Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN: 9780190698614
Author: Sadiku, Matthew N. O.
Publisher: Oxford University Press
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**Table 5.2: A Tabulation of Diffusion Data**

This table provides detailed information on diffusion data for various diffusing species in different host metals. The data includes diffusion coefficients, activation energies, and calculated diffusion values at different temperatures.

**Columns:**

1. **Diffusing Species:** Elements being diffused (e.g., Fe, C, Cu, Zn, Al, Mg).
2. **Host Metal:** Metal matrix in which diffusion occurs. This may include crystal structure types, such as α-Fe (BCC), γ-Fe (FCC), Cu, Al, and Ni.
3. **D₀ (m²/s):** Pre-exponential factor of the diffusion coefficient, indicating base diffusion rates before thermal activation.
4. **Activation Energy (Qᵈ):** Energy required for diffusion, shown in both kJ/mol and eV/atom.
5. **Calculated Value:**
   - **T (°C):** Temperature at which the diffusion coefficient (D) is calculated.
   - **D (m²/s):** Diffusion coefficient at the given temperature.

**Detailed Data:**

- **Fe in α-Fe (BCC):** 
  - D₀ = \(2.8 \times 10^{-4}\) m²/s
  - Activation Energy = 251 kJ/mol, 2.60 eV/atom
  - Diffusion coefficients: \(3.0 \times 10^{-21}\) (500°C), \(1.8 \times 10^{-15}\) (900°C)

- **Fe in γ-Fe (FCC):** 
  - D₀ = \(5.0 \times 10^{-5}\) m²/s
  - Activation Energy = 284 kJ/mol, 2.94 eV/atom
  - Diffusion coefficients: \(1.1 \times 10^{-17}\) (900°C), \(7.8 \times 10^{-16}\) (1100°C)

- **C in α-Fe:**
  - D₀ = \(6.2 \times 10^{-7}\) m²/s
  - Activation Energy = 80 kJ/mol, 0.83 eV/atom
  - Diffusion coefficients: \(2.4 \times 10^{-12}\) (500°C), \(1.7 \times 10^{-7}\
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Transcribed Image Text:**Table 5.2: A Tabulation of Diffusion Data** This table provides detailed information on diffusion data for various diffusing species in different host metals. The data includes diffusion coefficients, activation energies, and calculated diffusion values at different temperatures. **Columns:** 1. **Diffusing Species:** Elements being diffused (e.g., Fe, C, Cu, Zn, Al, Mg). 2. **Host Metal:** Metal matrix in which diffusion occurs. This may include crystal structure types, such as α-Fe (BCC), γ-Fe (FCC), Cu, Al, and Ni. 3. **D₀ (m²/s):** Pre-exponential factor of the diffusion coefficient, indicating base diffusion rates before thermal activation. 4. **Activation Energy (Qᵈ):** Energy required for diffusion, shown in both kJ/mol and eV/atom. 5. **Calculated Value:** - **T (°C):** Temperature at which the diffusion coefficient (D) is calculated. - **D (m²/s):** Diffusion coefficient at the given temperature. **Detailed Data:** - **Fe in α-Fe (BCC):** - D₀ = \(2.8 \times 10^{-4}\) m²/s - Activation Energy = 251 kJ/mol, 2.60 eV/atom - Diffusion coefficients: \(3.0 \times 10^{-21}\) (500°C), \(1.8 \times 10^{-15}\) (900°C) - **Fe in γ-Fe (FCC):** - D₀ = \(5.0 \times 10^{-5}\) m²/s - Activation Energy = 284 kJ/mol, 2.94 eV/atom - Diffusion coefficients: \(1.1 \times 10^{-17}\) (900°C), \(7.8 \times 10^{-16}\) (1100°C) - **C in α-Fe:** - D₀ = \(6.2 \times 10^{-7}\) m²/s - Activation Energy = 80 kJ/mol, 0.83 eV/atom - Diffusion coefficients: \(2.4 \times 10^{-12}\) (500°C), \(1.7 \times 10^{-7}\
## Educational Content: Determining Carburization Temperature of FCC Iron-Carbon Alloy

The following educational material provides guidance on solving the problem of determining the temperature at which an FCC iron-carbon alloy is carburized. This alloy initially contains 0.20 wt% carbon and is subjected to a controlled environment with a surface carbon concentration maintained at 1.0 wt%. After 51 hours, the carbon concentration reaches 0.35 wt% at a depth of 3.5 mm below the surface. 

### Problem Outline:

The task is to determine the temperature at which this treatment was carried out. This is accomplished using the provided tabulated data for error function values and diffusion coefficients.

### Table 5.1: Tabulation of Error Function Values

This table provides values of the error function, `erf(z)`, for various values of `z`.

```
|  z   | erf(z) |  z   | erf(z) |  z   | erf(z) |
|------|--------|------|--------|------|--------|
| 0    | 0      | 0.55 | 0.5633 | 1.3  | 0.9340 |
| 0.025| 0.0282 | 0.60 | 0.6039 | 1.4  | 0.9523 |
| 0.05 | 0.0564 | 0.65 | 0.6420 | 1.5  | 0.9661 |
| 0.10 | 0.1125 | 0.70 | 0.6778 | 1.6  | 0.9763 |
| 0.15 | 0.1680 | 0.75 | 0.7112 | 1.7  | 0.9838 |
| 0.20 | 0.2227 | 0.80 | 0.7421 | 1.8  | 0.9891 |
| 0.25 | 0.2763 | 0.85 | 0.7707 | 1.9  | 0.9928 |
| 0.30 | 0.3286 | 0.90 | 0.7970 | 2.0  | 0.9953 |
| 0.35 | 0.
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Transcribed Image Text:## Educational Content: Determining Carburization Temperature of FCC Iron-Carbon Alloy The following educational material provides guidance on solving the problem of determining the temperature at which an FCC iron-carbon alloy is carburized. This alloy initially contains 0.20 wt% carbon and is subjected to a controlled environment with a surface carbon concentration maintained at 1.0 wt%. After 51 hours, the carbon concentration reaches 0.35 wt% at a depth of 3.5 mm below the surface. ### Problem Outline: The task is to determine the temperature at which this treatment was carried out. This is accomplished using the provided tabulated data for error function values and diffusion coefficients. ### Table 5.1: Tabulation of Error Function Values This table provides values of the error function, `erf(z)`, for various values of `z`. ``` | z | erf(z) | z | erf(z) | z | erf(z) | |------|--------|------|--------|------|--------| | 0 | 0 | 0.55 | 0.5633 | 1.3 | 0.9340 | | 0.025| 0.0282 | 0.60 | 0.6039 | 1.4 | 0.9523 | | 0.05 | 0.0564 | 0.65 | 0.6420 | 1.5 | 0.9661 | | 0.10 | 0.1125 | 0.70 | 0.6778 | 1.6 | 0.9763 | | 0.15 | 0.1680 | 0.75 | 0.7112 | 1.7 | 0.9838 | | 0.20 | 0.2227 | 0.80 | 0.7421 | 1.8 | 0.9891 | | 0.25 | 0.2763 | 0.85 | 0.7707 | 1.9 | 0.9928 | | 0.30 | 0.3286 | 0.90 | 0.7970 | 2.0 | 0.9953 | | 0.35 | 0.
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