### Deriving Linear Density Expressions for FCC**Objective:** Derive linear density expressions for face-centered cubic (FCC) crystal structures in the [100] and [111] directions in terms of the atomic radius \( R \). Additionally, compute linear density values for these directions specifically for silver.---**(a) Linear Density Expressions:**1. **[100] Direction:** - Input box for calculation: \(\_\_\_\_\_\_\) atoms/R2. **[111] Direction:** - Input box for calculation: \(\_\_\_\_\_\_\) atoms/R---**(b) Computation of Linear Density Values:**1. **[100] Direction:** - Input box for calculation: \(\_\_\_\_\_\_\) 1/m2. **[111] Direction:** - Input box for calculation: \(\_\_\_\_\_\_\) 1/m---These sections require filling in the calculations based on the formulas derived in the [100] and [111] directions using the atomic radius \( R \) for silver. The results will be expressed in terms of atoms per unit distance or reciprocal meters.

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(a) Derive linear density expressions for FCC [100] and [111] directions in terms of the atomic radius R and (b) compute linear density values for these two directions for silver. (a) [100]: i [111]: i (b) [100]: i [111]: i atom/R atom/R 1/m 1/m

(a) Derive linear density expressions for FCC [100] and [111] directions in terms of the atomic radius R and (b) compute linear density values for these two directions for silver. (a) [100]: i [111]: i (b) [100]: i [111]: i atom/R atom/R 1/m 1/m

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

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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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### Deriving Linear Density Expressions for FCC

**Objective:**
Derive linear density expressions for face-centered cubic (FCC) crystal structures in the [100] and [111] directions in terms of the atomic radius \( R \). Additionally, compute linear density values for these directions specifically for silver.

---

**(a) Linear Density Expressions:**

1. **[100] Direction:**
- Input box for calculation: \(\_\_\_\_\_\_\) atoms/R

2. **[111] Direction:**
- Input box for calculation: \(\_\_\_\_\_\_\) atoms/R

---

**(b) Computation of Linear Density Values:**

1. **[100] Direction:**
- Input box for calculation: \(\_\_\_\_\_\_\) 1/m

2. **[111] Direction:**
- Input box for calculation: \(\_\_\_\_\_\_\) 1/m

---

These sections require filling in the calculations based on the formulas derived in the [100] and [111] directions using the atomic radius \( R \) for silver. The results will be expressed in terms of atoms per unit distance or reciprocal meters.

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