재료공학 12장
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경상대학교 재료공학 12장
목차
Crystal Structures
Silicate Ceramics
Imperfections in Ceramics
Ceramic Phase Diagrams
Brittle Fracture of Ceramics
Stress-Strain Behavior
Mechanisms of Plastic Deformation
Miscellaneous Mechanical Considerations
DESIGN PROBLEMS
Crystal Structures
Stress-Strain Behavior
본문내용
Crystal Structures
12.1 The two characteristics of component ions that determine the crystal structure of a ceramic compound are: 1) the magnitude of the electrical charge on each ion, and 2) the relative sizes of the cations and anions.
12.2 In this problem we are asked to show that the minimum cation-to-anion radius ratio for a coordination number of four is 0.225. If lines are drawn from the centers of the anions, then a tetrahedron is formed. The tetrahedron may be inscribed within a cube as shown below.
The spheres at the apexes of the tetrahedron are drawn at the corners of the cube, and designated as positions A, B, C, and D. (These are reduced in size for the sake of clarity.) The cation resides at the center of the cube, which is designated as point E. Let us now express the cation and anion radii in terms of the cube edge length, designated as a. The spheres located at positions A and B touch each other along the bottom face diagonal. Thus,
There will also be an anion located at the corner, point F (not drawn), and the cube diagonal AEF will be related to the ionic radii as
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