Materials Technology PDF

Chapter 1 The structure of metals 1.1 Introduction Consider the various metal objects shown in Fig. 1.1. The lathe tail- stock is made of cast iron; the spanners are made of steel and the electric cable is made of copper. Each metal is chosen because it has special and individual prop...

Chapter 1 The structure of metals 1.1 Introduction Consider the various metal objects shown in Fig. 1.1. The lathe tail- stock is made of cast iron; the spanners are made of steel and the electric cable is made of copper. Each metal is chosen because it has special and individual properties which make it different from the others and suitable for the application shown. But what have these metals got in common? No matter what changes they have undergone during extraction from the ore, refinement, processing, and final manufacture, the form they adopt in Fig. 1.1 is that of a crystalline solid. In fact, all metals are crystalline solids at room temperature, with the notable exception of the metal mercury. In order to assess the behaviour and properties of the many different metals and alloys available to them, so that they can select the most suitable for a given application, the engineer and the metallurgist must understand the crystalline structure of the metal. However, before studying the crystalline structure of metals and alloys it is advisable to revise some basic chemical concepts. 1.2 Atoms Figure 1.2 (a) shows, diagrammatically, an atom of hydrogen (the simplest atom) and Fig. 1.2 (b) shows an atom of the metal copper. It can be seen that both atoms consist of a nucleus around which one or more electrons are orbiting. 2 (a) (b) (c) Fig. 1.1 Typical metal components (a) Lathe tail-stock (b) Spanners and keys (c) Electric cable  3 Although the electrons spend most of their time in "shells' as shown in Fig.1.2 (a), these are not as rigid as the drawing implies and the electrons are free to wander anywhere round the nucleus as shown in Fig.1.2 (b) The dots show the location of the electrons at various times. The basic structure of the atom is as follows. 1 electron (shell 4) 18 electron (shell 3) 8 electron (shell 2) electron (shell 1) electron (total) (b) 4 Nucleus Dots represent location of electrons at various times (c) Fig. 1.2 Typical atomic structures {a) Hydrogen atom (b) Copper atom (c) Movement of electrons round the nucleus (a) Nucleus. This is the basic core of the atom and consists of protons and neutrons. (b) Protons. These are positively charged particles of very much greater mass than the electrons. (c) Neutrons. These particles have the same mass as protons but carry no electrical charge. (d) Electrons. These panicles are negatively charged and orbit the nucleus like planets around a sun. Although electrons are very small and have only 1/1836 the mass of a proton or neutron they are of supreme importance when considering how atoms bond together to form molecules. (e) Atoms can be considered as the smallest particle of a substance which can exhibit all the properties of that substance. An atom is electrically neutral because it has an equal number of electrons and protons. The chemical properties of an atom, that is, how.it combines with other atoms, are determined by the number of electrons that it has. (f) Ions are atoms which have gained or lost one or more electrons. Loss of an electron makes the atom electropositive and it is called a positive ion. Gaining an electron makes the atom electronegative and it is then called a negative ion. Since positive ions are attracted towards the cathode (negative electrode) of an electrolytic cell, positive ions are also called cations. Similarly, negative ions are attracted towards the anode (positive electrode) of an electrolytic cell, and are also called anions. (g) Isotopes. Since the electron is so small compared with the proton, the mass of the atom can - for all practical purposes - be considered as  5 concentrated in the nucleus. As has already been stated, the neutron has the same mass as the proton but no electrical charge. Therefore, if the number of neutrons in the nucleus changes, the mass of the atom changes but its chemical properties remain unchanged (although it can influence the radioactivity during nuclear reaction). Atoms which have the same chemical properties but different atomic masses are said to be isotopic and are referred to as isotopes of a given substance. 1.3 Molecules So far, the atom has been considered as a single free particle. However, apart from the noble gases such as neon (used in electric discharge tubes for advertising) and argon (used as a gas shield when welding), atoms rarely occur as single particles but are generally associated with other atoms in small or large groups. These groups of atoms are called molecules. Figure 1.3 shows a very simple molecule consisting of two hydrogen atoms. Since they share their electrons they are said to be joined by a covalent bond. Some molecules may contain thousands of individual atoms. In the hydrogen molecule the electrons are shared to give a covalent bond Fig. 1.3 The hydrogen molecule 1.4 Elements A substance composed of atoms all with the same number of electrons is an element. Elements are pure substances incapable of further division 6 and consisting of molecules formed entirely from one type of atom only. For example: iron, carbon, sodium, chlorine and copper. Steel is not an element since it contains both iron and carbon. Table salt is not an element since it consists of both sodium and chlorine (see section 1.6). There are 103 elements at present known to scientists. 1.5 Mixtures Mixtures are two or more substances in close association but not chemically combined, and which may be separated without recourse to chemical process. Fig. 1.4 Copper sulphate crystals growing from solution (J. Lewis)  7 For example, the grit and salt spread on the roads in the winter is a mixture. That is. the grit and the salt do not combine chemically and they can be easily separated. If the grit and salt are placed in sufficient water, the salt will dissolve to form a solution and the grit can be filtered off. The salt solution can then be boiled, and as the water evaporates the salt is left behind. 1.6 Compounds When two or more different types of atoms join together a compound is formed. Generally, this compound molecule will have totally different properties to either of the constituent atoms, and a chemical process is necessary to divide the compound into its constituent elements. For example, the metal sodium reacts violently with the poisonous gas chlorine to form the stable salt sodium chloride (common table salt). Metal alloys are sometimes formed by two metals reacting to form intermetallic compounds, but these are relatively rare compared with the number of compounds formed between metals and non-metals, or between non-metals and non-metals. 1.7 Crystals Many solid substances, including the metals, are crystalline in structure. That is, their basic particles are arranged in definite three- dimensional patterns of rigid geometrical form which are repeated many times. Allowed to grow freely, crystals take on a distinctive geometric form as shown in Fig. 1.4. Non-crystalline ‘solids’ such as pitch, glass and many ‘plastic’ materials are said to be amorphous (without shape) and are best understood if they are considered as being extremely viscous liquids. The structure of crystals may be understood if their constituent atoms are considered to be spherical in shape. Figure 1.5 (a) shows a simple cubic crystal built up from eight spherical particles. The dotted lines joining the centres of the spheres represent the unit cell of this simple crystal. The unit cell is the geometric figure which illustrates the fundamental grouping of the particles in the solid. To form the crystal this unit cell is repeated many times to form the space lattice as shown in Fig. 1.5 (b). It is this regular, repetitive pattern of particles which characterises crystalline materials. All crystal structures can be analysed into fourteen basic lattices. These are called the Bravais space lattices. For simplicity only the unit cells of each lattice is shown in Fig.1.6. P type. These are shown in Fig.1.6 (a) and are classified as primitive. C-type. These are shown in Fig. 1.6 (b) and are classified as centred on the ‘ab’ face. 8 I-type. These are shown in Fig. 1.6 (c) and are classified as body- centred. F-type. These are shown in Fig. 1.6 (d) and are classified as face- centred. R-type. and H-type are shown in Fig. 1.6 (e) and 1.6 (/) respectively. Of these fourteen possible space lattice formations, only six are met with in meta! crystals. Of these, the most common are: Fig. 1.5 The crystal structure (a) Unit cell tor sodium chloride (common salt) crystal (b) Part of the space lattice for sodium chloride (four unit cells shown)  9 a. _ t b a Triclinic Monoclinic Orthorhombic Cubic Petragonal (a) c b b Base-centred Base-centred orthorhombic monoclinic (b) Body-centred Body-centred Body-centred orthorhombic tetragonal cube (c) b Face-centred Fscn cunttart R hobohedral Close-packed orthorhombic hexagonal (d) (e) (f) Fig.1.6 Bravais space lattices (a) P-type (primitive space lattices) (b) C-type (base- centred on ‘ab’ face) (c) l-type (body-centred) (d) F-type (face-centred) (e) R-type (f) H- type 10 Body-centred cubic Face-centred cubic Close-packed hexagonal Chromium Aluminium Molybdenum Silver Beryllium Niobium Copper Cadmium Tungsten Lead Nickel Magnesium Gold Zinc 1.8 Allotropy Allotropy is the ability of a substance to exist in more than one physical form. The non-metal carbon is said to be allotropic since it can exist as both diamond and graphite. Both these substances consist solely of carbon atoms, but it is in the crystal structure and the way in which the atoms are bonded together where the difference lies. The metal iron is another allotropic substance which is why it was not included in the examples given in section 1.6. Below 910 °C iron has a body-centred cubic space lattice and is referred to as α iron. Between 9)0°C and 1400°C iron has a face-centred cubic space lattice and is referred to as y iron. Above 1400’C iron has a body-centred cubic space lattice again and is referred to as 6 iron. The allotropy of solids which relies solely on difference in the crystal structure (space lattice) is referred to as polymorphism. Many metals are allotropic. 1.9 Grain structure Although metals are crystalline solids this is not immediately apparent when they are examined under the microscope. Figure 1.7 (a) shows the appearance under the microscope of a typical metal specimen which has been polished and etched. Although obviously granular, it is difficult to identify the geometric regularity expected of crystals. This is because crystals can only achieve geometric regularity when they are free to grow without interference. In a metal many crystals commence growth at the same time and eventually collide with each other so that their boundaries are distorted. The term grain is used to describe crystals whose geometric shape has been distorted by contact with adjacent crystals so that their growth is impeded. Figure 1.7 (b) shows, diagrammatically, how the atoms within a grain can have the regular geometric pattern expected of a crystal, but how that pattern breaks down at the grain boundary to make way for the geometric pattern of particles in the adjacent grains.  11 (b) Fig. 1.7 Grain structure (a) Appearance of granular structure of metal under the microscope after etching (b) Despite the irregular appearance of the grain structure due to boundary interference, the crystal lattice within the grain is correctly ordered 1.10 Crystal growth All pure elements exist as gases, liquids or solids depending upon the combination of temperature and pressure to which they are exposed at any one time. This is not necessarily true of compounds, many of which break down and decompose at temperatures below their boiling points and some even below their melting points. In the case of metals, only mercury is a liquid at room temperature, though some metals melt below red heat. A few such as cadmium, mercury and zinc will even boil at low temperatures and can be refined by distillation. 12 In the liquid state there is no orderly arrangement of atoms in a pure meta! and the atoms are free to move with respect to each other, thus a liquid possesses mobility. As the temperature of the molten metal falls, a point is reached where the metal starts to solidify. At this point the atoms change from a disordered or amorphous state to an ordered or crystalline state. Like other pure crystalline substances, pure metals solidify at a fixed single temperature as shown in Fig. 1.8 (a). Under industrial conditions the crystal nucleus forms around an impurity particle such as a grain of slag. However, as shown in Fig. 1.8 (b), in a very pure metal some under-cooling may occur before nucleation sets in. Amorphous (non-crystalline) solids such as glass, pitch and some ‘plastics’ exhibit no such change point and, as has been previously stated, these so-called solids are more akin to extremely high-viscosity liquids. Fig. 1.8 Cooling curves (a) Pure metal: no undercooling (b) Pure metal: some undercooling (c) Amorphous solid: no single freezing temperature Once the nucleus of the crystal forms it provides a soiid/liquid interface where crystallisation can proceed. The nuclei which form will be crystal unit cells, generally face-centred cubic, body-centred cubic or close-packed hexagonal. As the crystal grows on these nuclei it tends to develop spikes and changes into a tree-like' shape called a dendrite. (Greek dendron = a tree). Figure 1.9 shows a typical metal dendrite. The dendritic crystal grows until the spaces between the branches fill up. Growth of the dendrite ceases when the branches of one dendrite meet those of an adjacent dendrite, and eventually the entire liquid solidifies. At this point there is little trace of the dendritic structure left, and it is only possible to see the grains into which the dendrites have grown. The steps in the growth pattern of a crystal from nuclei to grain are shown in Fig. 1.10. The reason for dendritic growth is as follows. When a liquid at its fusion point (melting point) solidifies it gives up latent heat energy. This is the latent heat of the fusion taken in when the solid was originally melted.  13 Fig. 1.9 Metallic dendrite growth (R. A. Higgins) When a solid is heated, the atoms vibrate about fixed points, called lattice points, each atom being held in place by forces of attraction. As the temperature increases, the energy of vibration of each atom increases. At a certain point (temperature) they can overcome the forces binding them to the lattice points, and can escape from their fixed positions. Thus the structure begins to lose its rigidity, that is, it begins to melt. In moving from their fixed positions the atoms or molecules do work against the binding forces, and also as a result energy is used up. This energy is replaced by the heat source of the furnace. Thus the heat energy supplied is used to produce fusion (melting) rather than causing a rise in temperature. The energy that is used as work to cause the change of state from solid to liquid is called the latent heat of fusion. The amount of latent heat energy required to melt 1 kg of a substance is called the specific latent heal. Thus the metal/liquid interface is warmed up by the release of the latent heat energy as solidification occurs. This slows or stops further solidification occurring in that direction. The result of this action is for spikes to develop into regions where the liquid is coolest. As these spikes warm up in turn, due to the release of latent heat energy, forward growth of the crystal is again retarded and secondary and even tertiary spikes are formed. Although it is hard to relate a dendrite to the well-ordered crystal structures previously considered, it must be remembered that the unit cells and space lattices are very, very small even when compared in size with the dendritic spike. Thus during solidification and crystallisation the ordered pattern of the space lattice is still being built up, but the rate of growth is not uniform in all directions. 14 Fig. 1.10 Crystal growth  Chapter 2 Binary equilibrium diagrams 2.1 Alloys A number of metal objects were shown in Fig. 1.1. The conductors in the electric cables are made from copper because of its high electrical conductivity. The connecting rod is made from an alloy steel to give it great strength. The lathe tail- stock is made from cast iron. This is an iron-carbon alloy which melts relatively easily and can be cast into complex shapes. Pure metals are used where good electrical conductivity, good thermal conductivity good corrosion resistance or all of these properties are required. Since pure metals usually lack the strength required for structural materials, alloys are designed to give superior mechanical properties and they can be ‘tailored’ to suit a particular application. An alloy is an intimate association of two or more component materials which form a metallic liquid or solid. The component materials may be metal elements, or they may be metal and non-metal elements. They may also be metal elements and chemical compounds. Useful alloys can only be produced from component materials which are soluble in each other in the molten state. That is, they are completely miscible. It would be useless to try and form an alloy from lead and zinc. The molten zinc would float on the molten lead and, on cooling, they would form two separate layers in the solid state with only tenuous bonding at the interface. Alloys are formed in one of three ways: 1. If the alloying components in the molten solution have similar chemical properties, and their atoms are similar in size, they will not  17 react together but will form solid solutions upon cooling. 2. if the alloying components in the molten solution have different chemical properties they may attract each other and form chemical compounds. These are often referred to as intermetallic compounds. Upon cooling the crystals will consist of a mixture of such compounds. 3. Ina situation where atoms with different chemical properties attract each other less than those with similar chemical properties, then both intermetallic compounds and solid solutions will be present at the same time. Upon cooling they will tend to separate out at the grain boundaries to form a heterogeneous mixture. In any alloy the metal which is present in the larger proportion is referred to as the parent metal or solvent, whilst the metal (or non-metal) present in the smaller proportion is known as the alloying component or solute. 2.2 Solubility In order to understand the formation of alloys, it is first necessary to understand the basic principles of solubility in the liquid and solid states. Sodium chloride (common table salt) dissolves readily in water. In cold water, at room temperature, approximately 35 g of sodium chloride will dissolve in 100g of water. The exact amount will depend upon the temperature of the water. If more sodium chloride is added to the solution it will not dissolve because the solution is saturated'. The excess salt will remain as a solid residue. The solubility of the sodium chloride increases only slightly as the temperature of the water increases. In this example the sodium chloride is dissolved in water, thus: 1. The water is called the solvent. 2. The sodium chloride is called the solute. 3. The resulting liquid is called the solution. Figure 2.1 shows the difference between complete and partial solubility. Copper sulphate can also be dissolved in water but, unlike sodium chloride, its solubility increases substantially as the temperature of the solvent increases. This is shown in Fig. 2.2. Consider 50g of copper sulphate being dissolved in 100g of water as shown by the broken line. (a) Above 80 °C the water is capable of dissolving more than 50 g of copper sulphate, so the solution is said to be unsaturated. (b) At 80 °C the water will dissolve a maximum of 50 g of copper sulphate, so the solution is said to be saturated. (c) Below 80 °C the water dissolves less than 50 g of copper sulphate. For example, at 40 °C only 30 g of copper sulphate can be dissolved in 100 g of water (only 30 g of CuS04 can be ‘held in solution’) and 18 the balance of 20 g of copper sulphate will be precipitated out of solution as a solid residue. Substances which will not dissolve in a solvent are said to be insoluble. Note: A substance may be insoluble in one solvent, but soluble in another. (a) Fig. 2.1 Solubility (A) Complete solubility (B) Partial solubility Mass of copper sulphate per 100 g water Fig. 2.2 Solubility curve for copper sulphate 2.3 Solid solutions Most metals are completely and mutually soluble (they are miscible) in the liquid state, that is, when they are molten. Some, such as copper and nickel, not only form solutions in the molten or liquid state, but remain in solution upon cooling and become solid solutions. There are two sorts of solid solution: 1. substitutional solid solutions; 2. interstitial solid solutions.  19 The copper-nickel alloy mentioned previously is a substitutional solid solution. The more important factors governing the formation of a substitutional solid solution are: (a) Atomic size. The atoms of the solvent and solute must be approximately the same size. If the atom diameters vary by more than 15 per cent the formation of a substitutional solid solution is highly unlikely. (b) Electrochemical series. All metals are electropositive to some degree. If there is only a small difference in charge between the alloying components then they will probably form a solid solution. Conversely if their positive charges are very dissimilar they are more likely to form intermetallic compounds. (c) Valency. A metal of lower valency is more likely to dissolve one of higher valency than the other way round, assuming the conditions set out in (a) and (b) are also favourable. This holds good particularly for monovalent metals such as copper, silver and gold. (c) Fig. 2.3 Substitutional solid solution (a) Face-centred cubic crystal of copper (b) Face- centred cubic crystal of nickel (c) Substitutional solid solution of copper and nickel 20 Figure 2.3 shows that both copper and nickel form face-centred cubic crystals. When these two metals are in solid solution they form a single face- centred cubic lattice with atoms of nickel replacing atoms of copper in the lattice. Hence the term substitutional solid solution. The substitution can be ordered, with the atoms taking up regular fixed positions of geometric symmetry in the lattice. However, most solid solutions are disordered, with the solute atoms appearing virtually at random throughout the solvent lattice. Interstitial solid solutions are formed when the solute atoms are small enough to lie between the solvent atoms as shown in Fig. 2.4. For example, carbon atoms can form an interstitial solid solution with face- centred cubic crystals of iron. Fig. 2.4 Interstitial solid solution 2.4 Intermetallic compounds It has already been stated that where the components of the alloy are sufficiently different chemically, they will tend to form compounds rather than solid solutions. In general, intermetallic compounds tend to be hard and brittle and are thus less useful for engineering alloys than the tough and ductile solid solutions. Intermetallic compounds are most widely found in bearing metals where they form hard, wear- resistant pads with a low coefficient of friction, set in a matrix of a tough solid solution.  21 2.5 Cooling curves Most substances can exist as gases, liquids and solids, depending upon their temperature. Water is one such substance, which can exist as a gas or vapour (steam) if it is sufficiently hot; as a liquid; and as a solid (ice) if it is sufficiently cold. Fig. 2.5 Cooling curve for water If water is raised to its boiling point and allowed to cool slowly, the change in temperature with time can be plotted as a graph as shown in Fig. 2.5. Such a graph is called a cooling curve. It will be seen that when a change of state occurs (such as liquid water to solid ice) there is a short pause in the cooling process. This pause is referred to as an arrest point and is the result of the substance absorbing or giving out latent heat. Latent heat is the heat energy required to produce a change of state in a substance at a constant temperature. The gaseous, liquid and solid states of a substance are often referred to as phases. A substance is said to be in the gaseous phase, the liquid phase or the solid phase. It will be seen later that phase changes can also occur in solids. A physical change of state during the cooling, or heating, of a substance is always accompanied by an arrest point in the cooling or heating curve. 22 The cooling curve shown in Fig. 2.5 is typical of pure substances and applies equally well to any pure metal. Alloys consist of two or more components and, to understand their behaviour on cooling, the above explanation must now be extended to encompass a solution. A suitable solution is that of domestic table salt (sodium chloride) in water. Figure 2.6 shows the cooling curve for pure water compared with the cooling curve for a salt-water solution for the temperature range covering the liquid and solid phases. It will be seen that the saltwater solution has two arrest points and that both these are below the freezing point of water. A salt-water solution has a lower freezing point than pure water and at 0 ’C no change of state occurs. However, as cooling continues, droplets of pure water separate out from the solution and immediately change into ice particles. This occurs at the upper arrest point, which is not usually too well defined, and the process of separation continues as the temperature of the remaining solution is further reduced. Thus, as the temperature continues to fall, more and more water separates out and freezes, causing the concentration of the remaining salt water to increase. When the lower arrest point is reached, even the concentrated salt- water solution freezes and no liquid phase is left. The solid so formed consists of a mixture of fine crystals of pure water (ice) and fine crystals of salt. Time Fig. 2.6 Cooling curve for a salt-water solution  23 If the experiment is repeated several times using stronger and weaker salt- water solutions it will be seen that the upper arrest points vary as shown in Fig. 2.7, whilst the lower arrest points remain constant. The family of cooling curves so produced show some interesting trends. Reference to Fig. 2.7 shows that: 1. The temperature of the lower arrest point remains constant. 2. The temperature of the upper arrest point falls as the concentration of the solution-increases until a point is reached where the temperatures of the upper and lower arrest points coincide. 3. The ratio of solid to liquid at the point where the temperatures coincide is referred to as a eutectic. Solutions with a lower concentration of solid to liquid are referred to as hypo-eutectic solutions. Solutions with a higher concentration of solid to liquid are referred to as hyper-eutectic solutions. 4. When the concentration of the solution increases beyond that of the eutectic composition the temperature of the upper arrest point rises once more. Since water separates out as ice crystals between the arrest points of hypo- eutectic solutions, and since salt separates out between the arrest points of hyper-eutectic solutions, the remaining solution is always of a constant concentration. This concentration is the same as for the eutectic solution. The logic for this is apparent if reference is again made to Fig. 2.7. The fact that excess water or salt is rejected from the solution so that a eutectic ‘balance’ is always ultimately achieved, results in the 24 diagram formed from the cooling curves (Fig. 2.7) being referred to as a thermal equilibrium diagram. 2.6 Alloy types Alloys containing two components are referred to as binary alloys. Even when more than two components are present, a lot of useful information can be obtained from a study of the binary diagram of the two principal components present. The constituent components of most commercially available binary alloys are soluble in each other in the liquid (molten) state and, in general, do not form intermetallic compounds. (The exceptions are some bearing alloys.) However, upon cooling into the solid state, binary alloys can be classified into three main types. 1. Simple eutectic type. The two components are soluble in the liquid state, but completely insoluble in each other in the solid state. 2. Solid solution type. The two components are completely soluble in each other both in the liquid state and in the solid state. 3. Combination type. The two components are completely soluble in each other in the liquid state, but are only partially soluble in each other in the solid state. Thus this type combines some of the characteristics of both 1 and 2 above, hence the name ‘combination type’ thermal equilibrium diagram. These three types of binary alloy and their thermal equilibrium diagrams will now be considered in greater detail. 2.7 Thermal equilibrium diagrams (eutectic type) Figure 2.8 shows a eutectic-type thermal equilibrium diagram and it will be seen that it is identical with the diagram produced for a common salt solution (Fig. 2.7). That is, complete solubility of salt in water in the liquid state and complete insolubility (crystals of ice and separate crystals of salt) in the solid state. In the general case of Fig. 2.8 the two components present are referred to as metal A and metal B. In the solid state both components retain their individual identities as crystals of A and crystals of B. Reference to Fig. 2.8 shows that the line joining the points where solidification begins is referred to as the liquidus. The line joining the points where solidification is complete is referred to as the solidus. This type of equilibrium diagram gets its name from the fact that at one particular composition (E), the temperature at which solidification starts to occur is a minimum for the alloying components present. With this composition the liquidus and the solidus coincide at the same temperature, thus the liquid changes into a solid with both A crystals and B crystals forming instantaneously at the same temperature. This point  25 on the diagram is called the eutectic; the temperature at which it occurs is the eutectic temperature, and the composition is the eutectic composition (see Fig. 2.10). CiW’ipixutwxi Fig. 2.8 Thermal equilibrium diagram (eutectic type) ' Figure 2.8 also shows that when both alloying components arc liquid (molten), this region of the diagram is referred to as the liquid phase. The term ‘phase’, when related to a thermal equilibrium diagram. is defined as a region on that diagram which has the same chemical composition or structure throughout.’Thus above the liquidus the A and B components form a homogeneous solution and the definition is applicable. Il is not applicable between the liquidus and solidus, neither is it applicable below the solidus in this diagram.* In practice, few metal alloys form simple eutectic type thermal equilibrium diagrams. Exceptions to this are the cadmium-bismuth alloys. The thermal equilibrium diagram for cadmium-bismuth alloys is shown in Fig. 2.9. It can be seen that the eutectic composition occurs when the alloy consists of 40 per cent cadmium and 60 per cent bismuth. Solidification occurs at just over 140°C with both metals crystallising out of solution simultaneously. The eutectic structure is usually lamellar in form, as shown in Fig. 2.10. In this instance there are alternate layers of cadmium and bismuth. Consider the cooling of an alloy consisting of 80 per cent cadmium and 20 per cent bismuth (hyper-eutectic). 1. Above the liquidus there is a liquid solution of molten bismuth and molten cadmium. 26 Temperature (°C) Composition Fig. 2.9 Cadmium-bismuth thermal equilibrium diagram 2. As the solution cools to the liquidus temperature for the alloy under consideration crystals of pure cadmium start to precipitate out ( Fig. 2.9). This increases the concentration of bismuth and reduces the concentration of cadmium-present in the remaining solution. Thus the solidification temperature is reduced to that appropriate for this new ratio of cadmium and bismuth, and further crystals of pure cadmium precipitate out. This again reduces the percentage of cadmium present in the remaining solution and the solidification temperature is further reduced with more pure cadmium crystals being precipitated out. This process repeats itself until the eutectic composition is reached ( Fig. 2.9). 3. At the eutectic composition, crystals of cadmium and bismuth precipitate out simultaneously to form lamellar eutectic crystals of the two metals as shown in Fig. 2.10. Thus the final composition of the solid alloy will consist of crystals of pure cadmium in a matrix of crystals of eutectic composition. Cadmium Bismuth Fig. 2.10 Lamellar structure of eutectic composition  27 Similarly for an alloy of 80 per cent bismuth and 20 per cent cadmium (hypo- eutectic), the amount of cadmium present in solution compared with the amount of bismuth present in solution will gradually increase as pure crystals of bismuth precipitate out until the eutectoid composition is reached. Thus in this instance the composition of the solid alloy will consist of crystals of pure bismuth in a matrix of crystals of eutectic composition. For an alloy of 60 per cent bismuth and 40 per cent cadmium only crystals of eutectic composition will be present. These solid alloy compositions are shown in Fig. 2.11. (a) Fig. 2.11 Solid composition of cadmium-bismuth alloys (a) 20% Cd 80% Bi (b) 40% Cd 60% Bi {c) 80% Cd 20% Bi 2.8 Thermal equilibrium diagram (solid solution type) It has already been stated that copper and nickel are not only mutually soluble in the liquid (molten) state, but are also mutually soluble in the solid state. They form a substitutional solid solution. The thermal equilibrium diagram for copper-nickel alloys is shown in Fig. 2.12. Again, the line marked liquidus joins all the points where solidification commences, whilst the line marked solidus joins all the points where solidification is complete. This time there is no eutectic composition. Thus for 100 per cent copper, 0 per cent nickel (pure copper) there is a single solidification temperature of 1084 °C. This is to be expected since for a pure metal (in fact any pure substance) the transition from liquid to solid takes place at a constant temperature. For an alloy of 80 per cent copper and 20 per cent nickel Fig. 2.12 shows that solidification starts at 1190 °C and is complete at 1135 °C. Between the solidus and liquidus is a solution of molten copper and nickel together with crystals of a solid solution of copper and nickel. For an alloy of 80 per cent nickel and 20 per cent copper Fig. 2.12 shows that solidification starts at 1410 °C and is complete by 1380 °C. Finally, Fig. 2.12 shows that 100 per cent nickel, 0 per cent copper (pure nickel) solidifies at the single temperature of 1455 °C. Below the solidus the alloy consists entirely of crystals of copper and nickel in solid solution.  28 Hence in this diagram it is correct to refer to the liquid phase and the solid phase. Composition Fig. 2.12 Copper-nickei thermal equilibrium diagram 3 Thermal equilibrium diagram (combination type) Fig. 2.13 Combination type thermal equilibrium diagram  29 Many metals and non-metals are neither completely soluble in each other in the solid state, nor are they completely insoluble. They form a thermal equilibrium diagram of the type shown in Fig. 2.13. in this sys tem there are two solid solutions labelled a and. Tin-lead alloys (soft solders) are a typical example of this type of thermal equilibrium diagram as shown in Fig. 2.14. The use of the Greek letters a, p, etc. in thermal equilibrium diagrams may be defined, in general, as follows: 1. Solid solution of one component A in an excess of another component B such that A is the solute and B is the solvent. 2. Solid solution of the component B in an excess of component A so that now B becomes the solute and A becomes the solvent. a Phase. This is a solid solution of 19.2 per cent tin in 80.8 per cent lead at the eutectic temperature. P Phase. This is a solid solution of 2.6 per cent lead in 97.4 per cent tin at the eutectic temperature. 1. Above the liquidus ABC there is a homogeneous solution of molten tin and lead. 2. For hypo-eutectic alloys, the solidus is the line ADB. Between the liquidus and the solidus the hypo-eutectic alloys will consist of the liquid solution of tin and lead plus crystals of the solid solution of a composition. 3. Below the eutectic temperature, the line separating the a phase from the a + ' phase is called the solvus (see Fig. 2.13). Fig. 2.14 Tin-lead equilibrium diagram 30 4. For hyper-eutectic alloys, the solidus is the line BFC. Between the liquidus and the solidus the hyper-eutectic alloys will consist of the liquid solution of tin and lead plus crystals of the solid solution of /? composition. 5. Below the eutectic temperature, the line separating the /) phase from the a + fl phase is also called the solvus. Example 2.1 Consider an alloy of composition 10 per cent tin, 90 per cent lead. Upon cooling from the molten state, where both metals are completely soluble in each other, to a temperature below the liquidus ( Fig. 2.14) then crystals of the a phase solid solution start to grow. As in the previous diagrams solidification is complete when the solidus is reached and the solid alloy will consist of crystals of the a phase in solid solution ( Fig. 2.14). The composition of this solid solution will be 19.2 per cent tin in 80.8 per cent lead, as previously stated. However, as the temperature of the alloy continues to fall it will eventually meet the solvus ( Fig. 2.14). At this point the solid solution will be saturated with tin. Further cooling to room (ambient) temperature will result in the tin precipitating out to form the other solid solution possible in this system, the p phase. Thus the final composition of this alloy will consist of tin-rich crystals of the fl phase dispersed through a matrix of crystals of low tin content a phase. Example 2.2 Consider an alloy of composition 30 per cent tin and 70 per cent lead. Upon cooling from the molten state, where both metals are completely soluble in each other, to below the liquidus ( Fig. 2.14) then crystals of a phase solid solution start to grow. This increases the concentration of tin and reduces the concentration of lead in the remaining molten solution. The solidification temperature is reduced to that appropriate for this new ratio, and the process repeats itself with more and more a phase solid solution being precipitated out until the eutectic composition is reached ([5} Fig. 2.14). At this point crystals of both a and fl phase solid solutions arc precipitated out simultaneously to form lamellar eutectic crystals. (See Fig. 2.10). Thus the final composition of the solid alloy will consist of crystals of a phase solid solutions in a matrix of crystals of eutectic composition. These are important examples to the engineer as they explain the behaviour of the various types of soft solder in popular use. Thus the popular 60 per cent tin, 40 per cent lead alloy known as ‘tinman’s’ solder has the lowest melting and solidification temperature since it is approximately the eutectic alloy. This also accounts for its instant setting