27R
1639
Willems et aL(lss2) @ON
1600 0.2
k& AIN
Figure 4 : Detail of Figure 3.
0.4
0.6 ‘Al,O,
0.8
1 .O A’,%
(1983)
AIN-A&O,-THERMODYNAMIC REASSESSMENT
Gas+Liquid
I_ :
2400 -
_/r_
II
2200 0
0.2
I 0.4
\ 0.6
/’
/I
Liquid
I 0.8
: :
1Ya6.‘
li
d w 2300-
: /
2320 5 AIN+ iZ 2315Gas d q 231011ol.s ,E 2 2306-
201
-
!.+ e 22Q5-
-
22QO-
1.0
2286
P” nFi
0
I 0.1
I 0.2
I 0.3
I 0.4
, 0.6
I 0.8
I 0.7
0.
xW203) (b)
Figure 5: a) Calculated phase diagram of the pseudo-binary system AlN-AlsO3 according to t present optimization including the gas phase; b) Detail of Figure 5a.