Stress development during reaction of metallic nanospheres with gas

Svoboda, Jiřı́; Fischer, Franz Dieter

doi:10.1016/j.actamat.2010.09.001

Cited by 16 publications

(8 citation statements)

References 32 publications

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“…The diffusion data of Peterson and Wiley in contrast, acquired from bulk measurements on large‐grained polycrystals of Cu 2 O at 700 °C ≤ T ≤ 1153 °C and oxygen partial pressures of

10^{- 6} \leq p_{O_{2}} \leq 8 \times 10^{- 2}

atm, can be extrapolated to

D_{{CuinCu}_{2} O} = 1.4 \times 10^{- 18}

cm 2 s −1 at atmospheric pressures and T = 100 °C conditions. The faster diffusion observed here may result from diffusion along grain boundaries or through voids in the polycrystalline Cu 2 O shell, be facilitated by hydrostatic tensile stresses in the Cu core, or be enhanced by electric fields generated by adsorbed species on the nanoparticle surface …”

Section: Resultsmentioning

confidence: 91%

“…[ 28 ] The measured activation energy for diffusion at these relatively low temperatures is signifi cantly reduced, however, from those observed in high temperature oxidation ( 120~180 a E = kJ mol −1 for 550 °C ≤ T ≤ 1050 °C) due to the dominant diffusion mode being along the grain boundaries that form in the growing Cu 2 O shell. [ 28 ] In addition, the diffusion coeffi cient in Cu nanocrystals at 100 °C may be extrapolated from literature data taken at T ≥ 600 °C to be approximately 7.5 10 [ 43 ] in contrast, acquired from bulk measurements on large-grained polycrystals of Cu 2 O at 700 °C ≤ T ≤ 1153 °C and oxygen partial pressures of 10 8 10 [ 44 ] be facilitated by hydrostatic tensile stresses in the Cu core, [ 45 ] or be enhanced by electric fi elds generated by adsorbed species on the nanoparticle surface. [ 3 ]…”

Section: Diffusion Coeffi Cient and A Cuincu2mentioning

confidence: 99%

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Nanoscale Kirkendall Effect and Oxidation Kinetics in Copper Nanocrystals Characterized by Real‐Time, In Situ Optical Spectroscopy

Rice

Paterson

Stoykovich

2014

Part & Part Syst Charact

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The low‐temperature oxidation of ≈10 nm diameter copper nanocrystals is characterized using in situ UV–vis absorbance spectroscopy and observed to lead to hollow copper oxide shells. The kinetics of the oxidation of solid Cu nanocrystals to hollow Cu2O nanoparticles is monitored in real‐time via the localized surface plasmon resonance response of the copper. A reaction‐diffusion model for the formation of hollow nanoparticles is fit to the measured time for complete Cu nanocrystal oxidation, and is used to quantify the diffusion coefficient of Cu in Cu2O and the activation energy of the oxidation process. The diffusivity measured here in single‐crystalline nanoscale systems is 1–5 orders of magnitude greater than in comparable systems in the bulk, and have an Arrhenius dependence on temperature with an activation energy for diffusion of 37.5 kJ mol−1 for 85 °C ≤ T ≤ 205 °C. These diffusion parameters are measured in some of the smallest metal systems and at the lowest oxidation temperatures yet reported, and are enabled by the unique nanoscale single‐crystalline material and the in situ characterization technique.

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“…The diffusion data of Peterson and Wiley in contrast, acquired from bulk measurements on large‐grained polycrystals of Cu 2 O at 700 °C ≤ T ≤ 1153 °C and oxygen partial pressures of

10^{- 6} \leq p_{O_{2}} \leq 8 \times 10^{- 2}

atm, can be extrapolated to

D_{{CuinCu}_{2} O} = 1.4 \times 10^{- 18}

Section: Resultsmentioning

confidence: 91%

Section: Diffusion Coeffi Cient and A Cuincu2mentioning

confidence: 99%

Nanoscale Kirkendall Effect and Oxidation Kinetics in Copper Nanocrystals Characterized by Real‐Time, In Situ Optical Spectroscopy

Rice

Paterson

Stoykovich

2014

Part & Part Syst Charact

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“…Although the details of the nucleation and growth of the void(s) can be complicated due to different additional effects (stress development [4,10,14], non-steady state vacancy distribution [12], etc.) it is generally accepted that the overall growth of the hole is controlled by D A and t g ∼R o 2 /D A was obtained for the time to complete the shell formation [4,11] (R o is the initial particle radius).…”

Section: Introductionmentioning

confidence: 99%

Temperature-dependent formation and shrinkage of hollow shells in hemispherical Ag/Pd nanoparticles

Glodán

Cserháti

Beke

2012

Philosophical Magazine

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It is shown that both the growth and shrinkage of hollow shells in Ag/Pd hemispherical core-shell nano structures took place at the same temperature. The crossover time, t cr , between these regimes is shifted to smaller values with increasing temperatures. This result confirms that the growth and the shrinkage regimes are controlled by the faster as well as the slower diffusion coefficients (D Ag as well as D Pd ), respectively. The pore radius, confirming recent theoretical predictions, linearly depends on the initial particle radius and the slope of this straight line increases with the average composition of the faster component.

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“…The conventional interpretation has assumed that the void size is only dependent on the ratio of the metal and oxygen diffusivities in the binary phase [6,28]. These prior interpretations have assumed that D MM is much larger than D MX and, in most cases, have not justified this assumption.…”

Section: Nanocrystal Oxidation With Surface Energy Considerationsmentioning

confidence: 98%

Kinetic description of metal nanocrystal oxidation: a combined theoretical and experimental approach for determining morphology and diffusion parameters in hollow nanoparticles by the nanoscale Kirkendall effect

Watanabe

Mowbray

Rice

et al. 2014

Philosophical Magazine

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2014) Kinetic description of metal nanocrystal oxidation: a combined theoretical and experimental approach for determining morphology and diffusion parameters in hollow nanoparticles by the nanoscale Kirkendall effect, Philosophical Magazine, 94:30,[3487][3488][3489][3490][3491][3492][3493][3494][3495][3496][3497][3498][3499][3500][3501][3502][3503][3504][3505][3506] The oxidation of colloidal metal nanocrystals to form hollow shells via the nanoscale Kirkendall effect has been investigated using a combined theoretical and experimental approach. A generalized kinetic model for the formation of hollow nanoparticles describes the phenomenon and, unlike prior models, is applicable to any material system and accounts for the effect of surface energies. Phase diagrams of the ultimate oxidized nanoparticle morphology and the time to achieve complete oxidation are calculated, and are found to depend significantly upon consideration of surface energy effects that destabilize the initial formation of small voids. For the oxidation of Cu nanocrystals to Cu 2 O nanoparticles, we find that the diffusion coefficients dictate the morphological outcomes: the ratio of D oxygen in Cu2O to D Cu in Cu controls the void size, D Cu in Cu determines the time of oxidation and D Cu in Cu2O is largely irrelevant in the kinetics of oxidation. The kinetic model was used to fit experimental measurements of 11 nm diameter Cu nanocrystals oxidized in air from which temperature-dependent diffusivities of D oxygen in Cu2O ¼ 90 expðÀ43=R g T Þ nm 2 =s ð Þ and D Cu in Cu ¼ 6 expðÀ30=R g TÞ nm 2 =s ð Þ for 100 ≤ T ≤ 200°C were determined. In contrast to previous interpretations of the nanoscale Kirkendall effect in the Cu/Cu 2 O system, these results are obtained without any a priori assumptions about the relative magnitudes of D Cu in Cu and D Cu in Cu2O . The theoretical and experimental approaches presented here are broadly applicable to any nanoparticle system undergoing oxidation, and can be used to precisely control the final nanoparticle morphology for applications in catalysis or optical materials.

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Stress development during reaction of metallic nanospheres with gas

Cited by 16 publications

References 32 publications

Nanoscale Kirkendall Effect and Oxidation Kinetics in Copper Nanocrystals Characterized by Real‐Time, In Situ Optical Spectroscopy

Nanoscale Kirkendall Effect and Oxidation Kinetics in Copper Nanocrystals Characterized by Real‐Time, In Situ Optical Spectroscopy

Temperature-dependent formation and shrinkage of hollow shells in hemispherical Ag/Pd nanoparticles

Kinetic description of metal nanocrystal oxidation: a combined theoretical and experimental approach for determining morphology and diffusion parameters in hollow nanoparticles by the nanoscale Kirkendall effect

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