The thermochemical behavior of some binary shape memory alloys by high temperature direct synthesis calorimetry

Article abstract of DOI:10.1016/j.jallcom.2011.01.152

The standard enthalpies of formation of some shape memory alloys have been measured by high temperature direct synthesis calorimetry at 1373 K. The following results (in kJ/mol of atoms) are reported: CoCr (-0.3 ± 2.9); CuMn (-3.7 ± 3.2); Cu₃Sn

Full text of DOI:10.1016/j.jallcom.2011.01.152

Journal of Alloys and Compounds 509 (2011) 5256–5262
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Journal of Alloys and Compounds
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The thermochemical behavior of some binary shape memory alloys by high
temperature direct synthesis calorimetry
S.V. Meschela,b,∗, J. Pavluc, P. Nashb
a James Franck Institute, The University of Chicago, 5640 S. Ellis Avenue, Chicago, IL, 60637, USA
b Illinois Institute of Technology, Thermal Processing Technology Center, 10W. 32nd Street, Chicago, IL, 60616, USA
c Department of Chemistry, Masaryk University, Kotlarska 2, Brno, 61137, Czech Republic
a r t i c l e i n f o
a b s t r a c t
Article history:
The standard enthalpies of formation of some shape memory alloys have been measured by high tem-
perature direct synthesis calorimetry at 1373 K. The following results (in kJ/mol of atoms) are reported:
CoCr (−0.3 2.9); CuMn (−3.7 3.2); Cu3Sn (−10.4 3.1); Fe2Tb (−5.5 2.4); Fe2Dy (−1.6 2.9); Fe17Tb2
(−2.1 3.1); Fe17Dy2 (−5.3 1.7); FePd3 (−16.0 2.7); FePt (−23.0 1.9); FePt3 (−20.7 2.3); NiMn
(−24.9 2.6); TiNi (−32.7 1.0); TiPd (−60.3 2.5). The results are compared with some earlier exper-
imental values obtained by calorimetry and by EMF technique. They are also compared with predicted
values on the basis of the semi empirical model of Miedema and co-workers and with ab initio calcu-
lations when available. We will also assess the available information regarding the structures of these
alloys.
Received 18 November 2010
Received in revised form 19 January 2011
Accepted 20 January 2011
Available online 5 March 2011
Keywords:
Shape memory alloys
Enthalpy of formation
Calorimetry
© 2011 Elsevier B.V. All rights reserved.
1. Introduction
ever, there are exceptions, some of the Fe based alloys show a face
centered cubic to hexagonal close pack martensitic transformation
W.J. Buehler and F.E. Wang, two crystal physicists observed in
1959 that NiTi alloy (Nitinol) has unique characteristics [1]. This
alloy “remembers” its shape, and therefore such compounds are
called shape memory alloys (SMA). Compounds in this group are
held in the so called “parent” state, which is usually a cubic struc-
ture (Austenite) and heat treated to transform to another structure.
When for example the NiTi wire cools below its transition temper-
ature the atoms rearrange in another structure of lower symmetry,
the Martensite phase. These are solid state transformations. The
Martensite crystals are slightly flexible and can accommodate some
degree of deformation. When the NiTi wire is warmed up the
Martensite crystals revert to their undeformed, “parent” structure
(Austenite). The earliest observations of this effect are credited
to Olander in 1932 (Au–Cd), Greeninger and Mooradian (1938)
(Cu–Zn) and later to Kurdjumov and Khandros (1949) and also to
Chang and Read (1951) [2–5].
in a non-thermoelastic way [7,8].
In general, materials which allow structures to adapt to their
environment are known as actuators [9]. They can change shape,
hardness, position, frequency and other properties as a response
to temperature, electricity or magnetism. The thermoelastic shape
memory alloys (SMA) may respond to thermal stimuli, piezoelec-
tric ceramics to electric stimuli (PZT = lead zirconate titanate) and
magnetostrictive materials to changes of magnetic fields (Terfenol-
D, Samfenol, Galfenol) [10]. While this definition is the most general
one, we should keep it in mind that though SMA alloys are actuators
not all actuators display shape memory phenomenon.
When a SMA recognizes only its “parent” state, it is undergoing a
so called “one way” shape memory transition. If the sample under-
goes specific “training” treatments, it is possible for the alloy to
recognize both its “parent” shape and also its deformed state. The
result is the fascinating so called two-way shape memory effect,
which is much less well understood [11–14]. This is a unique effect
in inanimate materials, however there are similar manifestations in
the animal kingdom, for example in the training of homing pigeons.
The shape memory alloys are utilized in many areas of endeavor,
including electrical engineering, machinery design, transportation,
chemical engineering, space research and medicine. This indicates
a great demand for these materials. To 1994 more than 15,000
patents were applied for utilization of SMA-s [13], These include
such diverse specific uses as pipe joints, eyeglass frames, orthodon-
tic treatments, stents in bypass surgeries and many other ingenious
applications.
The shape memory phenomenon is associated with reversible
martensitic transformations [6]. Such transformations may take
place either by thermoelastic or by a non-thermoelastic process.
When the material is heated up and the structure reverts to the
original or “parent phase” it is called a thermoelastic process. How-
∗
Corresponding author at: Illinois Institute of Technology, Thermal Processing
Technology Center, 10W. 32nd Street, Chicago, IL, 60616, USA. Tel.: +1 773 684 7795;
fax: +1 773 702 4180.
E-mail address: meschel@jfi.uchicago.edu (S.V. Meschel).
0925-8388/$ – see front matter © 2011 Elsevier B.V. All rights reserved.
doi:10.1016/j.jallcom.2011.01.152

S.V. Meschel et al. / Journal of Alloys and Compounds 509 (2011) 5256–5262
5257
In both the experimental and the theoretical treatments of SMA-
s the stability of the alloy is considered very important [15,16].
Since the enthalpies of formation are excellent indicators of the
stability of alloys, we believe that understanding the thermochem-
ical behavior of such compounds would be helpful to members of
the scientific community who design new shape memory alloys
with specific applications in mind [17,18]. We found the list of
compounds where shape memory effect has been observed very
helpful in identifying the more important shape memory alloys
[13,19].
In some instances shape memory effects have been predicted
for metallic systems where compound formation has not been
reported. Some of the binary alloys which are reported to exhibit
shape memory phenomena have only one reported crystal modifi-
cation. It is questionable if the effect is due to thermoelastic SMA
phenomenon if the alloys have no apparent “deformed” modifica-
tion. We also noticed that in some studies compositions of binary
alloys were proposed as exhibiting shape memory effect which are
not stoichiometric. Therefore we assessed in the present commu-
nication the systems where shape memory effect was reported or
predicted and surveyed their basic characteristics. Subsequently
we prepared some stoichiometric compositions for detailed ther-
mochemical study.
their heat contents. Between the two sets of experiments the samples were kept in
a vacuum desiccator to prevent reaction with oxygen or moisture.
Calibration of the calorimeter was achieved by dropping weighed segments of
high purity, 2 mm diameter Cu wire into the calorimeter at 1373 2 K. The enthalpy
of pure copper at 1373 K, 43.184 kJ/mol of atoms was obtained from Hultgren et al.
[24]. The calibrations were reproducible to within 2.0–2.5% precision.
The reacted samples were examined by X-ray powder diffraction analyses to
assess their structure and to ascertain the absence of unreacted metals. In the course
of the present study we attempted to prepare 19 binary alloys. Among these, 14
were found acceptable for fully quantitative measurements. We did not attempt to
prepare compositions of binary alloys which were not indicated to exist in the phase
diagram collection of Massalski et al. [25]. These are for example alloys in the Ti–Nb,
U–Nb, In–Tl and Ti–V systems. We also did not include compounds which had no
reported crystal structures either in the ASTM Powder diffraction file or in Pearson’s
collection of crystallographic data [26], as for example in Ti3Ni4, Fe81.6Ga18.4
.
The physical characteristics and structures of the binary alloys we prepared
are summarized in Table 1. In the second column we list the Chemical Abstracts
(CAS) Registry Numbers (RN) of the compounds reported to display shape memory
phenomenon. As CA currently indexes over 10 million compounds and alloys, if
a compound has no RN assigned to it, it is unlikely to be appropriate for further
measurements. In the third column we list the melting points of the compounds
and alloys from the data available from the Massalski et al. [25] phase diagram
collection. In the fourth column we list the Pearson symbols assigned to the structure
of the compound available from the ASTM powder diffraction file and from Pearson’s
collection of crystallographic data [26]. In order to have a well defined shape memory
alloy, both the parent structure and the structure after the transition should be
well known. The fifth column designated as comments shows if the reaction was
complete and the modification observed in the calorimetric measurements. We did
not study the alloys in the systems Ag–Cd and Au–Cd, because the vapor pressure of
Cd is such that direct synthesis calorimetry at 1100 ◦C is not possible. The compounds
which we found to be ductile during the preparation could be quite suitable for
preparing thin wires and coils.
It is sometimes possible to find information regarding Gibbs’
energies or estimate these quantities from phase diagrams, but
enthalpies of formation are considerably more scarce. The entropy
in these compounds is also a very significant quantity [16]. This
quantity plays a crucial role in the transformation of the SMA from
the Austenite to the Martensite phase. If the enthalpies of forma-
tion are available, it would be possible in principle to evaluate or
at least estimate the entropies with existing or estimated Gibbs’
energies.
To prepare the samples for XRD analyses we used an agate mortar and pestle.
When this was not sufficient we used a hardened steel die and a hammer. In one
case we needed to use a diamond wheel to cut the samples. The alloys we studied
varied significantly in behavior, structure characteristics and physical properties.
We will discuss some of the more important characteristics in the next section.
Detailed knowledge of the specific heat could also be very
important in understanding the Austenite–Martensite transition.
One would anticipate a definite break or discontinuity in the rela-
tionship between the specific heat and the temperature at the
transition point. Further study of the transition temperature could
also advance our understanding of this fascinating process. Rane,
Navrotsky and Rossetti studied the detailed thermodynamic behav-
ior of one of the actuators, in a piezoelectric ceramics material (PZT)
[10,20].
Therefore we decided to embark on a study of the thermochem-
ical behavior of some SMA-s. In the current communication we
are reporting standard enthalpies of formation for some binary
SMA-s, namely FePd3, FePt, FePt3, Fe2Tb, Fe17Tb2, Fe2Dy, Fe17Dy2,
NiMn, FeMn, CoCr, Cu3Sn and CuMn. Even though the enthalpies
of formation for NiTi, TiPd and several Pt alloys have already
been measured by high temperature, direct synthesis calorimetry
[21,22], we decided to remeasure the enthalpies of formation of
NiTi and TiPd, because we felt that the information regarding their
structures were not sufficient in the previous studies.
3. Discussion
3.1. Physical properties and structures
3.1.1. Unreacted alloys: RuTa, Ru2Ta3, Ti4Mo9
These are all listed as shape memory alloys, however we found
that in our conditions they are unreacted. The XRD patterns clearly
showed the presence of unreacted elements. In the XRD pattern
of Ti4Mo9 we noticed the presence of approximately 20% reaction
of the expected compound and two unidentified phases. The XRD
equipment is sufficiently sensitive so that we could have observed
solid solution formation had there been any.
3.1.2. Fe–Pd system
FePd was ductile and could not be powdered in preparation for
XRD analysis. However, we performed an XRD analysis on a very
thin pellet and a subsequent SEM study. Both samples show the
presence of FePd and a substantial amount of unreacted Fe metal.
FePd3 was also ductile. However, the XRD pattern showed a sin-
gle phase, a cubic structure. This is the only modification listed in
both the ASTM powder diffraction file and Pearson’s collection of
crystallographic data [26].
2. Experimental
The experiments were carried out at 1373 2 K in a single unit differential
calorimeter which has been described in an earlier communication by Kleppa and
Topor [23] at the University of Chicago. The measurements in the current study were
made at IIT. The changes in the equipment have been reported in an earlier commu-
nication [22]. All the experiments were performed under the protective atmosphere
of Argon gas which was purified by passing it over titanium chips at 900 ◦C.
A boron nitride (BN) crucible was used to contain the samples.
All the metals were purchased from Johnson Matthey/Aesar (Ward Hill, MA,
USA).The Tb and Dy samples were filed from solid ingots immediately prior to the
experiments. For the alloys where we used Fe,Co, Ni or Cu, these were reduced prior
to the calorimetric experiments at 600 ◦C under hydrogen gas flow to insure that
we avoid surface oxidation of these metals. The two components were mixed in the
appropriate molar ratio, compressed into small pellets of about 2 mm diameter and
then dropped from room temperature into the calorimeter. In a subsequent set of
experiments the reaction products were dropped into the calorimeter to measure
3.1.3. Fe–Pt system
Our FePt sample could not be powdered, it yielded only small
flakes. However, the XRD pattern showed that this compound is a
single phase, a tetragonal structure. This is the only modification
listed in the ASTM powder diffraction file and in Pearson’s crys-
tallographic data [26,27]. FePt3 is ductile. We performed an XRD
analysis on a very thin pellet and found an excellent match of the
published cubic structure. Again, there is only one structure listed
[26].

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S.V. Meschel et al. / Journal of Alloys and Compounds 509 (2011) 5256–5262
Table 1
Physical properties of some binary shape memory alloys.
Compound
RN
Melting point T (◦C)
Structure Pearson symbol
Comment
tP2
NiTi
12035-60-8
59328-60-8
108503-16-8
105-884
12165-82-1
12333-98-1
12066-72-7
–
1310(c)
1380(c)
984(p)
–
1400(c)
960(c)
1530(c)
–
cP2, mP4
hP16
cF96
–
cP2, oP4
–
hP16
–
Ni3Ti
NiTi2
Ti3Ni4
TiPd
TiPd2
TiPd3
Ti4Mo9
TiNb
Both modif.
XRD, SEM incomplete
12384-42-8
123188-71-6
–
–
–
–
–
–
–
TiNb2
TiV
TiV2
Ti2V
12067-84-4
–
–
–
–
–
RuTa
Ru2Ta3
AgCd
Ag2Cd
AgCd2
AuCd
–
–
1667(p)
–
oF*
tP2
XRD, SEM, unreacted
XRD, SEM unreacted
12002-62-9
119187-00-7
276691-61-3
12044-73-4
cP2, hP2, cI2, oC4
–
–
–
–
629 (c)
oP4, t*4, cP2
hP27, hP18
InTl
-
–
–
InTl2
In2Tl
FePd
-
-
–
–
–
–
tP4
12022-86-5
790(p)
XRD, SEM
1304(ordering)
820(p)
1304(ordering)
∼1300(p)
∼1350(p)
Incomplete, ductile
XRD, single phase
ductile, cP4
XRD, Single phase, tP4
XRD, single phase
Ductile, cP4
FePd3
12310-93-9
cP4
FePt
FePt3
12186-46-8
57679-16-0
tP4
cP4
Fe3Tb
Fe2Tb
-
1212(p)
1187(p)
hR12
cF24, hR6
XRD, mixed phase
XRD, single phase
Both modif.
12023-38-0452
Fe17Tb2
Fe3Dy
Fe2Dy
Fe17Dy2
FeMn
Fe3Mn
Fe4Mn
Fe3Ga4
Fe3Ga
FeGa3
CoCr
12063-75-1
-
1312(p)
1305(c)
1270(p)
hR19, hP38
hR12
cF24, hR*
hP38
cF4, cI2, t**
-
hP2
mc42, t*63
hP8, hP2
tP16
cI2, cP8
–
hP8
cI2, tP2
cP4
XRD, two hexag. modif.
mixed phase
s.p., cF24
two hexag. modif.
ductile, tetrag.
12019-81-7
12060-29-6
12518-52-4
12182-95-5
117443-48-8
53237-41-5
12063-30-8
12062-72-5
12052-27-6
159201-78-2
15381-39-4
12263-28-4
–
12272-98-9
104251-06-1
68985-62-6
–
12019-61-3
12019-69-1
12134-36-0
12158-95-1
1375(c)
-(1246 ◦C, ordering)
–
–
906(p)
–
824(p)
∼1283(c)
SEM, 90% 1:1
CoCr2
Co3Cr
NiMn
–
–
911(c)
–
–
–
eutectic
–
676(c)
–
859(c)
698(p)
tP2
Ni3Mn
CuMn
Cu3Mn
CuGa2
Cu11Ga39
Cu3Sn
Cu6Sn5
Cu3Si
cF4, t*4
–
tP3
Tetrag., ss
–
oC80, cF16, m**
hP4, hR22
hP72, hR*
oP8, cI2, hP8, mP4
oC80
mP4
Cu3Ge
3.1.4. Fe–Tb and Fe–Dy systems
present. However, we noticed two unidentified lines in the pattern,
which closely matched the hR19 type hexagonal pattern pub-
lished for Tb2Fe17.This structure has not been published for Dy2Fe17
[26,28–30].
In both systems the 3:1 compound did not form quantita-
tively at our conditions. We observed mixed phases where the 1:2
compound was predominant. In both systems the 2:1 compound
formed quantitatively. In both 1:2 compounds two modifications
are listed, a cubic and a hexagonal phase [26]. In TbFe2 we observed
both modifications. In our sample of Fe17Tb2 the XRD pattern of our
sample clearly showed the presence of both the reported hexag-
onal modifications [26]. There were no indications of unreacted
elements or secondary phases. Dy2Fe17 was very difficult to pow-
der. We obtained the sample for the XRD analysis by placing it in
a hardened stainless steel die and hammering it 300 times. The
structure is a reasonably good match of the hP38 type hexagonal
pattern. There were no unreacted elements or secondary phases
3.1.5. FeMn
This sample is ductile. The XRD performed on a very thin pel-
let did not match either the Fe or the Mn patterns. Subsequent
SEM study showed that the large majority of the sample has
a 1:1 composition with a minor component of 1:2 composition
[31]. We will show the enthalpy of formation result as indica-
tive.

S.V. Meschel et al. / Journal of Alloys and Compounds 509 (2011) 5256–5262
5259
Table 2
3.1.6. CoCr
This sample did not melt, yielded light grey pellets. The sam-
Standard enthalpies of formation of some binary shape memory alloys. Data are in
kJ/mol of atoms.
ples are ductile and we could not crush them even in the hardened
steel die. The XRD pattern of a very thin pellet did not match the
tetragonal CoCr phase. The closest match was with the alpha-Co
pattern. A subsequent SEM study showed that our sample was
nearly 90% 1:1 composition. The study showed the presence of a
few percent of two secondary phases. This alloy has gained con-
siderable current significance by its use in hip joint arthroplasty
[32].
Compound
ꢀH(1)
14.4 1.1(5)
6.0 1.5(5)
9.0 1.3(5)
30.1 2.5(6)
25.1 1.6(7)
28.9 2.5(6)
28.6 2.3(5)
24.0 1.6(5)
33.0 1.9(4)
35.7 2.7(6)
34.3 2.4(5)
41.1 1.3(5)
−3.5 0.4(5)
−29.7 1.8(5)
ꢀH(2)
ꢀHfo
FePd3
FePt
30.4 2.5(5)
29.0 1.1(5)
28.7 1.9(4)
40.5 1.8(4)
30.6 1.8(5)
31.0 1.5(5)
30.2 1.8(5)
29.3 0.7(4)
57.9 1.8(5)
38.3 1.6(5)
34.6 1.7(4)
44.8 2.9(4)
29.2 0.9(5)
30.8 1.6(5)
−16.0 2.7
−23.0 1.9
−20.7 2.3
−10.4 3.1
−5.5 2.4
−2.1 3.1
−1.6 2.9
−5.3 1.7
−24.9 2.6
−2.6 3.1
−0.3 2.9
−3.7 3.2
−32.7 1.0
−60.3 2.5
FePt3
Cu3Sn
Fe2Tb
Fe17Tb2
DyFe2
Dy2Fe17
NiMn
FeMna
CoCr
3.1.7. NiMn
This sample melted, yielded a light grey bead. This alloy sample
was very difficult to powder to prepare the XRD samples. We placed
it in a hardened stainless steel die and hammered it several hundred
times for powder preparation. There are two compounds reported
in this system [25], however the XRD patterns are not listed in the
ASTM powder diffraction file. We generated the pattern of the 1:1
composition from unit cell parameters and the atomic coordinates
of the prototype structure [26]. The XRD pattern showed that we
had no unreacted elements or any secondary phases. The exper-
imental pattern closely matched the generated tP2 pattern. Heo
et al. report this composition as a solid solution [33].
CuMn
TiNi
TiPd
a
Indicative result.
Here m represents the molar ratio [A1]/[A2], where A1 and A2
represent the elements in the binary shape memory alloys, while s
denotes solid and l denotes liquid. The reacted pellets were reused
in a subsequent set of measurements to determine their heat con-
tents:
[A1][A2]m(s, 298 K) = [A1][A2]m(s or l, 1373 K)
The standard enthalpy of formation is given by:
ꢀHf◦ = ꢀH(1) − ꢀH(2)
(2)
3.1.8. CuMn
This sample melted, and yielded a light grey bead. We could not
powder it even in the hardened steel die. We cut the sample with
a diamond wheel to prepare for heat content measurements. The
XRD pattern showed solid solution formation. The pattern matched
closely the tetragonal Mn pattern with significant shift toward
the copper peaks [34]. Copper based shape memory alloys were
reviewed by Tadaki [8,19].
(3)
where ꢀH(1) and ꢀH(2) are the enthalpy changes per mole of
atoms in the compounds associated with the reactions in Eqs. (1)
and (2).
The experimental results are summarized in Table 2. The heat
effects associated with the reactions in Eqs. (1) and (2) are given
in kilojoules per mole of atoms as averages of about six consecu-
tive measurements with the appropriate standard deviations. The
fourth column shows the standardenthalpy offormation of thecon-
sidered phases. The standard enthalpy of formation in that column
also reflects the small contribution from the uncertainties in the
calibrations. All the measurements were performed in BN crucibles.
We compared the experimental heat contents of the compounds
we studied with the values calculated on the basis of the Neumann-
Kopp rule from the heat contents of the elements as listed in
Hultgren et al. [24] and found reasonable agreement for most com-
pounds. The average experimental heat content for 14 compounds
was 32.9 5 as compared with 37.9 3 kJ/mol of atoms for the
calculated values. The experimental and calculated heat contents
usually show better agreement when the component metals are
all transition metals. We observed some notable deviations for the
heat contents of Fe2Tb, Fe17Tb2, FePt, Fe2Dy, Fe17Dy2, FeMn and
NiMn where the differences between the experimental and the cal-
culated values are quite substantial. Since NiMn melted under our
conditions, some of the difference may be accounted for by the
heats of transformation and the heat of fusion.
In Table 3, we compare our results with experimental measure-
ments from the published literature and with predicted values.
Some of the enthalpies of formation of the shape memory alloys
listed in Table 3 have been measured by Guo and Kleppa [21], by
Topor and Kleppa [35] and by Gachon and Hertz [36]. It is notewor-
thy that our measurement for Cu3Sn agrees well with the earlier
measurement by Kleppa by tin solution calorimetry in 1957 [37].
We found reasonable agreement for the enthalpy of formation of
Dy2Fe17 with Norgren et al. by solution calorimetry [38]. How-
ever our result is significantly different for DyFe2. The authors
refer to errors due to oxidation on p1373 of their study. Also, if
we look at the enthalpies of formation of other Fe–LA systems by
3.1.9. Cu3Sn
The samples melted, yielded a light grey bead. This sample could
be powdered for XRD analysis. The XRD pattern clearly showed an
excellent match of the published orthorhombic structure. There is
no evidence for the presence of unreacted elements or secondary
phases such as Cu6Sn5.We observed two extra peaks in the pattern
which could possibly be attributed to the cubic modification. The
pattern of the cubic modification is not listed in the ASTM powder
diffraction file. Therefore we generated this pattern from available
unit cell parameters and the appropriate atomic coordinates.
3.1.10. TiNi
This sample was a gold toned silvery alloy partially melted,
which we could not crush. The sample for XRD analysis was filed
from the bead. The XRD pattern showed complete reaction and the
CsCl type cubic structure.
3.1.11. TiPd
This sample was partially melted, yielded a light grey alloy. Our
sample could not be crushed to powder, we were only able to get
chips for the XRD analyses.
The XRD pattern showed both the cubic and the orthorhombic
modifications.
3.2. Standard enthalpies of formation
The standard enthalpies of formation of the shape memory
alloys determined in this study were obtained as the difference
of two sets of measurements. In the first set the following reaction
takes place in the calorimeter:
[A1](s, 298 K) + m[A2](s, 298 K) = [A1][A2]m(s or l, 1373 K)
(1)

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S.V. Meschel et al. / Journal of Alloys and Compounds 509 (2011) 5256–5262
Table 3
Comparison of the standard enthalpies of formation of some binary shape memory alloys with literature and theoretical predictions. Data are in kJ/mol of atoms.
Compound
Current work
Literature
Method
Prediction
Miedema et al. [41] ab initio
NiTi
−32.7 1.0
−34(36)
DSC
DSC
−52
−33.1
−33.1 1.1(20)
TiNi3
−43(36)
DSC
DSC
−37
−42.2 1.2(20)
NiTi2
TiPd
−29(36)
DSC
−40
−97
−60.3 2.5
−51.6 6.4(20)
−53.3 1.8(20)
DSC
DSC
TiPd3
FePd3
FePt
−65.0 0.9(20)
DSC
−62
−4
−16.0 2.7
−23.0 1.9
−20.7 2.3
−10.4 3.1
−5.5 2.4
−2.1 3.1
−1.6 2.9
–
−10.0
−23.1
−19.2
−25(ꢀG) (40)
−17(ꢀG) (40)
−9.1(37)
–
EMF
EMF
SC
DSC
EMF
SC
−19
−11
−5.4
−4.4
−1.5
−4.4
FePt3
Cu3Sn
Fe2Tb
Fe17Tb2
Fe2Dy
−3.3(39)
−11.1(38)
Fe17Dy2
−5.3 1.7
−1.9(38)
−4.6(39)
SC
EMF
−1.6
NiMn
FeMn
CoCr
−24.9 2.6
−2.6 3.1a
−0.3 2.9
−3.7 3.2
–
–
–
–
DSC
DSC
DSC
DSC
−12.3
+0.4
−6.7
CuMn
+5.6
DSC = Direct synthesis calorimetry.
SC = Solution calorimetry.
EMF = Electromotive force measurement.
a
Indicative result.
different methodologies, the enthalpy values appear to be small,
between −1 and −5 kJ/mol of atoms. Therefore the reported value
of −11.1 kJ/mol of atoms for DyFe2 seems unusual. We also found
good agreement for the enthalpy of formation of Fe17Dy2 with the
measurements of Gozzi et al. [39]. We also found good agreement
with the enthalpies of formation for NiTi measured by Gachon et al.
by calorimetry [36] and for TiPd measured by Topor and Kleppa
[35]. The results of Gozzi et al. and Hultgren et al. were measured by
the EMF technique [39,40]. The fourth column indicates the method
used in the cited results. The predicted values in the fifth column are
from the semi empirical model of Miedema and co-workers [41].
We recently began comparing our results with predicted values
by ab initio calculations. This is completely the work of Dr. Pavlu
at Masaryk University, Czech Republic and all questions regard-
ing the details of the calculations should be addressed to her. The
energies of formation at 0 K temperature were evaluated using
the Vienna’s Ab initio Simulation Package (VASP), code working
within the Density Functional Theory (DFT) [42,43]. This method
utilizes the Projector Augmented Wave–Perdew–Burke–Ernzerhof
(PAW-PBE) pseudopotentials [44–46]. The Generalized Gradient
Approximation (GGA) program was used here to evaluate the
exchange correlation energy. The preliminary calculations were
accomplished using the experimentally found structural informa-
tion published in Pearson’s collection of crystallographic data and
listed in Table 4 [26]. The FePd, FePd3, FePt and FePt3 structures
considered here to be ferromagnetic (FM) whereas the NiTi inter-
metallics in both the cubic and in the monoclinic arrangement are
treated as nonmagnetic (NM). The structural parameters for the
standard element reference (SER) states: FM bcc Fe, NM fcc Pd and
Pt, FM fcc Ni and NM hcp Ti were also cited from [26].
values extends from a grid of 23 × 23 × 17 points for FePt, from
23 × 23 × 15 for FePd, from 23 × 23 × 23 points for FePd3 and mon-
oclinic NiTi, to 31 × 31 × 31 points for FePt3, and to 33 × 33 × 33
points for cubic NiTi.
In the case of the SER structures we used a grid of 9 × 9 × 9 points
for FM bcc Fe and FM fcc Ni, of 19 × 19 × 15 points for NM hcp Ti,
of 37 × 37 × 37 points for NM fcc Pd and of 41 × 41 × 41 points for
NM fcc Pt. After these calculations, each structure was fully relaxed,
which yielded the minimum total energy and the equilibrium struc-
tural parameters at 0 K. As the Fe, Pd, Pt and Ni SER structures, FePd3,
FePt3 and one of the NiTi modifications are cubic, only the volume
relaxation is necessary to obtain their lowest energy state.
The results are summarized in Table 4.The agreement of cal-
culated V/atom with experiments is very good as the deviations
of calculated values from experiments (given in % of experimen-
tal value) lie in the interval of −5%(Pd) to +9.5%(Fe) for SER states
and in the interval from −3.5%(FePd3) to +4.5%(FePt) for inter-
metallic phases. The relatively high deviation for pure FM bcc Fe
is given by the choice of experimental data. If this deviation is
calculated with respect to the second experimental number given
in Table 4 its value is only +2.3%. The comparison of found and
experimental magnetic moments (Table 4) in case of FM bcc Fe,
FM fcc Ni, FM FePd, FM FePd3 and FM FePt provides an excel-
lent agreement. In the case of FePt3 the antiferromagnetic (AFM)
arrangement of the structures is reported [50]. Nevertheless the
magnetic moments found in the literature agree very well with the
calculated ones.
The above described approach can in principle evaluate the
structural stabilities, precise heats of formation, electronic struc-
tural properties, chemical bonding, magnetic ordering and defect
properties. However, it must be kept in mind that the data rigor-
ously refer to 0 K. Therefore comparison with experimental data
at 298 K may give rise to some discrepancies and the ab initio
value should be recalculated. In general, the energy of formation
of a binary intermetallic compound is obtained as a difference
between its equilibrium total energy and the total energies of the
The cut off energy restricting the number of plane waves in the
basis set was 348 eV, 326 eV, 299 eV, 350 eV and 232 eV for Fe, Pd, Pt,
Ni and Ti respectively, both for pure constituents and constituents
in the intermetallic compounds.
We first performed convergence tests of the total energies
with respect to the number of k-points. The range of optimum

S.V. Meschel et al. / Journal of Alloys and Compounds 509 (2011) 5256–5262
5261
Table 4
Ab initio calculations.
A. Optimized structural parameters of the SER states found in this work and compared with experimental data.
3
˚
˚
˚
˚
Structure
a (A)
b (A)
c (A)
ˇ
V/atom (A )
FM bcc Fe Exp.
Expa
Calc.
2.9315
2.8576
2.8358
3.5236
3.52
3.5227
3.890
3.9540
3.923
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
90
90
90
90
90
90
90
90
90
12.5962
11.6669
11.4023
11.0623
10.9036
10.9286
14.7160
15.4538
15.0937
15.7281
17.6438
17.1204
FM fcc Ni Exp.
Exp.b
Calc.
NM fcc Pd Exp.
Calc.
NM fcc Pt Exp.
Calc.
NM hcp Ti Exp.
Calc.
a
a
3.9772
2.9504
2.9239
90
120
120
4.6810
4.6249
B. Optimized structural parameters of the intermetallic compounds found in this work and compared with experimental data. So-called internal parameters
of phase describe the positions of atoms within the unit cell and symbols x, y, z denote the axes in the direction of which the position of atoms is defined.
3
˚
˚
˚
˚
Structure
a (A)
b (A)
c (A)
ˇ
V/atom (A )
FePd exp.
Calc.
FePd3 Exp.
Calc.
FePt Exp.
Calc.
FePt3 Exp.
Calc.
NiTi Exp.
Cubic Calc.
NiTi Exp.
Monocl.Calc.
Internal par.
Exp.
3.8552
3.8360
3.8480
3.8919
4.0001
3.8619
3.8720
3.9122
3.0070
3.0047
4.6225
4.7812
2e − x Ni
0.8070
0.8288
a
a
a
a
a
a
a
a
3.7142
3.7690
a
90
90
90
90
90
90
90
90
13.8006
13.8649
14.2444
14.7378
14.6891
14.0230
14.5126
14.9692
13.5947
13.5633
13.9409
13.7361
a
3.6721
3.7609
a
a
a
a
a
90
90
a
4.2105
4.0343
2e − z Ni
0.9475
0.9362
2.8854
2.9147
2e − x Ti
0.2790
0.2851
96.8000
102.2351
2e − z Ti
0.5274
0.6147
Calc.
C. Optimized magnetic moments of the SER states and intermetallic compounds found in this work and compared with experimental data. ꢁ Denotes average
magnetic moment per atom.
Structure
FM bcc Fe
Ref.
ꢁFe (␮B)
ꢁNi/Pd/Pt (ꢁB)
Comment
[47]
This work
2.12
2.18
FM fccNi
FePd
[48]
This work
0.61 (Ni)
0.60 (Ni)
[49]
This work
2.85
2.96
0.35 (Pd)
0.36 (Pd)
FePd3
[49]
[49]
2.37(13)
3.10
0.51 (4) (Pd)
0.42 (Pd)
At 300 K
This work
3.30
0.35 (Pd)
FePt
[50]
2.8
0.4 (Pt)
This work
2.95
0.35 (Pt)
FePt3
[50]
[50]
This work
3.3
–
3.26
–
AFM arr.
FM arr.
0.38 (Pt)
0.38 (Pt)
D. Ab initio calculated total energy differences between the intermetallic compound and the weighted averages of total energies of the SER phases of pure
constituents. All values are given in kJ/mol of atoms.
Structure
ꢀ0Eintermet−SER
FePd
FePd3
FePt
FePt3
NiTi (cubic)
NiTi (monoclinic)
−6.036
−10.029
−23.095
−19.232
−33.056
−37.057
˚
A = Angstrom.
˚
1 A = 0.1 nm.
a
Ref. [47].
Ref. [48].
b

5262
S.V. Meschel et al. / Journal of Alloys and Compounds 509 (2011) 5256–5262
pure atomic constituents at the same conditions, both calculated
ab initio at 0 K. Since in the ab initio calculations the energy per
formula unit of the binary compound is evaluated at 0 K there is no
entropy contribution. The enthalpy of formation at 0 K is therefore
identical with the energy of formation at this temperature and can
be calculated at 298 K using Kirchoff’s law. Often the approxima-
tion of Neumann–Kopp’s rule is used and the value of the energy of
formation (at 0 K) is approximately compared with the value of the
enthalpy of formation (at higher temperatures) without further cal-
culation. The Gibbs’ energy of formation is derived from the Gibbs’
energy difference of the compound and the pure constituents. It
follows than that in the derivation of the formation Gibbs’ energies
it is necessary to know well the Gibbs’ energies of the pure phases
and include an entropy contribution. The fifth column in Table 3 and
part D in Table 4. list the predicted values by ab initio calculations
by Dr. Pavlu.
P108/10/1908), the Ministry of Education of the Czech Republic
(Project No. MSM0021622410) and the Academy of Sciences of
the Czech Republic (Project No. AV0Z20410507). We would like
to express our appreciation to Dr. Ian Steele and to Dr. Joseph Pluth
for help with the SEM and the XRD analyses.
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Acknowledgements
This investigation has benefited from the MRSEC facilities at
the University of Chicago and from the facilities in the Thermal
Processing Center at IIT. This study was supported by NSF Grant
# DMR 0964812 at IIT. Dr. Pavlu’s theoretical work was sup-
ported by the Grant Agency of the Czech Republic, (Project No.
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