2007
DOI: 10.1007/s10483-007-0201-1
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Scale effect and geometric shapes of grains

Abstract: The rule-of-mixture approach has become one of the widely spread ways to investigate the mechanical properties of nano-materials and nano-structures, and it is very important for the simulation results to exactly compute phase volume fractions. The nanocrystalline (NC) materials are treated as three-phase composites consisting of grain core phase, grain boundary (GB) phase and triple junction phase, and a two-dimensional three-phase mixture regular polygon model is established to investigate the scale effect o… Show more

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Cited by 4 publications
(3 citation statements)
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“…32,33 D polycrystal = fD GB + (1 − f ) D bulk Here f is the volume fraction of GBs in the Li anode, and D GB and D bulk are the self-diffusivities of the GB and bulk regions, respectively. The GB volume fraction, f , was calculated using the regular polygon model, 38 eqn (7), where w is the representative GB width at each temperature, and d is the grain size.…”
Section: Methodsmentioning
confidence: 99%
“…32,33 D polycrystal = fD GB + (1 − f ) D bulk Here f is the volume fraction of GBs in the Li anode, and D GB and D bulk are the self-diffusivities of the GB and bulk regions, respectively. The GB volume fraction, f , was calculated using the regular polygon model, 38 eqn (7), where w is the representative GB width at each temperature, and d is the grain size.…”
Section: Methodsmentioning
confidence: 99%
“…32,33 𝐷 𝑃𝑜𝑙𝑦𝑐𝑟𝑦𝑠𝑡𝑎𝑙 = 𝑓𝐷 𝐺𝐵 + (1 − 𝑓)𝐷 𝐵𝑢𝑙𝑘 (6) Here f is the volume fraction of GBs in the Li anode, and 𝐷 𝐺𝐵 and 𝐷 𝐵𝑢𝑙𝑘 are the self-diffusivities of the GB and bulk regions, respectively. The GB volume fraction, f, was calculated using the regular polygon model, 36 Equation 7, where w is the representative GB width at each temperature, and d is the grain size.…”
Section: Methodsmentioning
confidence: 99%
“…32,33 𝐷 789:;<:=>?9 = 𝑓𝐷 @A + (1 − 𝑓)𝐷 AB9C (6) Here f is the volume fraction of GBs in the Li anode, and 𝐷 /0 and 𝐷 01(2 are the self-diffusivities of the GB and bulk regions, respectively. The GB volume fraction, f, was calculated using the regular polygon model, 38 Equation 7, where w is the representative GB width at each temperature, and d is the grain size.…”
Section: Gb Diffusivity Gb Width Measurementmentioning
confidence: 99%