Surface stress induced structural transformations and pseudoelastic effects inpalladium nanowiresJijun Lao and Dorel Moldovan Citation: Applied Physics Letters 93, 093108 (2008); doi: 10.1063/1.2976434 View online: http://dx.doi.org/10.1063/1.2976434 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/93/9?ver=pdfcov Published by the AIP Publishing

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Surface stress induced structural transformations and pseudoelasticeffects in palladium nanowires

Jijun Lao and Dorel Moldovana�

Department of Mechanical Engineering, Louisiana State University, Baton Rouge, Louisiana 70803, USA

�Received 7 May 2008; accepted 7 August 2008; published online 3 September 2008�

Using molecular dynamics simulations, we investigate the surface stress induced structuraltransformations and pseudoelastic behaviors in palladium nanowires. For wires with a �100� initialorientation, the simulations indicate that when the cross-sectional area is less than 2.18�2.18 nm2, the nanowire undergoes spontaneous reversible phase transformation from fcc tobody-centered tetragonal structure. In wires with larger cross-sectional areas, the structuraltransformation is achieved via spontaneous reversible lattice reorientation. In both cases, undertensile loading and unloading, Pd nanowires reverse between the corresponding transformedstructure and the original structure, exhibiting pseudoelastic behaviors characterized by fullyrecoverable strains of up to 50%. © 2008 American Institute of Physics. �DOI: 10.1063/1.2976434�

With the miniaturization of electrical, optical, thermal,and mechanical systems, the feature size of relevant devicecomponents are reduced down to several nanometers. Whentwo spatial dimensions of the systems are in the nanometerrange �i.e., nanowire structures�, the structural characteristicsand stability are strongly influenced by both surface energyand surface stress. Several structures have been identified inmetallic nanowires including multishell helical goldnanowires,1,2 “weird” aluminum and lead nanowires,3 andbody-centered tetragonal �bct� gold nanowires.4,5 Recent ato-mistic simulation studies have identified two distinct mecha-nisms that mediate the spontaneous structural changes in me-tallic nanowires. In certain metals when the cross-sectionalarea is below 4 nm2, the surface stress can be large enoughto cause a phase transformation that drives the system fromthe initial fcc structure into a bct structure.4,6 Nanowires withlarger cross-sectional areas can undergo spontaneous crystalstructure reorientation; that is, fcc wires with initial �100�orientations can reorient spontaneously under the effect ofsurface stress into �110� orientations.6–9 Associated with theexistence of reversible crystallographic lattice reorientation,pseudoelastic behavior in these nanowires was discoveredand studied extensively.7–9 The temperature dependence ofthis behavior leads to shape memory effect. It has been dem-onstrated that under tensile loading and unloading, suchnanowires can exhibit recoverable strains of up to 50%, wellbeyond the recoverable strains of 5%–8% typical for mostbulk shape memory alloys.

In this study, using molecular dynamics �MD� simula-tions, we investigate the fundamentals of surface stress in-duced structural transformations and pseudoelastic behaviorsin palladium crystalline nanowires. For wires with a �100�initial orientation, the simulations indicate that when thecross-sectional area is less than 2.18�2.18 nm2, the nano-wire undergoes spontaneous reversible phase transformationfrom fcc to bct structure, provided that the temperature isabove the critical value Tc=22.5 K. In wires with largercross-sectional areas �i.e., 2.57 �2.57 nm2�, the structuraltransformation is achieved via spontaneous reversible latticereorientation leading to an fcc wire with �110� orientation. In

both cases, under tensile loading and unloading, Pd nano-wires reverse between the corresponding transformed struc-ture and the original structure, exhibiting pseudoelastic be-haviors characterized by fully recoverable strains of up to50%. While the pseudoelastic behavior in the lattice reorien-tation process is controlled by the propagation of twin �111�boundary that involves repetitive nucleation, gliding, and an-nihilation of Shockley partial dislocations,7,8 the pseudoelas-tic behavior associated with the reversible fcc to bct phasetransformation is mediated by short range atomic rearrange-ments similar to those found in austenite to martensite phasetransformations. As our studies indicate, the differences inthe controlling mechanisms of the two pseudoelastic behav-iors has strong bearing on the corresponding stress-straincurves obtained by external loading and unloading of thenanowires.

The MD simulations were performed using theembedded-atom method potential for Pd.10 Single crystallinePd �100� nanowires with a square cross section and surfaceorientation of �100�, �010�, and �001� were created with ini-tial atomic positions corresponding to the bulk fcc Pd crystal.To investigate the role of the diameter on wire structuralstability and mechanical behavior, we carried out MD simu-lations of Pd nanowire systems of various cross-sectionalareas. We focused our analysis on three wire systems havingoriginal cross-sectional areas of 1.78�1.78 nm2, 2.18�2.18 nm2, and 2.57�2.57 nm2, respectively. All wiresconsidered were 31.2 nm in length. Free boundary condi-tions were used in all directions.

Our MD simulations results indicate that due to the pres-ence of large intrinsic surface stresses, all three Pd wiresundergo spontaneous structural transformations. Namely, atT=100 K the two wires with cross-sectional areas of 1.78�1.78 nm2 and 2.18�2.18 nm2 undergo phase transforma-tions from the initial fcc to a bct crystal structure whereas thewire with 2.57�2.57 nm2 cross-sectional area experienceslattice reorientation into a �110� wire with �111� surfaces.Figure 1 illustrates the dynamic progression of the fcc to bctphase transformation. During the first 3.0 ps, the fcc wirerelaxes elastically and contracts longitudinally by about6.1%. After the elastic contraction, a bct crystalline phasenucleates at the ends and propagates with a speed of approxi-mately 538 m /s toward the center of the nanowire. The fcc

a�Author to whom correspondence should be addressed. Electronic mail:moldovan@me.lsu.edu.

APPLIED PHYSICS LETTERS 93, 093108 �2008�

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to bct phase transformation is completed in about 30 ps andleads to a further wire longitudinal contraction of about38.5%. Using the average positions of the atoms located in-side the wire and neglecting those located at the ends crys-tallographic analysis yields the lattice parameters a=4.884 /2=3.454 Å and c=2.724 Å for the bct crystalstructure. The lattice parameter of the original fcc Pd wire is3.95 Å.

After the completion of the spontaneous fcc to bct phasetransformation in the 1.78�1.78 nm2 wire, the bct wire wasloaded in the longitudinal direction to investigate the pseu-doelastic behavior. Both tensile loading and unloading stud-ies were conducted under simulated quasistatic conditions.Namely, at each load step, the coordinates of all atoms weremodified according to a prescribed uniform strain incrementof 0.125% in the length direction. To allow the wire to reachlocal microscopic equilibration, after each straining step thewire was relaxed for 15 ps at 100 K holding the wire ends atfixed positions consistent with the prescribed wire length.The relaxation process usually takes less than 10 ps and thestress evaluated and averaged over the subsequent 5 ps wastaken as the actual stress in the wire at the correspondingstrain state. The unloading process followed a similar proto-col with a strain decrement of −0.125% at each unloadingstep. Figure 2 shows the dynamic progression of the bct wireunder tensile loading at 100 K. Upon loading the wire trans-forms back to the original fcc crystal structure via a phasechange mechanism mediated by short range atomic rear-rangements that nucleate at the ends and propagate towardthe center of the wire.

Figure 3 shows the stress-strain curves for the 1.78�1.78 nm2 wire during loading and unloading at 100 K. Thecurves indicate that the Pd wire is indeed very ductile with

fracture strains of approximately 50%. During the loadingpart of the stress-strain curve, one can identify the followingstages. �i� During the stage delimited by points O and A onthe loading curve, the wire maintains its bct crystalline struc-ture while undergoing elastic straining. �ii� When the tensilestress reaches 7.5 GPa, corresponding to point A on thecurve, the nucleation of the fcc phase starts at the ends of thewire. The subsequent motion of the nucleated fcc regionsmarks the beginning of the bct to fcc phase transformation;process which is also associated with a sudden drop of theapplied stress from 7.5 to approximately 3.5 GPa. �iii� Be-tween points B and C, the linear portion of the curve corre-sponds to wire elongation caused by the steady advance ofthe bct to fcc phase change from the ends toward the centerof the wire. At point C, the entire wire has been converted tothe fcc structure. Interestingly, there is no strain hardeningduring this stage of deformation. �iv� The portion between Cand D corresponds to the elastic linear stretching of the fccwire. �v� Further loading beyond point D at a stress levelexciding 8.2 GPa, causes the fcc wire to neck and ultimatelyto fracture at point E.

The 1.78�1.78 nm2 fcc wire transforms spontaneouslyback to the 2.196�2.196 nm2 bct configuration via phasechange mediated by short range atomic rearrangement pro-cesses in reverse to what is described above when the tem-perature is above a certain value. The reversible fcc to bctphase transformation results from a cooperative and collec-tive motion of atoms over distances smaller than a latticeparameter in the absence of any diffusive processes. Thecurve depicted in red in Fig. 3 traces the stress-strain rela-tionship during the controlled simulated quasistatic unload-ing of the fcc wire. Similar to the behavior of traditional bulkshape memory alloys, the reversible phase change in Pdnanowire is temperature dependent. The spontaneous fcc tobct phase transformation in both 1.78�1.78 nm2 and 2.18�2.18 nm2 wires occurs only when the temperature is abovea critical value Tc. If the temperature is below Tc, the fccwire configuration is stable. Our MD simulations indicatethat the critical temperature Tc for the Pd nanowires investi-gated is around 22.5 K.

For reference and comparison, we also give in Fig. 4 thestress-strain curve obtained during loading and unloading at100 K of the 2.57�2.57 nm2 Pd wire that undergoes revers-ible �110� / �111� to �100� / �100� lattice reorientation. De-

FIG. 1. �Color online� Six snapshots depicting the time evolution of a Pdnanowire during the spontaneous, surface-stress-driven, fcc to bct phasetransformation at 100 K. Snapshots of the 1.78�1.78 nm2 Pd wire at 1, 7,11, 15, 20, and 30 ps, respectively, are shown here.

FIG. 2. �Color online� Snapshots of the 1.78�1.78 nm2 wire at strains0.125%, 6.6%, 15.4%, 36.8%, and 44.1%, respectively, depicting the dy-namic progression of the bct to fcc phase transformation in the Pd wireloaded in tension at 100 K.

FIG. 3. �Color online� Stress-strain curve for the 1.78�1.78 nm2 Pd wireundergoing reversible bct to fcc phase transformation during loading andunloading at 100 K.

093108-2 J. Lao and D. Moldovan Appl. Phys. Lett. 93, 093108 �2008�

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tailed analysis of similar pseudoelastic behavior has beencarried out extensively in Au, Cu, and Ni nanowires by Li-ang et al.7 Liang and Zhou,8 and Park et al.9 Comparison ofthe two stress-strain curves �Figs. 3 and 4�, quantifying thetwo pseudoelastic behaviors mediated by different mecha-nisms indicate that there are both similarities and differencesbetween the two systems. Namely, although both transforma-tions can achieve similar levels of strains, they differ quali-tatively and quantitatively in the plateau regions. While theloading stress-strain curve for the lattice reorientation-controlled pseudoelastic behavior exhibits a small strainhardening over the range of strains delimited by the beginand the end stage of the reorientation process �see Fig. 4�, nosuch phenomena is observed on the corresponding portion ofthe stress-strain curve for the fcc to bct phase transformation-controlled pseudoelastic behavior �see Fig. 3�. Moreover, al-though in both mechanisms the deformations are fully recov-ered when the stress is reduced to zero, there are majordifferences between the two stress-strain curves during theunloading stage. While for the fcc to bct phasetransformation-controlled pseudoelastic behavior the loadingand the unloading stress-strain curves follow almost thesame path �Fig. 3� for the lattice reorientation-controlledpseudoelastic behavior the loading and unloading paths forma well defined hysteresis loop �Fig. 4�. The differences be-tween the stress-strain curves depicted in Figs. 3 and 4 aredue to the major differences between the mechanisms medi-ating the two pseudoelastic behaviors. As mentioned previ-ously, the reversible fcc to bct phase transformation is medi-ated by short range atomic rearrangements, similar to thosefound in austenite to martensite phase transformations, anddoes not involve nucleation and propagation over large dis-tances of any structural defects. In contrast to this, in thelattice reorientation-controlled pseudoelastic behavior, bothstrain hardening and hysteresis loop observed are the prod-ucts of repetitive nucleation, gliding, and annihilation ofShockley partial dislocations.

The magnitude of the induced longitudinal compressivestress, estimated based on a continuum model, is approxi-mately given by �=− 4f l /A, where f is the surface stresscomponent on the �100� wire surfaces in the initial fcc

�100� / �100� configuration, l is the width of the wire, and A isthe cross section area.6 Figure 5 shows the stress-straincurves for both 1.78�1.78 nm2 and 2.18�2.18 nm2 wiresduring quasistatic loading at 100 K. The stress plateaus de-limited by the beginning and the end of the reversible bct tofcc phase transformation �i.e., the region of the stress-straincurve between 0.05 and 0.45 strain values� are approxi-mately 3.50 and 2.82 GPa, respectively. The ratio of thesetwo stress values 3.50 /2.82=1.24 is approximately equal tothe inverse ratio 2.18 /1.78=1.22, of the corresponding nano-wires widths.

In summary, we have shown that the surface stress cancause palladium nanowires to undergo spontaneous structuraltransformations. When the cross-sectional area is less than2.18�2.18 nm2 Pd nanowires undergo spontaneous revers-ible fcc to bct phase transformation. In wires with largercross-sectional areas, the structural transformation isachieved via spontaneous reversible lattice reorientation. Inboth cases, under tensile loading and unloading, Pd nano-wires transform reversibly between the corresponding trans-formed structure and the original �100� wire, exhibiting pseu-doelastic behaviors characterized by comparable, fullyrecoverable, strains of up to 50%. The temperature-dependence of the pseudoelastic behaviors enables the shapememory effects in Pd nanowires. These properties cangreatly impact nanowires usage in a large class of nanode-vices including sensors, actuators and transducers.

This work was supported in part by NSF-EPSCoRthrough Grant Nos. EPS-0701491 and EPS-0346411. Thework of J.L. was supported by a Graduate Fellowship fromLONI Institute. The simulations were performed at the LSUCenter for Computation & Technology.

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FIG. 4. �Color online� Stress-strain curve for the 2.57�2.57 nm2 Pd wireduring loading and unloading at 100 K. At this cross-sectional area, uponloading and unloading, the nanowire maintains the fcc crystal structure andundergoes reversible lattice reorientation from the �110� / �111� �original�structure to the �100� / �100� �stretched� wire structure.

FIG. 5. �Color online� Stress-strain response during quasistatic loading ofboth 1.78�1.78 nm2 and 2.18�2.18 nm2 Pd wires �the dotted lines indi-cate the plateau stresses during the bct to fcc phase transformation�.

093108-3 J. Lao and D. Moldovan Appl. Phys. Lett. 93, 093108 �2008�

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