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Smallman 4th ed Sec 5.7

Smallman 4th ed Sec 5.7 - Ihile each in weight 1 terms of d...

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Unformatted text preview: Ihile each in weight 1 terms of -. d out that 1 solution 3; for this ination of ;s and has 2 page 98) ten either luminium 3e valency make up a tin system eming e/a. : unit cell) ass phase, .st of some eg. CuSSi s,Ag3Al is fatures; at . It is also ratio the y be found ate d-band le, has an 1 the first 1rth shells, also shows ontributes '———' Jr The structure of alloys 16? valency electrons, it also absorbs an equal number from other atoms to fill up the third quantum shell so that the net effect is zero. Without doubt the electron concentration is the most important single factor which governs these compounds. However, as for the other intermediate phases, a closer examination shows that the interplay of all factors must be taken into account, and the easily classified compounds are merely those in which a clearly recognizable factor predominates. A consideration of the 3/2 electron compounds, for example, shows that several secondary factors are also of importance to their formation. These can be listed as follows. (i) Atomic size—In general the b.c.c. 3/2 compounds are only. formed if the _ size factor is less than i18%. Moreover, with increasing size factor difference the range of homogeneity is displaced towards a lower e/a concentration. (ii) Valendy of the solute—An increase in the valency of the solute tends to - favour c.p.h. and [i-Mn structures at the expense of the b.c.c. structure. However, the size factor principle interferes even in this generalization, since large size- factor differences favour the b.c.c. lattice at the expense of the other structures. In the copper—tin system, for example, because tin has a valency of 4, a c.p.h. or 3- Mn structure might be expected whereas, because tin has a borderline size-factor, - the 3/2 compound has a b.c.c. structure. (iii) Electrochemical facroi'wThe 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 gold alloys to become ordered solid solutions increases in the sequence copper—fir silver——> gold. A high electrochemical factor leads to ordering up to the melting 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 I exhibited by the gold—magnesium system. (iv) Temperature—An increase in temperature favours the b.c.c. structure in preference to the c.p.h. or B—Mn structure. 3 5.2 Order—disorder phenomena " I. which the A and B atoms are arranged in a regular pattern, or disordered in which _.- 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, to an ‘ ' ”I- ordered solid solution is that dissimilar atoms must attract each other more than - similar atoms. In addition, the alloy must exist at or near a composition which can be expressed by a simple formula such as AB, A3B or AB3. _ 5.7.1 Examples of ordered structures ' Cqui While the disordered solution is b.c.c. with equal probabilities of having " copper or zinc atoms at each lattice point, the ordered lattice has copper atoms _ and zinc atoms segregated to cube corners (0,0, 0) and centres (i i 51; , respectively. The superlattice in the [i—phase therefore takes up the CsCl ‘ structures as illustrated in Figure 5.80:1). Other examples of the same type, which ”I may be considered as being made up of two interpenetrating simple cubic lattices, are Ag (Mg, Zn or Cd), AuNi, NiAl, FeAl and FeCo. A substitutional solid solution can be one of two types, either ordered in - 188 The structure of alloys (C) (d) _ 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 1 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 cornplete 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 have 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 _ based on the ice. structure with copper atoms at the centres of the faces (0, 5,31) l ' N ICE parameter to Latt i lattice (e.g range of h ', nickel cor vacated b; structure . of such p( I anomalor reason f0: [“ governing , and not] . identical. towards p t0 prever. g PIOportiO ‘ constant 1 y the fact th I . is unimpc energy. The I regarded .‘ Containin . Would im; the crysta at low ten . ‘ that of a I range ord gmeralfo . an? achiet l i I. i ‘ 572 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 legAl with positions :1ties have ttice which ot by x-ray the defect r ,r_ - ._ _ _..._-.i-r_LflmL__~__—x__2s .. ., -: . w =. .- _ __ i E l The structure of alloys 169 9'87 Lattice parameter Figure 5.9 Variation of lattice parameter and density in the b.c.c. [l-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 b.c.c. 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 therrnodynamio 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 thevlattice 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 if; 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 form 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 T, 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?” _ ”W._ n. 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 ne 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 nours still complete I may be . At high AB atom .ally form nd hence sive, until g mesh of (cf. grain ility until :order by [g process )rder will uilibrium form, i.e. .th which lug-range the alloy 8 of order ‘different .d. ans of the _ atoms is is missing her hand, ,_._,___,._,«__4-.,.L_-____ —_-' ——' , ”ma—"m ,L__—.m_ —___.-—_.____I ——. J3——-A-—————-n————I —-.__._fi_n The structure of alloys l'Z'l .- Rays A/E out 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 1le 2S2 (1“,, — 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 .s i " :i w i ._ 1500 E l E 'D l o i“ “5 I . i. 92’ 1000 . !. 8' . 500 _ ' G t a o 1 2 50910? 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 Smallman. Phil. Mag. 29, 48. (1934]. Courtesy Taylor and Francis) . ll 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 ‘ L3 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 a? so that the domains are easily resolvable in TEM, as seen in Figure 5.14051). The . _ . 419. , 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 , y ' ' I these superlattice structures, annealing experiments inside the microscope also ‘ SPECI'fiC h I 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 - - a110ther.l place, as predicted, by the nucleation and growth of anti~phase domains. I ‘ range Ofl 1 form show s i by Dulor. l- ‘ existence the temps . . . . . Electrical Figure 5.13 One unit cell of the orthorhomb1c superlattioe 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. i l f .fii.._'4_____.na_- _‘_‘-_____,__‘._-—v—,,.—._H_.___+_____kr__1 —'___..____-_~_ 1.5—; w "h The structure of alloys 1T3 .05 LELJLI Figure 5.14 Electron micrographs of (a) CuAu 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 Specific hear The order—disorder transformation has a marked effect on the Vspecific heat, since energy is necessary to change atoms from one configuration to 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 TL, 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, e.g. impurities, dislocations or point defects, will make a 174 The structure of alloys . 15 “Disordered E , f” \ alloy " u E ‘5 Disordered é .C as" 9 9 10 x 3" >a 2: e E e E 'n s 5 s o: 0 200 400 O 25 50 75 100 Temperature—HJC . Gold ——-— At “A. (a) (b) A Quench-ed CuaAu alloy .19. _[ ____ $100 " ‘ E‘ .12 E 5” BO Annealed g Cu3Au alloy E U) III 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 sthn inFigure 5.15(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 F igure 5.15(b), at composition near C113Au 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 0113Au 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 criti...
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