### Derivation and Calculation of Linear Density for BCC Structure#### Problem Statement:(a) **Derive linear density expressions** for the Body-Centered Cubic (BCC) structure in the [110] and [111] directions in terms of the atomic radius \( R \).(b) **Compute linear density values** for these same two directions for tungsten.#### Solutions:**(a)**- **[110] Direction:** - Expression: \( \_\_\_ \) - Units: atom/R- **[111] Direction:** - Expression: \( \_\_\_ \) - Units: atom/R**(b)**- **[110] Direction:** - Value: \( \_\_\_ \) - Units: 1/m- **[111] Direction:** - Value: \( \_\_\_ \) - Units: 1/mThis exercise involves calculating linear densities based on atomic positions for a BCC metal such as tungsten.

BCC unit cell has one atom at each of the 8 corners and one atom at the body center. Linear density…

(a) Derive linear density expressions for BCC [110] and [111] directions in terms of the atomic radius R and (b) compute linear density values for these same two directions for tungsten. (a) [110]: i [111]: i (b) [110]: i [111]: i atom/R atom/R 1/m 1/m

(a) Derive linear density expressions for BCC [110] and [111] directions in terms of the atomic radius R and (b) compute linear density values for these same two directions for tungsten. (a) [110]: i [111]: i (b) [110]: i [111]: i atom/R atom/R 1/m 1/m

Chemistry

10th Edition

ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

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Question

### Derivation and Calculation of Linear Density for BCC Structure

#### Problem Statement:
(a) **Derive linear density expressions** for the Body-Centered Cubic (BCC) structure in the [110] and [111] directions in terms of the atomic radius \( R \).

(b) **Compute linear density values** for these same two directions for tungsten.

#### Solutions:

**(a)**

- **[110] Direction:**
- Expression: \( \_\_\_ \)
- Units: atom/R

- **[111] Direction:**
- Expression: \( \_\_\_ \)
- Units: atom/R

**(b)**

- **[110] Direction:**
- Value: \( \_\_\_ \)
- Units: 1/m

- **[111] Direction:**
- Value: \( \_\_\_ \)
- Units: 1/m

This exercise involves calculating linear densities based on atomic positions for a BCC metal such as tungsten.

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