Ordering and domain growth in Ni3Fe

GROWTH IN Ni3Fe D. C. &dORRIS,* G. T. BROWS. R. C. PILLER* and R. E. SN4LLICLS Department of Physical Metallurgy and Science of Materials. I.!niversity of Birmingham, Birmingham BI5 2-I-f. England

A~traet-~deri~g and domain growth kinetics of Ni3Fe have been studied over the temperature range 43&497’C using etectron microscopy and X-ray diffraction. Ordering, in general, takes place more quickly at higher temperatures, except for the highest temperatures studied where nucleation difficulties appear to become important. Domain growth takes place in a two stage manner, corresponding to (i) a nucleation and growth stage and (ii) a coalescence stage. The nucleation and growth stage cannot be detected at low temperatures because of the fast nucleation kinetics. The parameter n. defined at 6 = Kr”. is reduced from the value of 1.0 expected during nucleation and growth, and that of 05 expected during coalescence. with the reduction being more marked at high temperatures. These features may be interpreted either by taking into account domain nuclei sizes or by considering the effect of dissolved impurity. R&urn&-La cinitique de mise en ordre et croissance des domaines en Ni,Fe dans la gamme de temperatures de 434 a 497°C a fait f’objet dune etude par microscopic eIectronique et diffraction de rayons X. La mise en ordre est generalement plus rapide aux temperatures plus elevees sauf a Ia pius haute temperature Ctuditr. oii les di~eult~s de germination semblent jouer un role important. La croissance des domaines est un processus a deux itapes. (i) de germination et accroissement. (ii) de coalescence. A basses temperatures la vitesse de germination rend impossible de mettre en evidence la premiere ttape. Tandis qu’on attendrait pour le paramhre n dans i’equation 6 = Kr” ies valeurs de 1.0 dans la premiere phase et de 0,5 dans la seconde ii s’en avere moindre. et d’autant plus que les temperatures sent plus elevtes. Ces observations se laissent interpreter soit a partir des grandeurs des germes de domaines soit par l’effet des impure& dissoutes.

Zusammenfassung-Mittels Elektronenmikroskopie und Rontgenbeugung wurde die Kinetik der Ordnungseinstellung und des Domanenwachstums in Ni,Fe im Temperaturbereich 434-497’C untersucht. In allgemeinen Lluft die Ordnungseinstellung bei hiiheren Temperaturen schneller ab, at&r bei sehr hohen Temperaturen, bei denen Keimbildungsschwierigkeiten wesentlich zu werden scheinen. Das Domanenwachstum lIuft in zwei Stufen ab. (i) Keimbildung und Wachstum, und (ii) Zusammenwachsen. Die erste Stufe kann bei tiefen Temperaturen wegen der raschen Keimbiidungskinetik nicht gefunden werden. Der Parameter n, definiert als 6 = Kr”, ist erniedrigt auf einen Wert zwischen I, den er wlhrend KeimbiIdung und Wachstum haben so&e, und 0,s der wahrend des Zus~menwach~ns erwartet wird, wobei die Emiedrigung bei hohen Tempetaturen ausgeprlgter ist. Diese Eigenheiten kiinnen interpretiert werden bei Beriicksichtigung entweder der GroBen der Domanenkeime oder Effekte getlister Verunreinigungen.

1. INTRODUCTION The ordering kinetics of N&Fe have recently been studied [I] by X-ray difiaction and a two-stage domain growth behaviour observed. These stages have been related to (i) nucleation and growth, and (ii) coalscence, respectively. Rase and Mikkola [2] have shown that the normal behaviour of 6 vs t* of CuJAu, where 6 is the domain size and r time, may bc changed for slightly off-stoichiometric material annealed for long times and these workers have related this to the influence of the excess component. It is well known that impurities in general affect

*Now at Metallurgy Division. A.E.R.E. Harweli. Didcot, Oxon, E&and.

domain kinetics [3.4] and it is therefore possible that the two stages observed may correspond to (i) impurity-unaffected and (ii) impurity-affected growth, respectively. The present paper reports the results of a closer exam~ation of domain growth kinetics covering a wide range of tem~ratures and domain sixes. Both X-ray diffraction and electron microscopy techniques have been used to achieve a high accuracy of domain measurement for all domain sizes. It was hoped, in addition. that electron microscopy would enable the ordered structures to be observed directly. This is especially relevant in view of recent suggestions [5] of modular ordering in Ni3Fe. In addition it was possible to correlate the electron microscopy and X-ray diffraction results in a manner similar to that carried out C6.71 for Cu3Au.

22

MORRIS et al:

ORDERING

AND DOIMAIN GROWTH IN X&Fe

tilt stage. Optimum contrast was achieved in dark field using the 100 reflection with this beam set to the Bragg position. Domain sizes were measured directly from the micrographs as the mean intercept distance, without the need to apply correction factors [6,7].

Table 1. Material composition

Nickel

72.5%

Iron

27.4%

Carbon

0.015%

Magnesium

0.05%

Sulphur +

0.005%

3. EXPERi~~E~~.~L

2. EXPENSE

PROCED~

2.1 Specimen preparation The material was obtained in the form of approximately 25 mm dia. bar and was from the same stock as that used by Besag and Smallman [83 for mechanical property studies. The material composition is shown in Table 1; the @OS%Mg present was added to combine with the small amount of sulphur as impurity. The bar was cold rolled directly to ca. 2 mm thick strip and annealed for 45 min in vacuum at 600°C to give a recrystallised, small grain size. This treatment produced a strong [IOOt (010) texture which was desirable to facilitate the X-ray measurements. Material for electron microscopy was given a longer annealing treatment of 2j h to produce a larger grain size more suitable for such studies. These annealing treatments were terminated by quenching into water to retain the disordered structure. Pieces of the strips were then ordered by annealing in a salt bath for the required time, which was terminated by quenching into water. The temperatures used ranged from 434A97”C, and were controlled to within +2”C. The specimens were electropolished using a phosphoric and-sulphuric acid mixture, and foils for electron microscopy obtained using the window technique.

2.2 Determination of degree of order and domain size X-ray investigations were carried out on a Siemens di~a~ometer equipped with step counting facilities using unfiltered Co I&-radiation. Pulse height discrimination was used with a proportional counter and for each specimen the 100 superlattia: and the 200 fundamental peaks were recorded, from which the integrated peak intensities and half-peak breadths were determined. From these measurements the degree of order and the domain size may be determined. No corrections for anomalous broadening were made [9,7, IO] since the domain boundaries are randomly oriented [l 1J in ordered N&Fe. Examination of peak breadths of reflections other than IlOO: is $ifficult because of the very weak intensity, but it would appear that no anomalous effects occur [12], Electron microscopy was carried out using a Philips EM300 microscope equipped with a high angle

RESULTS

3.1 Degree of order measurements For full order, the ratio of superlattice to fundamental intensity should be given by 1100/1200= 19.5 x IO-), although larger values are often achieved Cl] as a result of extinction reducing the intensity of the 200 reftection, and hence a determination of the actual degree of order is difficult. In the present work, the ratio I,OO;?~~Oreached a maximum value of 20 x 1O-3 for those materials annealed for Iong times at the lower temperatures. Relative degrees of order have therefore been calculated for each specimen by comparing the value of the ratio with this maximum value, i.e. S’ = [Iloo/Itoo],,,J [I,00/1200]max.Degree of order values obtained in this way are plotted in Fig. 1 as a function of annealing time for the several annealing temperatures used. There are several observations that can be made from this figure, namely (i) at each temperature the degree of order vs log time plot shows the expected S shape, (ii) the equilibrium degree of order decreases as the annealing temperature increases towards the critical temperature, and (iii) in general, the ordering kinetics are faster at higher temperatures, except close to the critical temperature when the kinetics are slowed by, for example, inhibited nucleation. The effect on ordering kinetics near T, may clearly be seen in the iso-order plots of Fig. 2. 3.2 Domain size measurements 3.21 ConI~arisan of electron rnj~oscop~ and X-ray dr@acrion results. Micrographs illustrating the

domain structure in three differently ordered specimens are shown in Fig. 3. The domain boundaries are randomly oriented with no tendency to lie on

Oyy

wer 5

O:. 10

M

la0 3w l.aw Annealing (hours!

time

3X0

Fig. 1. Relative degree of order as a function of annealing time for the various temperatures studied.

preferred plsn:s, as previously [6.7] found for Cuj.Au. The domain kes were determined from these micrographs as the mean int&rpt distance on randoml) oriented Straight lines. In each case. several hundred domain boundary intcrsectiom were counted. and the mean values obtained are shown in Table 2. Because of the poor domain boundary contrast obtained for Ni3Fe (a result of the similar scattering factors for Ni and Fe) it was only possible to make measurements on very thin regions of the foil, and rhz minimum domain size which could be esamined was of the order of 10&3O~k In addition. the curwture of the domain sAls means that thz projected tvall thickness is ahvays large and it is impossible to determine whether any disorder ma) occur in this region. Far each of the three materials examined by electron microxopy. three differem domain size values were obtained from the X-ray diffraction results corresponding to three different wars of correcting for instrumental broadeninp. Domain sizes were then calculated using the Scherrer equation d = Ki,/kosfl. kvhere ti is the domain size. K the Scherrer constant. i the wavelength of the cobalt I& radiation, f; the half-breadth. and tj the Bragg angle. These results are shown in Table 2 for comparison with the electron microscopy figures. It is sew, that u&g the espression domain sizes obtained r fi6 = , /3: - fly are in very good agreement with the electron microscope results i&here @* fi, ax? /3, are the domain size produced. ~sp~rimentai, and instrumental half-bre~~~iths respectirelyf. The same espression was used previously [7] for work on Cu&u. since the superlattice peaks were approximately Gaussian in form. Although the X-ray value for domain size is a harmonic mean and the electron microscope value an arithmetic mean. the two sets of values obtained are in good agreement. It has previously been show that a comparison may be carried out using these different averagin_e methods [7]. 3.22 Dor~rlitl qwwrh. Domain growth is shown in Fig. 4 for the \:arious annealing temperatures used. At the higher temperatures, 197470-C. domain growth occurs in a two stage manner, while at lower temperatures only one stage is observed. In each stage domain growth can be represented by the expression j - j,, = Kt”,

(11

where & is a critical domain nucleus size and K and Table 7. Comparison of domain sizes obtained b! Axtron microscopy and N-ray diffraction

Fig. 3. Electron micrographs iflusrratinp domsin boundaries in three ditkrent mnteri&. Dark tieId micwgr=raphs usinr It31 beam. on Brag 100. (i) Annealed for 1070 hr at 457-C. Orientation :Oll:. (ii) Anne&d for lit32 hr at 45-C. Orientation ;oOl:. (iii\ Annealed for 1700 hr at 460-C. Orientation i@N!.

02y 0 0

Fig.

02 CL c-s 08 10

4. Domain

12 IC 16 18 2c lxJthursl

22 N

growth as a function temperature.

26

23 3c 3.2 3.4

of

time

and

n are constants. Ignoring for the moment do, log d may be plotted against log t (Fig. 4) and values for log K and n are shown in fib/e 3. The transition from stage I to II occurs at smaller domain sizes and shorter times as the temperature is decreased from 497 to 470°C. It therefore seems logical to consider that at lower temperatures the transition takes place at very short times. and below the Emit of domain size dete~ination. This argument is confirmed by the continuous variation of log f( and rr for stage II at all tem~ratur~s. Table 3. Values of log K and n in the expression d = Ki” for stages I and II at each temperature

L

From the present results. activation energy values may be ~~etermined in several ways. Figure 5 illustrates the detestation of the activation energy of ordering, by plotting the logarithm of the time to a given degree of order (normalised for the equilibrium degree of order at that temperature) as a function of the reciprocal absolute temperature. The kinetics of ordering at high temperatures may be affected by the two-phase. ordered and disordered, nature of the material at relatively short times. It will be shown later that stage I corresponds to a nucleation stage so that materials have a two-phase structure. The time to a measured degree of order consequently depends on both ordering and domain kinetics. Ordering kinetics at 497’C may be further affected by nucleation difficulties, ‘and points corresponding to high degrees of order, especially at high temperatures may be affected by the approach to equilibrium degree of order. The value of activation energy determined is independent of the degree of order considered and corresponds to j0K calimole. This figure is close to the vaiues determined by Suzuki and Yamamoto [13], namely 455 K caljmole for disordered and 475 K cai mole for ordered Si,Fe. The activation eners for domain growth Q, may be determined in two ways. Firstly, from the rate of domain growth at a given domain size as a function of reciprocal absolute temperature, and secondly. from the variation of log K with 1;T. where K is defined in equation (1). The results are shown in Figs. 6 and 7. Figure 6 may be separated into two parts. At low temperature the activation ener=- is independent of the domain size and has a value of 45 K Cal/ mole. At high temperature the measured activation energy is dependent on domain size, ranging from about 60 K Cal/mole at a domain size of 40 A to cn. 120 K Cal/mole at a domain size of 2OOA. A comparison with Fig. 4 shows that the transition from stage I to II growth does not affect the plot, which indicates a similar energy for both stages. Figure 7 shows a curve tending to a straight line at low temperatures

Mean Wue WiO r5 K callmole

01 . 1.29

I

1.31

L

1.33 1.35 -.I--*lO“ T"K

Fig. 5. The determination

1.37

of the activation

l-39

energy

l-L1

of ordering.

MORRIS et al:

ORDERING

AND DOMAIN GROWTH IN N&Fe MC 260 2x

1.32

1.3‘

&

*lo”

136

136

1Lo

Fig, 6. Determination of the activation energy for domain growth from the growth rate at a given size. indicating that the Arrhenius equation is not satisfied at all temperatures. The activation energy determined from the slope of this line, i.e. below 46O”C, is 27 K Cal/mole, which corresponds to a value of Q, of 54 K Cal/mole since in the low temperature regime 6’ = fCt. This value is in fair agreement with the value determined from Fig. 6 for small domain sizes.

4. DISCUSSION As found previously [l] it is observed in the present work that domain growth takes place in a two stage manner. It was impossible to examine the first stage directly by electron microscopy, but the following arguments serve to show that stage I corresponds to a nucleation and growth stage and stage II to a coalescence stage. The values of n (where 6 = W) obtained in stage I he in the range 050-O-85, and for stage II in the range 021449. It has been shown on several occasions[i,4, 14,15-J that values of n lower than the theoretical values l*O (for nucleation and growth stage) and 050 (for coalescence) may be obtained, and an impurity-affected mechanism has been suggested [3,4]. In no case, however, has an increase in the expected values of n been obtained. Stage I cannot therefore correspond to coalescence, and must relate to the nucieation and growth stage, while stage II corresponds to the coalescence stage. Decreases in the values for the two slopes may be achieved by impurity effects, and if this is the case

24

16. logK 12.

al

I;?9

1.31

,,

/KM k--w PlOl

p

“,

.

130

I

25

133

1.3

I.37

1.39

i&l

75, .lo-3

Fig. 7. ~termination of the activation energy for domain growth from the variation of K.

Fig. 8. Values for critical domain size obtained by assuming n = 1 (stage I) and n = 05 (stage II). Domain sizes at which a kink in the log J-log t plot occurs are shown for comparison. it seems that the effect of the impurity

on kinetics is greater at higher temperatures. An alternative explanation of these features may follow from the effect introduced by neglecting the Jr, term in equation (1). The inclusion of a non-zero 6, in equation (1) would increase the slopes of both stages I and II. Thus, making the assumption that the real value of n should be 1.0 for stage I and &5 for stage II, allows values of 6, to be computed for each of the temperatures examined; these values are shown in Fig, 8. Two features are immediately obvious. Firstly, the predicted values of &, for stages I and II are different, and secondly the value determined for each stage increases with temperature. It is considered that 6e corresponds to the critical nucleus size for the particular mechanism and temperature being considered. It then follows that for stage I be will correspond to the critical size of an ordered domain nucleated in a disordered matrix (assuming a classical nucleation mechanism) or to a critical modulation size (according to the recent mechanism discussed by Taunt and Ralph [S]). It has not been possible experimentally to examine the nucleation stage in detail so that it is not possible to distinguish between the possible mechanisms. However a comparison of the modulation sizes of Taunt and Ralph [S] with the present X-ray diffraction measured domain sizes shows very good agreement. The field-ion microscope data obtained at 4WC corresponds to stage I in the present paper so that the absence of a two phase region must ehminate classical nucleation as the ordering mode. Furthermore, the modulation size corresponding to zero annealing time at 48O’C was 15A which is in agreement with the value of 6, predicted for that temperature in the present paper. Taunt and Ralph [5] did not obtain values for modulation size at zero time at other temperatures, but it seems likely from their results that the modulation size at zero time at 460°C was somewhat smaller. The values of de observed corresponding to stage I are thus consistent with the size of the critical nucleus corresponding to ordering and the increase in 6,, with temperatures is brought about by the more difficult nucleation near the critical temperature.

26

MORRIS et al:

ORDERING AND DOMAiN

The values of de corresponding to stage II are larger at all temperatures and may be seen (Fig. 8) to agree fairly well with the domain sizes corresponding to the kink in the log d vs log t plots. The critical size in this case is that at which domain impingement occurs and coalescence takes over. The decrease in the value of Se at lower temperatures in in accord with easier domain nucleation and consequently earlier domain impingement at such temperatures. It thus appears that it is important to describe domain growth using equation (1) and take into account the critical domain size, or the domain size at zero time. In most observations, 6e is very small while measured domain sizes are large [7], and the effect of ignoring So is not great. In measurements involving small domain sizes, however, and also for heat treatments carried out close to the critical temperature, where the critica nucleus sizes are large, the influence of the critical domain size on subsequent domain growth is important. It may be seen, for example. in Fig. 7 of the paper by Poquette and Mikkola [lo] that the slope of the log (domain size) versus log (time) plot increases with ageing time to achieve a value of O-5 which corresponds to domain coalescence. Lower slopes at short ageing times may then be explained in terms of the influence of the critical domain size. It thus appears that at least some of the slope changes observed in the present work may be explained by the inclusion of the ri, term. This does not, however, eliminate entirely the suggestion of impurity affected domain growth [3,4,15] which may still play a part. Taking this alternative view, then domain growth during coalescence may be expressed as drjldr = r$&$

(2)

where z is a constant, y the domain boundary energy, M the wall mobility and S the domain size. A different expression holds for domain growth during stage I, but nevertheless a similar impurity argument can be made. The dependence’ of growth rate on domain size occurs because the driving force for domain growth is related to the curvature of the domain walls, and this is related to the domain size. Integrating this expression the normal 6’ = Kt relationship is obtained. The impurity may, of course, affect the mobility term or the APB energy. The segregation of solute to a domain wall has recently been shown [16] to decrease the APB energy and any general impurity may be expected to act similarly. The mobility of the impurity-affected domain wall depends on the migration of both impurity and solsent atoms, and may be changed accordingly. It is ~portant to notice, however. that the mere presence of impurity at the domain wall is not sufficient to affect the value of II. For n to be altered it is essential that the concentration of impurity in the domain wall increases with domain size. For a slow-diffusing impurity, the mobi-

GROWTH IN NiJFe

lity of the domain wall will be decreased by the presence of impurity and as the wall moves dragging along the impurity, it encounters more and more impurity so that the concentration builds up. However, for a fast-diffusing impurity, all the impurity in solution will rapidly move to the domain wall, where its effect wiI1 mainly be to affect the APB energy. In the former case, before the beginning of the coalescence stage, the concentration of impurity will be linearly dependent on the distance moved by the domain wall, i.e. proportionat to the domain size. After this stage, and for all stages in the case of the fast diffuser, all the available impurity will be present in the domain wall. The concentration of impurity in the wall is therefore determined by the domain wall area and is given by c = c06/3a, where a is the domain wall thickness and ce the average impurity content of the material in atomic per cent. In all cases, therefore, the concentration of solute, increases linearly with the domain size. Equation (2) may be modified to include the impurity effect, viz. dS/dt = &M’/6 = f(l/~)~(l/~~ d,

(3)

where 7’ is the impurity dependent APB energy which decreases as the impurity content increases and iM the impurity affected mobility. Both these terms are also related to the domain size and the integrated form of the impurity modified equation (3) shows that the parameter n is related in a compIex way to the effect of the impurity on both the APB energy and the mobility. A decrease in the APB energy and the mobility leads to a decrease in n, while a decrease in the APB energy and an increase in the mobility may lead to either a decrease or increase in n, depending on the relative strengths of the two effects. The model just described relates the amount of solute at the domain wali to the decrease in the parameter n. For a given impurity content, co. the value of n may be determined if the functions describing the behaviour of the mobility APB energy are known. It appears, furthe~ore, that for a given ca a unique value of n is determined. The variation of n observed should therefore be related to a change in co with temperature. If the assumption is made that n varies linearly with impurity content, then it is possible to examine the experimental results more closely. The value of n is taken to be related to impurity according to (05 - n) = PC,,

(4)

where P is a constant for a particular impurity acting in a particular alloy system, and using the data of Table 1 reported by Ling and Starke [3] (where n is the reciprocal of the present n) P has a value of approx. 1. However. as shown by Gordon and El-Bassyouni [is], some impurities are much more potent than others, and in their case the value of P is approx. 300. Because of this wide variation in P. it is not possible to determine the actual value of the impurity

MORRIS er ai: ORDERING AND DOMAIN GROWTH IN Ni3Fe

Fig. 9. Variation of impurity content with temperature for two different values of P.

but nevertheless, the variation with temperature for a particular value of P may be determined. This is shown in Fig. 9 for the two extreme values of P: it will be noted that the impurity content is plotted logarithmically on the abscissa. The experimental situation may be expected to correspond to some intermediate range. The curves are seen to be similar in form to solid solubility boundaries on an equiIibrium diagram, and lead to the suggestion that the amount of impurity affecting domain growth is not the total alloy impurity content, but the amount in solid solution. In the subsequent discussion the impurity affecting domain growth is assumed to be sulphur, since this is known to have a profound effect upon the properties of N&Fe, and the results observed in the present work may be explained fairly well in terms of sulphur action. Although the solid solubility of sulphur in nickel or in y-iron at these temperatures is very low [17]. the amount in solution is probably determined by dissociation of the magnesium sulphide precipitate formed by the addition of magnesium to scavenge the alloy. Plotting ln(O.5 - n) against I/T allows the activation energy of solution of the impurity element to be determined and a value of 504OK Cal/mole is obtained. In the case considered this activation ener_By probably corresponds to the dissociation of magnesium sulphide and the subsequent solution of sulphur in the nickel-based solution. The reaction to be considered is content.

M?r Sprecipilatc

=

Win

solution +

4"

rolution

(5)

and, [18] using a heat of dissociation of about 80K Cal/mole and heats of solution of a few K Cal/mole, the energy required for dissociation is approximately 70 K cal,mole. In view of the assumptions involved in the arguments, this value is believed to correspond well with the experimental value deduced from the variation in II. Thus. the variation in domain growth behaviour may be explained either in terms of the effect of the critical domain nucleus size, or in terms of the effect of an impurity element. Both effects, acting independently or in conjunction, may lead to decreases in the sfope of the log 5 vs log t curve, as observed in Fig. 3. Further work on material with a very low

‘7

sulphur content may provide more evidence to differentiate between these two alternative models. Ordering in Ni,Fe at the temperature examined takes place firstly through a nucleation stage (which may correspond to a modular-type mechanism) followed by a coalescence stage during which the degree of order within the domains may increase slightly while the domains coarsen. Ordering has been examined by Dienes [I93 using chemical rate theory. and some analogies may be drawn between his results and the present ones. The order-time plots shown in Fig. 1 of the present work are very similar to Fig. 4 of the Dienes paper in showing the fastest ordering kinetics at some temperature below the critical temperature, with kinetics both above and below this temperature being slower. The slower ordering kinetics near the critical temperature may be related to inhibited nucleation or may follow from the chemical rate theory without considering change in rate of nucleation. The rate of ordering is shown in Fig. 10 as a function of degree of order and tem~rature. The form of these curves is similar to that predicted by Dienes, illustrated in the inset of Fig. 10. The activation energy of ordering may correspond to diffusion in either the disordered or the ordered phase so that it is not possible to relate the experimental value (of 50 K cal!mole) to diffusion at any particular state of order. It appears, however, from the work of Suzuki and Yamamoto [13] that there is little increase in the activation energy on ordering, and hence the experimental value gives the approximate activation energy both for ordered and for disordered Ni3Fe. There are several physical processes occurring in the order-time plots used to determine activation energies, Initially, the rate of increase of measured order is determined both by the rate of homogeneous ordering inside ordered domains and by the rate of nucleation and growth of these domains. In stage II, after domain impingement, the rate of ordering observed is that determined by homogeneous ordering and by a decrease in the volume of disordered domain walls. Nevertheless, the activation energy obtained appears to be a constant, irrespective of whether the domains are growing according to stage I or II. This observation is presumably a result of very similar activation energies in the ordered and disordered materials.

Fig. IO. Rate of ordering as a function of degree of order for several temperatures. Inset shows a typical plot from Dienes Ei93.

MORRIS et at:

2s

ORDERING

AND DOMAIN GROWTH IN Ni3Fe

The determination of the activation energy of domain growth is greatly complicated by the apparent variation of n with temperature. Expressing the domain growth rate as d6jdt = (A/am) exp[ - Q/RT]

(6)

leads to the following expressions on integrating (&,+ t/m + I) + (6;;’ t/m + 1) = A exp[-Q/Rat (7) or, ignoring be 6 = &, exp[ - nQ/RTft”,

(8)

where K0 = f A(m + 1): ” and n = (l/m + 1). The effect of varying n on the measured activation energy can now be seen. In Fig. 6 the activation energy was determined from the variation of (dJ/dt) with 1/‘1; i.e. through equation (6). For constant M and 6 the correct value of activation energy will be determined, but a variation of m with temperature means that incorrect values will be obtained, with the calculated value depending on the domain size. At the lower tem~ratu~s where n is approximately constant at O-5(and therefore m is approx~ately constant at 1-O) correct values may be expected and no domain size dependence should be observed. In a similar way, the determination of activation energy in Fig. 7 (using equation (8)) may be expected to lead to spurious results whenever n varies with temperature. Again, at low temperatures for n 2: 0.5, the correct value may be expected, and a measured activation energy Q/2 is obtained. The values for the activation energy of domain growth obtained are in reasonable agreement (45 K Cal/mole, cf: 54 K cal/mole) and they also agree with the activation energy of ordering (50 K Cal/mole). As before, however, it is not possible to d~er~tiate between diffusion in either the ordered or disordered material.

5. CONCLUSIONS 1. Ordering and domain growth of N&Fe in the range 434-497”C has been examined, principally by X-ray diffraction, and found to take place in two stages. It was not possible to examine stage I directly by electron microscopy, but it is evident that this stage corresponds to a nucleation and growth period. This stage may correspond to a modular type of ordering mechanism. Stage II has been found to correspond to domain coalescence. 2. Domain sizes have been measured both by X-ray diffraction and by electron microscopy and a very good correlation of results is obtained when the_X-ray domain sizes are calculated using the expression /ld = Jflz - /32 to remove instrumental broadening. The electron microscope technique is not generally suitable in this case, however, because of the poor contrast obtained and the small domain sizes generally examined.

3. Domain growth, plotted as log 6 against log t. occurs with a slope decreased from the expected values of I.0 for stage I and 05 for stage II. This may be caused by ignoring the effect of the critical domain size or by the effect of impurity on domain growth. 4. According to the critical domain size hypothesis larger nuclei are required at higher temperatures. The critical nucleus for stage I corresponds to the order modulation period, and that for stage II corresponds, approximately, to the domain size at which impingement occurs and coalescence takes over. 5. According to the impurity hypothesis. the impurity species segregate to domain walls thereby reducing domain growth. The impurity. believed to be sulphur, plays a greater part at higher temperatures as the sulphur-bearing precipitate dissociates. 6. Activation energies may be determined from ordering kinetics or from domain growth kinetics. Variations in the parameter n make determination from domain growth difficult at high temperatures but values obtained at lower temperatures agree with that obtained from ordering kinetics and with previously published figures.

REFERENCES 1.

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