Journal of Non-Crystalline Solids 337 (2004) 101–108

www.elsevier.com/locate/jnoncrysol

Liquid properties of Pd–Ni alloys

S. €Ozdemir Kart a,*, M. Tomak a, M. Uludo�gan b, T. C�a�gın c

a Department of Physics, Middle East Technical University, 06531 Ankara, Turkeyb School of Materials Science and Engineering, Georgia Institute of Technology, 771 Ferst Dr., Atlanta, GA 30332-0245, USA

c Materials and Process Simulation Center, California Institute of Technology, Pasadena, CA 91125, USA

Received 23 January 2004; received in revised form 25 March 2004

Available online 18 May 2004

Abstract

Liquid properties of Pd–Ni metal alloys are computed by molecular dynamics (MD) simulation with the use of quantum Sutton–

Chen potential (Q-SC) model. The thermodynamical, structural, and transport properties of the alloy are investigated. The melting

temperatures for Pd–Ni system are predicted. The temperature and concentration dependence of diffusion coefficient and viscosity

are reported. The transferability of the potential is tested by simulating the liquid state. The values of melting point are in excellent

agreement with the experiment. Comparison of calculated structural and dynamical properties with the available experiments and

other calculations shows satisfactory consistency.

� 2004 Elsevier B.V. All rights reserved.

PACS: 61.20.Ja; 61.25.Mv; 66.20.+d; 66.30.Fq

1. Introduction

The study of the liquid metals and their alloys has

attracted considerable interest, especially in the atomic

simulations ranging from first-principle [1,2] to empiri-

cal potential methods [3–6]. It is known that thefirst-principle molecular dynamics simulation is very

successful in calculating properties of materials to high

accuracy, but they cannot be as fast as empirical meth-

ods for the studies of larger systems. For providing a

satisfactory and quick description of energetics in

metallic systems, the empirical potentials are extremely

useful for the investigation of liquid properties, provided

that a suitable realistic interatomic potential model ischosen.

The study of melting points, static structure, i.e. pair

distribution function and static structure factor, and

transport properties, such as diffusion and viscosity

provides an understanding of behavior of liquid metals.

* Corresponding author. Tel.: +90-312 2104 332; fax: +90-312 2101

281.

E-mail address: ozsev@newton.physics.metu.edu.tr (S. €OzdemirKart).

0022-3093/$ - see front matter � 2004 Elsevier B.V. All rights reserved.

doi:10.1016/j.jnoncrysol.2004.03.121

Melting process of fcc transition metals has been

investigated in several theoretical studies [7–12]. Most of

them are carried out by applying the embedded atom

method (EAM) to metals. Foiles and Adams [7] deter-

mined the melting points (Tm) of Cu, Ag, Au, Ni, Pd andPt from intersection of the solid and liquid free energiesby using Monte-Carlo (MC) simulations. Tm of Cu, Ag

and Ni are consistent with experiments, but the model

fails to describe Tm of the rest. The same method was

applied to Al by performing molecular dynamics (MD)

simulations by Mei and Davenport [8]. Their Tm result is

below experimental value by about 130 K. MD simu-

lations of Cu [9] and Ni [10] show that, using EAM, the

system melts at 1370 and 1705 K, respectively, com-patible with the experiments. Gomez and Dobry [11]

studied the melting properties of nine fcc transition

metals described by second-moment tight-binding

method (SM-TBM) using a constant-pressure MC sim-

ulation. However, their results, except for Pb, are not

satisfactory with the experimental results. More re-

cently, Cherne et al. [12] have calculated the melting

temperature of Ni with two different EAM and fourvariations of the modified embedded atom model

(MEAM) by using the moving interface method [13].

They found Tm below the experimental value for the

102 S. €Ozdemir Kart et al. / Journal of Non-Crystalline Solids 337 (2004) 101–108

EAM function, while above the experimental result,except one, for the MEAM functions.

The melting process of metal alloys has been studied

much less than pure liquids. Hence the simulation of the

liquid Pd–Ni metal alloys is of interest in several re-

spects. The Pd–Ni system has technological importance

because of their hardness and resistance to corrosion.

Hence the understanding of its physical properties re-

mains a challenge. This alloy has also glass formingproperties at the eutectic region around 45% of Pd. Thus

the knowledge of the liquid properties of Pd–Ni alloys is

required for investigating the solidification process.

The transport properties (viscosity and diffusivity) are

important for metallurgical processes as well as for

understanding the dynamics of liquids. However,

experimental data for the self-diffusivities of liquid

metals are relatively scarce, mainly due to a lack ofspecific radio-isotopes. Experimental diffusion data are

only available for about a dozen liquid metals [14].

Moreover there are variations between the experimental

viscosity data [15]. The accurate measurement of these

quantities is a difficult task due to difficult experimental

conditions at high temperature and pressure. In addi-

tion, available data are limited to a few specific tem-

peratures. Indeed, little attention has been paid totemperature dependence of transport properties by

theoretical studies.

In this study, we have performed MD simulations

using the Sutton–Chen (SC) potential with a new po-

tential parameter set, namely the quantum Sutton–Chen

potential (Q-SC) developed by C�a�gın and co-workers

[16]. This potential has been applied to study various

problems successfully ranging from alloys, glass for-mations, crystallization, clusters, nanowires and single

crystal plasticity of pure metals and transport properties

of fcc transition metals [17–21]. This paper is devoted to

test the transferability of the potential for liquid Pd–Ni.

That is, the problem we are interested in is whether the

potential derived from elemental pure solid properties is

able to describe the behavior of the liquid Pd, Ni and

especially their binary alloys. To the best of ourknowledge, the liquid properties of Pd–Ni alloys pre-

sented in this work have not been studied before. The

melting temperatures for Pd–Ni alloys are predicted by

observing the discontinuity in the density and enthalpy,

and the change in the pair distribution function and

diffusion coefficients. Temperature and concentration

dependence of the physical properties studied in this

work are analyzed.The layout of the paper is as follows. The many-body

potential model and the method of calculation are de-

scribed in Section 2. The methods we follow to investi-

gate transport properties, self-diffusion coefficient and

shear viscosity, are presented in the same section. In

Section 3, we show and discuss the numerical results.

Whenever possible these results are compared with

experimental values and other calculations. Finallyconclusions are given in Section 4.

2. Method

The SC potentials describe the energetics of fcc

transition metals. They are of the Finnis–Sinclair type

and moderately long range in comparison to EAMpotentials. The total potential energy of the metals and

alloys is written as [22,23]

Utot ¼Xi

Ui ¼Xi

Xj 6¼i

1

2�ijV ðrijÞ

"� ci�iiðqiÞ

12

#; ð1Þ

where

V ðrijÞ ¼aijrij

� �nij

; ð2Þ

and

qi ¼Xj 6¼i

/ðrijÞ ¼Xj 6¼i

aijrij

� �mij

: ð3Þ

The power-law form of the potential terms construct

a unified model that can combine the short-range

interactions afforded by many body density ðqiÞ term

and long range interactions with a van der Waals tail

between the i and j atomic cores supported by pair-wise

potential term ðV ðrijÞÞ. In the Eqs. (1)–(3), rij is the

distance between atoms i and j, � is a parameter with thedimension of energy, a is a length parameter, c is a

dimensionless parameter scaling the cohesive second

term relative to repulsive first term, and m and n are

positive integer with n > m.We have used the following combination rules to

extend the SC model to alloys [23]:

�ij ¼ffiffiffiffiffiffiffi�i�j

p; ð4Þ

mij ¼mi þ mj

2; ð5Þ

nij ¼ni þ nj

2; ð6Þ

aij ¼ai þ aj

2: ð7Þ

Recently, C�a�gın and co-workers [16] reparametrized

the SC potential so as to improve the results of the

potentials for elevated temperatures by fitting to some

experimental properties, such as density, cohesive en-

ergy, bulk modulus and phonon frequencies at the X

point. This parametrization also includes quantum

corrections to account for zero point energy. Hence thismodified set of SC potential is referred as Q-SC poten-

tial. This potential gives better results for surface ener-

gies, vacancy energy and stacking fault energy. The

parameters used in this simulation are listed in Table 1.

Fig. 1. The melting temperatures of Pd–Ni alloys as a function of Pd

concentration in Ni. The experimental points are from Ref. [30].

Table 1

Quantum Sutton–Chen (Q-SC) [16] and Sutton–Chen (SC) [23] potential parameters

Metal Model n m � (eV) c a (�A)

Pd Q-SC 12 6 3.2864E)3 148.205 3.8813

SC 12 7 4.1260E)3 108.526 3.8900

Ni Q-SC 10 5 7.3767E)3 84.745 3.5157

SC 9 6 1.5714E)2 39.756 3.5200

S. €Ozdemir Kart et al. / Journal of Non-Crystalline Solids 337 (2004) 101–108 103

We have performed molecular dynamics (MD) sim-

ulations whose algorithms are based on extended

Hamiltonian formalism [24–28] using three successive

ensembles in a cubic box of 864 atoms. Q-SC potential

parameters are used to describe the interactions between

the atoms. At the beginning of the simulations, atoms

are randomly arranged on a fcc lattice subject to peri-

odic boundary conditions in three dimensions. Fifthorder Gear predictor–corrector algorithm is used to

investigate Newton’s equations of motion with a time

step of Dt ¼ 0:002 ps. The system is then heated up from

0.1 to 3000 K with increasing of 100 K by scaling the

velocities using a constant enthalpy and constant pres-

sure (HPN) ensemble. Near the melting temperature this

increment is reduced to 10 K to get more accurate values

of the melting temperature. The system reaches theequilibrium state over 2000 time steps. We have checked

for 1500 and 3000 time steps. The results for thermo-

dynamical properties of the system are not changed.

Therefore, 2000 time steps are taken to equilibrate the

system. Then 20 000 additional steps in the TPN (con-

stant pressure and constant temperature) dynamics are

taken to calculate the volume, density and enthalpy of

the system for each concentration. Finally, 50 000 stepsof microcanonical dynamics (EVN, constant energy

and constant volume) follow by using the resultant

zero strain average matrix hh0i to obtain pressure

dependent properties of the system. In these calcula-

tions, we have cut-off our interaction potential at a

range of two lattice parameters where the forces are

negligibly small. An additional distance of half a lattice

parameter is also added to this range to consider thetemperature effects. We adopt the random binary fcc

metal alloy method developed by Rafii–Tabar and Sut-

ton [23]; two types of atoms occupy the sites completely

randomly.

In the MD simulations, the self-diffusion coefficients

D can be determined either from an integral over the

velocity auto-correlation function CvðtÞ using Green–

Kubo relation (GK) [29]

D ¼ 1

3

Z 1

0

CvðtÞdt; ð8Þ

where CvðtÞ ¼ hviðtÞ � við0Þi, or from the long behavior of

mean square displacement r2ðtÞ by means of the Einsteinrelation (E)

D ¼ limt!1

r2ðtÞ6t

; ð9Þ

where r2ðtÞ ¼ h½riðtÞ � rið0Þ�2i.In the Eqs. (8) and (9), viðtÞ is the center of velocity

and riðtÞ is the position of the ith particle at time t.The shear viscosity is also calculated by using GK

relation as a transport property in this work. The vis-

cosity g is given by [29]

g ¼ VkBT

Z 1

0

dthPxyðtÞPxyð0Þi; ð10Þ

where V is the total volume of the system, Pxy is the off-diagonal component of the stress tensor with x and y ofthe Cartesian components. h i denotes the averages over50 time origins along a trajectory. The simulations of

self-diffusion coefficient and shear viscosity are per-

formed using EVN ensemble. The results are obtained

by using an average of 2000 individual correlation

function spaced 0.002 ps.

3. Results

The melting temperatures of Pd–Ni alloys are deter-

mined by examining the behavior of density, enthalpy,

and pair distribution function as a function of temper-

ature. To better describe the melting points, we also

check the diffusion coefficients of Pd–Ni alloys. We

obtain the same melting temperatures from all these

physical properties. The melting temperatures of Pd–Nialloys are plotted in Fig. 1, along with experimental

104 S. €Ozdemir Kart et al. / Journal of Non-Crystalline Solids 337 (2004) 101–108

results [30]. As shown in the figure, the melting points ofpure Pd (1820� 10 K) and pure Ni (1710� 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 5.3%. This is due to the

potential parameters of binary metal alloys calculated

by using those of pure metals using the combina-

tion rules (Eqs. (4)–(7)). Our results follow the trend

of the experiments. The calculated values are slightlylower than the experimental ones. We find eutectic

region between concentrations around Pd0:5Ni0:5 and

Pd0:3Ni0:7, supporting the critical experimental concen-

tration of Pd0:45Ni0:55. The region over the data points

shows the alloy in liquid phase and the region below the

points gives the alloy in solid phase. We have also ob-

tained the melting temperatures of pure Pd and pure

Ni metals by using SC potential parameters. The meltingpoints of Pd and Ni are found to be 1760� 10 K (65 K

lower than experimental value) and 1420� 10 K (306 K

lower than experimental value), respectively. Since Q-SC

potential parameters are working better in predicting

the melting temperatures of Pd–Ni alloys, we present

the results obtained from Q-SC parameters in this study.

The temperature dependence of density and enthalpy

of Pd, Ni and Pd0:4Ni0:6 are shown in Fig. 2(a) and (b),respectively. The discontinuity in the figures shows the

structural transformation from solid phase to liquid

phase. The melting temperature is identified by moni-

toring the jump in the figures. At the melting tempera-

Fig. 2. (a) Density and (b) enthalpy of Pd, Ni, and Pd0:4Ni0:6 as a

function of temperature.

tures, we find the density for Pd and Ni to be10.53 ± 0.06 and 7.94± 0.05 g/cm3, respectively. These

values are consistent with experimental values which are

10.49 and 7.90 g/cm3, respectively [15].

Our results for the pair distribution function gðrÞ arepresented in Fig. 3 for Pd, Ni and Pd–Ni alloy. Fig. 3(a)

shows the pair distribution function computed for Pd at

1853 K and Ni at 1873 K. The position of the first peak

compares well with the experimental results; for Ni, it isthe same as Waseda’s results [31] which is 2.40 �A, whilefor Pd it is 2.67 �A and experimental result is 2.60 �A.

The way we follow to predict the melting tempera-

tures from gðrÞ is observed in Fig. 3(b) plotted at se-

lected temperatures: 1600, 1810, 1820 and 2000 K for

Pd. The metal shows the structure with the peaks at

solid or near some of the ideal fcc position at 1600 and

Fig. 3. Pair distribution function ðgðrÞÞ: (a) for Pd at 1853 K and Ni at

1873 K, (b) for Pd at various temperatures and (c) partial pair distri-

bution function gabðrÞ for Pd0:45Ni0:55 at 1800 K.

S. €Ozdemir Kart et al. / Journal of Non-Crystalline Solids 337 (2004) 101–108 105

1810 K. The peaks are broadened and lowered at 1820K. Some peaks disappear, indicating that the liquid

dynamics is activated. After this temperature, the metal

goes into the liquid state (2000 K).

Partial pair distribution functions gabðrÞ for

Pd0:45Ni0:55 at 1800 K are given in Fig. 3(c) to see their

Fig. 4. Static structure factor ðSðqÞÞ: (a) for liquid Ni at 1873 K and (b)

for liquid Pd at 1853 K. The solid line is the simulation results and the

points are the experimental data [31].

Table 2

Arrhenius equation parameters for self-diffusion and shear viscosity values c

the Einstein (E) relation and viscosity from the Green–Kubo (GK) relation

Metal Diffusion

Pd

D0 Ea

Pd 89.896± 5.018 0.463± 0.011

Pd0:8Ni0:2 113.815± 8.520 0.514± 0.014

Pd0:6Ni0:4 90.890± 6.351 0.468± 0.013

Pd0:4Ni0:6 88.656± 5.121 0.462± 0.011

Pd0:2Ni0:8 87.631± 5.488 0.455± 0.012

Ni – –

Viscosity

g0

Pd 0.479± 0.062

Pd0:8Ni0:2 0.429± 0.047

Pd0:6Ni0:4 0.444± 0.070

Pd0:4Ni0:6 0.595± 0.079

Pd0:2Ni0:8 0.578± 0.068

Ni 0.624± 0.016

The units of D0, g0, and Ea and Evis are in nm2/ns, mPa s, and eV, respectiv

contributions to total pair distribution function. Thefirst peak in the gPd–NiðrÞ curve lies midway between the

first peaks in the gPd–PdðrÞ and gNi–NiðrÞ curves. We have

also studied concentration effect on gabðrÞ at the same

temperature. It is observed that Ni causes to reduce the

height of the first peaks in Pd–Pd and Ni–Ni pairs and

does not affect that of Pd–Ni pairs. The height of total

gðrÞ decreases up to the concentration around 60% of

Pd. Also the slight shift towards to left is observed in thetotal gðrÞ as the concentration of Ni in Pd increases,

while not in gabðrÞ. In the other peaks, shift is shown,

while their heights does not change.

The static structure factor, Fourier transform of gðrÞ,gives the experimentally measurable structural infor-

mation [29]. The simulation results for the static struc-

ture factor for Ni and Pd are shown in Fig. 4(a) and (b),

respectively, along with the X-ray scattering experimentstaken from Waseda [31]. The height of main SðqÞ peakof Ni is in agreement with the experiment, while the

position of the first peak appears to be slightly shifted

from the experimental data. Our result of Ni is also

comparable with that of MEAM [12]. On the other

hand, the EAM [32–34] underestimates the height of

main SðqÞ peak of Ni and leads to the discrepancy with

Waseda’s results. Foiles [32] and Holzman et al. [33]attributed discrepancy with Waseda’s x ray data to the

method which was not convenient for Ni or to the po-

tential parameters that they used, while Alemany et al.

[34,35] reported that there was a systematic error in the

method used by Waseda. As far as Pd is concerned,

main peak is lower than experimental data, whereas the

position of first peak agrees well with the experiment.

These problems may be inherent any parametrizationbased only solid data.

omputed by fitting to the MD simulation results of self-diffusion from

Ni

D0 Ea

– –

116.706± 7.153 0.486± 0.012

109.644± 7.619 0.467± 0.013

102.868± 3.917 0.457± 0.007

100.644± 2.675 0.448± 0.005

103.361± 5.946 0.449± 0.011

Evis

0.288± 0.027

0.314± 0.021

0.304± 0.030

0.239± 0.025

0.232± 0.023

0.213± 0.055

ely.

Fig. 5. Arrhenius plot of diffusion coefficients computed from: (a)

Green–Kubo (GK) and Einstein (E) relations for Pd, (b) GK and E

relations for Ni, and (c) E relation for Pd0:6Ni0:4.

106 S. €Ozdemir Kart et al. / Journal of Non-Crystalline Solids 337 (2004) 101–108

We have obtained the melting temperatures by alsochecking the diffusion coefficients. The diffusivities of

the order of 10�3 nm2 ps�1 helps us to distinguish the

liquid state from the solid state [15]. We now present our

results for the self-diffusion coefficient. First, we will

analyze the diffusion coefficients as a function of tem-

perature. Second, we will compare them with the

experimental data and other calculations, where avail-

able. The diffusion coefficients of Pd–Ni alloys arecomputed from GK (Eq. 8) and E (Eq. 9) relations. The

temperature dependence of our diffusion coefficient data

exhibits the Arrhenius-type behavior:

DðT Þ ¼ D0 expð�Ea=kBT Þ; ð11Þ

where D0 is the self-diffusion prefactor and Ea is the

diffusional activation energy. The values for Arrhenius

diffusion parameters are given in Table 2. D0 and Ea of

Ni are comparable in values of 108.0 nm2/ns and 0.476

eV, respectively, with Cai–Ye embedded atom method

(CY-EAM) used by Cherne et al. [12]. However, Ea

predicted by Protopapas et al. [14] is higher by a factor

greater than 2 for our results of Ni. Logarithmic rep-

resentation displayed in the Arrhenius-type diagram,

with D as a function of 1000=T for Pd, Ni and Pd0:6Ni0:4are given in Fig. 5. The solid line in the first two figures

represents an Arrhenius best fit for curve through data

points evaluated from GK relation. Dashed line corre-

sponds to fit for E. As shown in the figures, the values ofD computed by using the GK and E relations are

mutually consistent. The data in the figures fit well to

Eq. 11. The Arrhenius curve of E for Pd0:6Ni0:4 is illus-

trated in Fig. 5(c). As we see in this figure, D of Ni is

larger than that of Pd because the atomic size of Ni is

smaller than that of Pd. Table 3 lists the computed

values of D fitted to Arrhenius equation for Pd and Ni

along with the available experimental data [14] and theother simulation results. Also included in Table 3 are the

D computed from E relation for Pd–Ni alloys. The only

metal studied here for which the experimental values of

D are available is Ni [14]. Our simulation results for Ni

are consistent with the experimental values. This value is

also more compatible with the value predicted by Yo-

koyama [36] using a hard sphere (HS) description than

the previous works using SM-TBA [35] and EAM[34,37]. Our results for D of Pd at 1853 K agree with the

values calculated by the previous works reported in

Refs. [35,37,38]. There are no experimental and theo-

retical results for Pd–Ni alloys to compare with our

simulations. As seen in Table 3, self-diffusion coefficients

of Pd and Ni increases with increasing the concentration

of Ni in Pd–Ni alloys. This value does not change sig-

nificantly at the around of the eutectic region. This eventcould be also seen in the time dependence on the

neighbor list correlation function ðC‘ðtÞÞ, the measure-

ment of the change in the nearest neighbor numbers

during the simulation time [39]. Fig. 6 illustrates the

normalized C‘ðtÞ as a function of time for differentconcentration of Pd–Ni alloys at 1800 K. As shown in

the figure, atoms at the concentration of Pd0:8Ni0:2 are

less diffusive than that of Pd0:2Ni0:8. That is, as the

concentration of Ni increases in Pd–Ni alloys, pair

atoms survive less time in a chosen cut-off distance.

We have also studied the viscosity of the Pd–Ni metal

alloys as a liquid property. Our results obey an Arrhe-

nius relationship over the temperature range we havestudied:

gðT Þ ¼ g0 expðEvis=kBT Þ; ð12Þwhere values for the parameters g0 and Evis are tabulated

in Table 2. The activation energy for viscosity Evis of Ni

is in agreement with the results of Cherne et al. [12],

while it is lower than the experimental range of 0.311–

0.374 eV [15]. We report the viscosity results compared

to the experimental data and other calculations, where

Table 3

Diffusion coefficients D in nm2 ns�1 as evaluated by using the Green–Kubo (GK) and Einstein (E) relations at the shown temperatures for pure Pd,

Ni and their binary alloys

Metal T (K) D (nm2 ns�1) Ref.

Simulation Experimental Other calculations

GK E GK E

Pd 1853 4.98± 0.05 4.94± 0.07 3.80± 0.04 3.83± 0.04 [38]

4.03± 0.03 4.07± 0.03 [35]

Melting 4.49± 0.07 [37]

Ni 1773 5.48± 0.07 5.46± 0.04 4.61 2.52± 0.04 2.54± 0.04 [35]

3.52± 0.05 3.56± 0.04 [34]

4.49� [36]

Melting 3.85± 0.09 [37]

1873 6.39± 0.06 6.39± 0.04 5.96 4.31± 0.04 4.34± 0.04 [34]

5.60� [36]

Self-diffusion from E

Pd Ni

Pd0:8Ni0:2 1873 4.70± 0.07 5.74± 0.06

Pd0:6Ni0:4 1873 5.00± 0.06 6.07± 0.08

Pd0:4Ni0:6 1873 5.06± 0.05 6.03± 0.04

Pd0:2Ni0:8 1873 5.21± 0.06 6.28± 0.03

Here calculated diffusion coefficients are obtained from Arrhenius equation. Experimental data are taken from Ref. [14]. The values with � have beencalculated by using hard sphere model (HS) used in Ref. [36].

Fig. 6. Neighbor list correlation function ðC‘ðtÞÞ for Pd–Ni metal al-loys at 1800 K.

S. €Ozdemir Kart et al. / Journal of Non-Crystalline Solids 337 (2004) 101–108 107

available, in Table 4. The calculated viscosity of Ni is

lower than the experimental data [40] and other calcu-

lations obtained by Yokoyama and Arai [41] by up to a

Table 4

Values of shear viscosity g of pure Pd, Ni and Pd–Ni metal alloys, as compu

Metal T (K) g (mPa s)

Simulation E

Pd 1853 2.91± 0.86

Ni 1773 2.50± 0.97 4

1873 2.33± 0.86 4

1923 2.24± 0.80 4

Pd0:8Ni0:2 1873 3.06± 0.74

Pd0:6Ni0:4 1873 2.98± 1.02

Pd0:4Ni0:6 1873 2.66± 0.76

Pd0:2Ni0:8 1873 2.48± 0.65

Here calculated shear viscosities are obtained from Arrhenius equation. Exp

factor of 2.0. But temperature variation of the calcula-

tion is similar to that of experiment. As has also been

pointed out in the study of viscosity for Pu [42], the

experimental methods are employed in the errors of

±1% to ±20% [15]. Hence this fact may explain the

difference between the calculated and experimental vis-

cosities. In addition, experimental viscosity values for

liquid Ni at melting temperature vary from 4.5 to 6.4mPa s [15]. Therefore, it is difficult to trust in the reli-

ability of the experimental values. There are also vast

differences in the values of viscosity for Ni calculated by

using other potential models [12,35]. Our result for Pd

whose experimental values are non-existent is consistent

with the viscosity calculated by using the SM-TBM [35].

Concentration dependence on viscosity at 1873 K is also

given in Table 4. Decreasing in the viscosity withincreasing of Ni in Pd–Ni alloy is observed.

ted by using the Green-Kubo (GK) relation at the shown temperatures

Ref.

xperimental Other calculations

3.68± 0.48 [35]

.8 5.76± 0.80 [35]

4.06 [41]

.2 3.92 [41]

.0 2.60 [41]

erimental data are taken from Ref. [40].

108 S. €Ozdemir Kart et al. / Journal of Non-Crystalline Solids 337 (2004) 101–108

4. Conclusion

The results of applicability of the Q-SC many-body

potential for the properties of liquid Pd–Ni metal alloys

over wide range of temperatures are presented in this

study. The simulation results are in good agreement

with the available experimental values, except for the

shear viscosity of the alloy. One of the achievements of

this work is to predict the melting temperatures of Pd–Ni metal alloys with the same trend as the existing

experimental curve. The values of melting temperatures

especially for Pd and Ni agree quite well with the

experiment. The height of main SðqÞ peaks for Ni is

found to be quite encouraging if we take into account

the other simulation results in the literature.

Temperature and concentration dependence on the

self diffusion coefficient D and the shear viscosity g forthe Pd–Ni alloy are reported. The simulation results for

these transport properties seem to exhibit Arrhenius

behavior. It is also remarkable that the concentration of

Ni in Pd leads to increase the diffusivity in the alloy,

while reduce the shear viscosity of the system. The

experimental data on the diffusion coefficient D and

shear viscosity g for Pd–Ni alloys except for Ni are not

available for comparison, but the values of D computedfrom Einstein and Green–Kubo relations are nearly

equal to each others. These data may also encourage the

experimentalist to verify our results. The values of D for

pure systems are comparable to experiment, where

available, and the other simulation results, while those

of g are lower than them. This discrepancy for viscosity

can be improved by trying the other method, the non-

equilibrium molecular dynamics (NEMD) technique.Because the only experimental data for Pd–Ni metal

alloys exists for the melting points, we can test the

transferability from elemental case to alloy case for

melting. That the results for density, static structure

factor, and diffusion coefficients of pure metals show

satisfactory agreement with available experimental val-

ues leads us to conclude that transferability of the

potential is proved for pure metal cases. In other words,Q-SC model is able to reproduce the thermodynamical,

structural and dynamical properties of liquid Pd, Ni,

and Pd–Ni metal alloys, even though the potential

parameters have been fitted solely to solid state prop-

erties of pure system.

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