materials science i 5-alloy systems & phase diagrams 5-1-utility

Materials Science I

Dr Ali Salami Golezani

5-Alloy Systems & Phase Diagrams

5-1-Utility & Limitations to Use of Phase Diagrams

Utility Limitations

Phase Transformation Phase Diagrams are also known as Equilibrium Diagrams

Welding & Casting Rate of Transformation is missing

Soldering & Brazing TTT (Time-Temperature-Transformation)

Electromigration & Diffusion Problems

Kirkendahl Voiding

Corrosion

Electrical Resistivity

5-2- Concepts

Phase

A phase is a homogenous, physically distinct and mechanically separable portion of the material with a given chemical composition and structure.

For solids: Chemically and structurally distinct

For liquids: Miscibility

For gases: Always 1 phase

Metals and Alloys

A pure metal solidifies at a constant temperature equal to its freezing point (same as melting point)

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Components

Pure metals and/or compounds of which a system is made up,

ie: Brass has the components Cu and Zn. Or Ceramic systems normally have compound components ie SiO2 and Al2O3

Solubility

1. Total solubility (miscibility), ie alcohol+water(one phase) 2. Total immiscibility, ie water+sand(two phases) 3. Limited solubility, ie salt, or sugar+water, A certain amount of salt, or sugar, will dissolve

Metallic Solution

Most, but not all, metals will mix completely in the liquid phase. When they freeze the solids that they form can have different forms. These are solid solutions, inter-metallic compounds and intermediate phases. Similar behavior is found in ceramic systems.

a) Solid Solutions

A solid solution is formed when the impurity atoms mix with the host atoms in the solid without hange of crystal structure. There are two types:

Substitutional S.S The substitutional atoms replace atoms of the solvent. Small atoms (C N) can fit in the holes in the solute lattice.

Interstitial S.S The interstitial atom fits into the spaces in the solute lattice. Hume Rothery Rules Structure: crystal structure-must be the same Size: The atoms sizes should not differ by more than 15%. Electronegativity: The atoms should have similar electronegativity, or Elements should not form compounds with each other Valence: Elements should have the same valence.

Unsaturated Saturated Supersaturated

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b) Intermediate Phases When two metals have widely divergent electrochemical properties they are likely to associate to form a chemical compound. Thus strongly electropositive magnesium will combine with weakly electropositive tin to form the substance Mg2Sn. This is generally described as an intermetallic compound. Between these two extremes of substitutional solid solution on the one hand and intermetallic compound on the other, phases are formed which exhibit a gradation of properties according to the degree of association which occurs between the atoms taking part. These phases are collectively termed intermediate phases. At one extreme we have true intermetallic compounds whilst at the other ordered structures which can be more accurately classed as secondary solid solutions. These intermediate phases can be classified into three main groups: 1 Intermetallic compounds in which the laws of chemical valence are apparently obeyed as in Mg2Sn, Mg2Pb, Mg3Sb2 and Mg3Bi2. These valence compounds are generally formed when one metal (such as mag-nesium) has chemical properties which are strongly metallic, and the other metal (such as antimony, tin or bismuth) chemical properties which are only weakly metallic and, in fact, bordering on those of non-metals. Frequently such a compound has a melting point which is higher than that of either of the parent metals. For example, the intermetallic compound Mg2Sn melts at 7800C, whereas the parent metals magnesium and tin melt at 650 and 232°C respectively. This is an indication of the high strength of the chemical bond in Mg2Sn. 2 Electron Compounds the chemical valence of a metal is a function of the number of electrons in the outer 'shell' of the atom, whilst the nature of the metallic bond is such that wholesale sharing of umbers of electrons takes place in the crystal structure of a pure metal. In these 'electron compounds' the normal valence laws are not obeyed, but in many instances there is a fixed ratio between the total number of valence bonds of all the atoms involved and the total number of atoms in the empirical formula of the compound in question. There are three such ratios, commonly referred to as Hume-Rothery ratios:

(i) Ratio 3/2 (21/14)—(3 structures, such as CuZn, Cu3Al, Cu5Sn, Ag3Al, etc. (ii) Ratio 21/13—y structures, such as Cu5Zn8, G19Al4, Ag5Zn8, Na3iPb8, etc. (iii) Ratio 7/4 (21/12)—e structures, such as CuZn3, Cu3Sn, AgCd3, Ag5Al3, etc.

Size-factor Compounds These are intermediate phases in which compositions and crystal structures arrange themselves in such a way as to allow the constituent atoms to pack themselves closely together. In the Laves phases compositions are based upon the general formula AB2, eg MgNi2, MgCu2, TiCr2 and MnBe2. Their formation depends upon the fact that the constituent atoms vary in size by about 22.5% but that they can none the less pack closely together in crystal structures. A very important group of size-factor compounds are the interstitial compounds formed between some transition metals and certain small nonmetallic atoms. When the solid solubility of an interstitially dissolved element is exceeded a compound is precipitated from the solid solution. In this type of compound the small non-metal atoms still occupy interstitial positions but the overall crystal structure of the compound is different from that of the original interstitial solid solution. Compounds of this type have metallic properties and comprise hydrides, nitrides, borides and carbides of which TiH2, TiN, Mn2N, TiB2, TaC, W2C, WC, Mo2C and Fe3C are typical. All of these compounds are extremely hard and the carbides find application in tool steels and cemented-carbide cutting materials. Fe3C is of course the phase cementite of ordinary carbon steels. Many of these carbides are extremely refractory, having melting points well in excess of 3000oC.

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Note: Tm Comparison: Understanding interactions on bond energies Interaction between 2 species: A and B Thermodynamic Parameter: Melting Point (T) How does mixing of A-A and B-B bonds affect T? The Ideal Case (S.S) Eutectic Behavior Intermetallic CompoundFormation (A-B) = x(A-A) + (1-x) (B-B) Where x is the mole fraction of A in B TAlloy = TA + x ( TB-TA) Examples: Copper–Nickel, Silicon–Germanium

A-B < 0.5 (A-A + B-B) TAlloy < TA , TB Examples: Lead-Tin, Gold-Silicon

A-B > 0.5 (A-A + B-B) TAlloy > TA , TB Example: Gallium-Arsenic

5-3-Unary or One Component Phase Diagram The simplest case-Water, Also known as a P-T diagram and Sign of [dP/dT] for:

Solid-Liquid, Liquid-Gas and Gas-Solid equilibrium.

P-T Diagram for Water α-quartz � β-quartz � β-tridymite � β-cristobalite � liquid

5-4-Binary System or Binary Diagram If we consider the binary A-B system and add a second axis for composition, the behavior illustrated in Fig. A is commonly observed. A phase diagram (or equilibrium diagram) is a diagram with T and composition as axes, showing the equilibrium constitution.

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Composition Presentation

Mol (n) Weight % (Wt%) Atom (or Mol) % (at%)

n=(M/m) Wt%A=(weight of component A/Σ weights of all components)×100

XA=(number of atoms (or mols) of component A/Σ number of atoms (or mols) of all components) ×100

The Phase Rule or Phase Equilibrium

It refers to the set of conditions where more than one phase may exist. It can be reflected by constancy with time in the phase characteristics of a system.

1. Phase rule: P+F=C+2 2. Condensed Phase Rule: P+F = C+1

P: number of phase, (e.g. Polymorphism, solid solution) F: number of degrees of freedom (temperature, pressure and composition of phases) C: number of components (minimum number of constituents in composition)

Working with Phase Diagrams

1. Overall Composition 2. Solidus

Temperature at which alloy is completely solid or Temperature at which liquefaction begins

3. Liquidus Temperature at which alloy is completely liquid or Temperature at which solidification begins

4. Limits of Solid Solubility Unlimited Solid Solubility: Solute and solvent are mutually soluble at all concentrations, e.g., Cu-Ni system Meets the requirements of the Hume-Rothery Rules Result is a “single phase alloy”

Limited or Partial Solid Solubility: There is a limit to how much of the solute can dissolve in the solvent before “saturation” is reached, e.g., Pb-Sn and most other systems Does not meet the requirements of the Hume-Rothery Rules Results in a “multi-phase alloy”

5. Chemical Composition of Phases at any temperature It is the chemical composition of each phase in the system In a system having more than one phase,

each phase will have a unique chemical composition which will be different from each other, and will also be different from the overall composition

6. Amount of Phases at any temperature Level rule: relative amounts of two phases in a mixture

7. Invariant Reactions Eutectic: L = α (s) + β (s); e.g., Pb-Sn

Peritectic: α (s) + L = β (s); e.g., Pb-In

Monotectic: L1 = α (s) + L2; e.g., Cu-Pb

Syntectic: L1 + L2 = α (s); e.g., Na-Zn

Metatectic: β (s) + α (s) = L1 e.g., U-Mn

8. Development of Microstructure The microstructure developed depends on the overall composition and the cooling rate

9. Chemical Activity

A measure of the “escaping tendency

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Phase diagram for the Pb-Sn system

Chemical Composition of Phases at any temperature Consider points A and B on the Pb-Sn phase diagram in Figure (above). At a constitution point in a single-phase region, the phase composition is simply the composition of the alloy itself. Constitution point A (temperature 250ºC, alloy composition Pb-30wt% Sn) lies in the single-phase liquid field; the phase composition is also Pb-30wt% Sn. In two-phase regions, the phase compositions are given by the values on the phase boundaries at the ends of the tieline through the constitution point. Recall that these are the saturation limits of the single-phase fields on the other sides of the boundaries. Constitution point B (temperature 130ºC, alloy composition C = 40wt% Sn) lies in a two phase field with two solid phases identified from the ends of the tie-line: (Pb) and (Sn); the phase compositions are Pb-7wt% Sn and Pb-98wt% Sn respectively

Amount of Phases at any Temperature Consider the alloy with composition WSn = 20 wt% Sn at 250ºC in Figure, a constitution point in the two-phase field: liquid plus Pb-rich solid. To find the proportions of each phase, first construct a tie-line through

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the constitution point and read off the compositions of the phases: Pb-rich solid (Pb) with composition (Pb) WSn = 12 wt% Sn; Liquid L with composition WSn = 34 wt% Sn. The tie-line is of length l , while the lengths of the segments to either side of the constitution point are a and b respectively (all compositions in wt% Sn). For the example alloy of composition WSn = 20 wt% Sn:

The weight fractions of liquid and solid in the alloy are: FL= a / l and F(Pb) = b / l . Hence:

FL = 8/22 = 36% and F(Pb) = 14/22 = 64%

Determination of Phase Diagrams

1. Cooling Curves 2. Differential Scanning Calorimetry 3. Thermomechanical Analysis 4. Differential Thermal Analysis 5. Metallography

6. Energy Dispersive X-ray Spectroscopy 7. Electron Microprobe Analyzer 8. X-ray Diffraction 9. Transmission Electron Microscopy

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Cooling Curves

5-5-Types of Thermal Equilibrium Diagram

We will now consider the main types of thermal equilibrium diagram which are of use in studying metallic alloy systems. Generally a useful alloy will only be formed when the two metals are completely soluble in each other in the liquid state; but in some instances the two metals are only partially soluble as liquids. We will begin with a brief study of one such case.

5-5-1- Two metals, Mutually Soluble in all Proportions in the Liquid State, Remain Mutually Soluble in all Proportions in the Solid State

liquidus and solidus are congruent

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Development of Microstructure in Equilibrium (very slow) Cooling

Solidification in the solid+liquid phase occurs gradually upon cooling from the liquidus line. The composition of the solid and the liquid change gradually during cooling (as can be determined by the tie-line method.). Nuclei of the solid phase form and they grow to consume all the liquid at the solidus line.

Solidification

Development of Microstructure in Non-equilibrium Cooling 1. Compositional changes require diffusion in solid and liquid phases 2. Diffusion in the solid state is very slow.⇒The new layers that solidify on top of the existing grains

have the equilibrium composition at that temperature but once they are solid their composition does not change. ⇒ Formation of layered (cored) grains and the invalidity of the tie-line method to determine the composition of the solid phase.

3. The tie-line method still works for the liquid phase, where diffusion is fast. Average Ni content of solid grains is higher. ⇒ Application of the lever rule gives us a greater proportion of liquid phase as

compared to the one for equilibrium cooling at the same T. ⇒ Solidus line is shifted to the right (higher Ni contents), solidification is complete at lower T, the outer part of the grains are richer in the low-melting component (Cu).

4. Upon heating grain boundaries will melt first. This can lead to premature mechanical failure.

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Note: Diffusion

Diffusion is the migration of atoms from a region of high concentration to a region of low concentration. Interdiffusion: in a solid with more than one type of element (an alloy), atoms tend to migrate from regions of large concentration. Self-diffusion: In an elemental solid, atoms also migrate.

Diffusion Mechanisms are, Interstitial, Vacancy and Substitutional,

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Processing Using

Diffusion FASTER for... Diffusion SLOWER for...

1. Open crystal structures 2. Lower melting temp. mat’ls 3. Mat’ls w/secondary bonding 4. Cations 5. Smaller Diffusing atoms 6. Lower density mat’ls

1) Close packed structures 2) High melting temp. mat’ls 3) Mat’ls w/covalent bonding 4) Anions 5) Larger diffusing atoms 6) Higher density mat’ls

5-5-2-Two Metals Mutually Soluble in all Proportions in the Liquid State Becoming Completely Insoluble in the Solid State Consider the solidification of an alloy of composition x, ie containing about 80% cadmium and 20% bismuth. When the temperature falls to T, crystal nuclei of pure cadmium begin. (The temperature horizontal or tie-line, T, cuts the liquidus at the chosen composition, x, and the other phase boundary is the 100% cadmium ordinate.). Since pure cadmium is deposited, it follows that the liquid which remains becomes correspondingly richer in bismuth. Therefore the composition of the liquid moves to the left—say, to x\— and, as indicated by the diagram, no further deposition of cadmium takes place until the temperature has fallen to Ti. When this happens more cadmium is deposited, and dendrites begin to develop from the nuclei which have already formed. The growth of the cadmium dendrites, on the one hand, and the consequent enrichment of the remaining liquid in bismuth, on the other, continues until the

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temperature has fallen to 1400C. The remaining liquid then contains 40% cadmium and 60% bismuth, ie the eutectic point E has been reached. At this point the two metals are in equilibrium in the liquid, but, due to the momentum of crystallisation, the composition swings a little too far past the point E, resulting in the deposition of a little too much cadmium. In order that equilibrium shall be maintained, a swing back in composition across the eutectic point takes place by the deposition of a layer of bismuth. In this way the composition of the liquid oscillates about E by depositing alternate layers of cadmium and bismuth, whilst the temperature remains at 1400C until the remaining liquid has solidified. Thus the final structure will consist of primary crystals of cadmium which formed between the temperature T and 1400C, and a eutectic consisting of alternate layers of cadmium and bismuth which formed at 1400C.

Hypo-Eutectic Microstructure -Eutectic Microstructure Hyer-Eutectic Microstructure

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5-5-3-Two Metals Mutually Soluble in all Proportions in the Liquid State but only Partially Soluble in the Solid State

Three single phase regions (α - solid solution of Ag in Cu matrix, β = solid solution of Cu in Ag matrix, L - liquid) & Three two-phase regions (α + L, β +L, α +β)

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Development of Microstructure

Several different types of microstructure can be formed in slow cooling an different compositions. Let’s consider cooling of liquid lead – tin system as an example. In the case of lead-rich alloy (0-2 wt. % of tin) solidification proceeds in the same manner as for isomorphous alloys (e.g. Cu-Ni) that we discussed earlier.

L → α+L → α

At compositions between the room temperature solubility limit and the maximum solid solubility at the eutectic temperature, β phase nucleates as the α solid solubility is exceeded upon crossing the solvus line.

L → α+L→ α→ α + β

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Note: Age Hardening Treatment

Hypothetical phase diagram for a precipitation-hardenable alooy

of composition Co Age Hardenind haet treatment cycle, showing both solution and

aging treatment

5-5-4-Systems containing one or more Compound Phase

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5-5-5-System in which a Peritectic Transformation is Involved Sometimes in an alloy system two phases which are already present interact at a fixed temperature to produce an entirely new phase. This is known as a peritectic transformation.

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5-5-6-System in which a Monotectic Transformation is Involved

5-5-7-Solid State Reaction

Eutectoid Reactions The eutectoid (eutectic-like in Greek) reaction is similar to the eutectic reaction but occurs from one solid phase to two new solid Eutectoid structures are similar to eutectic structures but are much finer in scale (diffusion is much slower in the solid state). Upon cooling, a solid phase transforms into two other solid phases (δ - γ + ε in the example below)

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Peritectoid is a three-phase reaction similar to peritectic but occurs from two solid phases to one new solid phase

α + β = γ. Order-Disorder Transformation

Allotropy

Summary of reactions

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materials science i 5-alloy systems & phase diagrams 5-1-utility

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