Interface - Modern Physical Metallurgy and Materials Engineering

Figure 3.4 Plane-front solidification (a) and dendritic solidification (b) of a pure metal, as determined by thermal conditions.

Figure 3.4a illustrates the case where all the latent heat evolved at the interface flows into the solid and the temperature gradients in solid and liquid, Gs and GL, are positive. The solidification front, which moves at a velocity R, is stable, isothermal and planar. Any solid protuberance which chances to form on this front will project into increasingly hotter, superheated liquid and will therefore quickly dissolve and be absorbed by the advancing front. Planar-front solidification is char- acterized by a high G L / R ratio (e.g. slow cooling). If the solid is polycrystalline, emerging grain boundaries will form grooves in the stable planar front.

in the alternative scenario (Figure 3.4b), for which G L / R has relatively low values, latent heat flows into both solid and liquid and GL becomes negative. A planar interface becomes unstable. Dendritic protu- berances (spikes) grow rapidly into the undercooled liquid, which quickly absorbs their evolved latent heat.

Thermal undercooling is thus an essential prerequi- site for dendritic growth; this form of growth becomes more and more likely as the degree of thermal undercooling increases. Melts almost invariably undercool slightly before solidification so that dendritic mor- phologies are very common. (The ability of dilute alloy melts to produce a cellular morphology as a result of constitutional undercooling will be described in Section 3.2.4.3.)

as those discussed in the previous two sections.

When solidification commences at the flat surface of a metallic ingot mould there is usually an extreme undercooling or chilling action which leads to the heterogeneous nucleation of a thin layer of small, randomly-oriented chill crystals (Figure 3.5). The size of these equiaxed crystals is strongly influenced by the texture of the mould surface. As the thickness of the zone of chill crystals increases, the temperature gradient GL becomes less steep and the rate of cooling decreases. Crystal growth rather than the nucleation of new crystals now predominates and, in many metals and alloys, certain favourably-oriented crystals at the solid/liquid interface begin to grow into the melt. As in the case of the previously-described

3.1.3 Forms of cast structure

Because of the interplay of a variety of physical and chemical factors during freezing, the as-cast grain

structure is usually not as uniform and straightforward Figure 3.5 Chill-cast ingot structure.

Structural phases: their formation and transitions 45 dendrites, the rapid growth directions are (100) for

fcc and bcc crystals and lie along the direction of heat flow. Sideways growth is progressively hindered so that the crystals develop a preferred orientation and a characteristic columnar form. They therefore introduce directionality into the bulk structure; this effect will be most pronounced if the metal itself is strongly anisotropic (e.g. cph zinc). The preferred growth directions for cph crystals are (1 0 1 0). The growth form of the interface between the columnar crystals and the liquid varies from planar to dendritic, depending upon the particular metal (or alloy) and thermal conditions.

As the columnar zone thickens, the temperatures within the liquid become more shallow, undercooling more prominent and the presence of kindred nuclei from dendritic multiplication more likely. Under these conditions, independent nucleation (Section 3.1.1) is favoured and a central zone of equiaxed, randomly- oriented crystals can develop (Figure 3.5). Other factors such as a low pouring temperature (low superheat), moulds of low thermal conductivity and the presence of alloying elements also favour the development of this equiaxed zone. There is a related size effect, with the tendency for columnar crystals to form decreasing as the cross-section of the mould cavity decreases.

However, in the absence of these influences, growth predominates over nucleation, and columnar zone may extend to the centre of the ingot (e.g. pure metals).

The balance between the relative proportions of outer columnar crystals and inner equiaxed crystals is important and demands careful control. For some purposes, a completely fine-grained stucture is preferred, being stronger and more ductile. Furthermore, it will not contain the planes of weakness, shown in Figure 3.5, which form when columnar crystals impinge upon each other obliquely. (In certain specialized alloys, however, such as those for high-power magnets and creep- resistant alloys, a coarse grain size is prescribed.)

The addition of various 'foreign' nucleating agents, known as inoculants, is a common and effective method for providing centres for heterogeneous nucleation within the melt, inhibiting undercooling and producing a uniform fine-grained structure. Refining the grain structure disperses impurity elements over a greater area of grain boundary surface and generally benefits mechanical and founding properties (e.g. ductility, resistance to hot-tearing). However, the need for grain refinement during casting operations is often less crucial if the cast structure can be subsequently worked and/or heat-treated. Nucleating agents must remain finely dispersed, must survive and must be wetted by the superheated liquid. Examples of inoculants are tita- nium and/or boron (for aluminium alloys), zirconium or rare earth metals (for magnesium alloys) and aluminium (for steel). Zirconium is an extremely effective grain-refiner for magnesium and its alloys. The close similarity in lattice parameters between zirconium and magnesium suggests that the oriented overgrowth (epi- taxy) of magnesium upon zirconium is an important

factor; however, inoculants have largely been developed empirically.

3.1.4 Gas porosity and segregation

So far we have tended to concentrate upon the behaviour of pure metals. It is now appropriate to consider the general behaviour of dissimilar types of atoms which, broadly speaking, fall into two main categories: those that have been deliberately added for a specific purpose (i.e. alloying) and those that are accidentally present as undesirable impurities. Most metallic melts, when exposed to a furnace atmosphere, will readily absorb gases (e.g. oxygen, nitrogen, hydrogen). The solubility of gas in liquid metal can be expressed by Sievert's relation, which states that the concentration of dissolved gas is proportional to the square root of the partial pressure of the gas in the contacting atmosphere. Thus, for hydrogen, which is one of the most troublesome gases:

[Hsolution] -- K{p(H2)} 1/2 (3.1)

The constant K is temperature-dependent. The solubility of gases decreases during the course of freezing, usually quite abruptly, and they are rejected in the form of gas bubbles which may become entrapped within and between the crystals, forming weakening blow- holes. It follows from Sievert's relation that reducing the pressure of the contacting atmosphere will reduce the gas content of the melt; this principle is the basis of vacuum melting and vacuum degassing. Similarly, the passage of numerous bubbles of an inert, low-solubility gas through the melt will also favour gas removal (e.g.

scavenging treatment of molten aluminium with chlo- rine). Conversely, freezing under high applied pressure, as in the die-casting process for light alloys, suppresses the precipitation of dissolved gas and produces a cast shape of high density.

Dissolved gas may precipitate as simple gas bubbles but may, like oxygen, react with melt constituents to form either bubbles of compound gas (e.g. CO2, CO, 502, H2Ovap) or insoluble non-metallic particles. The latter are potential inoculants. Although their presence may be accidental, as indicated previously, their delib- erate formation is sometimes sought. Thus, a specific addition of aluminium, an element with a high chemical affinity for oxygen, is used to deoxidize molten steel in the ladle prior to casting; the resultant particles of alumina subsequently act as heterogeneous nucleants, refining the grain size.

Segregation almost invariably occurs during solidification; unfortunately, its complete elimination is impossible. Segregation, in its various forms, can seri- ously impair the physical, chemical and mechanical properties of a cast material. In normal segregation, atoms different to those which are crystallizing can be rejected into the melt as the solid/liquid interface advances. These atoms may be impurities or, as in the case of a solid solution alloy, solute atoms. Insolu- ble particles can also be pushed ahead of the interface.

46 Modern Physical Metallurgy and Materials Engineering Eventually, pronounced macro-segregation can be produced in the final regions to solidify, particularly if the volume of the cast mass is large. On a finer scale, micro-segregation can occur interdendritically within both equiaxed and columnar grains (coring) and at the surfaces of low- and high-angle grain boundaries. The modern analytical technique of Auger electron spec- troscopy (AES) is capable of detecting monolayers of impurity atoms at grain boundary surfaces and has made it possible to study their very significant effect upon properties such as ductility and corrosion resistance (Chapter 5).

in the other main form of separation process, 1 which is known as inverse segregation, thermal contraction of the solidified outer shell forces a residual melt of low melting point outwards along intergranular channels until it freezes on the outside of the casting (e.g. 'tin sweat' on bronzes, 'phosphide sweat' on grey cast iron). The direction of this remarkable migration thus coincides with that of heat flow, in direct contrast to normal macro-segregation. Inverse segregation can be prevented by unidirectional solidification. Later, in Section 3.2.4.4, it will be shown how the process of zone-refining, as used in the production of high-purity materials for the electronics industry, takes positive advantage of segregation.

3.1.5 Directional solidification

The exacting mechanical demands made upon gas turbine blades have led to the controlled exploitation of columnar crystal growth and the development of directional solidification (DS) techniques for superalloys. 2 As the turbine rotor rotates, the hot blades are subject to extremely large centrifugal forces and to thermal excursions in temperature. Development has proceeded in two stages. First, a wholly columnar grain structure, without grain boundaries transverse to the major axis of the blade, has been produced during preci- sion investment casting by initiating solidification at a watercooled copper chill plate in the mould base and then slowly withdrawing the vertically-positioned mould from the hot zone of an enclosing furnace. Most of the heat is removed by the chill plate. A restricted number of crystals is able to grow parallel to the major axis of the blade. Transverse grain boundaries, which have been the initiation sites for intergranular creep failures in equiaxed blade structures, are virtually elim- inated. Grain shape is mainly dependent upon (I) the thermal gradient GL extending into the melt from the melt/solid interface and (2) the growth rate R at which this interface moves. Graphical plots of GL versus R

I Like all separation processes, even so-called chemical separations, it is essentially a physical process.

2Directional solidification of high-temperature alloys was pioneered by F. L. VerSnyder and R. W. Guard at the General Electric Company, Schenectady, USA, in the late 1950s; by the late 1960s, DS blades were being used in gas turbines of commercial aircraft.

Figure 3.6 A single-crystal blade embodying a DS-starter block and helical constriction and a test plate facilitating orientation check by XRD.

have provided a useful means for predicting the grain morphology of DS alloys.

In the second, logical stage of development, a single- crystal (SC) turbine blade is produced by placing a geometrical restriction between a chilled starter block and the mould proper (Figure 3.6). This spiral selector causes several changes in direction and ensures that only one of the upward-growing columnar crystals in the starter block survives. A typical production unit is illustrated in Figure 3.7. The orientation of every blade is checked by means of a computerized X-ray diffraction procedure (e.g. the SCORPIO system at Rolls-Royce). In the fcc nickel-based superalloys, the favoured [1 00] growth direction coincides with the major axis of the blade and fortunately offers the best overall mechanical properties. For instance, the modu- lus of elasticity is low in the (1 0 0) directions; conse- quently, thermal stresses are reduced and the resistance to thermal fatigue enhanced. If full three-dimensional control of crystal orientation is required, a seed crystal is precisely located close to the chill plate and gives the desired epitaxial, or oriented, overgrowth. The production of single-crystal turbine blades by directional solidification (DS) techniques has increased blade life

Structural phases: their formation and transitions 47

Figure 3.7 Schematic diagram of directional solidification plant for turbine blades.

substantially and has enabled operating temperatures to be raised by 30~ thus improving engine efficiency.

It has also had a far-reaching effect upon the philoso- phy of alloy design. Previously, certain elements, such as carbon, boron, hafnium and zirconium, were added in order to strengthen grain boundary surfaces. Unfor- tunately, their presence lowers the incipient melting point. The DS route dispenses with the need for them and permits beneficially higher temperatures to be used during subsequent heat-treatment. The DS approach requires to be carefully matched to alloy composition;

it is possible for it to lower the creep strength of certain superalloys.

3.1.6 Production of metallic single crystals for research

Development of highly-specialized industrial-scale techniques, such as the directional solidification (DS) of turbine blades and the production of silicon, germanium and various compounds for semiconductors, owes much to expertise gained over many years in producing small single crystals for fundamental research. Several methods originally developed for metals have been adapted for ceramics.

Experiments with single crystals of metals (and ceramics and polymers) have a special place in the history of materials science. The two basic methods for preparing single crystals involve (1) solidification from the melt and (2) grain growth in the solid state.

In the simplest version of the solidification method, the polycrystalline metal to be converted to a single crystal is supported in a horizontal, non-reactive boat (e.g. graphite) and made to to freeze progressively from one end by passing an electric furnace, with its peak temperature set about 10~ above the melting point, over the boat. Although several nuclei may

form during initial solidification, the sensitivity of the growth rate to orientation usually results in one of the crystals swamping the others and eventually forming the entire growth front. The method is particularly useful for seeding crystals of a predetermined orientation.

A seed crystal is placed adjacent to the polycrystalline sample in the boat and the junction is melted before commencing the melting/solidification process. Wire specimens may be grown in silica or heat-resistant glass tubes internally coated with graphite (Aquadag).

In a modem development of these methods, the sample is enclosed in an evacuated silica tube and placed in a water-cooled copper boat; passage through a high- frequency heating coil produces a melt zone.

Most solidification techniques for single crystals are derived from the Bridgman and Czochralski methods.

In the former, a pure metal sample is loaded in a vertical mould of smooth graphite, tapered to a point at the bottom end. The mould is lowered slowly down a tubular furnace which produces a narrow melt zone.

The crystal grows from the point of the mould. In the Czochralski method, often referred to as 'crystal- pulling', a seed crystal is withdrawn slowly from the surface of a molten metal, enabling the melt to solidify with the same orientation as the seed. Rotation of the crystal as it is withdrawn produces a cylindrical crystal.

This technique is used for the preparation, in vacuo, of Si and Ge crystals.

Crystals may also be prepared by a 'floating-zone' technique (e.g. metals of high melting point such as W, Mo and Ta). A pure polycrystalline rod is gripped at the top and bottom in water-cooled grips and rotated in an inert gas or vacuum. A small melt zone, produced by either a water-cooled radio-frequency coil or electron bombardment from a circular filament, is passed up its length. High purity is possible because the specimen has no contact with any source of con- tamination and also because there is a zone-refining action (Section 3.2.4.4).

Methods involving grain growth in the solid state (2) depend upon the annealing of deformed samples. In the strain-anneal technique, a fine-grained polycrystalline metal is critically strained approximately 1 - 2 % elongation in tension and then annealed in a moving- gradient furnace with a peak temperature set below the melting point or transformation temperature. Light straining produces very few nuclei for crystallization;

during annealing, one favoured nucleus grows more rapidly than the other potential nuclei, which it con- sumes. The method has been applied to metals and alloys of high stacking-fault energy, e.g. AI, silicon- iron, (see Chapter 4). Single crystals of metals with low stacking-fault energy, such as Au and Ag, are difficult to grow because of the ease of formation of annealing twins which give multiple orientations.

Hexagonal metals are also difficult to prepare because deformation twins formed during straining act as effective nucleation sites.

48 Modern Physical Metallurgy and Materials Engineering

3.2 Principles and applications of phase diagrams

3.2.1 The concept of a phase

The term 'phase' refers to a separate and identifi- able state of matter in which a given substance may exist. Being applicable to both crystalline and non- crystalline materials, its use provides a convenient way of expressing a material's structure. Thus, in addition to the three crystalline forms mentioned in Section 2.5.1, the element iron may exist as a liquid or vapour, giving five phases overall. Similarly, the important refractory oxide silica is able to exist as three crystalline phases, quartz, tridymite and cristo- balite, as well as a non-crystalline phase, silica glass, and as molten silica. Under certain conditions, it is possible for two or more different phases to co-exist. The glass-reinforced polymer (GRP) known as Fibreglass is an example of a two-phase structure.

When referring to a particular phase in the structure of a material, we imply a region comprising a large number of atoms (or ions or molecules) and the exis- tence of a bounding surface which separates it from contiguous phases. Local structural disturbances and imperfections are disregarded. Thus, a pure metal or an oxide solid solution are each described, by conven- tion, as single-phase structures even though they may contain grain boundaries, concentration gradients (coring) and microdefects, such as vacancies, dislocations and voids (Chapter 4). Industrial practice understand- ably favours relatively rapid cooling rates, frequently causing phases to exist in a metastable condition. Some form of 'triggering' process, such as thermal activa- tion, is needed before a metastable phase can adopt the stable, or equilibrium, state of lowest energy (e.g.

annealing of metals and alloys). These two features, structural heterogeneity on a micro-scale and non- equilibrium, do not give rise to any untoward scientific difficulty.

The production of the thermal-shock resistant known as Vycor provides an interesting example of the potential of phase control. 1 Although glasses of very high silica content are eminently suitable for high- temperature applications, their viscosity is very high, making fabrication by conventional methods difficult and costly. This problem was overcome by taking advantage of phase separation in a workable silica containing a high proportion of boric oxide. After shaping, this glass is heat-treated at a temperature of 5 0 0 - 6 0 0 ~ in order to induce separation of two distinct and interpenetrating glassy phases. Electron microscopy reveals a wormlike boron-rich phase sur- rounded by a porous siliceous matrix. Leaching in hot acid dissolves away the former phase, leaving a porous I Vycor, developed and patented by Corning Glass Works (USA) just before World War II, has a final composition of 96SIO2-4B203. It has been used for laboratory ware and for the outer windows of space vehicles.

silica-rich structure. Consolidation heat-treatment at a temperature of 1000~ 'shrinks' this skeletal structure by a remarkable 30%. This product has a low linear coefficient of thermal expansion (or---0.8 x 10-6~

0-300~ and can withstand quenching into iced water from a temperature of 900~ its maximum service temperature.

3.2.2 The Phase Rule

For a given metallic or ceramic material, there is a theoretical condition of equilibrium in which each constituent phase is in a reference state of lowest energy. The independent variables determining this energy state, which are manipulated by scientists and technologists, are composition, temperature and pressure. The Phase Rule derived by Willard Gibbs from complex thermodynamical theory provides a device for testing multi-phase (heterogeneous) equilibria and deciding the number of variables (degrees of freedom) necessary to define the energy state of a system. Its basic equation, P + F -- C + 2, relates the number of phases present at equilibrium (P) and the number of degrees of freedom (F) to the number of components (C), which is the smallest number of sub- stances of independently-variable composition making up the system. For metallic systems, the components are metallic elements: for ceramics, the components are frequently oxides (e.g. MgO, SiO2, etc.).

Consider Figure 3.8, which is a single-component (unary) diagram representing the phase relations for a typical pure metal. Transitions such as melting, subli- mation and vaporization occur as boundaries between the three single-phase fields are crossed. Suppose that conditions are such that three phases of a pure metal co-exist simultaneously, a unique condition rep- resented by the triple-point O. Applying the Phase Rule: P = 3, C = 1 and F = 0. This system is said to be invariant with no degrees of freedom. Having stated that 'three phases co-exist', the energy state is fully defined and it is unnecessary to specify values for variables. One or two phases could be caused to disappear, but this would require temperature and/or pressure to be changed. Similarly, at a melting point on the line between single-phase fields, a solid and a liquid phase may co-exist (i.e. P = 2, C = 1 and F = 1). Specification of one variable (either temperature or pressure) will suffice to define the energy state of a particular two-phase equilibrium. A point within one of the single-phase fields represents a system that is bivariant (F = 2). Both temperature and pressure must be specified if its state is to be fully defined.

Let us consider some practical implications of Figure 3.8. The line for the solid/liquid transition is shown with a slight inclination to the right in this schematic diagram because, theoretically, one may reason from Le Chatelier's principle that a pressure increase on a typical melt, from P I to P2, will favour a constraint-removing contraction and therefore lead to freezing. (Bismuth and gallium are exceptions: like

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