The dihedral angle needs to be determined, for which the interfacial energy of the matrix-precipitate boundary and the grain boundary energy of the matrix will be equal. Concept introduction: A dihedral angle is defined as the angle among the two interconnecting planes. The angles between the planes over the two sets of three atoms, which have two atoms in communal. The grain boundary is defined as the border between the two grains, or crystallites which are existing in the polycrystalline material. The grain boundaries are important in various mechanisms of creep. The grain boundaries also disrupt the dislocation motion through a material, eventually reducing the crystallite size.

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Answer 1

Question

Chapter 12, Problem 12.15P

Interpretation Introduction

Interpretation:

The dihedral angle needs to be determined, for which the interfacial energy of the matrix-precipitate boundary and the grain boundary energy of the matrix will be equal.

Concept introduction:

A dihedral angle is defined as the angle among the two interconnecting planes. The angles between the planes over the two sets of three atoms, which have two atoms in communal. The grain boundary is defined as the border between the two grains, or crystallites which are existing in the polycrystalline material. The grain boundaries are important in various mechanisms of creep. The grain boundaries also disrupt the dislocation motion through a material, eventually reducing the crystallite size.

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Answer 2

Question

Chapter 12, Problem 12.15P

Interpretation Introduction

Interpretation:

The dihedral angle needs to be determined, for which the interfacial energy of the matrix-precipitate boundary and the grain boundary energy of the matrix will be equal.

Concept introduction:

A dihedral angle is defined as the angle among the two interconnecting planes. The angles between the planes over the two sets of three atoms, which have two atoms in communal. The grain boundary is defined as the border between the two grains, or crystallites which are existing in the polycrystalline material. The grain boundaries are important in various mechanisms of creep. The grain boundaries also disrupt the dislocation motion through a material, eventually reducing the crystallite size.

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Answer 3

Question

Chapter 12, Problem 12.15P

Interpretation Introduction

Interpretation:

The dihedral angle needs to be determined, for which the interfacial energy of the matrix-precipitate boundary and the grain boundary energy of the matrix will be equal.

Concept introduction:

A dihedral angle is defined as the angle among the two interconnecting planes. The angles between the planes over the two sets of three atoms, which have two atoms in communal. The grain boundary is defined as the border between the two grains, or crystallites which are existing in the polycrystalline material. The grain boundaries are important in various mechanisms of creep. The grain boundaries also disrupt the dislocation motion through a material, eventually reducing the crystallite size.

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Answer 4

Question

Chapter 12, Problem 12.15P

Interpretation Introduction

Interpretation:

The dihedral angle needs to be determined, for which the interfacial energy of the matrix-precipitate boundary and the grain boundary energy of the matrix will be equal.

Concept introduction:

A dihedral angle is defined as the angle among the two interconnecting planes. The angles between the planes over the two sets of three atoms, which have two atoms in communal. The grain boundary is defined as the border between the two grains, or crystallites which are existing in the polycrystalline material. The grain boundaries are important in various mechanisms of creep. The grain boundaries also disrupt the dislocation motion through a material, eventually reducing the crystallite size.

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Answer 5

Chapter 12, Problem 12.15P

Interpretation Introduction

Interpretation:

The dihedral angle needs to be determined, for which the interfacial energy of the matrix-precipitate boundary and the grain boundary energy of the matrix will be equal.

Concept introduction:

A dihedral angle is defined as the angle among the two interconnecting planes. The angles between the planes over the two sets of three atoms, which have two atoms in communal. The grain boundary is defined as the border between the two grains, or crystallites which are existing in the polycrystalline material. The grain boundaries are important in various mechanisms of creep. The grain boundaries also disrupt the dislocation motion through a material, eventually reducing the crystallite size.

Answer 6

Chapter 12, Problem 12.15P

Interpretation Introduction

Interpretation:

The dihedral angle needs to be determined, for which the interfacial energy of the matrix-precipitate boundary and the grain boundary energy of the matrix will be equal.

Concept introduction:

A dihedral angle is defined as the angle among the two interconnecting planes. The angles between the planes over the two sets of three atoms, which have two atoms in communal. The grain boundary is defined as the border between the two grains, or crystallites which are existing in the polycrystalline material. The grain boundaries are important in various mechanisms of creep. The grain boundaries also disrupt the dislocation motion through a material, eventually reducing the crystallite size.

Answer 7

Chapter 12, Problem 12.15P

Interpretation Introduction

Interpretation:

The dihedral angle needs to be determined, for which the interfacial energy of the matrix-precipitate boundary and the grain boundary energy of the matrix will be equal.

Concept introduction:

A dihedral angle is defined as the angle among the two interconnecting planes. The angles between the planes over the two sets of three atoms, which have two atoms in communal. The grain boundary is defined as the border between the two grains, or crystallites which are existing in the polycrystalline material. The grain boundaries are important in various mechanisms of creep. The grain boundaries also disrupt the dislocation motion through a material, eventually reducing the crystallite size.

Answer 8

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Answer 9

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Answer 10

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Answer 11

Ch. 12 - Prob. 12.1P Ch. 12 - Prob. 12.2P Ch. 12 - Prob. 12.3P Ch. 12 - Prob. 12.4P Ch. 12 - Prob. 12.5P Ch. 12 - Prob. 12.6P Ch. 12 - Prob. 12.7P Ch. 12 - Prob. 12.8P Ch. 12 - Prob. 12.9P Ch. 12 - Prob. 12.10P

Solution Summary: The author defines the dihedral angle as the angle between the two interconnecting planes, and the grain boundary, which governs the shape of the precipitate.

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Chapter 12 Solutions