An x-ray investigation of age hardening in alag

AN X-RAY

INVESTIGATION

OF

C. B. WALKERt

AGE HARDENING

IN AlAg*

and A. GUINIER$:

,411 r4l.Q alloy containing 20 per cent Ag by weight has been investigated with both low angle and high angle X-ray scattering techniques. The diffuse scattering from samples quenched from the region of solid solubility has shown that during the quench the majority of the Ag atoms of the alloy have clustered together into small spherical aggregates, each of which is surrounded by regions low in .b\g content. \%?th annealing the clusters first grow in size, the atoms continuing to remain on the matrrx lattice sites. After sufficient annealing the hexagonal y’ precipitate. of composition AgsAl abruptly appears in the form of platelets thin in the (000.1) d’n-ection, which exhibit faults in the stacking of the (000.1) planes. On further annealing the platelets grow and become more perfect. The interpretation of the mechanism of precipitation offered by Guinier thus appears to be justified for this alloy. IJNE

IN\‘E.STIGATION

AUX

RAYONS

X DU VIEILLISSEMENT

DrWS

AlAg

Un alliage contenant 20 pour cent d’Ag en poids a et& investigue au moyen des methodes de dispersion des rayons X a petit angle et a grand angle. La dispersion diffuse donnee par les echantillons trempes a partir de la region de solubilite solide a montre que pendant la trempe, la majorite des atomes d’Ag contenus dans I’alliage se sont group& en petits amas spheriques, entour& d’une region a faible teneur en Ag. Un recuit provoque, au commencement, une croiseance des amas, !es atomes continuant a occuper leurs places dans le reseau de la matrice. Aprils un temps suffisant de recuit, le pr&ipitC hexagonal y’, de composition AgsAl apparait subitement sous la forme de lamelles amincies dans la direction [OOOl] et presentant des defauts d’empilage dans les plans (0001). Si on prolonge le recuit au dela de ce stade, les lamelles continuent a croitre et deviennent plus parfaites. _4insi I’interpretation du mecanisme de precipitation, due a Guinier, est just.iliCe dans le cas de cet alliage. RONTGENUNTERSUCHUNG

DES

AUSHARTENS

EINER

Al-.4g LEGIERUSG

Eine AI-Ag Legierung mit 20 Gew. prozent Ag wurde sowohl mit Kleinwinkelals such Weitwinkelstreuungsmethoden untersucht. Die diffuse Streuung, die bei Proben gefunden wurde, die aus dem Phasenbereich dcr festen Msung abgeschreckt worden waren, zeigte, dass sich die Mehrzahl der Silberatome wahrend des Abschreckens zu kleinen kugelformrgen .4ggregaten zusammenballen. Jedes dieser Aggregate ist von einem Bereich verminderten Ag-Gehalts umgeben. Beim Gltihen wachsen die Aggregate zuerst, und die Atome verbleiben in den Gitterplatzen der Metrix. Nach weiterem Gltihen tritt pl6tzlich das y’ Precipitat dcr Zusammensetzung .4gs.4l auf. Dies sind Plattchen, deren kurze Achse in der (000.1) Richtung liegt, und die Stapelfehler (“stacking faults”) in der (000.1) Ebene aufweisen. Die Plattchen wachsen bei weiterem Gltihen und werden gleichfiirmiger. Im Falle dieser Legierung erscheint die von Guinier gegebene Erklarung des Ausscheidungsmechanismus gerechtfertigt.

Introduction In studying the course of the age hardening .transformation in various alloys X-ray diffraction techniques have provided information otherwise unattainable. This is particularly so in the study of the early stages of age hardening, where, following techniques introduced by Guinier [l] and Preston [2], the investigation is focussed primarily on the diffuse scattering outside of the normal Bragg reflections. While different investigators have agreed on descriptions of the final stages of the phenomenon of precipitation, disagreement still exists concerning the description of the first stages, this disagreement generally being over the manner of interpretation of the diffuse X-ray scattering. Guinier [3], in studying several alloy systems showing precipitation, has interpreted the scattering as s&owing that the solute atoms in the alloy first clty@r together in&o zones, ., *Received April 13, 1953. tDepartment of Physics, Mchusetts nology, Cambridge, Mass., # .$.A. SConservatoire Nationale des Arts et Saint Martin, Paris, France. ACTA

METALLURGICA,

VOL.

Institute

of Tech-

MCtiers,

292,

1, SEPT.

1953

rue

regions which may show irregularities in terms of interatomic spacings but which are coherent with the parent matrix in that the general disposition of atoms is the same as that for the matrix. On annealing these zones first increase in size, generally showing some modification of internal atomic arrangements tending towards some regular structure, but after further annealing there is an abrupt transition, the zones disappearing and the true precipitate, with its different structure, appearing. Thus this interpretation basically requires the existence of two distinct stages in the precipitation transformation. A different description is offered by Geisler and his associates [4], who maintain that the diffraction patterns “can be interpreted as evidence for precipitation particles which are only a few unit cells in size. Anisotropic growth can be followed until the particles exceed the size in all dimensions necessary for sharp diffraction effects. Interpretation involving pre-precipitation phenomena again can be abandoned.” In view of this difference in interpretation, it was thought worthwhile to make a further investigation of some alloy system which

WALKER

AA-D GliISIER:

had already been studied by both authors in order to determine which interpretation seemed to be justified. Of the several age hardening alloys which have been studied, the system of aluminum rich AlAg seemed to be one which should give the clearest answer to this problem, since not only does the large difference in atomic scattering factors render the diffuse scattering more easily observable, but also the equal atomic “radii” eliminates possible diffuse scattering due to lattice distortion caused simply by the different sizes of the constituents [5]. Several investigations of this system have been reported, beginning with those of Barrett and Geisler [6] and Guinier [7]. with two of the more recent studies being those by Geisler and Hill [4] and Guinier [3]. One fact stands out in a comparison of the experimental results of these investigations: whereas most investigators have found rods of diffuse scattering extending along various matrix (111) directions through reciprocal lattice points, Guinier reported essentially the same phenomenon, but as a characteristic of the second stage of precipitation, since earlier in the annealing history, before the appearance of these rods, a quite different scattering distribution was found. This first type of scattering, found for alloys immediately after sharp quenching from the solid solution and after short anneals at low temperatures, is best described as a distribution of scattering power in the form of spherical shell-like regions surrounding each of the reciprocal lattice points.* ‘To explain this scattering distribution, Guinier [8] offered an interpretation based on an analogy with the scattering from amorphous bodies, describing the Ag atoms as clustered together into spherical zones, with these zones displaying a liquidlike distribution with a marked most probable nearest neighbor distance, and from the positions and breaclths of the shells he determined the nearest neighbor separation and the size of the zones. This interpretation met with some difficulties, particularly in the matter of the quantitative determination of cluster size and inter-cluster distances, as was pointed out by Jagodzinski and Lnves [9]. To clarify this point, it was felt that the primary objective of this study should be a quantitative study of the intensity distribution in this first type of scattering, which, it was hoped, would make possible a more accurate interpretation of the

*In this article the term reciprocal lattice point corresponds to each reciprocal lattice intersection having a non-zero scattering power (P # 0).

:\GE

lI;\ICI)ENISG

atomic

distribution

IS

;\L.\(;

in this

569

first stage of the precipi-

tation. Of the several experimental techniques available, the study of small angle scattering was chosen as the basic technique to be employed. This method, though not used in the most recent investigations [lo ; 111, is particularly powerful for several reasons. First, at low angles not only do the atomic scattering factors have their largest values but also there is a minimum amount of Compton and temperature diffuse scattering present. _\gain, in the stud>- of single crystals where the sharpest possible Bragg reflections are demanded, the extent of the (000) reflection is determined only by the sharpness of focus of the primary beam, whereas the extent of other Bragg reflections is a function not only of the divergence of the beam but also of the degree of perfection of the single crystal. While singlecrystals could be grown with a fair degree of perfection, maintenance of this degree of perfection while at the same time reducing the crystal thickness to the optimum thickness for transmission patterns (0.04 mm.) was found extremely difficult. Lastly, for this particular system the diffuse scattering is found in the form of spherical shells surrounding each reciprocal lattice point as will be further discussed below, so that for measurements of the scattering about the (000) reciprocal lattice point, easily preparable polycrystalline foils would give the same scattering as that from single crystals.

Experimental

Study of the First Stage of Age Hardening

The alloy studied, of 20 per cent Ag by weight (i.e. 5 per cent atomic), was prepared in ingot form and given homogenizing treatment bq- the Office National d’l?tudes et Kecherches A&-onautiques. By successive annealing and cold rolling this was reduced to strips of 1 mm. thickness. While several of these strips were used in preparing single crystals by strain-anneal processes, the others were reduced by further cold rolling and annealing to polycr>-stalline foils 0.04 mm. thick. Some of the singlecrystals were reduced to thicknesses of the order of 0.06 mm. for transmission studies by a combination of polishing and etching, two etches being found suitable: H2F, followed by HNOa, and a solution of NaOH followed by HNO,. Samples of the polycr).stalline foil were annealed at 520°C for periods of the order of 24 hours, quenched in water and studied with the small angle scattering equipment developed by Fournet and Guinier [12]. This had as a source of X-rays an

570

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METALLURGICA,

electron beam focussed on a rotating Cu anode. The CuKa radiation was monochromated and focussed by successive diffraction from the (10il) planes of first one, then a second bent and ground quartz crystal, the focus of the first monochromator serving as a source for the second. The beam from the second monochromator was focussed on the flat film, excessive blackening from the direct beam being prevented by the presence of a thin Cu strip as beam stop placed 2 mm. before the film. Sets of slits limited the vertical and horizontal divergence of the beam, and further slits limited the parasitic scattering from the monochromators and from the edges of the first slits, so that with monochromators, slits and film contained in an evacuated chamber, extraneous scattering was reduced to a minimum. Resolution was excellent; with a sample to film distance of approximately 10 cm., scattering at angles down to 20 = 24’ was clearly visible; and with the X-ray tube operating at 45 kv and 45 ma legible patterns were obtained with only two hour exposures. The typical pattern for a quenched foil showed a diffuse ring surrounding the trace of the direct beam ; one such pattern, enlarged three times, is reproduced in Figure la. The diameter of the ring depended noticeably on the speed of quenching, slower rates giving rise to smaller ring diameters. When single crystal specimens were given the same anneals and quenched, it was confirmed that their transmission patterns showed this same ring of circularly, symmetric scattering, independent of the orientation of the crystal relative to the X-ray beam. ri description of these results in terms of the matrix reciprocal lattice is then that the (000) reciprocal lattice point is surrounded by a spherically symmetric, shell-like region of scattering power. When these quenched samples were annealed for various lengths of time at several temperatures between 20°C and 4OO”C, the diameter of the ring of diffuse scattering diminished and the intensity increased as the anneal progressed as is shown in Figure lb. The rate of decrease of diameter was greater, the higher the annealing temperature; Figure 2 is a graph of the diameter as a function of time and temperature. For each temperature, as the anneal continued the ring eventually diminished to such an extent that all details were obscured by the beam stop, the pattern showing only a blur of scattering, as is shown in Figure lc. Photographic studies of the large angle scattering from single crystals showed that when the (000) reciprocal lattice point was surrounded by its shell of

VOL.

1,

1953

a

c

d.

:

t FIGURE 1. Small a?gle scattering of CuKol radiation by polycrystalline AlAg m various stages of age hardening; (a) quenched from 520°C; (b) quenched from .i2O”C, annealed 25 minutes at 205°C; (c) quenched from 52O”C, annealed 65 minutes at 205°C; (d) quenched from 52O”C, annealed lO.days at 140°C.

scattering power, each of the other reciprocal lattice points was also surrounded by a similar scattering distribution. The Bragg reflections were rather distorted, a result of crystal imperfection and beam divergence, but the shell was clearly evident and its position, relative intensity, and diameter could be determined. The results of those measurements showed that each of these shells of scattering power had the same diameter and scattering power in reciprocal space as that of the shell surrounding the (000) reciprocal lattice point, and eaclz shell was centered on its respective matrix reciprocal lattice point. This requires that, whatever the form of the atomic distribution giving rise to this anomalous scattering, the atoms of the alloy must be situated on lattice sites having interatomic spacings and

WALKER

AND

GUINIER:

AGE

HARDENING

IN

571

ALAG

starts apparently from zero, mounts rapidly to a peak at 20 = 2”20’, then decreases more slowly, reaching zero at an angle of 26 = 9”.

.6

Interpretation

of the Diffuse Scattering

The observed periodicity of the diffuse scattering in reciprocal space having shown that the atoms still remained on the matrix lattice sites during this first stage of the transformation, it seemed appropriate to attempt an analysis based on the theory of scattering by binary alloys with local order config-

8 FIGURE 2. Change in diameter of ring of diffuse scattering as a function of time for several annealing (A) 100°C; (B) 140°C; (C) 165°C; (D) 205°C;

temperatures: (E) 255°C.

orientations identical to those of the parent matrix, i.e., a most probable supposition, the atoms are located on lattice sites of the parent matrix. Accurate quantitative determination of the intensity of diffuse scattering with photographic techniques is difficult, given, among others, the problem of subtraction of parasitic and background scattering, whereas this is much more simply done when the detection and enregistry of the scattering is done with a Geiger-Mtiller counter and associated scaling circuits. Thus for our quantitative measurements of intensity we employed equipment developed by Blin [13] for the particular study of small angle scattering. Radiation from a sealed, Cu target tube was monochromated by the (lOi1) planes of an asymmetrically cut, bent quartz crystal and focussed at a point on the circle traversed by the counter slits. An evacuable glass chamber with thin polystyrene windows was mounted on the arm supporting the G.M. counter, in between the counter slits and the sample at the center of the table, so that all but 3 or 4 mm. of the beam path between sampleand counter could be maintained in vacuum. With this arrangement, by carefully adjusting the monochromator and slits, intensities could be measured down to an angle of 20 = 50’ without the corrections for parasitic scattering becoming too large. The necessary corrections were made from measurements taken without the sample in position, these being corrected for absorption in the sample. The measured intensity distribution, corrected for parasitic scattering, obtained with this apparatus for a polycrystalline specimen quenched in water after a 24-hour anneal at 520°C is reproduced in Figure 3. This distribution, characteristic of quenched single crystals as well as polycrystalline foils,

7 6

FIGURE. 3. Intensity of diffuse scattering by a polycrystalline sample quenched from 520°C as a function of scattering angle, 20. Radiation: CuKol.

uration, best expressed in a recent article by Cowley 1141. Though all applications to date of this theory have been concerned with alloys showing the order-disorder transformation, there is no such limitation contained in the theory. The only serious limitation in the theory is that the atoms remain on the matrix lattice sites. Within this limitation, the diffuse scattering from a binary aHoy due to the particular arrangements of its two types of atoms is described by a three-dimensional Fourier series:

(1)

ID.” = NWd'h(fA -

exp y

(S -

f~)’ i F G

z %n,na

I)

So). ( nlal’ + 12282’+ n3a3’)

where: ID,” is the scattered intensity in electron units; NmAma (f~ - fs)’ is the Laue monotonic scattering resulting from a perfectly random distribution of the N atoms of the alloy of mA atomic per cent A atoms;

where P (AA .,,,,,,) is the probability of finding an atom of type A at a position %,a,’ + ma2 + n3a3’ from another A atom, the vectors al’, a?‘, and a3’ being the largest fractions of the unit cell axes such that any atomic position can be described by some combination of the integers nr, n2, nB (for face-centered cubic lattices, al’ = ial, az’ = +a2, as’ = Ias) and S and So are unit vectors in the directions of the diffracted and incident beams, respectively. Then, by a Fourier transformation:

(2) %n.na =

1- “e

exp

sss .

I DS”

--

Nm,m,(f, - fi+>'

(S

so)

(nlal’

+ tz2a2’ + w,l)]

_ dv

the integration extending over one cell of reciprocal space. Application of this theory to determine the desired parameters requires a knowledge of ID_ throughout a cell of reciprocal space, and determination of the parameters with reasonable accuracy integration over several requires a numerical thousand points in the cell. A simplification of the technique was possible in this case, since we had determined experimentally that the diffuse scattering was distributed in a spherically symmetric fashion about each reciprocal lattice point, with the intensity in any such “shell” dropping to zero close enough to its reciprocal lattice point so that there was no overlapping of contributions from adjacent “shells.” By virtue of this resolution and the symmetry of the reciprocal lattice, not only could the integration be limited to the region surrounding the (000) reciprocal lattice point, but also by expressing the reciprocal lattice vector, (S - So)/h, in spherical coordinates and integrating over the angular variables, equation (2) could be reduced to a simple, one-dimensional integration. After such manipulation, equation (2) becomes:

where

R = la’ld n”,+

n;+ ni,

a radius vector in the crystal lattice; h = lb’l-\/h21+_+ radius vector in reciprocal space, where b’ is the length of the reciprocal cell edge and hr, hz, and h3 are the independent variables, fractions of the reciprocal cell edge, which define the point in reciprocal a

space under consideration ; and where when h = IT, the intensity has dropped to zero. Further, since a(O) = 1, and since in the angular region concerned the atomic scattering factors remain essentially constant, this equation becomes finally: (4) a(R)

= $ ,l”l,(h) - ”

h sin (27rRh) dh

nH

J” I,(h)

4nh* dh

where I, is now expressed in arbitrary units. Using the intensity distribution from a quenched sample, that shown in Figure 3, a numerical integration furnished values for a(R), from which the probability distribution of Figure 4 was obtained.

.9-

PAG-A0

Ii

1.0

.8.7 .6.5.4 .3.2-\

.I bR,,, IO

20

30

40

FIGURE 4. Probability distribution characteristic of AIAg quenched from 520°C; PAPAL is the probability that one Ag atom will be at a distance R from another Ag atom.

This probability, P,,., (R), that of finding one Ag atom on a lattice site a distance R from another Ag atom, decreases from the value 1.0 at R = 0, reaching a minimum value well below that for a perfectly random distribution at R = 20 A, and rises again, attaining the average value, $j = 0.05, at about R = 36 A. While this function has meaning only for discrete values of R, those corresponding to actual interatomic distances, the continuous curve is drawn in to make more easily visible the significant variation of this function with increasing atomic separation. The interpretation of this Patterson-like probability function seems straightforward. The free energy of this system evidently is lowered when Ag atoms surround themselves with other -4g atoms. While

for temperatures above the limiting temperature for solid solubility thermal motion tends to overcome this “ordering,” during the quench this clustering becomes pos&ble and Ag atoms in regions about certain nuclei assemble into more or less spherical aggregates.* This clustering takes place so rapidl) that around each cluster there is left a shell like region with less than ayr%rage Ag c0ntent.t If we consider this phenomenon from a diffusion standpoint, with an “uphill” diffusion of atoms in clustering as opposed to the normal “downhill” diffusion which renders a uniform atomic distribution, then apparently the activation energy for “uphill” diffusion is less than that for “downhill” diffusion, so that the first varies much less quickly with temperature than the second, making possible the clustering during the quench. Having determined the Patterson-like probability distribution function for the quenched sample, one would like to determine an average cluster size and a measure of the percentage of Ag atoms in the alloy which have formed these clusters. This can be done by assuming different models for the clusters, calculating the probability distributions corresponding to the different models, and comparing these distributions with the distribution determined experimentally. For our calculations we considered a very simple basic model, a homogeneous spherical cluster of high Ag content surrounded by a shell-like region of low Ag content, with variables of cluster composition, cluster size, and percentage of Ag atoms collected in clusters. Calculations of first neighbor Ag-Ag bonds showed quickly that the experimentally determined probability fop first neighbors, pApdg (2.8 A) = 0.89, could only be obtained by considering clusters whose compositions were practically pure Ag, with the added restriction that almost all of the Ag atoms of the alloy be in such clusters. The single model which gave the best fit between calculated and observed distribution functions was that of a spherical cluster of Ag atoms of *The actual shape of any one aggregate cannot be determined from the X-ray diffraction data. The diffraction is influenced by a very large number of aggregates so that what is determined is an average shape. Thus if the aggregates actually had the shape of very slightly flattened ellipsoids of revolution, the short axes occurring with equal probability in several directions, such as the various (111) directions, then the diffraction by these aggregates w-ould be practically indistinguishable from that by spherical aggregates. Large departures from spheroidal shapes could of course be remarked, unless more orientations became equally probable. yl‘he atl.endant diffraction effect must be classified as a phenomenon which, cmce seen, becomes obvious. It is the combination of regions with greater than average scattering factor surrounded by shell like regions with less than average scattering factor which produces the shells of scattering pow er in reciprocal space.

8 w radius, containing 125 Ag atoms, this surrounded by a shell of Al atoms of 28 A outer radius. ;1 consideration of the departures of this calculated distribution function from the experimental distribution function then described the clusters as being of a range of sizes, with over 50 per cent of the clusters being the size described above and the rest being of somewhat smaller size. The extreme simplicity of our models forbade any attempt to determine a quantitative distribution of cluster sizes. A check of this calculation can be made by use of the theory of small angle scattering by small particles as developed by Guinier [17]. This predicts the amplitude of radiation scattered by spherical particles as: E,,

= N&n exp

4a2 - -Iox~ & c2

where N is the number of particles; n is the number of excess electrons in a particle (excess in the sense of the number of electrons above that for a similar volume of the homogeneous medium surrounding the particle) ; R,, is the radius of the particle; and e is the scattering angle measured in radians. The amplitude scattered by a cluster surrounded by a shell, the whole being contained in a homogeneous lattice, can then be calculated by adding the amplitude scattered by the cluster, with a positive excess of electrons, to the amplitude scattered by the shell, with its negative excess of electrons, and the scattered intensity is then given by the square of the amplitude. With a cluster of radius 10 A surrounded by a 0 shell of outer radius 30 A, the predicted intensity agreed remarkably well with the observed intensity for all angles above 28 = 1.5”, when the curves are matched at 20 = 2’. The calculations of the percentage of total Ag atoms to be found in clusters then could be made, since the scattered intensity had been determined in electron units; this calculation again resulted in a value of approximately 50 per cent. The calculations from these simplified models have thus permitted us to determine that during the quench more than 50 per cent of the Ag atoms have clustered into relatively large aggregates, the remaining Ag atoms probably being found in smaller clusters. The average cluster may be described as having a radius of approximately 8 A and contains on the order of 100 Ag atoms. Around this cluster there is to be found a shell-like region low in Ag content, of an outer radius of the order of 30 fi. Outside of this region on the average is found a region of homogeneous atomic distribution, but in

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the real crystal randomly distributed Ag atoms are few, so that actually beyond any cluster and its shell of Al atoms one finds primarily other clusters of varying sizes and positions. When the alloy is quenched and left at room temperature, the clusters formed during the quench do not noticeably change in size, owing to the very slow rates of diffusion at this temperature. The initial size does depend on the speed of quenching, slower rates allowing the formation of larger clusters. Mlhen the quenched alloy is annealed at higher temperatures, the decrease in diameter of the shells of scattering power in reciprocal space together with the increase in their intensities indicates that the average size of these clusters is increasing. This growth is probably accomplished by two mechanisms-the absorption by the larger clusters of the remaining “free” Ag atoms brought into their regions of influence by thermal diffusion, and also by coalescence of adjacent large clusters, again as a result of thermal notions. On continued annealing the Ag clusters grow to such a size that experimentally only a blur of scattering is found around the reciprocal lattice points. During this growth another diffraction phenomenon has been observed at large angles by Geisler and Hill [3] and others. This scattering, weaker in intensity than the spherical shells of scattering power, has been described as having the appearance of a “doubled cross” on transmission Laue patterns. NO detailed investigations of the intensity distribution of this scattering has been made, so that any interpretation must be qualitative in nature. Geisler and Hill have interpreted this phenomenon in terms of the formation of “onedimensional” precipitates. This conclusion does not seem valid, since the existence of such precipitates would in general create intersecting bands of scattering through the (000) reciprocal lattice point, a scattering which has not been found. Instead we offer the interpretation that during the growth of the clusters of Ag atoms some Al atoms have been incorporated into them, and that these exist in some crudely ordered arrangement which might give rise to the observed scattering. More quantitative measurements must be made before this or any other interpretation can be considered as validated. However, since this scattering is much weaker than the “spherical shells” of scattering, it seems reasonable to consider this as a second order effect which may modify slightly the description of the growth of the Ag clusters.

\‘OL.

1, 1953

Examination

of the Second Stage of Age Hardening

The first stage of age hardening has been characterized by the appearance of shells of scattering power in reciprocal space, which, on annealing, diminish in size and increase in intensity until only a blur of scattering is visible. With still further annealing a completely different type of scattering is observed at small angles-the appearance of short streaks passing through the trace of the direct beam. One such pattern, made from an annealed polycrystalline foil, is reproduced in Figure Id. The length of anneal necessary for the appearance of these streaks varies with temperature; Table I tabulates some of these values. TABLE

~-

I

ANNEALING TIME TO PRODUCE CENTRAL STREAKS AS A FUNCTION OF TEMPERATURE .- _____ ________. -. T”(C) t _. 20 not observed after three months 140 100 hours 165 22 hours 255 18 minutes 300 3 minutes 342 1 minute 405 15 seconds

Two of the dimensions of these streaks were quite sharp, apparently depending only on the dimensions of the crystals and the primary X-ray beam. Examination of a single crystal displaying this scattering showed that the long dimensions of the streaks were directed along the four (111) directions of the matrix reciprocal lattice. The total length of these rods or streaks in reciprocal space was found to be approximately one tenth the distance in reciprocal space from the (000) to the (111) reciprocal lattice point. Investigation of scattering at large angles revealed that further diffuse streaks had appeared around other reciprocal lattice points. These streaks also were directed along matrix (111) directions in reciprocal space and were not symmetric about the matrix reciprocal lattice points to which they were joined. These large angle rods of scattering were generally rather long, having a total length in reciprocal space of approximately fourtenths the distance from the (000) to the (111) reciprocal lattice points. However, certain of these rods were much shorter; these, the rods passing through the (Ill)-reciprocal lattice point directed towards the origin, had a total length of only one tenth the (OOO)-( 111) distance.

b’\rALIiER

IND

GUISIER:

These l,lrge rmgle diffraction effects are similar to those which have been reported by several investigators [4; 30; II]. Ziegler [II], in the most recent investigation of this phenomenon, shows diffuse rods of two types. Those which pass through the (111‘) and (222) reciprocal lattice points directed towards the origin have a length of roughly one-tenth the (000).-(ill) distance. All other rods observed such as n-hat from the (lli) toward the (200), have lengths of roughly one-half this dist-ante. These results agree quite well with our own, considering the differences in annealing history. Geisler and Hill have interpreted these diffraction effects as showing the existence of small platelets of the hexagonal close packed y’ precipitating phase, of composition AgzAl, having large dimensions in the (000.1) planes, corresponding to the matrix (111) planes, but which are thin in the direction perpendicular to these planes. A full criticism of this interpretation will not be given here, since this has been thoroughly done in two recent papers [3; 111. These investigators, Guinier and Ziegler, have shown that this by itself is not correct, proposing the modification that the y’ phase is forming as platelets, with these platelets exhibiting faults in the stacking of the (000.1) planes. With this mechanism one can easily obtain qualitative agreement with the experimentally observed scattering, the quantitative agreement depending on the accuracy of assumptions as to the distribution of faults. The origin of these platelets of the precipitating y’ phase must lie in the clusters of Ag atoms, for it is there that all the Ag atoms have collected. This second stage might well be described as a nucleation and growth phenomenon, the nucleation taking place in a cluster of favorable size and the growth occurring at the expense of the clusters. Barrett and Mehl suggest that the motion of half dislocations along (111) planes may be pictured as one grolvth mechanism, which would explain the existence of the stacking faults. On further annealing the platelets become more perfect and grow larger, so that the rods in reciprocal space break up and shorten, eventually becoming the reciprocal lattice points of the y’ precipitate. One interesting fact concerning the first appearance of these platelets can be seen in Figure Id. The streaks corresponding to any one of the crystallites appear as double streaks, indicating that the formation of these platelets takes place more rapidly in the grain boundaries than in the interior of the crystallite.

.4GE

HARDENING

IT\‘

575

.ALAG

High Temperature State Alloy

of the

In discussing the appearance of the Xg clusters in the quenched alloy, we suggested that the clusters form during the quench, this clustering taking place probably about some nuclei which exist at high temperatures. One of us [7], using high temperature photographic techniques, had previously found no evidence of such nuclei in the temperature range for solid solubility, but we felt that better experimental resolution could be attained with Geiger counter spectrometer techniques. =\ small furnace was constructed for the spectrometer described in a preceding section, and measurements of the low angle scattering were made at two temperatures within the solid solubility range. The results of this investigation will be mentioned only briefly here, since they do not actually fall within the scope of an article on age hardening, and they will be more completely discussed in a forthcoming article. These measurements showed that the alloy does not exist in a homogeneous state in the solid solubility region, but instead there is a tendency to form small clusters, these probably containing less than six Ag atoms. The results of a recent investigation by Rudman [16], who has been investigating this phenomenon by a study of Iarge angIe scattering, agree with this description, though his measurements indicate an even smaller size for the cluster. These clusters serve as the nuclei for the formation of the larger clusters during quenching.

Correlation of X-Ray Data with Measurements of Other Properties This X-ray investigation has shown the existence of two distinct stages in the age hardening transformation-first the appearance and growth of Ag rich clusters, then the appearance and growth of the hexagonal -y’ precipitate. Koster and Braumann’s [15] measurements of hardness, elastic limit, thermoelectric force, and conductivity likewise indicate the presence of two stages in this transformation, a cold hardening stage followed by a warm hardening stage. Both our own X-ray measurements and those of Glocker, Koster, Scherb and Ziegler [lo] show that the appearance of platelets of the 7’ phase is directly correlated to the appearance of the warm hardening stage. The period during which cold hardening exists is just the period in which the clusters are present in the alloy. However, Koster and Braumann show that the AlAg alloy with 38 per cent Ag by weight is capable of a marked

_\CTt\

576

SIETALLURGICX,

degree of reversion, (retrogression or “Riickbildung”), and their data indicates that for an alloy of 20 per cent Ag the phenomenon, though less marked, may still be possible. A visual examination of the small angle scattering pattern of a sample which had been given thermal treatment to produce reversion did not show any comparable change in the scattering. When the alloy was annealed in the cold hardening region, the clusters increased in size, and when the alloy was heated at the reversion temperature of 2OO”C, the clusters apparently remained the same or increased in size very slightly, whereas in AlCu, where a similar phenomenon is evidenced, such treatment produces a dissolution of the Guinier Prestor zones. It is possible that the reversion is rather small in this alloy, and that only the small fraction of clusters under a critical size should dissolve. If such were the case, a visual examination of the scattering patterns might not be sufficient to reveal this change. Further examination with the object of quantitatively measuring the intensity distribution after such treatment is now in progress. At the moment, though the warm hardening stage is clearly demonstrated to be the result of the formation of the platelets of the y’ precipitate, the exact relation between the cold hardening stage and the Ag clusters cannot be considered as fully determined.

Summary

and Conclusions

Our investigation has shown that the age hardening process in AlAg alloys of high percentage Al takes place in two separate stages. When the alloy is quenched from the region of solid solubility, during the quench Ag atoms cluster into small aggregates of approximate spherical shape, these containing the order of 100 Ag atoms for fast quenches. This clustering takes place so rapidly that there is left a shell-like region surrounding each cluster which is low in Ag content. For the most rapid quenches calculations indicate that at least 50 per cent of the Ag atoms have formed these clusters, with the remaining Ag atoms mostly dispersed in smaller clusters, so that actually in the real lattice outside of any cluster and its associated shell of Al atoms are to be found other clusters of varying sizes and positions. On annealing, these clusters grow in size both by absorption of the Ag atoms not contained in the large clusters and by coalescence of some of the larger clusters, so that as the average size of the clusters increases, the number of clusters decreases. At the same time, there may also be an introduction of some Al atoms

VOL.

I., 1953

into the clusters, these taking up a roughly ordered arrangement. During this first stage the atoms remain on the lattice sites of the parent matrix. With further annealing the alloy exhibits a new phase, the formation and growth of platelets of the -y’ phase, the hexagonal close-packed Ag,Al precipitate, this occurring at the expense of the Ag clusters. These platelets exhibit stacking faults along the (000.1) planes, so that it is thought that a part of the mechanism of formation may be a motion of half dislocations along the matrix (111) planes. On further annealing, the platelets grow and become more perfect. Satisfactory correlation of these two stages with the two-stage course of the variation of physical properties has not been accomplished. While the appearance of the platelets of the y’ phase has been correlated with the warm hardening stage of hardening, the cold hardening stage has not been simply linked to the formation of the Ag clusters, since the physical properties exhibit some reversible dependence on temperature which has not been discerned with X-rays. The definite existence of two stages in the transformation in this alloy, with the atoms in the first stage remaining on the lattice sites of the parent matrix, agrees well with the general interpretation of age hardening transformations offered by Guinier and cannot be explained on the basis of the simplified nucleation and anisotropic growth interpretation offered by Geisler. Though these results cannot be taken as proof of a generalization concerning all alloy systems, at least for this system we believe we have demonstrated that an aggregation of solute atoms into zones precedes the formation of the platelet structure which is the beginning of a true precipitate.

Acknowledgment Our thanks are extended to M. Jean apparatus was generously loaned for the measurements, and to the U.S. Fulbright for the grant of a Fulbright scholarship possible this dual investigation.

Blin, whose quantitative Commission which made

References 1. 2. 3. 4.

GUINIEK, A. Ann. Phys., 12 (1939) 192. PRESTON, B. D. Proc. Roy. Sot., Al67 (1938) 526. GUINIER, ,4. Acta Cryst., 5 (1952) 212. GEISLER, A. H. and HILL, J. K. Acta Cryst., 1 (1948) 238. 5. WARREN, B. E., AVERBACH, B. L., and ROBERTS, B. W. J. Appl. Phys., 22 (1951) 1493.

WALKER 6.

7. 8. 9. 10. 11. 12.

ASD

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AGE

RARRI:TT, C. S. and GEISLER, A. H. J. -4~~1. Phys., 11 (1940) i33. GUI~IEI~, A. Journal de Physique, 8 (1942) 124. GUINIEII, A. Physica, 15 (1949) 148. JAGODZINSKI,~<.andLAx%, F. Z. Metallk., 40(1949)296. GLOCKEK, R., KOSTER, W., SCHERB, J., and ZIEGLER, G. Z. Metallk., 43 (1952) 208. ZIEGLEIL,G. Z. Metallk., 43 (1952) 213. FOURNI:T, G. and GUINIER, A. Bull. Sot. franG. Min., 74 (1951) 39.

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13. BLIN, J. C. R. Acad. Sci., Paris, 233 (1951) 1288. 14. CO\VLEP,J. J. Appl. Phys., 21 (1950) 21. 15. KOSTER, W. and BRAUMANN, F. Z. Metallk., 43 (1952) 193. 16. RUD~IAN, P. S. MS. thesis, Dept. of Metallurgy, Massachusetts Institute of Technology (January, 1953). 17. GC.INIER, A. X-Ray Crystallographic Technology (Hilger and Watts Ltd., 1952), pp. 284-286.