Smallman 4th ed Ch5 exerpt - in Press, 1965 is and Alloys,...

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Unformatted text preview: in Press, 1965 is and Alloys, I11 Press, 1958 '3, Van Nostrand Chapter 5 The structure of alloys 5.1 Introduction When a metal 13 is alloyed to a metal A several different structures and atomic arrangements may be obtained in the alloy, depending upon the relative _ amounts of the component metals and upon the temperature of the alloy. Thus, if 7 - the two types of atoms behave as if they were similar and become homogeneously dispersed amongst each other, a solid solution of the type shoWn in Figure 1.80:1) - will be formed. However, in only a few alloy systems does the solid solution exist over the entire composition range from pure A to pure B, one example being the ‘ copper—nickel system. More usually, the second element enters into solid solution only to a limited extent and, in this case, a primary solid solution is formed which has the same crystal structure as the parent metal (see for example the copper— _ vzinc system, Figure 3.5(a). Then at higher concentrations of the second element, 1 new phases, generally termed intermediate phases, are formed in which the crystal " ‘ structure usually differs from that of the parent metals. These intermediate phases '_ . are also called secondary solid solutions if they exist over wide ranges of ' composition, or intermetallic compounds if the range of homogeneity is small. 5.2 Primary substitutional solid solutions As a result of a comparison of the solubilities of various solute elements in ‘If the noble metals, copper, silver and gold, several general rules* governing the y H; extent of the primary solid solutions haVe been formulated. Extension of these _' experimental observations to solvents from other groups such as magnesium and '- iron show that, in general, these rules form a useful basis for predicting alloying ' '_ behaviour. In brief the rules are as follows: ' (l) The atomic size factor—If the atomic diameter of the solute atom differs 'by more thanlS per cent from that of the solvent atom the extent of the primary Solid solution is small. In such cases it is said that the size-factor is unfavourable ‘ 3 I airfor extensiye solid solution. * These are usually called the Hume-Rother rules because it was chiefly Hume-Rothery and his colleagues who formulated them. 153 i ‘I I i -| "I 154 The structure of alloys I ‘ “critical valu T Liq. - T Li'q. I p I \ relative to s . The sir g E . consideratic E g associated v g g the heat of : g £ regarded as Compositionf—u— Compesition ——-— the dome-sl (b) (Figure 5.1(i . ‘ by r Liq. i m J 1H“! where ,u is tl constant an (r1 _ Ina/re) V respectively must be eqL' limited prin Temperature -——-— Temperature Composition ————-r (c) (d) Composition ——-- Figure 5.1 Effect of size factor on the 'form of the equilibrimn diagram; lsl> (kr- examples include (a) Cu—Ni, Au—Pt. (b) Ni—Pt. (o) Air—Ni. and (d) Ctr—Ag ' For most m shoWs that (2) The electrochemical reflect—The more electropositive the one com- penent and the more electronegative the other, the greater is the tendency for the 5.2.2 1 two elements to form compounds rather than extensive solid solutions. _ (3) Relative valency efl’eet—A metal of higher valency is more likely to . _ T1115 dissolve to a large extent in one of lower valency than vice versa. " electrF’pOSlt negativity c period and: 5.2.1 The state factor effect 7 elements of Clearly, two metals are able to form a continuous range of solid solutions Stable in the only if they haVe the same crystal structure, e.g. copper and nickel both have f.C.G. 1085 TC {351 structures. HOWever, even when the crystal structures of the two elements are the' 501“th 13 same, the extent'of the primary solubility is limited if the. atomic size of the two ' reSPeCthely silicon. Sin . includes the (Bl: Sb or it metals, usually taken as the CIOSest distance of approach of atoms in the crystal of the pure metal, is unfavourable. This is demonstrated in Figure 5.1 for alloy systems where rules 2 and 3 have been observed, i.e. the electrochemical Properties of the two elements are similar and the solute is dissolved in a metal of . The in lower valency. As the size difference between the atoms of the two component . Enmary SOl metals A and B approaches 15 per cent, the equilibrium diagram changes frOII_1 ‘ [LIVES 1'3th that of the copper—nickel type to one of a eutectic system with limited primafY Segse and 0 solid solubility. . p In. Deratur. The size-factor effect is due to the distortion produced in the parent latthe ‘ lxture (05 ‘1 around the dissolved misfitting solute atom. In these localized regions the flora Stabl' interatomic distance will differ from that given by the minimum in the E — r cul'V6 -r:rreSPOnd of Figure 4.1, so that the internal energy and hence the free energy, G, of the ‘ ngeTEVlllctl e a system is raised. In the limit when the lattice distortion is greater than some ODE 00111- :ncy for the 0118 is likely to I d solutions hhave f.c.c. ants are the : of the two Le crystal of - ‘_ _ - includes the elements bismuth, antimony and arsenic, when the compounds Mg3 '3 (Bi, Sb or As)2 are formed. ' J for alloy rochemical 1 a metal of :omponent anges from ed primary rent lattice 'egions the E—r curve t, ,G, 01" the than some . _ ; - ' _i -———..—A.o-4-____/‘-"———P4"-—‘——r‘-r' ‘ —' '—" , 4. _ - The structure of alloys 155 critical value the primary solid solution becomes thermodynamically unstable ' relative to some other phase. The size factor rule may be deduced semi-quantitatively from elasticity H Considerations, since this allows a calculation of the strain energy (ES: 8mg?) associated with the solution of a solute atom in an alloy of concentration, c, i.e. the heat of solution, to be made. According to this theory, in which atoms are . regarded as rigid spheres and electronic considerations are ignored, the height of .the dome-shaped two—phase region on the temperature~composition diagram .. (Figure 51(0)) increases with increasing misfit, and the maximum at c =% is given by T: Zngz/k (5.1) where ,u is the shear modulus of the alloy, (2 its atomic volume, it is Boltzmann’s constant and e is the misfit of the solute atom in the solvent which is equal to (r1 —r,,/r,) where r1 and 7-,, are the atomic radii of the solute and solvent atoms respectively. If there is to be no complete solid solution at any temperature, then T _' must be equal to the melting point Tm of the alloy, which gives the condition for - limited primary solid solubility to be when l6] > (Wm/2119)” 2 (5-2) For most metals, kTm Au!) is ab out 0.04 and substitution in the above relationship shows that the limiting misfit value ]s| is 14 per cent. 5.2.2 The electrochemical effect This effect is best demonstrated by reference to the alloying behaviour of an electropositive solvent with solutes of increasing electronegativity. The electro- . negativity of elements in the Periodic Table increases from left to right in any . period and from bottom to top in any group. Thus, if magnesium is alloyed with ; elements of Group IV the compounds formed, Mg2(Si, Sn or Pb), become more stable in the order lead, tin, silicon, as shown by their melting points, 550, 778 and 1085 °C respectively. In accordance with rule 2 the extent of the primary solid solution is small (z7.75 atomic per cent, 3.35 atomic per cent, and negligible, respectively at the eutectic temperature) and also decreases in the order lead, tin, silicon. Similar effects are also observed with elements of Group V, which The importance of compound formation in controlling the extent of the l "2 primary solid solution can be appreciated by reference to Figure 5.2, where the curves represent the free-energy versus composition relationship between the ot- t‘ phase and compound at a temperature T. It is clear from Figure 5.2(a) that at this '5 l ‘ temperature the tic—phase is stable up to a composition c1, above which the phase ' .‘ mixture (oz + compound) has the lower free energy. When the compound becomes more stable, as shown in Figure 5.20:), the solid solubility decreases, and 5-. correspondingly the phase mixture is now stable over a greater composition : '. j-. range which extends from as to c4. ' The above example is an illustration of a more general principle that the 186 ‘ ' The structure of alloys 91,100 5 Limit of lad-solid solution Limit eta-solid solution at this temperature T 1900 >1 at this temperature T . E” GED or C CD 3 800 ,_ a: . u. '5 E 700 A “c1 . . . . E 600 Composttlon -—---— CompOSItion —-~-— ,2 (a) (b) 500 Figure 5.2 Influence of compound stability on the solubility limit of the tit-phase at a given temperature [.00 solubility of a phase decreases with increasing stability, and may also be used to ' i show that the concentration of solute in solution increases as the radius of f- curvature of the precipitate particle decreases. Small precipitate particles are less .. stable than large particles and the variation of solubility with particle size is ' Figure recognized in classical thermodynamics by the Thomson—Freundlich equation _ ‘ Egg; ln [c(r)/c] = EyQ/k Tr Meta]: where C(r) is the concentration of solute in equilibrium with small particles of radius r, c the equilibrium concentration, y the precipitate/matrix interfacial 5.3(n), sugg _ concentrat energy and Q the atomic volume (See Chapters 9 and 11). COmPOSifiC number of- 5.2.3 The relative valency effect l fhislbwzlyoz This is a general rule for alloys of the univalent metals, copper, silver and t ‘ _ demonstra gold, with those of higher valency. Thus, for example, copper will dissolve _ ' When’ approximately 40 per cent zinc in solid solution but the solution of copper in Zinc ‘ - but an exa is limited. For solvent elements of higher valencies the application is not SO ‘j‘f [and solidu general, and in fact exceptions, such as that exhibited by the magnesium-indium ‘ _ increasing system, occur. ' ' ' Solidus cu: l ' - magnesiur . _ -i Complicati 5.3 The form of the liquidus and solidus curves ' valency. T :2 (2:3), or The fact that the primary solid solubility is affected by the three factorS more stee; discussed above, implies that the form of the liquidus and solidus curves will also be influenced. This may be demonstrated if we alter any one of the three alloying 5A factors while keeping the other two constant. For example, if we take copper?r T silver as solvents and add to them elements which have favourable size factorS, 1-37 ‘ _ It is those elements which follow copper or silver in the Periodic Table, it is found that i " boundary a definite valency effect exists. In each series, increasing the valency of the solut6 ' 1 i: F0 results in a more restricted solid solution and a steeper fall in both the liquidus 1.4, i and solidus curves. These observations, an example of which is shown in F igure are 2 The structure of alloys ' 15? m “E sass 8 c: solution § Temperature 3.58 300 0 l0 20 30 40 0 H 1'2 1'3 1‘1: 1'5 1 be used to Zinc or gallium Electron concentration 3 radius of atomic per cent ‘ cles are less (a) ' (b) ticle size is :h equation Figure 5.3 Solidus and solid solubility curves for the copper—zinc and copper—gallium systems (after Hume—Rotitery. Smallman and Howath, Structure of Metals and Alloys, by courtesy of the Institute of Metals) 5.3(a), suggest that if the curves were plotted in terms of the product of the atomic concentration of solute and valency they would superimpose. The equivalent composition used in practice is the electron concentration, or the ratio of the number of- valency electrons to atoms in the alloy*, to. the 6/0. ratio, and Figure _ ‘ 5.3(b) shows the data for the copper—zinc and copper—gallium systems plotted in _ ' this way against the e/a ratio. A comparisonrof Figure 5.305;) and (13) clearly ‘ . demonstrates the important role played by electronic structure in alloying. When all the factors affecting alloying are operativa the situation is less clear, ” but an examination of many systems suggests that the depression of the liquidus I I '- I and solidus curves increases both with increasing difference in size factor and with I ' -. increasing difference in valency between the solute and solvent. Moreover, the ' solidus curves appear to be much more affected than the liquidus cuIVes. With ' 7 magnesium as solvent, although the tendency to compound formation tends to complicate the observations, it is nevertheless still possible to see the effect of valency. The addition of solute elements such as cadmium (Z =2), aluminium ' j (2 =3), or tin (Z =4), causes both the liquidus and solidus curves to fall more and 3 more steeply with increasing valency. ' ' particles of ; interfacial ', silver and 'ill dissolve pper in zinc n is not so urn—indium tree factors ves will also ree alloying e copper or 3 factors, is. 5 found that )f the solute the liquidus (11 in Figure 5.4 The primary solid solubility boundary I _ i It is not yet possible to predict the exact form of the oc-solid solubility . - (boundary, but in general terms the boundary may be such that the range of I I' * For example, a copper—zinc alloy containing 40 atomic per cent zinc has an e/a ratio of 1.4, is. for every 100 atoms, 60 are copper each contributing one valency electron and 40 are zinc each contributing] valency electrons, so that e/a= (60 x 1 +40 x 2)/100= 1.4. 158 The structure of alloys primary solid solution either (a) increases, or (b) decreases with rise of temperature. Both forms arise as a result of the increase in entropy which occurs when solute atoms are added to a solvent. It will be remembered that this entropy of mixing is a measure of the extra disorder of the solution compared to the pure metal, and takes the form shown in Figure 4.13051). . The most common form of phase boundary is that indicating that the solution of one metal in another increases with riSe in temperature. This follows from thermodynamic reasoning since increasing the temperature favours the structure of highest entropy (because of the — TS term in the relation G=H — TS) and in alloy systems of the simple eutectic type an Ot-SOlld solution has a higher entropy than a phase mixture (cc—l— [3). Thus, if the alloy exists as a phase mixture (at + B) at the lower temperatures, it does so because the value of H happens to be less for the mixture than for the homogeneous solution at that composition. However, because of its greater entropy term, the solution gradually becomes preferred at high temperatures. In more complex alloy systems, particularly those containing intermediate phases of the secondary solid solution type (eg. copper—zinc, copper—gallium, copper—aluminium, etc), the range of primary solid solution decreases with rise in temperature. This is because the fi-phase, like the oc-phase, is a disordered solid solution. However, since it occurs at a higher Composition, it is evident from Figure 4.13051) that it has a higher entropy of mixing, and consequently its free energy will fall more rapidly with rise in temperature. This is shown schematically in Figure 5 .4. The point of contact on the free energy curve of the oc-phase, determined by drawing the common tangent to the or and )8 curves, governs the solubility c at a given temperature T. The steep fall with temperature of this common tangent automatically gives rise to a decreasing solubility limit. As discussed in the previous section, the electron concentration is all important factor controlling the slope of the liquidus and solidus curves, and consequently this factor must also be reflected in the composition limit of the 0!- phase. In support of this it is observed that in many alloys of copper or silver the fee. oc-solid solution reaches the limit of its solubility at an electron to atom ratio of about 1.4. The divalent elements zinc, cadmium and mercury have solubilities of approximately 40 atomic per cent* (cg. copper—zinc, silver—cadmium, silver“ mercury), the trivalent elements approximately 20 atomic per cent (eg. copperr aluminium, copper—gallium, ' silver—aluminium, Silva—indium) and the tetra- valent elements about 13 per cent (e.g. copper—germanium, copper—silicon silver—tin), respectively. The valency factor, therefore, has the same influence on these primary solubility values as it does on the liquidus and solidus curves. In all the above examples the solute and solvent atoms have favourable size factors, bat if this is not the case the solubility limit is less than that given by an electronéto' atom ratio of 1.4; tin is on the borderline of size factor favourability and hence dissolves in copper only up to 9.2 atomic per cent. It is also found that alloys with gold as solvent show much lower electron—atom ratios at saturation even when * When using this rule in practice remember that x atomic per cent is equal to [xWB/ng +(100—x)WA x 100 Weight per cent, where W3 is the atomic weight of the solute and WA that of the solvent. Free energy N“! Temperature ——-— _."‘| l l ~ t Figure 5.- of the oc- having a the size facto gold—tin is l. ‘ The limi 'zone Stmctm Curve for thet 0f the form . Parabolic rel: ’7‘ r the solute is a - the top of the and the total the number 0 11 rise of - icli occurs _ is entrepy - o the pure 5 that the tie followg vours the 3 relation :1 solution exists as a value of H on at that : solution olexr alloy dary solid , etc), the . 3 I is because 3r, since it it it has a ll‘C rapidly ie point of awing the it a given [1 tangent :ion is an urves, and it of the o:- r silver the atom ratio :olubilities 1m, silver— g. copper— the tetra- let—silicon, fluence on .rves. In all actors, but lectron-to— and hence alloys with even when J t of the The structure of alloys 159 Low temperature T, High temperature T2 Compoéition (b) Figure 5.4 (a) The effect of temperature on the relative positions of the (ya-and B—phase free energy curves for an alloy system having a primary solid solubility of the form shown in (b) ‘ - , the size factor is favourable; the value for gold—cadmium is 1.33, and that for gold—tin is 1.205. The limit of solubility has been explained by Jones in terms of the Brillouin _ I. zone structure of alloy phases. It is assumed that the density of states—energy ” ' .‘ curve for the two phases, at (the close packed phase) and ,8 (the more open phase), is . of the form shown in Figure 5.5 (a) where the N (E) curve deviates from the parabolic relationship as the Fermi surface approaches the zone boundary. As . the solute is-added to the solvent lattice and more electrons are put into the zone, the top of the Fermi level moves towards A, i.e. where the density'of states is high ‘ _ and the total energy E for a given electron concentration is low. Above this point the number of available energy levels decreases so markedly that the introduction Lof a few more electrons per atom causes a sharp increase in energy. Thus, just i '. "above this critical point the or structure becomes unstable relative to _. the " alternative ,8 structure which canaccommodate the electrons within a smaller _ _' " energy range, i.e. the energy of the Fermi level is lower if the J8-phase curve is '1 fellowed rather than the cx—phase curve. The composition for which ErnaLx reaches :1 I 'Itghe point E A is therefore a critical one, since the alloy will adopt that phase which ' l has the lowest energy. It can be shown that this point corresponds to an electron- . 'L-toaatom ratio of approximately 1.4, which appears to show successfully why the T‘—, as! 160 The structure of alloys Unbound states Bound states Denally of states Denalty of states Energy ._.. (a) (b) Figure 5.5 Density of states—energy curves (after Raynor; in Structure of Metals: ' courtesy of the Institute of Metals) ‘ . solubilities of many elements in copper or silver occur up to concentrations of 1.4 electrons per atom but no further. If it is assumed that the electrons are free and the Fermi surface approximates to a sphere when it touches the zone boundary then, since E :h2/2m/12 and the Fermi energy E}: [J’IZ/Sm)(31\J'/rrV)?!3 the electron wavelength at the Fermi level is I i=2(nV/3N)1/3 For the Fermi surface touching at the nearest point, the wavelength is the Bragg wavelength 1:252 for waves normal to the reflecting planes responsible for the zone boundary. In f.c.c. crystals these are the {111} planes for which at =a/\/ 3 where the lattice parameter a is given by (4 V/N [01/3 with N o the number of atoms in a volume V. Hence, eon/sierrth and eliminating ,1 between these equations, gives N /N o=7r\/ 3/4: 1.36 for the electron concentration above which the ice. or-phase should become unstable. For b.c.c. crystal structure the {110} planes are responsible for the zone boundary and N /No 21.48 for the B-phase. The lower solubilities in gold could be accounted for by the fact that the Fermi surface is slightly distorted from the spherical shape (see below) in such a way that it will need less solute metal than in the case of copper or silver to raise the electron energy level to the critical point E A. ‘ A similar reasoning to that of J Ones may be used to account for the occurrence of the electron compounds (see section 5.6.3), at 3/2, 21/13 and 7/4 electrons per atom, respectively. While there is little doubt that the energy band picture of a metal is justified: many quantitative details are in doubt. Work by Friedel, for example, suggests that when a polyvalent metal such as aluminium dissolves in copper it does not exist as an Al3 + ion with three valency electrons per atom belonging to the lattice as a whole, but instead contributes only one valency electron to the first alloys”?d energy band for the alloy. The remainder are effectively tied to the solute atoms and may be considered to occupy what are known as ‘bound states”. On this p electron p: _ A .F picture, the per atom, ; solid solub: more detail states of lo bound stat the areas b atom. Thus the curve 1 corresponc Consequer progressiv: still be use Nowa surface frc known as ( frequency ’ Alphen efi magnetizir is mapped in a single that the F tending to surface. H becomes 11 reduction region of e .the fi-phar To 31: levels are understoo electrons 1' (See also C simple th experimen 5.5 I‘ Inter: Interstices CWStal lat Consequel With atorr ITlost com "“V. . if Metals; tions of 1.4 .re free and : boundary Til/)2” the a" the Bragg ible for the s d=a/\/3 er of atoms .36 for the .e unstable. 3 boundary 1 could be :d from the etal than in itical point int for the ’13 and 7/4 . is justified, lle, suggests it does not 0 the lattice irst allowed olute atom, es’. On this l I i I I I I 'A A - - I ' A ' ' AKH4____,-__'r_ _... Us. _ gs, A '_ _ 1.. - ' s... __,. .__;_,u-_’V_.__._.__-v._r__._.,(fl___n._—_——-——‘————r— , _ rl‘he structure of alloys 161 picture, therefore, the valency band for the alloy still contains only one electron per atom, as for the solvent copper itself, and consequently the dependence of solid solubility on electron concentration is a little more difficult to understand. A more detailed consideration of the theory, hOWever, shows that in general, it is the states of lowest energy in the band system for the solvent that give rise to the bound states in the alloy. This is schematically shown in Figure 5.5 (b), where it is the areas beneath both curves which now correspond to a total of 2 electrons per atom. Thus, for every bound state introduced by a solute atom, the area beneath the curve for the unbound states between EU and E A in Figure 5.5(b) will be correspondingly decreased by the equivalent of one energy level per atom. Consequently, the Fermi level, although correSponding to effectively only one electron per atom in the unbound energy levels, will nevertheless be shifted progressively toward‘EA, so that an explanation such as that used by I ones can still be used. Nowadays there are several ways of determining the shape of the Fermi surface from physical property measurements (see Chapter 2). One method ‘ known as the anomalous skin effect, measures the surface resistance to a high- frequency current at low temperatures. Another, known as the De Haas—Van Alphen effect, measures the variation of the magnetic suscepibility with the magnetizing field strength. In both experiments, the contour of the Fermi surface _‘ is mapped out by measuring the physical property as a function of the orientation . in a single crystal of the material. Using the anomalous skin effect, Pippard finds that the Fermi surface in copper is distorted from the spherical shape, thus tending to invalidate the free electron model which assumes a spherical Fermi surface. However, work by Cohen and Heine indicates that the Fermi surface becomes more nearly spherical in copper alloys than in pure copper, owing to the . reduction by alloying of the energy gaps across the zone surfaces._Thus in-the region of electron concentration where the or-phase becomes unstable relative to the fi~phase, it is quite possible that the free electron model is valid.’ To summarize, it would appear that the precise details of how the energy .‘1 levels are occupied by electrons remain,'e3pecially in alloys, incompletely understood. Nevertheless, the application of the simple theory of quasi-free electrons is useful, since it allows a general interpretation of metallic behaviour (see also Chapter 1). As forthe details, it is not surprising that modifications to the simple theory are necessary as more work, of both a computational and experimental nature, is done. 5.5 Interstitial solid solutions Interstitial solid solutions are formed when the solute atoms can fit into the interstices of the lattice of the solvent. However, an examination of the common Crystal lattices shows that the size of the available interstices is restricted, and Consequently only the small atoms, such as hydrogen, boron, carbon or nitrogen, with atomic radii very much less than one nanometre form such solutions. The most common examples occur in the transition elements and in particular the solution of carbon or nitrogen in iron is of great practical importance. In f.c.c. iron 162. The structure of alloys Figure 5.6 (a) Body centred cubic lattice showing the relative positions of the main lattice sites, the octahedral interstices marked 0. and the tetrahedral interstices marked T. (13) Structure cell of iron showing the distortions produced by the two different interstitial sites. Only three of the iron atoms surrounding the octahedral sites are shown. the fourth, centred at A, has been omitted for Clarity (after Williamson and Smallrnan. Acts Cyst. 1953, 6, 381) (austenite) the largest interstice 'or ‘hole’ is at the centre of the unit cell (60- : ordinates gfié) Where there is space for an atom of radius 52 pm (0.52 A), is. 0.41r if r is the radius of the solvent atom. A carbon atom (80 pm (0.8 A) diameter) or a nitrogen atom (70 pm (0.7 A) diameter) therefore eXpands the lattice on solution, but nevertheless dissolves in quantities up to 1.7 weight per cent and 2.8 weight per cent respectively. Although the b.c.c. lattice is the more open structure. the largest interstice is smaller than that in the f.c.c. In b.c.c. iron (ferrite) the largest hole is at the position i i, O) and is a tetrahedral site where four iron atoms are situated symmetrically around it; this can accommodate an atom 0f radius 36 pm, is. 0.29r, as shown in Figure 5 .6 (a). However, internal friction and 7 X-ray diffraction experiments show that the carbon or nitrogen atoms do not use this site, but instead occupy a smaller site which can accommodate an atom only 0.154r, or 19 pm. This position (0, 0, a at the mid-points of the cell edges is known as the octahedral site since, as can be seen from Figure 5.6(b), it has a distorted octahedral symmetry for which two of the iron atoms are nearer to the centre 0f the site than the other four nearest neughbours. The reason for the interstitial b.c.c. lattice. The two iron atoms which lie above and below the interstice, and which are responsible for the smallness of the hole, can be pushed away more easily than the four atoms around the larger interstice. As a result, the solution 0f carbon in oc-iron is extremely limited (0.02 weight per cent) and the struCtUTe becomes distorted into a body-centred tetragonal lattice; the c axis for each interstitial site is, however, disordered, so that this gives rise to a structure whiGh is statistically cubic. The body-centred tetragonal structure forms the basis 0f martensite (an extremely hard metastable constituent of steel), since the quenching treatment given to steel retains the carbon in supersaturated solution (see Chapter 12). , atoms preferring this small site is thought to be due to the elastic properties of thfi, l " -- 5.6 The p ‘ equilibriur _ (2)5ize—fac1 ‘ persists ev :_ chemistry ' exists betv. _manyfactc , phases obs 5.6.1 We ht _When one magnesiur the formul salt-like ct ' their rang ‘ Moreover ' with defin fluoride, C Can fluo ' the non-Ir take up ti Even ' familiar w For exam] 8/3 electr ; 00111130111111 is also fu behaviour liquid sta indicates semicondi Second B: I In ge cOmplete Chemical Properties up Orders 5.6.2 Whe- coItlpoun difference it cell (00- ' ).52 A), i.e. )diameter) lattice on ant and 2.8 1 structure ferrite) the a four iron Ln atom of fiction and do not use atom only :5 is known 1 distorted ,e centre of interstitial :rties of the ‘rstice, and may more solution of 3 structure .s'for each ture which 1e basis of since the 3d solution .li, rf‘he structure of alloys 163“ 5.6 Intermediate phases The phases which form in the intermediate composition regions of the equilibrium diagram may be either (1) electrochemical or full-zone compounds, (2) size—factor compounds, or (3) electron compounds. The term ‘compound‘ still persists even though many of these phases do not obey the valency laws of chemistry and often exist over a wide composition range. No sharp distinction exists between these three different types of compound and, as We shall see later, many factors may be involved in their formation, so that the characteristics of the phases observed are those which arise from the resultant of these various factors. 5.6.1 Electrochemical compounds We have already seen that a strong tendency for compound formation exists when one element is electropositive and the other is electronegative. The magnesium-based compounds are probably the most Common examples having the formula Mg2(Pb, Sn, Ge or Si). These haVe many features in common with salt~like compounds since their compositions satisfy the chemical valency laws, their range of solubility is small, and usually they have high melting points. Moreover, many of these types of compounds have crystal structures identical with definite chemical compounds such as sodium chloride, NaCl,'or calcium fluoride, Can. In this respect the Mng series are anti-isomorphous with the (3an fluorspar structure, i.e. the magnesium metal atoms are in the position of the non—metallic fluoride atoms and the metalloid atoms such as tin or silicon take up the position of the metal atoms in calcium fluoride. Even though these compounds obey all the chemical principles that we are familiar with, they may in fact often be considered as special electron compounds. For example, the first Brillouin zone of the Cal?2 structure is completely filled at .8/3 electrons per atom, which significantly is exactly that supplied by the compound Mgsz, Sn, . . ., etc. Justification for calling these full-zone compounds is also furnished by electrical conductivity measurements. Contrary to the behaviour of salt-like compounds which exhibit low conductivity even in the liquid state, the compound Mgsz shows the normal conduction (which indicates the possibility of zone overlapping) while MgZSn behaves like a semiconductor (indicating that a small energy gap exists between the first and second Brillouin zones). In general, it is probable that both concepts are necessary to describe the complete situation. As we shall see in Section 5.6.3, with increasing electro- chemical factor even true electron compounds begin to show some of the properties associated with chemical compounds, and the atoms in the lattice take up ordered arrangements. 5.6.2. Size—factor compounds When the atomic diameters of the two elements differ-only slightly, electron compounds are formed, as discussed in the next section. However, when the =. difference in atomic diameter is appreciable, definite size—factor compounds are 1611 The structure of alloys formed which may be of the (a) interstitial, or (b) substitutional type. _. A consideration of several interstitial solid solutions has shown that if the interstitial atom has an atomic radius 0.41 times that of the metal atom then it can fit into the largest available lattice interstice without distortion. When the ratio of the radius of the interstitial atom to that of the metal atom is greater than 0.41. but less than 0.59, interstitial compounds are formed; hydrides, borides, carbides and I nitrides of the transition metals are common examples. These compounds usually take up a simple structure of either the cubic or hexagonal type, with the metal atoms occupying the normal lattice sites and the non-metal atoms occupying the- interstices. In general, the phases occur over a range of composition which is often _ centred about a simple formula such as MEX and MX. Common examples are carbides and nitrides of titanium, zirconium, hafnium, vanadium, niobium and tantalum, all of which crystallize in the NaCl structure. It is clear, therefore, that these phases do not form merely as a result of the small atom fitting into the ' interstices of the solvent lattice, since vanadium, niobium and tantalum are b.c_.c., while titanium, zirconium and hafnium are c.p.h. By changing their structure to f.c.c. the transition metals allow the interstitial atom not only a larger ‘hole’ but also six metallic neighbours. The formation of bonds in three directions at right angles, such as occurs in the sodium chloride arrangement, imparts a condition of _ great stability to these MX carbides. _ .' When the ratio' rantmmial) to ammo exceeds 0.59 the distortion becomes appreciable, and consequently more complicated crystal structures are formed. Thus, iron nitride, Where rN/rFe = 0.56, takes up a structure in which nitrogen lies at the centre of six atoms as suggested above, while iron carbide, i.e. cementite, Fe3C, for which the ratio is 0.63, takes up a more complex structure. For intermediate atomic size difference, i.e. about 20 to 30 per cent, an efficient packing of the atoms can be achieved if the crystal structure common to the Laves phases is adOpted. These phases, classified by Laves and his co-workers, have the formula AB2 and each A atom has 12 B neighbours and 4 A neighbours, while each B atom is surrounded by six like and six unlike atoms. The average co- ordination number of the structure (13 .33) is higher, therefore, than that achieved by the packing of atoms of equal size. These phases crystallize in one of three closely related structures which are isomorphous with the compounds MgCuz (cubic), MgNiz (hexagonal) or Man2 (hexagonal). The secret of the close relationship between these structures is that. the small atoms are arranged on a: space lattice of tetrahedra. The different ways of joining such tetrahedra account for the different structures. This may be demonstrated by an examination of the MgCu2 structure. The small B atoms lie at the corners of tetrahedra which are joined point—to-point throughout space, as shown in Figure 5. 7(a). Such an arrangement provides large holes of the type shown in Figure 5 .7(b) and these are best filled when the atomic ratio thaw/emu”): 1.225. The complete cubic structure of MgCu2 is shown in Figure 5.7(c). The Man2 structure is hexagonal, and in this case the tetrahedra are joined alternately point—to-point and base-to-base in long chains to form a Wurtzite type of structure. The MgNi2 structure is also hexagonal and although very complex it is essentially a mixture of both the MgCu2 and MgNi2 types- The range of homogeneity of theSe phases is narrow. This limited range 0f _ governing is that the - there are ‘ example, is high (6. structure, MgCu2 t] the magr systems c . M gNiZn 5.] shows ' is evident TABI —__ MgCt AgBe: ‘ BiAu2 Nch TaCo Ti (Be U (A. Zr (C. -—_ 5.6.3 An e: The structure of alloys 165 hat if the 1en it can e ratio of 10.41 but aides and ls usually he metal pyin g the his often nples are nuns and l b) (C ) fore, that . Figure 5.7 (a) Framework of the MgCua structure. (1:) Shape of hole in which into the _ large Mg atom is accommodated. to} Complete MgCug structure (after Hume- are bile _- RotheIY. Smallrnan and Howathl Structure of Metals and Alloys, courtesy of the " Inshtute of Metals) ucture to £10131 bu}: ‘ homogeneity is not due to any ionic nature of the compound, since ionic S at Tight _ . compounds usually have low co—ordination numbers whereas Laves phases have ldition 0f -' .5 high co-ordination numbers, but because of the stringent geometrical conditions ' governing the structure. However, even though the chief reason for their existence becomes " is that the ratio of the radius of the large atom to that of the small is about 1.2, 3 formed I i there are indications that electronic factors may play some small part. For 0an lieS ' _' example, provided the initial size-factor condition is satisfied then if’the e/a ratio . smentitca - is high (eg. 2), there is a tendency for compounds to crystallize in the Man2 I structure, while if the 12/52 ratio is low (cg. 4/3), then there is a tendency for the ' cents an 1 . MgCu2 type of structure to be formed. This electronic feature is demonstrated in mmon t0 _ ' the magnesiumenickel—zinc ternary system. Thus, even though the binary Workers: : I systems contain both the Man2 and _MgNi2 phases the ternary compound ghboursa ' ' MgNiZn has the MgCu2 structure, presumably because its e/a ratio is 4/3. Table efage 00- ‘ -- ' 5.1 shows a few common examples of each type of Laves structure, from which it aChiEVEd : is evident that there is also a general tendency for transition metals to be involved. : of three 3 Mgcuz . TABLE 5.1 Compounds which exist in a Laves phase structure :he close ‘ , .ged 011 a ': Mac“?! type ‘ Mt?le U’Pe M92711 type - AgBe2 different half/in or Fe) NbCo :truCtui—e' 1 ' TaCoZ2 Taan 2 TaCoz2 with f 40-13mm _ Ti (Be, Co, or or), Ti (M11 or Fe)2 "nee, 333:; {133 large _ U (A., CO, Fe DI Mn)2 [Ile ZI'FBZ Le atomic .' Zr (Co, Fe or W)2 Zr 1{Crgn M12313, drown in u: S’ or 2 :trahedra 0 form a 5.6.3 Electron compounds although [12 typgs_ ' An examination of the alloys of copper, silver and gold with the B sub-group range of . metals shows that their equilibrium diagrams have many similarities. In general, 166 The structure of alloys all possess the sequence or, B, y, e of structurally similar phases, and while each phase does not occur at the same composition when this is measured in weight per cent or atomic per cent, they do so if composition is expressed in terms of electron concentration. Hume-Rothery and his co~workers have pointed out that the aft: ratio is not only important in governing the limit of the Ot-SOlld solutiori but also in controlling the formation of certain intermediate phases; for this reason they have been termed “electron compounds’. Structural determination of many intermediate phases, by Westgren, has confirmed this hypothesis and has allowed a general classifiCation of such compounds to be made. In terms of those phases observed in the copper—zinc system (see page 98) fi-phases are found at an e/a ratio of 3/2 and these phases are often either disordered b.c.c. in structure or odered CsCl~type, )5”. In the copper—aluminium system for example, the B-structure is found at CugAl, where the three valency electrons from the aluminium and the one from each copper atom make up a ratio of 6 electrons to 4 atoms, is e/a=3/2. Similariy, in the copper—tin system the fi—phase occurs at CuSSn with 9 electrons to 6 atoms giving the governing e/o ratio. The y~brass phase, CuSZnB, has a complex cubic (52 atoms per unit cell) structure, and is characterized by an e/a ratio of 21/13, while the s-brass phase, CuZn3, has a cp.h. structure and is governed by an e/a ratio of 7/4. A list of some of these structurally analogous phases is given in Table 5.2. TABLE 5.2 Some selected structurally analogous phases Electroneatom ratio 3 :2 E lec tron—atom E l ectronearom . ratio 21:13 ratio 7:4 fi—brass (b.c.c.) iii—manganese (cp.h.) y-brass a-brass (cp.h.) (complex cubic) (complex cubic) (Cu, Ag or Au)Zn Aan (Cu, Ag or Au) (Cu, Ag or Au) (Zn or Cd)B (Zn or Cd)3 CuBe (Ag or Au)3Al Ang . Cussi CagAl4 Cussn (Ag or Au)Mg CoZna Ag3Al Cussi (Ag or Au)Cd AusA CumSna Ag5A13 (Cu or Ag),A1 ‘1 (Cussn or Si) (Fe, Co, Ni, Pd or Pt)52n21 (Fe, Co or Ni)Al _____W——___—4H____d__— A close examination of this table shows that some of these phases, e.g. C1155i and Ag3 AI, exist in different structural forms for the same e/a ratio. Thus, AgaAl is' basically a 3/2 b.c.c. phase, but it only exists as such at high temperatures; at intermediate temperatures it is cp.h. and at low temperatures B—Mn. It is also noticeable that to conform with the appropriate electron-to-atom ratio the transition metals are credited with zero valency. The basis for this may be found in their electronic structure which is characterized by an incomplete d-band below an occupied outermost s—band. The nickel atom, for example, has all electronic structure denoted by (2) (8) (16) (2), Le. two electrons in the first quantum shell, eight in the second, sixteen in the third and two in the fourth Shells, and While this indicates that the free atom has two valency electrons, it also shows two electrons missing from the third quantum shell. Thus, if nickel contributes W ' , J‘"_"F; *W. "I Jim—n .“""‘W R '-"‘ _“ f“ I _ I valency ele third quan Withr factor whit phases, a G into accou clearly rec compounc' importanc (i) At - size factor the range (ii) l/E favour c.p. the size fa factor diffs the copper Mn structt - the 3/2 co: (iii) r , dominates electron cr .' gold alloys silver ——> gr point, and _shown by exhibited 1 (iv) '1' . Preference 5.2 A sul: Which the . the distrib Clear that ' ordered so Similar at: can be ex; 5.7.1 CuZn W ' COpper or and zinc respectivel Structures may be cc: are Ag (M The structure of alloys 16? rhile each valency electrons, it also absorbs an equal number from other atoms to fill up the 111 Weight third quantum shell so that the net effect is zero. Items of -- Without doubt the electron concentration is the most important single d out that factor which governs these compounds. However, as for the other intermediate 1 solutiOn phases, a closer examination shows that the interplay of all factors must be taken 3; for this into account, and the easily classified compounds are merely those in which a ination of clearly recognizable factor predominates. A consideration of the 3/2 electron ;s and has compounds, for example, shows that several secondary factors are also of importance to their formation. These can be listed as follows. 2 page 98) (i) Atomic size—In general the b.c.c. 3/2 compounds are only. formed if the ten either _ size factor is less than i18%. Moreover, with increasing size factor difference, luminium the range of homogeneity is displaced towards a lower c/a concentration. 3e valency (ii) Valerie}; of the solute—An increase in the valency of the solute tends to make up a - favour c.p.h. and [i-Mn structures at the expense of the b.c.c. structure. However, tin System the size factor principle interferes even in this generalization, since large size- eming 9/3 factor differences favour the b.c.c. lattice at the expense of the other structures. In T unit cell) ‘the copper—tin system, for example, because tin has a valency of 4, a c.p.h. or 3- 335 Phase, Mn structure might be expected whereas, because tin has a borderline size-factor, Sl- Of 301113 - the 3/2 compound has a b.c.c. structure. (iii) Electrochemical factor-—The electrochemical factor whiCh pre- _ dominates in compounds such as Mgzsn is also present to some degree in the electron compounds. Thus, the tendency for these phaSes in copper, silver and n—atom gold alloys to become ordered solid solutions increases in the sequence copper—fir ’4 silver——> gold. A high electrochemical factor leads to ordering up to the melting {C'p'h'} point, and the liquidus curve rises to a maximum in a similar manner to that I shown by electrochemical compounds such as Mngn; a good example is s or Au) I exhibited by the gold—magnesium system. or Cd)3 (iv) Temperature—An increase in temperature favours the b.c.c. structure in , preference to the c.p.h. or B—Mn structure. , 5.2 Order—disorder phenomena _ A substitutional solid solution can be one of two types, either ordered in - " . which the A and B atoms are arranged in a regular pattern, or disordered in which _l- the distribution of the A and B atoms is random. From the previous section it is _' clear that the necessary condition for the formation of a superlattice, is. an eg. C115 31 ‘ ' ordered solid solution is that dissimilar atoms must attract each other more than s,Ag3 A1 is :- similar atoms. In addition, the alloy must exist at or near a composition which ratures; at can be expressed by a simple formula such as AB, A3B or AB3. _ . It is also _ 7‘ . - ratio the ' . 5.7.1 Examples of ordered structures 5’ be found ' - * Cqui While the disordered solution is b.c.c. with equal probabilities of having Vie til-band ' copper or zinc atoms at each lattice point, the ordered lattice has copper atoms 13: has an _ _ _ and zinc atoms segregated to cube comers (0,0, 0) and centres (i i 51; , 1 the firSt .- respectively. The superlattice in the [i—phase therefore takes up the CsCl 111111 8113115: ‘ structures as illustrated in Figure 5.80:1). Other examples of the same type, which 3180 Shows 'I may be considered as being made up of two interpenetrating simple cubic lattices, ontributes are Ag (Mg, Zn or Cd), AuNi, NiAl, FeAl and FeCo. 188 The structure of alloys 0 Al oFe Figure 5.8 Examples of ordered structures. (a) CuZn, (b) Cu3i'5lu1 (c) CuAu, (d) Fe3A1 AuCu3 This structure, which occurs less frequently than the B—brass type, is based on the f.c.c. structure with copper atoms at the centres of the faces (mi-1g) and gold atoms at the corners (0, 0, 0), as shown in Figure 5 .805). Other examples include PtCua, (Fe or Mn) Nia, and (MnFe)Ni3. - AuCu The AuCu structure shown in Figure 5.8(0) is also based on the f.c.c. lattice, but in this case alternate (001) layers are made up of copper and gold. atoms respectively. Hence, because the atomic sizes of copper and gold differ, the lattice is distorted into a tetragonal structure having an axial ratio c/a=0.93L Fe3Al Like FeAl, the Fe3Al structure is based on the b.c.c. lattice but, as shown in Figure 5 .8(d), eight simple cells are necessary to describe the c0mp1ete ordered arrangement. In this structure any individual atom is surrounded by the maximum number of unlike atoms and the aluminium atoms are arranged tetrahedrally in the cell. M 93 Cd This ordered structure is based on the c.p.h. lattice. Other examples art? Mng3 and Nigsn. ' Ordered structures can occur not only in binary alloys but also in ternary and quaternary alloys. The Heusler alloy, CuzMnAl, which is ferromagnetic ' when in the ordered condition, has a structure which is based on Fe3Al with manganese and aluminium atoms taking alternate body centring positionS respectively. In fact many alloys with important magnetic properties ha“ ordered lattices, and some (antiferromagnetic) have a form of superlattice which is based on the magnetic moment of the atoms and hence is shown up not by x-Iay but by neutron diffraction (see section 5.7.3). Another important structure which occurs in certain alloys is the defflct _ Lattice parameter to N N range of h nickel cor ' vacated b; - structure ‘ of such p( anomalor reason f0: governing , and not] ‘ identical. towardsp t0 prever. g PIOportiO ‘ constant 1 y the fact th I . is unimpc energy. ; lattice (e.g The I regarded , Containin . Would im; the crysta at low ten . ‘ that of a I raIlge 0rd generalfo . an? achiet l l I. i ‘ 57.2 i I - t .ss type, is CBS (0. i, i) t examples [1 the ice. 3 and gold ldiffer, the c/a:0.93. :, as shown :te ordered ed by the : arranged amples are in ternary omagnetic iegAl with positions :1ties have ttice which ot by x-ray the defect r ,r_ - ._ _ _—._:1_LflmL__~__—x__a .. -A -: . w =. .- _ __ l E l The structure of alloys 169 9'87 Lattice parameter Figure 5.9 Variation of lattice parameter and density in the hue. [S-phase NiAl (after Bradley and Taylor, Proc. Phys. Soc. 193?. 159, BB) 2'85 46 50 54 58 Atomic percent nickel —--- I, lattice (eg. the hue. NiAl phase). This ordered 3/2 electron compound has a wide range of homogeneity about the 50/50 composition and it is found that when the nickel content is reduced below 50 atomic per cent some of the lattice sites vacated by the nickel atoms are not taken up by the aluminium atoms so that the structure as a whole contains a large number of lattice vacancies. The influence I of such point defects on the physical properties is shown in Figure 5.9, where an anomalous decrease in both density and lattice parameter is observed. The reason for the thermodynamic stability of these vacancies is that the true factor governing the formation of 3/2 compounds is the number of electrons per unit cell and not the number of electrons per atom: in general these two ratios are identical. In the compound NiAl, as the composition deviates from stoichiometry '- . towards pure aluminium, the electron to atom ratio becomes greater than 3/2, but to prevent the compound becoming unstable the lattice takes up a certain proportion of vacancies to maintain the number of electrons per unit cell at a constant value of 3. Such defects obviously increase the entropy of the alloy, but i ' the fact that these phases are stable at low temperatures, where the entropy factor is unimportant, demonstrates that their stability is due to a lowering of internal energy. 5.7.2 Long- and short—range order The discussion so far suggests that in an ordered alloy thelattice may be regarded as being made up of two or more interpenetrating sub-lattices, each containing different arrangements of atoms. Moreover, the term ‘superlattice‘ ‘ would imply that such a coherent atomic scheme extends over large distances, i.e. the crystal possesses long-range order. Such a perfect arrangement can exist only at low temperatures, since the entropy of an ordered structure is much lower than that of a disordered one, and with increasing temperature the degree of long- range order, 8, decreases until at a critical temperature 'I; it becomes zero; the general form of the curve is as shown in Figure 5.10. Partially ordered structUres are achieved by the formation of small regions (domains) of order, each of which 170 lI'he structure of alloys Is ooopooo em ooompoo g oooodoo m oooogoo s 0000300 00 0000000 TC ' Temperature -—c» - (a) (b) Figure 5.10 (a) Influence of temperature on the degree of order; (13) an antiphase domain boundary are separated from each other by domain or anti-phase domain boundaries, across which the order changes phase (Figure 51003)). However, even when long- range order is destroyed, the tendency for unlike atoms to be neighbours still exists, and short—range order results above TC- The transition from complete disorder to complete order is a nucleation and growth process and may be likened to the annealing of a cold worked structure (see Chapter 10). At high temperatures well above 1",, there are more than the random number of AB atom pairs, and with the lowering of temperature small nuclei of order continually fonn and disperse in an otherwise disordered matrix. As the temperature, and hence thermal agitation, is lowered these regions of order become more extensive, until at Tc they begin to link together and the alloy consists of an interlocking mesh of small ordered regions. Below Tc these domains absorb each other (cf. grain growth, see Chapter 10) as a result of antiphase domain boundary mobility until long-range order is established. Some order—disorder alloys can be retained in a state of disorder by quenching to room temperature while in others, e.g. fi~brass, the ordering process occurs almost instantaneously. Clearly, changes in the degree of order will depend on atomic migration, so that the rate of approach to the equilibrium configuration will be governed by an exponential factor of the usual form, is. Rate=Ae"Q’RT. However, Bragg has pointed out that the ease with which interlocking domains can absorb each other to develop a scheme of long-range order, will also depend on the number of possible ordered schemes the alloy possesses. Thus, in fi-brass (see Figure 5.8(a)) only two different schemes of order are possible, while in f.c.c. lattices such as CusAu (Figure 5.8(b)) fOur different schemes are possible and the approach to complete order is less rapid. 5.7.3 The detection of order The determination of an ordered superlattice is usually done by means of the X-ray powder technique. In. a disordered solution every plane of atoms is statistically identical and, as discussed in Chapter 2, there are reflections missing in the powder pattern of the material. In an ordered lattice, on the other hand, [ him?” _ mw—q—h._ Figure the int alternate r reflections seen from J ' out of phas a weak ref Applil superlattic that in the In some al appreciabl detectable. copper—zit are very Vt superlattic special x-rz X~ray wave the f-facto: the differer. is to use no in the Pet indicates, r in CuaAuj approxima Sharp _ regions of . long-range estimate 0 breadth, as domain sir lines. The d in very goc more diffic intensities - Info Imatio intensity 0 vvkuw undaries, hen long-r tours still complete I may be . At high AB atom .ally fOIrn nd hence iive, until g mesh of (cf. grain ility until :order by [g process )rder will uilibrium form, i.e. .th which ing-range the alloy 8 of order ‘different .d. ans of the _ atoms is is missing her hand, ,_._,___,._,«__4-.,.L_-____ —_-' ——' A awn—"m ,L__—.m_ —___.-—_.____I ——I J3——-‘——————-n————I —-.__._fi_n The structure of alloys 1'21 ut of phase but amplitude not the same Figure 5.11 Formation of a Weak 100 reflection from an ordered lattice by the interference of difh'acted rays of unequal amplitude alternate planes become A-rich and B—rich respectively so that these ‘absent’ reflections are no longer missing but appear as extra superlattice lines. This can be ' seen from Figure 5.1] ; while the diffracted rays from the A planes are completely out of phase with those from the B planes their intensities are not identical, so that .a weak reflection results. Application of the structure factor equation indicates that the intensity of the superlattice lines is proportional to [Fa] =S2 (fl, — fB)2, from which it can be 'seen that in the fully disordered alloy, where S =0, the superlattice lines must vanish. In some alloys such as copper—gold, the scattering factor difference 01— fly) is appreciable and the superlattice lines are, therefore, quite intense and easily detectable. In other alloys, however, such as iron—cobalt, nickel—manganese, copper—zinc, the term ( f A— f3) is negligible for X-rays and the superlattice lines are very weak; in copper—zinc, for example, the ratio of the intensity of the superlattice lines to that of the main lines is only about 1:3500. In some cases special X-ray techniques can enhance this intensity ratio; one method is to use an x-ray wavelength near to the absorption edge when an anomalous depression of the f—factor occurs which is greater for oneelement than for the other. As a result, ‘ the difference between 1:, and fl, is increased. A more general technique, however, is to use neutron diffraction since the scattering factors for neighbouring elements I_ in the Periodic Table can be substantially different. Conversely, as Table 2.2 indicates, neutron diffraction is unable to show the existence of superlattice lines .in CugAu, because the scattering amplitudes of copper and gold for neutrons are approximately the same, although x-rays show them up quite clearly. Sharp superlattice lines are observed as long as order persists over lattice regions of about 10—3 mm, large enough to give coherent X—ray reflections. When long—range order is not complete the superlattice lines become broadened, and an estimate of the domain size can be obtained from a measurement of the line breadth, as discussed in Chapter 2. Figure 5.12 shows variation of order S and domain size as determined from the intensity and breadth of powder diffraction . lines. The domain sizes determined from the Scherrer line broadening formula are ‘ in very good agreement with those observed by TEM. Short-range order is much i." more difficult to detect but nowadays direct measuring devices allow weak it—ray _ __ intensities to be measured more accurately, and as a result considerable _ information on the nature of short-range order has been obtained by studying the intensity of the diffuse background between the main lattice lines. 1'12. The structure of alloys 3000 . x degree of order 0 domain size (13‘) 2500 2000 . i E - i .a i " :i w i ._ 1500 E l E 'D l o i“ “5 I I 92’ 1000 I !. 8' . 500 _ ' G i II o 1 2 iogIIIt 3 4 5 -; s _ | I 'l ‘10 100 1000 10 000 100 000 1: (min) Figure 5.12 Degree of order and domain size during isothermal annealing at 350°C after quenching from 465°C (after Morris. Besay and Smalhnan. Phil. Mag. 29, 48. (1934]. Courtesy Taylor and Francis) . if} High—resolution transmission microscopy of thin metal foils allows the structure of domains to be examined directly. The alloy CuAu is of particular interest, since it has a face~centred tetragonal structure, often referred to as CuAu 1 (see Figure 5.8(c)), below 380°C, but between 380°C and the disordering temperature of 410 0C it has the CuAu 11 structures shown in Figure 5.13. The (002) planes are again alternately gold and copper, but half-way along the a-axis I L i of the unit cell the copper atoms switch to gold planes and vice versa. The spacing _ _ between such periodic anti-phase domain boundaries is 5 unit cells or about 2mm, ' . i .i I so that the domains are easily resolvable in TEM, as seen in Figure 5.14051). The . _ . 419I , isolated domain boundaries in the simpler superlattice structures such as CuAu 1, although not in this case periodic, can also be revealed by electron microscope, ’ 5 7 4 and an example is shown in Figure 5.14(b). Apart from static observations 0f , t ' ' I these superlattice structures, annealing experiments inside the microscope also ‘ SPECI'fiC h 1 allow the effect of temperature on the structure to be examined directly. Such ' SPECifiC he [I ‘ observations have shown that the transition from CuAu 1 to CuAu 11 takes - - anotherl place, as predicted, by the nucleation and growth of anti~phase domains. I ‘ range 0“ 1 form shat s i by Dulor l- ‘ existence the temps . . . . . Electrical Figure 5.13 One unit cell of the orthorhombm superlattice of CuAu, re. CuAu 11 (from .. Inst. Metals, 195843, 32, 419. by courtesy of the institute of Metals) 1“ 3 meta allows the particular 0 as CuAu tisordering a 5.13. The ; the a-axis he spacing .bout 2 nm, .14 (a). The as CuAu l, iicroscope, rvations of :scope also ectly. Such u 11 takes mains. l t f r -;-—'r—.__—_;—r—~———-‘ _‘_‘ -—___j __ ,__‘._-—~'—,,.—._H_._—.+——..__,.Lr.__1 —'_r—..____-—~— new w in Specific heat Vspecific heat, since energy is necessary to change atoms from one configuration to The structure of alloys 1T3 v05 Figure 5.14 Electron inicrographs of (a) CuAn ll, and (b) Colin 1 {from Pashley and Freeland]. Inst. Metals, 1958—9, 82, 419, courtesy of the Institute of Metals) 5.7.4 The influence of ordering on properties The order—disorder transformation has a marked effect on the another. However, because the change in lattice arrangement takes place over a range of temperature, the specific heat versus temperature curve will be of the form shown in Figure 4.3 (b). In practice the excess specific heat, above that given by Dulong and Petit’s law, does not fall sharply to zero at TC owing to the existence of short-range order, which also requires extra energy to destroy it as _ the temperature is increased above Tc. _‘ _, Electrical resistivity As discussed in both Chapters 1 and 2 any form of disorder ‘ “ _ in a metallic structure, eg. impurities, dislocations or point defects, will make a 174 rPhe structure of alloys . 15 “Disordered E , f “" a. alloy " u E ‘5 Disordered é .C as" 9 9 10 x 3" >a 2: a 3% 'fi __ 'fi s 5 a o: 0 200 400 O 25 50 75 100 Temperature—+°C . Gold ——-— At “A. (a) (b) A Quench-ed CuaAu alloy .12 _[ ____ E100 " ‘ E" .13 E 3 Bo Annealed g Cu3Au alloy E U) Ill cc 60 0'25 50 75 100 Reduction in cross ‘1. sectional area (c) Figure 5.15 ‘ Effect of (a) temperature. (13) composition, and (c) deformation on the resistivity of copper—gold alloys (after Barrett. Structure of Metals, 1952, courtesy of McGraw—Hill Book Co. large contribution to the electrical resistance. Accordingly, superlattices below T. have a low electrical resistance, but on raising the temperature the resistivity increases, as shovvn inFigure 5.J5(a) for ordered Cu3Au. The influence of order on resistivity is further demonstrated by the measurement of resistivity as a. function of composition in the copperwgold alloy system. As shown in Figure 5.15(b), at composition near Cu3Au and CuAu, where ordering is most complete, the resistivity is extremely low, while away from these stoichiometric com- positions the resistivity increases; the quenched (disordered) alloys given by the dotted curve, also have high resistivity values. Mechanical properties The mechanical properties are altered when ordering occurs. The change in yield stress is not directly related to the degree or ordering however, and in fact CL13Au crystals have a lower yield stress when well ordered than when only partially ordered. Experiments show that such effects can be accounted for if the maximum strength as a result of ordering is associated with critical domain size. In the alloy CuaAu, the maximum yield strength is exhibited by quenched samples after an annealing treatment of 5 min at 350 °C which give5 a domain size of 6 nrh (see Figure 5.12). However, if the alloy is well ordered and I 4. I,I_._+_ ?w__._w—.I—..T ‘ the domai Cu Au or C lattice stra dislocatior Them order, but shows that (disordere: ' Irradiatior Chapter 9: Adagnefic impo rtanc Order affec disordered bouundari magnetic 1 5.8 ' As on known, di; because of complex e consequen _ magnetisrr ferrimagne 5.8.1 Diam . motion of Way repres altered by diatnagnet Shell it is r radius of t ‘ Paramagni Each elect: of two ori _ depending Electron is .' the band i halves, as 5 Spin, it foil their allegi in both. It 5 below T, resistivity e of order ivity as a in Figure complete, :tric com- Jen by the l ordering r ordering :11 ordered :ts can be iated with texhibited rhich gives 'dered and :5 The structure of alloys 175 the domain size larger, the hardening is insignificant. In some alloys such as CuAu or CuPt, ordering produces a change of Ciystal structure and the resultant . lattice strains can also lead to hardening. Interpretation of such effects in terms of dislocation is discussed in Chapters 8 and 10. Thermal agitation is the most common means of destroying long-range order, but other methods, e.g. deformation, are equally effective. Figure 515(0) shows that cold work has a negligible effect upon the resistivity of the quenched (disordered) alloy but considerable influence on the well annealed (ordered) alloy. Irradiation by neutrons or electrons also markedly affects the ordering (see Chapter 9). Magnetic properties The order—disorder phenomenon is of considerable importance in the application of magnetic materials. The kind and degree of order affects the magnetic hardness, since small ordered regions in an otherwise disordered lattice induce strains which affect the mobility of magnetic domain bouundaries. To understand such behaviour more fully it is necessary to examine magnetic materials in greater detail. 5.8 The magnetic properties of metals and alloys As outlined in Chapter 2, three types of magnetic materials are commonly known, dia-, para- and ferromagnetic. Interest in magnetism is large not only because of the practical importance, but also because it throws light on the complex electronic structure of the rare-earth and transition elements. As a consequence, it is customary nowadays to speak of five rather than three kinds of magnetism, since to the above list have been added antiferromagnetism and ferrimagnetism. 5.8.1 Dia— and paramagnetism Diamagnetism is a universalproperty of the atom since it arises from the motion of electrons in their orbits around the nucleus. Electrons moving in this way represent electrical circuits and it follows from Lenz’s law that this motion is altered by an applied field in such a manner as to set up a repulsive force. The diamagnetic contribution from the valency electrons is small, but from a closed shell it is proportional to the number of electrons in it and to the square of the radius of the ‘orbit’. In many metals this diamagnetic effect is outweighed by a, paramagnetic contribution, the origin of which is to be found in the electron spin. Each electron behaves like a small magnet and in a magnetic field can take up one of two orientations, either along the field or in the other opposite direction, depending on the direction of the electron spin. AcCordingly, the energy of the electron is either decreased or increased and may be represented conveniently by the band theory. Thus, if we regard the band of energy levels as split into two ‘- halves, as shown in Figure 5.1901), each half associated with electrons of opposite ‘_ I spin, it follows that in the presence of the field, some of the electrons will transfer their allegiance from one band to the other until the Fermi energy level is the same in both. It is clear, therefore, that in this state there will be a larger number of ...
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This note was uploaded on 12/05/2011 for the course MSE 4100 taught by Professor Hennig during the Fall '11 term at Cornell University (Engineering School).

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Smallman 4th ed Ch5 exerpt - in Press, 1965 is and Alloys,...

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