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13. Show that the minimum cation-to-anion radius ratio for a coordination number of 4 is 0.225. Hint: Anion (A) Cation ()

13. Show that the minimum cation-to-anion radius ratio for a coordination number of 4 is 0.225. Hint: Anion (A) Cation ()

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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### Problem 13: Minimum Cation-to-Anion Radius Ratio **Objective:** Demonstrate that the minimum cation-to-anion radius ratio for a coordination number of 4 is 0.225. **Hint:** Refer to the diagram of a cubic geometry containing ions. **Diagram Explanation:** The diagram illustrates a portion of a cubic lattice featuring a coordination number of 4. The key components are: - **Cube Structure:** The cube has its corners labeled as \( A, B, C, \) and \( F \). - **Ions:** - **Anion (\( r_A \)):** Represented by circles at the corners of the cube. - **Cation (\( r_C \)):** Positioned in the center of the cube face, labeled as \( E \). - **Cube Edges:** - Each edge of the cube is labeled with a length \( a \). This geometrical representation is used to derive the minimum radius ratio by analyzing the spatial arrangement of cations and anions within the cube. The goal is to optimize stability by calculating the smallest \( r_C/r_A \) ratio that maintains the structure without distortion or overlap.
Transcribed Image Text:### Problem 13: Minimum Cation-to-Anion Radius Ratio **Objective:** Demonstrate that the minimum cation-to-anion radius ratio for a coordination number of 4 is 0.225. **Hint:** Refer to the diagram of a cubic geometry containing ions. **Diagram Explanation:** The diagram illustrates a portion of a cubic lattice featuring a coordination number of 4. The key components are: - **Cube Structure:** The cube has its corners labeled as \( A, B, C, \) and \( F \). - **Ions:** - **Anion (\( r_A \)):** Represented by circles at the corners of the cube. - **Cation (\( r_C \)):** Positioned in the center of the cube face, labeled as \( E \). - **Cube Edges:** - Each edge of the cube is labeled with a length \( a \). This geometrical representation is used to derive the minimum radius ratio by analyzing the spatial arrangement of cations and anions within the cube. The goal is to optimize stability by calculating the smallest \( r_C/r_A \) ratio that maintains the structure without distortion or overlap.
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