Molecular Dynamics Simulation Study of Phase Transformations in

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J. Phys. Chem. C 2007, 111, 2430-2439

Molecular Dynamics Simulation Study of Phase Transformations in Transition Bimetallic Nanowires Subramanian K. R. S. Sankaranarayanan, Venkat R. Bhethanabotla,* and Babu Joseph Sensors Research Laboratory, Department of Chemical Engineering, UniVersity of South Florida, Tampa, Florida 33620 ReceiVed: September 19, 2006; In Final Form: October 24, 2006

Molecular dynamic simulations were carried out to study the thermal characteristics of Pd-Rh and Pd-Cu nanowires of approximately 2.3 nm diameter using the quantum Sutton-Chen potential function to model the metal-metal interactions. Monte Carlo simulations employing the bond order simulation model were used to generate the initial configurations. Melting temperatures for these bimetallic nanowires of varying composition were estimated based on variations in thermodynamic properties such as potential energy and specific heat capacity. These melting temperatures were found to be much lower than those of bulk alloys of same composition and at least 100-200 K higher than same-diameter nanoclusters. Density distributions along the wire cross-section and axis as well as components of velocity auto-correlation function and shell based diffusion coefficients were used to identify the mechanism of nanowire melting. It is found to be surface initiated, the onset of which is triggered by predominantly cross-sectional or in-plane atomic movement. This twodimensional melting mechanism differs from that observed in nanoclusters (3-D) where atomic movement is isotropic. The differences in melting mechanism manifest themselves in the form of differences in the simulated phase transition diagrams of wires and clusters. Nanowire and nanocluster melting mechanisms are associated with two competing processes (i.e., solid-solid and solid-liquid transition). Structural transitions (fcc to hcp) in the simulated phase diagram identified using bond orientational order parameters reveal the existence of low-temperature hcp phases prior to the melting transition. The composition dependence of existence of hcp structures is influenced by the competition between surface melting (solid-liquid) and fcc-hcp (solidsolid) transition. The temperature range of existence of these structures varies with bimetallic composition and is influenced by the melting mechanism and nanomaterial geometry as well as the relative strengths of metal-metal interactions in the bimetallic. Investigations into the thermal stability of low temperature solid phases of these bimetallic nanowires were carried out by simulating alternative starting configurations such as hypothetical hcp and glassy annealed structures for 50% Pd composition. The simulated phase diagrams of the corresponding bulk systems agree well with experimentally reported ones.

I. Introduction Nanomaterials such as nanowires and nanoclusters exhibit mechanical,1 thermal,2,3 electrical,4 and magnetic5 properties which are different from bulk materials as well as single molecules. Focus on nanoscale research over the past decade has increased as a result of promising applications arising from enhanced properties at nanoscale.6-9 Enhancements are primarily due to size effects, surface effects, and interface effects. Metal nanowires, in particular, have several uses which were identified in nanoscale wiring of integrated circuits,10 nanowire arrays for optoelectronic applications,11 and usage as tips for scanning electron microscopy (SEM) and atomic force microscopy (AFM). Other important areas of applications of metal nanowires include catalysis and sensing.12 Our focus is on Pd and its alloy nanowires which find extensive use in hydrogen sensing.13,14 Numerous studies have focused on fabrication and experimentation with and simulation of single component as well as bimetallic nanoclusters and nanowires.15-18 Synthesis procedures include template methods,19,20 lithographic techniques14,21 and solution techniques22,23 among several others.24-26 The most * Author to whom correspondence should be addressed. Phone: 813974-2116. Fax: 813-974-3651. E-mail: [email protected].

challenging issue in all of the synthesis methods is control over the size and morphology of these nanowires. Knowledge of the thermal properties of metallic nanowires and their effect on size, shape, and composition would have a bearing on the method of synthesis, processing, and performance of nanowires in their various areas of applications. It is well-known that the melting behavior of nanowires differs significantly from the bulk with the melting temperatures decreasing with reduction in the wire diameter.27-32 This lowering effect is primarily attributed to the increase in the ratio of surface to bulk atoms with decreasing nanowire diameters.33 Experimental investigations into the melting phenomenon are limited by the problems associated with control over size and distribution of nanoclusters and nanowires. Computer simulations such as molecular dynamics (MD) offer an effective tool to study the various properties of nanowires and complement the ongoing experimental efforts.34 Investigations into the melting behavior of one-dimensional zirconium nanowires indicate that the initiation of melting occurs from inner core shell atoms.30 Similar behavior was observed in the case of palladium nanowires29 in which the onset of melting resulted from diffusion of central strand of atoms. The surface melting temperature was found to be representative of the overall wire melting temperature (liquidus point) in the case gold

10.1021/jp066132h CCC: $37.00 © 2007 American Chemical Society Published on Web 01/23/2007

Study of Bimetallic Nanowires nanowires.18 This behavior differs from that observed in nanoclusters35-37 and other metal nanowires16,27 where the onset of melting results from enhanced movement of less constrained surface atoms. Solid-liquid coexistence was observed in the melting of titanium nanowires.28 Ultrathin titanium nanowires with diameters less than 1.2 nm showed no clear characteristic first-order transition during the melting process.17 Titanium nanowires of 1.7 nm diameter were found to undergo a structural transition from helical multiwalled to bulk-like rectangular structure.28 Similar structural transformation from an initial fcc to hcp type was also observed in the case of 2.3 nm diameter Pd nanowires.16 An improved understanding of the nanowire melting phenomenon and the associated structural transformations is essential to gain insights into their special behavior. Most of the experimental and theoretical investigations have been limited to single component metal clusters and nanowires.27-30,38,39 Although bimetallic nanomaterials are better suited for catalysis and sensing applications than their monometallic counterparts,40 complex phenomena such as surface segregation and micromixing occurring in finite-sized alloy nanostructures have resulted in lesser attention being devoted to their study. For a given composition of bimetallic, the microstructure is dictated by surface energies and mixing energies of the constituent atoms.41-44 Atoms with lower surface energies segregate to lower coordination sites such as surfaces, corners, and edges. The extent of segregation is determined by the interplay between surface energies, mixing energies, and entropy.43,44 The occurrence of this phenomenon has been found in experimental investigations of nanowires of Pd-Ag and Pt-Ag.45 In the present work, we employ MD simulations to study the structural evolution and dynamics associated with the melting of bimetallic transition metal nanowires composed of Pd-Cu and Pd-Rh. The two bimetallic nanowires have contrasting segregation profiles of Pd. In the case of Pd-Cu, Cu with lower surface energy occupies most of the surface sites, whereas in Pd-Rh, Pd has lower surface energy than Rh and hence segregates to the surface. Investigations into the thermal characteristics, low temperature solid phases, and melting transitions of these bimetallic nanowires of varying compositions form the focus of the current work. II. Initial Configuration Setup The transition elements employed in this study (Pd, Cu, and Rh) have an fcc structure in their bulk solid phase. Cylindrical structures, representing nanowires of Pd-Cu and Pd-Rh of approximately 2.3 nm diameter were created from a large block of fcc using that cutoff diameter. The length to diameter ratio was varied to ensure that the results are not influenced by the periodic boundary conditions. Alternative starting configurations comprising of hcp nanowires were also generated using hcp fractional coordinates. To identify the atomic distribution of the constituent atoms for a given composition of the bimetallic, these structures were subjected to a Metropolis Monte Carlo simulation employing a bond order simulation (BOS) model,43,44 to generate the minimum energy initial configuration which was subsequently used for studying the melting phenomenon. The BOS model was modified to include periodic boundary conditions along the nanowire axis. The stable configurations generated in the above simulations consisted of surface segregated structures with lower surface energy atoms preferentially located at the surface. The extent of segregation depends on factors such as surface energy, mixing energy, and entropy. The final microstructure depends

J. Phys. Chem. C, Vol. 111, No. 6, 2007 2431 TABLE 1: Potential Parameters Used in MD Simulations for Metal-Metal Interactions quantum Sutton-Chen Pd Rh Cu

n 12 13 10

m

(eV)

c

a (Å)

6 5 5

3.2864 × 2.4612 × 10-3 5.7921 × 10-3

148.205 305.499 84.843

3.8813 3.7981 3.603

10-3

on the interplay among these factors. Therefore, Cu in Pd-Cu and Pd in Pd-Rh nanowires occupied most of the surface sites. These structures were utilized as starting points for studying the thermal characteristics of bimetallic nanowires. III. Computational Details Molecular dynamics simulations using DLPOLY46 were performed to gain insights into the melting process at the atomic level. The thermodynamic and transport properties were derived as time averages over particle positions and velocities. The quantum Sutton-Chen (QSC) potential function47 was employed to model metal-metal interactions

Utot )

[∑ 1

N

N

∑ 2 i)1 j)1j*i

N

V(rij) - c

Fi1/2 ∑ i)1

]

(3.1)

Here, V(rij) ) (a/(rij))n and N

Fi )

∑ (a/(rij))m j ) 1;j * i

represent the pair potential accounting for the repulsion resulting from Pauli’s exclusion principle and the local density accounting for cohesion associated with any atom i, respectively. The potential parameters used in the simulations are listed in Table 1. The MD simulations were carried out in an ensemble approximating the canonical with a constant number of atoms N and nearly zero pressure P with periodic boundary condition applied only along the nanowire axis. A constant temperature Berendson thermostat48 with a relaxation time of 0.4 ps was used. The equations of motion were integrated using a Verlet leapfrog algorithm34 with a time step of 0.001 ps. The nanowires were initially subjected to mild annealing in the 0-300 K interval which was followed by heating to 1800 K in increments of 100 K. Near the melting point, the temperature increments were reduced to 10 K to account for the large temperature fluctuations. The simulations were carried out for 400 ps of equilibration followed by 200 ps of production time for generating time-averaged properties. In the present work, the initial configurations were not optimized using genetic algorithms17,29 or typical simulated annealing procedures49 which consist of heating till 75% of the bulk melting point of alloy and subsequent quenching. These procedures are more appropriate for wires which are extremely thin17,29 in which case the helical structures are found to be more stable. However, for the size of nanowires (2.3 nm diameter) employed in this work, the fcc structures similar to the ones used in this work are known to give reasonable predictions of thermal properties.16 The wire structures generated after the mild annealing are closer to an fcc (or hcp) closed packing. IV. Results and Discussion The following subsections discuss identification of the melting point as well as characterization of the structural changes associated with the phase transitions in Pd-Rh and Pd-Cu bimetallics nanowires at 50% Pd representative composition.

2432 J. Phys. Chem. C, Vol. 111, No. 6, 2007

Sankaranarayanan et al. TABLE 2: Bond Orientational Order Parameter Values for Various Geometries geometry fcc hcp liquid

Q4

Q6

0.19094 0.09722 0

0.57452 0.48476 0

The potential energy of the new solid phase (termed glassy annealed henceforth) is not very different from the initial fcc. The thermal stability of this glassy annealed structure as well as other starting configurations is discussed in a subsequent section. The constant pressure specific heat capacity in a weak coupling ensemble such as that achieved with Berendson thermostat can be written as a function of fluctuations in instantaneous enthalpy 〈δH2〉

Cp )

Figure 1. Temperature dependence of potential energy and specific heat capacity (Cp) for (a) (Pd0.5-Rh0.5)2.31nm and (b) (Pd0.5-Cu0.5)2.26nm nanowires. Solid line with squares and dashed line with circles represent heating and cooling of wires, respectively. Solid line with triangles represents the specific heat capacity of the wires.

Dynamic properties calculated at different temperatures leading up to the melting transition and beyond are used to gain insights into the mechanism of nanowire melting. Phase diagrams representing composition dependency of various simulated phase transitions for the two alloy nanowires are generated and compared to same-diameter nanoclusters as well as bulk alloys. 4.1. Melting Point Identification. The melting transition is identified by studying variations in thermodynamic properties such as potential energy and specific heat capacity as well as structural properties such as bond order parameter and Wigner values. The details are discussed below. 4.1.1. Variation of Thermodynamic Properties (Potential Energy and Specific Heat Capacities). Figure 1 , panels a and b, shows the temperature dependence of the potential energy as well as the specific heat capacity for (Pd0.5-Rh0.5)2.31nm and (Pd0.5-Cu0.5)2.26nm nanowires, respectively. The transition from solid to liquid phase can be identified by a jump in the total potential energy curve. This corresponds to melting temperatures of 1610 ( 10 and 1010 ( 20 K for (Pd0.5-Rh0.5)2.31nm and (Pd0.5-Cu0.5)2.26nm nanowires, respectively. The Pd-Cu nanowire shows a more continuous transformation in comparison to the Pd-Rh nanowire. This feature could be attributed to increased surface melting of Cu atoms in Pd-Cu nanowires than Pd atoms in Pd-Rh nanowires. On cooling, the nanowires show a strong hysteresis and undergo a sharp liquid-solid transition. The calculated freezing points for (Pd0.5-Rh0.5)2.31nm and (Pd0.5-Cu0.5)2.26nm nanowires correspond to 1330 ( 10 and 760 ( 10 K, respectively. However, nucleation is a stochastic process, and hence, the calculated freezing points would vary for different cooling runs. The hysteresis is a consequence of the need of supercooling in the transition from liquid to crystal.

〈δH2〉NPT NkBT2

)

〈H2〉 - 〈H〉2 NkBT2

(4.1)

Cp at different temperatures is shown in Figure 1 for the two bimetallic nanowires having 50% Pd composition. The phase transition from solid to liquid is identified by the maximum in the Cp curve. This corresponds to 1610 ( 10 and 1010 ( 20 K for (Pd0.5-Rh0.5)2.31nm and (Pd0.5-Cu0.5)2.26nm nanowires, respectively. In addition, a sharp peak is observed at 1000 K for the (Pd0.5-Rh0.5)2.31nm nanowire which is ∼600 K below the melting point for the same. This could be attributed to isomerization or structural changes in the nanowire. Such a peak in the Cp curve at temperatures much below the melting transition is observed in Pd-Rh bimetallic nanowires over the entire composition range of Pd. On the other hand, Pd-Cu bimetallic nanowires exhibit this behavior over a limited composition range (lower than 40% Pd). Similar characteristic also occurred in Pd-Pt nanowires over a different composition range (15-40% Pd).50 Our findings indicate that the bimetallic nanowires undergo structural transformation on heating with wide differences in the onset of solid-solid and solid-liquid phase transformation observed in a particular bimetallic composition range for a given nanowire size. The onset of solidsolid transformation occurs at different temperatures for a given Pd composition in the two bimetallics and appears to be dictated by the relative strengths of the metal-metal interactions. Better insights into the nature of solid-solid transformation could be obtained by utilizing bond orientational order parameters. 4.1.2. Variation of Structural Properties (Bond Orientational Order Parameter). Different signatures of bond orientational order parameters51 can be used to analyze the nanowire structure as well as distinguish between atoms in solid (closed packed) and liquid environments generated during the melting process. The value of the global bond orientational order parameter Ql (Table 2) in a solid structure depends on the relative bond orientations and is unique for each crystal structure. The temperature dependence of the bond orientational order parameters (Q4 and Q6) is shown in Figure 2 for the two bimetallics. The bond orientational order parameter values of the initial annealed structures at 300 K (Figure 2) indicate that the annealed configuration is not a perfect fcc structure (perfect fcc has Q6 ) 0.575 and Q4 ) 0.190 from Table 2), possibly due to the presence of some defects. Although the starting configurations are structures which are not entirely defect free, they are still closer to an ideal fcc structure. The atoms in a solid undergo vibrations about their equilibrium positions leading to distortion of the crystal structure which

Study of Bimetallic Nanowires

J. Phys. Chem. C, Vol. 111, No. 6, 2007 2433

Figure 2. Temperature dependence of bond orientational order parameters for alloy nanowires. Solid line with circles and squares represent Q4 and Q6 parameters, respectively for (Pd0.5-Cu0.5)2.26nm wire. Dashed line with circles and squares represent Q4 and Q6 parameters, respectively for (Pd0.5-Rh0.5)2.26nm wire.

is characterized by Q4 and Q6 values. Comparison of the Q4 and Q6 order parameters in Figure 2 with those given in Table 2 indicates structural transformation to occur in (Pd0.5-Rh0.5)2.31nm bimetallic nanowires which is absent in (Pd0.5-Cu0.5)2.26nm wires. The solid-solid transformation from fcc to hcp occurs at ∼1000 K for Pd-Rh nanowires of 50% Pd composition. While PdRh nanowires exhibit such a sharp fcc-hcp transition over the entire range of Pd composition studied (5-95%), Pd-Cu nanowires undergo such transformation over a limited composition range (5-40% Pd). Comparisons with the melting points for nanowires in these composition ranges indicate the existence of these metastable hcp structures over a much broader temperature range in the case of Pd-Rh nanowires. At the melting point, all of the order parameters show a sudden decrease to near zero indicative of the phase transformation to liquid. These agree well with the melting points calculated using simulated potential energy and specific heat capacity data. Similar BOP calculations were also carried out for same diameter Pd-Rh and Pd-Cu nanoclusters over a range of Pd compositions. Hcp structures exist in Pd-Cu nanoclusters over a wider composition range (5-70% Pd) and narrower temperature range than same diameter wires. Pd-Rh nanoclusters exhibit hcp phases over the entire range of Pd composition at temperatures close to the melting transition. The existence of low temperature (temperatures much below the melting transition) hcp phases is unique to nanowires and might be attributed to the differences in the melting mechanism of wires and clusters. These details are discussed in subsequent sections. 4.2. Mechanism of Melting in Nanowires. Insights into the nanowire melting mechanism can be obtained through analysis of various density profiles, shell based diffusion coefficients and components of velocity auto-correlation functions. The following subsections discuss the structural and dynamical changes associated with the nanowire melting. 4.2.1. Axial and Radial Density Profiles. The atomic distribution profiles of Pd atoms along the axial direction (termed axial henceforth), during the melting of (Pd0.5-Cu0.5)2.26nm nanowire are shown in Figures 3. At low temperatures, solid like features are preserved as indicated by the distinct peaks in the axial density profile. With an increase in temperature, the peaks become broader, suggestive of a relatively larger movement of metal atoms. A similar axial density profile exists for Cu atoms in (Pd0.5-Cu0.5)2.26nm nanowire. The peaks in the axial density profile remain distinct in the 300-900 K range for both Cu and Pd atoms in (Pd0.5-Cu0.5)2.26nm nanowire. Even at temperatures as high as 900 K, the shift in the peak is very small

Figure 3. Atomic distribution profiles along Pd-Cu nanowire axis for Pd atoms at temperatures leading up to and beyond the melting transition.

Figure 4. Atomic distribution profiles along Pd-Cu nanowire crosssection for Pd atoms at temperatures leading up to and beyond the melting transition.

suggesting a much smaller movement of the metal atoms along the axial direction (5 Å) than along axial, indicating much larger movement of atoms along the nanowire crosssection than along the wire axis. A similar argument can be extended for Cu atoms in Pd-Cu. The wire diameter increases as a result of such movement. At the melting point, the distribution becomes smooth indicative of a transformation to the liquid phase. Similar surface melting characteristics are also observed for Pd-Rh nanowires. A relatively larger axial movement as suggested by the shift in the peaks is observed in the case of Pd-Rh than Pd-Cu nanowires. At temperatures much closer to the wire melting point (within 100 K), the axial movement also becomes significant.


Sankaranarayanan et al.

Figure 5. Atomic distribution profiles along Pd-Cu nanowire crosssection for Cu atoms at temperatures leading up to and beyond the melting transition.

Surface segregation of Cu atoms in Pd-Cu is evident from the atomic radial density profiles at 300 K (Figures 4 and 5). With an increase in temperature, the atomic movement (especially cross-sectional at ∼700-900 K) becomes higher. As a result, intermixing of atoms in the alloy nanowire occurs, leading to reduced segregation. The atomic distribution profile of the constituent atoms in the bimetallic alloys becomes more uniform with increasing temperature which could be attributed to increased interatomic mixing. At temperatures well beyond the melting transition (i.e., in the liquid phase), the density profiles of both Pd and Cu atoms become similar indicative of a more completely mixed state. Similar mixing characteristics are also observed in case of Pd-Rh nanowires. It, therefore, appears from the nanowire axial and radial density profiles that the melting process is surface initiated, the onset of which occurs from the predominantly cross-sectional movement of surface atoms. Additional insights into the surface melting phenomenon as well as the diffusional movement of the atoms can be obtained by analyzing shell-based diffusion coefficients and components of velocity auto-correlation function. 4.3. Surface Melting Phenomenon. Surface melting refers to the formation and propagation of a quasi-liquid film that thickens with increasing temperature and ends with sharp melting of the solid core. The initiation of surface melting occurs at temperatures much below the melting transition depending on the composition of the bimetallic. To gain insights into the surface melting phenomenon, the diffusional movements of the constituent atoms in the bimetallic nanowires are analyzed using shell-based diffusion coefficients and velocity auto-correlation functions. 4.3.1. Shell-Based Diffusion Coefficients. The surface melting characteristics of the bimetallic nanowires were explored using shell-based diffusion coefficients. The nanowire cross-section was partitioned into different radial shells of equal width (dR). The mean square displacement (MSD)52 calculated within each shell was used to obtain the self-diffusion coefficient using eq 4.2 for atoms in that shell. The average interatomic distance between atoms in the bimetallic was used as dR. These values are 2.66 and 2.72 Å for Pd-Cu and Pd-Rh, respectively. The atoms were assigned to each bin based on the initial position obtained at the end of the equilibration period. The MSD for each shell was generated by averaging over a 200 ps trajectory sampling every 0.1 ps. In this work, the radial diffusion

Figure 6. Shell-based diffusion coefficients characterizing (a) radial (x-y plane) and (b) axial (z direction) movement of atoms in (Pd0.5Rh0.5)2.31nm nanowire.

coefficient for each shell was obtained from the two-dimensional (d ) 2) square displacement, for the five different shells cut across the wire cross-section

Di )

1 〈|r (t + s) - ri (s)|2〉 2d∆t i

(4.2)

where ri(t + s) is the vector position of the ith atom on the x-y plane (cross-section), the average is over atoms of type i and over choices of time origin s. The diffusion coefficient calculated above reflects the mobility of the atoms along the wire crosssection and characterizes the in-plane or radial movement. Similarly, the axial or out-of-plane movement refers to mobility of the atoms in the radial shells along the wire axis (z direction) and is the one-dimensional (d ) 1) diffusion coefficient calculated based on the axial position vector of atoms (by replacing ri(t + s) with zi(t + s)). These radial and axial diffusion coefficients calculated based on MSD were assigned to each shell. To facilitate comparisons between the axial and radial diffusion coefficients for the same shells, their dependence on radial distance of the wire was plotted. The components of shell-based diffusion coefficients calculated in the radial and z directions for (Pd0.5-Rh0.5)2.31nm and (Pd0.5-Cu0.5)2.26nm nanowires are shown in Figures 6 and 7. These depict the in-plane (cross-sectional) and out-of-plane (axial) movements, respectively. For both the bimetallic nanowires, the diffusivities of the outer shells (4 and 5) are higher than the inner ones (shells 1-3) indicative of a surface initiated melting process. The onset of surface melting occurs at ∼900 K for (Pd0.5Rh0.5)2.31nm and ∼600 K for (Pd0.5-Cu0.5)2.31nm nanowire. The



Figure 9. Snapshots showing side views of (Pd0.5-Rh0.5)2.31nm nanowires at (a) 300, (b) 1000, (c) 1400, and (d) 1620 K. Light colored spheres represent Pd atoms whereas dark ones represent Rh atoms.

Figure 7. Shell-based diffusion coefficients characterizing (a) radial (x-y plane) and (b) axial (z direction) movement of atoms in (Pd0.5Cu0.5)2.26nm nanowire.

Figure 8. Snapshots showing top views of (Pd0.5-Rh0.5)2.31nm nanowires at (a) 300, (b) 1000, (c) 1400, and (d) 1620 K. Light colored spheres represent Pd atoms whereas dark ones represent Rh atoms.

initiation of surface melting arises from predominantly radial movement, as seen from the in-plane and axial diffusion coefficients for the outermost shell 5 (Figure 6, panels a and b). As the temperature increases, atoms in the shell 4 also show much higher diffusivity, whereas those in the first three remain solid-like. At temperatures close to the melting transition (i.e., ∼1600 K), shell 3 also exhibits similar behavior. Above the melting transition temperature, atoms in all of the shells have much higher diffusivities indicative of phase transition from solid to liquid. The surface melting phenomenon is clearly evident from the snapshots taken at various temperatures (Figures 8 and 9). Similar surface melting characteristics are also observed in the case of Pd-Cu nanowires (Figure 7). Samediameter nanowires richer in Cu (in case of Pd-Cu) and Pd (in Pd-Rh) compositions surface melt more in comparison to wires having higher Pd (in Pd-Cu) and Rh (in Pd-Rh) composition. For example, our calculations based on the deviations in potential energy curve36 indicate that the thickness of the liquid film formed as a result of surface melting at 1200 K is ∼ 25%

Figure 10. Temperature dependence of potential energy for alternative configurations (a) (Pd0.5-Rh0.5)2.31nm and (b) (Pd0.5-Cu0.5)2.26nm. The solid lines with squares and diamonds represent heating of hcp and glassy annealed wires, respectively. Solid line with circles represents the cooling of hcp wires.

and 5% of the initial solid radius for Pd-Rh wires having 5% and 75% Rh, respectively. The onset of surface melting in PdRh wires having compositions greater than 75% Rh occurs at temperatures greater than 1200 K. Comparison of the radial and axial diffusion coefficients for the two bimetallic nanowires (Figure 6, panels a and b, and Figure 7, panels a and b) reveals that all of the shells have higher radial diffusion coefficients compared to axial at temperatures below their melting transition. At lower temperatures (300800 K in Pd-Rh and 300-500 K in Pd-Cu), the atoms are mostly solid-like and only vibrate about their equilibrium positions. As the temperature increases (900-1500 K for PdRh and 600-900 K for Pd-Cu), the radial components of diffusion coefficients in shells 4-5 become much larger than the corresponding axial components. This behavior extends to shell 3 at ∼1600 K for Pd-Rh and ∼1000 K for Pd-Cu. All of this indicates the increased tendency of the atoms to move along the cross-section than along the axis before the



TABLE 3: Stability of Alternative Starting Configurations Tm (K) starting configuration fcc hcp glassy

crystal structure of annealed structures at 300 K

(Pd0.5-Rh0.5)2.31nm

(Pd0.5-Cu0.5)2.26nm

(Pd0.5-Rh0.5)2.31nm

(Pd0.5-Cu0.5)2.261nm

1610 ( 10 1450 ( 10 1630 ( 10

1010 ( 10 880 ( 10 1050 ( 10

fcc fcc

fcc fcc

melting transition. At temperatures close to the melting transition and in the liquid phase, the atomic movements in both the axial and radial directions become comparable. The snapshots showing the cross-sectional (Figure 8) and axial (Figure 9) views of (Pd0.5-Rh0.5)2.31nm at various temperatures as well as analysis of radial, tangential, and axial components of normalized velocity autocorrelation function at 1000 K corroborate the arguments presented above and reveal the surface melting characteristics in nanowires. The surface melting mechanism in our study differs from that observed by Hui et al. where the melting of nanowires is seen to begin from the interior atoms.27-30 The differences arise from the difference in nanowire structures. In our case, the initial configurations are closer to an ideal fcc structure with surface segregation of lower surface energy atoms such as Cu in PdCu and Pd in Pd-Rh. It is well-known from the available thermodynamic models33 that the melting points of lower surface energy atoms are lower than those of higher surface energy. Additionally, for a near perfect crystal lattice such as that for ideal fcc, the degree of freedom of surface atoms (with coordination numbers less than 12) is much more than for those in the interior (coordination number ) 12). Hence, for the alloy structures studied in this work, it can be expected that the surface atoms would melt first followed by the core. On the other hand, the configuration obtained by Hui et al. after genetic algorithm optimization were multishell structures

Figure 11. Simulated phase diagram of bimetallic nanowires (a) PdRh and (b) Pd-Cu.

composed of coaxial cylindrical shells. The presence of defects allows several different local clusters (of various symmetries) to exist in such nanowires. With an increase in temperature, the diffusion of local atomic clusters formed in the wire interior leads to the formation of new defects which lowers the thermal stability of nanowires and results in the onset of melting. Thus, the differences in the atomic structures of the nanowires play a significant role in the melting behavior of nanowires. 4.4. Thermal Stability of Alternative Starting Configurations. As brought out in section 4.1, structural transition from fcc to hcp type occurs in alloy nanowires, with the transition temperatures dependent on the wire composition and diameter. The most stable low-temperature solid-phase configurations for the bimetallic nanowires can be identified by simulating alternative starting configurations comprised of a hypothetical hcp structure and a glassy annealed structure obtained at the end of the heating-cooling cycle shown in Figure 1. Simulations for representative composition of 50% Pd in the two bimetallics were performed. A thermally stable starting configuration is expected to yield a higher melting point for a given nanowire diameter and composition, when subjected to heating-cooling schedule as described in the earlier sections. The temperature dependence of the potential energy for the alternative starting configurations (hcp and glassy annealed) of the two bimetallics is shown in Figure 10. The melting points as well as the crystal type of the low temperature solid phases (at 300 K) for hcp and glassy annealed structures are summarized in Table 3. For both (Pd0.5-Rh0.5)2.31nm and (Pd0.5Cu0.5)2.26nm nanowires, the melting point of hcp configuration is at least 200 K lower than that of fcc and glassy annealed structures. Also, the melting temperatures of glassy annealed structures are slightly higher than fcc and, therefore, as expected are more stable. Investigations into the crystal type of the glassy annealed structure for the two bimetallic using bond orientational order parameters also suggest that fcc is the stable configuration for low temperature solid phases. Bond orientational order parameters of the cooled solid-phase obtained at the end of hcp as well as fcc heating-cooling runs for (Pd0.5-Rh0.5)2.31nm as well as (Pd0.5-Cu0.5)2.26nm nanowire indicate that the crystal type is closer to fcc than hcp, thereby corroborating the fact that an fcc low-temperature configuration is more stable for this nanowire composition. These simulations clearly indicate that an fcc starting configuration is better than hcp for 50% Pd composition for both the bimetallic nanowires. Similar behavior was observed at other nanowire compositions also. By utilizing fcc starting configurations, the simulated phase diagram of both Pd-Cu and Pd-Rh nanowires can be constructed in order to identify the various phase transitions/ boundaries as shown in subsequent section. 4.5. Simulated Phase Transition Diagram of Alloy Nanowires. The stability of different starting configurations for nanowires when subjected to an annealing and heating schedule was discussed in the previous section and is summarized in Table 3. Fcc clearly appears to be the more stable low temperature solid phase than hcp for the two bimetallics. Also, the crystal structure of the bulk solid phase for all the transition metals employed in this study corresponds to fcc. In this section,


Figure 12. Simulated phase diagram of bimetallic nanoclusters (a) Pd-Rh and (b) Pd-Cu.

the phase diagrams showing simulated phase boundaries of bimetallic Pd-Cu and Pd-Rh nanowires are constructed from an fcc starting configuration and compared with those of same diameter nanoclusters as well as with those of bulk Pd-Cu and Pd-Rh alloys. The nanoscale alloy simulated phase diagrams are known to differ from those observed in bulk.53,54 The melting mechanism of nanowires differs from that of nanoclusters36 as well as that of bulk alloys. Pd-Cu and Pd-Rh nanowires exhibit a twodimensional surface melting mechanism characterized by greater cross-sectional movement when compared to axial. The nanoclusters of these bimetallic alloys undergo a three-dimensional surface melting mechanism characterized by atomic movement which is more isotropic. The observed differences in the melting mechanisms result in a phase transition diagram which presents features that are unique to nanowires. To explore these features, phase transition temperatures for Pd-Cu and Pd-Rh nanowires of different compositions were identified by employing the thermodynamic and structural properties discussed in section 4.1. Figures 11 and 12 show the simulated composition dependence of the various phase transitions for bimetallic nanowires and same-diameter nanoclusters. The bulk alloy simulations were also carried out using the QSC potential, with periodic boundary conditions in a constant NPT ensemble. The calculated bulk melting points of Pd, Cu, and Rh agree well with the experimentally reported values.55,56 The simulated bulk phase diagram for Pd-Rh and Pd-Cu showing the liquidus curves is presented in Figure 13. Although, the nature of the liquidus curve in the nanocluster phase diagram is similar to that observed in bulk, the melting transitions occur at much lower temperatures than in bulk alloys of the same composition which could be attributed to the finite size effect. Nanowires of Pd-Cu and Pd-Rh exhibit liquidus


Figure 13. Simulated bulk phase diagram of (a) Pd-Rh and (b) PdCu.

curves which differ from bulk and same-diameter nanoclusters and vary nonmonotonically with Pd and Rh composition, respectively. For a given alloy composition, the melting transition temperatures of nanowires lies in between that of bulk and same-diameter nanoclusters. The main difference between the nanoscale (Figures 11 and 12) and bulk alloy phase diagrams (Figure 13) lies in the existence of metastable hcp phases prior to the melting transition in the case of nanowires and nanoclusters. The atomic rearrangement associated with the melting phenomenon in finitesized structures leads to changes in the crystal type (fcc to hcp) resulting in the existence of hcp phases over temperature ranges which vary with bimetallic composition. The presence of hcp phases in nanostructures of transition metals is not unusual and has been found experimentally as well as theoretically in the case of Au,57 Pd,16 as well as over certain composition ranges in alloys such as Pt-Ru54 which otherwise have an fcc structure in their bulk phases. The simulated phase boundaries in bimetallic nanowires and nanoclusters are shown in Figures 11 and 12. We find the absence of a sharp fcc-hcp transition for Pd compositions greater than 40% and 70% Pd in Pd-Cu wires and same-diameter clusters, respectively. In this composition range, the fcc-hcp transitions are more continuous and hence there are no observable (sharp) changes in the thermodynamic or structural properties. The melting of nanowires and nanoclusters is associated with two competing processes (i.e., solid-liquid (surface melting) and solid-solid (fcc-hcp) transitions). If the solidliquid transition point is below that of solid-solid transition, then the melting point is reached before a complete transformation to an hcp structure might occur. The sharp fcc-hcp transition for this composition range lies above the melting point and is not seen in the simulated phase transition diagram of bimetallic



TABLE 4: Comparison of Ratios of Melting Point Depression of Wire to Cluster Pd-Cu alloy

Pd-Rh alloy

simulation composition (% Pd) 5% 25% 50% 75% 95%

model

Tbm

)

(∆T)nc/(∆T)nw

(∆T)nc/(∆T)nw

Tm (bulk) K

(∆T)nc/(∆T)nw

(∆T)nc/(∆T)nw

1360 1410 1470 1600 1740

1.36 1.27 1.33 1.29 1.31

1.90 1.89 1.87 1.85 1.84

2250 2180 2050 1910 1790

1.47 1.45 1.40 1.35 1.32

1.87 1.87 1.85 1.84 1.83

[ () ]

Fs 2 γsv b Fl FsL R

2/3

γlv

(4.3)

Extension of the melting theory developed for nanoclusters to predict melting point depression from bulk value for nanowires results in the following expression

Tbm - Tm(R) Tbm

)

model

Tm (bulk) K

nanostructures. Pd-Rh nanoclusters and nanowires employed in this study have much higher melting points than Pd-Cu. Hence, the solid-solid (fcc-hcp) transition is observed over the entire range of Pd composition for Pd-Rh nanostructures. The temperature range of existence of hcp phases varies with the composition of the bimetallic. The hcp phases exist over a much broader temperature range in the case of Pd-Rh and PdCu nanowires, whereas same-diameter nanoclusters of these bimetallics exhibit hcp phases over a narrower temperature range (

Molecular Dynamics Simulation Study of Phase Transformations in

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