**Problem 5: Calculate the Planar Density (\( \rho_{hkl} \))**Given: Calculate \( \rho_{hkl} \) for the (100), (110), and (111) planes of a monoatomic face-centered cubic (fcc) crystal.This exercise focuses on determining the planar density of different crystallographic planes in a monoatomic fcc crystal structure. Planar density is defined as the number of atoms per unit area on a specific crystal plane.**Tips for solving this problem:**- Consider the arrangement of atoms in each of the specified planes.- Remember that a face-centered cubic structure has atoms at each corner of the cube and in the center of each face.- Calculate the area of the plane within the unit cell for each orientation.- Determine the contribution of atoms that are part of each plane and calculate \( \rho_{hkl} \). Understanding the atomic arrangement on these planes will help illustrate the material's properties, such as cleavage, slip, and other deformation processes in crystalline solids.

The given planes are (1 0 0), (1 1 0) and (1 1 1) and the crystal is FCC crystal

Answered: 5. Calculate Phki for the (100), (110),…

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5. Calculate Phki for the (100), (110), and (111) planes of a monoatomic fcc crystal.

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.

Question

**Problem 5: Calculate the Planar Density (\( \rho_{hkl} \))**

Given: Calculate \( \rho_{hkl} \) for the (100), (110), and (111) planes of a monoatomic face-centered cubic (fcc) crystal.

This exercise focuses on determining the planar density of different crystallographic planes in a monoatomic fcc crystal structure. Planar density is defined as the number of atoms per unit area on a specific crystal plane.

**Tips for solving this problem:**
- Consider the arrangement of atoms in each of the specified planes.
- Remember that a face-centered cubic structure has atoms at each corner of the cube and in the center of each face.
- Calculate the area of the plane within the unit cell for each orientation.
- Determine the contribution of atoms that are part of each plane and calculate \( \rho_{hkl} \).

Understanding the atomic arrangement on these planes will help illustrate the material's properties, such as cleavage, slip, and other deformation processes in crystalline solids.

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