Invariant Reactions
Eutect and peritectic reactions were discussed. In a eutect reaction, a phase disappears upon cooling.
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<math>\gamma \right \alpha + \beta</math>
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Peritectic reactions were also discussed. Below is a reaction that occurs upon cooling.
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<math>\alpha + \beta \right \gamma</math>
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While reactions occur, the temperature does not change. The phase conversion occurs at one temperature.
Gibbs Phase Rule
There is a mathematical expression that tells how many degrees of freedom there are in equilibrium. The term <math>P</math> denotes the number of phases and a term <math>C</math> denotes the number of components or chemical species. For each species, there is an equilibrium condition.
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<math>\mu_L^
= \mu_L^
= \mu_L^
...</math>
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<math> \mbox
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<math>P-1</math>
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<math> \mbox
</math>
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<math>C(P-1)</math>
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Consider <math>C</math> components and <math>C-1</math> concentrations. For each phase, there are <math>C-1</math> variables. Below is an expression used in calculating the number of degrees of freedom, <math>F</math>.
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<math>F = P(C-1) + 2 - C(P-1)</math>
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<math>F = 2 + C -P</math>
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In a one component system, <math>C</math> is equal to one, and the number of degrees of freedom is given by an expression below, where <math>P</math> is the number of phases.
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<math>F = 3 - P</math>
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When the number of phases is equal to one, there are two degrees of freedom. It would be possible to independently vary temperature and pressure.
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Below are terms related to binary systems.
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<math>C = 2</math>
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<math>F = 4 - P</math>
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<math>P = 3 \right F = 1</math>
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The pressure is fixed
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<math>F_
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The temperature is fixed.
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Two phase equilibrium is different.
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<math>P = 2</math>
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<math>F_
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Pick a temperature.
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Consider how many phases are possible.
Complex Phase Diagrams
NiTi
Give an idea of how to build complex phase diagrams. Compound formation has been seen. The phase diagram of <math>NiTi</math> is provided in a handout. Single phase regions are drawn as a line. The solubility is so small that it can't be drawn. In less famous systems, solubilities may not be known. Line is drawn because the solubility is not known. Consider where new phases are appearing. Consider reactions that occur as temperature is dropped at a particular composition.
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<math>1250^
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<math>L \right L + TiNi</math>
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<math>984^
</math>
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<math>L + TiNi \right Ti_2Ni</math>
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<math>L + TiNi \right TiNi + Ti_2Ni</math>
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<math>630^
</math>
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<math>TiNi + Ti_2Ni \right Ti_2Ni + TiNi_3</math>
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<math>TiNi \right Ti_2Ni + TiNi_3</math>
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The lever rule does not tell about composition.
Ytrium stabilized zirconium
Add <math>Y_2O_3</math> to <math>ZrO_2</math> to produce a classic high temperature oxygen conductor. A 3+ cation is placed on a 4+ site. There is not enough positive charge, and vacancies with oxygen result. There can be five to ten percent oxygen vacancies. There is good oxygen conductivity and it is a compound that can be used as sensor to detect whether burning rich or lean. It is used in solid oxide fuel cells, and the phase diagram is classic.
Aluminum Magnesium
A phase diagram of this material is provided. Reconstruct out of three phase equilibria, and make out of two invariants. Give leeway. Come to one point.
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<math>L \right Al + Al_
Mg_
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Additional information. Melting congruently would not be correct. Consider two eutectics next to each other.
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Compound appears through peritectic reaction from melt. The compound <math>Al_3Mg_2</math> appears as peritectic from liquid. There are two versions. Appear with <math>Al</math> or with <math>Al_
Mg_
</math>. Try at home.
Aluminum Copper
The use of this material helps planes be able to fly. As the material is heat treated, the hardness increases and then decreases. A eutectic composition is about <math>5.5%</math>. Heat a system with <math>4.4%</math> copper high enough and it can become a single phase. If a second phase forms, there may be precipitates, and they can block dislocation motion. There are obstacles to motion.
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There is a fixed volume fraction of the second phase. Heating can cause coarsening, which causes bigger precipitates to form. There are a lot fewer obstacles. There is a sweet spot with regard to heat treatment, and this there would not be high strength alloys. The yield strength of pure aluminum is about <math>30 MPa</math>, and small amounts of precipitate can cause the yield strength to rise to <math>300-400 MPa</math>.\
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There was a hope to replace copper with a lighter material. Replacing copper with lithium could reduce a lot of weight. There is a metastable precipitate that is a very effective hardener, but it is only used in seat frames. There could not be found an inexpensive way to join this material.
Melting Point
In most metals, melting point goes down.
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In the solid state, solubility is much harder. Mix more easily. Mixing always gives entropy. Liquid create high entropy. Liquid stability increased. Harder to mix.
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A lens phase diagram occurs when there is good solubility in the solid. There is good solubility among elements that are close in placement in the periodic table.
Transient Liquid Phase Bonding (TLP)
Consider a joining process that begins with placing a small amount of <math>B</math> between two pieces of <math>A</math>. A phase diagram aids in understanding a joining process.
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After the materials are placed in contact, elements start diffusing. A small amount of B diffuses into A, and vice versa. The composition moves from right to left along the gray line in the diagram above, and the material melts as A diffuses into the piece that is used to join the materials. After a sufficient amount of A diffuses into B, the material solidifies.
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An advantage is that the joining process occurs at a constant temperature. The joint solidifies without temperature gradients. In othe joining techniques, there is a temperature gradient, and the joint shrinks more than other regions.
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The technique of TLP is a way to bind titanium with copper. There is a high melting temperature of <math>1700</math>. Join at <math>1084</math> with, say, 100 mm of copper.
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Transient liquid phase bonding was used in creating Egyptian decorations. A copper paste may have been added. The technique may be a mix between TLP and using fluxes. The multing points of cupper and gold are 1064 and 1084, respectively. Melting point is lowered by the phenomenon of melting point depression, and it is lowered more with fluxes.
Non-Equilibrium Conditions
Consider a lack of diffusion and lack of nucleation. As temperature is lowered, a shell of <math>x_2</math> forms. If the temperature is lowered quickly, a layer is deposited. There is a need of solid state diffusion to reach the lowest energy state, and over time, interdiffusion may occur.
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When forming a solid, the average composition does not precisely follow the phase diagram. The actual composition is lower in B and drifts off.
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Solidification spans a larger range. What happens when the material is heated? It melts sooner than expected. Stuff solidifies rich in B. Inhomogeneity results in a varying melting point. Etching based on composition. Outside etches away.
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How is this issue resolved in industry? Mix samples mechanically.
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Cold-rolling is related to surface characteristics.
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Prevent nucleation of compounds by doing process quickly. Consider a complicated crystal structure. Cool a sample fast enough to avoid nucleation. When <math>\gamma</math> cannot nucleate, disregard the <math>\gamma</math> free energy curve. Keep equilibrium between liquid, <math>\alpha</math>, and <math>\beta</math>.
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Regarding amorphous metals, look for systems with potential for low eutectics. There is a risk that <math>\gamma</math> precipitates. It is possible to heat metallic glasses and precipitate equilibrium compounds. Most common glass formers are complicated compounds that are hard to form our of liquid. A special property of metallic glasses is enormous elasticity. There is research that involves investigating magnetic metallic glasses. There is a search of iron based amorphous glass.