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Isokinetic analysis of nanocrystalline nickel electrodeposits upon annealing
Pergamon PII: S1359-6454(96)00254-6
Actu maler. Vol. 45, No. 4, pp. 1655-1669, 1997 IC 1997 Acta Metallurgica Inc. Published by Elsevier Science Ltd Printed in Great Bntain. All rights reserved
1359-6454197 $17.00+ 0.00
ISOKINETIC ANALYSIS OF NANOCRYSTALLINE ELECTRODEPOSITS UPON ANNEALING NING WANG’?, ‘Department ‘Department
NICKEL
ZHIRUI WANG’S, K. T. AUST’ and U. ERB’
of Metallurgy and Materials Science, University of Toronto, Toronto, M5S 3E4 and of Materials and Metallurgical Engineering. Queen’s University, Kingston, K7L 3N6, Ontario, Canada (Received
31 May 1995; accepted
4 June
1996)
Abstract-The grain growth kinetics of nanocrystalline nickel electrodeposits was studied by transmission electron microscopy and differential scanning calorimetry at different heating rates. It was found that, upon annealing, the nanocrystals in the nickel electrodeposits appeared to grow abnormally and released about 415.7 k 3.5 Jjmol of heat. The mechanism of the abnormal grain growth was attributed to the subgrain coalescence. The method for determination of the grain growth activation energy as well as all the other kinetic parameters in the Johnson-MehlPAvrami equation was proposed based on an isokinetic analysis. This method is applicable to general types of transformation process governed by a single activation energy under the isokinetic condition. The activation energy for the grain growth of nanocrystalline nickel electrodeposits was found to be about 131.5 kJ/mol using this method. The difference between the present method and the Kissinger and Ozawa method was addressed in terms of their physical backgrounds. % 1997 Acta Metallurgica Inc.
1. INTRODUCTION
Nanocrystalline materials, due to the unique properties which make them distinct from their counterparts, conventional polycrystalline materials, have attracted a great deal of attention from material scientists in recent years. The development of this research field in the last few years has been comprehensively reviewed by a number of researchers [l&3]. From a thermodynamic point of view, a polycrystalline material is in a metastable state because of the excess free energy associated with the intercrystalline components. For polycrystalline single-phase material, the excess free energy arises mainly from the grain boundaries, triple lines and quadruple nodes. The overall contribution of these intercrystalline components to the total free energy of the system becomes more and more significant when the grain size of the material becomes smaller and smaller and especially when it falls into the nanometer range. The excess free energy of the system due to the presence of intercrystalline components is proportional to the volume fraction of these components within the materials. In the previous work [4], a polycrystalline material has been viewed as a composite material which consists of crystalline components and intercrystalline components (grain boundaries, triple lines and quadruple nodes), and the variation of each component with grain size was analyzed by assuming the grain shape to be tetrakaidecahedral with grain tPresent address: Chalk River Laboratories, ON Canada KOJ IJO. ICorresponding author.
Chalk River,
boundary thickness 1 nm. As seen in Fig. 1, when the grain size decreases from 1 pm, as often observed in conventional polycrystalline materials, to 10 nm, the summation of volume fraction of intercrystalline components increases from a value of about 0.3% to a significant value of 27.1% in which 24.3% is grain boundaries, 2.7% triple lines, and 0.1% quadruple nodes. And if the grain size is further reduced to 5 nm, then approximately half of the material is composed of intercrystalline components. The presence of large amounts of intercrystalline components in nanometer-grained polycrystalline materials provides us with a great opportunity to study the properties of these intercrystalline components since such materials have a strong tendency to transform into conventional polycrystals with coarser grain sizes and less intercrystalline volume fraction. The crystallization kinetics of nanocrystalline materials has been the subject of intense study in the last few years, due to this fact. A number of studies on the thermal stability of nanocrystalline materials have shown that the materials, upon heating, will exhibit a quasi nucleation-growth process [5-81. A quasi nucleationgrowth process is, in a sense, that in which, when nanocrystalline materials are brought to an elevated temperature, the nanometer-sized crystallites in the materials always start to grow in a random, non-uniform manner and some of the nanocrystallites appear to act as “nuclei” and preferentially start to grow at the expense of the surrounding nanocrystalline matrix. With increasing time, the grains become larger; meanwhile, new “nuclei” appear to form and grow in the same way.
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The process described above allows us to model the process with the existing kinetic theories of phase transformations. In this study, we will show that nanocrystalline materials can also provide us with the possibility to study (i) isokinetics of the transformation and (ii) the intercrystalline enthalpy using differential scanning calorimetry (DSC) measurement. As for (ii), nanocrystalline materials produced by electrodeposition possess the unique advantage over other production techniques for this type of measurement due to its pore-free and reduced lattice distortion characteristics. 2. THEORETICAL
CONSIDERATION
Non-isothermal DSC measurement has been commonly used to study the nature of structural change processes in amorphous and nanocrystalline materials due to the significant thermal effect upon heating these materials up to elevated temperatures. During a non-isothermal DSC experiment, the temperature of the furnace is changed linearly with time t at a given rate p (degree per minute). The furnace temperature in Kelvin is T=
T”+pt
(1)
where To is the initial temperature. Assuming that the dynamic case is a close succession of isothermal ones, then the well-known Johnson-Mehl-Avrami (JMA) equation [9-l l] for the fraction of transformed material can be used to describe the non-isothermal continuous heating process, as in DSC measurement with a constant heating rate, i.e. x(t) = 1 - exp(-kt”). where x completed
is the fraction of the at time t, k is a constant
(2) transformation associated with
NICKEL
ELECTRODEPOSITS
nucleation rate and growth rate, both being dependent on temperature, and n is a constant which reflects the nucleation and growth morphology. It is noteworthy that many people have used the analogy of a chemical reaction rate equation and interpreted the factors, k and n, in equation (2) in the same way as chemical reaction rate constants [ 121. This is rather misleading as we will see later that the factors, k and n, in the JMA equation should not be generally understood as chemical reaction rate constants. The difficulties in treating non-isothermal reactions are mainly due to the independent variations of growth and nucleation rate with temperature. Therefore, the JMA equation is in general not a valid description of transformation kinetics occurring under non-isothermal conditions. However, a nonisothermal transformation consisting of nucleation and growth can still be described by the JMA equation if it meets the following conditions [13]: (a) all nucleation occurs during the early stage in the process leading to the so-called site saturation and, for the rest of the time, only growth is significant, (b) the growth rate depends only on instantaneous temperature and is independent of time, (c) nucleation is random. The first condition also implies that the transformation rate depends only on the state variables x and T and not on the thermal history. Avrami [lo, 111 concluded, in his classic studies on kinetics of phase change, that equation (2) can be generally applied to a non-isothermal transformation if temperatures and concentrations are within the isokinetic range, in which the ratio of growth rate to the probability of formation of growth nuclei per germ nucleus per unit time becomes a constant. The definition of an isokinetic transformation was further modified by Cahn [14]. This leads to the concept of addivity [15]. Alternatively, taking into account that the temperature is a function of time in non-isothermal experiments, the transformation rate for an isokinetic reaction, 1 = dx/dt, can be obtained from equation (2) by differentiating x with respect to t, X = K”-‘t”+‘(nK+
n&)(1
where k = Km, and K, a function the Arrhenius type: s ‘f
-x)
(3)
of temperature,
has
K = K. exp( - E/RT)
0.6
E
(44
and
&KPE RT’
1
10
100
1000
Grain Size (nm) Fig.
1. The volume fractions of crystalline and intercrystalline components as a function of grain size.
where K. is a constant associated with the jump frequency of atoms, E the activation energy, R the universal gas constant, and T the absolute temperature. m is a constant which reflects the grain growth geometry. When a reaction occurs during a DSC measurement, the change in heat content and in the thermal properties of the sample is indicated by a heat flow deflection, or a peak in the plot of heat flow from the
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reference to the sample vs temperature. Kissinger [16] has shown that the temperature of maximum deflection (peak temperature) in a DSC plot is also the temperature at which the transformation rate reaches maximum. That is, the heat flow measure in DSC measurement is proportional to transformation rate, i. By inspecting equation (3) one can see that there are six parameters involved in a DSC measurement. As shown in Fig. 2, all the six parameters affect the curve shape and peak position. The peak temperature on the DSC curve can be found by setting the second order derivative of x with respect to t equal to zero, i.e. 2 = P-Q-*(1
- x)[(m - l)kt(nK+
mtk)
+ (n - l)K(nK + mt@ + Kt(mtI? + nk + rnk) - K”t”(nK + rn@
= 0 (5)
or
heating rate. We will see later that this result is so crucial that the activation energy of a transformation can be worked out by measuring the peak temperature at different heating rates. Thirdly, by substituting the value of Kp in equation (9) for the corresponding value according to equation (4a), it is found that
= - &
+ Kt(mtI?
+ mtk)
+ (n - l)K(nK
If all nucleation takes place at the beginning of the process, such as the case of annealing nanocrystalline materials, then m can be set to be equal to n. In such a process, all individual “nucleus” sites are quickly exhausted at the early stage in the process [17] due to the existence of nanometer-sized crystallites throughout the material. Then the JMA equation (2) becomes x(t) = 1 - exp[ - (Kt)“]
Kxand RT’
(6)
(7) we have (see Appendix)
(KJ’(tJ
= 1-
(8)
where T,, is the peak temperature, and K,, and t, are the values of K and t at the peak temperature T,,, respectively. There are a few interesting results we may draw from equation (8). Firstly, the value of (Kp)m(tp)n is never greater than unity since the second term on the right hand side of the equation is always positive. This results in the volume fraction transformed at the peak temperature never exceeding 63.2%. Secondly, for those cases in which the second term on the right hand side of the above equation is much less than unity, as in most solid-state reactions, one can simply write (KZ(fp)n
(12)
(5’)
Since k=
(11)
(10)
= -&+lnKo P
= 0
(10)
+ mtk)
+ nk + mk)
- K”t”(nK + mt@
+ In K. P
and the equation (m - l)kt(nK
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NICKEL ELECTRODEPOSITS
= 1
(9)
Substituting equation (9) in equation (2) leads to the approximation x(tp) z 0.632, that is, the maximum of the transformation rate takes place when the transformation is completed at about 63.2% of the volume percent of the sample and is independent of
Thus, by varying the scan rate p in a series of DSC measurements, different values of T, and To will be determined for a constant x (such as the value corresponding to the peak on the DSC plots). The result will be the existence of a linear relationship between the experimental values of ln[fl/(TP - To)] and the inverse of peak temperature on the plot of heat flow vs temperature. The slope of this straight line will give the activation energy, E/R, and the pre-exponential factor K. can be obtained from the intersection point on the ordinate. This special case has been reported by Augis and Bennett [18]. However, it is seen that (i) the JMA equation can be expressed in the form of equation (11) only if m = n, a typical example of which has been given as all nucleation centres are exhausted at the early stage in the reaction [17]; (ii) while for general isokinetic processes, equation (10) should be used; the modification we made on Kissinger [16] and Ozawa [19], and the Augis and Bennett [ 181 method for the activation energy determination have shown that, when DSC measurement is carried out under an isokinetic condition, normally a factor m/n is involved in the activation energy obtained from the slope of ln[b/( T, - To)] vs l/T plot, and a good approximation of the activation energy can be obtained only if m and n are very closely equal to each other. As stated earlier, that is when the nucleation rate decreases very quickly at the beginning of the transformation process. The condition, m = 1, set by Henderson [20] could not be applied to the transformation process in the present system. At this moment, it should be pointed out that there is one term missing in Augis and Bennett’s expression of their second derivative of u (u = Kt) 1181. Otherwise,
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I
I
700
800
(a) lmect of Em
1
NICKEL
ELECTRODEPOSITS
1.6
mi
a” 3
0.8 -
Fi % E
0.4 -
0.0
600
900
700
1.6
I
(e)
g
I
800
Temperature (K)
Temperature (K)
1.6
I
lmectof m
I
(d) Effect of n
0.8 -
ii 4 E
0.4 -
0.0
L
600
700
Temperature (K)
Temperature (K)
1.6
I
(e)
I
Effect of To
(f)mectof
2.0 1
800
1.2
!3
1
ii B .g iii E z P
0.8
I-’ 5 0.4
0.0 600
700
800
Temperature (K)
600
800
700
Temperature (K)
Fig. 2. The effect of (a) E/R, (b) Ko, (c) m, (d) n, (e) TO, and (f) /l on the transformation to equation (3).
rate according
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equation (8) should agree with Augis and Bennett’s result for the special case, m = n. After the activation energy E and the parameter ZG are determined, we can further estimate the values of m and n. On the one hand, the following relation exists according to the approximation made for equation (9):
*
In t,
m -=
In KP
n
Or
m=
-
In KP
(13)
On the other hand, the parameters, m and n, can also be linked by combining equations (9) and (3), that is,
1, = G’
(14)
By inserting equation (13) into (14) and rearranging the terms, one obtains the expression for estimating the parameter n: XPt,
?l= o’37
(15)
In t E /?t P-2 ’ - In KP RT, T,,
The analysis above has shown that all the parameters in the JMA equation (2) can be determined by DSC measurements, in which only the values of /I, T, and TO need to be measured. 3. EXPERIMENTAL
The nanocrystalline pure nickel samples used in this study were produced by the recently developed electrodeposition technique [21]. Density measurements on nickel electrodeposits have shown that the materials produced by this technique are essentially fully dense [22]. The impurities, S and C, in the samples were found to be under the EDX detectable level. The grain sizes of the samples were determined using X-ray diffraction technique combined with dark field observation in transmission electron microscope. The TEM samples were prepared with Tenupol-3 jet polisher in an electrolyte consisting of 10% perchloric acid, 15% acetic acid and 75% methanol at 40 V and a temperature of 263 K. Thermal behaviour was tested using a Du Pont 1000 Differential Scanning Calorimeter. Temperature and energy calibration of the instrument were performed using the well-known melting temperatures and enthalpies of high-purity tin, lead and indium. Disc-shaped bulk samples, weight about 20 mg and 3 mm in diameter, were sealed in aluiminium pans and scanned from room temperature up to 878 K at different heating rates of 5, 10, 20, 40, and 80 K/min. An empty aluminium pan was used as reference, and in all cases a constant 21 ml/min flow of purging gas, Ar, was maintained. Each sample, after cooling to room temperature, was run by the same heating procedure accordingly, to obtain the baselines. The
NICKEL
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ELECTRODEPOSITS
microstructural characterization was performed using transmission electron microscopy (Hitachi H-800, operating at 200 keV). 4. RESULTS
4.1. Microstructural
AND DISCUSSION
development
upon heating
Figure 3 shows a typical DSC trace upon heating the nanocrystalline nickel deposits used in this study. The heating rate in this particular case is 40 K/min. The exothermal and irreversible structural changing process is indicated by the appearance of the heat release peak at about 606 K on the first heating trace (a) and disappearance of the same peak on the second heating trace (b) at the same temperature. The endothermal peaks at 627 K appeared on both curves and corresponded to the reversible magnetic phase transformation of nickel and the peak temperature is the so-called Curie temperature. Subtracting the second heating curve from the first one gives the third trace (c) in Fig. 3, which reflects the net thermal effect of the irreversible structural changing process within the operating temperature range. According to this observation, the microstructural development of the samples during DSC measurements was further investigated by quenching the samples from different temperatures. As shown in Fig. 4, the average grain size of the as-plated nanocrystalline nickel deposits is about 20 nm. Upon heating at 40 K/min, the nickel deposits appear to be stable in their grain size when the temperature is below 533 K. No significant grain growth was observed. Continuous heating above this temperature at the same heating rate (40 Kjmin) up to 658 K results in grain growth. Figure 5(a)-(h) presents the microstructural evolution at the given temperatures. The coincidence of the significant grain growth temperature range observed under transmission electron microscope with the one covered by
0.4
300
I
I
I
400
500
600
’
1
700
800
Temperature (K) Fig. 3. The typical DSC traces of nanocrystalline nickel electrodeposits upon heating at 40 K/mix (a) the first heating trace; (b) the second heating trace; and (c) = (a) - (b), the net irreversible heat flow.
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the exothermal peak on the DSC trace shown in Fig . 3 indicates that the grain growth occurring in nan locrystalline materials releases a significant amcaunt of heat. In Figs 5(a) and (b), it is seen that,
NICKEL ELECTRODEPOSITS when the sample was heated up to 533 K, gr.ain growth had taken place in the nanocrystal mat rix, indicated by few individual large grains less tlhan 0.5 pm in size, which is significantly greater than the
Fig. 4(a-b) (caption opposite)
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NICKEL ELECTRODEPOSITS
Fig 4(c) Fig. 4. TEM micrographs of nanocrystalline nickel electrodeposits (as-deposited) (a) bright field; (b) dark field; (c) diffraction pattern.
matrix grain size. A detailed inspection under transmission electron microscope, as shown in Fig. 6, reveals that many Moire fringes are present in the microstructure of the nanocrystalline nickel samples produced by the electrodeposition technique, which suggests that those nano-grains showing Moire fringes are only slightly misoriented to each other and could be the potential “nucleation sites” during the process of DSC measurements since these crystals can easily rearrange their orientation and merge into a significantly larger grain. Although the appearance of bigger grains in the nanocrystalline matrix should not be understood as nucleation in the classical transformation theories, the statement we made in Section 2 and the TEM observation both suggest that, phenomenologically, one can still use the classical transformation theories to treat the grain growth process in nanocrystalline materials by analogy. The most extensive grain growth was observed when the sample temperature reached 593 - 613 K (Figs 5(e)-(f)). Up to 628 K after the sample was heated at the constant heating rate, the grain size was increased to a mean value of 1.25 pm (shown in Fig. 5(g)). Further increasing of temperature results in normal grain growth (Fig. 5(h)). Abnormal grain growth has also been observed in many other nanocrystalline systems, such as Al-Mn and AllMn-Si [S]; Al and Ag [23]; Ni-P [6]; Cu, Ag and Pd [24]; Ni-Si [25]. However, the mechanism of
abnormal growth in nanocrystalline materials is not fully understood. The thermodynamic term, excess free energy due to the existence of large amounts of intercrystalline components, can explain the spontaneous process of grain growth and the significant heat release, which is determined by the initial and final states of the system. But it seems to be difficult to explain why the grain growth occurs in such a manner. More dedicated work is needed to reveal the mechanism. In the case of nanocrystalline nickel deposits, the nanocrystalline “clusters” with small misorientations, indicated by the Moire patterns in the TEM micrograph (Fig. 6) could be the origin of the observed abnormal grain growth because the nanometer sized crystals within the clusters only need to rotate slightly to join the others, i.e., by the mechanism of subgrain coalescence. However, for those nanocrystalline materials produced by other techniques, this mechanism may not apply. The abnormal grain growth may be also associated with other properties observed with nanocrystalline materials, such as grain boundary structures and selective solute segregation to different boundaries [l,
261.
4.2. Grain growth activation
energy
The activation energy of a thermally activated transformation is a very important parameter which reflects the nature of the transformation.
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Traditionally, the energy is obtained by measuring the peak temperature at different constant heating rates and working out the slope of a plot of either log(BIT&
log(P),
or log[Bl(T,
-
TONagainst l/T,.
Fig. 5(aPb).
(caption
NICKEL
ELECTRODEPOSITS
The principles behind these plots were developer 4 by Kissinger [ 161, Ozawa [ 191, and Augis and Ben lnett [18], respectively. Graydon et al. [27] analyzed the activation energies obtained from non-isothet -mal
on page
1665)
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trar tsformations of amorphous metals and found that energies calculated by the Kissinger the activation and Ozawa methods are virtually identical. The small diffi erences in activation energies arise from different
Fig 5(c4)
NICKEL
ELECTRODEPOSITS
1663
mathematical approximations used in developing the two methods. As discussed in Section 2 earl lier, Kissinger and Ozawa plots require the transforr ned volume fraction to be a constant at peak tempera1 .ure
(caption on page 1665)
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for dilfferent heating rates. According to the theory de\ relc)ped in this study, a series of DSC measurein me nts ; at different heating rates were performed the activation energy for grain ord ler to determine
NICKEL
ELECTRODEPOSITS
All the growth in nanocrystalline nickel deposits. The DSC traces obtained are represented in Fig. peak temperatures for different heating rates at-e li in Table 1. After fitting the data to equatic 3n
Fig. 5(e-f). (caption opposite)
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NICKEL
ELECTRODEPOSITS
Fig. 5(g-h) Fig. 5. The microstructural evolution of nanocrystalline nickel electrodeposits upon heating at 40 K/min. (a) bright field (BF), 553 K; (b) dark field corresponding to (a), 553 K; (c) BF, 573 K; (d) BF, 583 K; (e) BF, 593 K; (f) BF, 613 K; (g) BF, 628 K; and (h) BF, 658 K.
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NICKEL ELECTRODEPOSITS
Fig. 6. TEM micrograph of nanocrystalline nickel electrodeposits (as-deposited), showing Moirt fringes which indicate the grains are slightly misoriented to each other.
using the least square method, it is found that the activation energy for grain growth of nanocrystalline nickel deposits is 131.5 kJ/mol. Figure 8 illustrates the plot as a result of the fitting process. The
activation energy obtained in this study is close to the activation energy of grain boundary self-diffusion [28] but on the lower value side, which indicates that grain growth in the nanocrystalline nickel deposits is similar to a grain boundary diffusion controlled process and that other diffusion short-cuts, in addition to grain boundaries, exist in nanocrystalline materials. This observation also further confirms the single-process theory of grain boundary migration [29, 301. For comparison, these data are also represented in Fig. 9 using Kissinger and Ozawa methods. It is seen that the activation energies derived from the different plots using the same data are found to be very close to each other and the relative differences are within 5%. However, the near equality of the activation energy values does not necessarily mean that all the
Table 1. Exothermal peak temperature (L’-,) and total exothermal enthalpy (AH’o’~‘) at different heating rates (8) for an as-plated nanocrystalline nickel deposit (20 nm)
400
500
600
700
800
Temperature (K)
Fig. 7. A series of DSC traces of nanocrystalline electrodeposits at different heating rates.
nickel
p (Kimin.) TP (K) AH’“‘“’(J/mol) AH’“‘“’(Jjmol) AH’“‘“’is the average
5 563.2 415.4
IO 578 412.8
value of AHto"'.
20 40 587 606 411.6 421.6 415.1 * 3.5
80 619.0 417.3
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NICKEL
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ELECTRODEPOSITS
shown that, if the grain polyhedral and the grain the intercrystalline volume in terms of grain size [4],
shape is assumed to be boundary thickness 1 nm, fraction can be expressed i.e.
&=l-
l-‘,j (
(17) >
where d (in nm) is the inscribed sphere diameter of the regular polyhedron. Thus, the change in the intercrystalline volume fraction after the grain size changes from L&before grain growth to d, after grain growth,
AL=(l-;)i-(l-;)r 1.60
1.65
1.70
1.75
(18)
1.80
1000/T, (K-1)
Fig. 8. The activation energy plot for the grain growth of nanocrystalline nickel electrodeposits according to equation (12).
. / I I /lM2(i.6kJhjol ia,’ ~i / I
___A----_
methods are the same in nature. On the contrary, some of them are quite different in terms of the basis of their physical fundamentals. The most obvious difference is that the Kissinger and Ozawa methods start from the chemical reaction rate equation; while the Augis and Bennett method and the present analysis assume the JMA equation (2) which generally describes the kinetics of solid state transformations. The difference in these models can be further appreciated by simply differentiating the JMA equation with respect to time under the isothermal condition. One can get the transformation rate from equation (2) 1=
nkt”_‘(l
Pk y& /
1
-4.0
/
_Lj_
-__+___f:
I____; 1 L____‘_____L_______I_____I_____L___
$ -4.5
t
---~--__l----+----~-~~---i_---_j
III,/,
I,:;:, 24 1
1
____I________i____- ----+----
1.60
I
1.65
1
1.70
b---
1____
1.75
1.80
1.75
1.80
1OOOrr,(K-’)
-x);
while the chemical reaction rate that Kissinger Ozawa used in their models is expressed as
I
:____-:---_:____:----+----
(a)
and 2.0
P = k’(1 - x) where n is the order of the chemical reaction, and k’ is an Arrhenius type parameter as equation 4(a). The coincidence of activation energies from the two physical models has been further discussed by Augis and Bennett [ 181.
Eb
1.2
if
4.3. Excess enthalpy In order to estimate the intercrystalline enthalpy, we assume that (i) the irreversible process is caused by grain growth only, (ii) the intercrystalline enthalpy is independent of grain size, and (iii) the integrated area under the peak on a DSC curve, i.e. the total intercrystalline enthalpy, Afl:“‘, is proportional to the intercrystalline volume fraction. Then AT:“’ = AAc.AH,,
1.6
(16)
where Aft is the change in intercrystalline volume fraction before and after grain growth and AH,, is the mean (specific) intercrystalline enthalpy. It has been
0.8
0.4 1.60
1.65
1.70 1000/T, (K’) (b)
Fig. 9. (a) Kissinger plot for nanocrystalline electrodeposits; (b) Ozawa plot for nanocrystalline electrodeposits.
nickel nickel
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10
NANOCRYSTALLINE
------
1
10
100
1000
10000
Grain She (nm) Fig. 10. The intercrystalline volume fraction changes as a result of grain growth. do is the grain size before grain growth.
By substituting equation equation (16) as
(18) in (16), one can write
For a given initial grain size, d, the intercrystalline volume fraction change due to grain growth is illustrated in Fig. 10. It can be seen that AJc decreases as the initial grain size increases and levels off when grain size becomes larger than 1000 nm. This result suggests that Afl:“‘, as the heat release in DSC measurements, can only be measurable when the grain size before grain growth is within the nanometer range. In the present work, the total enthalpy of the irreversible process is calculated by integrating the area under the exothermal peaks after the background subtraction and dividing the area by the corresponding heating rates. The results are listed in Table 1. The mean value of the total enthalpy was found to be 415.7 J/mol. By applying equation (16’) and inserting the grain size values before and after grain growth (L&= 20 nm and d, = 1250 nm), one can calculate the estimated intercrystalline enthalpy, AH,, = 2943 J/mol.
NICKEL ELECTRODEPOSITS process. By varying the heating rates and measuring the exothermal peak temperatures, a plot of ln(/?/(rp - TO)) us l/T,, has yielded the activation energy to be 13 1.5 kJ/mol. This value is very close to those obtained from Kissinger and Ozawa techniques; however, the physical difference between these techniques has been addressed. ??In addition to the activation energy, all the other parameters in the JMA equation (2) can be estimated by DSC measurements at constant heating rates. ??The activation energy obtained from this study falls in the range covered by the literature values of activation energy for grain boundary diffusion, but on the lower limit side, which indicates that the grain growth of nanocrystalline nickel deposits bears some similarities to grain boundary diffusion controlled processes and diffusion short circuits exist in nanocrystalline materials. This observation also further confirms the single-process theory of grain boundary migration. ??Nanocrystalline nickel deposits used in this study are stable in their grain size when the temperature is below 553 K. However, continuous heating to higher temperatures results in abnormal grain growth. The reason for abnormal grain growth has been attributed to subgrain coalescence of the slightly misoriented nanocrystal clusters in the as-deposited materials. ??The abnormal grain growth is found to be coincident with the exothermal peaks on DSC traces. The excess enthalpy released from this process is 415.7 f 3.5 J/mol. If all the enthalpy is attributed to the heat release due to the change in the intercrystalline volume fraction, the mean specific intercrystalline enthalpy is estimated to be AH,, = 2943 J/mol. Acknowledgements-The authors wish to express their gratitude to Dr J. W. Graydon for his assistance with the DSC measurements and valuable discussion. Comments from Profs G. C. Weatherly and D. D. Perovic are highly appreciated. Thanks are also due to Dr A. M. Sherik for his assistance with material production. Financial support provided by Natural Science and Engineering Research Council of Canada is gratefully acknowledged. N.W. has been supported by an Ontario Graduate Scholarship and a University of Toronto Open Scholarship. REFERENCES
5. CONCLUSIONS According to the present work, including the theoretical treatment of the JMA equation, the DSC measurements and TEM studies on nanocrystalline nickel produced by the electrodeposition technique, the following conclusions can be drawn: ??Nanocrystalline materials provide us with a great opportunity to study grain boundary properties. Based on the JMA equation, a technique, which is derived from an isokinetic analysis, has been developed to determine the activation energy of this
1. H. Gleiter,
Progress
in Materials
Science
33, 223
(1989). 2. R. Birringer, Muter.
Sci. Eng. A117, 33 (1989). 3. V. G. Gryaznov and L. I. Trusov, Progress in Materials
Science 37, 289 (1993). 4. Ning Wang, G. Palumbo, Zhirui Wang, U. Erb and K. T. Aust, Scripta Metall. et Mater. 28, 253 (1993). 5. L. C. Chen, F. Spaepen, J. L. Robertson, S. C. Moss and K. Hiraga, J. Mater. Res. 5, 1871 (1990). 6. K. Lu, W. D. Wei, and J. T. Wang, J. Appl. Phys. 69, 7345 (1991). 7. R. S. Averback, H. J. Hiifler, H. Hahn and J. C. Logas, Nanostructured Materials 1, 173 (1992).
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et al.:
NANOCRYSTALLINE
NICKEL
ELECTRODEPOSITS
8. U. Klement, 9. 10. 11. 12.
13. 14. 15.
16. 17.
18. 19. 20. 21. 22.
23. 24. 25. 26. 27. 28.
29. 30.
U. Erb, A. M. El-Sherik, K. T. Aust, (to be published). W. A. Johnson and R. F. Mehl, Truns. AIME, Iron & Steel DiGsion 135, 416 (1939). M. Avrami, J. C/rem. Phys. 7, 1103 (1939). M. Avrami, J. Chem. Phys. 8, 212 (1940). J. W. Christian, The Theory qf Transformation in Metals und Alloys, 2nd ed., p. 543. Pergamon Press, Hungary (1975). J. W. Graydon, S. J. Thorpe and D. W. Kirk, J. Non-Crystalline Solids 175, 31 (1994). J. W. Cahn, Acta Metall. 4, 572 (1956). J. W. Christian, The Theory of Transformation in Metals and Alloys. 2nd ed. Pergamon Press, Hungary (1975). H. E. Kissinger, Anal. Chem. 29, 1702 (1957). J. W. Christian, The Theory of Tramformation in Metals and Alloys, 2nd ed., p. 19. Pergamon Press, Hungary (1975). J. A. Augis, and J. E. Bennett, J. Thermal Anal. 13,283 (1978). T. Ozawa, J. Thermal Anal. 2, 301 (1970). D. W. Henderson, J. Non-Cryst. Solids 30, 301 (1979). A. M. El-Sherik and U. Erb, J. Muter. Sci. (to be published). T. R. Haasz, K. T. Aust, G. Palumbo, A. M. El-Sherik and U. Erb, Scripta Metall. et Mater. 32, 423 (1995). A. M. Chaplanov, Phys. Met. Metall. 70(2), 124 (1990). B. Gunther, A. Kumpmann and H.-D. Kunze, Scripta Metall. et Mater. 27, 833 (1992). P. Knauth, A. Charai’ and P. Gas, Scripta Metall et Mater. 28, 325 (1993). K. T. Aust, Can. Metall. Quar. 33, 265 (1994). J. W. Graydon, S. J. Thorpe and D. W. Kirk, Acta Metall. Mater. 42, 3163 (1994). I. Kaur and W. Gust, Handbook qf Grain and Interphase Press, Stuttgart Boundary D@sion Data. Ziegler ( 1989). K. T. Aust and J. W. Rutter, Trans. Metall. Sot. AIME 215, 820 (1959). D. G. Cole, P. Feltham and E. Gilliam, Proc. PhJx. Sot. B67, 131 (1954).
1669
APPENDIX By substituting have
equations
(6) and (7) in equation
(5’) we
(m-l)$(n+m+?j+(n-l)(n+m$?)
+mu
(A.11 where u = E/RT.
Expand
(A.1)
(A.2) Rearrange the terms in (A.2) so that only the term Pt” is left on the left side of the equation and put back the original expression for u
K”‘y =
1_
This is equation
L4.3)
(5’).
Actu maler. Vol. 45, No. 4, pp. 1655-1669, 1997 IC 1997 Acta Metallurgica Inc. Published by Elsevier Science Ltd Printed in Great Bntain. All rights reserved
1359-6454197 $17.00+ 0.00
ISOKINETIC ANALYSIS OF NANOCRYSTALLINE ELECTRODEPOSITS UPON ANNEALING NING WANG’?, ‘Department ‘Department
NICKEL
ZHIRUI WANG’S, K. T. AUST’ and U. ERB’
of Metallurgy and Materials Science, University of Toronto, Toronto, M5S 3E4 and of Materials and Metallurgical Engineering. Queen’s University, Kingston, K7L 3N6, Ontario, Canada (Received
31 May 1995; accepted
4 June
1996)
Abstract-The grain growth kinetics of nanocrystalline nickel electrodeposits was studied by transmission electron microscopy and differential scanning calorimetry at different heating rates. It was found that, upon annealing, the nanocrystals in the nickel electrodeposits appeared to grow abnormally and released about 415.7 k 3.5 Jjmol of heat. The mechanism of the abnormal grain growth was attributed to the subgrain coalescence. The method for determination of the grain growth activation energy as well as all the other kinetic parameters in the Johnson-MehlPAvrami equation was proposed based on an isokinetic analysis. This method is applicable to general types of transformation process governed by a single activation energy under the isokinetic condition. The activation energy for the grain growth of nanocrystalline nickel electrodeposits was found to be about 131.5 kJ/mol using this method. The difference between the present method and the Kissinger and Ozawa method was addressed in terms of their physical backgrounds. % 1997 Acta Metallurgica Inc.
1. INTRODUCTION
Nanocrystalline materials, due to the unique properties which make them distinct from their counterparts, conventional polycrystalline materials, have attracted a great deal of attention from material scientists in recent years. The development of this research field in the last few years has been comprehensively reviewed by a number of researchers [l&3]. From a thermodynamic point of view, a polycrystalline material is in a metastable state because of the excess free energy associated with the intercrystalline components. For polycrystalline single-phase material, the excess free energy arises mainly from the grain boundaries, triple lines and quadruple nodes. The overall contribution of these intercrystalline components to the total free energy of the system becomes more and more significant when the grain size of the material becomes smaller and smaller and especially when it falls into the nanometer range. The excess free energy of the system due to the presence of intercrystalline components is proportional to the volume fraction of these components within the materials. In the previous work [4], a polycrystalline material has been viewed as a composite material which consists of crystalline components and intercrystalline components (grain boundaries, triple lines and quadruple nodes), and the variation of each component with grain size was analyzed by assuming the grain shape to be tetrakaidecahedral with grain tPresent address: Chalk River Laboratories, ON Canada KOJ IJO. ICorresponding author.
Chalk River,
boundary thickness 1 nm. As seen in Fig. 1, when the grain size decreases from 1 pm, as often observed in conventional polycrystalline materials, to 10 nm, the summation of volume fraction of intercrystalline components increases from a value of about 0.3% to a significant value of 27.1% in which 24.3% is grain boundaries, 2.7% triple lines, and 0.1% quadruple nodes. And if the grain size is further reduced to 5 nm, then approximately half of the material is composed of intercrystalline components. The presence of large amounts of intercrystalline components in nanometer-grained polycrystalline materials provides us with a great opportunity to study the properties of these intercrystalline components since such materials have a strong tendency to transform into conventional polycrystals with coarser grain sizes and less intercrystalline volume fraction. The crystallization kinetics of nanocrystalline materials has been the subject of intense study in the last few years, due to this fact. A number of studies on the thermal stability of nanocrystalline materials have shown that the materials, upon heating, will exhibit a quasi nucleation-growth process [5-81. A quasi nucleationgrowth process is, in a sense, that in which, when nanocrystalline materials are brought to an elevated temperature, the nanometer-sized crystallites in the materials always start to grow in a random, non-uniform manner and some of the nanocrystallites appear to act as “nuclei” and preferentially start to grow at the expense of the surrounding nanocrystalline matrix. With increasing time, the grains become larger; meanwhile, new “nuclei” appear to form and grow in the same way.
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The process described above allows us to model the process with the existing kinetic theories of phase transformations. In this study, we will show that nanocrystalline materials can also provide us with the possibility to study (i) isokinetics of the transformation and (ii) the intercrystalline enthalpy using differential scanning calorimetry (DSC) measurement. As for (ii), nanocrystalline materials produced by electrodeposition possess the unique advantage over other production techniques for this type of measurement due to its pore-free and reduced lattice distortion characteristics. 2. THEORETICAL
CONSIDERATION
Non-isothermal DSC measurement has been commonly used to study the nature of structural change processes in amorphous and nanocrystalline materials due to the significant thermal effect upon heating these materials up to elevated temperatures. During a non-isothermal DSC experiment, the temperature of the furnace is changed linearly with time t at a given rate p (degree per minute). The furnace temperature in Kelvin is T=
T”+pt
(1)
where To is the initial temperature. Assuming that the dynamic case is a close succession of isothermal ones, then the well-known Johnson-Mehl-Avrami (JMA) equation [9-l l] for the fraction of transformed material can be used to describe the non-isothermal continuous heating process, as in DSC measurement with a constant heating rate, i.e. x(t) = 1 - exp(-kt”). where x completed
is the fraction of the at time t, k is a constant
(2) transformation associated with
NICKEL
ELECTRODEPOSITS
nucleation rate and growth rate, both being dependent on temperature, and n is a constant which reflects the nucleation and growth morphology. It is noteworthy that many people have used the analogy of a chemical reaction rate equation and interpreted the factors, k and n, in equation (2) in the same way as chemical reaction rate constants [ 121. This is rather misleading as we will see later that the factors, k and n, in the JMA equation should not be generally understood as chemical reaction rate constants. The difficulties in treating non-isothermal reactions are mainly due to the independent variations of growth and nucleation rate with temperature. Therefore, the JMA equation is in general not a valid description of transformation kinetics occurring under non-isothermal conditions. However, a nonisothermal transformation consisting of nucleation and growth can still be described by the JMA equation if it meets the following conditions [13]: (a) all nucleation occurs during the early stage in the process leading to the so-called site saturation and, for the rest of the time, only growth is significant, (b) the growth rate depends only on instantaneous temperature and is independent of time, (c) nucleation is random. The first condition also implies that the transformation rate depends only on the state variables x and T and not on the thermal history. Avrami [lo, 111 concluded, in his classic studies on kinetics of phase change, that equation (2) can be generally applied to a non-isothermal transformation if temperatures and concentrations are within the isokinetic range, in which the ratio of growth rate to the probability of formation of growth nuclei per germ nucleus per unit time becomes a constant. The definition of an isokinetic transformation was further modified by Cahn [14]. This leads to the concept of addivity [15]. Alternatively, taking into account that the temperature is a function of time in non-isothermal experiments, the transformation rate for an isokinetic reaction, 1 = dx/dt, can be obtained from equation (2) by differentiating x with respect to t, X = K”-‘t”+‘(nK+
n&)(1
where k = Km, and K, a function the Arrhenius type: s ‘f
-x)
(3)
of temperature,
has
K = K. exp( - E/RT)
0.6
E
(44
and
&KPE RT’
1
10
100
1000
Grain Size (nm) Fig.
1. The volume fractions of crystalline and intercrystalline components as a function of grain size.
where K. is a constant associated with the jump frequency of atoms, E the activation energy, R the universal gas constant, and T the absolute temperature. m is a constant which reflects the grain growth geometry. When a reaction occurs during a DSC measurement, the change in heat content and in the thermal properties of the sample is indicated by a heat flow deflection, or a peak in the plot of heat flow from the
WANG et al.:
NANOCRYSTALLINE
reference to the sample vs temperature. Kissinger [16] has shown that the temperature of maximum deflection (peak temperature) in a DSC plot is also the temperature at which the transformation rate reaches maximum. That is, the heat flow measure in DSC measurement is proportional to transformation rate, i. By inspecting equation (3) one can see that there are six parameters involved in a DSC measurement. As shown in Fig. 2, all the six parameters affect the curve shape and peak position. The peak temperature on the DSC curve can be found by setting the second order derivative of x with respect to t equal to zero, i.e. 2 = P-Q-*(1
- x)[(m - l)kt(nK+
mtk)
+ (n - l)K(nK + mt@ + Kt(mtI? + nk + rnk) - K”t”(nK + rn@
= 0 (5)
or
heating rate. We will see later that this result is so crucial that the activation energy of a transformation can be worked out by measuring the peak temperature at different heating rates. Thirdly, by substituting the value of Kp in equation (9) for the corresponding value according to equation (4a), it is found that
= - &
+ Kt(mtI?
+ mtk)
+ (n - l)K(nK
If all nucleation takes place at the beginning of the process, such as the case of annealing nanocrystalline materials, then m can be set to be equal to n. In such a process, all individual “nucleus” sites are quickly exhausted at the early stage in the process [17] due to the existence of nanometer-sized crystallites throughout the material. Then the JMA equation (2) becomes x(t) = 1 - exp[ - (Kt)“]
Kxand RT’
(6)
(7) we have (see Appendix)
(KJ’(tJ
= 1-
(8)
where T,, is the peak temperature, and K,, and t, are the values of K and t at the peak temperature T,,, respectively. There are a few interesting results we may draw from equation (8). Firstly, the value of (Kp)m(tp)n is never greater than unity since the second term on the right hand side of the equation is always positive. This results in the volume fraction transformed at the peak temperature never exceeding 63.2%. Secondly, for those cases in which the second term on the right hand side of the above equation is much less than unity, as in most solid-state reactions, one can simply write (KZ(fp)n
(12)
(5’)
Since k=
(11)
(10)
= -&+lnKo P
= 0
(10)
+ mtk)
+ nk + mk)
- K”t”(nK + mt@
+ In K. P
and the equation (m - l)kt(nK
1657
NICKEL ELECTRODEPOSITS
= 1
(9)
Substituting equation (9) in equation (2) leads to the approximation x(tp) z 0.632, that is, the maximum of the transformation rate takes place when the transformation is completed at about 63.2% of the volume percent of the sample and is independent of
Thus, by varying the scan rate p in a series of DSC measurements, different values of T, and To will be determined for a constant x (such as the value corresponding to the peak on the DSC plots). The result will be the existence of a linear relationship between the experimental values of ln[fl/(TP - To)] and the inverse of peak temperature on the plot of heat flow vs temperature. The slope of this straight line will give the activation energy, E/R, and the pre-exponential factor K. can be obtained from the intersection point on the ordinate. This special case has been reported by Augis and Bennett [18]. However, it is seen that (i) the JMA equation can be expressed in the form of equation (11) only if m = n, a typical example of which has been given as all nucleation centres are exhausted at the early stage in the reaction [17]; (ii) while for general isokinetic processes, equation (10) should be used; the modification we made on Kissinger [16] and Ozawa [19], and the Augis and Bennett [ 181 method for the activation energy determination have shown that, when DSC measurement is carried out under an isokinetic condition, normally a factor m/n is involved in the activation energy obtained from the slope of ln[b/( T, - To)] vs l/T plot, and a good approximation of the activation energy can be obtained only if m and n are very closely equal to each other. As stated earlier, that is when the nucleation rate decreases very quickly at the beginning of the transformation process. The condition, m = 1, set by Henderson [20] could not be applied to the transformation process in the present system. At this moment, it should be pointed out that there is one term missing in Augis and Bennett’s expression of their second derivative of u (u = Kt) 1181. Otherwise,
1658
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et al.:
NANOCRYSTALLINE
I
I
700
800
(a) lmect of Em
1
NICKEL
ELECTRODEPOSITS
1.6
mi
a” 3
0.8 -
Fi % E
0.4 -
0.0
600
900
700
1.6
I
(e)
g
I
800
Temperature (K)
Temperature (K)
1.6
I
lmectof m
I
(d) Effect of n
0.8 -
ii 4 E
0.4 -
0.0
L
600
700
Temperature (K)
Temperature (K)
1.6
I
(e)
I
Effect of To
(f)mectof
2.0 1
800
1.2
!3
1
ii B .g iii E z P
0.8
I-’ 5 0.4
0.0 600
700
800
Temperature (K)
600
800
700
Temperature (K)
Fig. 2. The effect of (a) E/R, (b) Ko, (c) m, (d) n, (e) TO, and (f) /l on the transformation to equation (3).
rate according
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et al.:
NANOCRYSTALLINE
equation (8) should agree with Augis and Bennett’s result for the special case, m = n. After the activation energy E and the parameter ZG are determined, we can further estimate the values of m and n. On the one hand, the following relation exists according to the approximation made for equation (9):
*
In t,
m -=
In KP
n
Or
m=
-
In KP
(13)
On the other hand, the parameters, m and n, can also be linked by combining equations (9) and (3), that is,
1, = G’
(14)
By inserting equation (13) into (14) and rearranging the terms, one obtains the expression for estimating the parameter n: XPt,
?l= o’37
(15)
In t E /?t P-2 ’ - In KP RT, T,,
The analysis above has shown that all the parameters in the JMA equation (2) can be determined by DSC measurements, in which only the values of /I, T, and TO need to be measured. 3. EXPERIMENTAL
The nanocrystalline pure nickel samples used in this study were produced by the recently developed electrodeposition technique [21]. Density measurements on nickel electrodeposits have shown that the materials produced by this technique are essentially fully dense [22]. The impurities, S and C, in the samples were found to be under the EDX detectable level. The grain sizes of the samples were determined using X-ray diffraction technique combined with dark field observation in transmission electron microscope. The TEM samples were prepared with Tenupol-3 jet polisher in an electrolyte consisting of 10% perchloric acid, 15% acetic acid and 75% methanol at 40 V and a temperature of 263 K. Thermal behaviour was tested using a Du Pont 1000 Differential Scanning Calorimeter. Temperature and energy calibration of the instrument were performed using the well-known melting temperatures and enthalpies of high-purity tin, lead and indium. Disc-shaped bulk samples, weight about 20 mg and 3 mm in diameter, were sealed in aluiminium pans and scanned from room temperature up to 878 K at different heating rates of 5, 10, 20, 40, and 80 K/min. An empty aluminium pan was used as reference, and in all cases a constant 21 ml/min flow of purging gas, Ar, was maintained. Each sample, after cooling to room temperature, was run by the same heating procedure accordingly, to obtain the baselines. The
NICKEL
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ELECTRODEPOSITS
microstructural characterization was performed using transmission electron microscopy (Hitachi H-800, operating at 200 keV). 4. RESULTS
4.1. Microstructural
AND DISCUSSION
development
upon heating
Figure 3 shows a typical DSC trace upon heating the nanocrystalline nickel deposits used in this study. The heating rate in this particular case is 40 K/min. The exothermal and irreversible structural changing process is indicated by the appearance of the heat release peak at about 606 K on the first heating trace (a) and disappearance of the same peak on the second heating trace (b) at the same temperature. The endothermal peaks at 627 K appeared on both curves and corresponded to the reversible magnetic phase transformation of nickel and the peak temperature is the so-called Curie temperature. Subtracting the second heating curve from the first one gives the third trace (c) in Fig. 3, which reflects the net thermal effect of the irreversible structural changing process within the operating temperature range. According to this observation, the microstructural development of the samples during DSC measurements was further investigated by quenching the samples from different temperatures. As shown in Fig. 4, the average grain size of the as-plated nanocrystalline nickel deposits is about 20 nm. Upon heating at 40 K/min, the nickel deposits appear to be stable in their grain size when the temperature is below 533 K. No significant grain growth was observed. Continuous heating above this temperature at the same heating rate (40 Kjmin) up to 658 K results in grain growth. Figure 5(a)-(h) presents the microstructural evolution at the given temperatures. The coincidence of the significant grain growth temperature range observed under transmission electron microscope with the one covered by
0.4
300
I
I
I
400
500
600
’
1
700
800
Temperature (K) Fig. 3. The typical DSC traces of nanocrystalline nickel electrodeposits upon heating at 40 K/mix (a) the first heating trace; (b) the second heating trace; and (c) = (a) - (b), the net irreversible heat flow.
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WANG et al.:
NANOCRYSTALLINE
the exothermal peak on the DSC trace shown in Fig . 3 indicates that the grain growth occurring in nan locrystalline materials releases a significant amcaunt of heat. In Figs 5(a) and (b), it is seen that,
NICKEL ELECTRODEPOSITS when the sample was heated up to 533 K, gr.ain growth had taken place in the nanocrystal mat rix, indicated by few individual large grains less tlhan 0.5 pm in size, which is significantly greater than the
Fig. 4(a-b) (caption opposite)
WANG et al.:
NANOCRYSTALLINE
NICKEL ELECTRODEPOSITS
Fig 4(c) Fig. 4. TEM micrographs of nanocrystalline nickel electrodeposits (as-deposited) (a) bright field; (b) dark field; (c) diffraction pattern.
matrix grain size. A detailed inspection under transmission electron microscope, as shown in Fig. 6, reveals that many Moire fringes are present in the microstructure of the nanocrystalline nickel samples produced by the electrodeposition technique, which suggests that those nano-grains showing Moire fringes are only slightly misoriented to each other and could be the potential “nucleation sites” during the process of DSC measurements since these crystals can easily rearrange their orientation and merge into a significantly larger grain. Although the appearance of bigger grains in the nanocrystalline matrix should not be understood as nucleation in the classical transformation theories, the statement we made in Section 2 and the TEM observation both suggest that, phenomenologically, one can still use the classical transformation theories to treat the grain growth process in nanocrystalline materials by analogy. The most extensive grain growth was observed when the sample temperature reached 593 - 613 K (Figs 5(e)-(f)). Up to 628 K after the sample was heated at the constant heating rate, the grain size was increased to a mean value of 1.25 pm (shown in Fig. 5(g)). Further increasing of temperature results in normal grain growth (Fig. 5(h)). Abnormal grain growth has also been observed in many other nanocrystalline systems, such as Al-Mn and AllMn-Si [S]; Al and Ag [23]; Ni-P [6]; Cu, Ag and Pd [24]; Ni-Si [25]. However, the mechanism of
abnormal growth in nanocrystalline materials is not fully understood. The thermodynamic term, excess free energy due to the existence of large amounts of intercrystalline components, can explain the spontaneous process of grain growth and the significant heat release, which is determined by the initial and final states of the system. But it seems to be difficult to explain why the grain growth occurs in such a manner. More dedicated work is needed to reveal the mechanism. In the case of nanocrystalline nickel deposits, the nanocrystalline “clusters” with small misorientations, indicated by the Moire patterns in the TEM micrograph (Fig. 6) could be the origin of the observed abnormal grain growth because the nanometer sized crystals within the clusters only need to rotate slightly to join the others, i.e., by the mechanism of subgrain coalescence. However, for those nanocrystalline materials produced by other techniques, this mechanism may not apply. The abnormal grain growth may be also associated with other properties observed with nanocrystalline materials, such as grain boundary structures and selective solute segregation to different boundaries [l,
261.
4.2. Grain growth activation
energy
The activation energy of a thermally activated transformation is a very important parameter which reflects the nature of the transformation.
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Traditionally, the energy is obtained by measuring the peak temperature at different constant heating rates and working out the slope of a plot of either log(BIT&
log(P),
or log[Bl(T,
-
TONagainst l/T,.
Fig. 5(aPb).
(caption
NICKEL
ELECTRODEPOSITS
The principles behind these plots were developer 4 by Kissinger [ 161, Ozawa [ 191, and Augis and Ben lnett [18], respectively. Graydon et al. [27] analyzed the activation energies obtained from non-isothet -mal
on page
1665)
WANG
et al.:
NANOCRYSTALLINE
trar tsformations of amorphous metals and found that energies calculated by the Kissinger the activation and Ozawa methods are virtually identical. The small diffi erences in activation energies arise from different
Fig 5(c4)
NICKEL
ELECTRODEPOSITS
1663
mathematical approximations used in developing the two methods. As discussed in Section 2 earl lier, Kissinger and Ozawa plots require the transforr ned volume fraction to be a constant at peak tempera1 .ure
(caption on page 1665)
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WANG
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NANOCRYSTALLINE
for dilfferent heating rates. According to the theory de\ relc)ped in this study, a series of DSC measurein me nts ; at different heating rates were performed the activation energy for grain ord ler to determine
NICKEL
ELECTRODEPOSITS
All the growth in nanocrystalline nickel deposits. The DSC traces obtained are represented in Fig. peak temperatures for different heating rates at-e li in Table 1. After fitting the data to equatic 3n
Fig. 5(e-f). (caption opposite)
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er al.:
NANOCRYSTALLINE
NICKEL
ELECTRODEPOSITS
Fig. 5(g-h) Fig. 5. The microstructural evolution of nanocrystalline nickel electrodeposits upon heating at 40 K/min. (a) bright field (BF), 553 K; (b) dark field corresponding to (a), 553 K; (c) BF, 573 K; (d) BF, 583 K; (e) BF, 593 K; (f) BF, 613 K; (g) BF, 628 K; and (h) BF, 658 K.
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WANG et al.:
NANOCRYSTALLINE
NICKEL ELECTRODEPOSITS
Fig. 6. TEM micrograph of nanocrystalline nickel electrodeposits (as-deposited), showing Moirt fringes which indicate the grains are slightly misoriented to each other.
using the least square method, it is found that the activation energy for grain growth of nanocrystalline nickel deposits is 131.5 kJ/mol. Figure 8 illustrates the plot as a result of the fitting process. The
activation energy obtained in this study is close to the activation energy of grain boundary self-diffusion [28] but on the lower value side, which indicates that grain growth in the nanocrystalline nickel deposits is similar to a grain boundary diffusion controlled process and that other diffusion short-cuts, in addition to grain boundaries, exist in nanocrystalline materials. This observation also further confirms the single-process theory of grain boundary migration [29, 301. For comparison, these data are also represented in Fig. 9 using Kissinger and Ozawa methods. It is seen that the activation energies derived from the different plots using the same data are found to be very close to each other and the relative differences are within 5%. However, the near equality of the activation energy values does not necessarily mean that all the
Table 1. Exothermal peak temperature (L’-,) and total exothermal enthalpy (AH’o’~‘) at different heating rates (8) for an as-plated nanocrystalline nickel deposit (20 nm)
400
500
600
700
800
Temperature (K)
Fig. 7. A series of DSC traces of nanocrystalline electrodeposits at different heating rates.
nickel
p (Kimin.) TP (K) AH’“‘“’(J/mol) AH’“‘“’(Jjmol) AH’“‘“’is the average
5 563.2 415.4
IO 578 412.8
value of AHto"'.
20 40 587 606 411.6 421.6 415.1 * 3.5
80 619.0 417.3
WANG
et al.:
NANOCRYSTALLINE
NICKEL
1661
ELECTRODEPOSITS
shown that, if the grain polyhedral and the grain the intercrystalline volume in terms of grain size [4],
shape is assumed to be boundary thickness 1 nm, fraction can be expressed i.e.
&=l-
l-‘,j (
(17) >
where d (in nm) is the inscribed sphere diameter of the regular polyhedron. Thus, the change in the intercrystalline volume fraction after the grain size changes from L&before grain growth to d, after grain growth,
AL=(l-;)i-(l-;)r 1.60
1.65
1.70
1.75
(18)
1.80
1000/T, (K-1)
Fig. 8. The activation energy plot for the grain growth of nanocrystalline nickel electrodeposits according to equation (12).
. / I I /lM2(i.6kJhjol ia,’ ~i / I
___A----_
methods are the same in nature. On the contrary, some of them are quite different in terms of the basis of their physical fundamentals. The most obvious difference is that the Kissinger and Ozawa methods start from the chemical reaction rate equation; while the Augis and Bennett method and the present analysis assume the JMA equation (2) which generally describes the kinetics of solid state transformations. The difference in these models can be further appreciated by simply differentiating the JMA equation with respect to time under the isothermal condition. One can get the transformation rate from equation (2) 1=
nkt”_‘(l
Pk y& /
1
-4.0
/
_Lj_
-__+___f:
I____; 1 L____‘_____L_______I_____I_____L___
$ -4.5
t
---~--__l----+----~-~~---i_---_j
III,/,
I,:;:, 24 1
1
____I________i____- ----+----
1.60
I
1.65
1
1.70
b---
1____
1.75
1.80
1.75
1.80
1OOOrr,(K-’)
-x);
while the chemical reaction rate that Kissinger Ozawa used in their models is expressed as
I
:____-:---_:____:----+----
(a)
and 2.0
P = k’(1 - x) where n is the order of the chemical reaction, and k’ is an Arrhenius type parameter as equation 4(a). The coincidence of activation energies from the two physical models has been further discussed by Augis and Bennett [ 181.
Eb
1.2
if
4.3. Excess enthalpy In order to estimate the intercrystalline enthalpy, we assume that (i) the irreversible process is caused by grain growth only, (ii) the intercrystalline enthalpy is independent of grain size, and (iii) the integrated area under the peak on a DSC curve, i.e. the total intercrystalline enthalpy, Afl:“‘, is proportional to the intercrystalline volume fraction. Then AT:“’ = AAc.AH,,
1.6
(16)
where Aft is the change in intercrystalline volume fraction before and after grain growth and AH,, is the mean (specific) intercrystalline enthalpy. It has been
0.8
0.4 1.60
1.65
1.70 1000/T, (K’) (b)
Fig. 9. (a) Kissinger plot for nanocrystalline electrodeposits; (b) Ozawa plot for nanocrystalline electrodeposits.
nickel nickel
1668
WANG et al.:
10
NANOCRYSTALLINE
------
1
10
100
1000
10000
Grain She (nm) Fig. 10. The intercrystalline volume fraction changes as a result of grain growth. do is the grain size before grain growth.
By substituting equation equation (16) as
(18) in (16), one can write
For a given initial grain size, d, the intercrystalline volume fraction change due to grain growth is illustrated in Fig. 10. It can be seen that AJc decreases as the initial grain size increases and levels off when grain size becomes larger than 1000 nm. This result suggests that Afl:“‘, as the heat release in DSC measurements, can only be measurable when the grain size before grain growth is within the nanometer range. In the present work, the total enthalpy of the irreversible process is calculated by integrating the area under the exothermal peaks after the background subtraction and dividing the area by the corresponding heating rates. The results are listed in Table 1. The mean value of the total enthalpy was found to be 415.7 J/mol. By applying equation (16’) and inserting the grain size values before and after grain growth (L&= 20 nm and d, = 1250 nm), one can calculate the estimated intercrystalline enthalpy, AH,, = 2943 J/mol.
NICKEL ELECTRODEPOSITS process. By varying the heating rates and measuring the exothermal peak temperatures, a plot of ln(/?/(rp - TO)) us l/T,, has yielded the activation energy to be 13 1.5 kJ/mol. This value is very close to those obtained from Kissinger and Ozawa techniques; however, the physical difference between these techniques has been addressed. ??In addition to the activation energy, all the other parameters in the JMA equation (2) can be estimated by DSC measurements at constant heating rates. ??The activation energy obtained from this study falls in the range covered by the literature values of activation energy for grain boundary diffusion, but on the lower limit side, which indicates that the grain growth of nanocrystalline nickel deposits bears some similarities to grain boundary diffusion controlled processes and diffusion short circuits exist in nanocrystalline materials. This observation also further confirms the single-process theory of grain boundary migration. ??Nanocrystalline nickel deposits used in this study are stable in their grain size when the temperature is below 553 K. However, continuous heating to higher temperatures results in abnormal grain growth. The reason for abnormal grain growth has been attributed to subgrain coalescence of the slightly misoriented nanocrystal clusters in the as-deposited materials. ??The abnormal grain growth is found to be coincident with the exothermal peaks on DSC traces. The excess enthalpy released from this process is 415.7 f 3.5 J/mol. If all the enthalpy is attributed to the heat release due to the change in the intercrystalline volume fraction, the mean specific intercrystalline enthalpy is estimated to be AH,, = 2943 J/mol. Acknowledgements-The authors wish to express their gratitude to Dr J. W. Graydon for his assistance with the DSC measurements and valuable discussion. Comments from Profs G. C. Weatherly and D. D. Perovic are highly appreciated. Thanks are also due to Dr A. M. Sherik for his assistance with material production. Financial support provided by Natural Science and Engineering Research Council of Canada is gratefully acknowledged. N.W. has been supported by an Ontario Graduate Scholarship and a University of Toronto Open Scholarship. REFERENCES
5. CONCLUSIONS According to the present work, including the theoretical treatment of the JMA equation, the DSC measurements and TEM studies on nanocrystalline nickel produced by the electrodeposition technique, the following conclusions can be drawn: ??Nanocrystalline materials provide us with a great opportunity to study grain boundary properties. Based on the JMA equation, a technique, which is derived from an isokinetic analysis, has been developed to determine the activation energy of this
1. H. Gleiter,
Progress
in Materials
Science
33, 223
(1989). 2. R. Birringer, Muter.
Sci. Eng. A117, 33 (1989). 3. V. G. Gryaznov and L. I. Trusov, Progress in Materials
Science 37, 289 (1993). 4. Ning Wang, G. Palumbo, Zhirui Wang, U. Erb and K. T. Aust, Scripta Metall. et Mater. 28, 253 (1993). 5. L. C. Chen, F. Spaepen, J. L. Robertson, S. C. Moss and K. Hiraga, J. Mater. Res. 5, 1871 (1990). 6. K. Lu, W. D. Wei, and J. T. Wang, J. Appl. Phys. 69, 7345 (1991). 7. R. S. Averback, H. J. Hiifler, H. Hahn and J. C. Logas, Nanostructured Materials 1, 173 (1992).
WANG
et al.:
NANOCRYSTALLINE
NICKEL
ELECTRODEPOSITS
8. U. Klement, 9. 10. 11. 12.
13. 14. 15.
16. 17.
18. 19. 20. 21. 22.
23. 24. 25. 26. 27. 28.
29. 30.
U. Erb, A. M. El-Sherik, K. T. Aust, (to be published). W. A. Johnson and R. F. Mehl, Truns. AIME, Iron & Steel DiGsion 135, 416 (1939). M. Avrami, J. C/rem. Phys. 7, 1103 (1939). M. Avrami, J. Chem. Phys. 8, 212 (1940). J. W. Christian, The Theory qf Transformation in Metals und Alloys, 2nd ed., p. 543. Pergamon Press, Hungary (1975). J. W. Graydon, S. J. Thorpe and D. W. Kirk, J. Non-Crystalline Solids 175, 31 (1994). J. W. Cahn, Acta Metall. 4, 572 (1956). J. W. Christian, The Theory of Transformation in Metals and Alloys. 2nd ed. Pergamon Press, Hungary (1975). H. E. Kissinger, Anal. Chem. 29, 1702 (1957). J. W. Christian, The Theory of Tramformation in Metals and Alloys, 2nd ed., p. 19. Pergamon Press, Hungary (1975). J. A. Augis, and J. E. Bennett, J. Thermal Anal. 13,283 (1978). T. Ozawa, J. Thermal Anal. 2, 301 (1970). D. W. Henderson, J. Non-Cryst. Solids 30, 301 (1979). A. M. El-Sherik and U. Erb, J. Muter. Sci. (to be published). T. R. Haasz, K. T. Aust, G. Palumbo, A. M. El-Sherik and U. Erb, Scripta Metall. et Mater. 32, 423 (1995). A. M. Chaplanov, Phys. Met. Metall. 70(2), 124 (1990). B. Gunther, A. Kumpmann and H.-D. Kunze, Scripta Metall. et Mater. 27, 833 (1992). P. Knauth, A. Charai’ and P. Gas, Scripta Metall et Mater. 28, 325 (1993). K. T. Aust, Can. Metall. Quar. 33, 265 (1994). J. W. Graydon, S. J. Thorpe and D. W. Kirk, Acta Metall. Mater. 42, 3163 (1994). I. Kaur and W. Gust, Handbook qf Grain and Interphase Press, Stuttgart Boundary D@sion Data. Ziegler ( 1989). K. T. Aust and J. W. Rutter, Trans. Metall. Sot. AIME 215, 820 (1959). D. G. Cole, P. Feltham and E. Gilliam, Proc. PhJx. Sot. B67, 131 (1954).
1669
APPENDIX By substituting have
equations
(6) and (7) in equation
(5’) we
(m-l)$(n+m+?j+(n-l)(n+m$?)
+mu
(A.11 where u = E/RT.
Expand
(A.1)
(A.2) Rearrange the terms in (A.2) so that only the term Pt” is left on the left side of the equation and put back the original expression for u
K”‘y =
1_
This is equation
L4.3)
(5’).