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Electron microscopic investigation of long period order in Ag3Mg
ELECTRON
MICROSCOPIC K.
INVESTIGATION
HANHI,?
J.
OF LONG
and
MAKIt
PERIOD
ORDER
IN A&M%*
P. PAALASSALOt
The anti-phase domain structure of the ordered alloy Ag,Mg was studied by means of electron transThe microstructure of Ag,Mg was confirmed mission and diffraction using polycrystalline bulk samples. to be composed of fairly large areas with common c-axis of the tetragonal crystal. Besides the periodic rectilinear anti-phase domains, these areas consist of domains which have different sublattice occudomains have pations. The nonlinear anti-ph&se boundaries (APB’s) separatin, v the last mentioned not been detected previously in the alloys which have periodically ordered structures. On the basis of the higher order satellite configurations observed in the diffraction patterns, the distribution of the periods for which fif = 1 among t,hose for which M = 2 is obviously uniform. The diffraction patterns confirm the theory of Fujiwara. ‘I) On the other hand, the transmission images suggest that the mixing of M = 1 and _84 = 2 also shows some regularity The distribution cannot be perfectly regular, because the measured average value of M varies contmuously between 1.67 and 2.00 as a function of composition. This implies that several lengths [(2n + l)a,] of the superlong periods occur at the same time in the ordered crystal. This was really observed in t,he present investigation. ETUDE
AU
MICROSCOPE
ELECTRONIQUE
DE
DISTANCE
LA
PERIODICITE
DANS
DE
L’ORDRE
A LONGUE
Ag,Mg
La structure de l’alliage ordonnb Ag,Mg dans le domaine antiphase a BtB &udi&e par microscopic 6lectronique par transmission et par dlffraction 6lectronique sur des &zhantillons polycristallins. Ces mesures ont confirm8 que la microstructure de Ag,Mg est composbe de zones asses grandes ayant l’axe c du cristal tetragonal en commun. En dehbrs des domaines antiphases p&iodiques rectilignes, ces zones sont constitubes de domaines ayant diffbrentes positions dans le sous-r&eau. Les front&es antiphases non linbaires (APB’s) sbparant ces derniers domaines n’ont pas QtB d&ectbes auparavant dans les alliages ayant des structures pbriodiquement ordonnbes. A partir des configurations satellites d’ordre plus 6levB observees dans les diagrammes de diffraction, la distribution des pbriodes pour lesquelles M = 1 parmi celles pour lesquelles M = 2 est manifestement uniforme. Les diagrammen de drffraction confirment la thborie de Fujiwara. D’autre part, les images de transmission suggerent l’idbe que le melange de M = 1 et M = 2 indique 6galement une certaine rbgularit& La distribution ne peut pas 6tre parfaitement rBgulibre, car la valeur moyenne mesurbe pour M varie de fapon continue entre I,67 et 2,00 en fonction de la composition. Ceci implique que plusieurs longueurs [ (27~ + l)a,] de pPriodes superlongues se prbsentent au m&me moment dans le cristal ordon&. Ceci a BtB reellement observ6 dans les experiences prt%entees ici. ELEKTRONENMIKROSKOPISCHE
UNTERSUCHUNG
DER
FERNORDNUNG
IN
Ag,Mg
An polykristallinen Proben der geordneten Legierung Ag,Mg wurde die Struktur der Antiphasendomilnen mit Hilfe der Durchstrahlung und Feinbereichsbeugung im Elektronenmikroskop untersucht. Ei:swurde bestiitigt, da5 die Mikrostruktur des Ag,Mg aus recht gro5en Kristallbereichen mit der c-Achse des tetragonalen Kristalls besteht. Au5er den periodischen langgestreckten Antiphasenbereichen oxistieren such Kristallgebiete aus Domiinen mit verschiedener Untergitterbesetzung. Die die zuletzt genanntnn Bereiche trennenden nichtlinearen Antiphasengrenzen (APB) sind in Legierungen mit period&h geordneten Strukturen friiher nicht beobachtet worden. Die in den Beugungsbildern auft,retenden Satellitenreflexe hijherer Ordnung deuten darauf hin, da5 die Perioden mit M = 1 unter jenen mit M = 2 offensichtlich gleichfijrmig verteilt sind. Die Beugungsbilder bestlitigen die Theorie x-on Fyjiwara.“’ Andererseits zeigen die Durchstrahlungsaufnahmen, da5 Regelmh5igkeiten der Verteilung von M = 1 in 111 = 2 auftreten. Die Verteilung kann nicht vollkommen regelm(l5ig sein, da die gemessenen Durchschnittswerte von M mit der Zusammensetzung zwischen 1,67 und 2,OO variieren. Das impliziert, da5 mehrere Liingen [(2n + l)ao] der superlangen Periode gleichzeitig im geordneten Kristall auftreten. Genau das wurde in den gegenwiirtigen Untersuchungen beobachtet.
INTRODUCTION
an integer.
According
to Fujiwara,(l)
this fact can be explained if M is the mean value of the different not
The long period order in alloys has been investigated very intensively in the recent years. Especially the periodic structures of the alloys CuAu 11,(2*3) CusAu
with lengths M, and M,, occurring
II,(*,5) Cu,Pd,(6)
n1:n2, the reflections
Au,Mg,(‘)
have been of interest. alloys indicate periodic
Au,Mn@’
and Ag3Mg@-14)
The results obtained
that in an ordered
domain lengths.
for these
would
crystal there exist
distance
M,
the lengths of the anti-phase
which domains,
is between the
not
values of 1.0 (Au,,Mn(*)) and 10 (Cu,Au(12)), when M expressed in fundamental unit vectors of the ordinary crystal. As a rule: the value of M, which can be calculated
* Received Fi;rl?=u-i ACTA
from
the diffraction
Mav IL, 1970. Physical Laboratory,
METALLURGICA,
VOL.
University 19, JANUARY
patterns, of
periodic
is
models
of Fujiwara’l)
an essentially
a regular
anti-phase
domains
is required
results.
However,
mental
of the exact
and of
uniform,
arrangement
the experimental evidence
to the
but
of different to explain
the final experi-
arrangement
is still
lacking. The value of x
Turkn. 1971
necessarily
periodicity
corresponding
+ n2M2)/(nl + n2). Accord-
Perio and Tournarie,(15)
is
directly
= (n,M,
ing to the theoretical
also represents
in the proportion
due to the lattice
at the positions
mean value fl
slips repeating after certain atomic distances.
This out-of-step
appear
In the case of two kinds of domains
exists between 15
for an alloy Ag-(21-28.5)
at. y. Mg
1.7 and 2.0.(12) This range is formed
16
ACTA
METALLURGICA,
VOL.
19, 1971
by
mixing domain lengths for which M = 1 and M = 2.(l) Because of the very great difference in the ratio of the two possible values of M, AgsMg is very appropriate
for the investigations
of the various object
anti-phase
This is the main
of the present study.
ELECTRON When tions
of the distribution
domains.
CONTRAST
calculating
in Ag,Mg,
concerns
are four possibilities
a model
: (1) regular uniform, (2) irregular and (4) random
Fujiwara (l) has derived the expressions
for the intensities
for each of the above-mentioned
In cases 1, 2 and 4, the expressions
intensity
maxima
in the l-direction
(n, m = 0 or integers).
peaks
(2m + 1)/(2x)
For case 4, the background
is the greater the more random
In addition to the above-mentioned defined
appear
give sharp
of the reciprocal
lattice, when h + k is odd and 1 = n f intensity
which
of M = 1 with M = 2. There
(3) regular but not uniform,
arrangement. cases.
of satellite reflec-
one has to choose
the mixing
uniform,
CIRCUMSTANCES
the intensities
at 1 = k/211x
by the condition
2vg
the mixing.
maxima, excessive
in case 3. = positive
Here
v is
integer and
k = 0, 1, 2, . . . . The intensities of the fundamental and of the superlattice reflections are defined by similar expressions as those of an ordinary
ordered f.c.c. structure.
matter of fact, Ag,Mg has a tetragonal the ratio c/a differs only slightly
As a
symmetry,
from unity
but
(C/U =
1.0000 -- 1 .0055’13)) so that the cubic approximation is justified.
Because the uniform and somewhat
lar arrangement
intensities and the coordinates reflections
FF*
=
2 1
from
exp
Tr2?n=o2?n+1
the
of the possible satellite
can be calculated(l)
-t
regu-
seems to be the most probable,
the expression
1+
2m
+
___ 2iV
1)
I
The intensity distribution in the Z-direction of the reciprocal lattice of Ag,Mg calculated from equat,ion (1) for Z = 13/7.
FIG. 1.
is about 1317, the intensity distribution
The results are given in Fig. 1.
If all three directions
of the periodicity
the diffraction
pattern,
the common
flections will be surrounded Besides
the reflections
flanking
the direct spot.
been observed Recently, intensive
for instance
in CuAuc3) and Cu,Au.c12)
Fitzgerald’l@ reflections
proposed that this kind of would appear due to Fraunhofer Here
n is an integer and d is the spacing between the antiphase domain boundaries. The transmission contrasts of the nonperiodio APB’s are primarily determined by the extinction distance of the diffracted
wave.(l’)
The values of the extinction
are generally
calculated
from
expression
?TV cos e P)
(2)
/IF
1
(N -
1)
1
1. The structure
the formulas
factors
were calculated
The scattering factors were taken from Hirsch et aI.
treated the case & = 1.80
Since the writers were especially at.%Mg,
from
of Gangulee and Moss(ll) taking M = 2.
On the basis of the values of the extinction distances to given by Table 1 the normal nonperiodical APB’s would have contrasts of one or two fringes, when the specimen is oriented exactly for a superlattice reflection.(17*14) Furthermore,
(1).
those
These extra satellites have
effects at distances of n/d from the direct spot.
Table
(1)
in the alloy Ag-24
there still
namely
F is the structure factor for the unit cell of V, 8 is the Bragg angle and 1 is the wavelength. The values of to, together with the phase angles tl = 27r?j . R for some reflections, are shown in
sin 77
interested
above,
maxima,
volume
X
using formula
to re-
where
sin Nrr
Fujiwara
contribute superlattice
by satellite cross-patterns.
mentioned
exist one group of diffraction
to=
sin i7
As an example,
was calculated
for this value of B.
1
1
‘s
0
distances
sin NT
x (N-
I
for which x
the first satellites
also have t, values small enough to reveal the APB’s in the transmission
image.
One should point out that
ct # 0 always for the satellite reflections.
HANHI
et al.:
LONG
PERIOD
TABLE 1. Values of the structure factor P, the extinction distance t, for 100 kV electrons, and the phase angle a (R = +a,, (S), fundamental (P) and (1101) for some superlattice satellite (Sat) reflections F CA)
Reflert,ion 100 110 210 III 200
s s F P
1270 1307 1605 273 :05
*7roro +7rooro &TrorO 0 0
I&O
Sat
2.298
2564
+ 7r or
130
Sat
2.008
2934
rt r or i(2n
contrasts
to Marcinkowski
of the periodic These
of the specimens,
different
rates below
temperature
out to be very quick. few hours. 1);
h(2f-L +
type. or more
satellite
+
1):
observed
cooled
with This
the phase diagram
by
two
with also
each been
after an annealing
The slices obtained
of a sparking
machine
were thinned
acetic-acid
for a
from bulks by means electrolytically
solution, recommended
by Tegart w for Mg. The transmission electron microwork was done by using a JEM-6A
microscope
operating RESULTS
The
writers
literature
have
electron
at 100 kV. AND
not
any detailed
DISCUSSION
found
from
experimental
the
available
analysis
of the
in the bright field images as a result of the
interference mentioned
of
the
direct
beam
flanking satellites.
the periodical Cu,Au
when
reflections interfere the periodicity has
However,
other.
formed
were
So, the ordered configurations
essentially
in a perchloric-acid
are of a sine-periodic
are
they
the critical temperature.
was taken from
did not change
and Zwell,f4) the electron
APB’s
contrasts
I7
Ag,Mg
ordering
scopic According
IN
Gangulee and Bever. (lo) In the alloys of Mg compositions greater than about 23 at. %, the ordering turned
c(
4.639 4.507 3.670 21.60 19.30
ORDER
APB’s
with
the
above-
The contrast theory of
was originally
developed
for
II, for which
the value of M is about four times greater than for AgaMg. If the model of regular mixing of M = 1 with M = 2 in AgsMg is accepted, the unit cell of this alloy would same size as that of CusAu II. ,q = 4:jyJ
be roughly
of the
For instance,
when
= a , the large unit cell of AgsMg con-
4n + 1
sists of 7 usual cubic unit cells (Fig. 2). If g
= __ 2n+l’
the greater long period unit cell would include 2(4~ + 1) cubic cells.
According
and Zwell,o4) periodic
APB’s
a periodic
to the theory of Marcinkowski
the minimum
intensities
in the transmission
sum contrast
the superlong
was expected
periodicity
successive APB’s
represent
of AgsMg,
to arise from caused
by the FIG. 3. Selected area diffraction pattern of Ag-25 at. % Mg alloy which was homogenized for 12 hr at 75O”C, annealed for 24 hr at 365°C and cooled l.B’C/hr.
for which M = 1.
EXPERIMENTAL
METHOD
The used alloys were prepared of 99.99% magnesium
the
image. Therefore,
ingots
helium atmosphere.
by induction
melting
The bulk specimens were homog-
enized at 750 or 550°C in a graphite quartz or Pyrex capsules. have any contact
silver and in argon or
crucible
inside
Thus, the alloy could not
with the glass material.
For the
satellites
of higher
order,
nor
AgaMg flanking the direct spot. microscopic
investigation
thin film specimens, such reflections. schaeveo4)
paid
of the
satellites
of
In the first electron
of AgaMg using evaporated
Fujiwara
In another no further
spots which he interpreted
et CL(~) could not find investigation, attention
Vander-
to the extra
to be double
diffraction
spots. In the present study, these satellites were observed to arise from all samples. It was possible
n”
to explain
them by using the model
of Fujiwara.o)
As said before, Fujiwara has published the intensity distribution of the reciprocal lattice when a = 1.80. FIO. 2. The long period unit cell of Ag,Mg to the value
z
corresponding
= 7/4 and to the regular arrangement of&Z = 1 withM = 2.
This value of L%! corresponds to the composition of at. y0 Mg. tg) Figure 3 shows a selected area
24.8
ACTA
18
VOL.
19,
0
present
investigation
n
fujiwan
et al “I
A
Vanderschaeve
METALLURGICA,
1971
i;i 2.10
-
(IL)
1.60 -
4
1 20
21
FIG. 4. Average
22 out-of-step
23 distance
diffraction pattern from which one can measure the value of iw = 1.80. The positions of the higher order satellites agree to an accuracy of about 1 per cent with those predicted theoretically by Fujiwara.(l) Figure 3 shows also quite intensive satellites flanking the direct spot. According to Fitzgerald,(16) the distance between these satellites would be l/d, where d is the long period distance. The distance measured from Fig. 3 is quite accurately + d&. Thus the spacing of the planes giving rise to these reflections equals to 9a,, which is the distance between M = 1 domains when x = 915. The composit,ion of the specimen, from which the value &? = 1.80 was obtained, was 25.0 at.% Mg according to the spectrophotometric analysis. This differs slightly from the corresponding value of Fujiwara et aZ.(g) Because of this difference, the i@ values were measured also for some other compositions. The results are given in Fig. 4 together with the values of Fujiwara et al. In Fig. 4, there is also the curve corresponding to the theoretical values calculated from the equation e -=
a
&
(2 + 2x + S)3’2
Here, x stands for 1/(2n), and t is the so-called truncation factor assumed to be 0.962 in the caloulations.(12) The present experimental data in Fig. 4 lie between the theoretical and the earlier experimental values. The experimental curve in Fig. 4 can be used for the determination of the compositions by means of the measured values of &!. A typical diffraction pattern of the composition 24.2 at. “/b Mg is illustrated by Fig. 5. The positions
2.4
25
26
% as B function
27
28 at.v. k.tg
of Ng composition.
of the satellites are quite near to the theoretical ones of Fig. 1 (p. 16). The two strong flanking satellites in Fig. 5 are obviously formed by a superposition of 6 7 6 Thus, the satellite pairs -!__ and=.--. 1la, ’ 13a, 0 13@0 the value d = 12a, measured from these satellites could be explained. On the other hand, the measured value w = 1.85, whioh is between ‘_Aand ‘4, agrees well with the above-mentioned value of it. The variation of the values of g, measured from several diffraction patterns which were obtained from the specimens of a fixed composition, was smaller than0.01. Figure 6 represents a bright field image of a sample with the same imposition as in Fig. 5. The diameter of the areas which have the same direction of periodicity is of the order of magnitude 1 ,u. In the diffraction pattern of Fig. 6, no satellites can be seen. This is caused by the fact that t,he c-axis of the selected area (the middle of Fig. 6) is parallel to the beam. The symmetrical contrasts of the curved APB’s are typical for the case tc = I. As far as the writers know, this kind of thermal APB’s have not previously been observed in a periodically ordered alloy. The mean value of the periodical fringe spacing, measured from Fig. 6, is about 60 if. The distances of periodicity in Fig. 6 sre thus formed mainly of a unit of length 15U,. Another bright field image of specimens containing 24.2 at. y0 Mg is shown by Fig. 7. In the whole area of this image the direction of periodicity is the same. The disturbance in the periodic fringe contrasts (e.g. points A) is caused by the above-mentioned curved APB’s, which separate the domains of different sublattice occupations.
HANHI
et al.:
LONG
PERIOD
FIG. 5. Selected area diffraction patstern of Ag-24.2 for 10 days at. o? Mg alloy, which was homogenized at, 550°C ordered by coolingO.!Y’C/hr between (390-37O)“C and then 40”Cjhr.
The microfotometric measurements of Pig. 7 gave the results d = (54 f 2) A for about 60 per cent, (45 i 2) A for about 20 per cent and (62 j= 2) L%for about 15 per cent of the measured distances. The remaining 5 per cent of distances did not fit to any of the above-nlentioned limits. The corresponding structure units have the lengths of 13, 11 and 15 cubic unit cells, respectively. From all these distances the mean
ORDER
IN
Ag,Mg
FIG. 7. Bright field image of Ag-24.2 at. y/oMg alloy. The whoIe area has the same direction of c-axis. The influence of the nonlinear APB’s is seen, e.g. at points A. The heat treatment is similar to that of the specimen of the Fig. 5. Normal to the foil is [OIO]. x 63,000. value @ = 1.853 was obtained. This is in good agreement with that found from Figs. 4 and 5. It is therefore evident that the fringe distances, measured from the bright field transmission images, really represent those between the out-of-step slips for which Ail = 1. The difference between the mean fringe spacings, measured from Figs. 6 and 7, represents the irregularity in the mixing of M = 1 with M = 2. On the other hand, this difference can also be caused by a slight variation of the composition. Figure 8 represents a dark field image which is
taken by using reflections from 101 to 101 -
Fro. 6. Bright field image of Ag-24.2 at. % Mg alloy. Normal to the foil is [OOI]. The contrasts of the nonlinear APB’s originate chiefly from reflection 110. The treat,ment is similar to that of the specimen of Fig. 5. X 28,000.
19
d2M’
Fro. 3. Dark field image of Ag-24.2 at. % Mg alloy. obtained with the reflections from 101 to lOi.l/2@. same specimen as in Fig. 7. Normal to the foil is jorol. s 317,000.
ACTA
20
The average
distance
of periodicity,
this image, is about 54 A. field image.
measured
from
Thus, the dark field image
reveals the same periodical bright
METALLURGICA,
arrangement
A similar
to the experimental
is met,
for
also shows that the distribution
flanking the central spot give information On the other about the superlong periodicity.
ACKNOWLEDGEMENTS
only
scholarship
hand, the satellites around the superlattice
found.
contrasts APB’s
resolution,
Nevertheless, which
this periodicity
could
not be
from
the
two
of (2% + l)a,
neighbouring
from each other,
were observed. The average distance between the out-of-step for which
M = 1 was determined
slips
in the following
ways : 1. Using the value of x
which was measured from 1 satellites at the distances of from 2X
the cross-pattern the superlattice
reflections,
2. measuring
the distances
between
the satellites
flanking the direct spot, and 3. measuring
the fringe spacings in the bright and
dark field images. All these procedures
led essentially
to the same
results which were in good agreement with those predicted
previously
results confirmed
in papers.(l*g) the conclusion
M = 1 with M = 2 in Ag,Mg completely
regular.
The
experimental
that the mixing is uniform
but
of not
The fact that the measured value
of iE varies continuously
as a function
of composition
and encouragement
One of us (K. H.) is indebted
Suomalainen
Yliopistoseura,
Finland,
to the for
a
in 1969.
reflections
in the dark field images the sum
arise
at a distance
V. Hovi for his advice
to this work. Turun
should also reveal the shorter periodicity which repeats itself after 2n, and la,. However, because of the
cannot be completely
The writers wish to express their cordial thanks to Professor
results, the satellite
1971
regular.
reflections
insufficient
19,
as does the
situation
instance, in the case of Cu,Au 11.c4) According
VOL.
REFERENCES 1. K. FUJIWARA, J. phys. Sot. *lapan 12, 7 (1957). 2. A. B. GLOSSOP and D. W. PASHLEY. Proc. R. Sot. A250. 132 (1959). 3. S. OGAWA, D. WATANABE, H. WATANABE and T. KOMODA, Acta crystallogr. 11,872 (1958). 4. M. J. MARCINKOWSKI and L. ZWELL, Acta Met. 11.
373 (1963).
5. R. S. TOTH and H. SATO, J. appZ. Phys. 33, 3250 (1962). 6. S. OGAWA and D. WATANABE. in Direct Observation of Imperfections in Crystals, p. 523; edited by J. B. NEWKIR; and J. H. WTERNICK. Interscience (1962). 7. H. SATO and R. S. TOTH, J. phys. Chem. Solids 29, 2015 (1968). 8. D. WATANABE, J. phys. Sot. Japan 15, 1030 (1960). 9. K. FUJIWARA, M. HIRABAYASHI, D. WATANABE and S. OGAWA, J. phys. Sot. Japan 13, 167 (1958). 10. A. GANQ~JLEEand B. BEVER, Trans. metall. Sot. A.I.M.E. 242, 278 (1968). .J. appl. Crystallogr. 11. A. GANGULEE and S. C. Moss, 1,61 (1968). 12. H. SATO and R. S. TOTH, in Alloying Rehaviour and Effects in Concentrated Solid Solutions, p. 295. edited bv T. B. MASSALSKI. Gordon and Breach (19651. 13. k. SCHUBERT, B. KIEBER, M. WILKENS a& R. ~AUFLER, 2. MetaUk. 46, 692 (1955). 14. G. VANDERSCHAEVE, Phys. Status Solidi 36, 103 (1969). 15. P. PERIO and M. TOURNARIE, Acta crystallogr. 12, 1032
(1959). 16. A. G. FITZGERALD, Thin Films 1,83 (1968). 17. R. M. FISHER and M. J. MARCIWKOWSXI. Phil. Maq. 6. 1385 (1961). 18. P. B. HIRSCH, A. HOWIE, R. B. NICHOLSON, D. W. PASHLEY and M. J. WHELAN, Electron, Microscopy of Thin Crystals, p. 490. Butterworths (1965). 19. W. J. McG. TEGART, The Electvolytie and Chemical Polishing of Metals in Research and Industry. Pergamon Press (1959).
MICROSCOPIC K.
INVESTIGATION
HANHI,?
J.
OF LONG
and
MAKIt
PERIOD
ORDER
IN A&M%*
P. PAALASSALOt
The anti-phase domain structure of the ordered alloy Ag,Mg was studied by means of electron transThe microstructure of Ag,Mg was confirmed mission and diffraction using polycrystalline bulk samples. to be composed of fairly large areas with common c-axis of the tetragonal crystal. Besides the periodic rectilinear anti-phase domains, these areas consist of domains which have different sublattice occudomains have pations. The nonlinear anti-ph&se boundaries (APB’s) separatin, v the last mentioned not been detected previously in the alloys which have periodically ordered structures. On the basis of the higher order satellite configurations observed in the diffraction patterns, the distribution of the periods for which fif = 1 among t,hose for which M = 2 is obviously uniform. The diffraction patterns confirm the theory of Fujiwara. ‘I) On the other hand, the transmission images suggest that the mixing of M = 1 and _84 = 2 also shows some regularity The distribution cannot be perfectly regular, because the measured average value of M varies contmuously between 1.67 and 2.00 as a function of composition. This implies that several lengths [(2n + l)a,] of the superlong periods occur at the same time in the ordered crystal. This was really observed in t,he present investigation. ETUDE
AU
MICROSCOPE
ELECTRONIQUE
DE
DISTANCE
LA
PERIODICITE
DANS
DE
L’ORDRE
A LONGUE
Ag,Mg
La structure de l’alliage ordonnb Ag,Mg dans le domaine antiphase a BtB &udi&e par microscopic 6lectronique par transmission et par dlffraction 6lectronique sur des &zhantillons polycristallins. Ces mesures ont confirm8 que la microstructure de Ag,Mg est composbe de zones asses grandes ayant l’axe c du cristal tetragonal en commun. En dehbrs des domaines antiphases p&iodiques rectilignes, ces zones sont constitubes de domaines ayant diffbrentes positions dans le sous-r&eau. Les front&es antiphases non linbaires (APB’s) sbparant ces derniers domaines n’ont pas QtB d&ectbes auparavant dans les alliages ayant des structures pbriodiquement ordonnbes. A partir des configurations satellites d’ordre plus 6levB observees dans les diagrammes de diffraction, la distribution des pbriodes pour lesquelles M = 1 parmi celles pour lesquelles M = 2 est manifestement uniforme. Les diagrammen de drffraction confirment la thborie de Fujiwara. D’autre part, les images de transmission suggerent l’idbe que le melange de M = 1 et M = 2 indique 6galement une certaine rbgularit& La distribution ne peut pas 6tre parfaitement rBgulibre, car la valeur moyenne mesurbe pour M varie de fapon continue entre I,67 et 2,00 en fonction de la composition. Ceci implique que plusieurs longueurs [ (27~ + l)a,] de pPriodes superlongues se prbsentent au m&me moment dans le cristal ordon&. Ceci a BtB reellement observ6 dans les experiences prt%entees ici. ELEKTRONENMIKROSKOPISCHE
UNTERSUCHUNG
DER
FERNORDNUNG
IN
Ag,Mg
An polykristallinen Proben der geordneten Legierung Ag,Mg wurde die Struktur der Antiphasendomilnen mit Hilfe der Durchstrahlung und Feinbereichsbeugung im Elektronenmikroskop untersucht. Ei:swurde bestiitigt, da5 die Mikrostruktur des Ag,Mg aus recht gro5en Kristallbereichen mit der c-Achse des tetragonalen Kristalls besteht. Au5er den periodischen langgestreckten Antiphasenbereichen oxistieren such Kristallgebiete aus Domiinen mit verschiedener Untergitterbesetzung. Die die zuletzt genanntnn Bereiche trennenden nichtlinearen Antiphasengrenzen (APB) sind in Legierungen mit period&h geordneten Strukturen friiher nicht beobachtet worden. Die in den Beugungsbildern auft,retenden Satellitenreflexe hijherer Ordnung deuten darauf hin, da5 die Perioden mit M = 1 unter jenen mit M = 2 offensichtlich gleichfijrmig verteilt sind. Die Beugungsbilder bestlitigen die Theorie x-on Fyjiwara.“’ Andererseits zeigen die Durchstrahlungsaufnahmen, da5 Regelmh5igkeiten der Verteilung von M = 1 in 111 = 2 auftreten. Die Verteilung kann nicht vollkommen regelm(l5ig sein, da die gemessenen Durchschnittswerte von M mit der Zusammensetzung zwischen 1,67 und 2,OO variieren. Das impliziert, da5 mehrere Liingen [(2n + l)ao] der superlangen Periode gleichzeitig im geordneten Kristall auftreten. Genau das wurde in den gegenwiirtigen Untersuchungen beobachtet.
INTRODUCTION
an integer.
According
to Fujiwara,(l)
this fact can be explained if M is the mean value of the different not
The long period order in alloys has been investigated very intensively in the recent years. Especially the periodic structures of the alloys CuAu 11,(2*3) CusAu
with lengths M, and M,, occurring
II,(*,5) Cu,Pd,(6)
n1:n2, the reflections
Au,Mg,(‘)
have been of interest. alloys indicate periodic
Au,Mn@’
and Ag3Mg@-14)
The results obtained
that in an ordered
domain lengths.
for these
would
crystal there exist
distance
M,
the lengths of the anti-phase
which domains,
is between the
not
values of 1.0 (Au,,Mn(*)) and 10 (Cu,Au(12)), when M expressed in fundamental unit vectors of the ordinary crystal. As a rule: the value of M, which can be calculated
* Received Fi;rl?=u-i ACTA
from
the diffraction
Mav IL, 1970. Physical Laboratory,
METALLURGICA,
VOL.
University 19, JANUARY
patterns, of
periodic
is
models
of Fujiwara’l)
an essentially
a regular
anti-phase
domains
is required
results.
However,
mental
of the exact
and of
uniform,
arrangement
the experimental evidence
to the
but
of different to explain
the final experi-
arrangement
is still
lacking. The value of x
Turkn. 1971
necessarily
periodicity
corresponding
+ n2M2)/(nl + n2). Accord-
Perio and Tournarie,(15)
is
directly
= (n,M,
ing to the theoretical
also represents
in the proportion
due to the lattice
at the positions
mean value fl
slips repeating after certain atomic distances.
This out-of-step
appear
In the case of two kinds of domains
exists between 15
for an alloy Ag-(21-28.5)
at. y. Mg
1.7 and 2.0.(12) This range is formed
16
ACTA
METALLURGICA,
VOL.
19, 1971
by
mixing domain lengths for which M = 1 and M = 2.(l) Because of the very great difference in the ratio of the two possible values of M, AgsMg is very appropriate
for the investigations
of the various object
anti-phase
This is the main
of the present study.
ELECTRON When tions
of the distribution
domains.
CONTRAST
calculating
in Ag,Mg,
concerns
are four possibilities
a model
: (1) regular uniform, (2) irregular and (4) random
Fujiwara (l) has derived the expressions
for the intensities
for each of the above-mentioned
In cases 1, 2 and 4, the expressions
intensity
maxima
in the l-direction
(n, m = 0 or integers).
peaks
(2m + 1)/(2x)
For case 4, the background
is the greater the more random
In addition to the above-mentioned defined
appear
give sharp
of the reciprocal
lattice, when h + k is odd and 1 = n f intensity
which
of M = 1 with M = 2. There
(3) regular but not uniform,
arrangement. cases.
of satellite reflec-
one has to choose
the mixing
uniform,
CIRCUMSTANCES
the intensities
at 1 = k/211x
by the condition
2vg
the mixing.
maxima, excessive
in case 3. = positive
Here
v is
integer and
k = 0, 1, 2, . . . . The intensities of the fundamental and of the superlattice reflections are defined by similar expressions as those of an ordinary
ordered f.c.c. structure.
matter of fact, Ag,Mg has a tetragonal the ratio c/a differs only slightly
As a
symmetry,
from unity
but
(C/U =
1.0000 -- 1 .0055’13)) so that the cubic approximation is justified.
Because the uniform and somewhat
lar arrangement
intensities and the coordinates reflections
FF*
=
2 1
from
exp
Tr2?n=o2?n+1
the
of the possible satellite
can be calculated(l)
-t
regu-
seems to be the most probable,
the expression
1+
2m
+
___ 2iV
1)
I
The intensity distribution in the Z-direction of the reciprocal lattice of Ag,Mg calculated from equat,ion (1) for Z = 13/7.
FIG. 1.
is about 1317, the intensity distribution
The results are given in Fig. 1.
If all three directions
of the periodicity
the diffraction
pattern,
the common
flections will be surrounded Besides
the reflections
flanking
the direct spot.
been observed Recently, intensive
for instance
in CuAuc3) and Cu,Au.c12)
Fitzgerald’l@ reflections
proposed that this kind of would appear due to Fraunhofer Here
n is an integer and d is the spacing between the antiphase domain boundaries. The transmission contrasts of the nonperiodio APB’s are primarily determined by the extinction distance of the diffracted
wave.(l’)
The values of the extinction
are generally
calculated
from
expression
?TV cos e P)
(2)
/IF
1
(N -
1)
1
1. The structure
the formulas
factors
were calculated
The scattering factors were taken from Hirsch et aI.
treated the case & = 1.80
Since the writers were especially at.%Mg,
from
of Gangulee and Moss(ll) taking M = 2.
On the basis of the values of the extinction distances to given by Table 1 the normal nonperiodical APB’s would have contrasts of one or two fringes, when the specimen is oriented exactly for a superlattice reflection.(17*14) Furthermore,
(1).
those
These extra satellites have
effects at distances of n/d from the direct spot.
Table
(1)
in the alloy Ag-24
there still
namely
F is the structure factor for the unit cell of V, 8 is the Bragg angle and 1 is the wavelength. The values of to, together with the phase angles tl = 27r?j . R for some reflections, are shown in
sin 77
interested
above,
maxima,
volume
X
using formula
to re-
where
sin Nrr
Fujiwara
contribute superlattice
by satellite cross-patterns.
mentioned
exist one group of diffraction
to=
sin i7
As an example,
was calculated
for this value of B.
1
1
‘s
0
distances
sin NT
x (N-
I
for which x
the first satellites
also have t, values small enough to reveal the APB’s in the transmission
image.
One should point out that
ct # 0 always for the satellite reflections.
HANHI
et al.:
LONG
PERIOD
TABLE 1. Values of the structure factor P, the extinction distance t, for 100 kV electrons, and the phase angle a (R = +a,, (S), fundamental (P) and (1101) for some superlattice satellite (Sat) reflections F CA)
Reflert,ion 100 110 210 III 200
s s F P
1270 1307 1605 273 :05
*7roro +7rooro &TrorO 0 0
I&O
Sat
2.298
2564
+ 7r or
130
Sat
2.008
2934
rt r or i(2n
contrasts
to Marcinkowski
of the periodic These
of the specimens,
different
rates below
temperature
out to be very quick. few hours. 1);
h(2f-L +
type. or more
satellite
+
1):
observed
cooled
with This
the phase diagram
by
two
with also
each been
after an annealing
The slices obtained
of a sparking
machine
were thinned
acetic-acid
for a
from bulks by means electrolytically
solution, recommended
by Tegart w for Mg. The transmission electron microwork was done by using a JEM-6A
microscope
operating RESULTS
The
writers
literature
have
electron
at 100 kV. AND
not
any detailed
DISCUSSION
found
from
experimental
the
available
analysis
of the
in the bright field images as a result of the
interference mentioned
of
the
direct
beam
flanking satellites.
the periodical Cu,Au
when
reflections interfere the periodicity has
However,
other.
formed
were
So, the ordered configurations
essentially
in a perchloric-acid
are of a sine-periodic
are
they
the critical temperature.
was taken from
did not change
and Zwell,f4) the electron
APB’s
contrasts
I7
Ag,Mg
ordering
scopic According
IN
Gangulee and Bever. (lo) In the alloys of Mg compositions greater than about 23 at. %, the ordering turned
c(
4.639 4.507 3.670 21.60 19.30
ORDER
APB’s
with
the
above-
The contrast theory of
was originally
developed
for
II, for which
the value of M is about four times greater than for AgaMg. If the model of regular mixing of M = 1 with M = 2 in AgsMg is accepted, the unit cell of this alloy would same size as that of CusAu II. ,q = 4:jyJ
be roughly
of the
For instance,
when
= a , the large unit cell of AgsMg con-
4n + 1
sists of 7 usual cubic unit cells (Fig. 2). If g
= __ 2n+l’
the greater long period unit cell would include 2(4~ + 1) cubic cells.
According
and Zwell,o4) periodic
APB’s
a periodic
to the theory of Marcinkowski
the minimum
intensities
in the transmission
sum contrast
the superlong
was expected
periodicity
successive APB’s
represent
of AgsMg,
to arise from caused
by the FIG. 3. Selected area diffraction pattern of Ag-25 at. % Mg alloy which was homogenized for 12 hr at 75O”C, annealed for 24 hr at 365°C and cooled l.B’C/hr.
for which M = 1.
EXPERIMENTAL
METHOD
The used alloys were prepared of 99.99% magnesium
the
image. Therefore,
ingots
helium atmosphere.
by induction
melting
The bulk specimens were homog-
enized at 750 or 550°C in a graphite quartz or Pyrex capsules. have any contact
silver and in argon or
crucible
inside
Thus, the alloy could not
with the glass material.
For the
satellites
of higher
order,
nor
AgaMg flanking the direct spot. microscopic
investigation
thin film specimens, such reflections. schaeveo4)
paid
of the
satellites
of
In the first electron
of AgaMg using evaporated
Fujiwara
In another no further
spots which he interpreted
et CL(~) could not find investigation, attention
Vander-
to the extra
to be double
diffraction
spots. In the present study, these satellites were observed to arise from all samples. It was possible
n”
to explain
them by using the model
of Fujiwara.o)
As said before, Fujiwara has published the intensity distribution of the reciprocal lattice when a = 1.80. FIO. 2. The long period unit cell of Ag,Mg to the value
z
corresponding
= 7/4 and to the regular arrangement of&Z = 1 withM = 2.
This value of L%! corresponds to the composition of at. y0 Mg. tg) Figure 3 shows a selected area
24.8
ACTA
18
VOL.
19,
0
present
investigation
n
fujiwan
et al “I
A
Vanderschaeve
METALLURGICA,
1971
i;i 2.10
-
(IL)
1.60 -
4
1 20
21
FIG. 4. Average
22 out-of-step
23 distance
diffraction pattern from which one can measure the value of iw = 1.80. The positions of the higher order satellites agree to an accuracy of about 1 per cent with those predicted theoretically by Fujiwara.(l) Figure 3 shows also quite intensive satellites flanking the direct spot. According to Fitzgerald,(16) the distance between these satellites would be l/d, where d is the long period distance. The distance measured from Fig. 3 is quite accurately + d&. Thus the spacing of the planes giving rise to these reflections equals to 9a,, which is the distance between M = 1 domains when x = 915. The composit,ion of the specimen, from which the value &? = 1.80 was obtained, was 25.0 at.% Mg according to the spectrophotometric analysis. This differs slightly from the corresponding value of Fujiwara et aZ.(g) Because of this difference, the i@ values were measured also for some other compositions. The results are given in Fig. 4 together with the values of Fujiwara et al. In Fig. 4, there is also the curve corresponding to the theoretical values calculated from the equation e -=
a
&
(2 + 2x + S)3’2
Here, x stands for 1/(2n), and t is the so-called truncation factor assumed to be 0.962 in the caloulations.(12) The present experimental data in Fig. 4 lie between the theoretical and the earlier experimental values. The experimental curve in Fig. 4 can be used for the determination of the compositions by means of the measured values of &!. A typical diffraction pattern of the composition 24.2 at. “/b Mg is illustrated by Fig. 5. The positions
2.4
25
26
% as B function
27
28 at.v. k.tg
of Ng composition.
of the satellites are quite near to the theoretical ones of Fig. 1 (p. 16). The two strong flanking satellites in Fig. 5 are obviously formed by a superposition of 6 7 6 Thus, the satellite pairs -!__ and=.--. 1la, ’ 13a, 0 13@0 the value d = 12a, measured from these satellites could be explained. On the other hand, the measured value w = 1.85, whioh is between ‘_Aand ‘4, agrees well with the above-mentioned value of it. The variation of the values of g, measured from several diffraction patterns which were obtained from the specimens of a fixed composition, was smaller than0.01. Figure 6 represents a bright field image of a sample with the same imposition as in Fig. 5. The diameter of the areas which have the same direction of periodicity is of the order of magnitude 1 ,u. In the diffraction pattern of Fig. 6, no satellites can be seen. This is caused by the fact that t,he c-axis of the selected area (the middle of Fig. 6) is parallel to the beam. The symmetrical contrasts of the curved APB’s are typical for the case tc = I. As far as the writers know, this kind of thermal APB’s have not previously been observed in a periodically ordered alloy. The mean value of the periodical fringe spacing, measured from Fig. 6, is about 60 if. The distances of periodicity in Fig. 6 sre thus formed mainly of a unit of length 15U,. Another bright field image of specimens containing 24.2 at. y0 Mg is shown by Fig. 7. In the whole area of this image the direction of periodicity is the same. The disturbance in the periodic fringe contrasts (e.g. points A) is caused by the above-mentioned curved APB’s, which separate the domains of different sublattice occupations.
HANHI
et al.:
LONG
PERIOD
FIG. 5. Selected area diffraction patstern of Ag-24.2 for 10 days at. o? Mg alloy, which was homogenized at, 550°C ordered by coolingO.!Y’C/hr between (390-37O)“C and then 40”Cjhr.
The microfotometric measurements of Pig. 7 gave the results d = (54 f 2) A for about 60 per cent, (45 i 2) A for about 20 per cent and (62 j= 2) L%for about 15 per cent of the measured distances. The remaining 5 per cent of distances did not fit to any of the above-nlentioned limits. The corresponding structure units have the lengths of 13, 11 and 15 cubic unit cells, respectively. From all these distances the mean
ORDER
IN
Ag,Mg
FIG. 7. Bright field image of Ag-24.2 at. y/oMg alloy. The whoIe area has the same direction of c-axis. The influence of the nonlinear APB’s is seen, e.g. at points A. The heat treatment is similar to that of the specimen of the Fig. 5. Normal to the foil is [OIO]. x 63,000. value @ = 1.853 was obtained. This is in good agreement with that found from Figs. 4 and 5. It is therefore evident that the fringe distances, measured from the bright field transmission images, really represent those between the out-of-step slips for which Ail = 1. The difference between the mean fringe spacings, measured from Figs. 6 and 7, represents the irregularity in the mixing of M = 1 with M = 2. On the other hand, this difference can also be caused by a slight variation of the composition. Figure 8 represents a dark field image which is
taken by using reflections from 101 to 101 -
Fro. 6. Bright field image of Ag-24.2 at. % Mg alloy. Normal to the foil is [OOI]. The contrasts of the nonlinear APB’s originate chiefly from reflection 110. The treat,ment is similar to that of the specimen of Fig. 5. X 28,000.
19
d2M’
Fro. 3. Dark field image of Ag-24.2 at. % Mg alloy. obtained with the reflections from 101 to lOi.l/2@. same specimen as in Fig. 7. Normal to the foil is jorol. s 317,000.
ACTA
20
The average
distance
of periodicity,
this image, is about 54 A. field image.
measured
from
Thus, the dark field image
reveals the same periodical bright
METALLURGICA,
arrangement
A similar
to the experimental
is met,
for
also shows that the distribution
flanking the central spot give information On the other about the superlong periodicity.
ACKNOWLEDGEMENTS
only
scholarship
hand, the satellites around the superlattice
found.
contrasts APB’s
resolution,
Nevertheless, which
this periodicity
could
not be
from
the
two
of (2% + l)a,
neighbouring
from each other,
were observed. The average distance between the out-of-step for which
M = 1 was determined
slips
in the following
ways : 1. Using the value of x
which was measured from 1 satellites at the distances of from 2X
the cross-pattern the superlattice
reflections,
2. measuring
the distances
between
the satellites
flanking the direct spot, and 3. measuring
the fringe spacings in the bright and
dark field images. All these procedures
led essentially
to the same
results which were in good agreement with those predicted
previously
results confirmed
in papers.(l*g) the conclusion
M = 1 with M = 2 in Ag,Mg completely
regular.
The
experimental
that the mixing is uniform
but
of not
The fact that the measured value
of iE varies continuously
as a function
of composition
and encouragement
One of us (K. H.) is indebted
Suomalainen
Yliopistoseura,
Finland,
to the for
a
in 1969.
reflections
in the dark field images the sum
arise
at a distance
V. Hovi for his advice
to this work. Turun
should also reveal the shorter periodicity which repeats itself after 2n, and la,. However, because of the
cannot be completely
The writers wish to express their cordial thanks to Professor
results, the satellite
1971
regular.
reflections
insufficient
19,
as does the
situation
instance, in the case of Cu,Au 11.c4) According
VOL.
REFERENCES 1. K. FUJIWARA, J. phys. Sot. *lapan 12, 7 (1957). 2. A. B. GLOSSOP and D. W. PASHLEY. Proc. R. Sot. A250. 132 (1959). 3. S. OGAWA, D. WATANABE, H. WATANABE and T. KOMODA, Acta crystallogr. 11,872 (1958). 4. M. J. MARCINKOWSKI and L. ZWELL, Acta Met. 11.
373 (1963).
5. R. S. TOTH and H. SATO, J. appZ. Phys. 33, 3250 (1962). 6. S. OGAWA and D. WATANABE. in Direct Observation of Imperfections in Crystals, p. 523; edited by J. B. NEWKIR; and J. H. WTERNICK. Interscience (1962). 7. H. SATO and R. S. TOTH, J. phys. Chem. Solids 29, 2015 (1968). 8. D. WATANABE, J. phys. Sot. Japan 15, 1030 (1960). 9. K. FUJIWARA, M. HIRABAYASHI, D. WATANABE and S. OGAWA, J. phys. Sot. Japan 13, 167 (1958). 10. A. GANQ~JLEEand B. BEVER, Trans. metall. Sot. A.I.M.E. 242, 278 (1968). .J. appl. Crystallogr. 11. A. GANGULEE and S. C. Moss, 1,61 (1968). 12. H. SATO and R. S. TOTH, in Alloying Rehaviour and Effects in Concentrated Solid Solutions, p. 295. edited bv T. B. MASSALSKI. Gordon and Breach (19651. 13. k. SCHUBERT, B. KIEBER, M. WILKENS a& R. ~AUFLER, 2. MetaUk. 46, 692 (1955). 14. G. VANDERSCHAEVE, Phys. Status Solidi 36, 103 (1969). 15. P. PERIO and M. TOURNARIE, Acta crystallogr. 12, 1032
(1959). 16. A. G. FITZGERALD, Thin Films 1,83 (1968). 17. R. M. FISHER and M. J. MARCIWKOWSXI. Phil. Maq. 6. 1385 (1961). 18. P. B. HIRSCH, A. HOWIE, R. B. NICHOLSON, D. W. PASHLEY and M. J. WHELAN, Electron, Microscopy of Thin Crystals, p. 490. Butterworths (1965). 19. W. J. McG. TEGART, The Electvolytie and Chemical Polishing of Metals in Research and Industry. Pergamon Press (1959).