- Email: [email protected]
Distortion scattering due to guinier-preston zones in AlAg
Acta metall, mater. Vol. 38, No. 12, pp. 2583-2586, 1990
0956-7151/90 $3.00 + 0.00 Copyright © 1990 Pergamon Press plc
Printed in Great Britain. All rights reserved
DISTORTION SCATTERING D U E TO GUINIER-PRESTON ZONES IN AI-Ag T. UNGA, R t , PH. A. D U B E Y and G. KOSTORZ Institut fiir Angewandte Physik, ETH Ziirich, CH-8093 Zfirich, Switzerland (Received 23 April 1990)
Abstract--For a decomposing A1-3 at.% Ag alloy the mismatch of Guinie~Preston zones was determined from high-resolution measurements of the diffuse X-ray scattering near the 222 Bragg reflection. It was found that the mismatch of the Guinier Preston zones is largest directly after quenching and decreases monotonically with ageing time. In the temperature range from 110 to 200°C the rate of mismatch reduction increases with increasing temperature. R6sum~-Pour un alliage A1-3 at.% Ag 5. l'6tat de d6mixtion, la diff6rence de param6tre cristallin entre zones Guinier-Preston et matrice a 6td d&ermin6e fi partir des mesures de diffusion des rayons X au voisinage de la r6flection de Bragg 222. I1 en r6sulte que la diff6rence de paramdtre cristallin est la plus grande directement apr6s la trempe et d6croit d'une f~con monotone avec le temps de vieillissement. Dans la plage de temperatures comprises entre 110°C et 200°C, la vitesse de r6duction de la diff6rence de param6tre cristallin augmente avec la temperature. Zusammenfassung--Fiir eine entmischende AI-3 at.% Ag-Legierung wurde die Gitterfehlpassung der Guinier-Preston-Zonen aus diffusen R6ntgenmessungen hoher Aufl6sung in der Umgebung des 222-Braggreflexes bestimmt. Es ergab sich, dass die Fehlpassung der Guinier-Preston-Zonen unmittelbar nach dem Abschrecken am grbssten ist und monoton mit der Auslagerungszeit abnimmt. Im Temperaturbereich zwischen 110°C und 200°C nimmt die Geschwindigkeit des Fehlpassungsabbaus mit der Temperatur zu.
1. INTRODUCTION In a relatively wide temperature range the decomposition of aluminum-rich A1-Ag solid solutions starts by the formation of Guinier-Preston (GP) zones [1]. Baur and Gerold [2] using small-angle X-ray scattering (SAXS) found that the formation of G P zones was governed by a metastable miscibility gap with a critical point at about 450°C and a contraction on the silver-rich side in the temperature range from 140 to 220°C, where the silver concentration of the G P zones changes from about 55 to 35 at.%. It was assumed that two distinct G P zone states existed; the r/-state below 170°C and the E-state above this temperature. In a further X-ray investigation Auer and Gerold [3] concluded that the two states were related to an order~lisorder transformation, the r/-state being the ordered one. This provided an explanation for results of earlier investigations [4-6], where an abrupt and reversible change at about 170°C was reported for the hardness and electrical resistivity of A I - A g alloys. Later Gragg and Cohen [7], based on diffuse X-ray scattering measurements for an A1-5 at.% Ag single crystal aged for 14 h at 110°C, concluded that the G P zones formed below 170°C were octahedral in
shape--instead of spherical as thought before--with no internal order. They claimed the q-e-transition to be due to a change in shape and concentration of the G P zones and the extra scattering near superstructure positions previously attributed to order within the zones by Auer and Gerold [3] to be caused by the considerable elastic strains associated with the zones. Subsequently several authors using (high-resolution) transmission electron microscopy [8-11] and atomprobe field-ion microscopy [12, 13] have reported that the G P zones are actually facetted. Further SAXS studies by N a u d o n and Caisso [14] indicated that the composition of the G P zones remains nearly constant if the aging temperature is changed from 140 to 190°C. This is corroborated by a more recent study [15] using the same technique, where it has been found that the composition of the G P zones (i.e. ~ Ag2A1) remains nearly constant in a wide temperature range from 20 to 250°C. The aim of the present work is to reexamine the role of coherency strains caused by the G P zones, based on X-ray measurements of the broadening of Bragg peaks of differently aged single crystals. 2. X-RAY DIFFRACTION TECHNIQUE
tPermanent address: Institute for General Physics, E6tv6s University, Budapest, P.O.B. 323, H-1445, Budapest, Hungary. AM3S/I2--N
The intensity distribution of scattered X-rays in the vicinity of Bragg reflections was measured on a special double-crystal diffractometer [16, 17]. The
2583
2584
UNGAR et al.: GUINIER-PRESTON ZONES IN A1-Ag
normal line focus of a sealed Cu tube was used (at 35 kV and 22 mA). The primary X-ray beam was monochromatized by a plane, symmetrically cut Si monochromator, using its 444 reflection at about 71 °. The beam reflected from the monochromator passed through a thin diaphragm of about 0.2 mm x 2 mm which served to stop the parasitic background scattering. The monochromator was tuned for the CUK~l line so that the CuK~2 component was completely suppressed. The collimated and monochromatic Xray beam impinged on the fiat sample under a divergence angle of about 10 sec of arc. The scattered radiation was registered by a linear position-sensitive X-ray detector (Braun, Munich) connected to a multichannel analyzer. The linear resolution of the detector was about 80/~m, and the nominal distance between two adjacent channels was selected to be 28.1 #m. The sample-to-detector distance was set to 240 mm in order to cover the total angular range in which the GP zones contribute significantly to the scattering around the 222 Bragg reflection. In a few cases this distance was selected to be 940 mm in order to increase the resolution of the diffractometer and to measure the undistorted intensity distribution of the matrix peak itself. In order to obtain a measure of the average strain fields related to the GP zones, the intensity distribution around the 222 peak was integrated experimentally in the plane perpendicular to the diffraction vector. For this purpose the sample was rocked around the axis perpendicular to the plane of incidence. The rocking angle was about +__1°. Within one intensity-distribution measurement the sample was rocked a few hundred times. Thus, the reported intensity distributions represent the average distribution of lattice spacings in the sample. 3. SAMPLE PREPARATION AND HEAT TREATMENTS Single crystals were prepared by strain-annealing (10 mm in diameter, a few cm long) using aluminum alloys containing 3 at.% silver. Slices about 0.5 mm thick were cut along {111} by spark erosion. The sample surfaces were electropolished to remove any damage introduced during the sample preparation. The specimens were homogenized at 580°C for 2 h and quenched into water at room temperature. Subsequent heat treatments were performed in a silicon oil bath at 110, 140 and 200°C. The temperature of the oil bath was controlled to _+ I°C. 4. EXPERIMENTAL RESULTS The intensity distributions at the 222 Bragg position after different aging times at 200°C are shown in Fig. 1. The line profiles corresponding to different aging periods are shifted vertically. The following features are apparent: (i) the maxima of the matrix peaks remain unshifted within experimental error, i.e.
200°C "i 0,1
- -
i:t ,"i?\
5"-
/ : ,~.,~,
~:¢'~
/
.....
\,
, ~! \
.v..~...:.
: ~- ~
"~:~3..&t~~ .
/i..t.~ \ ~,
,.J"
:'::!
)iii
~
%%~..
/ii\. i --..
A
0,5 min
\
, m,0
8 1° (@)
Fig. 1. Intensity distributions of the 222 Bragg reflections of an A1-3 at.% Ag alloy single crystal after aging at 200°C for different periods of time.
~a/a <<.10 -'1, where a is the average lattice spacing of
the crystal, (ii) the intensity of the diffuse scattering around the matrix peaks increases monotonically with aging time, (iii) the diffuse scattering contribution is slightly but definitely asymmetric, i.e. its center of gravity is shifted towards smaller angles as compared to the position of the matrix peak (this asymmetry is visually most apparent on the profile corresponding to an aging time of 2 min). Similar asymmetries have been reported by Gerold [18] (Debye-Scherrer profiles), Dauger et al. [19] (diffuse X-ray scattering near Bragg peaks) and Gragg and Cohen [7]. The qualitative behavior of the line profiles corresponding to the aging sequences at 110 and 140°C was not different from that shown in Fig. 1. Some of these profiles will be shown in connection with the evaluation of the asymmetry of the diffuse scattering in the next paragraph. 5. A SEMI-QUANTITATIVE EVALUATION OF THE LINE PROFILES The asymmetry of the small-angle scattering contribution in the vicinity of the 222 Bragg reflection was evaluated on the basis of recent work by Iida, Larson and Tischler [20]. According to these authors the scattering amplitude for the diffuse scattering of
UNG,~R et al.: GUINIER-PRESTON ZONES IN Al-Ag coherent precipitates with a displacement field s(r) in a dilute alloy can be written as follows A ( K ) = ( f P ( K ) - 1) ~ e " " d T M \ f(K) /r< r 0
~
i
j.
2585
ii 200°E12rain i! 6= 2.6 I0"
~=&z~10-~
ili
I
"
.4/+2___ !~--~ ~-~ .
/I-',
+ ~ dq"iK's(r) r>0
1 I~
+ ~ e~'[e 'K'(') - 1 - iK.s(r)].
(1)
r>0
where f ( K ) is the average atomic scattering factor of the crystal,fp(K) is the average scattering factor of the precipitate atoms, re is the radius of the particles and K is the scattering vector given by K = H + q, where H is the reciprocal lattice vector and q is a vector joining the vector H with the appropriate corner of the Ewald triangle in the usual way. The first term on the right describes the so-called "direct scattering" generated by the difference in the scattering factors of the host and the precipitate atoms. The second term leads to first-order distortion scattering usually called Huang scattering, and the third term contains the higher-order distortions. Iida et aL [20] evaluated all three terms in equation (1) numerically for a monodisperse system of precipitate particles. The first term in equation (1) can be transformed into the following formula (for isotropic displacement fields)
J~
(fAK) 1)
F(q'Ro)
(2)
where F ( x ) is the form factor for scattering from the precipitates of radius R o, Vp/V~ is the volume fraction of the particles, q ' = q +EK, and E is the lattice mismatch of the precipitates. Since the form factor F is a function of q', this scattering is centered at the position q = - c K along H. The center of this "direct" scattering may be interpreted as the Bragg position corresponding to the average lattice spacing of the precipitates. Taking into account the coherency of the precipitates, e is a measure of the strength of the distortions caused by the precipitates. The value of E may be obtained from the X-ray diffraction line-profiles by determining the center of the diffuse scattering around the Bragg peak of the average crystal. The Huang scattering [cf. second term in equation (1)] is centered around q = 0 and, therefore, will not shift the center of the direct scattering. The third term of equation (1) is relatively small if: (a) the difference in the atomic scattering factors of solute and host atoms is large, (b) the average precipitate size is small and (c) the absolute value of the distortion E is small. In the alloy system investigated in the present work, all of these conditions are met, and the third term may therefore be neglected (cf. Ref. [20] for a situation where this is not the case). Based on these considerations the long-range order distortions e were determined by evaluating the shift of the diffuse
o.1~-
A 140°C110min ~i ~3.~1o-~
×t
Jli
' 200°E/8min !! S°UlO-'
I
/I !~
i
ii!:: L
1 ~V 0.1
! ill
1z*O°C/190hE:o.o
z"" /
g.o /
i
[
110°C11/*'3h ~=2.a I0 ~
" "',
/"
........ ............................
A8
"'"~' ......
I
"X...... '"',....,.
I
1°(8) Fig. 2. Determination of the centre of the scattering distribution due to Guinier-Preston zones relative to the fundamental reflection. The procedure is illustrated in the upper right-hand corner. In the other examples, the midpoints are indicated by a heavy line only. scattering of the precipitates relative to the matrix peak. For this purpose, the midpoint of the intensity profiles was determined at several heights. These points were connected with a continuous line as shown in Fig. 2. The figure shows that the center line clearly indicates two regimes. The first regime corresponds to large intensities where the midpoints give the exact Bragg position for the matrix. The second regime where diffuse scattering dominates is related to the average lattice spacing of the precipitates. The difference of the two line positions directly yields the distortion E. The evaluation is more efficient if the scattered intensity is plotted on a logarithmic scale. A few examples are shown in Fig. 2. The different values of E are shown in Fig. 3 as a function of aging time at different temperatures. E
5
x103 ~
~
Z~:Q e: 110°C o,1/,0°C °'200°E
3 2 1 0
1¢ 1
10 102 10~ 10' 1¢
t [rain]
Fig. 3. Mismatch between particles and matrix vs aging time at different aging temperatures. The open triangle indicates the value obtained after quenching.
2586
UNGAR et al.: GUINIER-PRESTON ZONES IN A1-Ag
5
E'R6 [10-3 nm]
2
/
o : It+OOC ~. : DAUGERET AL [19]
//
1 0 0
1
2
° ~
3
RG [,',tr,]
Fig. 4. The product of mismatch E and OP zone size Ro plotted as a function of RG. 6. DISCUSSION Figure 3 shows that the mismatch Eof the GP zones is largest directly after quenching and decreases monotonically with aging time. The rate of decrease increases with the temperature of aging. The GP zone size RG (where RG is the average radius of gyration) in the same alloy has been determined by X-ray small angle scattering by Dubey [15]. In Fig. 4, ERG is plotted as a function of Rc for aging at 140°C. It can be seen that ERG reaches a maximum for RG ~ 1.2 nm and decreases monotonically for larger zone sizes. This means that when the particles become larger than 1.2 nm, the mismatch E starts to decrease rather strongly. For / ~ >/2 nm the mismatch practically vanishes. The data points taken from Dauger et al. [19] for aging at 150°C agree well with the present data. The most important result of the present work, i.e. that the long-range distortions due to E are decreasing with aging time everywhere in the temperature range from 110 to 200°C, could be explained by considering an ordering process within the GP zones, as suggested by Auer and Gerold [3]. According to these authors, the zones acquire an ordered structure below 170°C. They suggested a layer structure for the GP zones in which {100} monolayers of AI alternate with two Ag layers (r/-state). This sequence of AI and Ag layers completely eliminates a net distortion of the zone. Assuming that the suggested ordered structure develops gradually as the zones grow, the distortions will gradually decrease as observed. However, an abrupt transition to a disordered state (E-state) above 170°C (E-state, [3]) would call for another mechanism for stress-relief at the higher aging temperatures. The present results do not exclude an ordered structure as suggested by Auer and Gerold [3] for temperatures below 170°C. However, the existence of an ordered structure has been questioned by Gragg and Cohen [7] who investigated the diffuse scattering of an A1-5 at.% Ag single crystal. The sample had been aged at l l0°C for 14h. According to these authors the diffuse scattering far from the Bragg reflections is due to atomic displacements within the GP zones and not to ordering. The heat treatment
used by Gragg and Cohen [7] corresponds to a situation near the black dot at higher E in Fig. 3, indicating a relatively high value of lattice mismatch. The other black dot in Fig. 3 corresponds to aging for 110 h at 110°C, indicating the same distortion as after 3 h of aging at 140°C. This latter state is near the one in which Auer and Gerold [3] observed ordering. The results of the present work suggest that distortions gradually decrease while the internal order of the zones may gradually increase during their growth. After aging for 14 h at 110°C, distortions still contribute an important part to scattering from the GP zones as found in [7]. At higher temperatures, however, more advanced zones are formed in considerably shorter periods of time. In these stages, internal order may be the main reason for the diffuse scattering far from the Bragg peaks. At 200°C the GP zones grow and evolve so fast that after a few minutes of aging, distortions are reduced to below one tenth of the value found at the beginning of decomposition (Fig. 3). Wide-angle diffuse scattering measurements for these states would be required to verify whether these zones are ordered. REFERENCES
1. 2. 3. 4. 5. 6. 7. 8. 9.
A. Guinier, J. Phys. Radium 8, 124 (1942). R. Baur and V. Gerold, Acta metall. 10, 637 (1962). H. Auer and V. Gerold, Z. Metallk. 56, 240 (1965). W. K6ster and F. Braumann, Z. Metallk. 43, 193 (1952). W. K6ster, H. Steinert and J. Scherb, Z. Metallk. 43, 202 (1952). V. Gerold, H. Auer and W. Merz, Adv. X-ray Anal. 7, 1 (1964). J. E. Gragg and J. B. Cohen, Aetametall. 19, 507 (1964). R. Gronsky, 40th EMSA Annual Meeting (edited by G. W. Bailey),p. 722. Claitors, Baton Rouge, La (1982). R. Gronsky, G. van Tendeloo and G. Thomas, Decomposition o f Alloys: the Early Stages, Proe. 2nd Acta-Scripta Metall. Conf. (edited by P. Haasen,
10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20.
V. Gerold, R. Wagner and M. F. Ashby), p. 198. Pergamon Press, Oxford (1984). K. B. Alexander, F. K. LeGoues, H. I. Aaronson and D. E. Laughlin, Acta Metall. 32, 2241 (1984). F. Ernst and P. Haasen, Physica status solidi (a) 104, 403 (1987). K. Hono and K.-I. Hirano, Scripta metall. 18, 945 (1984). K. Osamura, T. Nakamura, A. Kobayashi, T. Hashizume and T. Sakurai, Acta Metall. 34, 1563 (1986). A. Naudon and J. Caisso, 3. appl. Crystallogr. 7, 25 (1974). Ph. A. Dubey, Dr. sc. nat. Dissertation, ETH Ziirich (1990). M. Wilkens and K. Eckert, Z. Naturforsch. 19a, 459 (1964). T. Ungfir, L. S. Trth, J. Illy and I. Kov~ics,Acta Metall. 34, 1257 (1986). V. Gerold, Ergeb. Exakt. Natur. 33, 105 (1961). A. Dauger, J. P. Guillot and J. Caisso, Acta metall. 22, 733 (1974). S. Iida, B. C. Larson and J. Z. Tischler, J. Mater. Res. 3, 267 (1988).
0956-7151/90 $3.00 + 0.00 Copyright © 1990 Pergamon Press plc
Printed in Great Britain. All rights reserved
DISTORTION SCATTERING D U E TO GUINIER-PRESTON ZONES IN AI-Ag T. UNGA, R t , PH. A. D U B E Y and G. KOSTORZ Institut fiir Angewandte Physik, ETH Ziirich, CH-8093 Zfirich, Switzerland (Received 23 April 1990)
Abstract--For a decomposing A1-3 at.% Ag alloy the mismatch of Guinie~Preston zones was determined from high-resolution measurements of the diffuse X-ray scattering near the 222 Bragg reflection. It was found that the mismatch of the Guinier Preston zones is largest directly after quenching and decreases monotonically with ageing time. In the temperature range from 110 to 200°C the rate of mismatch reduction increases with increasing temperature. R6sum~-Pour un alliage A1-3 at.% Ag 5. l'6tat de d6mixtion, la diff6rence de param6tre cristallin entre zones Guinier-Preston et matrice a 6td d&ermin6e fi partir des mesures de diffusion des rayons X au voisinage de la r6flection de Bragg 222. I1 en r6sulte que la diff6rence de paramdtre cristallin est la plus grande directement apr6s la trempe et d6croit d'une f~con monotone avec le temps de vieillissement. Dans la plage de temperatures comprises entre 110°C et 200°C, la vitesse de r6duction de la diff6rence de param6tre cristallin augmente avec la temperature. Zusammenfassung--Fiir eine entmischende AI-3 at.% Ag-Legierung wurde die Gitterfehlpassung der Guinier-Preston-Zonen aus diffusen R6ntgenmessungen hoher Aufl6sung in der Umgebung des 222-Braggreflexes bestimmt. Es ergab sich, dass die Fehlpassung der Guinier-Preston-Zonen unmittelbar nach dem Abschrecken am grbssten ist und monoton mit der Auslagerungszeit abnimmt. Im Temperaturbereich zwischen 110°C und 200°C nimmt die Geschwindigkeit des Fehlpassungsabbaus mit der Temperatur zu.
1. INTRODUCTION In a relatively wide temperature range the decomposition of aluminum-rich A1-Ag solid solutions starts by the formation of Guinier-Preston (GP) zones [1]. Baur and Gerold [2] using small-angle X-ray scattering (SAXS) found that the formation of G P zones was governed by a metastable miscibility gap with a critical point at about 450°C and a contraction on the silver-rich side in the temperature range from 140 to 220°C, where the silver concentration of the G P zones changes from about 55 to 35 at.%. It was assumed that two distinct G P zone states existed; the r/-state below 170°C and the E-state above this temperature. In a further X-ray investigation Auer and Gerold [3] concluded that the two states were related to an order~lisorder transformation, the r/-state being the ordered one. This provided an explanation for results of earlier investigations [4-6], where an abrupt and reversible change at about 170°C was reported for the hardness and electrical resistivity of A I - A g alloys. Later Gragg and Cohen [7], based on diffuse X-ray scattering measurements for an A1-5 at.% Ag single crystal aged for 14 h at 110°C, concluded that the G P zones formed below 170°C were octahedral in
shape--instead of spherical as thought before--with no internal order. They claimed the q-e-transition to be due to a change in shape and concentration of the G P zones and the extra scattering near superstructure positions previously attributed to order within the zones by Auer and Gerold [3] to be caused by the considerable elastic strains associated with the zones. Subsequently several authors using (high-resolution) transmission electron microscopy [8-11] and atomprobe field-ion microscopy [12, 13] have reported that the G P zones are actually facetted. Further SAXS studies by N a u d o n and Caisso [14] indicated that the composition of the G P zones remains nearly constant if the aging temperature is changed from 140 to 190°C. This is corroborated by a more recent study [15] using the same technique, where it has been found that the composition of the G P zones (i.e. ~ Ag2A1) remains nearly constant in a wide temperature range from 20 to 250°C. The aim of the present work is to reexamine the role of coherency strains caused by the G P zones, based on X-ray measurements of the broadening of Bragg peaks of differently aged single crystals. 2. X-RAY DIFFRACTION TECHNIQUE
tPermanent address: Institute for General Physics, E6tv6s University, Budapest, P.O.B. 323, H-1445, Budapest, Hungary. AM3S/I2--N
The intensity distribution of scattered X-rays in the vicinity of Bragg reflections was measured on a special double-crystal diffractometer [16, 17]. The
2583
2584
UNGAR et al.: GUINIER-PRESTON ZONES IN A1-Ag
normal line focus of a sealed Cu tube was used (at 35 kV and 22 mA). The primary X-ray beam was monochromatized by a plane, symmetrically cut Si monochromator, using its 444 reflection at about 71 °. The beam reflected from the monochromator passed through a thin diaphragm of about 0.2 mm x 2 mm which served to stop the parasitic background scattering. The monochromator was tuned for the CUK~l line so that the CuK~2 component was completely suppressed. The collimated and monochromatic Xray beam impinged on the fiat sample under a divergence angle of about 10 sec of arc. The scattered radiation was registered by a linear position-sensitive X-ray detector (Braun, Munich) connected to a multichannel analyzer. The linear resolution of the detector was about 80/~m, and the nominal distance between two adjacent channels was selected to be 28.1 #m. The sample-to-detector distance was set to 240 mm in order to cover the total angular range in which the GP zones contribute significantly to the scattering around the 222 Bragg reflection. In a few cases this distance was selected to be 940 mm in order to increase the resolution of the diffractometer and to measure the undistorted intensity distribution of the matrix peak itself. In order to obtain a measure of the average strain fields related to the GP zones, the intensity distribution around the 222 peak was integrated experimentally in the plane perpendicular to the diffraction vector. For this purpose the sample was rocked around the axis perpendicular to the plane of incidence. The rocking angle was about +__1°. Within one intensity-distribution measurement the sample was rocked a few hundred times. Thus, the reported intensity distributions represent the average distribution of lattice spacings in the sample. 3. SAMPLE PREPARATION AND HEAT TREATMENTS Single crystals were prepared by strain-annealing (10 mm in diameter, a few cm long) using aluminum alloys containing 3 at.% silver. Slices about 0.5 mm thick were cut along {111} by spark erosion. The sample surfaces were electropolished to remove any damage introduced during the sample preparation. The specimens were homogenized at 580°C for 2 h and quenched into water at room temperature. Subsequent heat treatments were performed in a silicon oil bath at 110, 140 and 200°C. The temperature of the oil bath was controlled to _+ I°C. 4. EXPERIMENTAL RESULTS The intensity distributions at the 222 Bragg position after different aging times at 200°C are shown in Fig. 1. The line profiles corresponding to different aging periods are shifted vertically. The following features are apparent: (i) the maxima of the matrix peaks remain unshifted within experimental error, i.e.
200°C "i 0,1
- -
i:t ,"i?\
5"-
/ : ,~.,~,
~:¢'~
/
.....
\,
, ~! \
.v..~...:.
: ~- ~
"~:~3..&t~~ .
/i..t.~ \ ~,
,.J"
:'::!
)iii
~
%%~..
/ii\. i --..
A
0,5 min
\
, m,0
8 1° (@)
Fig. 1. Intensity distributions of the 222 Bragg reflections of an A1-3 at.% Ag alloy single crystal after aging at 200°C for different periods of time.
~a/a <<.10 -'1, where a is the average lattice spacing of
the crystal, (ii) the intensity of the diffuse scattering around the matrix peaks increases monotonically with aging time, (iii) the diffuse scattering contribution is slightly but definitely asymmetric, i.e. its center of gravity is shifted towards smaller angles as compared to the position of the matrix peak (this asymmetry is visually most apparent on the profile corresponding to an aging time of 2 min). Similar asymmetries have been reported by Gerold [18] (Debye-Scherrer profiles), Dauger et al. [19] (diffuse X-ray scattering near Bragg peaks) and Gragg and Cohen [7]. The qualitative behavior of the line profiles corresponding to the aging sequences at 110 and 140°C was not different from that shown in Fig. 1. Some of these profiles will be shown in connection with the evaluation of the asymmetry of the diffuse scattering in the next paragraph. 5. A SEMI-QUANTITATIVE EVALUATION OF THE LINE PROFILES The asymmetry of the small-angle scattering contribution in the vicinity of the 222 Bragg reflection was evaluated on the basis of recent work by Iida, Larson and Tischler [20]. According to these authors the scattering amplitude for the diffuse scattering of
UNG,~R et al.: GUINIER-PRESTON ZONES IN Al-Ag coherent precipitates with a displacement field s(r) in a dilute alloy can be written as follows A ( K ) = ( f P ( K ) - 1) ~ e " " d T M \ f(K) /r< r 0
~
i
j.
2585
ii 200°E12rain i! 6= 2.6 I0"
~=&z~10-~
ili
I
"
.4/+2___ !~--~ ~-~ .
/I-',
+ ~ dq"iK's(r) r>0
1 I~
+ ~ e~'[e 'K'(') - 1 - iK.s(r)].
(1)
r>0
where f ( K ) is the average atomic scattering factor of the crystal,fp(K) is the average scattering factor of the precipitate atoms, re is the radius of the particles and K is the scattering vector given by K = H + q, where H is the reciprocal lattice vector and q is a vector joining the vector H with the appropriate corner of the Ewald triangle in the usual way. The first term on the right describes the so-called "direct scattering" generated by the difference in the scattering factors of the host and the precipitate atoms. The second term leads to first-order distortion scattering usually called Huang scattering, and the third term contains the higher-order distortions. Iida et aL [20] evaluated all three terms in equation (1) numerically for a monodisperse system of precipitate particles. The first term in equation (1) can be transformed into the following formula (for isotropic displacement fields)
J~
(fAK) 1)
F(q'Ro)
(2)
where F ( x ) is the form factor for scattering from the precipitates of radius R o, Vp/V~ is the volume fraction of the particles, q ' = q +EK, and E is the lattice mismatch of the precipitates. Since the form factor F is a function of q', this scattering is centered at the position q = - c K along H. The center of this "direct" scattering may be interpreted as the Bragg position corresponding to the average lattice spacing of the precipitates. Taking into account the coherency of the precipitates, e is a measure of the strength of the distortions caused by the precipitates. The value of E may be obtained from the X-ray diffraction line-profiles by determining the center of the diffuse scattering around the Bragg peak of the average crystal. The Huang scattering [cf. second term in equation (1)] is centered around q = 0 and, therefore, will not shift the center of the direct scattering. The third term of equation (1) is relatively small if: (a) the difference in the atomic scattering factors of solute and host atoms is large, (b) the average precipitate size is small and (c) the absolute value of the distortion E is small. In the alloy system investigated in the present work, all of these conditions are met, and the third term may therefore be neglected (cf. Ref. [20] for a situation where this is not the case). Based on these considerations the long-range order distortions e were determined by evaluating the shift of the diffuse
o.1~-
A 140°C110min ~i ~3.~1o-~
×t
Jli
' 200°E/8min !! S°UlO-'
I
/I !~
i
ii!:: L
1 ~V 0.1
! ill
1z*O°C/190hE:o.o
z"" /
g.o /
i
[
110°C11/*'3h ~=2.a I0 ~
" "',
/"
........ ............................
A8
"'"~' ......
I
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I
1°(8) Fig. 2. Determination of the centre of the scattering distribution due to Guinier-Preston zones relative to the fundamental reflection. The procedure is illustrated in the upper right-hand corner. In the other examples, the midpoints are indicated by a heavy line only. scattering of the precipitates relative to the matrix peak. For this purpose, the midpoint of the intensity profiles was determined at several heights. These points were connected with a continuous line as shown in Fig. 2. The figure shows that the center line clearly indicates two regimes. The first regime corresponds to large intensities where the midpoints give the exact Bragg position for the matrix. The second regime where diffuse scattering dominates is related to the average lattice spacing of the precipitates. The difference of the two line positions directly yields the distortion E. The evaluation is more efficient if the scattered intensity is plotted on a logarithmic scale. A few examples are shown in Fig. 2. The different values of E are shown in Fig. 3 as a function of aging time at different temperatures. E
5
x103 ~
~
Z~:Q e: 110°C o,1/,0°C °'200°E
3 2 1 0
1¢ 1
10 102 10~ 10' 1¢
t [rain]
Fig. 3. Mismatch between particles and matrix vs aging time at different aging temperatures. The open triangle indicates the value obtained after quenching.
2586
UNGAR et al.: GUINIER-PRESTON ZONES IN A1-Ag
5
E'R6 [10-3 nm]
2
/
o : It+OOC ~. : DAUGERET AL [19]
//
1 0 0
1
2
° ~
3
RG [,',tr,]
Fig. 4. The product of mismatch E and OP zone size Ro plotted as a function of RG. 6. DISCUSSION Figure 3 shows that the mismatch Eof the GP zones is largest directly after quenching and decreases monotonically with aging time. The rate of decrease increases with the temperature of aging. The GP zone size RG (where RG is the average radius of gyration) in the same alloy has been determined by X-ray small angle scattering by Dubey [15]. In Fig. 4, ERG is plotted as a function of Rc for aging at 140°C. It can be seen that ERG reaches a maximum for RG ~ 1.2 nm and decreases monotonically for larger zone sizes. This means that when the particles become larger than 1.2 nm, the mismatch E starts to decrease rather strongly. For / ~ >/2 nm the mismatch practically vanishes. The data points taken from Dauger et al. [19] for aging at 150°C agree well with the present data. The most important result of the present work, i.e. that the long-range distortions due to E are decreasing with aging time everywhere in the temperature range from 110 to 200°C, could be explained by considering an ordering process within the GP zones, as suggested by Auer and Gerold [3]. According to these authors, the zones acquire an ordered structure below 170°C. They suggested a layer structure for the GP zones in which {100} monolayers of AI alternate with two Ag layers (r/-state). This sequence of AI and Ag layers completely eliminates a net distortion of the zone. Assuming that the suggested ordered structure develops gradually as the zones grow, the distortions will gradually decrease as observed. However, an abrupt transition to a disordered state (E-state) above 170°C (E-state, [3]) would call for another mechanism for stress-relief at the higher aging temperatures. The present results do not exclude an ordered structure as suggested by Auer and Gerold [3] for temperatures below 170°C. However, the existence of an ordered structure has been questioned by Gragg and Cohen [7] who investigated the diffuse scattering of an A1-5 at.% Ag single crystal. The sample had been aged at l l0°C for 14h. According to these authors the diffuse scattering far from the Bragg reflections is due to atomic displacements within the GP zones and not to ordering. The heat treatment
used by Gragg and Cohen [7] corresponds to a situation near the black dot at higher E in Fig. 3, indicating a relatively high value of lattice mismatch. The other black dot in Fig. 3 corresponds to aging for 110 h at 110°C, indicating the same distortion as after 3 h of aging at 140°C. This latter state is near the one in which Auer and Gerold [3] observed ordering. The results of the present work suggest that distortions gradually decrease while the internal order of the zones may gradually increase during their growth. After aging for 14 h at 110°C, distortions still contribute an important part to scattering from the GP zones as found in [7]. At higher temperatures, however, more advanced zones are formed in considerably shorter periods of time. In these stages, internal order may be the main reason for the diffuse scattering far from the Bragg peaks. At 200°C the GP zones grow and evolve so fast that after a few minutes of aging, distortions are reduced to below one tenth of the value found at the beginning of decomposition (Fig. 3). Wide-angle diffuse scattering measurements for these states would be required to verify whether these zones are ordered. REFERENCES
1. 2. 3. 4. 5. 6. 7. 8. 9.
A. Guinier, J. Phys. Radium 8, 124 (1942). R. Baur and V. Gerold, Acta metall. 10, 637 (1962). H. Auer and V. Gerold, Z. Metallk. 56, 240 (1965). W. K6ster and F. Braumann, Z. Metallk. 43, 193 (1952). W. K6ster, H. Steinert and J. Scherb, Z. Metallk. 43, 202 (1952). V. Gerold, H. Auer and W. Merz, Adv. X-ray Anal. 7, 1 (1964). J. E. Gragg and J. B. Cohen, Aetametall. 19, 507 (1964). R. Gronsky, 40th EMSA Annual Meeting (edited by G. W. Bailey),p. 722. Claitors, Baton Rouge, La (1982). R. Gronsky, G. van Tendeloo and G. Thomas, Decomposition o f Alloys: the Early Stages, Proe. 2nd Acta-Scripta Metall. Conf. (edited by P. Haasen,
10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20.
V. Gerold, R. Wagner and M. F. Ashby), p. 198. Pergamon Press, Oxford (1984). K. B. Alexander, F. K. LeGoues, H. I. Aaronson and D. E. Laughlin, Acta Metall. 32, 2241 (1984). F. Ernst and P. Haasen, Physica status solidi (a) 104, 403 (1987). K. Hono and K.-I. Hirano, Scripta metall. 18, 945 (1984). K. Osamura, T. Nakamura, A. Kobayashi, T. Hashizume and T. Sakurai, Acta Metall. 34, 1563 (1986). A. Naudon and J. Caisso, 3. appl. Crystallogr. 7, 25 (1974). Ph. A. Dubey, Dr. sc. nat. Dissertation, ETH Ziirich (1990). M. Wilkens and K. Eckert, Z. Naturforsch. 19a, 459 (1964). T. Ungfir, L. S. Trth, J. Illy and I. Kov~ics,Acta Metall. 34, 1257 (1986). V. Gerold, Ergeb. Exakt. Natur. 33, 105 (1961). A. Dauger, J. P. Guillot and J. Caisso, Acta metall. 22, 733 (1974). S. Iida, B. C. Larson and J. Z. Tischler, J. Mater. Res. 3, 267 (1988).