Closure to “Discussion of Iron-Molybdenum and Nickel-Molybdenum Alloys (pp. 7–15) [S. S. Brenner] and “Discussion of ‘Catastrophic Oxidation of Some’ [Molybdenum-Containing Alloys (pp. 16–21) S. S. Brenner]”

Brenner, S.S.

doi:10.1149/1.2429950

Cited by 58 publications

(97 citation statements)

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“…[1][2][3][4][5][6] Pure metals and some alloys exhibit strong size effects at the submicron scale. [1][2][3][4][5][6][7][8][9][10][11][12][13] Size effects in indentation, torsion, and bending have been understood in terms of the nonuniformity of the deformation, which sets up strain gradients leading to hardening. 7 Size effects are also found in thin films, where the strength scales inversely with film thickness and is usually attributed to the confinement of dislocations by the substrate.…”

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confidence: 99%

“…In addition, classic experiments on the initially dislocation-free metal whiskers indicated that whiskers with smaller diameters yielded at higher stresses. 13 In typical whiskerlike deformation behavior, initial elastic loading leads to a very high stress followed by a significant drop and continued plastic flow at low stresses. Finally, several molecular dynamics simulations [14][15][16] and more recent experiments on small pillars 17,18 all support the tenet that smaller is stronger.…”

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Nanoscale gold pillars strengthened through dislocation starvation

2006

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It has been known for more than half a century that crystals can be made stronger by introducing defects into them, i.e., by strain-hardening. As the number of defects increases, their movement and multiplication is impeded, thus strengthening the material. In the present work we show hardening by dislocation starvation, a fundamentally different strengthening mechanism based on the elimination of defects from the crystal. We demonstrate that submicrometer sized gold crystals can be 50 times stronger than their bulk counterparts due to the elimination of defects from the crystal in the course of deformation. DOI: 10.1103/PhysRevB.73.245410 PACS number͑s͒: 62.25.ϩg, 81.07.Bc, 81.16.Rf, 81.70.Bt Anyone who has ever repeatedly bent a copper wire knows that it gets progressively stronger as it becomes more deformed, through a phenomenon called strain-hardening. The strengths of cold-worked metals are known to be up to ten times greater than those of well-annealed crystals. Plasticity in metals occurs by the motion of dislocations, or line defects, which multiply in the course of plastic deformation. Impeding the motion of dislocations by introducing defects into crystals results in strengthening. Although these fundamental concepts are often assumed to be applicable to crystals of any dimensions, numerous recent studies have shown that conventional plasticity diverges at a certain length scale, with smaller samples reported to be stronger than their bulk counterparts. [1][2][3][4][5][6] Pure metals and some alloys exhibit strong size effects at the submicron scale. [1][2][3][4][5][6][7][8][9][10][11][12][13] Size effects in indentation, torsion, and bending have been understood in terms of the nonuniformity of the deformation, which sets up strain gradients leading to hardening. 7 Size effects are also found in thin films, where the strength scales inversely with film thickness and is usually attributed to the confinement of dislocations by the substrate. [8][9][10] Size effects are observed for pristine crystals, as well. 11,12 In the earliest stages of nanoindentation, for example, the crystal volume is extremely small and can be dislocation-free, requiring very large stresses to nucleate new dislocations. In addition, classic experiments on the initially dislocation-free metal whiskers indicated that whiskers with smaller diameters yielded at higher stresses. 13 In typical whiskerlike deformation behavior, initial elastic loading leads to a very high stress followed by a significant drop and continued plastic flow at low stresses. Finally, several molecular dynamics simulations 14-16 and more recent experiments on small pillars 17,18 all support the tenet that smaller is stronger. In spite of much progress on size effects research there is still no unified theory for plastic deformation at the submicron scale.We focus on size effects arising in unconstrained geometries, in the absence of strain gradients, and with nonzero initial dislocation densities. Gold nanopillars ranging in diameter between 200 nm and s...

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Nanoscale gold pillars strengthened through dislocation starvation

2006

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“…[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.…”

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Size-dependent mechanical properties of molybdenum nanopillars

Kim

Greer

2008

Applied Physics Letters

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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,...

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“…Большие величины характерны для отдельных «уникальных» образцов, основная же масса усов имеет меньшую прочность, но также значительно превышающую прочность обычных кристаллов. Почти для всех изученных веществ имеется явная зависимость прочности нитевидных кристаллов от диаметра 15 . После достижения напряжения, соответствующего пределу текучести, могут быть три возможности: или ус разрушается хрупко, или он дефор-мируется пластично, или испытывает ползучесть.…”

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The properties of whiskers

Nadgornyĭ¹

1962

Успехи физических наук

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ВВЕДЕНИЕРост кристаллов в форме нитей или волокон был известен очень давно 1 . Однако изучение свойств нитевидных кристаллов, или, как их часто назы-вают, «усов», практически не производилось до 1952 г., когда впервые были обнаружены их необычные механические свойства 2 . В последние годы ведется интенсивное исследование нитевидных кристаллов. Им были посвящены две международные конференции s > 4 и ряд совещаний; свыше 200 научных работ излагают результаты изучения их свойств. К настоя-щему времени получены нитевидные кристаллы 30 элементов и более 50 соединений; непрерывно ведется работа по изучению нитевидных кри-сталлов новых веществ.Такой большой интерес объясняется целым рядом свойств нитевидных кристаллов, относящихся к самым различным веществам: металлам, полу-проводникам, ионным, молекулярным или органическим кристаллам. В настоящее время нитевидными кристаллами, или усами, называют только те кристаллы, которые при малых диаметрах, порядка микрон, обладают некоторыми необычными свойствами и в первую очередь большой упругой деформацией. Это сразу позволяет предположить, что в нитевидных кри-сталлах на практике реализуются свойства, присущие совершенной кри-сталлической решетке, которые до сих пор не могли быть проверены экспериментально, а лишь предсказывались теоретически. В какой мере это верно, можно сказать, только подробно изучая нитевидные кристаллы.Наиболее характерными свойствами нитевидных кристаллов являются: 1) очень большая упругая деформация, доходящая до нескольких процентов;2) другой вид диаграммы растяжения (изгиба) в пластической области, чем у обычных кристаллов;3) ряд особенностей фазовых превращений; 4) меньшие скорости окисления, испарения и растворения; 5) высокая коэрцитивная сила (для железа), в несколько тысяч раз больше обычной.Оптические и электрические свойства нитевидных кристаллов пока изучены гораздо меньше, поэтому можно ожидать, что будут обнаружены новые особенности этих свойств, присущие нитевидным кристаллам.В настоящем обзоре излагаются, в основном, результаты исследований нитевидных кристаллов последних лет, опубликованные после появления обзора 6 в 1959 г.; иногда с целью сохранения последовательности изложе-1 УФН, т. LXXVII, вып. 2

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Closure to “Discussion of Iron-Molybdenum and Nickel-Molybdenum Alloys (pp. 7–15) [S. S. Brenner] and “Discussion of ‘Catastrophic Oxidation of Some’ [Molybdenum-Containing Alloys (pp. 16–21) S. S. Brenner]”

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Cited by 58 publications

References 0 publications

Nanoscale gold pillars strengthened through dislocation starvation

Nanoscale gold pillars strengthened through dislocation starvation

Size-dependent mechanical properties of molybdenum nanopillars

The properties of whiskers

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