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An FCC iron-carbon alloy initially containing 0.20 wt% C is carburized at an elevated temperature and in an atmosphere wherein the surface carbon concentration is maintained at 1.0 wt%. If after 51 h the concentration of carbon is 0.35 wt% at a position 3.5 mm below the surface, determine the temperature at which the treatment was carried out. You will need to use data in the two tables below to solve this problem. Diffusing Species Fe Table 5.1 Tabulation of Error Function Values erf(z) 0 0.0282 0.0564 0.1125 Fe Z 0 0.025 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 Table 5.2 A Tabulation of Diffusion Data Host Metal a-Fe (BCC) y-Fe (FCC) a-Fe 0.1680 0.2227 0.2763 0.3286 0.3794 y-Fe 0.4284 0.4755 0.5205 Z 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.0 1.1 1.2 Do(m²/s) 2.8 x 10-4 5.0 x 10-5 6.2 x 10-7 2.3 x 10-5 erf(z) 0.5633 0.6039 0.6420 0.6778 0.7112 0.7421 0.7707 0.7970 0.8209 0.8427 0.8802 0.9103 80 284 Z 1.3 1.4 1.5 1.6 1.7 1.8 1.9 Activation Energy Qa kJ/mol eVlatom 251 2.60 148 2.0 2.2 2.4 2.6 2.8 2.94 0.83 1.53 erf(z) 0.9340 0.9523 0.9661 0.9763 0.9838 0.9891 0.9928 0.9953 0.9981 0.9993 0.9998 0.9999 Calculated Value T(°C) 500 900 900 1100 500 900 900 1100 D(m²/s) 3.0 x 10-21 1.8 x 10-15 1.1 x 10-17 7.8 x 10-16 2.4 x 10-12 1.7 x 10-10 5.9 x 10-12 5.3 × 10-11

An FCC iron-carbon alloy initially containing 0.20 wt% C is carburized at an elevated temperature and in an atmosphere wherein the surface carbon concentration is maintained at 1.0 wt%. If after 51 h the concentration of carbon is 0.35 wt% at a position 3.5 mm below the surface, determine the temperature at which the treatment was carried out. You will need to use data in the two tables below to solve this problem. Diffusing Species Fe Table 5.1 Tabulation of Error Function Values erf(z) 0 0.0282 0.0564 0.1125 Fe Z 0 0.025 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 Table 5.2 A Tabulation of Diffusion Data Host Metal a-Fe (BCC) y-Fe (FCC) a-Fe 0.1680 0.2227 0.2763 0.3286 0.3794 y-Fe 0.4284 0.4755 0.5205 Z 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.0 1.1 1.2 Do(m²/s) 2.8 x 10-4 5.0 x 10-5 6.2 x 10-7 2.3 x 10-5 erf(z) 0.5633 0.6039 0.6420 0.6778 0.7112 0.7421 0.7707 0.7970 0.8209 0.8427 0.8802 0.9103 80 284 Z 1.3 1.4 1.5 1.6 1.7 1.8 1.9 Activation Energy Qa kJ/mol eVlatom 251 2.60 148 2.0 2.2 2.4 2.6 2.8 2.94 0.83 1.53 erf(z) 0.9340 0.9523 0.9661 0.9763 0.9838 0.9891 0.9928 0.9953 0.9981 0.9993 0.9998 0.9999 Calculated Value T(°C) 500 900 900 1100 500 900 900 1100 D(m²/s) 3.0 x 10-21 1.8 x 10-15 1.1 x 10-17 7.8 x 10-16 2.4 x 10-12 1.7 x 10-10 5.9 x 10-12 5.3 × 10-11

Elements Of Electromagnetics
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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**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}\
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.
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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