L. GOMID@ELOVI] et al.: THERMODYNAMIC PROPERTIES AND MICROSTRUCTURES ...
47–53
THERMODYNAMIC PROPERTIES AND MICROSTRUCTURES OF
DIFFERENT SHAPE-MEMORY ALLOYS
TERMODINAMI^NE LASTNOSTI IN MIKROSTRUKTURA
RAZLI^NIH ZLITIN Z OBLIKOVNIM SPOMINOM
Lidija Gomid`elovi}1, Emina Po`ega1, Ana Kostov1, Nikola Vukovi}2,
Dragana @ivkovi}3, Dragan Manasijevi}3
1Mining and Metallurgy Institute, Zeleni bulevar 35, 19210 Bor, Serbia
2University of Belgrade, Faculty of Mining and Geology, \u{ina 7, 11000 Belgrade, Serbia
3University of Belgrade, Technical Faculty, VJ 12, 19210 Bor, Serbia
lgomidzelovic@yahoo.com
Prejem rokopisa – received: 2014-08-26; sprejem za objavo – accepted for publication: 2015-02-06
doi:10.17222/mit.2014.212
The results of a thermodynamic-properties calculation conducted using a general solution model (GSM) and an experimental
investigation of the microstructures of different shape-memory alloys (SMAs) are presented in this paper. The investigated
alloys belong to ternary systems Cu-Al-Zn and Cu-Mn-Ni and to quaternary system Ni-Cu-Fe-Mn. The examinations were
conducted using light microscopy (LM) and scanning electron microscopy with energy-dispersive X-ray spectrometry
(SEM-EDX).
Keywords: thermodynamics, shape-memory alloys, microstructure, LM, SEM-EDX
V tem ~lanku so predstavljeni rezultati termodinami~nih izra~unov lastnosti, ki so bili izvr{eni z uporabo splo{nega modela
re{itev (GSM) in eksperimentalne preiskave mikrostrukture razli~nih zlitin z oblikovnim spominom (SMAs). Preiskovane zlitine
pripadajo ternarnim sistemom Cu-Al-Zn in Cu-Mn-Ni in kvaternarnem sistemu Ni-Cu-Fe-Mn. Preiskave so bile izvedene s
pomo~jo svetlobne mikroskopije (LM), z vrsti~no elektronsko mikroskopijo (SEM) in z rentgensko energijsko disperzijsko
spektrometrijo (EDX).
Klju~ne besede: termodinamika, zlitine z oblikovnim spominom, mikrostruktura, LM, SEM-EDX
1 INTRODUCTION
Shape-memory materials are able to recover their
original shape after being distorted, at the presence of the
right stimulus. These materials include: a) shape-me-
mory alloys, b) shape-memory polymers, c) shape-me-
mory composites and newly developed d) shape-memory
hybrids1.
The shape-memory effect was first discovered for a
gold-cadmium alloy in the 1930s, but this type of
behavior of materials did not attracted the attention of
the researchers until 1960s, when a significant recover-
able strain was observed for a Ni-Ti alloy, enabling
commercial applications.
Shape-memory alloys (SMAs) are characterized by
unique properties (pseudoelasticity and shape-memory
effect), which enable them to "remember" their original
shapes. These alloys are used as activators, changing
their shapes, positions and other mechanical characte-
ristics in a response to a variation in the temperature and
electromagnetic field.
SMAs can be classified, in accordance with the
alloying metals, into:
1. Alloys based on nickel (Ti-Ni, Ni-Mn-Ga)
2. Alloys based on copper (Cu-Zn-Al, Cu-Zn-Si, Cu-
Zn-Sn, Cu-Zn-Ga, Cu-Zn-Mn, Cu-Zn-Al-Ni, Cu-Zn-
Al-Mn, Cu-Al-Ni, Cu-Al-Be, Cu-Al-Mn)
3. Alloys based on iron (Fe-Mn, Fe-Ni-C, Fe-Mn-Cr,
Fe-Mn-Si, Fe-Ni-Nb, Fe-Co-Ni-Ti)
4. Alloys based on noble metals (Au-Cd, Au-Ag, Pt-Al,
Pt-Ga, Pt-Ti, Pt-Cr)
5. Exotic alloys (In-Te, In-Cd, V-Nb)2.
The interest in SMAs is continuously increasing as
new areas of application are discovered. Today, SMAs
are used in different areas such as civil engineering3,4, the
production of microsystems5, medicine6–8, earthquake
technologies9–11 and robotics12,13.
The first copper-based SMA to be commercially
exploited was the Cu-Al-Zn alloy and the shape-memory
alloys from this ternary system typically contain mass
fractions of w(Zn) = 15–30 % and w(Al) = 3–7 %.
Cu-Mn-Ni shape-memory alloys are magnetic, but
some of their properties (like the brittleness) limit their
applications, so the alloying elements like gallium, iron
or aluminum are added to an alloy in order to achieve
satisfying characteristics.
The objective of this work is to provide some new
information about the thermodynamics and microstruc-
tures of selected shape-memory alloys.
Materiali in tehnologije / Materials and technology 50 (2016) 1, 47–53 47
UDK 536.7:66.017 ISSN 1580-2949
Original scientific article/Izvirni znanstveni ~lanek MTAEC9, 50(1)47(2016)
2 EXPERIMENTAL WORK
The characterization of the selected shape-memory
alloys was done using light microscopy and a SEM-EDX
analysis. The samples were obtained from the industrial
production. The composition, shape and production
method of the investigated samples are given in Table 1.
The samples were used as prepared (no annealing).
The microstructural analysis of the investigated
samples was performed with light microscopy (LM),
using a Reichert MeF2 microscope (a magnification of
up to 500×) and a SEM-EDX analysis performed on a
JEOL JSM-6610LV scanning electron microscope (a
magnification of up to 300000×) coupled with an Oxford
Instruments, X-Max 20 mm2 SDD, energy-dispersive
X-ray spectrometer (an accelerating voltage of 20 kV
and a beam current of 1.25 nA). Prior to the
metallographic analysis, the surfaces of the polished
samples were etched with an appropriate etching
solution (Table 2) in order to reveal the structures of the
investigated alloys.
Table 2: Solutions used for sample etching
Tabela 2: Raztopine, uporabljene za jedkanje vzorca
Sample Etching solution
A1 HCl+H2O2+H2O
A2 FeCl3+HCl+H2O
A3 FeCl3+HCl+H2O
A4 FeCl3+HCl+H2O
3 THEORETICAL FUNDAMENTALS
Among many available methods for calculating the
thermodynamic properties of a ternary system based on
the information about the constitutive binary systems,
Chou’s general solution model (GSM)14,15 proved to be
the most reasonable in all respects, overcoming the inhe-
rent defects of the traditional symmetrical and asymme-
trical geometric models. This model breaks down the
boundaries between symmetrical and asymmetrical sys-
tems and generalizes various situations; the accuracy of
the calculation was also proven with practical
examples16,17.
Recently, a new, improved version of the general
solution model based on the Redlich-Kister parameters
was presented by Zhang and Chou18. As the older version
of GSM required a series of integration processes, which
significantly complicated the calculation, and a large
number of real systems can be approximately fit using a
Redlich-Kister polynomial, a new formalism, based on
the binary Redlich-Kister-type parameters, was pre-
sented.
Therefore, this new GSM version is utilized for cal-
culating the thermodynamic properties of the Cu-Al-Zn
and Cu-Mn-Ni ternary systems.
The basic equation of the general solution model for
a ternary system is:
ΔG x x L x x x
x x L
i
i
n
i
i
n
E = − + − +
+
=
=
∑1 2 12
0
1 2 12 3
2 3 23
1
0
2 1( ( ) )
∑
∑
− + − +
+ − + −
=
( ( ) )
( (
x x x
x x L x x
i
ik
k
n
2 3 23 1
3 1 31
0
3 1 31
2 1
2 1

 ) )x i2
(1)
Similarity coefficient  is defined as:
 
 
 
12 = +I I II/ ( ) (2)
 
 
 
23 = +II II III/ ( ) (3)
 
 
 
31 = +III III I/ ( ) (4)
and the deviation sum of squares can be calculated
using:

 I = + + +
− +
+
+ +
=
∑ 12 2 1 2 3 2 5
1
1
12
0
13
2
( )( )( )
( )
( )
i i i
L L
j k
i
l
n
i
( )( )
( )( )
j k j k
L L L L
k j
m
j
n
i i
+ + + +
− −
>=
∑∑ 3 50 12 13 12
1
13
1
(5)

 II = + + +
− +
+
+ +
=
∑ 12 2 1 2 3 2 5
1
1
21
0
23
2
( )( )( )
( )
(
i i i
L L
j k
i
l
n
i
)( )( )
( )( )
j k j k
L L L L
k j
m
j
n
i i k k
+ + + +
− −
>=
∑∑ 3 50 21 23 21 23
(6)

 III = + + +
− +
+
+ +
=
∑ 12 2 1 2 3 2 5
1
31
0
32
2
( )( )( )
( )
(
i i i
L L
j k
i
l
n
i
1 3 50
31 32 31 32)( )( )
( )( )
j k j k
L L L L
k j
m
j
n
i i k k
+ + + +
− −
>=
∑∑
(7)
The basic equation of the general solution model for
a quaternary system19 is:
L. GOMID@ELOVI] et al.: THERMODYNAMIC PROPERTIES AND MICROSTRUCTURES ...
48 Materiali in tehnologije / Materials and technology 50 (2016) 1, 47–53
Table 1: Composition, shape and production method of investigated samples
Tabela 1: Sestava, oblika in na~in izdelave preiskanih vzorcev
Sample Alloy
Composition (w/%)
Shape Production method
Al Cu Zn Mn Ni Fe
A1 NiCuFeMn / 32 / 1.5 65 1.5 rod, R 1.27 cm casting
A2 CuMnNi / 84 / 12 4 / wire, R 1 mm casting, extraction
A3 CuAlZn 4.54 68.14 27.31 / / / wire, R 3.5 mm casting
A4 CuAlZn 5.7 68.27 26.03 / / / rod, R 8 cm casting
ΔG x x L X x x L Xk
k
n
k k
k
n
E = − +
= =
∑ ∑1 2 12
0
1 12 1 3 13
0
1 132 1 2( ) (( ) ( )
( )
)
( ) (
− +
+ − +
= =
∑ ∑
1
2 1 21 4 14
0
1 14 2 3 23
0
2
k
k
k
n
k k
k
n
x x L X x x L X ( )
( )
)
( ) (
23
2 4 24
0
2 24 3 4 34
0
1
2 1
− +
+ − +
= =
∑ ∑
k
k
k
n
k k
k
n
x x L X x x L 2 13 34X
k
( ) )−
(8)
with
X x xi ij i i ij
k
k
k i j
k( ) ( )
,
= +
=
≠
∑ 
1
4
(9)
   i ij
k
(ij,ik) (ij,ik) (ji,jk)( ) / ( )= + (10)
and
 (ij,ik) ij
l
l
n
ik
l
l l l
L L=
+ + +
− +
+
=
∑ 12 2 1 2 3 2 5
1
0
2
( )( )( )
( )
(l m l m l m
L L L L
m l
m
l
n
ij
l
ik
l
ij
m
ik+ + + + + +
− −
>=
∑∑ 1 3 50 )( )( )
( )( m )
(11)
In Equation (11) the second part is different from
zero only if the sum of m and n is an even number, and it
applies to all the Lij parameters that Lkij = (-1)k Lkij. In all
the equations given, Lvij is the Redlich-Kister parameter
for the binary system ij, independent of the composition
and only dependent on the temperature; GE is the integ-
ral molar excess Gibbs energy for the ternary or quater-
nary system and xi is the mole fraction of component i.
Partial thermodynamic quantities are calculated
according to the equations:
G G x G x RTi i i i
E E E= + − =( )( / ) ln1 ∂ ∂  (12)
and:
a xi i i=  (13)
4 RESULTS AND DISCUSSION
The basic thermodynamic data on the constituent
binary subsystems, needed for the calculation of the
thermodynamic properties of the investigated systems,
were taken from the available literature data20–28 and
presented in the form of Redlich-Kister parameters in
Table 3.
The results for the integral molar excess Gibbs
energies of the investigated sections at the corresponding
temperatures, obtained with the general solution model,
are given analytically in polynomial forms (Table 4).
The general solution model and Equations (12) and
(13) were used for the calculation of the copper activities
in the selected sections of ternary systems Cu-Al-Zn and
Cu-Mn-Ni and for the calculation of the nickel activity in
the selected cross-section of quaternary system Ni-Cu-
Fe-Mn. The results of these calculations are presented in
a graphic form (Figures 1 to 3). The thermodynamic
L. GOMID@ELOVI] et al.: THERMODYNAMIC PROPERTIES AND MICROSTRUCTURES ...
Materiali in tehnologije / Materials and technology 50 (2016) 1, 47–53 49
Table 3: Redlich-Kister parameters for constitutive binary systems
Tabela 3: Redlich-Kister parametri za konstitutivne binarne sisteme
System ij Loij (T) L1ij (T) L2ij (T) L3ij (T)
Al-Cu20 –67094 + 8.555*T 32148 – 7.118*T 5915 – 5.889*T –8175 + 6.049*T
Cu-Zn21 –40695.54 + 12.65269*T 4402.72 – 6.55425*T 7818.1 – 3.25416*T 0
Al-Zn22 10465.55-3.39259T 0 0 0
Cu-Mn23 1118.55 – 5.6225T –10915.375 0 0
Cu-Ni24 11760 + 1.084T –1672 0 0
Mn-Ni25 –85853 + 22.715*T –1620 + 4.902*T 0 0
Fe-Ni26 –18782 + 3.7011*T 12308 – 2.7599*T 4457 – 4.1536*T 0
Cu-Fe27 +35625.8 – 2.19045*T –1529.8 + 1.15291*T +12714.4 – 5.18624*T +1177.1
Fe-Mn28 –3950 + 0.489*T +1145 0 0
Table 4: Polynomial form of integral molar excess Gibbs energies calculated using general solution model
Tabela 4: Oblika polinoma integralnih molskih odve~nih Gibbsovih energij, izra~unanih z uporabo splo{nega modela re{itev
System Cross-section T/K Gxs/J mol–1 R2
Ni-Cu-Fe-Mn Cu:Fe:Mn=20:1:1 1873 –2180.5*xNi3 – 6229*xNi2 + 7760.2*xNi + 643.38 1
Cu-Mn-Ni Mn:Ni=3:1 1773 13831*xCu3 – 24352*xCu2 + 18408*xCu – 7883.2 1
Cu-Al-Zn Al:Zn=1:2 1373 11751*xCu2 – 7231*xCu – 5241.8 0.9895
Figure 1: Dependence of nickel activity on the composition, for
cross-section Cu : Fe : Mn = 20 : 1 : 1 from quaternary Ni-Cu-Fe-Mn
system, calculated with GSM, at 1873 K
Slika 1: Odvisnost aktivnosti niklja od sestave, za presek Cu : Fe : Mn
= 20 : 1 : 1 v kvaternarnem sistemu Ni-Cu-Fe-Mn, izra~unana z upo-
rabo GSM, pri 1873 K
properties calculated with the general solution model are
related to the liquid phase of the system, so the tem-
perature, at which the calculation was carried out, was
selected according to that rule, taking into account the
melting points of all the metals in the investigated
system.
From Figure 1, it can be seen that the nickel activity
in section Cu : Fe : Mn = 20 : 1 : 1 and at T = 1873 K
shows a variable character of the deviation from Raoult’s
law, where up to xNi = 0.4 the deviation is positive, but
with a higher content of nickel in the alloy the deviation
becomes negative, indicating that a higher amount of
nickel in the alloy leads to a better miscibility of the
alloy components.
The copper activity in cross-section Mn : Ni = 3 : 1
and at T = 1773 K (Figure 2) shows a clear positive
deviation from Raoult’s law, which can even result in an
occurrence of layering.
The copper activity in cross-section Al : Zn = 1 : 2
and at T = 1373 K (Figure 3) exhibits an apparent
negative deviation from Raoult’s law, indicating that the
L. GOMID@ELOVI] et al.: THERMODYNAMIC PROPERTIES AND MICROSTRUCTURES ...
50 Materiali in tehnologije / Materials and technology 50 (2016) 1, 47–53
Figure 4: Microstructure of sample A1: a) LM (magnification of
500×), b) SEM (magnification of 4000×) and c) positions of EDX
analysis
Slika 4: Mikrostruktura vzorca A1: a) LM (pove~ava 500×), b) SEM
(pove~ava 4000×) in c) polo`aj EDX-analiz
Table 5: Results of EDX analysis of sample A1 in amount fractions,
(x/%)
Tabela 5: Rezultati EDX-analiz vzorca A1 v mno`inskih dele`ih,
(x/%)
Position
A1
Mn Fe Ni Cu
Spectrum 1 1.23 1.52 65.49 31.75
Spectrum 2 1.20 1.69 66.63 30.48
Spectrum 3 1.26 1.67 67.95 29.12
Spectrum 4 1.31 1.27 64.97 32.46
Figure 2: Dependence of copper activity on the composition, for
cross-section Mn : Ni = 3 : 1 from ternary Cu-Mn-Ni system, calcul
ated with GSM, at 1773 K
Slika 2: Odvisnost aktivnosti bakra od sestave, za presek Mn : Ni = 3 : 1
v ternarnem sistemu Cu-Mn-Ni, izra~unana z uporabo GSM, pri 1773
K
Figure 3: Dependence of copper activity on the composition, for
cross-section Al : Zn = 1 : 2 from ternary Cu-Al-Zn system, calculated
with GSM, at 1373 K
Slika 3: Odvisnost aktivnosti bakra od sestave, za presek Al : Zn = 1 : 2
v ternarnem sistemu Cu-Al-Zn, izra~unana z uporabo GSM, pri 1373 K
miscibility of the metals in the ternary Cu-Al-Zn system
is quite good.
The results of the microstructural analysis with light
optical microscopy and SEM-EDX for sample A1 are
given in Figure 4, with the chemical composition deter-
mined with EDX presented in Table 5.
The microphotograph obtained with LM (Figure 4a)
shows that the alloy structure consists of sharp-edged
polygonal grains.
The SEM image on Figure 4b reveals the structure of
sample A1 as a gray matrix with imbedded triangular
grains, but the EDX analysis shows that the grains and
the matrix have almost identical chemical compositions.
These findings are in agreement with the fact that copper
and nickel, two components that together account for
over 90 % of the alloy’s mass, form a continuous series
of solid solutions29.
L. GOMID@ELOVI] et al.: THERMODYNAMIC PROPERTIES AND MICROSTRUCTURES ...
Materiali in tehnologije / Materials and technology 50 (2016) 1, 47–53 51
Figure 5: Microstructure of sample A2: a) SEM (magnification of
2000×) and b) positions of EDX analysis
Slika 5: Mikrostruktura vzorca A2: a) SEM (pove~ava 2000×) in b)
polo`aj EDX-analiz
Table 6: Results of EDX analysis of sample A2 in amount fractions,
(x/%)
Tabela 6: Rezultati EDX-analiz vzorca A2 v mno`inskih dele`ih,
(x/%)
Position
A2
Mn Ni Cu
Spectrum 1 15.04 4.70 80.25
Spectrum 2 14.92 4.50 80.58
Spectrum 3 15.11 4.48 80.41
Spectrum 4 15.35 4.41 80.24
Figure 6: Microstructure of sample A3: a) LM (magnification of
500×), b) SEM-EDX (magnification of 1000×) and c) positions of
EDX analysis
Slika 6: Mikrostruktura vzorca A3: a) LM (pove~ava 500×), b)
SEM-EDX (pove~ava 1000×) in c) polo`aj EDX-analiz
Table 7: Results of EDX analysis of sample A3 in amount fractions,
(x/%)
Tabela 7: Rezultati EDX-analiz vzorca A3 v mno`inskih dele`ih,
(x/%)
Position
A3
Al Cu Zn
Spectrum 1 8.83 69.75 21.42
Spectrum 2 7.93 71.11 20.96
Spectrum 3 1.11 78.03 20.87
The results of the microstructural analysis with light
microscopy and SEM for sample A2 are given in Figure
5 and the chemical compositions determined with the
EDX analysis are presented in Table 6.
Technical difficulties like the fact that the maximal
magnification of the LM apparatus is just 500× and a
very small diameter (1 mm) of sample A2 prevented us
from getting a LM photograph.
The microstructure of sample A2 (Figure 5b) is
characterized by the grains irregular in the shape and
size, and the results of the EDX analysis presented in
Table 6 are consistent with the fact that copper forms
solid solutions with nickel and manganese29.
The results of the microstructural analysis with light
optical microscopy and SEM for sample A3 are given in
Figure 6, with the chemical compositions determined
with the EDX analysis presented in Table 7.
The microstructure of alloy A3, obtained with a LM
microphotograph (Figure 6a), consists of polygonal
grains with a significant variation in size.
The results of the microstructural analysis with light
optical microscopy and SEM-EDX for sample A4 are
given in Figure 7 and the chemical compositions deter-
mined with the EDX analysis are presented in Table 8.
The microstructure of sample A4 consists of polygonal
grains, which vary in size.
According to the phase diagram of the binary Cu-Zn
and Cu-Al systems29, the solid solubility of aluminum in
copper is approximately 18 % of amount fractions, and
for zinc it goes up to 30 % of amount fractions. Consi-
dering that the base material for samples A3 and A4 is
copper (w(Cu) = 68 %), it is reasonable to expect that
aluminum and zinc will dissolve in copper, creating solid
solutions. This was confirmed with the results of the
EDX analysis presented in Tables 7 and 8. In addition,
the EDX results indicate that the homogeneity of sample
A4 is quite good because there is no significant
difference in the chemical composition analyzed at
various measuring points.
5 CONCLUSION
Different shape-memory alloys belonging to ternary
systems Cu-Al-Zn and Cu-Mn-Ni and to quaternary sys-
tem Ni-Cu-Fe-Mn were investigated. The termodynamic
properties of these alloys were investigated analytically,
using the general solution model (GSM) and the known
Redlich-Kister parameters for the constitutive binary
systems. The thermodynamic analysis showed that the
alloys with high copper amounts from systems Cu-Al-Zn
and Ni-Cu-Fe-Mn display a good miscibility, while the
alloys from the Cu-Mn-Ni system tend to display
positive deviations from Raoult’s law, which can even
lead to layering.
The microstructures of the selected alloys were inve-
stigated experimentally by means of light optic micro-
scopy (LM) and scanning electron microscopy with
energy-dispersive X-ray spectrometry (SEM-EDX). The
microstructure analysis of the investigated alloy samples
L. GOMID@ELOVI] et al.: THERMODYNAMIC PROPERTIES AND MICROSTRUCTURES ...
52 Materiali in tehnologije / Materials and technology 50 (2016) 1, 47–53
Figure 7: Microstructure of sample A4: a) LM (magnification of
80×), b) SEM-EDX (magnification of 1000×) and c) positions of EDX
analysis
Slika 7: Mikrostruktura vzorca A4: a) LM (pove~ava 80×), b)
SEM-EDX (pove~ava 1000×) in c) polo`aj EDX-analiz
Table 8: Results of EDX analysis of sample A4 in amount fractions,
(x/%)
Tabela 8: Rezultati EDX-analiz vzorca A4 v mno`inskih dele`ih,
(x/%)
Position
A4
Al Cu Zn
Spectrum 1 12.14 63.45 24.41
Spectrum 2 11.95 64.22 23.83
Spectrum 3 12.03 63.60 24.37
Spectrum 4 12.09 63.66 24.25
Spectrum 5 12.10 63.15 24.76
revealed that the microstructure is built of polygonal
grains that can significantly vary in size. The EDX
analysis results provided the information about the alloy
chemical compositions and were, overall, in agreement
with the known facts about the investigated systems. The
results presented in this paper contribute to a better
understanding of the thermodynamic properties and mi-
crostructures of the investigated shape-memory alloys.
Acknowledgement
The authors are grateful to the Ministry of Education,
Science and Technological Development of the Republic
of Serbia for the financial support provided through
Projects 34005 "Development of ecological knowl-
edge-based advanced materials and technologies for
multifunctional application" and 172037 "Modern
multi-component metal systems and nanostructured
materials with different functional properties".
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