Thermodynamic Modeling of the Al-Ti-V Ternary System

Abstract

The sub-binary systems Al-Ti, Ti-V, and Al-V are reviewed and adopted from the previous assessments, the thermodynamic analysis of the Al-Ti-V ternary system is performed by the CALPHAD approach, and a set of self-consistent thermodynamic parameters of the ternary system are obtained. Furthermore, the isothermal sections of this system at 1073 K, 1173 K, 1273 K, 1373 K, and 1473 K (800 °C, 900 °C, 1000 °C, 1100 °C, and 1200 °C) and the ternary invariant equilibria are calculated and compared with the corresponding experimental data, and all are in good agreement with most of the experimental results. Thus, the optimized thermodynamic parameters in this study may provide more accurate guidance to develop the new alloys involving it.

Full text

Thermodynamic Modeling of the Al-Ti-V Ternary System
XIONGGANG LU, NA GUI, AITAO QIU, GUANGXIN WU, and CHONGHE LI
The sub-binary systems Al-Ti, Ti-V, and Al-V are reviewed and adopted from the previous
assessments, the thermodynamic analysis of the Al-Ti-V ternary system is performed by the
CALPHAD approach, and a set of self-consistent thermodynamic parameters of the ternary
system are obtained. Furthermore, the isothermal sections of this system at 1073 K, 1173 K,
1273 K, 1373 K, and 1473 K (800 C, 900 C, 1000 C, 1100 C, and 1200 C) and the ternary
invariant equilibria are calculated and compared with the corresponding experimental data, and
all are in good agreement with most of the experimental results. Thus, the optimized thermo-
dynamic parameters in this study may provide more accurate guidance to develop the new alloys
involving it.
DOI: 10.1007/s11661-014-2317-y
The Minerals, Metals & Materials Society and ASM International 2014
I. INTRODUCTION
THE Ti-based alloys with their high strength-to-
weight ratio, good toughness, and corrosion resistance
have been extensively used in aerospace engineering and
processing equipment. The compound TiAl typically has
a high-temperature property with relatively low ductility
and formability;
[1,2]
therefore, the addition of a third
element, vanadium, is needed to effectively improve the
room-temperature ductility of TiAl and Ti
3
Al interme-
tallic alloys.
[3]
In addition, the most widely used
titanium alloy in the world is Ti6Al4V. As early as the
1950s, the Al-Ti-V system was investigated,
[4–6]
and the
previous studies were mainly focused on the Ti-rich
corner.
[5,7]
Today, several thermodynamic descriptions
of the Al-Ti-V system are available.
[8–11]
For example,
Hayes
[8]
assessed the phase equilibria of the Al-Ti-V
ternary system in 1995, but there was disputation about
the phase relationship of the Al-Ti-V ternary system at
high temperature, and the thermodynamic database was
not published. Further thermodynamic evaluation was
also done by Zhang
[9]
in 1997; afterward, the sub-binary
(Al-Ti, Ti-V, and Al-V) parameters were updated, and
there are some differences between these
[8,9]
and the
latest ones. Recently, the thermodynamic optimization
of the ordered B2 phase in the Al-Ti-V ternary systems
was carried out by Wang et al.,
[10]
and Kostov and
Z
ˇivkovic
´
[11]
calculated the enthalpies of mixing of the
liquid phase and the integral excess Gibbs energy of the
Al-Ti-V system at 2200 K (1927 C).
The purpose of this study is to obtain a thermody-
namic description for the Al-Ti-V ternary system. First,
the available thermodynamic data for three binary
systems (Al-Ti, Ti-V, and Al-V)
[12–14]
are reviewed.
Then, the thermodynamic parameters of the Al-Ti-V
system are optimized, including the ternary interaction
parameters of bcc_A2, hcp, liquid, and some interaction
parameters involving the third element (for example, the
interaction between the elements Al and V in the TiAl
phase). Finally, several phase diagrams from 1073 K to
1473 K (800 C to 1200 C) and the invariant reactions
in this ternary system are calculated and compared to
the experimental results.
II. REVIEW OF LITERATURE INFORMATION
A. Binary Systems
1. Al-Ti system
The Al-Ti system consists of liquid (L), hcp(a),
bcc_A2(b), bcc_B2, fcc, Ti
3
Al(a2), TiAl(c), Ti
3
Al
5
,Ti
2
Al
5
,
TiAl
2
,Ti
5
Al
11
, the high-temperature phase H_TiAl
3
(D0
22
,
TiAl
3
type), and the low-temperature phase L_TiAl
3
.
Several thermodynamic descriptions of the Al-Ti
system are available now; for example, Okamoto,
[15]
Kattner et al.,
[16]
and Zhang et al.
[17]
studied the Al-Ti
system. Ohnuma et al.
[18]
confirmed the presence of
A2/B2, the second-order transition in the bcc phase, by
means of differential scanning calorimetry and extrap-
olation from Al-Ti-X (X = Cr, Fe) ternary systems.
Braun and Ellner
[19]
reported the transformation tem-
perature from H_TiAl
3
to L_TiAl
3
was between 1008 K
and 1223 K (735 C and 950 C). However, the results
assessed by Witusiewicz et al.
[12]
were in good agreement
with the latest experimental results,
[20]
in which TiAl
3
was treated as (Al,Ti)
0.75
(Al,Ti)
0.25
. Thus, Witusiewicz’s
thermodynamic parameters for the Al-Ti system are
adopted in our work. Figure 1shows the calculated
Al-Ti binary phase diagram.
2. Ti-V system
The Ti-V system is a relatively simple one; only three
phases exist: liquid (L), hcp (a), and bcc_A2 (b), all are
XIONGGANG LU and CHONGHE LI, Professors, are with the
Shanghai Key Laboratory of Modern Metallurgy & Materials Proces-
sing, Shanghai University, Shanghai 200072, P.R. China, and also with
the Shanghai Engineering Technology Research Center of Special
Casting, Shanghai, P.R. China. Contact e-mail: chli@staff.shu.edu.cn
NA GUI and AITAO QIU, Master Candidates, and GUANGXIN
WU, Associate Professor, are with the Shanghai Key Laboratory of
Modern Metallurgy & Materials Processing, Shanghai University.
Manuscript submitted August 12, 2013.
METALLURGICAL AND MATERIALS TRANSACTIONS A

disordered solution phases. This system was assessed
earlier by Kaufman and Bernstein
[21]
and Murray.
[22]
The latest assessment of the Ti-V binary phase diagram
was published in 2002 by Ghosh.
[13]
Ghosh’s thermo-
dynamic parameters for the Ti-V system are adopted in
this work. Figure 2is the phase diagram of the Ti-V
system.
3. Al-V system
The Al-V system consists of liquid (L), fcc, bcc_A2
(b), Al
21
V
2
,Al
45
V
7
,Al
23
V
4,
Al
3
V, and Al
8
V
5.
The first
assessment of this system was reported by Murray.
[23]
Later, based on the crystal structure data, the param-
eters for the intermediate phase Al
8
V
5
were reassessed
by Gong et al.,
[14]
who used a sublattice model, denoted
by Al
0.4616
(Al,V)
0.1538
(Al,V)
0.2308
V
0.1538
, to model the
Al
8
V
5
phase. The latest experimental results reported by
Richter and Ipser
[24]
can be reproduced well by Gong’s
result, so her thermodynamic parameters for the Al-V
system are used in this work. Figure 3shows the phase
diagram of the Al-V system.
B. Al-Ti-V Ternary System
The Al-Ti-V ternary phase diagram was investigated
by several groups; however, no new ternary phase was
reported until now. In the early 1960s, Farrar and
Margolin
[7]
investigated the Ti-rich region from 873 K
to 1673 K (600 C to 1400 C) by X-ray diffraction and
metallographic methods; they considered that the phase
Ti
3
Al(a
2
) decomposed easily and formed eutectoid
products Ti
2
Al and hcp(a) below 973 K (700 C).
However, the work of Hashimoto et al.
[25]
was signif-
icantly different from Farrar and Margolin;
[7]
the former
reported that phase Ti
3
Al(a
2
) and Ti
2
Al cannot coexist.
In addition, Hashimoto et al.
[25]
also reconstructed the
two isothermal sections of the system at 1073 K and
1273 K (800 C and 1000 C), employing scanning
electron microscopy (SEM), X-ray diffraction (XRD),
and electron microprobe analysis (EPMA). According
to their studies, 2 three-phase regions, TiAl(c)+
(Ti,V)Al
3
(n)+band (Ti,V)Al
3
(n)+Al
8
V
5
(r)+b, were
first proposed. Paruchuri and Massalski
[26]
studied the
annealed and as-cast alloys of the isothermal section at
1173 K (900 C) and attempted to depict the liquidus
projection by using optical metallographic analysis,
XRD, SEM, and energy dispersive X-ray analysis
(EDXA); the result was consistent with the phase
relationships reported by Hashimoto et al.
[25]
Chaudh-
ury and Rack
[27]
re-examined five Ti-rich alloys at
elevated temperatures of 1073 K, 1273 K, and 1373 K
(800 C, 1000 C, and 1100 C) using high-temperature
X-ray diffraction, in view of the tiny content of the
interstitial element including O and N.
Weight Fraction Al
Temperatrue,K
AlTi
β
L
α
α
2
α
γ
Ti2Al5
Ti3Al5
TiAl2
H_TiAl3
L_TiA l3fcc
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
300
1150
2000
Fig. 1—Al-Ti system assessed by Witusiewicz et al.
[12]
.
Weight Fraction V
Temperature,K
VTi
L
α
β
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
600
1400
2200
Fig. 2—Ti-V system assessed by Ghosh
[13]
.
Weight Fraction V
Temperature,K
VAl
L
fcc
β
Al8V
5
Al3V
Al21 V
2
Al45 V
7
Al23 V
4
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
300
1250
2200
Fig. 3—Al-V system assessed by Gong et al.
[14]
.
METALLURGICAL AND MATERIALS TRANSACTIONS A

Later, Ahmed and Flower
[28]
established isothermal
sections of the AL-Ti-V ternary system at 873 K, 973 K,
1073 K, 1173 K, and 1473 K (600 C, 700 C, 800 C,
900 C, and 1200 C) by means of optical microscopy,
SEM, transmission electron microscopy (TEM), XRD,
and EDXA. They first evidenced that the A2/B2
transition in the bcc phase existed in the ternary system
Al-Ti-V experimentally and then constructed a large
region of bcc_B2 phase at isothermal sections. Further-
more, Ahmed and Flower reported that at 1473 K
(1200 C) or above, the assumed one-phase (Ti,V)Al
3
(n)
can divide into two different phases.
Zhang
[9]
carried out the systematic thermodynamic
evaluation of the Al-Ti-V ternary system using some
necessary experiments. In her study, experiments of the
Al-Ti-V ternary system at x
Ti
<0.7 were investigated.
The phase equilibria among a
2
,b, and cat 1273 K and
1373 K (1000 C and 1100 C) were established by
electron-probe microanalysis. Only one three-phase
field, Ti
3
Al(a
2
)+b+TiAl(c), was detected at 1373 K
(1100 C). At 1273 K (1000 C), the three-phase field
b+Al
8
V
5
+(Ti,V)Al
3
(n) was also found.
In 2006, Zhang and Du
[29]
determined the phase
relationship of the Al-Ti-V system at 1373 K (1100 C)
through equilibrate alloys. Six samples of the Al-Ti-V
system were prepared by melting the starting materials
in a vacuum arc furnace and annealing at 1373 K
(1100 C) for 240 hours. Water-quenched samples were
analyzed by XRD, SEM, and EDS. The positions of five
phase fields, Ti
3
Al(a
2
)+b, TiAl(c)+b, (Ti,V)Al
3
+
Al
8
V
5
+b,Ti
3
Al(a
2
)+TiAl(c), and Ti
3
Al(a
2
)+TiAl(c)+
b, were obtained. It is obvious that the experimental
data reported by Zhang and Du
[29]
at 1373 K (1100 C)
are credible due to the prolonged annealing treatment of
samples.
Recently, Chang and Muddle
[30]
and Shao et al.
[31,32]
detected a new phase named H
2
in the alloys Al
62
Ti
10
V
28
and Al
55
Ti
10
V
35
after chill casting and homogenization
at 1523 K (1250 C); its crystal structure is similar to the
a
2
-Ti
3
Al phase. However, the specific composition of the
H
2
phase is still not established. Therefore, this phase is
not taken into account in this assessment.
III. THERMODYNAMIC MODELING AND
PARAMETERS OPTIMIZATION
A. Unary Phases
The Gibbs free energy function for the element i (i =
Al, Ti, and V) in the phase Ø (Ø = liquid, bcc, fcc, etc.)
is taken from the SGTE compilation of Dinsdale.
[33]
The
Gibbs free energy function for the unary phases is
described by Eq. [1]:
0G/
iðTÞ¼aþbT þcT ln TþdT2þe=Tþ... ½1
B. Solution Phases
In the Al-Ti-V ternary system, there exist several
solution phases, such as liquid, bcc, and hcp. Their
Gibbs free energies are described by the following
expression:
G[¼X
n
i¼1
x0
iG[
iþRTX
n
i¼1
xilnðxiÞþEG[;½2
where x
i
is the mole fraction of the component i,0G[
i
is the Gibbs free energy of the pure component iwith
structure Ø, Ris the gas constant, and Tis the abso-
lute temperature. EG[is the excess Gibbs free energy
of the phase, which is defined as
GE¼X
n
i;j¼1i6¼jðÞ
xixjX
m
k¼0
Lk
i;jðÞXiXj

k
þX
n
i;j;l¼1i6¼j6¼lðÞ
xixjxlX
k¼i;j;l
LkVk;½3
where the first term represents the binary interaction
terms and the second one represents the ternary inter-
actions. The Lk
i;jðÞ
term is the binary interaction param-
eter for the i-jbinary, and L
k
is the ternary interaction
parameter, which can be obtained by optimization
using available experimental data. V
k
is defined as
Vk¼xkþ
1P
p¼i;j;l
xp
n
C. Stoichiometric Compound Phases
The four binary compounds Ti
3
Al
5
,Al
21
V
2
,Al
45
V
7
,
and Al
23
V
4
are considered as stoichiometric compound
phases taken from the binary system.
[12,14]
In the ternary
system, there is no report of the third element dissolving
in these phases. The Gibbs energy can be expressed as
follows:
G¼X
n
i¼1
xiGo;/
iþaþbT ½4
where a+bT is the standard state of the Gibbs energy
of the stoichiometric phase.
D. Compound Energy Formalism Phases
In the Al-Ti-V ternary system, there exist many
intermediate phases, including Ti
3
Al(a
2
), TiAl(c), TiAl
2
,
Ti
2
Al
5
, H_TiAl
3
, (Ti,V)Al
3
(n), and Al
8
V
5
, which are
modeled using compound energy formalism (CEF).
[34]
Because there is no solubility information reported in
the ternary system, the phases Ti
2
Al
5
, TiAl
2
,and
H_TiAl
3
are modeled according to the models employed
in their binary system.
[12]
Several researchers, Erschbaumer et al.,
[35]
Wolf
et al.,
[36]
and Hao et al.,
[37]
who studied the atom site
preference in phase TiAl, found that element V substi-
tutes for both Ti and Al, so TiAl(c) is modeled as
METALLURGICAL AND MATERIALS TRANSACTIONS A

(Al,Ti,V)
0.5
(Al,Ti,V)
0.5
in the ternary system; its Gibbs
free energy can be expressed by Eq. [5]:
GTiAl ¼y0
Tiy00
TiGTiAl
Ti:Ti þy0
Aly00
AlGTiAl
Al:Al þy0
Vy00
VGTiAl
V:V
þy0
Tiy00
AlGTiAl
Ti:Al þy0
Tiy00
VGTiAl
Ti:V þy0
Aly00
VGTiAl
Al:V
þy0
Aly00
TiGTiAl
Al:Ti þy0
Vy00
AlGTiAl
V:Al þy0
Vy00
TiGTiAl
V:Ti
þ0:5RTðy0
Ti ln y0
Ti þy0
Al ln y0
Al þy0
Vln y0
VÞ
þ0:5RTðy00
Ti ln y00
Ti þy00
Al ln y00
Al þy00
Vln y00
VÞ
þy0
Aly0
Tiy00
Al½0LTiAl
Al;Ti:Al þðy0
Al y0
TiÞ1LTiAl
Al;Ti:Al
þðy0
Al y0
TiÞ22LTiAl
Al;Ti:Alþy0
Aly00
Aly00
Ti½0LTiAl
Al:Al;Ti
þðy00
Al y00
TiÞ1LTiAl
Al:Al;Ti þðy00
Al y00
TiÞ22LTiAl
Al:Al;Ti
þy0
Aly0
Tiy00
Ti
0LTiAl
Al;Ti:Ti þy0
Tiy00
Aly00
Ti
0LTiAl
Ti:Al;Ti
þy0
Vy00
Aly00
Ti
0LTiAl
V:Al;Ti þy0
Aly0
Vy00
Al
0LTiAl
Al;V:Al
þy0
Tiy0
Vy00
Al
0LTiAl
Ti;V:Al þy0
Aly0
Tiy0
Vy00
Al
0LTiAl
Al;Ti;V:Al
½5
where the parameters y¢
Al
,y¢
Ti
, and y¢
V
represent the site
fractions of Al, Ti, and V on the first sublattice,
respectively, and y¢¢
Al
,y¢¢
Ti
,andy¢¢
V
represent the site
fractions of Al, Ti, and V on the second sublattice,
respectively. The parameterG;
Ti:Aldenotes the Gibb free
energy of Ti
0.5
Al
0.5
. The terms0LAl;Ti:Al,0LAl:Al;Ti ,and
1LAl:Al;Tirepresent the ith interaction parameters, which
are functions of temperature.
It is reported by Hao et al.
[37]
and Yang et al.
[38]
that
the element V substitutes exclusively for Ti in the phase
Ti
3
Al(a
2
). Its model is (Al,Ti,V)
0.75
(Al,Ti)
0.25
in the
ternary system. By extending the binary models of
(Al,Ti)
0.75
(Al,Ti)
0.25
, the Gibbs free energy of the
Ti
3
Al(a
2
) can be written as:
GTi3Al ¼y0
Tiy00
TiGTi3Al
Ti:Ti þy0
Aly00
AlGTi3Al
Al:Al þy0
Aly00
TiGTi3Al
Al:Ti
þy0
Tiy00
AlGTi3Al
Ti:Al þy0
Vy00
TiGTi3Al
V:Ti þy0
Vy00
AlGTi3Al
V:Al
þ0:75RTðy0
Ti ln y0
Ti þy0
Al ln y0
Al þy0
Vln y0
VÞ
þ0:25RTðy00
Ti ln y00
Ti þy00
Al ln y00
AlÞ
þy0
Aly0
Tiy00
Al
0LTi3Al
Al;Ti:Al þy0
Tiy00
Aly00
Ti
0LTi3Al
Ti:Al;Ti
þy0
Tiy0
Vy00
Al
0LTi3Al
Ti;V:Al þy0
Aly0
Tiy0
Vy00
Al
0LTi3Al
Al;Ti;V:Al
½6
Several investigators
[25,26,28]
reported that phases
TiAl
3
and VAl
3
can be judged as one phase (Ti,V)Al
3
due to the continuous solid solutions existing between
them within a certain range of homogeneity. Thus, the
phases L_TiAl
3
and VAl
3
are dealt with as one phase
(Ti,V)Al
3
with model (Al,Ti)
0.75
(Al,Ti,V)
0.25
in the
present work. The phase’s Gibbs energy can be
described by the following expression:
GTiVAl3¼y0
Tiy00
AlGTiVAl3
Ti:Al þy0
Tiy00
TiGTiVAl3
Ti:Ti þy0
Tiy00
VGTiVAl3
Ti:V
þy0
Aly00
AlGTiVAl3
Al:Al þy0
Aly00
TiGTiVAl3
Al:Ti þy0
Aly00
VGTiVAl3
Al:V
þ0:75RTðy0
Al ln y0
Al þy0
Ti ln y0
TiÞ
þ0:25RTðy00
Al ln y00
Al þy00
Vln y00
Vþy00
Ti ln y00
TiÞ
þy0
Aly0
Tiy00
Al
0LTiVAl3
Al;Ti:Al þy0
Aly00
Aly00
Ti
0LTiVAl3
Al:Al;Ti
þy0
Aly0
Tiy00
Ti
0LTiVAl3
Al;Ti:Ti þy0
Tiy0
Aly0
Ti
0LTiVAl3
Ti:Al;Ti
þy0
Aly00
Tiy00
V
0LTiVAl3
Al;Ti:V þy00
Ti y00
V

1LTiVAl3
Al;Ti:V
hi
½7
By means of SEM and X-ray analysis, Hashimoto
et al.
[25]
suggested that phase Al
8
V
5
can dissolve a small
amount (1 to 5 wt pct) of Ti atom at a series of
experimental isothermal sections. Based on these results,
phase Al
8
V
5
is taken as Al
0.4616
(Al,Ti,V)
0.1538
(Al,Ti,V)
0.2308
V
0.1538
in the ternary. The following
expression gives the Gibbs energy of the phase Al
8
V
5
used in this study:
GAl8V5¼y0
Aly00
Aly000
Vy0000
VGAl8V5
Al:Al:V:V þy0
Aly00
Aly000
Aly0000
VGAl8V5
Al:Al:Al:V
þy0
Aly00
Vy000
Vy0000
VGAl8V5
Al:V:V:V þy0
Aly00
Vy000
Aly0000
VGAl8V5
Al:V:Al:V
þy0
Aly00
Aly000
Tiy0000
VGAl8V5
Al:Al:Ti:V þy0
Aly00
Vy000
Tiy0000
VGAl8V5
Al:V:Ti:V
þy0
Aly00
Tiy000
Tiy0000
VGAl8V5
Al:Ti:Ti:V þy0
Aly00
Tiy000
Vy0000
VGAl8V5
Al:Ti:V:V
þy0
Aly00
VGAl8V5
Al:Ti:Al:V þ0:4616RTy0
Al ln y0
Al
þ0:1538RTðy00
Al ln y00
Al þy00
Vln y00
VÞ
þ0:2308ðy000
Al ln y000
Al þy000
Vln y000
VÞ
þ0:1538RTy00000
Vln y00000
V
þy0
Aly00
Aly000
Aly0000
Vy00000
V
0LAl8V5
Al:Al:Al;V:V
þy0
Aly00
Vy000
Aly0000
Vy00000
V
0LAl8V5
Al:V:Al;V:V
þy0
Aly00
Aly00
Vy000
Aly00000
V
0LAl8V5
Al:Al;V:Al:V
þy0
Aly00
Aly00
Vy000
Vy0000
V
0LAl8V5
Al:Al;V:V:V
þy0
Aly00
Aly000
Vy000
Tiy0000
V
0LAl8V5
Al:Al:V;Ti:V ½8
E. Optimization of Thermodynamic Parameters
The ternary thermodynamic parameters of all the
phases listed in Table Iare optimized by using the Pan
optimizer included in the Software Pandat (Compu-
Therm LLC, Wisconsin, USA), which is a C/C++
software package designed for evaluating thermody-
namic, kinetic, and thermophysical model parameters
from experimental measurements. The optimization is
conducted until the sum of the squares of the errors
between the calculated and the experimental data and
the phase equilibria is minimized; then, the improved
METALLURGICAL AND MATERIALS TRANSACTIONS A

thermodynamic descriptions of the Al-Ti-V system can
be obtained.
This procedure can be conducted as follows. First, the
ternary interaction parameters of liquid, bcc, and hcp
are calculated; second, the interaction parameters
involving the third element in TiAl(c) and Ti
3
Al(a
2
)
are optimized. Finally, the thermodynamic parameters
of (Ti,V)Al
3
(n) and Al
8
V
5
(r) are optimized. During the
optimization process, the experimental data on each
phase field and tie-lines at 1073 K and 1173 K (800 C
and 900 C) by Reference 28 are assigned a weight of 2.
Data on each phase field, tie-lines at 1073 K and 1273 K
(800 C and 1000 C) measured by Reference 25,at
1373 K (1100 C) detected by References 9and 29 as
well as the solubility of Ti in Al
8
V
5
at 1073 K (800 C)
measured by Reference 25, and at 1173 K (900 C)
measured by Reference 28, were given a weight of 1.5.
Other data used a weight of 1.
IV. RESULTS AND DISCUSSION
The calculated isothermal sections at 1073 K, 1173 K,
1273 K, and 1373 K (800 C, 900 C, 1000 C, and
Table I. Optimized Thermodynamic Parameters of the Al-Ti-V System
Phases Models Parameters
L, liquid (Al,Ti,V) 0Lliquid
Al;Ti;V¼550;000
1Lliquid
Al;Ti;V¼50;000
2Lliquid
Al;Ti;V¼390;000
b, bcc_A2 (Al,Ti,V)
0.25
(Va)
0.75
0Lbcc A2
Al;Ti;V¼7315 100T
1Lbcc A2
Al;Ti;V¼113;926 þ40T
2Lbcc A2
Al;Ti;V¼75;972:5150T
a, hcp (Al,Ti,V)
0.67
(Va)
0.33
0Lhcp
Al;Ti;V¼0
1Lhcp
Al;Ti;V¼206;074 40T
2Lhcp
Al;Ti;V¼0
c, TiAl (Al,Ti,V)
0.5
(Al,Ti,V)
0.5
0GTiAl
V:Al ¼0:50Gfcc
Vþ0:50Gfcc
Al 15;000
0GTiAl
Al:V ¼0:50Gfcc
Al þ0:50Gfcc
V15;000
0GTiAl
V:Ti ¼0:50Gfcc
Vþ0:50Gfcc
Ti
0GTiAl
V:V ¼0Gfcc
V
0GTiAl
Ti:V ¼0:50Gfcc
Ti þ0:50Gfcc
V
0LTiAl
V:Al;Ti ¼109;815 þ100T
0LTiAl
Al;V:Al ¼22;500
0LTiAl
Ti;V:Al ¼19;037 20T
0LTiAl
Al;Ti;V:Al ¼150;000
a
2,
Ti
3
Al (Al,Ti,V)
0.75
(Al,Ti)
0.25
0GTi3Al
V:Al ¼0:750Ghcp
Vþ0:250Ghcp
Al 31;048:625 þ7:5T
0GTi3Al
V:Ti ¼0:750Ghcp
Vþ0:250Ghcp
Ti þ22;500
0LTi3Al
Ti;V:Al ¼10;100:6875 3:75T
0LTi3Al
Al;Ti;V:Al ¼62;500
r,Al
8
V
5
Al
0.4616
(Al,Ti,V)
0.1538
(Al,Ti,V)
0.2308
V
0.1538
0GAl8V5
Al:Al:Ti:V ¼0:61540Gfcc
Al þ0:23080Ghcp
Ti þ0:15380Gbcc
V
0GAl8V5
Al:V:Ti:V ¼0:46160Gfcc
Al þ0:23080Ghcp
Ti þ0:30760Gbcc
V
0GAl8V5
Al:Ti:Ti:V ¼0:46160Gfcc
Al þ0:38460Ghcp
Ti þ0:15380Gbcc
V
0GAl8V5
Al:Ti:V:V ¼0:46160Gfcc
Al þ0:15380Ghcp
Ti þ0:38460Gbcc
V
0GAl8V5
Al:Ti:Al:V ¼0:69240Gfcc
Al þ0:15380Ghcp
Ti þ0:15380Gbcc
V
0LAl8V5
Al:Al:V;Ti:V ¼4798:536:1538T
n, (Ti,V)Al
3
(Al,Ti)
0.75
(Al,Ti,V)
0.25
0GTiVAl3
Ti:V ¼0:750Ghcp
Ti þ0:250Gbcc
V
0LTiVAl3
Al:Ti;V¼15;062:95 7T
1LTiVAl3
Al:Ti;V¼10;000
METALLURGICAL AND MATERIALS TRANSACTIONS A

1100 C) with experimental data including tie-lines and
tie-triangles from the mentioned References 9,25,28,
and 29 are shown in Figures 4through 7, respectively.
The calculated equilibrium between the two phases a+b
and among the three phases a+b+a
2
are in reasonable
agreement with the experimental tie-lines except for the
c+b+(Ti,V)Al
3
phase fields. Table II lists the calcu-
lated phase boundaries and the experimental
ones
[25,28,29]
at a series of temperatures from 1073 to
1373 K (800 to 1100 C). It can be seen that the phase
boundaries calculated in this work correspond well with
most of the experimental results except for the points 15,
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Weight Fraction Al
Weight Fraction Ti
V
Ti
Al
1173K [28]
single phase
two phases
three phases
tie-line
α
β
α
2
γ
δ
ξ
+L
TiAl2
H_TiAl3
ξ
Fig. 5—Calculated isothermal section of the Al-Ti-V system at
1173 K (900 C) along with the experimental data measured by
Ahmed and Flower.
[28]
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Weight Fraction Al
Weight Fraction Ti
V
Ti
Al
1073K
[28]
single phase
two phases
three phases
tie-line
[25]
single phase
two phases
three phases
α
β
α
2
γ
TiAl2
δ
ξ
ξ
+L
H_TiAl3
Fig. 4—Calculated isothermal section of the Al-Ti-V system at
1073 K (800 C) along with the experimental data measured by
Hashimoto et al.
[25]
and Ahmed and Flower.
[28]
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Wei
g
ht Fraction Al
Weight Fraction Ti
V
Ti
Al
1273K
α
α
2
γ
β
δ
TiAl2
Ti2Al5
ξ
H_TiAl3
[25]
single phase
two phases
three phases
tie-line
tie-trangle
ξ
+L
Fig. 6—Calculated isothermal section of the Al-Ti-V system at
1273 K (1000 C) along with the experimental data measured by Ha-
shimoto et al.
[25]
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Weight Fraction Al
Weight Fraction Ti
V
Ti
Al
1373K [29]
two phases
three phases
[9]
tie-line
β
α
2
α
γ
δ
TiAl2
Ti2Al5
ξ
H_TiAl3
ξ
+L
Fig. 7—Calculated isothermal section of the Al-Ti-V system at
1373 K (1100 C) along with the experimental data measured by
Zhang and Du
[29]
and Zhang.
[9]
METALLURGICAL AND MATERIALS TRANSACTIONS A

Table II. Calculated and Experimental Points of Phase Boundary with Different Chemical Composition (Weight Percent) at a
Series of Temperature
Points
Chemical
Composition
(Wt Pct)
Temperature
[K (C)]
Phase Constitute
in Experimental
Work
[25,28,29]
Phase Constitute
in This WorkAl Ti
1 40 50 1073 (800) cc
1173 (900) cc
2 40 45 1073 (800) cc
1173 (900) cc
3 10.5 69 1073 (800) a
2
+b
2
a
2
+b
1173 (900) a
2
+b
2
near the boundary of a
2
+b
4 15 65 1073 (800) a
2
+b
2
a
2
+b
1173 (900) a
2
+b
2
a
2
+b
5 20 65 1073 (800) a
2
+b
2
a
2
+b
1173 (900) a
2
+b
2
a
2
+b
6 20 60 1073 (800) a
2
+b
2
a
2
+b
1173 (900) a
2
+b
2
a
2
+b
7 25 51 1073 (800) c+b
2
c+b+a
2
1173 (900) c+b
2
c+b
8 27 43 1073 (800) c+b
2
c+b
1173 (900) c+b
2
c+b
9 27 53 1073 (800) c+b
2
c+b+a
2
1173 (900) c+b
2
c+b
10 28 48 1073 (800) c+b
2
c+b
1173 (900) c+b
2
c+b
11 32 37 1073 (800) c+bc+b
1173 (900) c+bc+b
12 35 40 1073 (800) c+bc+b
1173 (900) c+bc+b
13 40 30 1073 (800) c+bc+b
1173 (900) c+bc+b
14 41 20 1073 (800) c+bnear the boundary of c+b
1173 (900) c+bnear the boundary of c+b
15 45 20 1073 (800) c+bc+b+n
1173 (900) c+bc+b+n
16 48 42 1073 (800) c+ TiA
2
c
1173 (900) c+ TiA
2
c
17 25 71 1073 (800) c+a
2
c+a
2
1173 (900) c+a
2
c+a
2
18 27 68 1073 (800) c+a
2
c+a
2
1173 (900) c+a
2
c+a
2
19 28 68 1073 (800) c+a
2
c+a
2
1173 (900) c+a
2
c+a
2
20 25 62 1073 (800) a
2
+b
2
+ca
2
+b+c
1173 (900) a
2
+b
2
+cnear the boundary of a
2
+b+c
21 26 58 1073 (800) a
2
+b
2
+ca
2
+b
2
+c
1173 (900) a
2
+b
2
+ca
2
+b
2
+c
22 27 63 1073 (800) a
2
+b
2
+cc+a
2
1173 (900) a
2
+b
2
+cnear the boundary of a
2
+b+c
23 48 22 1073 (800) c+b+nc+b+n
1173 (900) c+b+nc+b+n
24 15 80 1073 (800) a
2
a
2
1273 (1000) a
2
+ba
2
+b
25 35 60 1073 (800) cc
1273 (1000) cc
26 42.5 55 1073 (800) cc
1273 (1000) cc
27 42.5 52.5 1073 (800) cc
1273 (1000) cc
28 7 88 1073 (800) a+ba+b
1273 (1000) a+bb
29 20 70 1073 (800) a
2
+bnear the boundary of a
2
+b
1273 (1000) a
2
+ba
2
+b
METALLURGICAL AND MATERIALS TRANSACTIONS A

22, 31, 35, and 50; however, all of these points are close
to the related phase boundary within the error, as shown
in Table II.
Figure 4is the calculated isothermal section of the Al-
Ti-V system at 1073 K (800 C) along with the exper-
imental data measured by Ahmed and Flower
[28]
and
Hashimoto et al.
[25]
Though their results are similar to
each other at 1073 K (800 C), the composition of the
phase boundaries differs by about 5 to 10 wt pct due to
different experimental methods. Besides, the calculated
solubility of Ti in Al
8
V
5
is 0.77 wt pct at 1073 K
(800 C), which is in accord with the experiment
result
[25]
(1.0 wt pct). The solid solubility of V in the
phase TiAl(c) is 21.5 wt pct, which is similar to the
measured value (30 wt pct) at 1073 K (800 C).
[28]
The
phase boundaries of c+band c+a
2
calculated in
this work correspond well with most of the experi-
mental data except for the deviations from the related
phase fields c+b+ (Ti,V)Al
3
; however, all of the
deviations are close to the related phase boundaries
within the error.
Figure 5shows the comparison between Ahmed and
Flower’s
[28]
experimental results and our calculated
isothermal section of the Al-Ti-V ternary system at
1173 K (900 C). The calculated solubility of Ti in
Al
8
V
5
is 1.39 wt pct at 1173 K (900 C), which is close
to the experimental data of about 1.0 wt pct by Ahmed
and Flower. Wang et al.
[10]
assessed this system recently,
but they hardly considered that the phase Al
8
V
5
can
dissolve a certain amount of Ti atoms, which may lead
to no occurrence of the three-phase region: Al
8
V
5
+
b+ (Ti,V)Al
3
at 1173 K (900 C).
Figure 6is the calculated isothermal section of the
Al-Ti-V system at 1273 K (1000 C) along with the
experimental data reported by Hashimoto et al.
[25]
Compared to Figures 4and 5, the size of the
Table II. continued
Points
Chemical
Composition
(Wt Pct)
Temperature
[K (C)]
Phase Constitute
in Experimental
Work
[25,28,29]
Phase Constitute
in This WorkAl Ti
30 55 5 1073 (800) n+rn+r
1273 (1000) n+rn+r
31 45 10 1073 (800) n+bnear the boundary of n+b
1273 (1000) n+b+rn+b
32 40 7.5 1073 (800) n+bnear the boundary of n+b
1273 (1000) n+b+rn+b+r
33 50 10 1073 (800) n+bn+b
1273 (1000) n+rn+b
34 30 40 1073 (800) c+bc+b
1273 (1000) c+bc+b
35 27 53 1073 (800) c+ba
2
+b+c
1273 (1000) a
2
+b+cc+b
36 40 20 1073 (800) c+bc+b
1273 (1000) c+bc+b
37 9 86 1073 (800) a+b+a
2
a+b+a
2
1273 (1000) a+bnear the boundary of a+b
38 11 84 1073 (800) a+b+a
2
a+b+a
2
1273 (1000) a+b+a
2
near the boundary of a+b+a
2
39 25 65 1073 (800) a
2
+b+cnear the boundary of a
2
+b+c
1273 (1000) a
2
+b+ca
2
+b+c
40 30 60 1073 (800) a
2
+b+ca
2
+c
1273 (1000) a
2
+b+ca
2
+b+c
41 50 20 1073 (800) c+b+nc+b+n
1273 (1000) c+b+nc+b+n
42 55 20 1073 (800) c+b+nc+b+n
1273 (1000) c+b+nc+b+n
43 37.5 2.5 1073 (800) n+r+bn+r+b
1273 (1000) r+br+b
44 32 64 1173 (900) c+a
2
c+a
2
45 30 55 1173 (900) c+b
2
c+b
46 45 4 1173 (900) n+b+rn+b+r
47 42 18 1173 (900) c+b+nc+b+n
48 34.3 46.9 1373 (1100) b+cb+c
49 37.9 24.1 1373 (1100) b+cb+c
50 23.9 69.7 1373 (1100) a
2
+ba
2
+b+c
51 33.2 63.4 1373 (1100) a
2
+ca
2
+c
52 51 9.6 1373 (1100) n+r+bn+r+b
53 27.1 63.2 1373 (1100) a
2
+b+cnear the boundary of a
2
+b+c
METALLURGICAL AND MATERIALS TRANSACTIONS A

three-phase field a+Ti
3
Al(a
2
)+bdecreases, while the
b-phase region expands toward the Ti-Al side and the
TiAl(c) single-phase region increases, which is in accord
with the experimental data.
[25]
The calculated result is in
good agreement with the experimental data, except for
the occurrence of the phase Ti
2
Al
5
and the three-phase
fields Ti
2
Al
5
+c+ (Ti,V)Al
3
; neither exists in the exper-
imental isothermal sections.
[25,28]
The compound Ti
2
Al
5
appears at about 1249 K (976 C) in the Ti-Al binary
system;
[12]
therefore, its existence at 1273 K (1000 C)
may be reasonable, which will lead to the generation of
the three-phase fields TiAl
2
+c+Ti
2
Al
5
.
Figure 7is the calculated isothermal section of the
Al-Ti-V system at 1373 K (1100 C) along with the
experimental data reported by Zhang and Du
[29]
and
Zhang.
[9]
The difference of isothermal section at 1373 K
(1100 C) between Hayes’
[8]
and the recent work is
obvious. In his section, the existence of 1 three-phase
field, b+c+Al
8
V
5
, was unreasonable, because his
assessment was based on the earlier experiments
[39,40]
in which the b+c+Al
8
V
5
area existed down to 723 K
(450 C). However, Hashimoto et al.,
[25]
Paruchuri and
Massalski,
[26]
and Ahmed and Flower
[28]
recently con-
firmed no existence of this three-phase region at 1273 K
(1000 C) or even lower temperature.
Figure 8is the calculated isothermal section of the
Al-Ti-V system at 1473 K (1200 C); the calculated
single a-phase region hardly exists. However, by con-
trasting to Ahmed and Flower’s
[28]
experimental data at
1473 K (1200 C), the aphase field enlarged unexpect-
edly. Zhang
[9]
reported that the amount of oxygen has
quite an effect on the size of the a-phase region, which
leads to the dramatic enlargement of the experimental a-
phase region in Ahmed and Flower’s report. In addition,
with the temperature increasing from 1073 K to 1373 K
(800 C to 1100 C), the a-phase region becomes nar-
rower toward Al-rich composition and parallel to the
Ti-Al side, obviously, as shown in Figures 4,5,6, and 7.
As a result, the experimental data of Ahmed and Flower
at 1473 K (1200 C) are not taken into consideration in
the present assessment.
Furthermore, the phase (Ti,V)Al
3
(n) is treated with a
tiny homogeneity range in this calculation, as shown in
Figures 4,5,6,7, and 8. This treatment can describe the
reported phase relationship between (Ti,V)Al
3
and
other phases well; compared to the experimental iso-
thermal sections,
[25,28]
the calculated (Ti,V)Al
3
region is
smaller. Analyzing the experimental (Ti,V)Al
3
phase
region in detail, this region in all experimental isother-
mal sections are depicted by dashed lines, which may
imply that its exact composition and homogeneity range
were still undetermined.
As for the bcc_B2 phase in the Al-Ti-V system,
Ahmed and Flower pointed out that the exact experi-
mental phase boundaries between the band bcc_B2 and
the size of their phase fields were still not exactly
known;
[28]
further experimental studies are needed to
determine them. Otherwise, our focus is not on the
bcc_ A2/B2 order/disorder transition in the ternary
system. Therefore, for simplicity, in this calculation, the
ternary interaction parameters of the bcc_B2 phase are
not considered.
The calculated invariant equilibria in the Al-Ti-V
ternary system are listed in Table III and compared to
the experimental ones.
[8,9,26,42]
Obviously, the present
work is consistent with the recent reported data.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Weight Fraction Al
Weight Fraction Ti
V
Ti
Al
1473K
β
δ
γ
ξ
+L
H_TiAl3
ξ
TiAl2
Ti2Al5
γ
+
α
Fig. 8—Calculated isothermal section of the Al-Ti-V system at
1473 K (1200 C).
Table III. Calculated and Experimental Results of the Invariant Reaction in the Ternary System
Invariant Reactions
Temperature [K (C)]
Calculated
Ref. [42]
[K (C)]
Ref. [8]
[K (C)]
Ref. [26]
[K (C)]
Ref. [9]
[K (C)]
L+a-hcp = c-TiAl+bcc_A2 1724.09 1673 to 1723
(1400 to 1450)
1673 to 1773
(1400 to 1500)
— 1717 (1444)
L+Ti
2
Al
5=
n-(Ti,V)Al
3
+c-TiAl 1664.70 1633 to 1668
(1360 to 1395)
1633 to 1660
(1360 to 1387)
~1643 (1370) 1663 (1360)
L+ bcc_A2 = c-TiAl+ r-Al
8
V
5
1657.36 1663 (1360) 1663 (1360) — 1670 (1397)
L+c-TiAl = n-(Ti,V)Al
3
+r-Al
8
V
5
1630.11 1573 to 1633
(1300 to 1360)
———
METALLURGICAL AND MATERIALS TRANSACTIONS A

V. CONCLUSIONS
The previous investigations of the Al-Ti-V ternary system
and the thermodynamic descriptions of the binary systems
are reviewed. The model of Ti
3
Al(a
2
) is taken as (Al,
Ti,V)
0.75
(Al,Ti)
0.25,
, the model of TiAl(c) is taken as
(Al,Ti,V)
0.5
(Al,Ti,V)
0.5
, the model of (Ti,V)Al
3
is taken as
(Al,Ti)
0.75
(Al,Ti,V)
0.25
, and the model of Al
8
V
5
is Al
0.4616
(Al,Ti,V)
0.1538
(Al,Ti,V)
0.2308
V
0.1538
. Based on these models,
the Al-Ti-V ternary system is assessed by means of the
CALPHAD method using the ternary experimental data in
the literature. Then, a series of isothermal sections from
1073 K to 1473 K (800 C to 1200 C) and some invariant
reactions are calculated. It is shown that the present
thermodynamic assessment is in good agreement with the
updated experimental results within the error and the
thermodynamic parameters obtained in this study are self-
consistent. This thermodynamic assessment may provide
theoretical information for designing the novel alloys
involving the Al-Ti-V system.
ACKNOWLEDGMENTS
Thanks are due to Dr. S.L. Chen, CompuTherm
LLC, and Professor J.Y. Zhang, Shanghai University,
for the helpful discussions of this work. This work is
financially supported by the National Nature Science
Foundation of China (Grant Nos. 51074105, 51374142
and 51225401), the Science and Technology Fund of
Scientific Committee of Shanghai (Grant Nos.
11520500100 and 11DZ2283400), and the open project
of the State Key Laboratory of New Ferrous Metal-
lurgy Technology (Grant No. KF12-05).
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vol. 5, pp. 1373–81.
2. H.A. Lipsitt, D. Shechtman, and R.E. Schafrik: Metall. Trans. A,
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METALLURGICAL AND MATERIALS TRANSACTIONS A