Ken Gall Jiankuai Diao Martin L. Dunn Department of Mechanical Engineering, University of Colorado at Boulder, Boulder, CO 80309 Michael Haftel Noam Bernstein Michael J. Mehl Center for Computational Materials Science, Naval Research Laboratory, Washington, DC 20375-5345 Tetragonal Phase Transformation in Gold Nanowires First principle, tight binding, and semi-empirical embedded atom calculations are used to investigate a tetragonal phase transformation in gold nanowires. As wire diameter is decreased, tight binding and modified embedded atom simulations predict a surface- stress-induced phase transformation from a face-centered-cubic (fcc) 100 nanowire into a body-centered-tetragonal (bct) nanowire. In bulk gold, all theoretical approaches pre- dict a local energy minimum at the bct phase, but tight binding and first principle calculations predict elastic instability of the bulk bct phase. The predicted existence of the stable bct phase in the nanowires is thus attributed to constraint from surface stresses. The results demonstrate that surface stresses are theoretically capable of inducing phase transformation and subsequent phase stability in nanometer scale metallic wires under appropriate conditions. DOI: 10.1115/1.1924558 1 Introduction Gold Au nanowires have potential application in nanotechnol- ogy due to their relative ease of fabrication 1,2, stability at small scales 3–13, capacity for biomolecule functionalization 14–17, and high conductivity. Recent studies have demonstrated that low- dimension Au materials can exist in non-face centered cubic fcc structures. When thinned below a critical size, 110 Au nanowires have been observed to transform into a helical multi-shell struc- ture 10. Small 100 Au nanowires are predicted to undergo an fcc to body centered cubic bct phase transformation 18. Atoms in single chain Au nanowires have different spacing than atoms along close-packed directions in bulk Au 12. The formation of non-fcc crystal structures in Au nanowires is driven by surface stresses and the tendency to minimize surface energy. In order to fully exploit Au nanowires in emerging nanosystems, it is critical to understand their unique structures from a fundamental perspec- tive. In addition, the study of phase stability and transformation in nanometer scale solids has broad implications. From a basic sci- ence point of view, the study of phase changes in nanometer scale materials provides fundamental information on solid-state trans- formations not easily ascertained in bulk solids 19,20. From an application standpoint, control of metastable phases in nanometer scale materials may provide a means for small-scale actuation, analogous to martensitic transformations observed in nanoscale biological systems 21,22. Nanometer scale solids possess unique properties due in part to their large ratio of surface area to volume. Free surfaces in solids give rise to surface energy and surface stress. Surface stresses, which are typically tensile in metals, cause contraction of surface atoms relative to bulk atoms, resulting in “intrinsic” compressive stresses within materials. Intrinsic stresses are defined as stresses existing in a material in the absence of external applied load. Although free surfaces exist in macroscopic materials, surface- stress-induced intrinsic compressive stresses are significant only in materials with nanometer scale dimensions. The surface-stress- induced intrinsic compressive stress state depends on sample ge- ometry. Figure 1 is a schematic illustrating the effect of tensile surface stress on the development of intrinsic compressive stresses in the core of freestanding nanometer scale materials. The core of a nanometer scale solid is defined as the remainder of the material excluding the first few atomic surface layers. A nanofilm is de- fined by one dimension being nanometer scale, a boundary con- dition that creates intrinsic in-plane biaxial compression in the film core. Nanowires possess nanometer scales in two dimensions, and a resulting intrinsic stress state of triaxial compression in the wire core. Nanoparticles have nanometer scales in all three dimen- sions, and thus an intrinsic stress state of hydrostatic compression in the particle core. The intrinsic stress states depicted in Fig. 1 are ideal, since cross-sectional shape and exposed surface orien- tation can alter the resulting stress state. The magnitude of the intrinsic stresses in nanometer scale materials increases with de- creasing sample size in the nanometer scale dimension. Moreover, the intrinsic stresses in nanofilms or nanoparticles can be propor- tionately modified by experimental methods: forced epitaxial growth for nanofilms 23,24 and application of hydrostatic pres- sure for nanoparticles 19,20. On the other hand, the unique tri- axial stress state in nanowires hydrostatic pressure plus uniaxial compression is more difficult to uniformly adjust. The intrinsic stresses in nanowires can result in a tetragonal crystal lattice distortion 23–27, which can drive the formation of a bct lattice from a host fcc lattice. Theoretical predictions have revealed a local minimum energy bct phase formed by tetragonal distortion of the fcc lattice 23,27. However, the predicted bct structure is typically elastically unstable with respect to shear 23,27, thus requiring stabilization by “external” forces. In this sense, the bct structure is not a classical metastable phase, as defined for bulk materials. Although prior work has considered stabilization of the bct structure by epitaxial film growth 23,24, it may be possible to stabilize an elastically unstable phase in a freestanding material by surface stresses 18. The objective of the present paper is to explore the stability of tetragonal states in freestanding fcc Au nanowires using various theoretical ap- proaches. The present work provides a stronger theoretical foun- dation for initial semi-empirical atomistic predictions of the fcc to bct phase transformation in Au nanowires 18. 2 Simulation Methods Simulations were performed using the embedded atom method EAM28, the modified embedded atom method MEAM29, the tight binding TB30 method, and density functional theory Contributed by the Materials Division of ASME for publication in the JOURNAL OF ENGINEERING MATERIALS AND TECHNOLOGY. Manuscript received September 21, 2004. Final manuscript received December 28, 2004. Review conducted by: Min Zhou. Journal of Engineering Materials and Technology OCTOBER 2005, Vol. 127 / 417 Copyright © 2005 by ASME