Section 1 Introduction to Alloy Phase Diagrams

Hugh Baker, Editor

ALLOY PHASE DIAGRAMS are useful to exhaust system). Phase diagrams also are con- terms "phase" and "phase field" is seldom made, metallurgists, materials engineers, and materials sulted when attacking service problems such as and all materials having the same phase name are scientists in four major areas: (1) development of pitting and intergranular corrosion, hydrogen referred to as the same phase. new alloys for specific applications, (2) fabrica- damage, and hot corrosion. Equilibrium. There are three types of equili- tion of these alloys into useful configurations, (3) In a majority of the more widely used commer- bria: stable, metastable, and unstable. These three design and control of heat treatment procedures cial alloys, the allowable composition range en- conditions are illustrated in a mechanical sense in for specific alloys that will produce the required compasses only a small portion of the relevant Fig. l. Stable equilibrium exists when the object mechanical, physical, and chemical properties, phase diagram. The nonequilibrium conditions is in its lowest energy condition; metastable equi- and (4) solving problems that arise with specific that are usually encountered inpractice, however, librium exists when additional energy must be alloys in their performance in commercial appli- necessitate the knowledge of a much greater por- introduced before the object can reach true stabil- cations, thus improving product predictability. In tion of the diagram. Therefore, a thorough under- ity; unstable equilibrium exists when no addi- all these areas, the use of phase diagrams allows standing of alloy phase diagrams in general and tional energy is needed before reaching meta- research, development, and production to be done their practical use will prove to be of great help stability or stability. Although true stable equilib- more efficiently and cost effectively. to a metallurgist expected to solve problems in rium conditions seldom exist in metal objects, the In the area of alloy development, phase dia- any of the areas mentioned above. study of equilibrium systems is extremely valu- grams have proved invaluable for tailoring exist- able, because it constitutes a limiting condition ing alloys to avoid overdesign in current applica- from which actual conditions can be estimated. tions, designing improved alloys for existing and Common Terms Polymorphism.The structure of solid elements new applications, designing special alloys for and compounds under stable equilibrium condi- special applications, and developing alternative Before the subject of alloy phase diagrams is tions is crystalline, and the crystal structure of alloys or alloys with substitute alloying elements discussed in detail, several of the commonly used each is unique. Some elements and compounds, to replace those containing scarce, expensive, terms will be discussed. however, are polymorphic (multishaped); that is, hazardous, or "critical" alloying elements. Appli- Phases. All materials exist in gaseous, liquid, or their structure transforms from one crystal struc- cation of alloy phase diagrams in processing in- solid form (usually referred to as a phase), de- ture to another with changes in temperature and cludes their use to select proper parameters for pending on the conditions of state. State variables pressure, each unique structure constituting a dis- working ingots, blooms, and billets, fmding include composition, temperature, pressure, mag- tinctively separate phase. The term allotropy (ex- causes and cures for microporosity and cracks in netic field, electrostatic field, gravitational field, isting in another form) is usually used to describe castings and welds, controlling solution heat and so on. The term "phase" refers to that region polymorphic changes in chemical elements. treating to prevent damage caused by incipient of space occupied by a physically homogeneous Crystal structure of metals and alloys is discussed melting, and developing new processing technol- material. However, there are two uses of the term: in a later section of this Introduction; the allo- ogy. the strict sense normally used by physical scien- tropic transformations of the elements are listed In the area of performance, phase diagrams give tists and the somewhat looser sense normally used in the Appendix to this Volume. an indication of which phases are thermodynami- by materials engineers. Metastable Phases. Under some conditions, cally stable in an alloy and can be expected to be In the strictest sense, homogeneous means that metastable crystal structures can form instead of present over a long time when the part is subjected the physical properties throughout the region of stable structures. Rapid freezing is a common to a particular temperature (e.g., in an automotive space occupied by the phase are absolutely iden- method of producing metastable structures, but tical, and any change in condition of state, no some (such as Fe3C, or"cementite") are produced matter how small, will result in a different phase. at moderately slow cooling rates. With extremely For example, a sample of solid metal with an rapid freezing, even thermodynamically unstable apparently homogeneous appearance is not truly structures (such as amorphous metal "glasses") a single-phase material, because the pressure con- can be produced. dition varies in the sample due to its own weight Systems. A physical system consists of a sub- in the gravitational field. stance (or a group of substances) that is isolated In a phase diagram, however, each single-phase from its surroundings, a concept used to facilitate field (phase fields are discussed in a following study of the effects of conditions of state. "Iso- Ill section) is usually given a single label, and engi- lated" means that there is no interchange of mass neers often find it convenient to use this label to between the substance and its surroundings: The (a) (b) (c) refer to all the materials lying within the field, substances in alloy systems, for example, might regardless of how much the physical properties of be two metals, such as copper and zinc; a metal the materials continuously change from one part and a nonmetal, such as iron and carbon; a metal Fig. I Mechanical equilibria: (a) Stable. (b) Metas- of the field to another. This means that in en- and an intermetallic compound, such as iron and table. (c) Unstable gineering practice, the distinction between the cementite; or several metals, such as aluminum, 1*2/Introduction to Alloy Phase Diagrams magnesium, and manganese. These substances constitute the components comprising the system and should not be confused with the various quid) phases found within the system. A system, how- 4 ever, also can consist of a single component, such Solid 2 as an element or compound. Liquid / Solidus Phase Diagrams. In order to record and visual- ize the results of studying the effects of state variables on a system, diagrams were devised to show the relationships between the various I Ot phases that appear within the system under equi- Gas librium conditions. As such, the diagrams are variously called constitutional diagrams, equilib- f rium diagrams, or phase diagrams. A single- Temperature component phase diagram can be simply a one- or two-dimensional plot showing the phase changes in the substance as temperature and/or Fig. 2 Schematic pressure-temperature phase diagram pressure change. Most diagrams, however, are two- or three-dimensional plots describing the phase relationships in systems made up of two or more components, and these usually contain beled fields. Stable equilibrium between any two phases occurs along their mutual boundary, and fields (areas) consisting of mixed-phase fields, as Composition B well as single-phase fields. The plotting schemes invariant equilibrium among all three phases oc- A in common use are described in greater detail in curs at the so-called triple point, O, where the three boundaries intersect. This point also is Fig. 3 Schematic binary phase diagram showing mis- subsequent sections of this Introduction. cibility in both the liquid and solid states System Components. Phase diagrams and the called an invariant point because, at that location systems they describe are often classified and on the diagram, all externally controllable factors named for the number (in Latin) of components are fixed (no degrees of freedom). At this point, in the system: all three states (phases) are in equilibrium, but any The Gibbs phase rule applies to all states of changes in pressure and/or temperature will cause matter (solid, liquid, and gaseous), but when the Number of Name of one or two of the states (phases) to disappear. effect of pressure is constant, the rule reduces to: components system or diagrum Univariant Equilibrium. The phase rule says One Unary that stable equilibrium between two phases in a f=c-p+ 1 Two Binary unary system allows one degree of freedom (f= Three Temary 1 - 2 + 2). This condition, called univariant The stable equilibria for binary systems are sum- Four Quatemary equilibrium or monovariant equilibrium, is illus- Five Quinary marized as follows: Six Sexinary trated as lines 1, 2, and 3 separating the single- phase fields in Fig. 2. Either pressure or tempera- Seven Septenary Number of Number of Degrees of Eight Octanary ture may be freely selected, but not both. Once a components ph~es freedom Equilibrium Nine Nonary pressure is selected, there is only one temperature Ten Decinary that will satisfy equilibrium conditions, and con- 2 3 0 Invariant 2 1 Univariant versely. The three curves that issue from the triple 2 l 2 Bivariant point are called triple curves: line 1, representing Phase Rule. Thephase rule, first announced by the reaction between the solid and the gas phases, J. Willard Gibbs in 1876, relates the physical state is the sublimation curve; line 2 is the melting of a mixture to the number of constituents in the curve; and line 3 is the vaporization curve. The system and to its conditions. It was also Gibbs vaporization curve ends at point 4, called a criti- who first called each homogeneous region in a cal point, where the physical distinction between Miscible Solids, Many systems are comprised of components having the same crystal structure, system by the term "phase." When pressure and the liquid and gas phases disappears. temperature are the state variables, the rule can be Bivariant Equilibrium. If both the pressure and the components of some of these systems are written as follows: and temperature in a unary system are freely and completely miscible (completely soluble in each arbitrarily selected, the situation corresponds to other) in the solid form, thus forming a continu- f=c-p+2 having two degrees of freedom, and the phase rule ous solid solution. When this occurs in a binary says that only one phase can exit in stable equi- system, the phase diagram usually has the general appearance of that shown in Fig. 3. The diagram where f is the number of independent variables librium (p = 1 - 2 + 2). This situation is called (called degrees of freedom), c is the number of bivariant equilibrium. consists of two single-phase fields separated by a two-phase field. The boundary between the liquid components, and p is the number of stable phases field and the two-phase field in Fig. 3 is called the in the system. liquidus; that between the two-phase field and the Binary Diagrams solid field is the solidus. In general, a liquidus is Unary Diagrams the locus of points in a phase diagram representing the temperatures at which alloys of the Invariant Equilibrium. According to the phase If the system being considered comprises two various compositions of the system begin to rule, three phases can exist in stable equilibrium components, a composition axis must be added to freeze on cooling or finish melting on heating; a only at a single point on a unary diagram (f= 1 - the PT plot, requiring construction of a three- solidus is the locus of points representing the 3 + 2 = 0). This limitation is illustrated as point O dimensional graph. Most metallurgical problems, temperatures at which the various alloys finish in the hypothetical unary pressure-temperature however, are concerned only with a fixed pressure freezing on cooling or begin melting on heating. (PT) diagram shown in Fig. 2. In this diagram, the of one atmosphere, and the graph reduces to a The phases in equilibrium across the two-phase three states (or phases)--solid, liquid, and gas--- two-dimensional plot of temperature and compo- field in Fig. 3 (the liquid and solid solutions) are are represented by the three correspondingly la- sition (TX diagram). called conjugate phases. Introduction to Alloy Phase Diagrams/I-3

point P, an invariant point that occurred by coin- L L cidence. (Three-phase equilibrium is discussed in the following section.) Then, if this two-phase field in the solid region is even further widened so that the solvus lines no longer touch at the invariant point, the diagram passes through a series of configurations, finally taking on the more familiar shape shown in Fig. 6(b). The three-phase reaction that takes place at the invari- ro ant point E, where a liquid phase freezes into a 0E mixture of two solid phases, is called a eutectic I-- I reaction (from the Greek word for "easily melted"). The alloy that corresponds to the eutectic composition is called a eutectic alloy. An alloy having a composition to the left of the eutectic a b B point is called a hypoeutectic alloy (from the A Composition Greek word for "less than"); an alloy to the right (a) Composition is a hypereutectic alloy (meaning "greater than"). Schematic binary phase diagram with a mini- In the eutectic system described above, the two Fig. 5 mum in the liquidus and a miscibility gap in the components of the system have the same crystal L solid state structure. This, and other factors, allows complete miscibilitybetween them. Eutectic systems, however, also can be formed by two components If the solidus and liquidus meet tangentially at having different crystal structures. When this oc- some point, a maximum or minimum is produced curs, the liquidus and solidus curves (and their in the two-phase field, splitting it into two por- extensions into the two-phase field) for each of

:3 tions as shown in Fig. 4. It also is possible to have the terminal phases (see Fig. 6c) resemble those a gap in miscibility in a single-phase field; this is for the situation of complete miscibility between shown in Fig. 5. Point Tc, above which phases tXl system components shown in Fig. 3. a)E I.-- and ~2 become indistinguishable, is a critical Three-Phase Equilibrium. Reactions involv- point similar to point 4 in Fig. 2. Lines a-Tc and ing three conjugate phases are not limited to the b-Tc, called solvus lines, indicate the limits of eutectic reaction. For example, upon cooling, a solubilityof component B in A and Ain B, respec- single solid phase can change into a mixture of tively. The configurations of these and all other two new solid phases or, conversely, two solid phase diagrams depend on the thermodynamics phases can react to form a single new phase. A B Composition of the system, as discussed later in this Introduc- These and the other various types of invariant (b) tion. reactions observed in binary systems are listed in Eutectic Reactions. If the two-phase field in the Table 1 and illustrated in Fig. 7 and 8. solid region of Fig. 5 is expanded so that it touches Intermediate Phases. In addition to the three Fig. 4 Schematic binary phase diagrams with solid- the solidus at some point, as shown in Fig. 6(a), solid terminal-phase fields, (~, [~, and e, the dia- state miscibility where the liquidus shows a complete miscibility of the components is lost. gram in Fig. 7 displays five other solid-phase maximum (a) and a minimum (b) Instead of a single solid phase, the diagram now fields, 7, 5, fi', ~q, and ~, at intermediate composi- shows two separate solid terminal phases, which tions. Such phases are called intermediate are in three-phase equilibrium with the liquid at phases. Many intermediate phases, such as those

L+~ L+I3 / %SS,,, ~ .~ ~ % I

%• E % •p "t'... _~ i r" .s -S ~ ~+~ c~+B / A Composition B A Composition B A Composition (a) (b) (c)

Fig° 6 Schematic binary phase diagrams with invariant points. (a) Hypothetical diagram of the type shown in Fig. 5, except that the miscibility gap in the solid touches the solidus curve at invariant point P; an actual diagram of this type probably does not exist. (b) and (c) Typical eutectic diagrams for components having the same crystal structure (b) and components having different crystal structures (c); the eutectic (invariant) points are labeled E. The dashed lines in (b) and (c) are metastable extensions of the stable-equilibria lines. 1-4/Introduction to Alloy Phase Diagrams

Critical L Allotropl¢ ¢onsruent ~ruent I \ = +L \ / L, + ,/ --\ .o~=.o~o - \ "/; I \ V / \ 7 + Ls \/L + L2 t ::7 /" ......

7/Co~ngr~7 + 71 71 Monoteetold

Eutectoid ~ + 6'

...... Y_o_lLmo_r p_h_z c_ ......

~+~

A Composition B A Composition B

Hypothetical binary phase diagram showing intermediate phases formed by Fig, 8 Hypothetical binary phase diagram showing three intermetallic line com- Fig. 7 various invariant reactions and a polymorphic transformation pounds and four melting reactions illustrated in Fig. 7, have fairly wide ranges of dimensions becomes more compticated. One op- diagram, reading values from them is difficult. homogeneity. However, many others have very tion is to add a third composition dimension to the Therefore, ternary systems are often represented limited or no significant homogeneity range. base, forming a solid diagram having binary dia- by views of the binary diagrams that comprise the When an intermediate phase of limited (or no) grams as its vertical sides. This can be represented faces and two-dimensional projections of the homogeneity range is located at or near a specific as a modified isometric projection, such as shown liquidus and solidus surfaces, along with a series ratio of component elements that reflects the nor- in Fig. 9. Here, boundaries of single-phase fields of two-dimensional horizontal sections (iso- mal positioning of the component atoms in the (liquidus, solidus, and solvus lines in the binary therms) and vertical sections (isopleths) through crystal structure of the phase, it is often called a diagrams) become surfaces; single- and two- the solid diagram. compound (or line compound). When the compo- phase areas become volumes; three-phase lines Vertical sections are often taken through one nents of the system are metallic, such an interme- become volumes; and four-phase points, while comer (one component) and a congruently melt- diate phase is often called an intermetallic com- not shown in Fig. 9, can exist as an invariant ing binary compound that appears on the opposite pound. (Intermetallic compounds should not be plane. The composition of a binary eutectic liq- face; when such a plot can be read like any other confused with chemical compounds, where the uid, which is a point in a two-component system, true binary diagram, it is called a quasibinary type of bonding is different from that in crystals becomes a line in a ternary diagram, as shown in section. One possibility is illustrated by line 1-2 and where the ratio has chemical significance.) Fig. 9. in the isothermal section shown in Fig. 10. A Three intermetallic compounds (with four types Although three-dimensional projections can be vertical section between a congruently melting of melting reactions) are shown in Fig. 8. helpful in understanding the relationships in a binary compound on one face and one on a dif- In the hypothetical diagram shown in Fig. 8, an alloy of composition AB will freeze and melt isothermally, without the liquid or solid phases undergoing changes in composition; such a phase change is ailed congruent. All other reactions are Liquidus surfaces incongruent;, that is, two phases are formed from L+/~ one phase on melting. Congruent and incongruent \\\ L+a Solidus phase changes, however, are not limited to line Solidus compounds: the terminal component B (pure surface phase e) and the highest-melting composition of intermediate phase 8' in Fig. 7, for example, ~,e::,...... -~ freeze and melt congruently, while 8' and e freeze \ Solvus / and melt incongruently at other compositions. Solvus surface Metastable Equilibrium. In Fig. 6(c), dashed surface lines indicate the portions of the liquidus and solidus lines that disappear into the two-phase solid region. These dashed lines represent valu- able information, as they indicate conditions that would exist under metastable equilibrium, such as might theoretically occur during extremely rapid cooling. Metastable extensions of some stable-equilibria lines also appear in Fig. 2 and 6(b).

Ternary Diagrams A When a third component is added to a binary 9 Ternary phase diagram showing three-phase equilibrium. Source: 56Rhi system, illustrating equilibrium conditions in two Fig, Introduction to Alloy Phase Diagrams/I,5

C C C a:Z r, r, r, ,. A/VV\ r, r~ r, AA/kAAA/k r, r2

A B A xa ~ B A

Fig. 10 Isothermal section of a ternary diagram with Fig. 11 Triangular composition grid for isothermal sec- phase boundaries deleted for simplification tions; x is the composition of each constituent Fig. 12 Liquidus projection of a ternary phase diagram in mole fraction or percent showing isothermal contour lines. Source: Adapted from 56Rhi ferent face might also form a quasibinary section tion, component A is placed at the bottom left, B (see line 2-3). formed at the intersections of two surfaces. Ar- at the bottom right, and C at the top. The amount All other vertical sections are not true binary rowheads are often added to these lines to indicate of component A is normally indicated from point diagrams, and the term pseudobinary is applied the direction of decreasing temperature in the to them. A common pseudobinary section is one C to point A, the amount of component B from trough. where the percentage of one of the components is point A to point B, and the amount of component held constant (the section is parallel to one of the C from point B to point C. This scale arrangement faces), as shown by line 4-5 in Fig. 10. Another is often modified when only a comer area of the ThermodynamicPrinciples is one where the ratio of two constituents is held diagram is shown. Projected Views. Liquidus, solidus, and solvus constant and the amount of the third is varied from The reactions between components, the phases surfaces by their nature are not isothermal. There- 0 to 100% (line 1-5). formed in a system, and the shape of the resulting fore, equal-temperature (isothermal) contour Isothermal Sections. Composition values in phase diagram can be explained and understood lines are often added to the projected views of the triangular isothermal sections are read from a through knowledge of the principles, laws, and these surfaces to indicate their shape (see Fig. 12). triangular grid consisting of three sets of lines terms of thermodynamics, and how they apply to In addition to (or instead of) contour lines, views parallel to the faces and placed at regular compo- the system. often show lines indicating the temperature sition intervals (see Fig. 11). Normally, the point Internal Energy. The sum of the kinetic energy troughs (also called "valleys" or "grooves") of the triangle is placed at the top of the illustra- (energy of motion) and potential energy (stored energy) of a system is called its internal energy, Table I Invariant reactions E. Internal energy is characterized solely by the Type Reaction state of the system. Closed System. A thermodynamic system that Eutectic Lt undergoes no interchange of mass (material) with (involvesliquid and solid) I.,2> V < S Monoteetic its surroundings is called a closed system. A L closed system, however, can interchange energy S~ > \/ < $2 Eutectic with its surroundings. First Law. The First Law of Thermodynamics, S, as stated by Julius yon Mayer, James Joule, and L > V < S~ Catatectic (Metatectic) Hermann von Helmholtz in the 1840s, states that energy can be neither created nor destroyed. Eutectoid St Therefore, it is called the Law of Conservation of (involvessolid S~ > V < S~ Monotectoid Energy. This law means that the total energy of only) St an isolated system remains constant throughout ,%> \/ < S~ Eutectoid any operations that are carded out on it; that is, for any quantity of energy in one form that disappears from the system, an equal quantity of an- Peritectic other form (or other forms) will appear. (involvesliquid Lt > A < I.~ Syntectic and solid) S For example, consider a closed gaseous system to which a quantity of heat energy, ~Q, is added St Peritectic L> A < and a quantity of work, 5W, is extracted. The First ,% Law describes the change in intemal energy, dE, of the system as follows: Peritectoid (involvessolid St > A < ~ Peritectoid only) S~ dE = ~2-aW

In the vast majority of industrial processes and material applications, the only work done by or on a system is limited to pressure/volume terms. 1-6/Introduction to Alloy Phase Diagrams

Any energy contributions from electric, mag- C = 8Q Second Law. While the First Law establishes netic, or gravitational fields are neglected, except ST the relationship between the heat absorbed and for electrowinning and electrorefining processes the work performed by a system, it places no such as those used in the production of copper, However, if the substance is kept at constant restriction on the source of the heat or its flow aluminum, magnesium, the alkaline metals, and volume (dV = 0): direction. This restriction, however, is set by the the alkaline earths. With the neglect of field ef- Second Law of Thermodynamics, which was ad- fects, the work done by a system can be measured &2 = dE vanced by Rudolf Clausius and WilliamThomson by summing the changes in volume, dV, times (Lord Kelvin). The Second Law states that the each pressure causing a change. Therefore, when and spontaneous flow of heat always is from the field effects are neglected, the First Law can be higher temperature body to the lower tempera- written: ture body. In other words, all naturally occurring processes tend to take place spontaneously in the dE = ~3Q - PdV direction that will lead to equilibrium. Entropy. The Second Law is most conveniently Enthalpy. Thermal energy changes under con- If, instead, the substance is kept at constant pres- stated in terms of entropy, S, another property of stant pressure (again neglecting any field effects) sure (as in many metallurgical systems), state possessed by all systems. Entropy represents are most conveniently expressed in terms of the the energy (per degree of absolute temperature, enthalpy, H, of a system. Enthalpy, also called T) in a system that is not available for work. In heat content, is defined by: terms of entropy, the Second Law states that all natural processes tend to occur only with an H=E+PV increase in entropy, and the direction of the proc- CP= L dT Jp ess always is such as to lead to an increase in Enthalpy, like internal energy, is a function of the entropy. For processes taking place in a system in state of the system, as is the product PV. equilibrium with its surroundings, the change in Heat Capacity. The heat capacity, C, of a sub- and entropy is defined as follows: stance is the amount of heat required to raise its temperature one degree; that is: ~Q dE + PdV dS =_ T- T

r3 i i 2

A Composition A Composition C~ q

(a) (b) (c)

T~ ..... 4 ...... £ r, I I r2

r, (X i i i rs

A Composition B A Composition B A Composition

(d) (e) (f)

Fig. 13 Use of Gibbs energy curves to construct a binary phase diagram that shows miscibility in both the liquid and solid states. Source: Adapted from 66Pri Introduction to Alloy Phase Diagrams/lo7

r~ r2

t t == (D o~ .g_ L9 (.9 I T66 i 7 I I J I I I I I I I I I I I i I 1 I I A Composition B A Composition B A Composition B

(a) (b) (c)

r, rs 1 T 1 t t r~ r3 == L L /3 r,

1~9 ~ 10 i r5 I I I I [ ,' A Composition A Composition B A Composition

(d) (e) (f)

Fig. 14 Use of Gibbs energy curves to construct a binary phase diagram of the eutectic type. Source: Adapted from 68Gor

Third Law. A principle advanced by Theodore independent variables, pressure and absolute tem- equilibrium is altered, a reaction occurs that Richards, Walter Nemst, Max Planck, and others, perature, which are readily controlled experimen- opposes the constraint, i.e., a reaction that par- often called the Third Law of Thermodynamics, tally. If the process is carded out under conditions tially nullifies the alteration. The effect of this states that the entropy of all chemically homoge- of constant pressure and temperature, the change theorem on lines in a phase diagram can be seen neous materials can be taken as zero at absolute in Gibbs energy of a system at equilibrium with in Fig. 2. The slopes of the sublimation line (1) zero temperature (0 K). This principle allows its surroundings (a reversible process) is zero. For and the vaporization line (3) show that the system calculation of the absolute values of entropy of a spontaneous (irreversible) process, the change reacts to increasing pressure by making the denser pure substances solely from heat capacity. in Gibbs energy is less than zero (negative); that phases (solid and liquid) more stable at higher Gibbs Energy. Because both S and V are diffi- is, the Gibbs energy decreases during the process, pressure. The slope of the melting line (2) indi- cult to control experimentally, an additional term, and it reaches a minimum at equilibrium. cates that this hypothetical substance contracts on Gibbs energy, G, is introduced, whereby: freezing. (Note that the boundary between liquid water and ordinary ice, which expands on freez- G =_ E + PV- TS =_ H- TS Features of Phase Diagrams ing, slopes toward the pressure axis.) Clausius-Clapeyron Equation. The theorem and of Le Ch~telier was quantified by Benoit Clapey- The areas (fields) in a phase diagram, and the ron and Rudolf Clausius to give the following position and shapes of the points, lines, surfaces, dG = dE + PdV + VdP - TdS - SdT equation: and intersections in it, are controlled by thermodynamic principles and the thermodynamic prop- However, erties of all of the phases that constitute the sys- dP AH tem. dT TAV dE=TdS-PdV Phase-field Rule. The phase-fieM rule speci- fies that at constant temperature and pressure, the Therefore, number of phases in adjacent fields in a multi- where dP/dT is the slope of the univariant lines in component diagram must differ by one. a PT diagram such as those shown in Fig. 2, AV dG = VdP-SdT Theorem of Le Chfitelier. The theorem of is the difference in molar volume of the two Henri Le Ch~telier, which is based on thermody- phases in the reaction, and AH is the difference in Here, the change in Gibbs energy of a system namic principles, states that if a system in equi- molar enthalpy of the two phases (the heat of the undergoing a process is expressed in terms of two librium is subjected to a constraint by which the reaction). 1,8/IntroductionL to Alloy Phase Diagrams L

~ L+(x~ ~ i J"

" %~ Incorrect /// L+ccJ /

@ % I a+13 o¢+15 I G

(a) (b) A B Composition

Fig. 1 ~; Examplesof acceptable intersection angles for Fig. 16 An exampleof a binaryphase diagramwith a minimum in the liquidusthat violatesthe Gibbs-KonovalovRule. ~boundaries of two-phasefields. Source: 56Rhi Source: 81Goo

Solutions. The shapes of liquidus, solidus, and points 1 and 2, where these compositions intersect as diagrams with multiple three-phase reactions, solvus curves (or surfaces) in a phase diagram are temperature T3, is called a tie line. Similar tie lines also can be constructed from appropriate Gibbs determined by the Gibbs energies of the relevant connect the coexisting phases throughout all two- energy curves. Likewise, Gibbs energy surfaces phases. In this instance, the Gibbs energy must phase fields (areas) in binary and (volumes) in and tangential planes can be used to construct include not only the energy of the constituent ternary systems, while tie triangles connect the ternary phase diagrams. components, but also the energy of mixing of coexisting phases throughout all three-phase re- Curves and Intersections. Thermodynamic these components in the phase. gions (volumes) in temary systems. principles also limit the shape of the various Consider, for example, the situation of complete Eutectic phase diagrams, a feature of which is a boundary curves (or surfaces) and their intersec- miscibility shown in Fig. 3. The two phases, field where there is a mixture of two solid phases, tions. For example, see the PT diagram shown in liquid and solid tz, are in stable equilibrium in the also can be constructed from Gibbs energy Fig. 2. The Clausius-Clapeyron equation requires two-phase field between the liquidus and solidus curves. Consider the temperatures indicated on that at the intersection of the triple curves in such lines. The Gibbs energies at various temperatures the phase diagram in Fig. 14(f) and the Gibbs a diagram, the angle between adjacent curves are calculated as a function of composition for energy curves for these temperatures (Fig. 14a-e). should never exceed 180 ° or, alternatively, the ideal liquid solutions and for ideal solid solutions When the points of tangency on the energy curves extension of each triple curve between two phases of the two components, A and B. The result is a are transferred to the diagram, the typical shape must lie within the field of third phase. series of plots similar to those shown in Fig. 13(a) of a eutectic system results. The mixture of solid The angle at which the boundaries of two-phase to (e). c~ and g that forms upon cooling through the fields meet also is limited by thermodynamics. At temperature Th the liquid solution has the eutectic point k has a special microstructure, as That is, the angle must be such that the extension lower Gibbs energy and, therefore, is the more discussed later. of each beyond the point of intersection projects stable phase. At T2, the melting temperature of A, Binary phase diagrams that have three-phase into a two-phase field, rather than a one-phase the liquid and solid are equally stable only at a reactions other than the eutectic reaction, as well field. An example of correct intersections can be composition of pure A. At temperature T3, between the melting temperatures of A and B, the Gibbs energy curves cross. Temperature T4 is the Correct Incorrect melting temperature of B, while T5 is below it. Construction of the two-phase liquid-plus-solid L L field of the phase diagram in Fig. 13(f) is as follows. According to thermodynamic principles, the compositions of the two phases in equilibrium with each other at temperature T3 can be determined by constructing a straight line that is tangential to both curves in Fig. 13(c). The points of tangency, 1 and 2, are then transferred to the phase diagram as points on the solidus and liquidus, respectively. This is repeated at sufficient tem- Line peratures to determine the curves accurately. compound If, at some temperature, the Gibbs energy curves I Line for the liquid and the solid tangentially touch at compound some point, the resulting phase diagram will be similar to those shown in Fig. 4(a) and (b), where a maximum or minimum appears in the liquidus and solidus curves. A B A Mixtures. The two-phase field in Fig. 13(0 ComposlUon Composition consists of a mixture of liquid and solid phases. (a) (b) As stated above, the compositions of the two phases in equilibrium at temperature T3 are C1 glo. 1 7 Schematicdiagrams of binary systemscontaining congruent-meltingcompounds but having no associationof -'b the component atoms in the melt common. The diagram in (a) is consistent with the Gibbs-Konovalov Rule, and C2. The horizontal isothermal line connecting whereasthat in (b) violates the rule. Source: 81Goo Introduction to Alloy Phase Diagrams/11,9

Typical Phase-Rule Violations 10. When two phase boundaries touch at a point, Problems Connected With Phase-Boundary they should touch at an extremity of tempera- Curvatures (See Fig. 18) ture. 11. A touching liquidus and solidus (or any two Although phase rules are not violated, three addi- 1. A two-phase field cannot be extended to become touching boundaries) must have a horizontal tional unusual situations (21, 22, and 23) have also part of a pure-element side of a phase diagram common tangent at the congruent point. In this been included in Fig. 18. In each instance, a more at zero solute. In example 1, the liquidus and the instance, the solidus at the melting point is too subtle thermodynamic problem may exist related to solidus must meet at the melting point of the pure "sharp" and appears to be discontinuous. these situations. Examples are discussed below where element. 12. A local minimum point in the lower part of a several thermodynamically unlikely diagrams are 2. Two liquidus curves must meet at one composi- single-phase field (in this instance, the liquid) considered. The problems with each of these situ- tion at a eutectic temperature. cannot be drawn without an additional boundary ations involve an indicated rapid change of slope of 3. A tie line must terminate at a phase boundary. in contact with it. (In this instance, a horizontal a phase boundary. If such situations are to be associ- 4. Two solvus boundaries (or two liquidus, or two monotectic line is most likely missing.) ated with realistic thermodynamics, the temperature solidus, or a solidus and a solvus) of the same 13. A local maximum point in the lower part of a (or the composition) dependence of the thermody- phase must meet (i.e., intersect) at one compo- single-phase field cannot be drawn without a namic functions of the phase (or phases) involved sition at an invariant temperature. (There should monotectic, monotectoid, syntectic, and sintec- would be expected to show corresponding abrupt and not be two solubility values for a phase boundary toid reaction occurring below it at a lower tem- unrealistic variations in the phase diagram regions at one temperature.) perature. Alternatively, a solidus curve must be where such abrupt phase boundary changes are pro- 5. A phase boundary must extrapolate into a two- drawn to touch the liquidus at point 13. posed, without any clear reason for them. Even the phase field after crossing an invariant point. The 14. A local maximum point in the upper part of a onset of ferromagnetism in a phase does not normally validity of this feature, and similar features re- single-phase field cannot be drawn without the cause an abrupt change of slope of the related phase lated to invariant temperatures, is easily demon- phase boundary touching a reversed monotectic, boundaries. The unusual changes of slope considered strated by constructing hypothetical free-energy or a monotectoid, horizontal reaction line coin- here are: diagrams slightly below and slightly above the ciding with the temperature of the maximum. invariant temperature and by observing the rela- When a 14 type of error is introduced, a mini- 21. Two inflection points are located too closely to tive positions of the relevant tangent points to mum may be created on either side (or on one each other. 22. An abrupt reversal of the boundary direction the free energy curves. After intersection, such side) of 14. This introduces an additional error, (more abrupt than a typical smooth "retro- boundaries can also be extrapolated into metas- which is the opposite of 13, but equivalent to 13 grade"). This particular change can occur only table regions of the phase diagram. Such ex- in kind. if there is an accompanying abrupt change in the trapolations are sometimes indicated by dashed 15. A phase boundary cannot terminate within a temperature dependence of the thermodynamic or dotted lines. phase field. (Termination due to lack of data is, 6. Two single-phase fields (Ix and 6) should not be of course, often shown in phase diagrams, but properties of either of the two phases involved in contact along a horizontal line. (An invariant- this is recognized to be artificial.) (in this instance, ~ or ~, in relation to the bound- temperature line separates two-phase fields in 16. The temperature of an invariant reaction in a ary). The boundary turn at 22 is very unlikely to contact.) binary system must he constant. (The reaction be explained by any realistic change in the com- 7. A single-phase field (Ix in this instance) should line must he horizontal.) position dependence of the Gibbs energy func- not be apportioned into subdivisions by a single 17. The liquidus should not have a discontinuous tions. line. Having created a horizontal (invariant) line sharp peak at the melting point of a compound. 23. An abrupt change in the slope of a single-phase at 6 (which is an error), there may be a tempta- (This rule is not applicable if the liquid retains boundary. This particular change can occur only tion to extend this line into a single-phase field, the molecular state of the compound, i.e., in the by an abrupt change in the composition depend- Ix, creating an additional error. situation of an ideal association.) ence of the thermodynamic properties of the 8. In a binary system, an invariant-temperature line 18. The compositions of all three phases at an invari- single phase involved (in this instance, the should involve equilibrium among three phases. ant reaction must be different. phase). It cannot be explained by any possible 9. There should be a two-phase field between two 19. A four-phase equilibrium is not allowed in a abrupt change in the temperature dependence of single-phase fields (Two single phases cannot binary system. the Gibbs energy function of the phase. (If the touch except at a point. However, second-order 20. Two separate phase boundaries that create a temperature dependence were involved, there and higher-order transformations may be excep- two-phase field between two phases in equilib- would also be a change in the boundary of the e tions to this rule.) rium should not cross each other. phase.)

11 17 11 17 L

12 18 13

16 16 2 16

a 4

5 a+7 i 1D 2O

a i , ,

100 Composition B Composition B

:l:|~,,,b 1 ,.,R Hypothetical binary phase diagram showing many typical errors of construc- Fig. 19 Error-free version of the phase diagram shown in Fig. 18. Source: 910kal tion. See the accompanying text for discussion of the errors at points 1 to 23. Source: 910kal lol0/Introduction to Alloy Phase Diagrams seen in Fig. 6(b), where both the solidus and solvus lines are concave. However, the curvature of both boundaries need not be concave; Fig. 15 shows two equally acceptable (but unlikely) intersections where convex and concave lines are mixed. Congruent Transformations. The congruent point on a phase diagram is where different C f phases of same composition are in equilibrium. The Gibbs-Konovalov Rule for congruent points, which was developed by Dmitry Konovalov from a thermodynamic expression given by J. Willard Gibbs, states that the slope of phase boundaries at congruent transformationsmust be zero (horizontal). Examples of correct slope at the maximum cell / and minimum points on liquidus and solidus curves can be seen in Fig. 4. Often, the inner curve A "/ on a diagram such as that shown in Fig. 4 is erroneously drawn with a sharp inflection (see Fig. 20 a space lattice Fig. 16). Fig. 21 Crystal axes and unit-cell edge lengths. Unit- cell faces are shown, but to avoid confusion A similar common construction error is found they are not labeled. in the diagrams of systems containing congruently melting compounds (such as the line compounds shown in Fig. 17) but having little or or molecules in the interior of a crystal is called no association of the component atoms in the melt its crystal structure. The unit cell of a crystal is all three directions, all unequal lengths must be (as with most metallic systems). This type of error the smallest pattern of arrangement that can be stated to completely define the crystal. The same is especially common in partial diagrams, where contained in a parallelepiped, the edges of which is true if all interaxial angles are not equal. When one or more system components is a compound form the a, b, and c axes of the crystal. The defining the unit-cell size of an alloy phase, the instead of an element. (The slope of liquidus and three-dimensionalaggregation of unit cells in the possibility of crystal ordering occurring over sev- solidus curves, however, must not be zero when crystal forms a space lattice, or Bravais lattice eral unit cells should be considered. For example, they terminate at an element, or at a compound (see Fig. 20). in the copper-gold system, a supedattice forms having complete association in the melt.) Crystal Systems. Seven different crystal sys- that is made up of 10 cells of the disordered lattice, Common Construction Errors. Hiroaki tems are recognized in crystallography, each hav- creating what is called long-period ordering. Okamoto and Thaddeus Massalski have prepared ing a different set of axes, unit-cell edge lengths, Lattice Points. As shown in Fig. 20, a space the hypothetical binary phase shown in Fig. 18, and interaxial angles (see Table 2). Unit-cell edge lattice can be viewed as a three-dimensional net- which exhibits many typical errors of construc- lengths a, b, and c are measured along the corre- work of straight lines. The intersections of the tion (marked as points 1 to 23). The explanation sponding a, b, and c axes (see Fig. 21). Unit-cell lines (called lattice points) represent locations in for each error is given in the accompanying text; faces are identified by capital letters: face A con- space for the same kind of atom or group of atoms one possible error-free version of the same dia- tains axes b and c, face B contains c and a, and of identical composition, arrangement, and orien- gram is shown in Fig. 19. face C contains a and b. (Faces are not labeled in tation. There are five basic arrangements for lat- Higher-Order Transitions. Fig. 21.) Interaxial angle tx occurs in face A, tice points within a unit cell. The first four are: The transitions at considered in this Introduction up to this point angle [3 in face B, and angle y in face C (see Fig. primitive (simple), having lattice points solely have been limited to the common thermodynamic 21). cell comers; base-face centered (end-centered), types called first-order transitions---that is, Lattice Dimensions. It should be noted that the having lattice points centered on the C faces, or changes involving distinct phases having differ- unit-cell edge lengths and interaxial angles are ends of the cell; all-face centered, having lattice ent lattice parameters, enthalpies, entropies, den- unique for each crystalline substance. The unique points centered on all faces; and innercentered sities, and so on. Transitionsnot involvingdiscon- edge lengths are called lattice parameters. The (body-centered), having lattice points at the cen- tinuities in composition, enthalpy, entropy, or term lattice constant also has been used for the ter of the volume of the unit cell. The fifth ar- molar volume are called higher-order transitions length of an edge, but the values of edge length rangement, the primitive rhombohedral unit cell, and occur less frequently. The change in the mag- are not constant, varying with composition within is considered a separate basic arrangement, as netic quality of iron from ferromagnetic to param- a phase field and also with temperature due to shown in the following section on crystal struc- agnetic as the temperature is raised above 771 °C thermal expansion and contraction. (Reported lat- ture nomenclature.These five basic arrangements (1420 °F) is an example of a second-order transi- tice parameter values are assumed to be room- are identified by capital letters as follows: P for tion: no phase change is involved and the Gibbs temperature values unless otherwise specified.) the primitive cubic, C for the cubic cell with phase rule does not come into play in the transi- Interaxial angles other than 90 ° or 120° also can lattice points on the two C faces, F for all-face- tion. Another example of a higher-order transition change slightly with changes in composition. centered cubic, I for innercentered (body-cen- is the continuous change from a random arrange- When the edges of the unit cell are not equal in tered) cubic, and R for primitive rhombohedral. ment of the various kinds of atoms in a multicom- ponent crystal structure (a disordered structure) to an arrangement where there is some degree of Table 2 Relationshipsof edge lengths and of interaxial angles for the seven crystal systems crystal ordering of the atoms (an ordered struc- Crystal system Edge lengths lntera~dalangles Examples ture, or superlattice), or the reverse reaction. Tficlinic (anorthic) a ¢ b # c Ix # ~ # 7 ¢ 90° HgK Monoclinic a ¢ b ¢ c ~ = y = 90 ° # [3 13-S; CoSb2 Orthorhombic a # b # c 0t = 13 = 7 = 90° or-S; Ga; Fe3C (cementite) Crystal Structure Tetragonal a = b # c ot = 13 = 7 = 90° 13-Sn (white); TiO2 Hexagonal a = b ~ c o~ = 13 = 90°; y = 120 ° Zn; Cd; NiAs Rhombohedral(a) a = b = c ct = [5 = Y # 90° As; Sb; Bi; calcite Acrystal is a solid consisting of atoms or mole- Cubic a = b = c ot = 13 = T = 90° Cu; Ag; Au; Fe; NaCI cules arranged in a pattern that is repetitive in three dimensions. The arrangement of the atoms (a) Rhombohedral crystals (sometimes called trigonal) also can be described by using hexagonal axes (rhombohedral-hexagonal). Introduction to Alloy Phase Diagrams/I,11

~'~ 0 o?+. o+,,+?0 ?',6" 0 a ½0½ + )iI+++++,++o Origin = 0.361 nm Origin 1 nm ~ ~n Face-centerod cubic: Frn~lm,Cu cF4 Face-centerod cublc:F43m, ZnS (sphalerlte) cF8

~a 0 0 ' 0 ~ 0 0

r" " L~)'"--.~,,I~-'" I +~ a = 0.564nm- Origin = 0,357 nm O~,n -~'~ ~/ - O, + Face-centered cubic: Fm3m, NaCl Face-canterod cubic: Fd~lm, C (diamond) cF8 0 CI cF8

I o(~ 0 +0+ o ++'+ +(),0,(I I le+ "O+ ~o Origin ½ 0 Ca OF Face-cantered cubic: Fm3m, CaF2 (fluorite) cF12

t~--~ + "------~ ½ + + a .~. a ~ , 0 0

1 3 1 3 >_+ +_Oo

Origin a = 0.316nm gin~ igin Body-cantered cubic: Im~'lm,W Ori 2 8B i OZF 2 cl2

Face-centered cubic: superlatUce: Fm3m, BIF3 cF16

Schematic drawings of the unit cells and ion positions for some simple metal crystals, arrangedalphabetically according to Pearson symbol. Also listed are the space lattice Fig. 22 and crystal system, space-groupnotation, and prototype for each crystal. Repottedlattice parametersare for the prototype crystal. (continued) 1e12/Introduction to Alloy Phase Diagrams

~~ o~ 0

)0 a~a~ ~ Origin ~-.~_. no Ori~oO11 Primitivecubic: Pm~lm,(~Po cPl Cubic: Pm~n, CsCl cP2

• co ?o~,

Origin ,~°~o a = 0.374nm Origin n ~ O Cubic: Pm3n,Cr=Sl O O cFII Origin Cubic superletUce:Pm3m, AuCu a cP4

e B 0 AI

Origin ~n a = 0.300nm l c = 0.325nm

Hexagonal: P61mmm,AIB 2 hP3

Close-packed hexagonal: P631mmc, Mg hP2 -'~< a--~ a 0 382 nm

i~ l, 0371 120=

i O ~Origin ½\,') ~ \~ 0 / k. J Origin /~,,,- 0~71 / k__:__V o zo 0.37,~ ~o-~#._0.3,, ""2 a =0.246nm c=0.671nm x~?rj_Qi£_/" 0 Hexagonal: P631mmc, C (graphite) Hexagonal:/~3mc, ZnS (wurtzlte) hP4 hP4

Schematic drawings of the unit cells and ion positionsfor some simplemetal crystals,arranged alphabetically according to Pearsonsymbol. Also listedare the space lattice Fig. 22 and crystalsystem, space-group notation, and prototypefor each crystal. Reportedlattice parameters are for the prototypecrystal. (continued) Introduction to Alloy Phase Diagrams/lol 3 a d

a = 0.~8 nm c = 0.512nm J c = 0.423 nm J- / ~e- eV - 1 2 0 0 2 ~ / ~O-__e~_/

O In z O sn Origin NI3Sn Origin Hexagonal:/~31mm¢, Hexagonal: P63/rnmc, InNI 2 hP6

j a-~l ~-~ a-~.l

o ,o38 i ~,¶ 0 ~ Z \7, ~ ~:~o.~6;, , l ~li I1 ', II, /2 ~---~-/ o.,38 ' ! Yiilb', • I/~ '= !~-', h~,,.--,T~~Ln .o. O FeI ½~ O~ ~ Felt a = 0.586nm 0 Origin y M.~.~.._LL / a = 0.517nm 0 Mg p c = 0.346 nm ~__L~_~--£~/ c = O.=Onm O Zn Origin Hexagonal:/~ 2m, Fo2P hPO Hexagonal: P631mmc, MgZn 2 hP12

a = 0.467nm I•1 !1 I V.) I/ b=O.315nm

~m~~~ Origin 0 nm I~C-~.L~ f ', U / 0.313 0.687 Origin Ori~~ !--0 Rhombohedrll: R'~, c~ HO hR1 i0~ 0; i O,u 10~3 0~, I

Orthorhomblo: Pmma, AuCd oP4

I 0 I~ ', II 00,. I I I ~'~L_,

Origin ~Z ~ ! Origin b = 0.541 nm Or0gm ~ Fe I~-J '~- ,,41 It.. s,~ ~ b u O,E(~nm C = 0.338nm ~ Origi~ c = 0~8"~ nm ~) Fe Os Oc Orth~tmmblc: Pnnm, FeS2 (mlmeslto) Orthodmmblc: Prime, FolC (cementlto) oP6 oPl6 Fig, 22 Schematic drawings of the unit cells and ion positions for some simple metal crystals, arranged alphabetically according to Pearson symbol. Also listed are the space lattice and crystal system, space-group notation, and prototype for each crystal. Reported lattice parameters are for the prototype crystal (continued) 1.14/Introduction to Alloy Phase Diagrams

o() 0 )o

)~ ¼() ~ i I I o() ) Origin ~ ~ ~ -- ~:31~ nnmm Origin 3 0

Body-centered tetragonal: 1411emd , ~Sn .~/ t14 Ori

Tetregonal: 141mmm, MoSI 2 t16

Au W II~IT /Y_Y~

o ~ 17 ~-O.~om O~u Or _. °m O"O"'n l Origin ~ ©,, c = 0.367 nm Tetragonel: P41nmm, 7CuTI Tetragonal superlatUce:P41mmm,AuCu tP4 tP2 i ?023, o,,~ 11/::oo::: o: Telragoneh P4/nmm, PbO IP4

0.73 \ / 0.30

I o 1,.90 ,1 / '~'1 • oct, ,I I : Origin K._,/ a = 0.4Egnm Origin Ti / Ocu C = 0.296 nm eo Tetragonel: P4/2/mnm , TIO 2 (mUle) Tetragonal: P41nmm,Cu2Sb tPS IP6

Schematic drawings of the unit cells and ion positions for some simple metal crystals, arranged alphabetically according to Pearson symbol. Also listed are the space lattice Fig, 22 and crystal system, space-group notation, and prototype for each crystal. Reported lattice parameters are for the prototype crystal. Introduction to Alloy Phase Diagrams/I-15

Table 3 The 14 space (Bravais) lattices and their Pearson symbols C Solventatoms Solute atoms Crystal Space Pearson system lattice symbol

Triclinic (anorthic) Primitive aP Monoclinic Primitive mP Base-centered(a) mC © Otthorhombic Primitive oP ) Base-centered(a) oC Face-centered oF Body-centered ol Tetragonal Primitive tP ) Body-centered tl Hexagonal Primitive hP Rhombohedral Primitive hR Cubic Primitive cP ) Face-centered cF Body-o'mtered cl

(a) The face that has a lattice point at its c¢.d,er may be chosen as the c face (the xy plane), denoted by the symbol C, or as the a or b face, denoted by ) A orB, because the choice of axes is arbitrary and does not alter the actual ) translations of the lattice. Interstitial Substitutional along with schematic drawings illustrating the atom arrangements in the unit cell. It should be (a) (b) noted that in these schematic representations, the different kinds of atoms in the prototype crystal Fig. 23 Solid-solutionmechanisms. (a) Interstitial.(b) Substitutional illustrated are drawn to represent their relative sizes, but in order to show the arrangements more clearly, all the atoms are shown much smaller than their true effective size in real crystals. Crystal Structure Nomenclature. When the are widely used to identify crystal types. As can Several of the many possible crystal structures seven crystal systems are considered together be seen in Table 3, the Pearson symbol uses a are so commonly found in metallic systems that with the five space lattices, the combinations small letter to identify the crystal system and a they are often identified by three-letter abbrevia- listed in Table 3 are obtained. These 14 combina- capital letter to identify the space lattice. To these tions that combine the space lattice with the crys- tions form the basis of the system of Pearson is added a number equal to the number of atoms tal system. For example, bcc is used for body-cen- symbols developed by William B. Pearson, which in the unit cell conventionally selected for the particular crystal type. When determining the tered cubic (two atoms per unit cell), fcc for face-centered cubic (four atoms per unit cell), and number of atoms in the unit cell, it should be cph for close-packed hexagonal (two atoms per remembered that each atom that is shared with an adjacent cell (or cells) must be counted as only a unit cell). is a symbolic description fraction of an atom. The Pearson symbols for Space-group notation some simple metal crystals are shown in Fig. 22, of the space lattice and symmetry of a crystal. It consists of the symbol for the space lattice fol- 1 lowed by letters and numbers that designate the symmetry of the crystal. The space-group notation for each unit cell illustrated in Fig. 22 is identified next to it. For a more complete list of Pearson symbols and space-group notations, con- suit the Appendix. To assist in classification and identification, each crystal structure type is assigned a repre- / sentative substance (element or phase) having that structure. The substance selected is called the structure prototype. Generally accepted prototypes for some metal crystals are listed in Fig. 22. An important source of information on crystal structures for many years was Structure Reports (Strukturbericht in German). In this publication, crystal structures were classified by a designation consisting of a capital letter (A for elements, B for I AB-type phases, C for AB2-type phases, D for other binary phases, E for ternary phases, and L for superlattices), followed by a number consecu- tively assigned (within each group) at the time the type was reported. To further distinguish among crystal types, inferior letters and numbers, as well Time Time as prime marks, were added to some designations. Because the Strukturbericht designation cannot Fig. 24 Ideal coolin8 curve with no phase change Fig. 25 Idealfreezing curve of a pure metal be conveniently and systematically expanded to 1-16/Introduction to Alloy Phase Diagrams

Determination of Phase Diagrams from high-purity constituents and accurately analyzed. The data used to construct phase diagrams are Chemical analysis is used in the determination obtained from a wide variety of measurements, of phase-field boundaries by measuring compo- many of which are conducted for reasons other sitions of phases in a sample equilibrated at a than the determination of phase diagrams. No one fixed temperature by means of such methods as research method will yield all of the information the diffusion-couple technique. The composition needed to construct an accurate diagram, and no of individual phases can be measured by wet T~ . B ..... diagram can be considered fully reliable without chemical methods, electron probe microanalysis, corroborating results obtained from the use of at and so on. 0E / rature least one other method. Cooling Curves. One of the most widely used Knowledge of the chemical composition of the methods for the determination of phase bounda- #_ sample and the individual phases is important in ries is thermal analysis. The temperature of a the construction of accurate phase diagrams. For sample is monitored while allowed to cool natu- example, the samples used should be prepared rally from an elevated temperature (usually in the

Heating curve Cooling curve Time

~_Natural freezing and melting curves of a pure Liquidus [Zig• ~'Vmetal. Source: 56Rhi OOODQOQOQOOOQO@OOOOOQOO OQO9

..... ~ _Solidus cover the large variety of crystal structures cur- 0004 ~eeoetHeeo~ooeHeolet~ rently being encountered, the system is falling into disuse. The relations among common Pearson symbols, space groups, structure prototypes, and Struktur- bericht designations for crystal systems are given I in various tables in the Appendix. Crystal- lographic information for the metallic elements can be found in the table of allotropes in the Appendix; data for intermetallic phases of the systems included in this Volume are listed with the phase diagrams. Crystallographic data for an A Composition B Time exhaustive list of intermediate phases are presented in 91Vil (see the Bibliography at the end of this Introduction). Fig. 27 Ideal freezing curve of a solid-solution alloy Solid-Solution Mechanisms. There are only two mechanisms by which a crystal can dissolve atoms of a different element. If the atoms of the solute element are sufficiently smaller than the atoms comprising the solvent crystal, the solute atoms can fit into the spaces between the larger L atoms to form an interstitial solid solution (see Fig. 23a). The only solute atoms small enough to fit into the interstices of metal crystals, however, are hydrogen, nitrogen, carbon, and boron. (The other small-diameter atoms, such as oxygen, tend t to form compounds with metals rather than dis- 0J solve in them.) The rest of the elements dissolve in solid metals by replacing a solvent atom at a E lattice point to form a substitutional solid solution (see Fig. 23b). When both small and large solute atoms are present, the solid solution can be both interstitial and substitutional. The addition of for- eign atoms by either mechanism results in distortion of the crystal lattice and an increase in its internal energy. This distortion energy causes 1 2 3 some hardening and strengthening of the alloy, called solution hardening. The solvent phase be- A Composition comes saturated with the solute atoms and reaches Time its limit of homogeneity when the distortion energy reaches a critical value determined by the Ideal freezing curves of (I) a hypoeutecticalloy, (2) a eutecti£ alloy, and (3) a hypereutecticalloy superimposed thermodynamics of the system. lifor=n 28 on a portion of a eutecti¢ phasediagram. Source:Adapted from 66Pri Introduction to Alloy Phase Diagrams/1e17

I To" tions across the diagram, the shape of the liquidus I curves and the eutectic temperature of eutectic \ L system can be determined (see Fig. 28). Cooling T1-..1~ curves can be similarly used to investigate all

~-,. Or2 -)~ -- _ other types of phase boundaries. t Differential thermal analysis is a technique used O) O~ to increase test sensitivity by measuring the dif- (0 \ ference between the temperature of the sample =E =E L+c~ and a reference material that does not undergo I- k- phase transformation in the" temperature range i being investigated. A Y X Z B -'~ X B --~ Crystal Properties. X-ray diffraction methods are used to determine both crystal structure and (a) (b) lattice parameters of solid phases present in a To-" I system at various temperatures (phase identification). Lattice parameter scans across a phase field L are useful in determining the limits of homogene- T1-,i.- . _ ity of the phase; the parameters change with ~ -~-'--'-'-L- .:-~,~2 L3 t r,--~ kl changing composition within the single-phase = T3 --'- o~1 field, but they remain constant once the boundary cO is crossed into a two-phase field. Physical Properties. Phase transformations =E =E within a sample are usually accompanied by I- I- ot I L+ot changes in its physical properties (linear dimen- I sions and specific volume, electrical properties, A X B--=- A X B --~ magnetic properties, hardness, etc.). Plots of these Composition Composition changes versus temperature or composition can be used in a manner similar to cooling curves to (d) (c) locate phase boundaries. Metallographic Methods. Metallography can Fig, 29 Portion of a binary phase diagram containing a two-phase liquid-plus-solid field illustrating (a) the lever rule be used in many ways to aid in phase diagram and its application to (b) equilibrium freezing, (c) nonequilibrium freezing and (d) heating of a homogenized determination. The most important problem with sample. Source: 56Rhi metallographic methods is that they usually rely on rapid quenching to preserve (or indicate) elevated-temperature microstructures for room-temperature observation. Hot-stage metallography, c c however, is an altemative. The application of metallographic techniques is discussed in the section on reading phase diagrams. Thermodynamic Modeling. Because a phase diagram is a representation of the thermodynamic relationships between competing phases, it is theoretically possible to determine a diagram by considering the behavior of relevant Gibbs energy functions for each phase present in the system and physical models for the reactions in the system. How this can be accomplished is demon- strated for the simple problem of complete solid miscibility shown in Fig. 13. The models required to calculate the possible boundaries in the more A B A B complicated diagrams usually encountered are, of (a) (b) course, also more complicated, and involve the use of the equations governing solutions and solution interaction originally developed for physi- I::|n. 30 Alternative systems for showing phase relationships in multiphase regions of ternary diagram isothermal cal chemistry. Although modeling alone cannot /l~ sections. (a) Tie lines. (b) Phase-fraction lines. Source: 84Mot produce a reliable phase diagram, it is a powerful technique for validating those portions of a phase diagram already derived from experimental data. liquid field). The shape of the resulting curves of illustrated in the cooling and heating curves In addition, modeling can be used to estimate the temperature versus time are then analyzed for shown in Fig. 26, where the effects of both super- relations in areas of diagrams where no experi- deviations from the smooth curve found for ma- cooling and superheating can be seen. The dip in mental data exist, allowing much more efficient terials undergoing no phase changes (see Fig. 24). the cooling curve often found at the start of freez- design of subsequent experiments. When apure element is cooled through its freezing is caused by a delay in the start of crystal- ing temperature, its temperature is maintained lization. near that temperature until freezing is complete The continual freezing that occurs during cool- Reading Phase Diagrams (see Fig. 25). The true freezing/melting tempera- ing through a two-phase liquid-plus-solid field ture, however, is difficult to determine from a results in a reduced slope to the curve between the CompositionScales. Phase diagrams to be used cooling curve because of the nonequilibrium con- liquidus and solidus temperatures (see Fig. 27). by scientists are usually plotted in atomic percent- ditions inherent in such a dynamic test. This is By preparing several samples having composi- age (or mole fraction), while those to be used by 1-18/Introduction to Alloy Phase Diagrams

equilibrium by employing the lever rule. The parallel tie lines in the two-phase fields of isother- lever rule is a mathematical expression derived by mal sections (see Fig. 30a) are replaced with sets the principle of conservation of matter in which of curving lines of equal phase fraction (Fig. 30b). the phase amounts can be calculated from the bulk Note that the phase-fraction lines extend through composition of the alloy and compositions of the the three-phase region, where they appear as a conjugate phases, as shown in Fig. 29(a). triangular network. As with tie lines, the number At the left end of the line between al and Lh of phase-fraction lines used is up to the individual the bulk composition is Y% component B and 100 using the diagram. Although this approach to - Y% component A, and consists of 100% cx solid reading diagrams may not seem helpful for such solution. As the percentage of component B in the a simple diagram, it can be a useful aid in more bulk composition moves to the right, some liquid complicated systems. For more information on appears along with the solid. With further in- this topic, see 84Mot and 91Mor. creases in the amount of B in the alloy, more of Solidification. Tie lines and the lever rule can the mixture consists of liquid, until the material be used to understand the freezing of a solid-so- becomes entirely liquid at the right end of the tie lution alloy. Consider the series of tie lines at line. At bulk composition X, which is less than different temperatures shown in Fig. 29(b), all of halfway to point Lh there is more solid present which intersect the bulk composition X. The first than liquid. According to the lever rule, the per- crystals to freeze have the composition al. As the centages of the two phases present can be calcu- temperature is reduced to T2 and the solid crystals Fig. 31 Copper alloy C71500 (copper nickel, 30%) ingot. Dendritic structure shows coring: light lated as follows: grow, more A atoms are removed from the liquid areas are nickel rich; dark areas are low in nickel. 20x. than B atoms, thus shifting the composition of the Source: 85ASM length of line alXl % liquid = x 100 remaining liquid to L2. Therefore, during freez- length of line oqL1 ing, the compositions of both the layer of solid freezing out on the crystals and the remaining engineers are usually plotted in weight percent- %solida = length of line X1L l x 100 liquid continuously shift to higher B contents and age. Conversions between weight and atomic length of line alL1 become leaner in A. Therefore, for equilibrium to composition also can be made using the equations It should be remembered that the calculated be maintained, the solid crystals must absorb B given in the box below and standard atomic amounts of the phases present are either in weight atoms from the liquid and B atoms must migrate weights listed in the Appendix. or atomic percentages and, as shown in the box (diffuse) from the previously frozen material into Lines and Labels. Magnetic transitions (Curie on page 29, do not directly indicate the area or subsequently deposited layers. When this hap- temperature and N6el temperature) and uncertain volume percentages of the phases observed in pens, the average composition of the solid mate- or speculative boundaries are usually shown in microstructures. rial follows the solidus line to temperature T4, phase diagrams as nonsolid lines of various types. Phase-Fraction Lines. Reading the phase rela- where it equals the bulk composition of the alloy. The components of metallic systems, which usu- tionships in many ternary diagram sections (and Coring. If cooling takes place too rapidly for ally are pure elements, are identified in phase other types of sections) often can be difficult maintenance of equilibrium, the successive layers diagrams by their symbols. (The symbols used for because of the great many lines and areas present. deposited on the crystals will have a range of local chemical dements are listed in the Appendix.) compositions from their centers to their edges (a Allotropes of polymorphic elements are distin- Phase-fraction lines are used by some to simplify condition known as coring). The development of guished by small (lower-case) Greek letter pre- this task. In this approach, the sets of often non- fixes. (The Greek alphabet appears in the Appen- dix.) Terminal solid phases are normally designated by the symbol (in parentheses) for the allotrope of the component element, such as (Cr) or (aTi). Composition Conversions Continuous solid solutions are designated by the names of both elements, such as (Cu,Pd) or (I3Ti,I3Y). The following equations can be used to make conversions in binary systems: Intermediate phases in phase diagrams are normally labeled with small (lower-case) Greek let- at.% A × at. wt of A wt%A= x 100 ters. However, certain Greek letters are conven- (at.% A x at. wt of A) + (at.% B x at. wt of B) tionally used for certain phases, particularly disordered solutions: for example, 13 for disordered bcc, ~ or e for disordered cph, y for the wt% A / at. wt of A at.% A - x 100 "vbrass-type structure, and o for the aCrFe-type (at.% A / at. wt of A) + (wt% B / at. wt of B) structure. For line compounds, a stoichiometric phase name is used in preference to a Greek letter (for The equation for converting from atomic percentages to weight percentages in higher-order systems is similar example, A2B3 rather than ~5). Greek letter pre- to that for binary systems, except that an additional term is added to the denominator for each additional component. For ternary systems, for example: fixes are used to indicate high- and low-temperature forms of the compound (for example, aA2B3 for the low-temperature form and 13A2B3 for the at.% A x at. wt of A wt%A- ×100 high-temperature form). (at.% A x at. wt of A) + (at.% B x at. wt of B) + (at.% C x at. wt of C) Lever Rule. As explained in the section on the features of phase diagrams, a tie line is an imagi- wt% A / at. wt of A nary horizontal line drawn in a two-phase field at.% A - x 100 connecting two points that represent two coexist- (wt% A / at. wt of A) + (wt% B / at. wt of B) + (wt% C / at. wt of C) ing phases in equilibrium at the temperature indicated by the line. Tie lines can be used to deter- The conversion from weight to atomic percentages for higher-order systems is easy to accomplish on a computer mine the fractional amounts of the phases in with a spreadsheet program. Introduction to Alloy Phase Diagrams/l*19 this condition is illustrated in Fig. 29(c). Without Liquation also can have a deleterious effect on voids that decrease the strength of the sample. diffusion of B atoms from the material that solidi- the mechanical properties (and microstmcture) of Homogenization heat treatment will eliminate the fied at temperature T1 into the material freezing the sample after it returns to room temperature. coring, but not the voids. at T2, the average composition of the solid formed This is illustrated in Fig. 29(d) for a homogenized Entectie Mierostructures. When an alloy of up to that point will not follow the solidus line. sample. If homogenized alloy X is heated into the eutectic composition (such as alloy 2 in Fig. 28) Instead it will remain to the left of the solidus, liquid-plus-solid region for some reason (inad- is cooled from the liquid state,the eutectic reac- following compositions tx'l through ~x'5. Note vertently or during welding, etc.), it will begin to tion occurs at the eutectictemperature, where the that fmal freezing does not occur until tempera- mek when it reaches temperature 2"2; the first two distinctliquidus curves meet. Atthis temperature Ts, which means that nonequilibrium solidi- liquid to appear will have the composition L2. ture, both a and [3 solid phases must deposit on fication takes place over a greater temperature When the sample is heated at normal rates to the grain nuclei untilall of the liquidis converted range than equilibrium freezing. Because most temperature Th the liquid formed so far will have to solid. This simultaneous deposition results in metals freeze by the formation and growth of a composition L1, but the solid will not have time microstructures made up of distinctively shaped "treelike" crystals, called dendrites, coring is to reach the equilibrium composition IXl. The particles of one phase in a matrix of the other sometimes called dendritic segregation. An ex- average composition will instead lie at some in- phase, or alternate layers of the two phases. Ex- ample of cored dendrites is shown in Fig. 31. termediate value, such as tX'l. According to the amples of characteristic eutectic microstructures Liquation. Because the lowest freezing mate- lever rule, this means that less than the equilib- include spheroidal, nodular, or globular; acicular rial in a cored microstructure is segregated to the rium amount of liquid will form at this tempera- (needles) or rod; and lamellar (platelets, Chinese edges of the solidifying crystals (the grain ture. If the sample is then rapidly cooled from script or dendritic, or filigreed). Each eutectic boundaries), this material can remelt when the temperature T1, solidification will occur in the alloy has its own characteristic microstructure alloy sample is heated to temperatures below the normal manner, with a layer of material having when slowly cooled (see Fig. 32). More rapid equilibrium solidus line. If grain-boundary melt- composition o~1 deposited on existing solid cooling, however, can affect the microstructure ing (caned liquation, or "burning") occurs while grains. This is followed by layers of increasing B obtained (see Fig. 33). Care must be taken in the sample also is under stress, such as during hot content up to composition ct3 at temperature T3, characterizing eutectic structures, because elon- forming, the liquefied grain boundaries will rup- where all of the liquid is converted to solid. This gated particles can appear nodular and flat plate- ture and the sample will lose its ductility and be produces coring in the previously melted regions lets can appear elongated or needlelike when characterized as hot short. along the grain boundaries, and sometimes even viewed in cross section. If the alloy has a composition different from the eutectic composition (such as alloy 1 or 3 in Fig. 28), the alloy will begin to solidify before the eutectic temperature is reached. If the alloy is hypoeutectic (such as alloy I), some dendrites of will form in the liquid before the remaining liquid solidifies at the eutectic temperature. If the alloy is hypereutectic (such as alloy 3), the first (primary) material to solidify will be dendrites of [~. The microstructure produced by slow cooling of a hypoeutectic and hypereutectic alloy will consist of relatively large particles of primary constituent, consisting of the phase that begins to freeze first surrounded by relatively fine eutectic structure. In many instances, the shape of the particles will show a relationship to their dendritic origin (see Fig. 34a). In other instances, the initial dendrites will have filled out somewhat into idio- rnorphic particles (particles having their own characteristic shape) that reflect the crystal struc- (a) (b) ture of the phase (see Fig. 34b). v As stated earlier, cooling at a rate that does not allow sufficient time to reach equilibrium conditions will affect the resulting microstructure. For example, it is possible for an alloy in a eutectic system to obtain some eutectic structure in an alloy outside the normal composition range for such a structure. This is illustrated in Fig. 35. With relatively rapid cooling of alloy X, the composition of the solid material that forms will follow line (Xl-lX.rather than the solidus line to Ix4. As a /4 . . result, the last llqmd to solidify will have the eutectic composition L4, rather than L3, and will form some eutectic structure in the microstructure. The question of what takes place when the temperature reaches T5 is discussed later. (c) (d) Eutectoid Microstruetures. Because the diffusion rates of atoms are so much lower in solids Fig. 32 Examples of characteristic eutectic microstructures in slowly cooled alloys. (a) 50Sn-501n alloy showing than in liquids, nonequilibrium transformation is globules of tin-rich intermetallic phase (light) in a matrix of dark indium-rich intermetallic phase. 150x. (b) Al-13Si alloy showing an acicular structure consisting of short, angular particles of silicon (dark) in a matrix of aluminum. even more important in solid/solid reactions 200x. (c) AI-33Cu alloy showing a lamellar structure consisting of dark platelets of CuAI2 and light platelets of aluminum (such as the eutectoid reaction) than in liq- solid solution. 180x. (d) Mg-37Sn alloy showing a lamellar structure consisting of Mg2Sn "Chinese script" (dark) in a matrix uid/solid reactions (such as the eutectic reaction). of magnesium solid solution. 250x. Source: 85ASM With slow cooling through the eutectoid tempera- 1*20/Introduction to Alloy Phase Diagrams

cles are difficult to distinguish in the microstructure. Instead, there usually is only a general dark- ening of the structure. If sufficient time is allowed, the [3 regions will break away from their host grains of a and precipitate as distinct particles, thereby relieving the lattice strain and retum- ing the hardness and strength to the former levels. This process is illustrated for a simple eutectic system, but it can occur wherever similar conditions exist in a phase diagram; that is, there is a range of alloy compositions in the system for which there is a transition on cooling from a single-solid region to a region that also contains a second solid phase, and where the boundary (a) (b) between the regions slopes away from the com- ~"". 33 Effect of cooling rate on the microstructure of Sn-37Pb alloy (eutectic soft solder). (a) Slowly cooled sample position line as cooling continues. Several exam- shows a lamellar structure consisting of dark platelets of lead-rich solid solution and light platelets of tin. 375x. pies of such systems are shown schematically in (b) More rapidly cooled sample shows globules of lead-rich solid solution, some of which exhibit a slightly dendritic Fig. 38. structure, in a matrix of tin. 375x. Source: 85ASM Although this entire process is called precipitation hardening, the term normally refers only to the portion before much actual precipitation takes place. Because the process takes some time, the term age hardening is often used instead. The rate 0 at which aging occurs depends on the level of supersaturation (how far from equilibrium), the amount of lattice strain originally developed (amount of lattice mismatch), the fraction left to be relieved (how far along the process has pro- gressed), and the aging temperature (the mobility of the atoms to migrate). The [3 precipitate usually takes the form of small idiomorphic particles '~ ~ |i ~tl~ situated along the grain boundaries and within the grains of a phase. In most instances, the particles are more or less uniform in size and oriented in a systematic fashion. Examples of precipitation mi- crostluctures are shown in Fig. 39.

Examples of Phase Diagrams (a) (b) Fig. 34 Examples of primary particle shape. (a) Sn-30Pb hypoeutectic alloy showing dendritic particles of tin-rich solid The general principles of reading alloy phase solution in a matrix of tin-lead eutectic. 500x. (b) AI-19Si hypereutectic alloy, phosphorus-modified, showing diagrams are discussed in the preceding section. idiomorphic particles of silicon in a matrix of aluminum-silicon eutectic. 100x. Source: 85ASM The application of these principles to actual diagrams for typical alloy systems is illustrated be- ture, most alloys of eutectoid composition, such similar to that described in the discussion of eu- low. as alloy 2 in Fig. 36, transform from a single- tectic and eutectoid reactions to determine the The Copper-Zinc System. The metallurgy of phase microstructure to a lamellar structure con- microstructures expected to result from cooling brass alloys has long been of great commercial sisting of altemate platelets of ct and [3 arranged an alloy through any of the other six types of importance. The copper and zinc contents of five in groups (or "colonies"). The appearance of this reactions listed in Table 1. of the most common wrought brasses are: structure is very similar to lamellar eutectic struc- Solid-State Precipitation. If alloy X in Fig. 35 ture (see Fig. 37). When found in cast irons and is homogenized at a temperature between T3 and steels, this structure is called "pearlite" because T5, it will reach an equilibrium condition; that is, of its shiny mother-of-pearl appearance under the the [3 portion of the eutectic constituent will dis- Zinc content, wt% microscope (especially under oblique illumina- solve and the microstructure will consist solely of UNS No. Common name Nominal Range tion); when similar eutectoid structure is found in a grains. Upon cooling below temperature T5, C23000 Red brass, 85% 15 14.0-16.0 nonferrous alloys, it often is called "pearlite-like" this microstructure will no longer represent equi- C24000 Low brass, 80% 20 18.5-21.5 or "pearlitic." librium conditions, but instead will be supersatu- C26000 Cartridge brass, 30 28.5-31.5 The terms hypoeutectoid and hypereutectoid rated with B atoms. In order for the sample to 70% C27000 Yellow brass, 35 32.5-37.0 have the same relationship to the eutectoid com- retum to equilibrium, some of the B atoms will 65% position as hypoeutectic and hypereutectic do in tend to congregate in various regions of the sam- C28000 Muntz metal, 40 37.0-41.0 a eutectic system; alloy 1 in Fig. 36 is a hypoeu- ple to form colonies of new [3 material. The B 60% tectoid alloy, whereas alloy 3 is hypereutectoid. atoms in some of these colonies, called Guiniero The solid-state transformation of such alloys Preston zones, will drift apart, while other colo- As can be seen in Fig. 40, these alloys encompass takes place in two steps, much like the freezing of nies will grow large enough to form incipient, but a wide range of the copper-zinc phase diagram. hypoeutectic and hypereutectic alloys, except that not distinct, particles. The difference in crystal The alloys on the high-copper end (red brass, low the microconstituents that form before the eutec- structures and lattice parameters between the a brass, and cartridge brass) lie within the copper told temperature is reached are referred to as and [3 phases causes lattice strain at the boundary sohd-solution phase field and are called alpha proeutectoid constituents rather than "primary." between the two materials, thereby raising the brasses after the old designation for this field. As Microstructures of Other Invadant Reac- total energy level of the sample and hardening and expected, the micmstmcture of these brasses con- tions. Phase diagrams can be used in a manner strengthening it. At this stage, the incipient parti- sists solely of grains of copper solid solution (see Introduction to Alloy Phase Diagrams/1e21

0~2 °tl Xl L L _ L r,-3 -- _ .J_. ~ ~ "- ~.-£ --. --.. /

t \ ~ ~ Euteetoid point tU

I-- B5 c~ /i x` + I I /Solvus ~ + B Solvus T8 ---~ ----4 .,I x , I I I I I 31 x B i 11 2[ Composition ~= A Composition Schematic binary phase dia~ram," illustrating the effect of cooling rate on an Fig. 35 Fig. 36 Schematic binary phase diagram of a eutectoid system. Source: Adapted from alloy lying outside the equilibrium eutectic transformation line. Rapid solidifi- 56Rhi cation into a terminal phase field can result in some eutectic structure being formed; homogenization at temperatures in the single-phase field will eliminate the eutectic structure; ~ phase will precipitate out of solution upon slow cooling into the @-plus-~ field. Source: Adapted from 56Rhi

Fig. 41a). The strain on the copper crystals caused aluminum solid solution and the 0 (AI2Cu) phase. equilibrium conditions drastically decreases, by the presence of the zinc atoms, however, pro- This family of alloys (designated the 2xxx series) reaching less than 1% at room temperature. This duces solution hardening in the alloys. As a result, has nominal copper contents ranging from 2.3 to is the typical shape of the solvus line for precipi- the strength of the brasses, in both the work-hard- 6.3 wt%, making them hypoeutectic alloys. tation hardening; if any of these alloys are ho- ened and the annealed conditions, increases with A critical feature of this region of the diagram mogenized at temperatures in or near the solid- increasing zinc content. is the shape of the aluminum solvus line. At the solution phase field, they can be strengthened by The composition range for those brasses con- eutectic temperature (548.2 °C, or 1018.8 °F), aging at a substantially lower temperature. raining higher amounts of zinc (yellow brass and 5.65 wt% Cu will dissolve in aluminum. At lower The Titanium-Aluminum, Titanium-Chro- Muntz metal), however, overlaps into the two- temperatures, however, the amount of copper that mium, and Titanium-Vanadium Systems. The phase (Cu)-plus-13 field. Therefore, the micro- can remain in the aluminum solid solution under phase diagrams of titanium systems are domi- structure of these so-called alpha-beta alloys shows various amounts of 13 phase (see Fig. 41b and c), and their strengths are further increased over those of the alpha brasses. The Aluminum-Copper System. Another al- C~ loy system of great commercial importance is aluminum-copper. Although the phase diagram of this system is fairly complicated (see Fig. 42), the alloys of concern in this discussion are limited to the region at the aluminum side of the diagram where a simple eutectic is formed between the Miscibility gap Sloping solvus: Proeutectoid CXo'~l~l + ~2 decreasing solid reaction solubility with ~o--~ + decreasing temperature £[0 --4~ (y +

Intermediate phase

Intermediate Promonotectoid; similar Heterogeneous phase to miscibility gap ordering; -,/is Io--¢.-I + c~ Cto--~cq + tx2 an ordered phase "~s":"" 37 Fe4).8C alloy showing a typical pearlite eutectoid structure of alternate layers of light ferrite and dark cementite. 500x. Source: 85ASM Fig. 38 Examples of binary phase diagrams that give rise to precipitation reactions. Source: 85ASM 1*22/Introduction to Alloy Phase Diagrams hated by the fact that there are two allotropic forms of solid titanium: cph aTi is stable at room temperature and up to 882 °C (1620 °F); bcc 13Ti is stable from 882 °C (1620 °F) to the melting temperature. Most alloying elements used in commercial titanium alloys can be classified as alpha stabilizers (such as aluminum) or beta stabilizers (such as vanadium and chromium), de- pending on whether the allotropic transformation temperature is raised or lowered by the alloying addition (see Fig. 43). Beta stabilizers are further classified as those that are completely miscible (a) with 13Ti (such as vanadium, molybdenum, tanta- (b) lum, and niobium) and those that form eutectoid systems with titanium (such as chromium and iron). Tin and zirconium also are often alloyed in titanium, but instead of stabilizing either phase, they have extensive solubilities in both aTi and I~Ti. The microstructures of commercial titanium alloys are complicated, because most contain more than one of these four types of alloying elements. The Iron-Carbon System. The iron-carbon diagram maps out the stable equilibrium conditions between iron and the graphitic form of carbon (see Fig. 44). Note that there are three allotropic forms of solid iron: the low-temperature phase, a; the medium-temperature phase, y, and the high-temperature phase, 8. In addition, ferritic iron undergoes a magnetic phase transition at 771 °C (1420 °F) between the low-temperature ferromagnetic state and the higher-temperature para- magnetic state. The common name for bcc a-iron is "ferrite" (fromferrum, Latin for "iron"); the fcc Y phase is called "austenite" after William Roberts-Austen; bcc 8-iron is also commonly called ferrite, because (except for its temperature (c) (d) range) it is the same as a-iron. The main feature Fig. 39 Examples of characteristic precipitation microstructures. (a) General and grain-boundary precipitation of Co3Ti of the iron-carbon diagram is the presence of both (y' phase) in a Co-12Fe-6Ti alloy aged 3 x 103 rain at 800 °C (1470 °F). 1260×. (b) General precipitation a eutectic and a eutectoid reaction, along with the (intragranular Widmanst~itten) and localized grain-boundary precipitation in an AI-1 gAg alloy aged 90 h at 375 °C (710 great difference between the solid solubilities of °F), with a distinct precipitation-free zone near the grain boundaries. 500x. (c) Preferential, or localized, precipitation carbon in ferrite and austenite. It is these features along grain boundaries in a Ni-20Cr-IAI alloy. 500x. (d) Cellular, or discontinuous, precipitation growing out uniformly from the grain boundaries in an Fe-24.BZn alloy aged 6 min at 600 °C (1110 °F). 1000x. Source: 85ASM that allow such a wide variety of microstructures and mechanical properties to be developed in Atomic Percent Zinc iron-carbon alloys through proper heat treatment. 10 II00 The Iron-Cementite System. In the solidifica- I084.87*C tion of steels, stable equilibrium conditions do not exist. Instead, any carbon not dissolved in the iron 1000 is tied up in the form of the metastable intermetallic compound, Fe3C (also called cementite be- 900 cause of its hardness), rather than remaining as free graphite (see Fig. 45). It is, therefore, the 8OO iron-cementite phase diagram, rather than the o iron-carbon diagram, that is important to indus- 70O (Cu) trial metallurgy. It should be remembered, however, that although cementite is an extremely en- (~ 600 - during phase, given sufficient time, or the 500- presence of a catalyzing substance, it will break 0 down to iron and carbon. In cast irons, silicon is ,19.58°C the catalyzing agent that allows free carbon 400- (flakes, nodules, etc.) to appear in the microstructure (see Fig. 46). 300 The boundary lines on the iron-carbon and iron- cementite diagrams that are important to the heat 200- ! treatment of steel and cast iron have been as- i 100 I ...... ~ .... signed special designations, which have been 0 10 20 30 40 50 60 70 ~0 HO ]UU found useful in describing the treatments. These CU Weight Percent Zinc Zn lines, where thermal arrest takes place during I:~n 40 The copper-zinc phase diagram, showing the composition range for five common brasses. Source: Adapted "b heating or cooling due to a solid-state reaction, from 90Mas Introduction to Alloy Phase Diagrams/1.23

(b) (c)

Fig. 41 The microstruduresof two common brasses. (a) C26000 (cartridgebrass, 70%), hot rolled,annealed, cold rolled 70%, and annealed at 638 °C (1180 °F), showing equiaxed grains of copper solid solution.Some grains are twinned. 75x. (b) C28000 (Muntz metal, 60%) ingot, showingdendrites of copper solid solution in a matrixof 13. 200x. (c) C28000 (Muntz metal, 60%), showing feathers of copper solid solutionthat formed at I] grain boundariesduring quenching of the all-[~structure. 100x. Source:85ASM are assigned the letter "A" for arr~t (French for sisting of carbide and transformed austenite, plus microstructures that result from these treatments "arrest"). These designations are shown in Fig. carbide precipitated from austenite and particles is beyond the scope of a discussion of stable and 45. To further differentiate the lines, an "e" is of free carbon. For slowly cooled hypereutectic metastable equilibrium phase diagrams. Phase added to identify those indicating the changes cast iron (between 4.3 and 6.67% C), the micro- diagrams are invaluable, however, when design- occurring at equilibrium (to give Ae], Ae3, Ae4, structure shows primary particles of carbide and ing heat treatments. For example, normalizing is and Aecm). Also, because the temperatures at free carbon, plus grains of transformed austenite. usually accomplished by air cooling from about which changes actually occur on heating or cool- Cast irons and steels, of course, are not used in 55 °C (100 °F) above the upper transformation ing are displaced somewhat from the equilibrium their slowly cooled as-cast condition. Instead, temperature (A3 for hypoeutectoid alloys and Acre values, the"e"is replaced with"c" (for chauffage, they are more rapidly cooled from the melt, then for hypereutectoid alloys). Full annealing is done French for "heating") when identifying the subjected to some type of heat treatment and, for by controlled cooling from about 28 to 42 °C (50 slightly higher temperatures associated with wrought steels, some type of hot and/or cold to 75 °F) above A3 for both hypoeutectoid and changes that occur on heating. Likewise, "e" is work. The great variety of microconstituents and hypereutectoid alloys. All tempering and process replaced with "r" (for refroidissement, French for "cooling") when identifying those slightly lower temperatures associated with changes occurring Atomic Percent Copper on cooling. These designations are convenient 0 20 30 40 50 60 70 80 90 100 terms because they are used not only for binary 110o ,I..... I .... :I084.87"C alloys of iron and carbon, but also for commercial /- steels and cast irons, regardless of the other elements present in them. Alloying elements such as 100o -f14 manganese, chromium, nickel, and molybdenum, however, do affect these temperatures (mainly 900 L A3). For example, nickel lowers A3, whereas chromium raises it. The microstructures obtained in steels by ~o Boo slowly cooling are as follows. At carbon contents k~ from 0.007 to 0.022%, the microstructure consists = of ferrite grains with cementite precipitated in ~ 700 from ferrite, usually in too fine a form to be visible ~660.4~z by light microscopy. (Because certain other metal atoms that may be present can substitute for some 6oo= of the iron atoms in Fe3C, the more general term, ~__ 54B.2°C "carbide," is often used instead of "cementite" when describing microstructures.) In the hypoeu- 8oo tectoid range (from 0.022 to 0.76% C), ferrite and (c~) pearlite grains constitute the microstmcture. In 400 the hypereutectoid range (from 0.76 to 2.14% C), pearlite grains plus carbide precipitated from austenite are visible. 300 ,, ...... , ,, ..... , ,,,,11.... '~ q,, II I,.I, -~ Slowly cooled hypoeutectic cast irons (from 1ot 'lO" 20 ...... 30 .... 40 ...... 50 6'0 '"70 8'0 90 100 2.14 to 4.3% C) have a microstructure consisting A1 Weight Percent Copper Cu of dendritic pearlite grains (transformed from hypoeutectic primary austenite) and grains of Fig, 42 The aluminum-copper phase diagram, showing the composition range for the 2xxx series of precipitation-har- iron-cementite eutectic (called"ledeburite") con- denable aluminum alloys. Source: 90Mas 1.24/Introduction to Alloy Phase Diagrams

Atomic Percent Aluminum Atomic Percent Vanadium IO 20 30 40 50 60 70 80 90 I00 10 20 30 40 50 60 70 80 00 O0 ..... q . p.i ...... r i .... i ...... I. J i I i ~ ...... ~{ ...... ) ...... ,~ .... I I k I ...... 1910~ 1700 1670°C

1700- 1870"C 1500- 1805"C (BTi)~// 1500- , rj U o 1300 o

1300 (flTi,V) ~ n00

noo-

900 /.// 802*¢ 900

700 885"C 60.452"C ...... --.,,, : (hl)~ 5o0 .... , ; ...... ]II ...... , " ~aTiAla 500 +.i...... , ...... , ...... , ...... , ...... r ...... j..A .... 40 00 6o ...... 7'o7'~; ...... o ...... ~ ~oo 0 10 20 30 40 50 60 70 80 00 100 Ti Weight Percent Aluminum A1 Ti Weight Percent Vanadium V

Atomic Percent Chromium l0 20 30 40 50 60 ?0 00 90 100 2000 I i I J L i

1000 86-3*C

1670"C 1600 Z

1400 1370"C

(flTi,Cr) ~ "

tooo

882*0

0oo ~ aTiCr2

Ti Weight Percent Chromium Cr

Fig. 43 Three representative binary titanium phase diagrams, showing alpha stabilization (Ti-AI), beta stabilization with complete miscibility (Ti-V), and beta stabilization with a eutectoid reaction (Ti-Cr). Source: 90Mas

annealing opeF,ations are done at temperatures with txFe. This continuous bcc phase field con- steel, which contains about 8% Ni, is an all- below the lower transformation temperature (A1). firms that 8-ferrite is the same as ct-ferrite. The austenite alloy at 900 °C (1652 °F), even though Austenitizing is done at a temperature sufficiently nonexistence of T-iron in Fe-Cr alloys having it also contains about 18% Cr. above A3 and Acm to ensure complete transforma- more than about 13 % Cr, in the absence of carbon, tion to austenite, but low enough to prevent grain is an important factor in both the hardenable and growth from being too rapid. nonhardenable grades of iron-chromium stain- Practical Applications of Phase The Iron-Chromium-Nickel System. Many less steels. At these lower temperatures, a material Diagrams commercial cast irons and steels contain ferrite- known as sigma phase also appears in different stabilizing elements (such as silicon, chromium, amounts from about 14 to 90% Cr. Sigma is a The following are but a few of the many in- molybdenum, and vanadium) and/or austenite hard, brittle phase and usually should be avoided stances where phase diagrams and phase relation- stabilizers (such as manganese and nickel). The in commercial stainless steels. Formation of ships have proved invaluable in the efficient solv- diagram for the binary iron-chromium system is sigma, however, is time dependent; long periods ing of practical metallurgical problems. representative of the effect of a ferrite stabilizer at elevated temperatures are usually required. (see Fig. 47). At temperatures just below the The diagram for the binary iron-nickel system Alloy Design solidus, bcc chromium forms a continuous solid is representative of the effect of an austenite sta- solution with bcc (5) ferrite. At lower tempera- bilizer (see Fig. 47). The fcc nickel forms a con- Age Hardening Alloys. One of the earliest uses tures, the T-iron phase appears on the iron side of tinuous solid solution with fcc (7) austenite that of phase diagrams in alloy development was in the diagram and forms a "loop" extending to dominates the diagram, although the (x-ferrite the suggestion in 1919 by the U.S. Bureau of about 11.2% Cr. Alloys containing up to 11.2% phase field extends to about 6% Ni. The diagram Standards that precipitation of a second phase Cr, and sufficient carbon, are hardenable by for the ternary iron-chromium-nickel system from solid solution would harden an alloy. The quenching from temperatures within the loop. shows how the addition of ferrite-stabilizing age hardening of certain aluminum-copper alloys At still lower temperatures, the bcc solid solu- chromium affects the iron-nickel system (see Fig. (then called "Duralumin" alloys) had been acci- tion is again continuous bcc ferrite, but this time 48). As can be seen, the popular 18-8 stainless dentally discovered in 1904, but this process was Introduction to Alloy Phase Diagrams/l*25

Atomic Percent Carbon composition away from the 13Mn phase field. The 0 10 gO 30 carbon addition also would further stabilize the I ...... i 'I ...... t ..... I .... L ...... i ' j ...... i austenite phase, permitting reduced manganese content. With this information, the composition ~ooo L / of the alloy was modified to 7 to 10% A1, 30 to 35% Mn, and 0.75 to 1% C, with the balance iron. It had good mechanical properties, oxidation resistance, and moderate stainlessness. 1538 C~/~SFe) / L + C(graphite) Permanent Magnets. A problem with perma-

°~ 1394° nent magnets based on Fe-Nd-B is that they show high magnetization and coercivity at room tem- ] ~Ke~,.. \ "-..~ .~.c perature, but unfavorable properties at higher I ausz, emr.e/2.1 42 temperatures. Because hard magnetic properties 1000- are limited by nucleation of severed magnetic domains, the surface and interfaces of grains in \/ .o.o the sintered and heat-treated material are the con- 0.65 trolling factor. Therefore, the effects of alloying 500- additives on the phase diagrams and microstruc- tural development of the Fe-Nd-B ahoy system V-(aFe), ferrite plus additives were studied. These studies showed that the phase relationships and domain- nucleation difficulties were very unfavorable for ...... i ...... i ...... i ...... t ...... i 2 4 6 8 10 12 the production of a magnet with good magnetic Fe Weight Percent Carbon properties at elevated temperatures by the sinter- ing method. However, such a magnet might be

Fig. 44 The iron-carbon phase diagram. Source: Adapted from 90Mas produced from Fe-Nd-C material by some other process, such as melt spinning or bonding (see 91Hay). thought to be a unique and curious phenomenon. aluminum may substitute for chromium because The work at the Bureau, however, showed the it stabilizes the a-iron phase (ferrite), leaving Processing scientific basis of this process (which was dis- only a small T loop (see Fig. 47 and 49). Alumi- cussed in previous sections of this Introduction). num is known to impart good high-temperature Hacksaw Blades. In the production of hacksaw This work has now led to the development of oxidation resistance to iron. Next, the literature blades, a strip of high-speed steel for the cutting several families of commercial "age hardening" on phase diagrams of the aluminum-iron-manga- edges is joined to a backing strip of low-alloy steel alloys covering different base metals. nese system was reviewed, which suggested that by laser or electron beam welding. As a result, a Austenitic Stainless Steel. In connection with a range of compositions exists where the alloy very hard martensitic structure forms in the weld a research project aimed at the conservation of would be austenitic at room temperature. A non- area that must be softened by heat treatment be- magnetic alloy with austenitic structure contain- always expensive, sometimes scarce, materials, fore the composite strip can be further rolled or the question arose: Can manganese and alumi- ing 44% Fe, 45% Mn, and 11% A1 was prepared. set. To avoid the cost of the heat treatment, an However, it proved to be very brittle, presumably num be substituted for nickel and chromium in alternative technique was investigated. This tech- because of the precipitation of a phase based on stainless steels? (In other words, can standard nique involved ahoy additions during welding to chromium-nickel stainless steels be replaced with 13-Mn. By examining the phase diagram for car- create a microstructure that would not require an austenitic ahoy system?) The answer came in bon-iron-manganese (Fig. 50), as well as the dia- subsequent heat treatment. Instead of expensive gram for aluminum-carbon-iron, the researcher two stages---in both instances with the help of experiments, several mathematical simulations phase diagrams. It was first determined that man- determined that the problem could be solved were made based on additions of various steels or ganese should be capable of replacing nickel be- through the addition of carbon to the aluminum- pure metals. In these simulations, the hardness of cause it stabilizes the T-iron phase (austenite), and iron-manganese system, which would move the

Atomic Percent Carbon Atomic Percent Carbon Atomic Percent Carbon 5 1o 15 20 25 o oo5 ol o15 ....1600 ...... ,' ...... ,, L...... , ...... L ,, ...... /,I ...... , ...... leoo ...... , i...... , ...... , ..... , .... i .... o ...... i ...... L ...... i ..... (~F.I L 1400 13~'C t5:~"¢ L l~"C 771 e 0.022 72~C 1200 1500 A1 P o

4001 (TFe)' austenite

"A,,, 200

c°°~aFe), ferrite

0 I O;t O;Z 4oo~ ...... 1...... ~..... :~ ...... k ...... ~...... ~.... 02 0.4 06 08 ...... b;a...... 0 Fe Weight Percent Carbon Fe Weight Percent Carbon Fe Weight Percent Carbon

Fig, 45 The iron-cementite phase diagram and details of the (6Fe) and (aFe) phase fields. Source: Adapted from 90Mas 1e26/Introduction to Alloy Phase Diagrams the weld was determined by combining calcula- mium borides and chromium matrix were made eutectics could be causing the problem. Investi- tions of the equilibrium phase diagrams and avail- and tested. Subsequent fine tuning of the compo- gation of the furnace system resulted in the dis- able information to calculate (assuming the aver- sition to ensure fabricability of welding rods, covery that the tubes conveying protective atmos- age composition of the weld) the martensite weldability, and the desired combination of cor- phere to the furnace were made of sulfur-cured transformation temperatures and amounts of re- rosion, abrasion, and impact resistance led to a rubber, which could result in liquid metal being tained austenite, unWansformed ferrite, and car- patented alloy. formed at temperatures as low as 637 °C (1179 bides formed in the postweld microstructure. Of °F) (see Fig. 51). Armed with this information, a those alloy additions considered, chromium was Performance metallurgist solved the problem by substituting found to be the most efficient (see 91Hay). neoprene for the robber. Hardfaeing. A phase diagram was used to de- Heating elements made of Nichrome (a nickel- Electric Motor Housings. At moderately high sign a nickel-base hardfacing alloy for corrosion chromium-iron alloy registered by Driver-Harris service temperatures, cracks developed in electric and wear resistance. For corrosion resistance, a Company, Inc., Harrison, NJ) in a heat treating motor housings that had been extruded from alu- matrix of at least 15% Cr was desired; for abra- fumace were failing prematurely. Reference to minum produced from a combination of recycled sion resistance, a minimum amount of primary nickel-base phase diagrams suggested that low- and virgin metal. Extensive studies revealed that chromium-boride particles was desired. After melting eutectics can be produced by very small the cracking was caused by small amounts of lead consulting the B-Cr-Ni phase diagram, a series of quantities of the chalcogens (sulfur, selenium, or and bismuth in the recycled metal reacting to form samples having acceptable amounts of total chro- tellurium), and it was thought that one of these bismuth-lead eutectic at the grain boundaries at 327 and -270 °C (621 and -518 °F), respectively, much below the melting point of pure aluminum (660.45 °C, or 1220.81 °F) (see Fig. 52). The question became: How much lead and bismuth can be tolerated in this instance? The phase diagrams showed that aluminum alloys containing either lead or bismuth in amounts exceeding their respective solubility limits (<0.05% and .4).2%) can lead to hot cracking of the aluminum. Carbide Cutting Tools. A manufacturer of carbide cutting tools once experienced serious trouble with brittleness of the sintered carbide. No impurities were found. The range of compositions for cobalt-bonded sintered carbides is shown in the shaded area of Fig. 53, along the dashed line connecting pure tungsten carbide (marked "WC") on the right and pure cobalt at the lower left. At 1400 °C (2552 °F), materials with these compositions consist of particles of tungsten carbide (a) (b) suspended in liquid metal. However, when there is a deficiency of carbon, compositions drop into the region labeled WC + 1] + liquid, or the region Fig. 46 The microstructures of two types of cast irons. (a) As-cast class 30 gray iron, showing type A graphite flakes in labeled WC + q where tungsten carbide particles a matrix of pearlite. 500x. (b) As-cast grade 60-45-I 2 ductile iron, showing graphite nodules (produced by the addition of a calcium-silicon compound during pouring) in a ferrite matrix. 100x. Source: 85ASM are surrounded by a matrix of q phase. The TI

Atomic Percent Chromium Atomic Percent Nickel I0 20 30 40 50 60 70 80 90 100 10 20 30 40 50 60 ?0 80 90 100 1900 1538' 1514"C L 1440°C __ L455"C 1700 140( 67 1394"C

1538"C 1500! 1200 1394~C ]300; p 1000 (TFe,Hl)

1100

11.2 18,4 012"C 900 - E-= ~ (aFe,,~Fe) 630°C =~c ?7O'( ...... :-..T.c ~~g~-.. 800 ~...... To -"" ...... -" ...... ~S(Tr~'NI) 700

5OO 4OO " 354 8"C

30O 2O0 10 20 30 40 50 60 70 80 90 100 10 20 30 40 50 60 70 80 90 100 Fe Weight Percent Chromium Cr Fe Weight Percent Nickel Ni

Fig, 47 Two representative binary iron phase diagrams, showing ferrite stabilization (Fe-Cr) and austenite stabilization (Fe-Ni). Source: 90Mas Introduction to Alloy Phase Diagrams/1.27

Cr problem and its solution, which could have been avoided had the proper phase diagram been ex- amined (see Fig. 54). to /I \ A question concerning purple plague problems, ~// ~_9o however, has remained unresolved: whether or e0 / / \ not the presence of silicon near the gold-alumi- -// 'K- num interface has an influence on the stability and rate of formation of the damaging intermetallic / \ phase. An examination of the phase relationships in the A1-AI2Au-Si subtemary system showed no 40 stable ternary AI-Au-Si phases (see 91Hay). It was suggested instead that the reported effect of silicon may be due to a reaction between silicon ^b ,50 /,.7%%~,, (Cr) + (TFe,Ni) \ '~c" and alumina (A1203) at the aluminum-gold interface that becomes thermodynamically feasible in .'~ 6,, /-1~% \ ', ~ %, the presence of gold. -..'~ ~/,,~ '~ \-,, ~ o~ _y,/~ \-,, v_ ".~. ~? 40 BIBLIOGRAPHY

35Mar: J.S. Marsh, Principles of Phase Dia- grams, McGraw-Hill, 1935. This out-of-print oo /,, ..,.~/-- \ book is an early thorough presentation of the ~/,'.~ ~/' ~ z0 l/,~I;<~ ...... \ principles of heterogeneous equilibrium in or- ganic, inorganic salt, and metallic systems. 44Mas: G. Masing (B.A. Rogers, transl.), Ter- nary Alloys: Introduction to the Theory of Three Component Systems, Reinhold, 1944; available from U.M-I, 300 North Zeeb Rd., Ann Arbor, MI

Fe 10 Z0 30 40 50 60 70 80 90 Ni 48106. This out-of-print book, originally published in German in 1932, is one of the first to Weight Percent Nickel thoroughly discuss the theory underlying ternary alloy systems and their application to industrial Fig. 48 The isothermalsection at 900 °C (1652 °F) of the iron-chromium-nickelternary phase diagram, showingthe nominal compositionof 18-8 stainlesssteel. Source:Adapted from Ref 1 alloys. 56Rhi: EN. Rhines, Phase Diagrams in Metal- lurgy: Their Development and Application, McGraw-Hill, 1956. This out-of-print book is a phase is known to be brittle. The upward adjust- gold lead wires were fused to aluminized transis- basic text designed for undergraduate students in ment of the carbon content by only a few hun- tor and integrated circuits. A purple residue was metallurgy. dredths of a weight percent eliminated this prob- formed, which was thought to be a product of 66Pri: A. Prince, Alloy Phase Equilibria, El- lem. corrosion. Actually, what was happening was the sevier, 1966. This out-of-print book covers the Solid-State Electronics. In the early stages of formation of an intermetallic compound, an alu- thermodynamic approach to binary, ternary, and the solid-state industry, a phenomenon known as minum-gold precipitate (AlxAu) that is purple in quaternary phase diagrams. the "purple plague" nearly destroyed the fledg- color and very brittle. Millions of actual and 68Got: P. Gordon, Principles of Phase Dia- ling industry. Components were failing where the opportunity dollars were lost in identifying the grams in Materials Systems, McGraw-Hill, 1968;

Atomic Percent Aluminum Atomic Percent Manganese 10 20 30 40 50 60 70 80 90 lOO I0 20 30 40 50 60 70 80 90 oo 1600 I [ I I I ..L ~ I ...... 1600 "r ...... liSa'C: 1538"C

140o- 1400 1304"c 18ml,'C 1310"C 246"C 11~5"C 1200- 1200 L) p / '.. ~,~ o 1100"C

P 1000- 2 (TFe.7~n) 012*C i ; h BOO - Fekl ~ : • J iiII ¢: ,al~I~ i ~ 8002 -~.Te .i ,<~ . ) ,i.< ~,, i i i 600

H I Ill 400 \ 11 I II~ \ . i ii i •~--.Fesll II I l: ~ (kl

400 2o0 ...... I 10 0 30 40 50 60 70 80 00 100 ...... ~o...... ~'o...... ~'o...... 8"~o...... g'o...... i& Fe Weight Percent Aluminum AI Fe Weight Percent Manganese M~

Fig. 49 The aluminum-iron and iron-manganese phase diagrams. Source: Ref 2 1*28/Introduction to Alloy Phase Diagrams

reprinted by Robert E. Krieger Publishing, 1983. 81Goo: D.A. Goodman, J.W. Cahn, and L.H. 85ASM: Metals Handbook, 9th ed., Vol 9, Met- Covers the thermodynamic basis of phase dia- Bennett, The Centennial of the Gibbs-Konovalov allography and Microstructures, American Soci- grams; the presentation is aimed at materials Rule for Congruent Points, Bull. Alloy Phase ety for Metals, 1985. A comprehensive reference engineers and scientists. Diagrams, Vol 2 (No. 1), 1981, p 29-34. Presents covering terms and definitions, metallographic 70Kau: L. Kaufman and H. Bemstein, Com- the theoretical basis for the rule and its applica- techniques, microstructures of industrial metals puter Calculations of Phase Diagrams, Aca- tion to phase diagram evaluation. and alloys, and principles of microstructures and demic Press, 1970.A comprehensive presentation 81Hil: M. Hillert, A Discussion of Methods of crystal structures. of thermodynamic modeling with the aid of com- Calculating Phase Diagrams, Bull. Alloy Phase 89Mas: T.B. Massalski, Phase Diagrams in Ma- puters. Diagrams, Vol 2 (No. 3), 1981, p 265-268. Pre- terials Science, ASM News, Vol 20 (No. 7), July 75Gok: N.A. Gokcen, Thermodynamics, Tech- sents a brief description of the various methods 1989, p 8-9. A concise presentation of the role of science, 1975. Chapter XV discusses the role of for thermodynamic modeling ofphase diagrams. phase diagrams in materials science, and the thermodynamics in phase diagrams and Gibbs 82Peh A.D. Pelton, W.T. Thompson, and C.W. worldwide efforts to make reliable diagrams energy diagrams. Bale, F*A*C*T* (Facility for the Analysisof readily available. 77Luk: H.L. Lukas, E.T. Henig, and B. Zim- Chemical Thermodynamics), McGill University, 90Mas: T.B. Massalski, Ed., Binary Alloy merman, Optimization of Phase Diagrams by a 1982. Describes a thermodynamic database and Phase Diagrams, 2nd ed., ASM Intemational, Least Squares Method Using Simultaneously computer program for modeling phase diagrams. 1990. The most comprehensive collection of bi- Different Types of Data, Calphad, Vol 1 (No. 3), 84Mor: J.E. Mortal, Two-Dimensional Phase nary phase diagrams published to date: dia- 1977, p 225-236. Presents the use of a computer- Fraction Charts, Scr. Metall., Vol 18 (No. 4), grams for 2965 systems, presented in both atomic aided program for determining phase boundary 1984, p 407-410. Gives a general description of and weightpercent, with crystal data and discus- lines that best fit scattered data points. phase-fraction charts. sion.

Atomic Percent Sulfur 10 30 40 50 00 ..... I .... ,,j 20...... L, ...... I., ..... I .... , .... J .... r''

...... :Ill 1200 o ~o d

/ .....600000- (Ni) (Ni)++L8~ ,i ~ ~,Lc~CJ~ ~--~ ///': I

7 2oo- (Ni)

...... 1o 20 30 40 '5~' lee Weight Percent Manganese Mn Ni Weight Percent Sulfur

Fig. 50 The isothermal sedion at 1100 °C (2012 °F) of the iron-manganese-carbon Fig. 51 The nickel-sulfur phasediagram. Source: Adapted from 90Mas phase diagram. Source: Adapted from Ref 3

Atomic Percent Bismuth Atomic Percent Lead , Z 3 4 ..5.1 1 2 3 4 5 ...... , .... I ..... i ...... I..i, .I,i I,i 1200 ...... i .... i .... r ...... J . . i ...... I , i ...... I . i ...... l

1100

L L

gO0

U i/ o o 8OO- ¢~ 700-

~ 81111-

(AI) + L (AI) + L

~Z7~¢ ~AI) (bl) + (Pb) ----(AI) (A0 + (m) Ib ...... :,~ ...... ~ ...... ~5 ...... 3o 2oo! ...... ~ ...... ~b...... ~ ...... ~ ...... 2'5...... so Weight Percent Bismuth AI Weight Percent Lead

Fig. 52 The aluminum-bismuth and aluminum-lead phasediagrams. Source: Adapted from 90Mas Introduction to Alloy Phase Diagrams/I,,29

Atomic Percent Gold 5 1o 15 2O 30 40 50 6070 100 .~. llrl., I.....

I064.43"C 100o

o~ L (Au~

WC(tungsten carbide) 0oo ~ ~ -~C+n +liquid 660.452"( 7.,5 625"C 62 7AIAu --~ L'C aAIAu ~_ Liqu" ~(AI) BAIAu _

AIAu~ 400 ...... ~b...... z~6...... 3'0 ...... 4'6 ...... ~o ...... 0'0 ...... Vo...... 00 0o ioo Co W A] Weight Percent Gold Au

The isothermal section at 1400°C(2552 °F)ofthecobalt-tungsten-carbon phase Fig. 54 The aluminum-gold phasediagram, Source: Ref 5 Fig. 53 diagram. Source: Adapted from Ref 4

91Hay: EH. Hayes, Ed., User Aspects of Phase Diagrams, The Institute of Metals, London, 1991. A collection of 35 papers and posters presented Volume Fraction at a conference held June 1990 in Petten, The Netherlands. In order to relate the weight fraction of a phase present in an alloy specimen as determined from a phase 91Mor: J.E. Morral and H. Gupta, Phase diagramto its two-dimensional appearance as observed in a micrograph, it is necessary to be able to convert Boundary, ZPF, and Topological Lines on Phase between weight-fraction values and areal-fraction values, both in decimal fractions. This conversion can be Diagrams, Scr. Metall., Vol 25 (No. 6), 1991, p developed as follows: 1393-1396. The weight fraction of the phase is determined from the phase diagram, using the lever rule. Reviews three different ways of considering the lines on a phase diagram. 91Okal: H. Okamoto and T.B. Massalski, Volume portion of the phase = weight fraction of the phase phase density Thermodynamically Improbable Phase Dia- grams, J. Phase Equilibria, Vol 12 (No. 2), 1991, Total volume of all phases present = sum of the volume portions of each phase. p 148-168. Presents examples ofphase-rule violations and problems with phase-boundary curvatures; also discusses unusual diagrams. Volume fraction of the phase = weight fraction of the phase 91Oka2: H. Okamoto, Reevaluation of Ther- phase density x total volume modynamic Models for Phase Diagram Evalu- ation, J. Phase Equilibria, Vol 12 (No. 6), 1991, It has been shown by stereology and quantitative metallography that areal fraction is equal to volume fraction [85ASM]. (Areal fraction of a phase is the sum of areas of the phase intercepted by a microscopic p 623-643. Reviews the basic principles of ther- traverse of the observed region of the specimen divided by the total area of the observed region.) Therefore: modynamic calculation of phase diagrams, simplification of thermodynamic models, and reli- Areal fraction of the phase = weight fraction of the phase ability of thermodynamic data and parameters; phase density x total volume also presents examples of unlikely calculated phase diagrams. The phase density value for the preceding equation can be obtained by measurement or calculation. The 91Vih P. Villars and L.D. Calvert, Pearson's densities of chemical elements, and some line compounds, can be found in the literature. Alternatively, the Handbook of Crystallographic Data for Interme- density of a unit cell of a phase comprising one or more elements can be calculated from information about diate Phases, ASM International, 1991. This third its crystal structure and the atomic weights of the elements comprising it as follows: edition of Pearson's comprehensive compilation includes data from all the international literature atomic weight from 1913 to 1989. Weight of each element = number of atoms x Avogadro's number OTHER REFERENCES Total cell weight = sum of weights of each element 1. G.V. Raynor and V.G. Rivlin, Phase Equili- bria in Iron Ternary Alloys, Vol 4, The Density = total cell weight / cell volume Institute of Metals, London, 1988 2. H. Okamoto, Phase Diagrams of Binary For example, the calculated density of pure copper, which has a fcc structure and a lattice parameter of Iron Alloys, ASM International, 1992 0.36146 nm, is: 3. R. Benz, J.E Eiliott, and J. Chipman, Met- all. Trans., Vol 4, 1973, p 1449 4 atoms/cell x 63.546 g/tool 4. P. Rautala and J.T. Norton, p = = 8.937Mg/m 3 Trans. AIME, 6.0227 x 1023 atoms/mol x (0.36146 x 10-9 m) 3 Vol 194, 1952,p 1047 5. H. Okamoto, Ed., Binary Alloy Phase Dia- This compares favorably with the published value of 8.93. grams Updating Service, ASM Interna- tional, 1992