Cited by 2,629Fluid Dynamics and Thin FilmsThermodynamic and Structural Properties of Metals and AlloysSolidification and crystal growth phenomena

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Theory of Thermal Grooving

Mullins, W. W.·1957·Journal of Applied Physics

DOI 10.1063/1.1722742

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Abstract

A theory is presented which describes the development of surface grooves at the grain boundaries of a heated polycrystal. The mechanisms of evaporation-condensation and surface diffusion are discussed with the use of the Gibbs-Thompson formula and the assumption that the properties of an interface do not depend on its orientation. For the idealized case in which only one of the mechanisms is operative, the groove profile is shown to have a time-independent shape whose linear dimensions are proportional to t½ for evaporation-condensation, and to t½ for surface diffusion. The proportionality constants are evaluated, and criteria are developed which permit one to estimate which process predominates in practice. Order of magnitude agreement is obtained with estimates of actual grooving speeds and profiles.

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1950, Proc. Phys. Soc. B, 63, 350
1949, J. Metals, 1, 169
1948, Proc. Roy. Soc. (London) A, 193, 465
1951, J. Inst. Metals, 79, 415

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Background
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Method
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Background
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“[14] W. W. Mullins, Theory of thermal grooving, J. Appl.”
BackgroundInfluential
The role of the configurational force balance in the nonequilibrium epitaxy of films
Fried, E., & Gurtin, M. (2003) · doi:10.1016/s0022-5096(02)00077-7 · Cited by 31

Authors: Mullins, W. W.
Affiliations: Westinghouse Electric (United States) (US)
Corresponding author: Mullins, W. W.
Venue: Journal of Applied Physics
Publisher: AIP Publishing
Published: 1957-03-01
Volume: 28
Issue: 3
Pages: 333-339
ISSN: 0021-8979 (ISSN-L)
1089-7550
DOI: 10.1063/1.1722742
OpenAlex: W2017334281
Cited by: 2,629
References: 8
Citations by year: 2026: 62 · 2025: 72 · 2024: 73 · 2023: 55 · 2022: 63 · 2021: 102 · 2020: 84 · 2019: 68 · 2018: 57 · 2017: 72 · 2016: 71 · 2015: 57 · 2014: 78 · 2013: 74 · 2012: 71
FWCI: 11.00
Type: journal article
Language: en
Open access: closed
Locations: Journal of Applied Physics (publishedVersion)
Topics: Physical Sciences › Engineering › Computational Mechanics › Fluid Dynamics and Thin Films
Physical Sciences › Materials Science › Metals and Alloys › Thermodynamic and Structural Properties of Metals and Alloys
Physical Sciences › Materials Science › Materials Chemistry › Solidification and crystal growth phenomena
Keywords: thermal grooving, grain boundaries, polycrystalline materials, evaporation and condensation, surface diffusion, Gibbs-Thomson equation, groove profile

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Theory of Thermal Grooving

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