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Specify the number of degree of freedom for the following alloys. Refer to the pictures below. A) 95 wt% Ag-5 wt% Cu at 780C B) 2.5 wt% C-97.5 wt% Fe at 1000C

Specify the number of degree of freedom for the following alloys. Refer to the pictures below. A) 95 wt% Ag-5 wt% Cu at 780C B) 2.5 wt% C-97.5 wt% Fe at 1000C

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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Specify the number of degree of freedom for the following alloys. Refer to the pictures below. A) 95 wt% Ag-5 wt% Cu at 780C B) 2.5 wt% C-97.5 wt% Fe at 1000C
### Transcription and Explanation of Phase Diagram #### Title: Copper-Silver Phase Diagram This phase diagram shows the composition of copper (Cu) and silver (Ag) alloys. The x-axis represents the composition in both atomic percent (at% Ag) and weight percent (wt% Ag), while the y-axis represents temperature in both Celsius (°C) and Fahrenheit (°F). #### Key Phases and Lines: 1. **Phase Regions:** - **α (Alpha) Region:** This is found on the left side of the diagram. It exists at lower temperatures in the copper-rich portion. - **β (Beta) Region:** Found on the right side, representing the silver-rich phase existing at lower temperatures. - **Liquid Region:** Above both solidus and liquidus lines, where the alloy is completely liquid. - **α + L and β + L Regions:** These are two-phase regions where solid (α or β) coexists with liquid. 2. **Important Lines:** - **Liquidus Line:** Separates the liquid phase from the liquid and solid coexisting phases (α + L and β + L). - **Solidus Line:** Separates the completely solid phase from the regions where solid and liquid coexist. - **Solvus Line:** Located in the α and β phase regions, shows the limit of solubility of one component in the other. 3. **Key Points on the Diagram:** - **Point A:** Upper part of the α region. - **Point B (CαE):** Located on the line separating α from α + L, marking eutectic composition at 8.0 wt% Ag. - **Point E (TE):** Represents the eutectic temperature, 779°C (T_E), where liquid transitions directly to two solid phases (α + β). - **Point F:** Upper part of the β region. - **Point G (CβE):** Marks the boundary of the β + L region at 91.2 wt% Ag. - **Point C:** Lower cusp of the solvus line. - **Point H:** Lower terminus of β. #### Additional Information: - **Eutectic Reaction:** Occurs at 779°C, where a liquid alloy transforms into two solid phases (α + β) at a specific composition (C_E = 71.9 wt% Ag). -
Transcribed Image Text:### Transcription and Explanation of Phase Diagram #### Title: Copper-Silver Phase Diagram This phase diagram shows the composition of copper (Cu) and silver (Ag) alloys. The x-axis represents the composition in both atomic percent (at% Ag) and weight percent (wt% Ag), while the y-axis represents temperature in both Celsius (°C) and Fahrenheit (°F). #### Key Phases and Lines: 1. **Phase Regions:** - **α (Alpha) Region:** This is found on the left side of the diagram. It exists at lower temperatures in the copper-rich portion. - **β (Beta) Region:** Found on the right side, representing the silver-rich phase existing at lower temperatures. - **Liquid Region:** Above both solidus and liquidus lines, where the alloy is completely liquid. - **α + L and β + L Regions:** These are two-phase regions where solid (α or β) coexists with liquid. 2. **Important Lines:** - **Liquidus Line:** Separates the liquid phase from the liquid and solid coexisting phases (α + L and β + L). - **Solidus Line:** Separates the completely solid phase from the regions where solid and liquid coexist. - **Solvus Line:** Located in the α and β phase regions, shows the limit of solubility of one component in the other. 3. **Key Points on the Diagram:** - **Point A:** Upper part of the α region. - **Point B (CαE):** Located on the line separating α from α + L, marking eutectic composition at 8.0 wt% Ag. - **Point E (TE):** Represents the eutectic temperature, 779°C (T_E), where liquid transitions directly to two solid phases (α + β). - **Point F:** Upper part of the β region. - **Point G (CβE):** Marks the boundary of the β + L region at 91.2 wt% Ag. - **Point C:** Lower cusp of the solvus line. - **Point H:** Lower terminus of β. #### Additional Information: - **Eutectic Reaction:** Occurs at 779°C, where a liquid alloy transforms into two solid phases (α + β) at a specific composition (C_E = 71.9 wt% Ag). -
The image shows the iron-carbon phase diagram, which is critical in understanding the metallurgical properties of steel and cast iron. Here's a detailed breakdown: ### Phases and Regions: - **δ (Delta Ferrite):** Exists at high temperatures (above 1394°C) for low carbon concentrations. - **γ (Austenite):** Stable between 912°C and 1394°C, accommodating a higher carbon concentration. - **α (Alpha Ferrite):** Exists below 912°C with minimal carbon solubility (up to 0.022 wt% C). - **Cementite (Fe₃C):** A compound of iron and carbon with a fixed composition of 6.70 wt% C. ### Key Transformations: - **Peritectic Reaction:** Occurs at 1493°C, converting δ and liquid to γ. - **Eutectic Reaction:** At 1147°C in the iron-carbon system, liquid transforms into γ and cementite. - **Eutectoid Reaction:** At 727°C, austenite (γ) transforms to a mixture of ferrite (α) and cementite (Fe₃C). ### Critical Points: - **1538°C:** Melting point of pure iron. - **912°C:** Maximum temperature for α (ferrite). - **727°C (Eutectoid Temperature):** Critical for transformations between austenite and the mixture of ferrite and cementite. ### Axes: - **x-axis (Composition):** Ranges from 0 to 6.70 wt% carbon. Unit labels indicate weight percent and atomic percent carbon. - **y-axis (Temperature):** Displays temperature in Celsius (left side) and Fahrenheit (right side), ranging from 400°C to 1600°C and 1000°F to 2500°F, respectively. Understanding this diagram is essential for controlling heat treatment processes, predicting microstructure changes, and determining material properties in various steel and cast iron applications.
Transcribed Image Text:The image shows the iron-carbon phase diagram, which is critical in understanding the metallurgical properties of steel and cast iron. Here's a detailed breakdown: ### Phases and Regions: - **δ (Delta Ferrite):** Exists at high temperatures (above 1394°C) for low carbon concentrations. - **γ (Austenite):** Stable between 912°C and 1394°C, accommodating a higher carbon concentration. - **α (Alpha Ferrite):** Exists below 912°C with minimal carbon solubility (up to 0.022 wt% C). - **Cementite (Fe₃C):** A compound of iron and carbon with a fixed composition of 6.70 wt% C. ### Key Transformations: - **Peritectic Reaction:** Occurs at 1493°C, converting δ and liquid to γ. - **Eutectic Reaction:** At 1147°C in the iron-carbon system, liquid transforms into γ and cementite. - **Eutectoid Reaction:** At 727°C, austenite (γ) transforms to a mixture of ferrite (α) and cementite (Fe₃C). ### Critical Points: - **1538°C:** Melting point of pure iron. - **912°C:** Maximum temperature for α (ferrite). - **727°C (Eutectoid Temperature):** Critical for transformations between austenite and the mixture of ferrite and cementite. ### Axes: - **x-axis (Composition):** Ranges from 0 to 6.70 wt% carbon. Unit labels indicate weight percent and atomic percent carbon. - **y-axis (Temperature):** Displays temperature in Celsius (left side) and Fahrenheit (right side), ranging from 400°C to 1600°C and 1000°F to 2500°F, respectively. Understanding this diagram is essential for controlling heat treatment processes, predicting microstructure changes, and determining material properties in various steel and cast iron applications.
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