**Problem Statement**:Calculate the planar atomic density for the (100), (110), and (111) planes for a BCC (body centered cubic) crystal. Assume a BCC lattice parameter of \( a \).**Explanation**:In a BCC crystal structure, atoms are located at the corners of a cube and a single atom is positioned at the center of the cube. The planar atomic density is defined as the number of atoms per unit area in a specific crystallographic plane.- **(100) Plane**: - Visualize a square face of the cube. - Atoms at the corners contribute partially to this plane. - Central atom does not contribute directly to the (100) plane.- **(110) Plane**: - Visualize a rectangular face, crossing through the body center. - This plane contains atoms from both the face and the body center.- **(111) Plane**: - Visualizes a triangular slice passing through the body. - More complex interaction of atoms at corners and the body center.For each plane, you’ll calculate the effective number of atoms in the plane and divide by the area of the plane.These calculations provide insight into the distribution of atoms across different planes within a BCC structure, which is crucial for understanding the properties of materials such as metals.

Planar density is given as - Densityρ =Number of atomsArea of planeFor BCC (100) -ρ =1a2For BCC (110) -ρ =22a2For BCC (111) -ρ =1232a2ρ=13a2

Answered: 9. Calculate the planar atomic density…

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9. Calculate the planar atomic density for the (100), (110) and (111) planes for a BCC (body centered cubic) crystal, assume a BCC lattice parameter of a.

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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Concept explainers

The Space Lattice and Unit Cells

Every matter consists of atoms, molecules, and ions. If these atoms, molecules, and ions (micro-particles) are represented in a three-dimensional space-occupying certain specific points in space, then these arrangements are termed as space lattices and the specific points which are being occupied by atoms, molecules and ions are termed as lattice points. The atoms, molecules, and ions at the lattice points are generally grouped in a regular fashion and repeat periodically at the three-dimensional space.

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**Problem Statement**:
Calculate the planar atomic density for the (100), (110), and (111) planes for a BCC (body centered cubic) crystal. Assume a BCC lattice parameter of \( a \).

**Explanation**:

In a BCC crystal structure, atoms are located at the corners of a cube and a single atom is positioned at the center of the cube. The planar atomic density is defined as the number of atoms per unit area in a specific crystallographic plane.

- **(100) Plane**:
- Visualize a square face of the cube.
- Atoms at the corners contribute partially to this plane.
- Central atom does not contribute directly to the (100) plane.

- **(110) Plane**:
- Visualize a rectangular face, crossing through the body center.
- This plane contains atoms from both the face and the body center.

- **(111) Plane**:
- Visualizes a triangular slice passing through the body.
- More complex interaction of atoms at corners and the body center.

For each plane, you’ll calculate the effective number of atoms in the plane and divide by the area of the plane.

These calculations provide insight into the distribution of atoms across different planes within a BCC structure, which is crucial for understanding the properties of materials such as metals.

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