Density functional theory investigation of surface-stress-induced phase transformations in fcc metal nanowires

Abstract

We use density functional theory ͑DFT͒ and the tight-binding ͑TB͒ method to study the relaxation of narrow Cu, Ni, Au, Pt, and Ag nanowires originally oriented in the ͗001͘ direction with a fcc structure. For a small enough diameter ͑d Ͻ 2 nm͒ each nanowire, under the compressive influence of its own surface stress, spontaneously relaxes to either a ͗110͘ orientation ͑Cu, Ni, Ag͒ or to a bct ͗001͘ orientation ͑Au, Pt͒, both of which are characterized by a compression of the wire axis of at least 30%. To analyze the stability of bct structures, we calculate the elastic constants for the bct phases of these metals under bulk, slab, and nanowire conditions. DFT predicts that only the bct phase in Pt is stable with respect to shear distortions in both the bulk and in nanowires. We find that the surface contribution to the elastic constant for shear, C 66 , helps stabilize the bct phase in Au which would otherwise be unstable under bulk conditions. A large stabilization contribution from the surface also occurs in Ni and Cu, but not enough to overcome the shear instability in the bulk, and these nanowires do not transform to bct, although Cu is nearly stable for very narrow nanowires of width ϳ1 nm. We discuss the interplay of surface and edge effects in the phase change or reorientation of these nanowires and implications of these results on pseudoelasticity or shape memory in fcc metals.

Size effects in NiTi from density functional theory calculations

“…4,16,17 Surfaces are also known to drive phase transformations in nanoscale FCCwires. 18,19,20 MD simulations showedthat surface stresses cause<100> nano-wires to spontaneously change their orientation to<110> in Ni, Ag and Cu;in the case ofAu nanowireswith diameters less than 2 nm, a transformationto a body centered tetragonal structure has been observed. 18 Furthermore, Cu and Ni, square cross-section nanowires also exhibit shape memory and pseudoelasticity due to the above-mentioned structural relaxations and their large stacking fault energies.…”

“…18,19,20 MD simulations showedthat surface stresses cause<100> nano-wires to spontaneously change their orientation to<110> in Ni, Ag and Cu;in the case ofAu nanowireswith diameters less than 2 nm, a transformationto a body centered tetragonal structure has been observed. 18 Furthermore, Cu and Ni, square cross-section nanowires also exhibit shape memory and pseudoelasticity due to the above-mentioned structural relaxations and their large stacking fault energies. 21 Gold nano-films of thicknessless than 2 nm (8 atomic layers) have also been experimentally observed to transform from a(001) orientation to (111) spontaneously.…”

Surface-induced structural transformation in nanowires

“…Surface energy (Jm À2 ) (0 0 1) 1.21 (EAM) [18] 0.79 (EAM) [18] 1.57 (EAM) [18] 0.85 (EAM) [18] 1.35 (EAM) [19] 0.91 (EAM) [20] 1.88 (EAM) [19] 1.09(MEAM) [25] 1.45 (DFT) [27] 1.04 (MEAM) [23] 2.42 (MEAM) [25] 1.66(MEAM) [24] 1.25 (SEAM) [26] ( 1 1 1) 1.01 (EAM) [18] 0.62 (EAM) [18] 1.33 (EAM) [18] 0.69 (EAM) [18] 1.24 (EAM) [19] 0.79 (EAM) [20] 1.63 (EAM) [19] 1.09(MEAM) [25] 1.30 (DFT) [27] 0.92(MEAM) [20] 2.02(MEAM) [25] 1.41(MEAM) [24] 1.05 (SEAM) [26] Surface stress (Jm À2 ) (0 0 1) 0.90 (EAM) [18] 1.23 (EAM) [18] 0.75 (EAM) [18] 0.80 (EAM) [18] 2.11(MEAM) [24] 1.57 (EAM) [21] 2.37(MEAM) [25] 1.48(MEAM) [25] 1.38(EAM) [22] 1.03(MEAM) [21] 2.98 (DFT) [28] 1.00 (DFT) [28] 2.03 (DFT) [28] 3.25 (SEAM) [26] 3.00 (DFT) [29] 2.88 (DFT) [30] 1.39 (DFT) [31] 3.64 (TB) [21] 4.57 (DFT) …”

“…Hence, surface effects are dominant factors affecting the structure of nanowires and can even induce thorough structural transition. On the heels of these discoveries, other interesting materials properties such as surfaceinduced lattice reorientation, martensitic phase transformation (MT), pseudo-elastic behavior, and shape memory effects (SMEs) have been studied and observed from fcc [14,[19][20][21][22][23]28,[63][64][65][66][67][68][69][70][71][72][73][74][75], bcc [76][77][78][79][80][81][82], and hcp [83,84] single-element, layered composite [85][86][87][88][89], intermetallic alloy [90][91][92][93][94][95], and even metal oxide [96][97][98][99][100] or nitride [101] compound nanowires. The reversible strain can be as high as 40-70% and is much lar...…”

“…Although it is difficult to measure these two parameters experimentally, they have been predicted by theoretical methods such as the embedded atom method (EAM) [18][19][20][21][22], modified embedded atom method (MEAM) [20,21,[23][24][25], surface embedded atom method (SEAM) [26], density function theory (DFT) [27][28][29][30][31][32][33][34][35], and tight-binding (TB) [21]. Table 1 lists the results of typical face centered cubic (fcc) metals and only {1 0 0} and {1 1 1} planes are shown as examples.…”