Some key phase diagrams

3.2.8 Some key phase diagrams

3.2.8.1 Copper–zinc system Phase diagrams for most systems, metallic and

ceramic, are usually more complex than the examples discussed so far. Figure 3.20 for the Cu–Zn system illustrates this point. The structural characteristics and mechanical behaviour of the industrial alloys known as brasses can be understood in terms of the copper- rich end of this diagram. Copper can dissolve up to 40% w/w of zinc and cooling of any alloy in this range will produce an extensive primary solid solution (fcc- ˛ extremely limited. A special feature of the diagram is the presence of four intermediate phases (ˇ, , υ, ε). Each is formed during freezing by peritectic reaction and each exists over a range of composition. Another notable feature is the order–disorder transformation which occurs in alloys containing about 50% zinc over the temperature range 450–470 °

C. Above this

temperature range, bcc ˇ-phase exists as a disordered solid solution. At lower temperatures, the zinc atoms are distributed regularly on the bcc lattice: this ordered

phase is denoted by ˇ 0 .

Suppose that two thin plates of copper and zinc are held in very close contact and heated at a temperature

Figure 3.20 Phase diagram for copper–zinc (from Raynor; courtesy of the Institute of Metals) .

of 400 °

C for several days. Transverse sectioning of the diffusion couple will reveal five phases in the sequence ˛ face. The υ-phase will be absent because it is unstable at temperatures below its eutectoid horizontal ⊲560 ° C⊳. Continuation of diffusion will eventually produce one or two phases, depending on the original proportions of copper and zinc.

3.2.8.2 Iron–carbon system The diagram for the part of the Fe–C system shown

in Figure 3.21 is the basis for understanding the microstructures of the ferrous alloys known as steels and cast irons. Dissolved carbon clearly has a pro- nounced effect upon the liquidus, explaining why the difficulty of achieving furnace temperatures of 1600 ° C caused large-scale production of cast irons to predate that of steel. The three allotropes of pure iron are ˛-Fe

(bcc), -Fe (fcc) and υ-Fe (bcc). 1 Small atoms of car- bon dissolve interstitially in these allotropes to form three primary solid solutions: respectively, they are ˛- phase (ferrite), -phase (austenite) and υ-phase. At the other end of the diagram is the orthorhombic interme-

diate phase Fe 3 C, which is known as cementite. The large difference in solid solubility of carbon in austenite and ferrite, together with the existence of

a eutectoid reaction, are responsible for the versatile behaviour of steels during heat-treatment. Ae 1 , Ae 2 , Ae 3 and A cm indicate the temperatures at which phase changes occur: they are arrest points for equilibria detected during thermal analysis. For instance, slow cooling enables austenite (0.8% C) to decompose

eutectoidally at the temperature Ae 1 and form the microconstituent pearlite, a lamellar composite of soft,

1 The sequence omits ˇ-Fe, a term once used to denote a non-magnetic form of ˛-Fe which exists above the Curie

point.

Structural phases: their formation and transitions 61

Figure 3.21 Phase diagram for Fe–C system (dotted lines represent iron-graphite equilibrium) .

ductile ferrite (initially 0.025% C) and hard, brittle liquid miscibility is complete. The upper isothermal cementite (6.67% C). Quenching of austenite from a

represents a monotectic reaction, i.e. L 1 ⇀ ↽˛CL 2 . temperature above Ae 3 forms a hard metastable phase

On cooling, a hyper-monotectic 50Cu–50Pb melt known as martensite. From the diagram one can see

will separate into two liquids of different composition. why a medium-carbon (0.4%) steel must be quenched

The degree of separation depends on cooling condi- from a higher Ae 3 temperature than a high-carbon

tions. Like oil and water, the two liquids may form an (0.8%) steel. Temperature and composition ‘windows’

emulsion of droplets or separate into layers according for some important heat-treatment operations have

C, the copper-rich been superimposed upon the phase diagram.

to density. At a temperature of 954 °

liquid L 1 disappears, forming ˛ crystals and more of the lead-rich liquid L 2 . This liquid phase gets richer

3.2.8.3 Copper–lead system in lead and eventually decomposes by eutectic reac- The phase diagram for the Cu–Pb system (Figure 3.22)

tion, i.e. L 2 ⇀ ↽ ˛ C ˇ. (Tie-lines can be used for all provides an interesting example of extremely limited

two-phase fields, of course; however, because of den- solubility in the solid state and partial immiscibility

sity differences, mass ratios may differ greatly from in the liquid state. The two components differ greatly

observed volume ratios.)

in density and melting point. Solid solutions, ˛ and The hypo-monotectic 70Cu–30Pb alloy, rapidly ˇ , exist at the ends of the diagram. The ‘miscibility

cast, has been used for steel-backed bearings: dispersed gap’ in the liquid phase takes the form of a dome-

friction-reducing particles of lead-rich ˇ are supported

in a supporting matrix of copper-rich ˛. Binary above the top of the dome, the critical point,

shaped two-phase ⊲L 1 CL 2 ⊳ field. At temperatures

combinations of conductive metal (Cu, Ag) and

62 Modern Physical Metallurgy and Materials Engineering

Figure 3.22 Phase diagram for Cu–Pb system (by permission of the Copper Development Association, 1993) .

refractory arc-resistant metal (W, Mo, Ni) have make steel-making, glass-making, heat-treatment, etc. been used for electrical contacts (e.g. 60Ag–40Ni).

possible. The profile of its liquidus shows a minimum These particular monotectic systems, with their liquid

and thus mirrors the refractoriness of aluminosilicate immiscibility, are difficult to cast and are therefore

refractories (Figure 3.24). Refractoriness, the prime made by powder metallurgy techniques.

requirement of a refractory, is commonly determined by an empirical laboratory test. A sample cone of a

3.2.8.4 Alumina–silica system given refractory is placed on a plaque and located at The binary phase diagram for alumina–silica

the centre of a ring of standard cones, each of which (Figure 3.23) is of special relevance to the refractories

has a different softening or slumping temperature and industry, an industry which produces the bricks,

is identified by a Pyrometric Cone Equivalent (PCE) slabs, shapes, etc. for the high-temperature plant that

number. All cones are then slowly heated until the

Structural phases: their formation and transitions 63 of lime (CaO) flux at a temperature of 1450 °

C: the final structure consists of tridymite, cristobalite and a minimal amount of unconverted quartz. Tridymite is preferred to cristobalite because of the large volume change (¾1%) associated with the ˛/ˇ cristobalite inversion. The lime forms an intergranular bond of

SiO 2 –CaO glass. Chequerwork assemblies of silica bricks are used in hot-blast stoves that regeneratively preheat combustion air for iron-making blast furnaces to temperatures of 1200–1300 °

C. Silica bricks have

a surprisingly good refractoriness-under-load at tem- peratures only 50 °

C or so below the melting point of pure silica 1723 ° C⊳. Apparently, the fired grains of tridymite and cristobalite interlock, being able to withstand a compressive stress of, say, 0.35 MN m at these high temperature levels.

Firebricks made from carefully-selected low-iron clays are traditionally used for furnace-building. These

Figure 3.23 Phase diagram for SiO 2 –Al 2 O 3 system .

clays consist essentially of minute platey crystals of kaolinite, Al 2 ⊲ Si 2 O 5 ⊳⊲ OH⊳ 4 : the (OH) groups are expelled during firing. The alumina content (46%) of fired kaolinite sets the upper limit of the normal composition range for firebricks. Refractoriness rises steeply with alumina content and aluminous fireclays containing 40% or more of alumina are therefore par- ticularly valued. A fireclay suitable for refractories should have a PCE of at least 30 (equivalent to 1670 ° C): with aluminous clays the PCE can rise to 35 ⊲1770 ° C⊳. Firing the clay at temperatures of 1200–1400 °

C forms a glassy bond and an interlock- ing mass of very small lath-like crystals of mullite; this is the intermediate phase with a narrow range of composition which marks the edge of the important ⊲ mullite C corundum⊳ plateau. High-alumina bricks, with their better refractoriness, have tended to replace firebricks. An appropriate raw material is obtained by taking clay and adding alumina (bauxite, artifi-

cial corundum) or a ‘sillimanite-type’ mineral, Al 2 SiO 5 (andalusite, sillimanite, kyanite). Phase transformations in ceramic systems are Figure 3.24 Refractoriness of aluminosilicate ceramics .

generally more sluggish than in metallic systems and steep concentration gradients can be present on a micro-scale. Thus tie-lines across the silica–mullite

sample cone bends or slumps under gravity: the PCE field usually only give approximate proportions of of a standard cone that has behaved similarly is noted

these two phases. The presence of traces of catalysing and taken to represent the refractoriness of the sample.

mineralizers, such as lime, can make application of the It will be realized that the end-point of the PCE test

diagram nominal rather than rigorous. For instance, is rather arbitrary, being a rising-temperature value.

although silica bricks are fired at a temperature of (Other requirements may include refractoriness-under-

C, which is within the stability range of tridymite load, resistance to thermal shock, resistance to attack

⊲ 870–1470 ° C⊳, cristobalite is able to form in quantity. by molten slag, low thermal conductivity, etc.)

However, during service, true stability is approached The steeply-descending liquidus shows the adverse

and a silica brick operating in a temperature gradient effect of a few per cent of alumina on the refractori-

will develop clearly-defined and separate zones of

ness of silica bricks. (Sodium oxide, Na 2 O, has an

tridymite and cristobalite.

even more pronounced eutectic-forming effect and is By tradition, refractories are often said to be acid commonly used to flux sand particles during glass-

or basic, indicating their suitability for operation in melting.) The discovery of this eutectic point led to

contact with acid (SiO 2 -rich) or basic (CaO- or FeO- immediate efforts to keep the alumina content as far

rich) slags. For instance, suppose that conditions are below 5% as possible. Silica refractories are made by

reducing and the lower oxide of iron, FeO, forms firing size-graded quartzite grains and a small amount

in a basic steel-making slag ⊲1600 ° C⊳. ‘Acid’ silica

64 Modern Physical Metallurgy and Materials Engineering refractory will be rapidly destroyed because this fer-

rous oxide reacts with silica to form fayalite, Fe 2 SiO 4 , which has a melting point of 1180 °

C. (The SiO 2 –FeO phase diagram shows a sudden fall in the liquidus.) However, in certain cases, this approach is scientifi- cally inadequate. For instance, ‘acid’ silica also has a surprising tolerance for basic CaO-rich slags. Refer-

ence to the SiO 2 –CaO diagram reveals that there is a monotectic plateau at its silica-rich end, a feature that is preferable to a steeply descending liquidus. Its exis- tence accounts for the slower rate of attack by molten basic slag and also, incidentally, for the feasibility of using lime as a bonding agent for silica grains during firing.

3.2.8.5 Nickel–sulphur–oxygen and chromium–sulphur–oxygen systems

The hot corrosion of superalloys based upon nickel, iron or cobalt by flue or exhaust gases from the combustion of sulphur-containing fuels is a problem common to a number of industries (e.g. power generation). These gases contain nitrogen, oxygen (excess to stoichiometric combustion requirements), carbon dioxide, water vapour, sulphur dioxide, sulphur trioxide, etc. In the case of a nickel-based alloy, the principal corrosive agents are sulphur and oxygen. They form nickel oxide and/or sulphide phases at the flue gas/alloy interface: their presence represents metal wastage. A phase diagram for the Ni –S–O system, which makes due allowance for the pressure variables, provides a valuable insight into the thermochemistry of attack of a Ni-based superalloy. Although disregarding kinetic factors, such as diffusion, a stability diagram of this type greatly helps understanding of underlying mechanisms. Primarily, it indicates which phases are likely to form. Application of these diagrams to hot corrosion phenomena is discussed in Chapter 12.

Under equilibrium conditions, the variables gov- erning chemical reaction at a nickel/gas interface are

temperature and the partial pressures p o 2 and p s 2 for

the gas phase. For isothermal conditions, the gen- eral disposition of phases will be as shown schemat- ically in Figure 3.25a. An isothermal section (900 K) is depicted in Figure 3.25b. A comprehensive three- dimensional representation, based upon standard free energy data for the various competing reactions, is given in Figure 3.26. Section AA is isothermal (1200 K): the full diagram may be regarded as a par- allel stacking of an infinite number of such vertical sections. From the Phase Rule, P C F D C C 2, it fol-

gas and one condensed phase, there are three degrees of freedom and equilibrium is represented by a vol- ume. Similarly, equilibrium between gas and three condensed phases is represented by a line. The bivari- ant and univariant equilibrium equations which form the basis of the three-dimensional stability diagram are given in Figure 3.26.

Figure 3.25 (a) General disposition of phases in Ni–S–O system; (b) isothermal section at temperature of 900 K (after Quets and Dresher, 1969, pp. 583–599) .