The structure of short range ordered α-Cu-Al alloys and a new superlattice phase

THE STRUCTURE OF SHORT RANGE ORDERED a-Cu-Al ALLOYS AND A NEW SUPERLATTICE PHASE W. GAUDIG* Max-Planck-Institut

and H. WARLIMONTt

fur Metallforschung, 7 Stuttgart 1, Seestrasse 75. Federal Republic of Germany

(Receioed 27 December 1976; in revisedform 13 August 1977) Abstract-Electron micrographs of annealed Cu-15 at.% Al splats reveal strain contrasts which are assumed to be caused by internal strain fields due to short range order (SRO). A model is developed which characterizes the SRO structure of r-Cu-Al by a contiguous microdomain arrangement. The structure within the microdomains is assumed to be a two-dimensional antiphase shift structure with non-uniform and irregular shift spacings, based on the LIZ superlattice structure. The domain size for short range ordered Cu-16 at.% Al was obtained to be 1.7 nm using diffuse X-ray scattering data by Borie and Sparks. Electron diffraction experiments confirmed the theoretical relation between the SRO diffuse scattering and the Fermi surface, established by Moss. For Al concentrations exceeding the solubility limit of z-Cu-Al, two different superlattice phases were found by electron diffraction. At 34O’C, the known phase a1 was found, the structure of which is a one-dimensional antiphase shift structure with a step length of 4/3. At 250% a new one-dimensional antiphase shift structure with a step length of 715 was detected. The new phase was designated I~.

R&urn&-On emet l’hypothese que les contrastes de deformation que I’on observe dans les micrographies d’alliages Cu-15 at.% Al trempes rapidement et recuits, proviennent de champs de deformation internes dQs a l’ordre a courte distance (OCD). On prtsente un modtle qui dtcrit la structure de Cu-Al x ordonne a courte distance comme un arrangement de microdomaines contigus. On postule que la structure interne des microdomaines est une structure antiphase bidimensionneile, basee sur la structure Ll?, et dont I’espacement des decalage n’est ni uniforme, ni regulier. La taille des microdomaines dans Cu-16 at.‘4 Al ordonne a courte distance est tgale a 1.7 nm, d’apres les rtsultats d’intensite diffuse de rayons X de Borie et Sparks. Des experiences de diffraction electronique ont co&me la relations entre l’intensite de diffraction diffuse et la surface de Fermi, relations prevues theoriquement par Moss. Lorsque la concentration d’aluminium est supirieure a la limite de solubilitt dans CU-AI 2, la diffraction electronique permet d’observer deux surstructures differentes. On a trouve a 340°C la phase zs qui est connue, et dont la structure est une antiphase periodique unidimensionnelle de periode 4!3. A 25O’C, on a mis en evidence une nouvelle antiphase p6riodique unidimensionnelle de periode 715. On a appele cette nouvelle phase 2s. Zusammenfassung-Electronenmikroskopische Aufnahmen rasch abgeschreckter und angeiassener Legierungen Cu-15 At. % Al zeigen Spannungskontraste, von denen angenommen wird, daf.3 sie vou Verzerrungsfeldern durch Nahordnung herrtihren. Es wird ein Model1 entworfen, welches die Nahordnungsstruktur von z-Cu-AI mit einem benachbarten Mikrodomlnenarrangement beschreibt. Die Struktur innerhalb der Mikrodomfnen wird als eine zweidimensionale Antiphasenstruktur angesehen, basierend auf der Ll,-Struktur, mit uneinheitlichen und unregelmlBigen Verschiebungsabstlnden. Fiir nahgeordnetes Cu-16 At. y0 Al wurde die DomanengrGDe mit den Damn von Borie und Sparks iiber diffuse Riintgenstreuung zu 1.7 nm bestimmt. Elektronenbeugungsexperimente bestiitigten die theoretische Beziehung von Moss zwischen der diffusen Nahordnungsstreuung und der Fermiflache. Bei Aluminiumkonzentrationen, die fiber der Loslichkeitsgrenze von z-Cu-Al liegen, wurden mit Elektronenbeugung zwei verschieden ubergitterphasen beobachtet. Bei 340°C wurde die bekannte Phase xX1. gefunden, deren Struktur eine eindimensionale Antiphasenstruktur mit Schrittweite 4/3 ist. Bei 250°C wurde eine neue eindimensionale Antiphasenstruktur mit einer Schrittweite 715 entdeckt. Diese neue Phase wird mit zs bezeichnet.

1. INTRODUCTION Numerous studies have been carried out to examine the SRO state of r-Cu-Al alloys, to obtain informa* Now at: Department of Materials Science and Engineering. Cornell University. Ithaca. NY 14853. U.S.A. t Now at: Vacuumschmelze GmbH, 6450 Hanau, Federal Republic of Germany.

tion about its structure and to analyse the kinetics of short range ordering. The methods used were X-ray diffuse scattering [l-S], X-ray small angle scattering [6], electron microscopy and electron diffraction [7-143, measurements of the electrical resistivity [15-223, measurements of the specific heat or differential thermal analysis [2325], and measurements of the elastic [26] and plastic [ZS, 27-291 properties. 709

710

GAUDIG

A?jD

WARLIMONT:

THE STRUCTURE

Iveronova et al. [5] showed that short range ordering in deformed r-Cu-Al alloys (annealed below the recrystallization temperature) can be described in terms of the formation of ordered domains at lattice defects (dislocations, stacking faults). The assumption of a homogeneous distribution of SRO would not be compatible with their measured diffuse X-ray scattering data. Several authors [7.8,21,30] have concluded that in the case of formation of SRO in undeformed r-Cu-Al alloys. ordered domains can also occur. In the present paper, further evidence for the existence of ordered domains in short range ordered undeformed &u-Al alloys is given by electrical resistivity measurements and transmission electron microscopy. The electron micrographs were taken from specimens which were quenched from the liquid state (‘splat cooling’) such that thin foils were obtained which could be examined without further preparation. In this way it is possible to avoid surface roughness as it would arise from electropolishing, the contrast of which can interfere with the strain contrast. A microdomain model is formulated which complies with the present results and fits quantitatively the diffuse X-ray scattering data measured by Borie and Sparks [3]. Exceeding the solubility limit of &u-Al. besides the known superlattice phase xz [7], a new phase with a similar long period antiphase shift structure could be detected at a lower annealing temperature. 2. EXPERIMENTAL

PROCEDURES

OF x-Cu-Al

ALLOYS

an argon atmosphere. The electrical resistivity was measured at 2O’C as a function of the annealing time after interrupting the annealing by a water quench. The measurements were carried out with a Thomson bridge using a reference sample of the same material and size cooled from 450°C to room temperature at 5’C,%. During the measurement, both the sample measured and the reference sample were kept in an ethanol bath at 20 _+O.l”C. It was possible to detect resistivity changes of +0.005% whereas the absolute values of the electrical resistivity could only be determined with an accuracy of + 1%. For transmission electron microscopy, the homogenized sheets were quenched from 45O’C in water, isothermally annealed, and again water quenched. Disks of 2.3mm diameter were punched out and thinned electrochemically with a jet method, using an electrolyte consisting of 33 vol. % nitric acid and 67 vol. % methanol. The voltage was 7 V, the temperature of the electrolyte -40°C. The specimens were washed with methanol and then dried in a warm air stream. From the Cu-15 at.% Al alloy. some specimens were prepared for transmission electron microscopy by quenching from the liquid state at 115O’C under an argon atmosphere (splat cooling) using the shock wave method [31]. Some splats were subjected to the following heat treatment under high vacuum (z2.10-8Torr): room temperature + 275’C at 5’C/h, 24 h at 275”C, 275°C -+ room temperature at YC/ll. Transmission electron microscopy was performed using a Siemens Elmiskop I at an acceleration voltage V= 1OOkV and a JEOL Jem 200 at V=2OOkV. Bright field and dark field images were examined using dynamical two-beam conditions of fundamental reflections. Some dark field images were formed by superlattice reflections. The imaging conditions are characterized by the direction of the incident beam, n, and the imaging vector, g (in units of the reciprocal lattice parameter of the f,c.c. structure, l/u). The beam forming the image was always aligned along the optical axis of the microscope. Electron diffraction patterns of a Cu-18 at.% Al specimen were taken at different temperatures up to 400°C with the JEOL Jem 200 microscope using a hot stage. The hot stage was calibrated with a Ni-NiCr thermocouple inside the microscope with an accuracy of +_lO’C.

Eight Cu-AI alloys were melted in graphite crucibles under high vacuum and then cast into a copper mould under an argon atmosphere. The initial materials were 99.999% Cu and 99.9980/, Al. The compositions of the alloys were chemically analysed to be 10.0, 15.0, 17.0, 17.5, 18.0, 18.5, 19.0, 19.5 & 0.03 at.% Al. Cylindrical samples of 7.5 mm diameter and 1Omm length were machined for differential thermal analysis. Sheets of the Cu-18, 18.5 and 19.5 at.% Al alloys of about 90pm thickness were cold rolled for transmission electron microscopy. From the sheet of the Cu-18 at.% Al alloy, appropriate samples were punched for electrical resistivity measurements. The sheets and samples were homogenized by the following heat treatment (under an argon atmosphere): 1 h at 800°C. 800+ 650°C at 5’C/h, 650~ 520°C at l’C/h, 5904 540°C at O.Z’C/h, 540 + 500°C at l’C/h, 5004 450°C at 5”C/h, 24 h at 450°C. By this 3. RESULTS AND EVALUATIONS heat treatment, eutectoidal precipitation of the The differential thermal analyses (Fig. 1) display a y,-phase could be prevented even in the Cu-19.5 at.“,6 minimum of the AT/T curve (AT = T- To. T= temAl alloy. perature of the Cu-Al sample, To = temperature of The homogenized samples for differential thermal analysis were further cooled from 450°C to room tem- the Cu reference sample) at about 28O’C for all the Cu-AI alloys examined. This is a well known dynamiperature at 5’C/h. The analyses were run at a heating cal effect due to the relatively fast heating (S’C/min) rate of S”C/min, keeping the samples under an argon atmosphere. An annealed copper sample of the same of the slowly cooled (5’C/h) alloys [24]. The SRO begins to decay noticeably at about 24O’C when diffusize was used as a reference. sion becomes fast enough; at about 32O’C. the degree A Cu-18 at.% Al resistivity sample was quenched of SRO is reduced to the equilibrium value. At higher from 45O’C in water and annealed at 25O’C under

STRCCTCRE

OF I-CS-.A’: XLLOYS

:I:ii

Al concentrations

i.13 and 13.5 at.“, Ali. a second energ absorption was detected leading for 13.5 a:.“, Al to a second minimum of the JT Tcurve 2~ 37YC.

-2.8 -3 2 -

17 ot % AL

-1.8 .2.2. -2.6 -

17.3

ICC

at % API

l5C

2X

2x Temperature

‘CO

30

2CO

2%

300 r,

300

3M

4oc

430

4CQ

450

“C

35a

I

-0 3 ix

I

This is due to the dissolution of x3 precipitates formed during slow cooling [‘i]. Electricai resistivity measurements uere carried out for studying the kinetics of isothermal short range ordering. The resistivity of a Cu-lg at.“,, Al specimen was measured to be 11.716 /LRcm immediately after a water quench from 4SOC. After isothermal annealing at 25O’C for 1 h. the resistivity had dropped to 11.2-15@? cm. i.e. by about 4”,. During further annealing fl h to Y days). the resistivity- slowly increased by about O.l’?, up to an equilibrium value of 11.37 @2 cm (Fig. 21. This small :csistivit!- increase is reported here for the first time, whereas the resistivity drop at’ the beginning of annealing is a ~11 known effect [ 16, IS]. Figure 3 shows a [OOl] electron diffraction pattern of Cu-18 at.‘, Xl quenched from -I5OC, equilibrated at ZO’C, and finally again water quenched to retain the equilibrium state. Besides diffuse SRO maxima, streaks can be seen arranged around the origin and the f.c.c. reflections. The SRO maxima appear at intersections of such streaks. The streaks are due to SRO and can bz explained in terms of thz Fermi surface [4]. Figure i shows schematically the positions of the SRO maxima in terms of a parameter D which has been shown to be dependent on the composition of the ahoy [-I. 71. Comparing Figs. 3 and 4, D was obtained to be 0.337 2 0.007 (in units of l/a, where a is the lattice parameter of the f.c.c. structure) for 18 at.?, Al. Figures S(a)-(e) show how the SRO maxima get n-eaker and more diffuse during heating up the specimen inside the microscope. Diffuse maxima indicating SRO can still be detected at 4OO’C. The spacings of the SRO maxima (all not exactly lying in the IlO-plane of the reciprocal space) do not change during heating up, indicating that D is independent of temperature. Figure 6 shows a dark field image of a Cu-15 at.:: Al splat taken with a fundamental reflection in two

19.5 at % AL !50

200

250

Temperature

300 T,

350

400

450

‘C

Fig. 1. DifTerential thermal analyses of Cu-Al alloys with fO-19.5 at.“,, Al at a heating rate ol S’C:min’. Initial state: homogenized at 15O’C. 450’C-room temperature at 5’C h.

Fig. 2. Electrical resistivity of (3.1-18 at.“; .41 water quenched from JSO’C and annealed at 25O’C: measured at 20’C after water quenching.

7f?

GAUXG

AVT)W.~RLl>fOXT:

THE STRUCTL’RE OF +X-AI

ALLOYS

Fig. 3. G-18 at.:: Al, homogenized at 150% 450’C:HL0 + 125 days ZjO’C:HzO. Electron diffraction pattern, n = [COl], V = 200 kV.

beam condition (n = [m], g = [lli]). It reveals a tweed-like strain contrast pattern with apparent spacings of 3-4 nm. Dislocation loops as they occur in copper quenched from high temperatures were not detected. It is straightforward to assume that the observed contrasts are due to SRO associated with domains. However, splat cooling could also give rise to lattice defects such as vacancy clusters or vacancyj solute clusters. Therefore, annealed splats were also examined. Figure 7 shows a bright field image of a Cu-15 at.% Al splat annealed at 275°C (n = [no], g = [002]). It can be seen that the annealing treatment did not change the kind of the contrasts; thus it can be concluded that they are largely caused only by SRO. Stereo electron micrographs were taken from a short range ordered Cu-18 at.% Al specimen (homogenized at 45O’C, 430’C;HzO + 128 days 250C/;HzO) which was prepared electrolytically. The stereo pairs (not published) showed profuse contrasts caused by surface roughness, but also strain contrasts in the interior of the foil which are interpreted to be due to SRO. Figure 8(a) shows a [OOI] electron diffraction pattern of Cu-19.5 at.% Al annealed at 340°C. The following superlattice reflections could be detected (in units of l/u): 100, (1 l/S 0), 1 3$? 0, 1 5,‘s 0, (1 7/8 0), 110, (1 9,:8 O), 1 11!8 0, 1 13/8 0, (1 15,‘8 0), 120, . . . . indicating the presence of the phase z2 [7]. Furthermore, reflections of the type (0, 1 + I+, 0). . . . could be found which can be explained by periodic displacements of the atoms out of their ideal positions caused by the superlattice. Figure 8(b) shows a dark field image of the ~z precipitates formed by a

superlattice reflection. Figure 9 schematically shows the reciprocal lattice of the rZ superlattice structure if the parameter D is set 3:8 and the very weak reflections are ignored [7]. Figure IO(a) shows the unit cell of the rz superlattice, with the long axis in any (001) direction. Thus, three orientation variants of the structure are possible giving rise to three different sets 022

222

Fig. 4. The positions of the short range order diffuse scattering maxima in reciprocal space for x-Cu-Al alloys. D is dependent on the Al concentration

of the alloy.

GACDIG

&SD

WARLIMONT:

THE STRUZKXE

OF Ku-x!

ALLOYS

‘!J

Fig. 5. Cu-18 at.“i Al, homogenized at 45O’C. 450’C,‘HzO + 128 days 250°C/H,0. Electron diffraction patterns, n = [llO]. V= 2OOkV. taken at different temperatures: (a) room temperature: (b) ?WC; (c) XWC; (d) 35O’C; (e) 4OO’C.

of superlattice reflections labeled in Fig. 9 by x, r and :. Long time annealing (128 days) of Cu-18.5 and 19.5 at.:; Al at XO’C yielded diffraction patterns (Figs. lla and 12a) displaying the following superlattice reflections: 100, (1 1.14 O), (.l 3r1-1 0). 1 5 14 0, (1 7 11 O), 1 9114 0. (1 11 14 0). (1 13.14 0). 110. (I 15’1-l 0). (1 17:14 0). 1 1924 0. (1 I1 14 0). 1 ‘3-l-2

0, (1 25 ‘14 0), (1 27114 0). 110,. . . . Furthermore, reflections of the typx (0, 1 f 2.7, O)? . could also be detected. Very weak reflections are again written in parentheses. If the very weak reflections are ignored. the superiatrice reflections schematically shown in Fig. 9 can be made fo fit the experimental reelections by setting D = 5 1% Thus. a new superlattice phase

714

G.U:DIG

Fig. 6. G-15

.%%D W.4RLI%fONT:

at.*,, Al. splat cooled

from

THE

STRUCTURE

115O’C. Dark

has been found which shall be designated x3. Figure 10(b) shows the unit cell which is proposed for the new x3 superlattice structure. The three orientation variants yield all reflections experimentally detected including the very weak ones, with the exception of (0, 1 &-2!7. O),. . . The latter ones are assumed to be due to periodic atomic displacements caused by the superlattice. Figs. 1i(b) and 12(b) show dark field

field image.

OF

z-Cu-4

ALLOYS

n = [iZ]. g = [llf].

b’= IOOkV.

images of coherent x3 precipitates of about 25 nm diameter. Besides the superlattice reflections, Fig. 11(a) shows SRO streaks caused by the coexisting r-matrix phase. However, SRO maxima cannot be observed because they obviously are so close to much stronger superlattice reflections that they cannot be separated from them. In Fig. 12(a), SRO streaks cannot be observed. since at 250X. the fraction of the r-phase

Fig. 7. G-15 at.“; Al. splat cooled from IljO’C, room temperature--r 27S’C at 5.C:h, 24h 275’C, 27S’C -* room temperature at 5’C;h. Bright field image, B = [i?O]. g = [OG!]. V = 100 kV.

Fig. 3. Cu-19.5 at.“, .41. homogenized at -I50 C. 150’C/H20 + 8 days 3O’C,‘H,O. (a) Electron diffraction pattern. n = [OOl]. V= 3-00kV; (b) dark field image. n = [LlOj. g = [ITO], I-= 200 kV.

less than in in Cu-19.5 at.“, Xl is considerably Cu-lg.5 at.“, Al. The kinetics of the formation of z,-precipitates was studied taking electron diffraction patterns (Figs. 13a and 13a) and dark field images (Figs. 13b and 14b) from Cu-19.5 at.“; M specimens annealed at 250X for 5 min and 60 min. The electron diffraction patterns onI> display the superiattice reflections in the schematic Fig. 9. The tery weak reflections found in the equilibrium state (Fig. 13at could not be detected.

The parameter D turned out to increase with increasing time. After 5 min annealing, annealing D = 0.350 5 0.001: after 60min. D = 0.352 2 0.002. These values are clearly smaller than the equilibrium value 5:14 = 0.357 (after 128 days annealing). The diameter of the zj precipitates was measured to be 6nm after 5 min annealing, and 10nm after 60min. After 5 min annealing. streaks like those due to SRO could be detected which practically disappeared after 60 min annealing.

GAUDIG

0 f.c.c.fundamental superlattice

.ANDWXRLIMOAZ:

THE STRUCTIXE

reflections

0

LI,

reflection

0

Long period superlottice

positions reflection

positions

Fig. 9. Reciprocal lattice of the Cu-Al superlattice structures x1 (D = 3 5) and x3 1.D= 5,04j. Very weak reflections are ignorrd. The positions of the superlattice reflections are labeled by .Y..Yor z. which yields the long axis direction

OF x-Cu-At ALLOYS

the exampit draw% the .r-axis) is a preferred direction, so that three orientation variants are possible. In Fig. 15(a). these three orientation variants of the structure within the microdomains are symbolized by the preferred direction. The sharp boundaries separating the microdomains arise from changes of the preferred direction. Every antiphase shift system consists of an array of parallel shift planes the traces of which are drawn in Fig. 15(b). All initial AI positions on such a shift plane are shifted along this plane to a neighbouring lattice position of the f.c.c. disordered structure by shift vectors S, = (--u .2. 0, -n.2) or S, = (-(1.2, -rt$. 0) whose traces io the plane of projection are drawn. lf two perpendicular shift planes of the two antiphase shift systems intersect. then the two shift vectors S, and Sz are added to obtain the resultant shift vector (-0. -u/Z, -a 2~. The arrangement of the shift planes of either antiphase shift system is determined by a step function I&<) as proposed by Fujiwara [32]. ~~~j is defined to be + 1 or -1 depending on the spatial coordinate 2 in the direction of the shift plane normal (in the case draan, the I’- and z-coordinate). According to Fujiwars a (100) plane of the primitive lattice formed by the initial Al-positions will be a shift plane or not, depending on whether the step function I&<) at this positions is - 1 or + 1. This is sho&n in Fig. 15(b).

of the unit cell of the appropriate orientation variant.

4. FORMULAl-fON MODEL

OF A MICRODOMAIN

FOR I-G-AI

ALLOYS

The SRO diffuse X-ray scattering data for CL-16 at.“; Al measured by Borie and Sparks [3] are used to establish a quantitative microdomain model. Previously, Borie and Sparks explained their experimental results assuming the existence of tetrahedral clusters of 4 Al atoms each. It will be shown that their data can also be explained by assuming that the alloy consists of contiguous microdomains, that the structure within the microdomains is a two-dimensional antiphase shift structure, and that’adjacent microdomains have different orientation variants of the structure. Figure 15(a) schematically shows the suggested structure of a short range ordered single crystal of Ku-Al consisting of microdomains with sharp boundaries. In Fig. 15(b), the proposed structure within the microdomains is shown. The structure is a twodimensional antiphase shift structure based on the Cu,Au type superlattice structure (LIZ). Only the positions of the Al atoms need to be considered. The filled circles represent the initial AI positions of the L12 structure, located at the corners of the unit cells of the f.c.c. disordered structure, and forming a primitive lattice. Tao antiphase shift systems with shift plane normals in two of the three (lOO>-directions are constructed. Hence. the third -direction (in

D=3/8(a,l

(al Fig. 10. Unit cells of the Cu-AI superlactics phases %(Iand z~. The disordered structure is f.c.c. The positions of the Al-atoms are drawn as open circles. The dashed lines mark antiphase pianes. (a) x2 (0 = 3:S, M = 4.3): (b) xj CD= 5X-I. M = 7:jj.

Fig. 11. Cu-18.5 at.?: Al. homogenized at 45O’C, 4WC,H,O * 128 days 2jO’C,H10. (at Electron diffraction pattern. n = [OOl]. V = 200 kV; (b) dark field image, n = [llO]. g = [OOI]. i’ = XOkV.

GACDIG

*XI fVARLi~f0~~:

THE STRt‘CTCRE

OF r-C11-4: ALLOYS

Fig. 12. 0~19.5 at.?; Al, homogenized at 450X, 450’CHH30 + 125 days ZSOC’H~O. (a) Electron diffraction pattern, n - [Ool]. V = 200 kV; (b) dark field image. n = [I lo], g = [llO]. C;= 300 kV.

Fig. 13. Cu-19.5 at.“, Al. homogcnizcd at 4jO.C. 150’C;H,O + 5 min 250’C;H10. la) Electron ditfrxtion pattern. n = [0+X]. i’ = 200 kV; (bl dark field image. n = [1 LO],g = [ITO]. i’ = ‘00 kI’.

Fig. 14. Cu-19.5 at.:; Al, homogenized at 4%X, 450’C,‘H20 + 60 min Z503C;H@ (a) electron diffraction pattern n = [OOI]. Y= 200 kV; fb) dark field image n = [llO], g = [LIOJ. V= 100 kV.

GAUDIG

AND WARLIMONT:

THE STRUCTURE

OF x-Cu-Al ALLOYS

721

(a)

Antiphase

Fig. 15. Microdomain

function

of shifts in 2x plones

model. (a) Arrangement of the microdomains; (b) structure within the microdo. mains with shift plane normals parallel to the y and 5 axes.

Fujiwara’s step function can be defined as follows: $(5) = (-I)” for

(m = 42, 3, . . .). The M, (n = 1, 2, 3,. . .) and d, (m = 1, 2, 3,. . .) are chosen according to normal distributions with mean values M and zero, and standard deviations Go and uZ, respectively. M is the mean step length, crl determines the degree of ‘non-uniformity’, cr2 the degree of ‘irregularity’ of the arrangement of the shift planes. to gives the location of the Jr(t) step function on the t-axis and is chosen according to a rectangular distribution on an interval of length 2M. The two antiphase shift systems are chosen to be equivalent, which means that for either antiphase shift system the M, ol, and tr2 have the same values. Not every Al position can be occupied by an Al atom because l/4 of all lattice points are Al positions, and the mean atom fraction of the Al atoms of the alloy, 7, is less than l/4. Accordingly, every Al position has got to be occupied by an Al atom with a probability of R @ = 0.16 in the case treated).

The SRO X-ray intensity was calculated by summing up the scattered intensities from all microdomains. For this purpose, the microdomains are approximated as spheres of the same radius R, so that their total volume is equal to the volume of the specimen. One of these spheres is marked in Figs. 15(a) and (b) as a dashed circular line. The relative locations of the centers of the spheres in a f.c.c. unit cell are chosen according to a rectangular distribution. The microdomain model can be made to fit Borie and Sparks’ data of SRO X-ray scattering (that is the scattering after removal of the temperature-, Compton-, and atomic size effect) from a single crystal of Cu-16 at.% Al (2 h 75O”C, 75O’C-,room temperature at 2o”C/h, 54 h 150°C). The calculations were carried out using a computer with probability generator. 500 microdomains were taken into account to suppress statistical fluctuations. Figure 16 shows the comparison of the theoretical with the experimental SRO intensity along several scans in the 001 plane of reciprocal space, setting R = 2.3, ,M = 1.67, Q1 = 0.28, (Ft = 0.07 (in units of a). It can be seen that the microdomain model is suited to explain the With quantitatively experimental data. a = 0.365 nm, the domain size 2R is found to be about 1.7 nm. The calculations have shown the validity of the relation D = 1/2M which was originally found for the case of one-dimensional antiphase shift

GAUDIG

722

0.5

WARLIMONT:

THE STRUCTURE

___/w.._

hl0

r

AND

.

h I

-0.5 1,

I.5

2 I

2kO

=

“‘p=l_ I

“0.5

D = 2,/5 KP.iilJ -2

ro.5

K Fell0

I.5

2

I5

I

k

-

Fig. 16. Short range order X-ray scattering intensity I for Cu-16 at.?; Al in units of lfc.-j-~,l’ electron units/atom along the scans h 10, 2 k 0, 1.3 k 0, 1.7 k 0. Comparison of the experimental data by Borie and Sparks (full lines) with the theoretical results according to the microdomain model for R = 2.3 a, M = 1.67 a, o1 = 0.28 a. c2 = 0.07

u (dashed lines).

structures (based on the LIZ superlattice structure) [32]. The structure within the microdomains cannot be a one-dimensional antiphase shift structure since these structures give rise to intensity maxima at the Lls superlattice positions (100, 110, . . .) which are not observed in the case of SRO. By adding a second antiphase shift system, the L12 maxima are eliminated. 5. DISCUSSION 5.1 Short range order A statistical mechanical theory of homogeneous SRO [33] was used to explain the diffuse SRO scattering from binary copper alloys [4,34] taking into account periodic long range interactions caused by electronic screening of the ions. These interactions are effective in directions near (110) in which the Fermi surface is almost flat. The theory yields diffuse intensity streaks in the 001 plane of reciprocal space. The location of the streaks is given by the equation ZnK,/a

G,I,O(l

-

E +

Ey*,/V,“)’

31

0

and Kr,riO = magnitudes of KF in
(K~.llo

-x_______

k = g +

-

2 I

I

ALLOYS

(110) [34]. The SRO maxima are predicted at intersections of such streaks. To explain all of the SRO maxima in the (001) plane of reciprocal space, streaks lying in planes parallel to the (100) and (010) plane must also be taken into account. Assuming the Fermi surface has a completely flat area perpendicular to the (llO)-direction. the following formula for D (in units of I/a) for &u-AI alloys was found [4]:

k

I ,

‘0.5 I ,

OF PCU-AI

(I)

(g = 0 or any reciprocal lattice vector of the f.c.c. structure, h&/a = Fermi wave vector) and the condition that the direction of K, must be near

GAUDIG

AND

WARLIMONT:

THE STRUCTURE

tion by Gehlen and Cohen [37] yielded a SRO structure of Cu-14.5 at.:, Al which is characterized by row-like arrays of Al atoms in (lOO)-directions. However. this result cannot be considered to be realistic because only the first 3 SRO parameters were taken into account. Hashimoto developed a correlative microdomain model for short range ordered binary copper alloys [38]. He assumed spatially correlated Liz microdomains (e.g. in the case of a Cu,Au alloy) to be embedded in a disordered matrix. For z-Cu-Al however, a case not treated by Hashimoto, the Lll domains are supposed to be so close (because PI = 1/2D is small!) that there is no space left for a disordered matrix. Even if domains of only one L12 unit cell would be assumed, they would come in touch with each other forming antiphase boundaries. From the experiments carried out. no conclusion can be drawn whether the SRO structure (i.e. the microdomain arrangement) of a-Cu-Al alloys is metastable [30] or just due to equilibrium concentration fluctuations [39]. 5.2 Equilibrium

superlattice

strucrures

If the (coherent) solubility limit of r-Cu-Al is exceeded, the phase xl (at 340°C) or x3 (at 250°C) is coherently precipitated. The structures of the phases rz and Y) are one-dimensional antiphase shift structures based on the Lll superlattice structure, and can be constructed by assuming a uniform (ct = 0) and regular (az = 0) arrangement of shift planes with a step length of M = 1/2D [32]. For az, M = 4/3; for x), M = 7/S. 5.3 Transitional

superlattice

structures

Although equations (2) were developed for the SRO state, they also hold for the initial stage of precipitation of the superlattice phase (z)) when the precipitates are still very small. For Cu-19.5 at.% Al, equations (2) yield D = 0.345 which is smaller than the equilibrium value D = 5/14 = 0.357 of the phase r3. This explains the formation of transitional structures within the precipitates during annealing (at ZSO’C), with increasing values of D as the precipitates grow bigger, until the equilibrium superlattice structure of the phase xj is established. An independent study [40] of Cu-18.9 at.72 Al (quenched from 65O’C and annealed for 30min at 250°C) yielded D = 0.350. The authors [40] approximated the structure to correspond to D = l/3, and falsely considered it to be the equilibrium structure. Tomokiyo et al. [14] found D to be 0.339 + 0.008 for a Cu-18.6 at.% Al alloy (cold reduced by 25% and annealed for 400 h at 200°C). They assumed the alloy to be short range ordered. However, the state of the alloy should rather be considered to be an early stage of a superlattice precipitation (z3), since the Al concentration exceeds the (coherent) solubility limit of r-Cu-Al.

OF x-Cu-Al ALLOYS

723

Acknowfedyemenrs-We

are grateful to Professors V. Gerold and K. Schubert for helpful discussions. to Mr. L. Bitzek and Mr. H. Dorrer for extensive technical help, and to Mr. T. Godecke for carrying out the differential thermal analyses. The support of this work by the International Copper Research Association is gratefully acknowledged.

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29. R. 0. Scattergood and M. B. Bever, Phil. .\fag. 22, 501 (1970). 30. H. Warlimont and H. P. Aubauer. Z. ,Merolfk. 64, 484 (1973): ibid. 65, 297 (1974). 31. P. Furrer and H. Warlimont, Z. Merallk. 62, 12 (1971). 32. K. FuJiwara. J. phys. Sot. Japan 12, 7 (195i).

724

GAUDIG

I\,XD WARLIMONTi

THE STRUCTURE

33. P. C. Clapp and S. C. MOSS, Whys. Reo. 142, 418 (1966); 171, 754 (1968); ibid. 171, 764 (1968). 34. S. C. Moss, Phys. Rec. Left. 22, 1108 (1969). 35. 3. E. Warren, B. L. Averbach and 8. W. Roberts, f. UQQl.

PhyS.

22, 1493 (1951).

36. R. 0. Williams, Metali. Trans. 5, 1843 (1974).

OF r-&-Al

ALLOYS

37. P. C. GehIen and J. B. Cohen, Php. Rev. (A) 139, 844 (1965). 38. S. Nashimoto, Acta cr~stuliogr. ,430, 792 (1974). 39. 5%.E. Cook, J. Phys. Gem. Solids 30. 3427 (1969). 40. A. Varschavsky, M. I. Perez and T. LGbel, bferuif. Trans. (A) 6, 577 (1975).