MATEC Web of Conferences 5, 04032 (2013)
DOI: 10.1051/matecconf/20130504032
c Owned by the authors, published by EDP Sciences, 2013
Thermodynamic assessment of the Pd–Y binary system
S. Kardellass, N. Selhaoui, A. Iddaoudi, M. Ait Amar, R. Karioui, and L. Bouirden
Laboratory of Thermodynamics and Energy (L.T.E), Faculty of science, BP. 8106, University IbnZohr, Agadir,
Morocco
Abstract. The Pd–Y system was critically assessed using the CALPHAD technique. The solution phases (liquid, b.c.c., f.c.c. and
h.c.p.) were modeled using the Redlich–Kister equation. The intermetallic compounds Pd3 Y and PdY, which have homogeneity
ranges, were treated as the formula (Pd, Y)0.75 (Pd, Y)0.25 and (Pd, Y)0.5 (Pd, Y)0.5 by a two-sublattice model with a mutual
substitution of Pd and Y on both sublattices. The optimization was carried out in two steps. In the first treatment, Pd3 Y and
PdY are assumed to be stoichiometric compounds; in the second treatment they are treated by a sublattice model. The parameters
obtained from the first treatment were used as starting values for the second treatment. The calculated phase diagram and the
thermodynamic properties of the system are in satisfactory agreement with the experimental data.
1. INTRODUCTION
The rare earth elements exhibiting a good combination
of magnetic, optical, electrical and thermal properties
have been paid increasing attention and widely used to
prepare new high performance functional materials, such
as permanent magnet, magnetic refrigerant and hydrogen
storage material [1–3]. The CALPHAD technique, which
has been recognized to be an important tool to significantly
reduce time and cost during the development of materials,
can provide a clear guidance for the materials design
[4–6]. In order to develop the thermodynamic database of
the rare earth alloys for reliable predictions of liquidus,
phase fraction, equilibrium and non-equilibrium solidification behavior, etc. The thermodynamic assessment of
the Pd–Y binary system was carried out by means of the
CALPHAD method.
2. REVIEW OF EXPERIMENTAL DATA
The phase diagram of the Pd–Y system was first measured
by Loebich and Raub [7]. They found seven intermetallic
compounds in the Pd–Y system and called them Pd3 Y,
Pd2 Y, Pd5 Y4 , PdY, PdY3 , Pd3 Y2 and Pd2 Y5 , where Pd3 Y,
PdY and Pd5 Y4 melted congruently and Pd3 Y2 , Pd2 Y
and Pd2 Y3 formed by peritectic reactions. Later, Pd5 Y4
was identified to be Pd4 Y3 by Palenzona and Iandelli [8].
Pd7 Y and PdY3 were found to exist by Sanjines-Zeballos
et al. [9] and Takao et al. [10], respectively. The results
obtained have been taken by Massalski [22] to draw a
phase diagram. Kuentzler and Loebich [11] presented a
revised phase diagram and discussed the stability of the
existing ordered structures. The homogeneity range of the
intermetallic compound Pd3 Y and the solubility of Y in
f.c.c.(Pd) were measured by Loebich and Raub [7] and
Harris and Norman [12]. No appreciable solid solubility
of Pd in Y was observed [7]. Loebich and Raub [7]
indicated the presence of polymorphic transformation and
a small range of homogeneity for PdY (51–52 at.% Y).
Considering, however, the subsequent work of Kuentzler
and Loebich [11] and Palenzona and Cirafici [13], the
homogeneity range of PdY should be 50–51 at.% Y and
the maximum melting point attributed to the ideal 50 at.%
Y composition [14].
3. THERMODYNAMIC MODELS
3.1. Pure elements
The Gibbs energy function
Gi (T) =◦ Gi − HiSER (298.15 K)
(1)
(298.15) for the element i (i = Pd, Y) in the phase ϕ (ϕ =
Liquid, HCP A3, BCC A2 and FCC A1) is described by
an equation of the following form:
Gi (T) = a + bT + cT ln T + dT2 + eT3 + fT7
+ gT−1 + hT−9 .
(2)
Where HSER
(298.15 K) is the molar enthalpy of the
i
element i(i = Pd, Y) at 298.15 K in its standard element
reference (SER) state, FCC A1 for Pd and HCP A3 for Y.
In this article, the Gibbs energy functions are taken
from the SGTE compilation of Dinsdale [15].
3.2. Solution phases
The solution phases [(FCC A1) Pd, HCP A3 (αY),
BCC A2 (βY) and liquid] were modeled as substitutional
solutions according to the polynomial Redlich–Kister
model [16]. The Gibbs energy of one mol of formula unit
of phase ϕ is expressed as the sum of the reference part
ref ϕ
G , the ideal part id G ϕ , and the excess part exc G ϕ :
Gϕm = refG ϕ + idG ϕ + excG ϕ .
(3)
As used in the thermo-calc software [17]:
ref
ϕ
G ϕ (T) = (0 GPd (T) − HSER
Pd (298.15 K))xPd
ϕ
+ (0 GY (T) − HSER
Y (298.15 K))xY
(4)
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MATEC Web of Conferences
id
G ϕ = RT (xPd ln xPd + xY ln xY )
(5)
Where R is the gas constant, T the temperature, in Kelvin,
Warning: xPd and xY are the fraction of elements Pd and Y,
respectively.
The excess terms of all the solution phases were
modeled by the Redlich-Kister [16] formula:
exc
ϕ
ϕ
G ϕm (T ) = xPd xY [0 L Pd,Y (T ) + 1 LPd,Y (T )(xPd − xY )
ϕ
+ L Pd,Y (T )(xPd − xY )2 + · · · ]
i
LϕPd,Y (T ) = ai + bi T.
(6)
(7)
ϕ
Where i LPd,Y (T) is the interaction parameter between the
elements Pd and Y, which is evaluated in the presented
work, ai and bi are the coefficients to be optimized.
3.3. Stoichiometric compounds and intermediate
phases
The Gibbs energy of the stoichiometric compounds Ap Bq
is expressed as follows:
0
G A p Bq =
p 0
q 0
GA +
G B + a + bT.
p+q
p+q
(8)
Where 0 G A and 0 G B are the Gibbs energy of the pure
elements Pd and Y, respectively, a and b are parameters
to be determined.
The Pd3 Y (C14 Laves, isotypic with AuCu3 ) and PDY
are treated by a two-sublattice model [18, 19]. The Gibbs
energy function per mole (m) of the formula unit is the
following:
G Pd3Y
m
=
0
0
yPd
yPd
G Pd:Pd + yPd
yY 0 G Pd:Y + yY yPd
G Y:Pd
0
+ yY yY G Y:Y + p RT (yPd Ln yPd + yY Ln yY )
+ p RT (yPd
Ln yPd
+ yY Ln yY )
yY yPd
+ pyPd
n
L Pd,Y:Pd (yPd
− yY )n
n
+ yY
n
n
+ qyPd
yY yPd
n
L Pd:Pd,Y (yPd
− yY )n
n
+
yY
n
L Y:Pd:Y (yPd
−
occupied by element i or j · L i·Pd·Y and L PdY· j are the
interaction parameters between Pd and Y in the second or
first sublattice, when the other sublattice is occupied by
element i or j. 0 Gi, j , Li:Pd,Y and LPd,Y: j were evaluated in
the present work.
4. RESULTS AND DISCUSSIONS
L Pd,Y:Y (yPd
− yY )n
Figure 1. Comparison of the Pd-Y calculated phase diagram with
the experimental data. (b) Enlarged section of (Fig. 1).
yY )n
n
G PdY
= yPd 0 G Pd:Y + yY:Y 0 G Y:Y + RT (yPd Ln yPd )
m
+ yY Ln yY )
n
L Pd,Y:Y (yPd − yY )n
+ yY
n
Where yi and y j are the site fraction of component i and
j(i, j = Pd, Y) located on sublattice I and II, respectively,
and the parameter 0 Gi: j represents the Gibbs free energy
of the compound phase when the two sublattices are
The evaluation of the phase diagram was carried out with
the computer Thermo-Calcsoftoware [17] which makes
it possible to optimize the formation Gibbs energies of
the system phases by means of the least squares method
using simultaneously thermodynamic and phase diagram
data. The calculated phase diagram is shown in Fig. 1. It is
compared with the numerous experimental data in Fig. 1.
A good agreement is noted.
All the parameters were evaluated and listed in Table 1.
For the intermetallic compounds Pd3 Y, Pd4 Y3 , PdY ht, the
coefficients a and b in Eq. (7), were adjusted according to
the enthalpiesof formation measured by [22].
The calculated invariant equilibria in the Pd-Y system
are listed in Table 2, where the largest uncertainty is
about 4 ◦ C in the invariant temperature of the reaction
Liq ↔ Pd2 Y5 + Pd2 Y3 In the reaction Liq ↔ Pd2 Y5 +
Pd2 Y3 , the uncertainty in the invariant temperature is
about 13 ◦ C [11]. In view of the estimated experimental
04032-p.2
REMCES XII
Table 1. The optimized thermodynamic parameters of the Pd-Y system.
Phase
Liquid
Thermodynamic models
(Pd,Y)1
BCC A2
HCP A3
FCC A1
Pd7 Y
(Pd,Y)1 (Va)3
(Pd,Y)1 (Va)5
(Pd)0.875 :(Y)0.125
Parameters in SI
L = −344376.073 + 21.686T
1 liq
L = −209832.431 + 54.045T
No excess term
No excess term
0 FCC A1
L
= −640143 + 17.95T
7Y
298 FCC A1
GPd
HPd
− 0.125 298 HYHCP A3
Pd:Y − 0.875
0 liq
FCC A1
= 0.875GPd
+ 0.125GYHCP A3 − 54709 + 10.815T
Pd3 Y
(Pd)0.75 :(Y)0.25
0.75
GPd:pd
Pd
Y0.25
FCC A1
− HPd
= 80000 + GHSERPd
Pd
Y0.25
− 0.75HPd
0.75
GPd:Y
FCCA1
− 0.25 HYHCP A3
=+ 0.25 GHSERPd + 0.75 GHSERY − 88887.7
+ 6.135T
Pd0.75 Y0.25
GY:Pd
FCCA1
− 0.75HPd
− 0.25HYHCP A3
=+ 75000 + 0.75GHSERPd + 0.25 GHSERY
+ 88887.7 − 6.135T
Pd
Y
GY:Y0.75 0.25
Pd2 Y
(Pd)0.667 :(Y)0.333
Pd2 Y
GPd·Y
Pd3 Y2 bt
FCCA1
− 0.6HPd
− 0.4HYHCP A3
FCC A1
= 0.6HPd
+ 0.4HYHCP A3 − 90425 + 2.08T
(Pd)0.6 :(Y)0.4
(Pd)0.571 :(Y)0.429
= −103331.7 − 0.86T
FCC A1
=+ 0.667 298 HPd
+ 0.333 298 HYHCP A3 − 90302.78 + 3.7T
(Pd)0.6 :(Y)0.4
Pd Y bt
Pd4 Y3
= 75000 + GHSERY
FCC A1
− 0.667 298 HPd
− 0.333 298 HYHCP A3
3 2
GPd·Y
Pd3 Y2 ht
−
0 Pd0.75 Y0.25
LPd:Y,Pd
HYHCP A3
Pd Y ht
3 2
GPd·Y
FCCA1
− 0.6HPd
− 0.4HYHCP A3
FCC A1
= 0.6GPd
+ 0.4HYHCP A3 − 90107.45 + 1.84T
PdY bt
(Pd)0.5 :(Y)0.5
Pd Y
HCPA3
FCCA1
4 3
GPd·Y
− 0.571HPd
− 0.429HY
FCC A1
= 0.571GPd
+ 0.429GYHCP A3 − 90509 + 1.493T
Pd
0.5
GPd·Y
Y0.5
FCCA1
− 0.5HPd
HCPA3
− 0.5HY
=+ 0.5 GHSERPd + 0.5 GHSERY − 91389.8748
+ 3.16T
PdY ht
(Pd)0.5 :(Y)0.5
Pd Y
GY·Y0.5 0.5
− HYHCP A3 = 153095.5 + GHSERY
0 Pd0.5 Y0.5
LPd·Y:Y
Pd0.5 Y0.5
GPd·Y
= −141542.47
FCCA1
− 0.5HPd
− 0.5HYHCP A3
=+ 0.5 GHSERPd + 0.5 GHSERY − 91389.8743
Pd2 Y3
(Pd)0.4 :(Y)0.6
Pd2 Y5
(Pd)0.286 :(Y)0.714
+3.16T
Pd
GY:Y0.75
Y0.25
0 Pd0.5 Y0.5
LPd,Y:Y
PdY3
(Pd)0.25 :(Y)0.75
Pd2 Y3
GPd·Y
− HYHCP A3 =+ 183383.5 − 7.7T + GHSERY
= −162924.4
FCCA1
− 0.4HPd
− 0.6HYHCP A3
FCC A1
= 0.4GPd
+ 0.6GYHCP A3 − 81146.17 + 7.23T
Pd Y
FCCA1
2 5
GPd:Y
− 0.286HPd
− 0.714HYHCP A3
FCC A1
= 0.286GPd
+ 0.714GYHCP A3 − 57513.8 + 3.47T
PdY
FCCA1
GPd:Y3 − 0.25HPd
HCPA3
− 0.75HY
FCC A1
= 0.25GPd
+ 0.75GYHCP A3 − 50238.5 + 2.914T
04032-p.3
MATEC Web of Conferences
Table 2. Invariant reactions in the Pd-Y system.
Reaction
Present work
T(K) X(Y)
Liq + BCC A2 ↔ HCP A3 1751 0.980
1185 0.746
Liq + HCP A3 ↔ PdY3
Liq ↔ Pd2 Y5 + PdY3
1183 0.734
Liq ↔ Pd2 Y5
1187
Liq ↔ Pd2 Y5 + Pd2 Y5
1178 0.685
Liq + PdY ht ↔ Pd2 Y5
1233 0.649
Liq ↔ PdY ht
1723
Liq ↔ PdY ht + Pd4 Y3
1658 0.453
Liq ↔ Pd4 Y3
1683
Liq + Pd4 Y3 ↔ Pd3 Y2− ht
1546 0.376
Liq ↔ Pd3 Y2− ht + Pd2 Y
1519 0.367
Liq + Pd3 Y ↔ Pd2 Y
1578 0.342
Liq ↔ Pd3 Y
1973
Liq ↔ Pd3 Y + FCC A1
1478 0.147
FCC
0.132
Pd3Y
0.225
FCC A1 + Pd2 Y ↔ Pd7 Y
FCC
777 0.101
Pd3Y
0.224
Pd3 Y2− ht ↔ Pd3 Y2− bt
1318 0.369
PdY− ht + Pd2 Y3 ↔ PdY− b 1171
−
PdY− ht ↔ Pd4 Y3 + PdY− b 1149
−
Ref [7]
T(K) X(Y)
1751 0.980
1181 0.745
1168 0.730
1188
−
1176 0.700
1233 0.660
1723 0.500
1658 0.470
1683
−
1547 0.380
1518 0.370
1578 0.340
1973 0.250
1478 0.150
Figure 3. Calculated Pd-Y phase diagram when the liquid phase
is suspended.
777
0.105
1318
1173
1143
−
0.520
0.510
Figure 4. Gibbs energy of mixing of the liquid phase at different
temperature.
at high temperatures. A terminal solid solutions and a
two-phase domain existing between them are found to be
stable (Fig. 3).
Figure 4 shows the evolutions of Gibbs energy for
the liquid phase asa function of temperature (T) with our
optimization, when T is increasing up to 6000 K, the Gibbs
energyfor the liquid phase decreases.
The reference states were Pd and Y liquids.
Figure 2. Calculated and measured enthalpies of formation of the
intermetallic compounds.
5. CONCLUSIONS
errors (about 1–2 at. %), all experimental invariant reaction
compositions in the Pd–Y system are well reproduced.
The assessed enthalpies of formation of the intermetallic compounds compared with experimental measurements
are plotted in Fig. 2. The calculated enthalpies agree well
with the experimental data [20–22].
As mentioned by [23] in order to check that the
optimized thermodynamic parameters of the intermetallic
compounds are satisfactory, we verified that when the
liquid phase is suspended during the calculation of the
Pd-Y phase diagram, the stoichiometric phases disappear
All of the experimental phase equilibria and thermodynamic data of the Pd-Y system from the available
literature have been critically evaluated. Within the
regime of CALPHAD technique, the Redlich–Kister
polynomial, the sublattice-compound energy model and
the temperature dependant expression were adopted to
describe the solution phases, the non-stoichiometric phases
and the stoichiometric compounds, respectively. A set
of self-consistent thermodynamic parameters has been
obtained, which can reproduce satisfactorily most of the
experimental data on thermodynamic properties and phase
diagram within experimental uncertainties.
04032-p.4
REMCES XII
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