Size-dependent mechanical properties of molybdenum nanopillars

Abstract

We report the deformation behavior of single crystalline molybdenum nanopillars in uniaxial compression, which exhibits a strong size effect called the "smaller is stronger" phenomenon. We show that higher strengths arise from the increase in the yield strength rather than through postyield strain hardening. We find the yield strength at nanoscale to depend strongly on sample size and not on the initial dislocation density, a finding strikingly different from that of the bulk metal. © 2008 American Institute of Physics. ͓DOI: 10.1063/1.2979684͔Efforts to characterize the mechanical deformation behavior of materials at nanoscale have been driven by the need for precise fabrication and reliable operation of nanoscale devices as well as by fundamental scientific curiosity. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] Uniaxial compression tests of micropillars and nanopillars, recently used to investigate size-dependent mechanical properties at this scale, have shown that pure metals and metallic alloys exhibit strong size effects in plastic deformation, called the "smaller is stronger" phenomenon. [2][3][4][5][6][7][8][9][10] As metal sample sizes decrease to nanoscale, they are expected to contain few or no dislocations, and dislocations generated during plastic deformation tend to escape the crystal by annihilating at a nearby free surface, a condition known as hardening by dislocation starvation. 3-5,7-10 However, other origins of size effects in plastic deformation of nanocrystals remain somewhat controversial.Here we report the size dependence of mechanical behavior of single-crystal molybdenum ͑Mo͒ ͓body-centered cubic ͑bcc͔͒ nanopillars. The uniaxial stress-strain curves of these nanopillars appear to have the following two distinct features not present in previous experimental reports for Ni, Ni 3 Al, and Au ͓face-centered cubic ͑fcc͔͒: 2-4,7,8 ͑1͒ onset of plasticity is unambiguous allowing for precise yield strength determination, and ͑2͒ plastic deformation region is composed of discrete strain bursts ͑believed to be associated with dislocation annihilation͒ and continuous strain hardening ͑as-sociated with dislocation multiplication͒, which may lead to the overall increase in dislocation density during plastic deformation. In this study, smaller Mo nanopillars are found to sustain higher stress even though they do not meet the condition of dislocation starvation. We show that the fundamental origin of the observed size effect ͑higher strength for smaller sample͒ is the pronounced increase in yield strength, which is found to strongly depend on the pillar size and, surprisingly, to be independent of the initial dislocation density.Nanopillars with diameters from ϳ200 to ϳ900 nm and aspect ratios ͑height/diameter͒ of ϳ3 were made from electropolished and well annealed ͑100͒ single-crystal Mo using the focused ion beam ͑FIB͒ ͑Nova 200 NanoLab, FEI Co., Hillsboro, OR, USA͒ fabrication technique. 2,3 The nanopillars were subsequently compressed by a Nanoindenter G200 ͑Agilent Corp., Oak Ridge, TN,...

Fabrication, structure and mechanical properties of indium nanopillars

“…A technique is yet to be developed to analyze these hollow features. This type of "pop-in" displacement at small depths has been reported in gold, copper, molybdenum, molybdenum-alloy, and niobium pillar compression tests [4,6,7,[9][10][11]14,27]. It is often described as the incipient onset of plasticity where dislocations are nucleated within the pillars, allowing them to deform plastically.…”

“…This suggests non-uniform plastic deformation and the presence of fabrication-induced geometry necessary dislocations (GNDs) [22]. By using the Cahn-Nye analysis [25,26] and a Laue spot streak length of 1.20, the GND density in this grain was estimated to be 3.35 x10 9 cm -2 , which translates to 4.2 immobile geometrically necessary dislocations in this pillar. The number of dislocations in the h019i oriented grain is calculated by multiplying the measured dislocation density by the area of interest with respect to the relevant crystal dimensions.…”

“…The majority of research conducted in this area has focused on metals with cubic structures, i.e. nickel [1][2][3], gold [4][5][6], copper [7], molybdenum [8][9][10] and niobium [11]. The results of all these studies show that the uniaxial compressive yield strength of crystalline cubic metals increases with reduced sample sizes [12].…”

Flow Stress in Submicron BCC Iron Single Crystals: Sample-size-dependent Strain-rate Sensitivity and Rate-dependent Size Strengthening

“…In addition, it has been proposed previously that the sample-size-strengthening exponent α of BCC metals increases with a decrease in the 'critical temperature', [17] defined as the temperature above which the strain rate has little effect on the flow stress of BCC metals because screw and edge dislocations have equal mobility. However, as shown in Table 1, the α for single crystal Mo ranges from 0.29 to 1.0 [5,6,16,18,19] and that for single crystal Nb is from 0.48 to 1.07. [5,6,16] Apparently, just the critical temperature argument cannot rationalize the large scatter of α observed in different BCC metals (Table 1), neither can it explain the size effect on m.…”

“…[2,11] In addition, almost all previous studies of the size dependence of m of BCC metals used polycrystalline materials except the one by Schneider et al [14] They found that submicron-sized single crystal Mo pillars exhibited strain-rate sensitivity similar to their bulk counterpart. Moreover, compared with the widely studied size-strengthening effect and its underlying mechanism of single crystal BCC metals, [5,6,[14][15][16][17][18][19][20][21] much less work have been carried out on m. Recently, we demonstrated through molecular dynamics simulation [19] that very high applied stresses can diminish the velocity difference between screw and edge dislocations in single crystal Mo. As a consequence, BCC Mo behaves more like an FCC metal.…”