Molecular dynamics study of Cu-Pd ordered alloys
ABSTRACT Purpose: The goal of the paper is to study the molecular dynamics of Cu-Pd ordered alloys.Design/methodology/approach: The thermal and mechanical properties of Cu, Pd pure metals and their ordered intermetallic alloys of Cu3Pd(L12) and CuPd3(L12) are studied by using the molecular dynamics simulation. The melting behavior of the metals considered in this work is studied by utilizing quantum Sutton-Chen (Q-SC) many-body potential. The effects of temperature and concentration on the physical properties of Cu-Pd system are analyzed.Findings: A wide range of properties of Cu, Pd pure metals and their Cu3Pd and CuPd3 ordered intermetallics is presented. It was found that this potential is suitable to give the general characteristics of the melting process in these systems. Practical implications: The simulation results such as cohesive energy, density, elastic constants, bulk modulus, heat capacity, thermal expansion and melting points are in good agreement with the available experimental data and other theoretical calculations.Originality/value: To the best our knowledge this work presents, for the first time, a wide range of physical properties of alloys focusing on Cu-Pd ordered compounds.
- Citations (44)
- Cited In (0)
- [Show abstract] [Hide abstract]
ABSTRACT: We have evaluated interatomic potentials of Cu, Au and Cu-Au 0953-8984/10/48/018/img9 ordered alloys in the framework of the second-moment approximation to the tight-binding theory by fitting to the volume dependence of the total energy of these materials computed by first-principles augmented-plane-wave calculations. We have applied this scheme to calculate the bulk modulus and elastic constants of the pure elements and alloys and we have obtained a good agreement with experiment. We also have performed molecular-dynamics simulations at various temperatures, deducing the temperature dependence of the lattice constants and the atomic mean square displacements, as well as the phonon density of states and the phonon-dispersion curves of the ordered alloys. A satisfactory accuracy was obtained, comparable to previous works based on the same approximation, but resulting from fitting to various experimental quantities.Journal of Physics Condensed Matter 01/1998; 101(48):10979-10990. · 2.22 Impact Factor - [Show abstract] [Hide abstract]
ABSTRACT: We present a simple method to improve the accuracy of the calculated heat of mixing for the Cu-Pd alloy within the formalism of the molecular dynamics/ Monte Carlo-corrected effective medium (MD/MC-CEM) theory by adding a fitted Morse potential to the pair interaction between Cu and Pd atoms. This leads to a much better agreement between the theoretical and experimental values of heats of mixing for five different compositions of the Cu-Pd alloy in the bulk phases. Using this newly fitted model, we have performed simulations on CuPd clusters consisting of 50-10000 atoms with fcc and bcc structures. Our calculations show that in the range of cluster sizes of several thousand atoms, the fcc structure is energetically favoured over the bcc structure. We estimate an approximate size for the fcc to bcc (CsCl, known bulk structure for CuPd) transition in these clusters to be around 10000 atoms. Additionally, we have also performed calculations of the X-ray diffraction patterns of a variety of cluster geometries and sizes. The calculated X-ray diffraction pattern of a slightly distorted fcc cluster exhibits the main features observed in the available experimental diffraction patterns of colloidal bimetallic catalysts of CuPd. The calculated diffraction patterns of bcc clusters are quite different from the experimental data.Philosophical Magazine A 08/1999; 79(8):2025-2049. - [Show abstract] [Hide abstract]
ABSTRACT: The structures and energetics of Cu-Au alloys over a wide range of temperatures are studied using a combination of quasi-harmonic (QH) lattice dynamics and Monte Carlo (MC) simulations at constant temperature and constant pressure. The many-body potential used is fitted to room-temperature experimental data taking vibrational contributions into account. Transitions to the disordered phases are studied using MC simulations in which not only anisotropic deformation of the unit cell and atomic movements are allowed, but also exchange of atoms of different type is explicitly considered. Our calculations reproduce all characteristic features of the order-disorder transitions, including the characteristic peaks in the plots of heat capacity as a function of temperature.Modelling and Simulation in Materials Science and Engineering 05/2000; 8(3):389. · 1.93 Impact Factor
Page 1
© Copyright by International OCSCO World Press. All rights reserved. 2008
VOLUME 31
ISSUE 1
November
2008
Research paper
41
of Achievements in Materials
and Manufacturing Engineering
and Manufacturing Engineering
of Achievements in Materials
Molecular dynamics study
of Cu-Pd ordered alloys
S. Özdemir Kart a,*, A. Erbay a, H. Kılıç a, T. Cagin b, M. Tomak c
a Department of Physics, Pamukkale University, 20020 Denizli, Turkey
b Department of Chemical Engineering, Texas A&M University, TX77845-3122 Texas, USA
c Department of Physics, Middle East Technical University, 06531 Ankara, Turkey
* Corresponding author: E-mail address: ozsev@pau.edu.tr
Received 27.06.2008; published in revised form 01.11.2008
Analysis and modelling
AbstrAct
Purpose: The goal of the paper is to study the molecular dynamics of Cu-Pd ordered alloys.
Design/methodology/approach: The thermal and mechanical properties of Cu, Pd pure metals and their ordered
intermetallic alloys of Cu3Pd(L12) and CuPd3(L12) are studied by using the molecular dynamics simulation. The
melting behavior of the metals considered in this work is studied by utilizing quantum Sutton-Chen (Q-SC) many-body
potential. The effects of temperature and concentration on the physical properties of Cu-Pd system are analyzed.
Findings: A wide range of properties of Cu, Pd pure metals and their Cu3Pd and CuPd3 ordered intermetallics
is presented. It was found that this potential is suitable to give the general characteristics of the melting process
in these systems.
Practical implications: The simulation results such as cohesive energy, density, elastic constants, bulk modulus,
heat capacity, thermal expansion and melting points are in good agreement with the available experimental data
and other theoretical calculations.
Originality/value: To the best our knowledge this work presents, for the first time, a wide range of physical
properties of alloys focusing on Cu-Pd ordered compounds.
Keywords: Cu-based intermetallic alloys; Molecular dynamics simulations; Quantum Sutton-Chen potentials;
Melting properties
1. Introduction
1.?? Introduction
With the rapid development of advanced technologies, the
demands for the design of components and the production of new
materials which are strong, stiff and ductile at high temperature
and the study of the final product properties are increasing. Stable
materials responding these requirements are the intermetallic
compounds. They have structural properties which differ greatly
from constituent metals.
Cu-based intermetallics have motivated the strong interest in
their fundamental properties including interatomic bonding, long
range order, crystalline defects, order-disorder transition and
diffusion [1-14]. Among them, CuPd has receiving considerable
attention due to their promising use as catalysts in many
technologically important areas, including petroleum refining and
automotive emission control, and membrane for hydrogen
production and purification. On the other hand, Cu3Pd and CuPd3
being ordered alloys of Cu-Pd system offer to be investigated due
to a little of theoretical and experimental studies. In fact,
relatively attention has been paid to the temperature dependence
of the thermodynamical and mechanical properties of the ordered
Cu3Pd and CuPd3 intermetallic compounds. In this work this
specific problem is addressed.
Some first principles (ab initio) calculations responsible for the
physical properties of Cu-Pd system have recently been carried out
successfully [1, 2, 11-13]. Because ab initio methods are
computationally expensive, the calculations have been limited to
short time scales and to a few hundred atoms. On the other hand,
Page 2
Research paper
42
Journal of Achievements in Materials and Manufacturing Engineering
S. Özdemir Kart, A. Erbay, H. Kılıç, T. Cagin, M. Tomak
Volume 31 Issue 1 November 2008
there are empirical and more practical approaches that can afford to
investigate many system and trends in physical properties [15-18].
These potentials provide sufficiently accurate and quick description
in metallic systems. Molecular dynamics (MD) simulation can
provide an important insight by allowing one to determine static
and dynamical properties of materials at finite temperatures, when
provided with suitable interatomic potentials.
In this study, we have performed MD simulations using
Sutton-Chen (SC) [18] potential with new potential parameter set,
namely the Quantum Sutton-Chen (Q-SC) potential developed by
Ça?n and co-workers [19] to investigate the physical properties
of Cu and Pd pure metals and ordered Cu-Pd alloys (especially,
Cu3Pd(L12)and CuPd3(L12)). This potential has been used in
various applications, ranging from random alloys, glass
formation, crystallization, surfaces, clusters, nanowires and single
crystal plasticity of pure metals to transport properties of fcc
metals [20-26]. One purpose of this study is to verify the validity
of potential parameters to show their transferability from pure
elements to ordered alloys, from low temperatures to high
temperatures. Another aim is to obtain comprehensive data of the
physical properties of ordered Cu-Pd, which is scientifically and
technologically important material. In this study, we have
calculated the lattice parameter, cohesive energy, density, elastic
constant and bulk modulus at various temperatures and deduced
the melting temperature, heat capacity and thermal coefficient of
the volume expansion by using Q-SC potential parameters. The
results are compared with experimental and theoretical data
available in the literature. To the best our knowledge this work
presents, for the first time, a wide range of physical properties of
alloys focusing on Cu-Pd ordered compounds.
This paper has the following structure: simulation details are
presented in Section 2. Section 3 deals with the results of computer
simulations. The final section gives the conclusion of the results.
2. Simulation details
2.?? simulation?details
Three successive simulations are performed for heating
process of Cu-Pd alloys by using the algorithm based on extended
Hamiltonian formalism [27-31]. First, constant-enthalpy constant-
pressure (HPN) MD simulation is carried out to heat the system
from 0.1 K to 2500 K with the increments of 50 K. This
increment is reduced to 10 K near the melting temperature to get
more accurate values of the melting temperature. The heating
procedure is carried out by scaling velocities with the ratio of the
increment temperature to the specific number of steps depending
on target temperature, (1 K/step). At each temperature, 2000 time
steps are carried out for equilibrium. Then 20000 additional steps
in constant-temperature constant-pressure (TPN) dynamics are
taken to obtain some statistical properties, such as volume,
density and energy of the system. Finally, 50000 steps of
microcanonical ensemble (EVN) dynamics follows by using the
resulting zero strain average matrix to obtain pressure dependent
properties of the system, such as elastic constant.
The simulation box is made up of 2048 particles arranged on
the fcc structure for the pure Cu and Pd, L12 structure for the
Cu3Pd and CuPd3 ordered intermetallic systems. In the case of
Cu3Pd, the Pd atoms occupy the corner cites, while Cu atoms
occupy the face centres of the basis cube; the opposite occurs for
CuPd3. The MD simulation performed in this study uses the
Sutton-Chen (SC) type potential [18]. This potential is recently
reparametrized by Ça?n et al. [19] by including quantum
corrections accounting for zero-point energy, hence called
quantum Sutton-Chen (Q-SC) potential, to improve some physical
properties at high temperatures. The potential parameters are
obtained by fitting to some experimental properties, such as lattice
parameter, cohesive energy, bulk modulus, phonon frequency at
the X point, vacancy formation energy and surface energy. The
total potential energy has the following form:
?
??
?
?
?
i
?
i
?
?
i
?
?
j
?
?
?
?
?
?
?
?
?
??
?
?
?
??
?
?
?
??
?
?
??
?
?
?
?
??
?
??
NN
j
ij
m
ij
ij
iii
ij
n
ij
ij
i
iji tot
r
a
c
r
a
UU
2 / 1
2
1
??
(1)
The first term in Eq. 1 is a two body repulsive interaction
between the atoms i and j, separated by a distance rij. The second
term represents the many-body cohesion term associated with
atom i. The square root term introduces a many-body component
into the energy summation. The popularity of SC potentials is
partly due to the computationally tractable form adopted for the
many-body forces. It is the relatively simple analytic form of the
potential that enables one to calculate the many physical
properties of the materials.
In the Eq. 1, a is a length parameter scaling to the lattice
spacing of the crystal, c is a dimensionless parameter scaling the
attractive terms, ? is an energy parameter determined from
experiment, and
mn,
are integer parameters with
determine the range of the two components of the potential. The
interaction length of potential is taken as two lattice parameters for
the efficiency of the computer simulation time. The temperature
effects in the simulations are considered by giving an additional
length of half the lattice parameter. The parameters for the Cu-Pd
alloys are obtained through the following mixing rules [32]:
?
ji ij
????
,
ij
a
?
mn ?
which
?
2 / 1
2
ji
aa
?
,
(2)
2
ji
ij
mm
m
?
?
,
2
ji
ij
nn
n
?
?
Q-SC potential parameters [19] for pure Cu and Pd metals are
given in Table 1.
Table1.
Q-SC potential parameters for Cu and Pd pure metals
Metal
n m
)(meV
?
c
)(
?
Aa
3.6030 Cu 10 5 5.792184.843
Pd 12 6 3.2864 148.205 3.8813
The fluctuation formula for the calculation of the elastic
constants [33-35] is given as:
?
klij
B
T Nk
??
????
0
?
??
ijkljk iljlik
B
klijijkl
V
PPPP
Tk
V
C
??
??
0
2
(3)
Page 3
43
Analysis and modelling
Molecular dynamics study of Cu-Pd ordered alloys
The first term represents the contribution of the fluctuation of the
microscopic stress tensor
energy contribution, and third term is the so-called Born term. <>
denotes the averaging over time and
volume for the model system. The bulk modulus for the cubic
systems can be obtained from
B
?
and coefficient of thermal volume expansion can be determined
from the differential of the enthalpy and that of volume,
respectively, as follows:
ij P , the second term is the kinetic
00
dethV ?
is the reference
3 / )
12
C
2(
11
C
?
. Specific heat
P
p
T
TH
?
TC
?
?
?
?
?
?
?
?
)(
)(
, (4)
P
p
T
TV
?
TV
T
?
?
?
?
?
?
?
??
)(
)(
1
)(
?
. (5)
3. Results
3.?? results
Table 2 shows some thermodynamical properties, namely
density ? , lattice constanta ,
compressibility ? of CuPd ordered metal alloys calculated from
TPN ensemble average over 20000 time steps at 300 K, together
with available experimental or theoretical data. The results for Cu
and Pd pure metals are in good agreement with the experimental
data [36]. The discrepancy between Q-SC and experimental
values for the first three properties is less than 1%, for
compressibility of Cu 20.5% and for that of Pd 12.5%. We expect
that the results of compressibility will be improved at high
temperatures because Q-SC potential describes well temperature
dependent properties. There is not any experimental data for
Cu3Pd and CuPd3 alloys to compare our results with them. The
values of lattice constants calculated for the ordered alloys are
cohesive energy
c
E and
close to that of other theoretical studies [10, 37]. The increasing
concentration of Pd in Cu-Pd compounds gives rise to decreasing
the cohesive energy of the Cu-Pd intermetallics, while it causes an
increment in lattice parameter and density, as expected.
We calculated the heat capacity as a function of temperature
and concentration by fitting the enthalpy of Cu-Pd alloys to a
quadratic polynomial using the data below the melting
temperature. The quadratic function form may be given as
2
)(
cTbTaT
Here T is the temperature. Heat capacity can be found by
taking the derivative of the polynomial function of Eq. 6
according to Eq. 4. The resulting
H
???
(kJ/mole).
(6)
p
C should not be extrapolated
)(TH
which is fitted to to T=0 K, as it is derived from
simulation results between 100 K and 700 K. The coefficients of
expression in Eq.6 are given in Table 3.
As shown in Table 3, the agreement between the simulated results
and experimental data [38] is very good. For example, the heat
capacities of Cu and Pd at 300 K are reported as 26.359 Jmole-1K-1 and
25.791 Jmole-1K-1, respectively. Deviations from the experimental
values for Cu and Pd are 7.75 % and 0.73 %, respectively.
We have also fitted the volume and temperature curve by the
same type of quadratic polynomial function as done in the heat
capacity to analyze further the volume thermal expansion
behaviour. The function used in the fitting procedure is
2
)(
cT bTaTV
???
(nm3mole-1). (7)
The coefficients in Eq.7 and the values of the thermal volume
expansion calculated from Eq. 5 at 300 K are presented in Table 4.
The value for copper, 7.642x10-5 K-1, is in better agreement with the
value from the experiment [38] than other experimental value
measured by Moruzzi et al. [39]. For palladium, our simulation
result is greater than experimental value of 1.160x10-5 K-1 [39].
Table 2.
Density ? , lattice constanta , cohesive energy
300 K, together with a comparison with available experimental [36] or theoretical data. Stars correspond to other theoretical results [10, 37]
E (kJ/mol)
Exp Q-SC
Exp Q-SC
Cu -336.0 -339.58 3.61
Cu3Pd -339.89 3.694*, 3.705**
CuPd3 -358.87 3.839*, 3.834**
Pd -376.0 -377.91 3.89
* from [37], ** from [10]
c
E and compressibility ? of CuPd ordered metal alloys calculated by using Q-SC potential parameters at
Material
c
)(
?
Aa
? (g/cm3)
Exp Q-SC
8.93
12.00
? (10-11m2/N)
Exp Q-SC
0.73
0.55
3.62
3.70
3.84
3.90
8.93
9.73
11.22
11.96
0.58
0.62
Table 3.
Coefficients of polynomial function used to find the heat capacity of Cu, Pd pure metals and their alloys. Heat capacity values of the metals along
with whenever available experimental data [38] at 300 K
Material
a
4
10?
bx
6
10?
cx
p
C (J/moleK)
Q-SC Exp
Cu
Cu3Pd
CuPd3
Pd
-339.672
-347.680
-366.437
-377.824
249.787
255.138
244.646
246.235
2.300
1.609
2.247
1.945
26.359
26.479
25.813
25.791
24.464
25.980
Page 4
Research paper
44
Journal of Achievements in Materials and Manufacturing Engineering
S. Özdemir Kart, A. Erbay, H. Kılıç, T. Cagin, M. Tomak
Volume 31 Issue 1 November 2008
We calculated the elastic constants of Cu-Pd ordered alloys to
study the mechanical and dynamical properties. The elastic constants,
in particular, provide valuable information on the stability and
stiffness of materials. In this study, elastic constants are calculated by
using the fluctuation expression (3) by taking the average ensemble of
EVN over the 50000 time steps. The elastic constants and bulk
modulus results for Cu and Pd pure metals and their ordered alloys
are listed in Table 5. At each temperature, the density obtained from
TPN ensemble by averaging over the 20000 time step is used to
specify the volume of the EVN ensemble. The detailed calculation
methodology related to the elastic constants can be found in Refs.
[35]. The elastic constants and bulk modulus of Cu and Pd pure
metals predicted from Q-SC parameters are compared with the
available experimental values and the results of previous works using
different potential models at 0 K in Table 5. As shown, the potential
used by Cleri and Rosato [40] for the elastic constants is yielding
better results. The elastic constants and bulk modulus from Q-SC
agree with the available experiment and other calculations except for
elastic constant of C12. The percentage differences of C11, C12 and C44
of Cu for the Q-SC are 9.8%, 2.9% and 11.1% at 0 K, respectively.
The accuracy of the Q-SC elastic constant of C11 for Pd, showing a
deviation of 8% from experiment, is comparable to that of the
embedded atom model (EAM) [41]. The experimental data on the
elastic constants for Cu-Pd alloys are not available for comparison.
Table 4.
Coefficients of polynomial function used to find the thermal
volume expansion of Cu, Pd pure metals and their alloys. Thermal
expansion values of the metals along with whenever available
experimental data [38, 39] at 300 K
Material
4
10?
ax
9
10?
bx
12
10?
cx
5
10?
x
p
?
Q-SC Exp
(K-1)
Cu 116.023 734.596 281.536 7.642
1.6701
4.9502
25.980
Cu3Pd
CuPd3
Pd
1 from [39], 2 from [38]
124.252
139.136
145.387
757.483
749.161
748.575
232.696
200.403
179.893
7.090
6.149
5.802
Table 5.
Comparison of calculated and experimental (Exp) [42] values for
elastic constants (Cij) and bulk modulus (B) at 0 K for pure metals
in the units of GPa. For Cu-Pd alloys, the elastic constants are
predicted from Q-SC potential parameters at 300K. Our results
(Q-SC) for Pd and Cu are compared with the other potential
models: embedded atom model (EAM) [41] and tight binding
second moment approximation (TBSMA) [40, 43]
Metals Model C11
Q-SC
Exp1
TBSMA2
TBSMA3
142.00
Cu3Pd Q-SC 166.71
CuPd3 Q-SC 190.44
Q-SC
Exp1
TBSMA2
EAM4
218.00
1 from [42], 2 from [40], 3 from [43], 4 from [41]
C12
121.30
124.94
125.00
180.00
117.97
132.90
150.25
176.14
178.00
184.00
C44
72.74
81.80
82.00
122.00
67.85
77.08
91.66
71.17
73.00
65.00
B
Cu
159.00
176.20
176.00
127.50
142.03
142.00
142.00
134.22
152.08
172.17
195.00
196.00
195.00
Pd
216.00
234.12
232.00
We are also interested in investigating the temperature and
concentration dependence of elastic constants of Cu-Pd ordered
system to see the effect. The variation of elastic constants of Cu-
Pd in the fcc structure for pure metals and in the L12 structure for
Cu3Pd and CuPd3ordered alloys as a function of temperature are
given in Figure 1a-d, respectively. These quantities decrease
linearly with increasing temperature, as seen in the Figures.
Thermal softening increases with increasing the concentration of
Cu in Cu-Pd system at each temperature.
The melting temperatures of Cu-Pd ordered alloys have been
determined by analyzing the behaviour of density, energy, volume
and pair distribution function as a function of temperature. We
obtain the same melting temperatures from all these physical
properties. Computer simulations are carried out by 10 K
increments around the melting point in order to make better
predictions of the melting point. In this manner, the melting points
of the pure elements and intermetallic systems are predicted for
Q-SC parameters. The results are listed in Table 6, along with the
available experimental [44] and other theoretical data [41, 45, 46].
As shown in the table, the melting points of pure Cu (1370±10 K)
and Pd (1820 ±10 K) metals are in very good agreement with
experimental values. As we go into the alloy, this accuracy
decreases with the maximum deviation of 3.20%. This is due to
the potential parameters of binary metal alloys calculated by using
those of pure metals using combination rules (Eq. 2). Our result
for the melting temperature of Cu are in excellent agreement with
the other calculation based on EAM [35].
Fig. 1. The variation of elastic constants as a function of temperature
for a) Cu, b) Cu3Pd, c) CuPd3 and d) Pd
Page 5
45
Analysis and modelling
Molecular dynamics study of Cu-Pd ordered alloys
Table 6.
Melting points of Cu-Pd ordered alloys and Cu and Pd pure
metals along with experimental [44] and other calculation results
[41, 45, 46], where available
Tm(K)
Q-SC Exp Other calculations
Cu 1370±10 1356 13701,10732±17,13403
Cu3Pd 1450±10 1405
CuPd3 1700±10 1650
Pd 1820±0 1825
1 from [45], 2 from [46], 3 from [41]
Mater.
Devia.
(%)
1.03
3.20
3.03
0.27
1215±202,13903
The temperature dependence of density, volume and energy of
Cu, Pd, Cu3Pd and CuPd3 are shown in Fig. 2(a), (b) and (c)
respectively. The discontinuity in the Figures shows the structural
transformation from solid phase to liquid phase. The melting
temperature is identified by monitoring the jump in the Figures. At
the melting temperatures, we find the density for Pd and Cu to be
10.53±0.06 and 7.64 g/cm3, respectively. These values are consistent
with experimental values which are 10.49 and 8.00, respectively [47].
The way we follow to predict the melting temperatures from
the pair distribution function g(r) is observed in Fig. 3 plotted at
the selected temperatures; 1600, 1810, 1820 and 2000 K for Pd.
The peaks at 1600 K could be one by one related to the different
coordination shells of a perfect fcc structure. With increasing
temperature up to 1810 K the peaks are broadened and lowered,
showing the structure with the peaks at near some of the ideal fcc
position. At the temperature of 1820 K some peaks disappear,
indicating that a diffusion dynamics is thermally activated.
Finally, the crystal order is broken and melting occurs after this
temperature. That is, the metal goes into the liquid state (2000 K).
Fig. 2. (a) Density, (b) energy and (c) volume of Cu, Pd , Cu3Pd
and CuPd3 as a function of temperature
Fig. 3. Pair distribution function g(r) for Pd at various temperatures
4. Conclusion
4.?? conclusions
We have presented a wide range of properties of Cu, Pd pure
metals and their Cu3Pd and CuPd3 ordered intermetallics. We have
found that this potential is suitable to give the general characteristics of
the melting process in these systems. The transferability of the potential
is an important conclusion which can be made from this work.
Although the potential parameters were fitted to solid experimental
properties of the pure system, the Q-SC model describes the thermal
and mechanical properties of the liquid Cu-Pd system. Because the only
experimental data for Cu-Pd metal alloys exits for the melting points,
we can test the transferability from experimental case to alloy case for
melting. That the results for density, lattice constants, cohesive energy,
compressibility, elastic constants, heat capacity and thermal expansion
coefficients of pure metals show satisfactory agreement with available
experimental values leads us to conclude that transferability of the
potential is proved for pure metal cases.
To our knowledge, the temperature dependence of physical
properties for Cu3Pd and CuPd3 ordered alloys are presented for the
first time, in this study. If the potential energy function considered
here is fitted to the solid properties of the intermetallic compounds
of Cu3Pd and CuPd3, the results may be improved further.
Acknowledgements
Acknowledgements
This work is supported by Pamukkale University Scientific
Research Fund through Project No: BAP-2006-FEF-019.
References
references
[1]Z.W. Lu, S.H. Wei, A. Zunger, S. Frota-Pessoa, L.G. Ferreira,
First-principles statistical mechanics of structural stability of
intermetallic compounds, Physical Review B 44 (1991) 512-544.
S. Taizawa, S. Blugel, K. Terakura, Theoretical study of the
structural stability of CuPd and CuPt alloys: Pressure-induced phase
transition of CuPt alloy, Physical Review B 43 (1991) 4947-955.
P. Deurinck, C. Creemers, Monte Carlo simulation of Cu
segration and ordering at the (110) surface of Cu75Pd25,
Surface Science 419 (1998) 62-77.
[2]
[3]
Page 6
Research paper
46
READING DIRECT: www.journalamme.org
Journal of Achievements in Materials and Manufacturing EngineeringVolume 31 Issue 1 November 2008
[4]N.I. Papanicolaou, G.C. Kallinteris, G.A. Evangelakis, D.A.
Papaconstantopoulos, M.J. Mehl, Second-moment interatomic
potential for Cu-Au alloys based on total-energy calculations
and its application to molecular-dynamics simulations, Journal
of Physics Condensed Matters 10 (1998) 10979-10990.
V. Shah, L. Yang, Nanometre fcc clusters versus bulk bcc
alloy: the structure of Cu-Pd catalysts, Philosophical
Magazine A 79 (1999) 2025-2049.
G.D. Barrera, R.H. de Tendler, E.P. Isoardi, Structure and
energetics of Cu-Au alloys, Modelling Simulations
Materials Science Engineering 8 (2000) 389-401.
N. Metadjer, A. Laref, Tight-binding calculation of
structural properties of bulk Cu3Au and its corresponding
clusters, Superlattices and Microstructures 30 (2001) 21-28.
X. Wang, K.F. Ludwig, O. Malis, J. Mainville, Temperature
dependence of the diffuse-scattering fine structure in Cu-Pd
alloys, Physical Review B 63 (2001) 092201 1-4.
W. Pfeiler, B. Sprusil, Atomic ordering in alloys: stable states and
kinetics, Materials Science and Engineering A 324 (2002) 34-42.
[10] G. Bozzolo, J.E. Garces, R.D. Noebe, P. Abel, H.O. Mosca,
Atomistic modelling of surface and bulk properties of Cu, Pd and
Cu-Pd system, Progress in Surface Science 73 (2003) 79-116.
[11] P. Kamakoti, D.S. Sholl, A comparison of hydrogen
diffusivities in Pd and CuPd alloys using density functional
theory, Journal of Membrane Science 225 (2003) 145-154.
[12] E.J. Wu, G. Ceder, Using bond-length-dependent transferable
force constants to predict vibrational entropies in Au-Cu, Au-Pd,
and Cu-Pd alloys, Physical Review B 67 (2003) 134103 1-7.
[13] P. Kamakoti, D.S. Sholl, Ab initio lattice-gas modeling of
interstitial hydrogen diffusion in CuPd alloys, Physical
Review B. 71 (2005) 014301 1-9.
[14] H.H. Kart, M. Tomak, T. Cagin, Thermal and mechanical
properties of Cu-Au intermetallic alloys, Modelling Simulations
Materials Science Engineering 13 (2005) 357-669.
[15] J.K. Norskov, Covalent effects in the effective medium
theory of chemical binding: Hydrogen heats of solutions in
3d metals, Physical Review B 26 (1982) 2875-2885.
[16] M.S. Daw, M.I. Baskes, Embedded-atom method:
Derivation and application to impurities, surfaces, and other
defects in metals, Physical Review B 29 (1984) 6443-6453.
[17] M.W. Finnis, J.E. Sinclair, A simple empirical N-body potential
for transition metals, Philosophical Magazine A 50 (1984) 45-55.
[18] A.P. Sutton, J. Chen, Long-range Finnis-Sinclair potentials,
Philosophical Magazine Letters 61 (1990) 139-146.
[19] T. Çagin, Y. Qi, H. Li, Y. Kimura, H. Ikeda, W.L. Johnson, W.A.
Goddard III, The quantum Sutton-Chen many-body potential for
properties of fcc metals, MRS Symposium Ser. 554 (1999) 43.
[20] H. Ikeda, Y. Qi, T. Cagin, K. Samwer, W.L. Johnson,
W.A. Goddard III, Strain rate induced amorphization of metallic
nanowires, Physical Review Letters 82 (1999) 2900-2903.
[21] Y. Qi, T. Cagin, K. Samwer, W.L. Johnson, W.A. Goddard III,
Melting and crystallization in Ni nanoclusters: The mesoscale
regime, Journal of Chemical Physics 115 (2001) 385-394.
[22] A. Strachan, T. Cagin, K. Samwer, W.A. Goddard III,
Critical behavior in spallation failure of metals, Physical
Review B 63 (2001) 060103 1-4.
[23] Y. Qi, T. Cagin, Y. Kimura, W.A. Goddard III, Viscosities of
liquid metal alloys from nonequilibrium molecular dynamics,
Journal of Computer-Aided Materials Design 8 (2002) 233-243.
[24] S. Ozdemir Kart, M. Tomak, M. Uludogan, T. Cagin, Liquid
properties og Pd-Ni alloys, Journal of Non-Crystalline
Solids 337 (2004) 101-108.
[5]
[6]
[7]
[8]
[9]
[25] S. Ozdemir Kart, M. Tomak, T. Cagin, Phonon dispersions
and elastic constants of disordered Pd-Ni alloys, Physica B
355 (2005) 382-391.
[26] S. Ozdemir Kart, M. Tomak, M. Uludogan, T. Cagin,
Structural, thermodynamical, and transport properties of
undercooled binary Pd-Ni alloys, Materials Science
Engineering A 435-436 (2006) 736-744.
[27] H.C. Andersen, Molecular dynamics simulations at constant
pressure and/or temperature, Journal of Chemical Physics
72/4 (1980) 2384-2393.
[28] M. Parrinello, A. Rahman, Crystal structure and pair
potentials: A molecular-dynamics study, Physical Review
Letters 45 (1980) 1196-1199.
[29] S. Nose, A unified formulation of the constant temperature
molecular dynamics method, Journal of Chemical Physics
81 (1984) 511-519.
[30] W.G. Hoover, Canonical dynamics: Equilibrium phase space-
distributions, Physical Review A 31 (1985) 1695-1697.
[31] T. Çagin, B.M. Pettitt, Molecular dynamics with a variable
number of molecules, Molecular Physics 72 (1991) 169-175.
[32] H. Rafii-Tabar, A.P. Sutton, Long-range Finnis-Sinclair
potentials for f.c.c. metallic alloys, Philosophical Magazine
Letters 63 (1991) 217-224.
[33] T. Çagin, R. Ray, Third-order elastic constants from
molecular dynamics: Theory and an example calculation,
Physical Review B 38 (1988) 7940-7946.
[34] T. Çagin, R. Ray, Elastic constants of sodium from
molecular dynamics, Physical Review B 37 (1988) 699-705.
[35] G. Dereli, T. Çagin, T.M. Uludogan, M. Tomak, Thermal
and mechanical properties of Pt-Rh alloys, Philosophical
Magazine Letters 75 (1997) 209-218.
[36] C. Kittel, Introduction to solid state physics, Seventh
Edition, John Wiley and Sons, New York, 1996.
[37] W.B. Perason, Handbook of lattice spacings and structure of
metals, Pergamon Press, New York, 1967.
[38] I. Barin, Thermochemical data of pure substances, VCH,
Verlagsgesellschaft mbH, Weinheim, 1989.
[39] V.L. Moruzzi, J.F. Janak, K. Schwarz, Calculated thermal
properties of metals, Physical Review B 37 (1988) 790-799.
[40] F. Cleri, V. Rosato, Tight-binding potentials for transition
metals and alloys, Physical Review B 48 (1993) 22-32.
[41] S.M. Foiles, J.M. Adams, Thermodynamic properties of fcc
transition metals as calculated with the embedded-atom
model, Physical Review B 40 (1989) 5909-5915.
[42] G. Simmons, H. Wang, Single crystal elastic constants and
calculated aggregate properties, Second Edition, MIT Press,
Cambridge, 1991.
[43] G.C. Kallinteris, N.I. Papanicolaou, G.A. Evangelakis, D.A.
Papaconstantopoulos, Tight-binding interatomic potentials
based on total-energy calculation: Application to noble
metals using molecular-dynamics simulation, Physical
Review B 55 (1997) 2150-2156.
[44] R. Hultgren, D.D. Desai, D.T. Hawkins, Selected values of
thermodynamic properties of binary alloys, ASM, Ohio, 1973.
[45] B. Sadigh, G. Grimvall, Molecular-dynamics study of
thermodynamical properties of liquid copper, Physical
Review B 54 (1996) 15742-15746.
[46] L. Gomez, A. Dobry, Melting properties of fcc metals using a
tight-binding potential, Physical Review B 55 (1997) 6265-6271.
[47] T. Iida, R.I.L. Guthrie, The physical properties of liquid
metals, Clarendon Press, Oxford, 1993.
View other sources
Hide other sources
- Available from S. Özdemir Kart · May 21, 2014
- Available from 157.158.19.167