Dic 05 Hume Rothery soluciones sólidas

Metals – Phase diagram for Iron and Carbon

• Iron: - pure iron (99.99 %),

- ingot iron (some carbon, 0.1 % impurities),

- wrought iron (3% slag with low carbon).

• Solubility of carbon in iron will depend on solid phases of iron: Ferrite 0.02%; Austenite 2.1 %;

• Steel: 0.02 – 2.1 %; Cast iron: 2.1-4 %

• Cementite, Fe3C: hard and brittle

• Carbon: an element increasing strength; Fe is soft.


3. Steel

- Steel is an alloy of iron that contains carbon ranging by weight between 0.02% and 2.11%

-It often includes other alloying ingredients as well: manganese, chromium, nickel, molybdenum

- classification of steels:

plain carbon, low-alloy, stainless, tool


3. Steel

Plain carbon steel: low-carbon (<0.2%), medium-carbon (0.2%< and <0.5%), high-carbon (>0.5%).

Low-alloy steel: Cr, Mn, Mo, Ni, V; alloying elements <5%

Stainless steels: highly alloyed steels; Cr >15%, Ni

Tool steel: highly alloyed steels designed for use as industrial cutting tools, dies, and molds.

Metals – Nonferrous metals

1. Metals

Ferrous and nonferrous

2. Nonferrous

Aluminum, copper, magnesium, nickel, titanium, and zinc and their alloys.

General features of non-ferrous metals:

(1)Strength is not as good as steel

(2)Corrosion resistance and/or strength-to-weight ratios for certain non-ferrous alloys are higher than steels

• Lower electrical resistance – copper

• Higher thermal conductivity – aluminum

• Lower melting point – Zinc (die casting)

• Superalloys - Substantial amount of 3 or more metals rather than one

base metal + alloying elements - 3 groups: iron, nickel, or cobalt (based on the main

element) - Used in high strength and wear applications at high

temperatures (>1100 C)

• Processing of metals - Shaping (i.e. casting, forming, material removal) - Assembly (i.e. welding, mechanical fastening) - Finishing process (i.e. electroplating, painting) - Property Enhancement (Alloying, Cold working, and Heat

treatments)

IMPACTO

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Alloying: atoms mixed on a latticeSolid Solutions and Ordered Compounds

Two Possibilities for Solid Solutions: B atoms in A atoms

Substitutional Interstitials‘new element replaces host atoms’ ‘new element goes in holes’

Can we roughly estimate what atoms will form solid solutions?

e.g. semiconductor devices: doped-Si C in Fe

e.g. Ni in Cu, steels

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Ordered Substitutional and Interstititials Compounds

Substitutional Interstitial element replaces host atoms element goes into holes in an orderly arrangement in an orderly arrangement

e.g., Ni3Al (hi-T yield strength), Al3(Li,Zr) (strengthening)

e.g., small impurities, claysionic crystals, ceramics.


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Hume-Rothery Rules for Alloys (atoms mixing on a lattice)

Will mixing 2 (or more) different types of atoms lead to a solid-solution phase?

Empirical observations have identified 4 major contributors through :

+1 +2

Atomic Size Factor , Crystal Structure, Electronegativity, Valences

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Hume-Rothery Rules for Mixing

Empirical rules for substitutional solid-solution formation were identified from experiment that are not exact, but give an expectation of formation. Briefly,

1) Atomic Size Factor The 15% RuleIf "size difference" of elements are greater than ±15%, the lattice distortions (i.e. local lattice strain) are too big and solid-solution will not be favored.

DR%= < ±15% will not disallow formation.

2) Crystal Structure Like elemental crystal structures are betterFor appreciable solubility, the crystal structure for metals must be the same.

3) Electronegativity DE ~ 0 favors solid-solution.The more electropositive one element and the more electronegative the other, then "intermetallic compounds" (order alloys) are more likely.

4) Valences Higher in lower alright. Lower in higher, it’s a fight.A metal will dissolve another metal of higher valency more than one of lower valency.

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Two Possibilities for Solid Solutions: B atoms in A atoms

Substitutional Interstitials‘new element replaces host atoms’ ‘new element goes in holes’

Can we roughly estimate what atoms will form solid solutions?

e.g. semiconductor devices: doped-Si C in Fe

e.g. Ni in Cu, steels

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Ordered Substitutional and Interstititials Compounds

Substitutional Interstitial element replaces host atoms element goes into holes in an orderly arrangement in an orderly arrangement

e.g., Ni3Al (hi-T yield strength), Al3(Li,Zr) (strengthening)

e.g., small impurities, claysionic crystals, ceramics.


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Hume-Rothery Rules for Alloys (atoms mixing on a lattice)

Will mixing 2 (or more) different types of atoms lead to a solid-solution phase?

Empirical observations have identified 4 major contributors through :

+1 +2

Atomic Size Factor , Crystal Structure, Electronegativity, Valences

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©2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under license.

Figure 9.1 Illustration of phases and solubility: (a) The three forms of water – gas, liquid, and solid – are each a phase. (b) Water and alcohol have unlimited solubility. (c) Salt and water have limited solubility. (d) Oil and water have virtually no solubility.

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Figure 9.2 Schematic unary phase diagram for magnesium, showing the melting and boiling temperatures at one atmosphere pressure.

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Figure 9.3 (a) Pressure-temperature diagram for H2O. The triple point temperature is 273.0098 K and the triple point pressure is 4.6 torr. Notice the solid-liquid line sloping to the left. At normal pressure (1 atm or 760 torr), the melting temperature is 273 K. A possible scheme for freeze drying is shown as starting with point S and following the dashed line to the left. (b) Pressure-temperature diagram for CO2. Many researchers are examining the applications of super-critical CO2 for use as a solvent for applications related to the processing of plastics and pharmaceuticals. (c) Pressure-temperature diagram for Si02, The dotted line shows the 1 atm pressure.

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Solubility - The amount of one material that will completely dissolve in a second material without creating a second phase.

Unlimited solubility - When the amount of one material that will dissolve in a second material without creating a second phase is unlimited.

Limited solubility - When only a maximum amount of a solute material can be dissolved in a solvent material.

Solubility and Solid Solutions

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(a) Liquid copper and liquid nickel are completely soluble in each other. (b) Solid copper-nickel alloys display complete solid solubility, with copper and nickel atoms occupying random lattice sites. (c) In copper-zinc alloys containing more than 30% Zn, a second phase forms because of the limited solubility of zinc in copper.

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(c)2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under license.

(a) In an ordered structure, the substituting atoms occupy specific lattice points,(b) while in normal structure, the constituent atoms are randomly located at different lattice points.

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The unit cells of two intermetallic compounds: (a) TiAl has an ordered tetragonal structure, and (b) Ni3Al has an ordered cubic structure.

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Hume-Rothery rules - The conditions that an alloy or ceramic system must meet if the system is to display unlimited solid solubility. Hume-Rothery’s rules are necessary but are not sufficient for materials to show unlimited solid solubility.

Hume-Rothery rules: - Size factor - Crystal structure- Valence- Electronegativity

Conditions for Unlimited Solid Solubility

Reglas de Hume Rothery

1. Relación de tamaño[(radio solvente – radio soluto ) / radio solvente] = (∆r / r ) 100

< 8% solubilidad total 8 – 15 % solubilidad parcial < 15% solubilidad nula

2. Estructura cristalina

Estructura del solvente vs estructura del solutoIdéntica : solubilidad totalIgual número de coordinación : solubilidad parcial altaIgual sistema : solubilidad parcial bajaDiferente : solubilidad nula

3. Electronegatividad

A mayor semejanza en la electronegatividad y valencia de soluto y solvente, más fácilmente se promueve la generación de una solución sólida.

4.Valencia

Entre metales de diferente valencia actúa el de mayor valencia como soluto.

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Mg0 and Ni0 have similar crystal structures, ionic radii, and valences; thus the two ceramic materials can form solid solutions.

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NiO can be added to MgO to produce a solid solution. What other ceramic systems are likely to exhibit 100% solid solubility with MgO?

SOLUTION

From Appendix B, some other possibilities in which the cation has a valence of +2 include the following:

Ceramic Solid Solutions of MgO

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SOLUTION

The percent difference in ionic radii and the crystal structures are also shown and suggest that the FeO-MgO system will probably display unlimited solid solubility. The CoO and ZnO systems also have appropriate radius ratios and crystal structures.

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Solid-solution strengthening - Increasing the strength of a metallic material via the formation of a solid solution.

Dispersion strengthening - Strengthening, typically used in metallic materials, by the formation of ultra-fine dispersions of a second phase.

Solid-Solution Strengthening

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Figure 9.8 The effects of several alloying elements on the yield strength of copper. Nickel and zinc atoms are about the same size as copper atoms, but beryllium and tin atoms are much different from copper atoms. Increasing both atomic size difference and amount of alloying element increases solid-solution strengthening.

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For atoms larger than copper—namely, zinc, aluminum, and tin— increasing the size difference increases the strengthening effect. Likewise for smaller atoms, increasing the size difference increases strengthening.

The atomic radii and percent size difference are shown below:

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Figure 9.9 The effect of additions of zinc to copper on the properties of the solid-solution-strengthened alloy. The increase in % elongation with increasing zinc content is not typical of solid-solution strengthening.

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Peritectic - A three-phase reaction in which a solid and a liquid combine to produce a second solid on cooling.

Monotectic - A three-phase reaction in which one liquid transforms to a solid and a second liquid on cooling.

Miscibility gap - A region in a phase diagram in which two phases, with essentially the same structure, do not mix, or have no solubility in one another.

Metastable miscibility gap - A miscibility gap that extends below the liquidus or exists completely below the liquidus.

Phase Diagrams Containing Three-Phase Reactions

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The five most important three-phase reactions in binary phase diagrams.

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Consider the binary phase diagram in Figure 10.7. Identify the three-phase reactions that occur.

Identifying Three-Phase Reactions

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Figure 10.7 A hypothetical phase diagram (for Example 10.2)

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SOLUTION

We find horizontal lines at 1150oC, 920oC, 750oC, 450oC, and 300oC: 1150oC: The in-betwen point is at 15% B. δ + L are present above the point, γ is present below. The reaction is:

δ + L γ, a peritectic

920oC: This reaction occurs at 40% B:

L1 γ + L2 a monotectic


L γ + β, a eutectic


γ α + β, a eutectoid


α + β μ or a peritectoid

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Solvus - A solubility curve that separates a single-solid phase region from a two-solid phase region in the phase diagram.

Isopleth - A line on a phase diagram that shows constant chemical composition.

Hypoeutectic alloy - An alloy composition between that of the left-hand-side end of the tie line defining the eutectic reaction and the eutectic composition.

Hypereutectic alloys - An alloy composition between that of the right-hand-side end of the tie line defining the eutectic reaction and the eutectic composition.

The Eutectic Phase Diagram

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The lead-tin equilibrium phase diagram.

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Solidification and microstructure of a Pb-2% Sn alloy. The alloy is a single-phase solid solution.

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Solidification, precipitation, and microstructure of a Pb-10% Sn alloy. Some dispersion strengthening occurs as the β solid precipitates.

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Solidification and microstructure of the eutectic alloy Pb-61.9% Sn.

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The cooling curve for a eutectic alloy is a simple thermal arrest, since eutectics freeze or melt at a single temperature.

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(a) Atom redistribution during lamellar growth of a lead-tin eutectic. Tin atoms from the liquid preferentially diffuse to the β plates, and lead atoms diffuse to the α plates. (b) Photomicrograph of the lead-tin eutectic microconstituent (x400).

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The solidification and microstructure of a hypoeutectic alloy (Pb-30% Sn).

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The cooling curve for a hypoeutectic Pb-30% Sn alloy.

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The effect of the composition and strengthening mechanism on the tensile strength of lead-tin alloys.

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The aluminum-silicon phase diagram.

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A phase diagram for the CaO-SiO2 system. (Source: Adapted from Introduction to Phase Equilibria, by C.G. Bergeron and S.H. Risbud, pp. 44 and 45, Figs. 3-36 and 3-37. Copyright © 1984 American Ceramic Society.)

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Ternary alloy - An alloy formed by combining three elements or components.

Ternary phase diagram - A phase diagram between three components showing the phases present and their compositions at various temperatures. This diagram requires a three-dimensional plot or is presented as two-dimensional isothermal sections of a three-dimensional diagram.

Ternary Phase Diagrams

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Hypothetical ternary phase diagram. Binary phase diagrams are present at the three faces.

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A liquidus plot for the hypothetical ternary phase diagram. The circles labeled x, y, and z refer to the different compositions discussed in Example 10.10.

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Binary phase diagrams for the (a) copper-zinc, (b) copper-tin, (c) copper-aluminum, and (d) copper-beryllium systems

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The aluminum-copper phase diagram and the microstructures that may develop during cooling of an Al-4%-Cu alloy (for Problem 10.24).

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The aluminum-lithium phase diagram (for Problem 10.25).

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Portion of the aluminum-magnesium phase diagram (for Problem 10.31).

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A portion of the magnesium-aluminum phase diagram

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A portion of the Fe-Fe3C phase diagram. The vertical line at 6.67% C is the stoichiometric compound Fe3C

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The Mg0-Al203 phase diagram, showing limited solid solubility and the presence of MgAl204 or spinel (for Problem 10.42).

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Cooling curve for a Pb-Sn alloy

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Cooling curve for an Al-Si alloy

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Cooling curves for a series of Cu-Ag alloys

Dic 05 Hume Rothery soluciones sólidas

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