# Difference between revisions of "Grooving of a grain boundary by evaporation-condensation processes: Surface evolution below the roughening transition."

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== Summary == | == Summary == | ||

− | + | [[Image:stone-aziz-margetis_fig1.jpg|thumb|450px|right|alt=Schematic diagram.|'''Figure 1:''' Schematic diagram of the evolution of a grain boundary.]] | |

This paper's focus is understanding and mathematically defining how grooves form at grain boundaries at the intersection of a planar surface. This is important in describing grain growth of thin films since the deepening of grain boundary grooves along the surface will set the boundaries resulting in slower grain growth. The specific condition studied here is how these grooves evolve when below the thermodynamic roughening transition by evaporation–condensation processes. Also, the case examined is a solid–vapor interface. It turns out the dynamics are governed by a nonlinear partial differential equation and the groove profile is defined by a nonlinear ordinary differential equation. This groove profile is important since the slope determines the driving force for how much grain growth is required for the boundary to break free of the groove. Both numerical and approximate analytical solutions are presented and agree with each other: the grooves' width and depth vary as <math>t^{1/2}</math> where <math>t</math> is time. | This paper's focus is understanding and mathematically defining how grooves form at grain boundaries at the intersection of a planar surface. This is important in describing grain growth of thin films since the deepening of grain boundary grooves along the surface will set the boundaries resulting in slower grain growth. The specific condition studied here is how these grooves evolve when below the thermodynamic roughening transition by evaporation–condensation processes. Also, the case examined is a solid–vapor interface. It turns out the dynamics are governed by a nonlinear partial differential equation and the groove profile is defined by a nonlinear ordinary differential equation. This groove profile is important since the slope determines the driving force for how much grain growth is required for the boundary to break free of the groove. Both numerical and approximate analytical solutions are presented and agree with each other: the grooves' width and depth vary as <math>t^{1/2}</math> where <math>t</math> is time. | ||

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== Soft Matter == | == Soft Matter == | ||

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[[Image:stone-aziz-margetis_table1.jpg|thumb|500px|right|alt=Table of results.|]] | [[Image:stone-aziz-margetis_table1.jpg|thumb|500px|right|alt=Table of results.|]] | ||

Currently writing... | Currently writing... |

## Revision as of 21:56, 7 November 2009

Original Entry by Michelle Borkin, AP225 Fall 2009

## Contents

## Overview

H.A. Stone, M. Aziz and D. Margetis, J. Appl. Phys. 97, 113535-1-6, 2005

## Keywords

grain boundary, solid–vapor interface, evaporation–condensation, thermodynamic roughening

## Summary

This paper's focus is understanding and mathematically defining how grooves form at grain boundaries at the intersection of a planar surface. This is important in describing grain growth of thin films since the deepening of grain boundary grooves along the surface will set the boundaries resulting in slower grain growth. The specific condition studied here is how these grooves evolve when below the thermodynamic roughening transition by evaporation–condensation processes. Also, the case examined is a solid–vapor interface. It turns out the dynamics are governed by a nonlinear partial differential equation and the groove profile is defined by a nonlinear ordinary differential equation. This groove profile is important since the slope determines the driving force for how much grain growth is required for the boundary to break free of the groove. Both numerical and approximate analytical solutions are presented and agree with each other: the grooves' width and depth vary as <math>t^{1/2}</math> where <math>t</math> is time.

## Soft Matter

Currently writing...