Mat sci homework 6 solutions sp2015 1
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The document provides information about phase diagrams for several metal alloy systems and asks homework problems related to interpreting the phase diagrams and determining phase equilibria. Specifically, it discusses the binary molybdenum-vanadium, silver-copper, and molybdenum-rhenium phase diagrams. It asks students to determine phase compositions, temperatures of phase changes, and possible strengthening mechanisms based on interpreting the provided phase diagrams.
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The document describes slow cooling and rapid cooling of an isomorphous alloy using a Cu-Ni system. For slow cooling, the alloy solidifies completely with a uniform composition along the solidus line. For rapid cooling, solidification takes longer and is incomplete, resulting in segregation of grains with non-uniform composition. The document also describes a binary eutectic system using Cu-Ag, which has three single-phase regions (α, β, liquid), limited solid solubility, and a eutectic reaction that occurs at a single temperature and composition.
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This document provides an overview of phase diagrams and transformations. It discusses:
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The document discusses phase diagrams, including:
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2) Binary eutectic systems have a specific eutectic composition that results in the lowest melting temperature. At the eutectic point, the liquid phase transforms directly into two solid phases upon cooling.
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This document provides information about phase diagrams:
[1] Phase diagrams graphically show the phases present in a material system at different temperatures and compositions. They can indicate properties like the number, type, and amount of phases.
[2] There are several common types of phase diagrams including complete solid solution, eutectic, and peritectic diagrams. Cooling curves are also used to experimentally determine phase boundaries.
[3] The phase rule relates the number of phases, components, and degrees of freedom in a system. Lever rule calculations use tie lines on phase diagrams to determine the composition and relative amounts of coexisting phases.
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The document provides information on phase diagrams including:
- Phase diagrams represent the phases present in materials at different conditions of temperature, pressure, and composition. They indicate solubility, solidification ranges, and melting points.
- Pure substances have solid, liquid, and vapor phases separated by phase boundaries and coexisting at triple points, as shown in pressure-temperature diagrams.
- Binary alloy phase diagrams show the phases present at different compositions and temperatures, including solid solutions, eutectic points where two solids form from liquid, and peritectic reactions where a solid and liquid form a new solid phase.
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The document provides information about phase diagrams and the different types of phases that can exist in alloy systems. It discusses the following key points:
- Phase diagrams show the phases in equilibrium for a given alloy composition at different temperatures. They indicate solidification processes and phase changes with heat treatment.
- Solid solutions are homogeneous solid mixtures where one element dissolves uniformly in the crystal lattice of another. They can be substitutional or interstitial.
- Intermediate phases form in alloy systems with high chemical affinity between elements. They range from ideal solid solutions to ideal chemical compounds.
- The phase rule establishes the relationship between phases, components, and degrees of freedom in a system. It can be used to
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The document discusses time-temperature-transformation (TTT) diagrams and the phase transformations they describe. TTT diagrams show the percentage of a phase transformation completed over temperature and time for a given alloy composition. They can indicate the microstructural phases like pearlite, bainite, and martensite that form during heating and cooling processes. The document explains how TTT diagrams are constructed from isothermal experiments and describes the various diffusion-controlled and diffusionless transformations that occur for a eutectoid steel depending on the cooling rate.
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The document discusses phase diagrams, including:
1) Phase diagrams show the phases present in a material at different temperatures and compositions.
2) Binary eutectic systems have a specific eutectic composition that results in the lowest melting temperature. At the eutectic point, the liquid phase transforms directly into two solid phases upon cooling.
3) The copper-silver phase diagram is a binary eutectic system. It has a eutectic point at 779°C and 71.9% silver composition, where the liquid transforms into solid copper and silver phases.
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This document provides information about phase diagrams:
[1] Phase diagrams graphically show the phases present in a material system at different temperatures and compositions. They can indicate properties like the number, type, and amount of phases.
[2] There are several common types of phase diagrams including complete solid solution, eutectic, and peritectic diagrams. Cooling curves are also used to experimentally determine phase boundaries.
[3] The phase rule relates the number of phases, components, and degrees of freedom in a system. Lever rule calculations use tie lines on phase diagrams to determine the composition and relative amounts of coexisting phases.
TTT diagram of eutectoid steel and martensitic transformation
The document discusses TTT diagrams and phase transformations in steel. It explains that TTT diagrams plot transformation over time and temperature, showing the different phases formed. The C-shaped curve represents the austenitic, pearlitic, bainitic, and martensitic regions. Ms and Mf lines mark the start and end of martensite formation. Martensite has a body-centered tetragonal crystal structure formed by atomic realignment without diffusion. The document also discusses order and disorder in alloy solutions above and below the critical temperature.
TTT Diagram
The document discusses time-temperature-transformation (TTT) diagrams, which show the kinetics of isothermal transformations in steel alloys. TTT diagrams plot temperature versus the logarithm of time and indicate when specific transformations start and end. They show that austenite is stable above the lower critical temperature but unstable below it. Depending on the cooling rate, austenite can transform into pearlite, bainite, or martensite. Slow cooling leads to full pearlite transformation, while very fast cooling results in full martensite formation. TTT diagrams provide information about transformation rates, temperatures, phases, and microstructure sizes.
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This document discusses phase diagrams and related concepts. It covers:
- What phase diagrams are and how they are used to show phase structure under different conditions.
- The Gibbs phase rule and how it relates to phase diagrams.
- Examples of binary phase diagrams and how they show equilibrium between phases.
- Equilibrium and non-equilibrium solidification processes depicted on phase diagrams.
- Intermediate phases and reactions shown on iron-carbon alloy diagrams.
- Additional concepts like lever rule, eutectic and eutectoid systems, and development of microstructure.
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The document provides information about phase diagrams and equilibrium diagrams. It defines a phase as a state of matter that has uniform structure, composition, and properties throughout, with a clear interface between it and other phases. A phase diagram graphically represents the phases present in a material at different temperatures, pressures, and compositions, describing equilibrium conditions. It indicates melting/solidification temperatures and phase formation ranges. General types of solid solutions and Hume-Rothery's rules for substitutional solutions are discussed. Gibbs' phase rule relates the number of coexisting phases to components and degrees of freedom. Different types of phase diagrams including unary, binary, ternary and quaternary are classified.
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Phase diagrams for Different Alloy
By
P.SENTHAMARAIKANNAN,
ASSISTANT PROFESSOR ,
DEPARTMENT OF MECHANICAL ENGINEERING,
KAMARAJ COLLEGE OF ENGINEERING AND TECHNOLOGY,
VIRUDHUNAGAR, TAMILNADU,
INDIA
Types of phase daigram
This document discusses different types of phase diagrams that can be used to represent alloy systems. It describes four main types:
1) Complete solid solubility - The metals are soluble in both the liquid and solid states, forming a substitutional solid solution.
2) No solid solubility - The metals are soluble only in the liquid state and insoluble in the solid state, resulting in separate metal phases.
3) Partial solid solubility - The metals are soluble in the liquid state but only partially soluble in the solid state, allowing for intermediate phases.
4) Congruent melting - One phase changes isothermally into another phase without changing composition, represented as a vertical line on the phase diagram
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The iron-carbon diagram (also called the iron-carbon phase or equilibrium diagram) is a graphic representation of the respective microstructure states depending on temperature (y axis) and carbon content (x axis).
Ch09
This document discusses phase diagrams and microstructures in binary alloy systems. It begins by outlining key questions that can be addressed using phase diagrams, such as the phases present at a given temperature and composition. It then provides examples of using a Cu-Ni phase diagram to determine phase compositions and fractions. The document discusses eutectic systems and uses a Pb-Sn phase diagram to solve examples determining phase properties. It concludes by describing microstructures that form in the Pb-Sn system depending on alloy composition.
Phase diagrams.ppt
This document discusses phase diagrams and binary alloy systems. It defines key terms like phase, solubility limit, and equilibrium. It describes two main types of binary alloy systems - isomorphous systems which have complete solubility, and eutectic systems which have a eutectic point. For isomorphous systems, it discusses microstructure development and how properties vary with composition. For eutectic systems, it outlines the phase diagram features and eutectic reaction. It also provides an example problem calculating phase amounts in the Pb-Sn system at a given temperature and composition.
fe-c diagram
The document discusses the iron-carbon phase diagram and the microstructures that form in steels of different carbon compositions. It describes the phases in the Fe-C system including α-ferrite, γ-austenite, δ-ferrite, and Fe3C cementite. The eutectic and eutectoid reactions are identified. Microstructures that form in hypoeutectoid, eutectoid, and hypereutectoid steels upon slow cooling are discussed. These include proeutectoid ferrite or cementite plus pearlite. The lever rule is used to determine the fraction of phases. An example problem demonstrates using the phase diagram and lever rule to calculate phase compositions and
PHASE DAIGRAM 1.pptx
Let's solve this problem step-by-step:
(a) Given: Find the maximum solubility of Pb in Sn at 100°C (temperature is along the x-axis)
From the Pb-Sn phase diagram:
- At 100°C, follow the vertical line upwards until it intersects the liquidus line for the β (Sn-rich) phase
- This intersection point is at about 5% Pb
Therefore, the maximum solubility of Pb in Sn at 100°C is about 5%
(b) Given: Find the maximum solubility of Sn in Pb at 100°C
From the Pb-Sn phase diagram:
- At 100°C
Thermodynamics Hw#4
This document provides the solutions to homework problems assigned in a thermodynamics course. It summarizes the key steps and conclusions for 6 problems involving concepts like approximations for enthalpy of compressed water, properties of water at different temperatures and pressures, heat transfer for a refrigerant, the Rankine cycle diagram, and properties of propane using different equations of state. The last problem calculates about 700 kJ/kg of work done by steam expanding adiabatically between two states.
CONSTITUTION OF ALLOYS
1. Alloys are made of two or more metals to obtain desired properties like strength, toughness, corrosion resistance that pure metals lack.
2. A solid solution is a homogeneous mixture of atoms where solute atoms substitute or fit in the lattice structure of the solvent metal.
3. Cooling curves and phase diagrams are used to understand the solidification process of alloys and predict the phases present at various temperatures and compositions.
UNIT - I.pptx
Constitution of alloys – Solid solutions, substitutional and interstitial – phase diagrams, Isomorphous, eutectic, eutectoid, peritectic, and peritectoid reactions, Iron – carbon equilibrium diagram. Classification of steel and cast Iron microstructure, properties and application.
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Mat sci homework 6 solutions sp2015 1
- 1. Use the binary, isomorphous, molybdenum-vanadium phase diagram for Problems 2-4. Note: the dashed curve in the phase diagram indicates that there is some error or uncertainty in the location of the liquidus line; the uncertainty in the liquidus line should not affect your calculations. NOTE: I recognize that you have not yet been assigned reading on solid solution strengthening (this will come in the next assignment), so you may have had some trouble with the hardness vs. composition curve. 2. 3. 4. HOMEWORK 6. SCI 1410: materials science & solid state chemistry solutions
- 2. Use the following silver-copper phase diagram for Problems 5-9. 5. What are the solubility limits of Ag in (Cu) and Cu in (Ag)? Recall that (Cu) and (Ag) are the same as α and β, respectively. The solubility limit of Ag in (Cu) is 7.9 wt. % Ag. The solubility limit of Cu in (Ag) is 8.8 wt.% Cu. Note that these solubility limits are found at the ends of the eutectic line (780 ºC). 6. For equilibrium solidification of a Cu-Ag alloy containing 40 weight percent Ag, a. State the temperature at which solidification begins. Solidification starts at about 905 ºC. b. State the temperature at which solidification is complete. Solidification is complete at 780 ºC (eutectic line). 7. For a Cu-Ag alloy of 50 wt.% Ag, a. Determine the phases present, compositions of the phases, and relative amounts (weight fractions) of the phases at a temperature just above the eutectic temperature. b. Determine the phases present, compositions of the phases, and relative amounts of the phases when solidification is just complete (at a temperature just below the eutectic temperature).
- 3. 8. For a 50 wt.% Ag alloy, determine the fractional amounts of microconstituents when solidification is just complete. 9. Sketch the 50 wt.% silver alloy at a temperature just below the eutectic temperature. Label both the phases and the microconstituents.
- 4. 10. The molybdenum-rhenium phase diagram is provided below. Note that all the single-phase regions labeled. b. Label all two-phase regions. c. Specify the temperatures and compositions for all 3-phase equilibria in this system. For each 3-phase equilibrium, write the reaction upon cooling. d. Assuming no phase transformations occur at lower temperatures, specify the strengthening mechanisms that are possible for an alloy of Mo with 18 wt. % Re. e. BONUS (don’t you love how I give bonus questions for homework that isn’t graded?): How would you actually form an alloy of Mo with 10 wt. % Re? Could you make it in one of our mat sci lab furnaces?