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In-situ annealing experiments of octachloropropane as a rock analogue: kinetics and energetics of grain growth
ELSEVIER
Tectonophysics 304 (1999) 57–70
In-situ annealing experiments of octachloropropane as a rock analogue: kinetics and energetics of grain growth Tran Ngoc Nam a,1 , Shigeru Otoh b , Toshiaki Masuda a,* a
Institute of Geosciences, Faculty of Science, Shizuoka University, Ohya 836, Shizuoka 422-8529, Japan b Department of Earth Sciences, Faculty of Science, Toyama University, Toyama 930-8555, Japan Received 3 March 1998; accepted 9 December 1998
Abstract Two-dimensional in-situ observation of the change of size of individual grains of octachloropropane (OCP) during post-deformation annealing revealed that grain boundary migration occurred to reduce the grain boundary energy. Within the polycrystalline aggregate studied some grains show a cyclic change in grain size, others have a stable grain size, while most grains were consumed and disappeared in order that the mean grain size could increase. During grain coarsening, some grains were dissected, then coalesced, amalgamated with others and their centers migrated across the aggregate. The average grain size (D) can be expressed by D D k0 exp. Q=RT /t n , where k0 is a constant, Q is the activation energy, R is the gas constant, T is the temperature, t is the annealing time and n is a constant. We obtained n D 0.1–0.2 and Q D 6.2 kcal=mol. The driving force .P/ is the surface energy stored at grain boundaries. The driving force can be expressed as 0 0 P / t m , where m is the constant, and hence the grain growth rate (D ) can be expressed as D / P .n 1/=m . The value of .n 1/=m ranges from 4 to 10. 1999 Elsevier Science B.V. All rights reserved. Keywords: annealing experiments; energetics; kinetics; normal grain growth; octachloropropane; rock analogue
1. Introduction Octachloropropane (OCP) is an analogue material for quartz, and the microstructures of OCP are very similar to those of metamorphosed and deformed quartz aggregates (e.g., Means, 1989 and references therein). The study of microstructural development using OCP may greatly help our understanding of natural processes under metamorphic conditions, beŁ Corresponding
author. Tel.: C81 (54) 2384794; Fax: C81 (54) 2379895; E-mail: [email protected] 1 Present address: Geological Institute, Faculty of Science, University of Tokyo, Tokyo 113-0033, Japan.
cause OCP enables us to obtain two-dimensional in-situ observations using an optical microscope. This allows us to monitor how each grain changes its shape and size with time at specific conditions (e.g., Means, 1983; Jessell, 1986; Bons and Urai, 1992; Ree and Park, 1997). Although we can only observe frozen natural quartz microstructures which do not change under the microscope, we will speculate on predecessor microstructures and even successor microstructures by the knowledge of the in-situ observations of OCP so that we can understand their real microstructural history (cf. Means, 1995). Most in-situ experiments of OCP have been performed to trace microstructural changes during plas-
0040-1951/99/$ – see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 4 0 - 1 9 5 1 ( 9 8 ) 0 0 2 9 7 - 2
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tic deformation, and many processes such as new grain formation and grain boundary migration have been described (e.g., McCrone and Cheng, 1949; Means, 1983, 1989 and references therein; Bons and Urai, 1992; Bons et al., 1993). These studies, however, have been mostly qualitative with no consideration given to the energetics of the processes studied. Since use of in-situ observation provides us with quantitative data, this technique can produce much more quantitative analyses of microstructural development. This paper deals with the energetics of normal grain growth of OCP under static conditions, aiming at (1) precisely describing grain growth processes, and (2) quantifying the grain growth rate as a function of the driving force. Normal grain growth is a thermally activated process by which the average grain size of a polycrystalline aggregate increases with the annealing time, its driving force being the reduction of surface energy stored at grain boundaries (e.g., Hobbs et al., 1976; Joesten, 1991). As the surface energy can be evaluated by measuring the length of grain boundaries of all the grains, in-situ observation is suitable for a quantitative study. Hillert (1965) proposed a theory for normal grain growth. Assuming the grain growth rate of each grain to be a function of its size, he derived a relationship between the average grain size and time. This paper also compares our data with the results derived using his theory. The results of our experiments will help considering coarsening processes of quartz in contact aureoles where static recrystallization took place. Such examples are the evolution of the microstructure of quartz aggregates in the Ballachulish contact aureole (Buntebarth and Voll, 1991; Joesten, 1991) and the kinetic analysis of grain growth of quartz in nodular chert in the Christmas Mountains contact aureole (Joesten, 1983).
2. Experiments 2.1. Apparatus We used a torsional ring shear apparatus designed by Mark Jessell. The apparatus, similar to that described by Jessell and Lister (1991) and ten Brink
and Passchier (1995), was mounted on a microscope and allowed us to make in situ observations of microstructural development that took place in rockanalogue materials at room temperatures. A specimen was placed between two frosted glass plates. The rotation of the upper plate around a central axis with respect to the lower plate induced an in-plate torsional deformation geometry, and produced a 1.7 mm wide annular shear zone in the sample. The sample was heated using an electric heater. The temperature of the sample was monitored with a copper–constantan thermocouple and kept constant to within š2ºC. The microstructures were recorded as digitized images on a computer using a video microscopy system and a RasterOps 24STV video card. 2.2. Procedure A specimen of OCP was mixed with 0.1 weight percent of silicon carbide grit of about 9–10 µm in diameter. The grit acted as marker particles, allowing the motion of material points and grain boundaries to be traced. When the sample was placed between two glass plates, a very thin film of silicone oil was coated on the plates to reduce the friction of the interface between the plates and the sample. The thickness of the sample was kept at approximately 0.1 mm, but could not be controlled exactly during deformation and annealing. The sample was first deformed by switching on an electric motor. The start of the annealing experiment was defined as the time when the electric motor stopped driving the deformation. Digitized images of a selected area of 6 mm2 were taken at certain time intervals during the annealing. Hundreds of digitized images for each experiment allowed us to trace the progressive microstructural development. 2.3. Conditions Six annealing experiments were performed at atmospheric pressure, temperatures .T / of 20 and 60ºC and an annealing time .t/ up to 1127.5 h (Table 1). Pre-annealing deformation was done at the same temperature for each experiment. The conditions of the deformation can be represented by the angular velocity and the rotated angle of the inner wall (Table 1). The shear strain rate in the annular shear zone is pro-
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Table 1 Experimental conditions and results Run no.
ANO4 ANO5 ANO6 ANO1 ANO8 ANO7
Pre-annealing deformation a (º=h)
b (º)
165 165 870 870 870 870
205 270 270 200 360 360
Temperature (ºC)
Time (hours)
60 60 60 20 22 20
230.5 192.0 144.0 1127.5 336.4 196.0
D D K tn
B D Ct m
K
n
C
39 40 39 12 37 64
0.20 0.21 0.20 0.19 0.16 0.10
0.06 0.05 0.05 0.14 0.05 0.03
.n
m 0.21 0.22 0.20 0.19 0.16 0.09
1/=m
3.7 3.7 4.0 4.3 5.1 9.9
a: Angular velocity of the inner wall of the annular shear zone. b: Rotation angle of the inner wall.
Fig. 1. Photomicrographs (digitized images) of OCP aggregates (crossed polarizers). Scale bar D 1 mm. (a) Starting microstructure (t D 0) of ANO1. Most of the grains were not clear with unclear grain boundaries. Microstructures of the sample annealed for t D 10 h (b), t D 107:5 h (c) and t D 1007:5 h (d). Primary recrystallization took place more rapidly in the inner part of the annular shear zone. (b) and (c) show the co-existence of two processes: normal grain growth in the inner part and primary recrystallization in the outer part. These processes took place diachronously.
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portional to r 2n s where r is the distance from the center of the rotation and n s is the stress exponent for power-law creep (Masuda et al., 1995): it maximizes at the inner wall of the shear zone and decreases with increasing distance from the inner wall. At n s D 4:5 (Bons, 1993) or n s D 5 (ten Brink and Passchier, 1995), the shear strain rate at the inner wall of the shear zone is about 5 ð 102 –103 times larger than that at the outer wall. Strain rate during the annealing experiments is not exactly zero. Our brief estimation using the marker particles is about 10 7 =s for the first 100 h and less than that for the next hours.
3. General observations Fig. 1 shows the microstructural development of ANO1 during the annealing. The starting microstruc-
ture at t D 0 is shown in Fig. 1a. Grains commonly show undulatory extinction, and since most grain boundaries were not clear, it was difficult to measure the grain size, although we can perceive that grains situated in the inner half of the shear zone appeared larger than those in the outer half. A foliation could not be detected, although some grains were elongated. Microstructures in the frosted-glass area looked less clear, and were not the site for further observations. Analogous to the metallurgical and ceramic sciences, the annealing process of OCP can be explained by two mechanisms: primary recrystallization and normal grain growth (e.g., Hobbs et al., 1976; Urai et al., 1986). The deformation microstructures changed rapidly in the inner half of the shear zone in the first few hours of annealing. Grains showing no signs of undulatory extinction devel-
Fig. 2. Grain boundary angles at triple junctions (ANO1). N D number of measured angles. t D annealing time in hours. The distributions are symmetric and centered at 120º. The range narrowed and the peak sharpened with increasing t.
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oped, their grain boundaries being clear and straight or only slightly curved. A similar change took place much slower in the outer half. This stage is called primary recrystallization. The driving force is the strain energy stored at dislocations plus surface energy stored at grain boundaries. After the microstructures resulting from deformation have been completely replaced by clear (strain-free) ‘two-dimensional’ equigranular polygonal grains through primary recrystallization, the mean grain size still increases gradually with increasing annealing time (Fig. 1b–d). This process results from normal grain growth (e.g., Hobbs et al., 1976; Urai et al., 1986) for which the driving force is the surface energy. Since an increase in mean grain size is accomplished by a decrease in the number of grains in a certain area, many grains disappear during annealing. The transition of mechanisms from primary recrystallization to normal grain growth took place earlier in the inner half of the shear zone than
61
in the outer half. Fig. 1b and c shows that the domain of primary recrystallization, characterized by unclear grains, diminished with annealing time. This transition took place earlier for the 60ºC than the 20ºC experiments. The following description deals with the normal grain growth stage unless stated otherwise. Fig. 2 shows the typical distribution of angles at triple junctions during normal grain growth. The angle gradually converges to 120º with increasing annealing time.
4. Observation of individual grains Two-dimensional in situ observation enables us to trace the change of size and shape of individual grains during annealing. The change was mostly accomplished by grain boundary migration. There was an exception that we describe later involving amalgamation of grains. We document the change in terms
Fig. 3. Sketch of typical shrinking grains (shaded) of ANO1. The same number refers to the same grain from sketch to sketch. t D annealing time in hours. See text for explanation.
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of diameter (Di ), area (Ai ) and perimeter (L i ) of individual grains, the latter two of which were measured using a computerized image processor from a video camera p with an accuracy of š3%. Di is defined as Di D 2 Ai =³ where ³ is the ratio of a circle’s
circumference to its diameter. Di is the diameter of a circle which has the same area as the grain. Most grains were short-lived and consumed by surrounding grains (Figs. 3–5). Typically, five- or six-sided grains developed less sides as they became
Fig. 4. Grain size distributions with respect to annealing time for ANO1. For N and t, see Fig. 2. SD D standard deviation. The mean grain diameters are indicated by arrows. ∆t D time interval between two photomicrographs used for identifying whether grains were growing, shrinking or others. This classification was based on a comparison of grain sizes and grain growth histories of two photomicrographs taken at a different interval of time ∆t.
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Fig. 5. Sketches of grains (ANO1). Height of each sketch D 1 mm. t in hours. We used 105 images to prepare (a) to (i). Shaded grains were shrinking and disappeared. The same label refers to the same grain from sketch to sketch. New grains p* and 6* formed by progressive misorientation of grains p and 6, respectively. A small grain (7) survived for 1127 h, while larger grains such as f, p and q disappeared earlier.
smaller. Ultimately, after they became three-sided, they rapidly disappeared (Fig. 3). As a result, other grains became larger. Fig. 4 shows typical distributions of the diameter. Obviously, the average diameter of growing grains was larger than that of shrinking ones. However, no critical diameter exists
separating growing grains from shrinking ones (cf. theory by Hillert, 1965). Fig. 5 shows sketches of microstructures demonstrating how grains changed their diameter and shape. Fig. 6 shows how the diameter of typical long-lived grains changed with increasing annealing
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Fig. 6. Change of the diameter with increasing the annealing time .t/ in seconds. Only data of typical long-lived grains are plotted. (a) ANO1; (b) ANO5.
time. The two figures show a slow increase and a rather rapid decrease in diameter. The history of the diameter looks unique for each grain. Several grains are characterized by a cyclic change in the diameter. The timing of growth and shrinkage differs from grain to grain. Fig. 7 shows one such grain. This grain rapidly grew from a nucleus at t D 0 to Di D 480 µm at t D 9 h. This stage is related to primary recrystallization. Then it shrank to Di D 150 µm at t D 36 h. However, then it enlarged causing an increase in surface energy. This behavior is ‘irrational’. Some relatively small grains surrounded by larger grains were ‘stable’ in size as exemplified in Fig. 5: one grain survived for 1127 h, while surrounding larger grains completely disappeared.
New grain formation preceded by progressive misorientation were recognized as shown in Fig. 5. The new grain formation caused a temporal decrease in the local mean diameter. An exceptional new grain appeared at a quadruple junction at 1:33 < t < 2:08 h in ANO1 (Fig. 8). It grew as large as Di D 70 µm at t D 6 h and disappeared by t D 20 h (Fig. 8). Such a new grain formation in the course of normal grain growth has not been theoretically predicted. An example of coalescence (Means, 1989) is shown in Fig. 9. New subgrain boundaries (type IV of Means and Ree, 1988) are usually straight. Fig. 9 also shows examples of amalgamation (Means, 1989). Progressive reduction of misorientation in crystallographic axes between neighboring grains changes the grain boundary between them into a subgrain boundary (type III of Means and Ree, 1988) leaving one amalgamated grain. No effective grain boundary migration occurred in this case. The subgrain boundaries were usually straight. Coalescence and amalgamation contributed to the grain growth of OCP after the grain size exceeded 400 µm. Fig. 10 shows an example of dissection (Urai et al., 1986; Means, 1989). Dissection was locally observed when the grains became large (>500 µm). It is related to the non-homogeneous migration rate of a grain boundary. Fig. 7 and 10 show examples of grain migration (Urai et al., 1986; Urai, 1987). Grain migration can be seen when a grain shifts its position in relation to marker particles. In these figures the marked grains have migrated so far that they did not contain any former material inside.
5. Grain growth traced with statistical parameters 5.1. Grain size Fig. 4 shows typical distributions of the diameter. Each distribution is approximately log-normal. The mean diameter (D) is defined as: 1 X log.Di / log.D/ D (1) N where N is the number of grains. D increases with increasing the annealing time .t/. The relationship between log.D/ and log.t/ can be fitted by a straight
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Fig. 7. An example of cyclic change in grain size and grain migration (ANO5). Solid squares (A and B) D marker particles. t in hours.
line (Fig. 11), which indicates the following form of equation: D D K tn
(2)
where K is a constant and n is the time exponent. In a strict sense, we should use the form: D
1=n
1=n
D0
D kt
(3)
where D 0 is the initial mean grain diameter at t D 0. However, as we cannot measure D 0 , due to unclear microstructures, we prefer to use Eq. 2 to Eq. 3. We have until now used an hour as the unit of time to
describe the microstructural development. From now on we will use a second to show the quantitative relationship between the mean diameter and time. Eq. 2 is the same as the empirically established formula for normal grain growth of metals, ceramics, silicates and ice (Hu and Rath, 1970; Wilson, 1982; Karato, 1989). K varies from experiment to experiment in the range from 12 to 64, while n is between 0.1 and 0.2 irrespective of the temperature (Table 1). K can be expressed as: K D K 0 exp. Q=RT /
(4)
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Fig. 8. Sketches of a new grain formation (black grain) by grain boundary migration in ANO1. t in hours.
where K 0 is a constant, Q is the activation energy, R is the gas constant and T is the absolute temperature (e.g., Hu and Rath, 1970). The value of Q D 6:2 kcal=mol was obtained using ANO1 at 20ºC and ANO4–6 at 60ºC assuming n D 0:2. The standard deviation of the diameter does not change greatly during annealing, mostly ranging from 0.18 to 0.26. The magnitudes show that sizes of the individual grains are relatively uniform during normal grain growth. The skewness is also stable, mostly between 0.8 and 0.
As the driving force .P/ for normal grain growth is the surface energy of grain boundaries, P D B where is the specific surface energy and B is the grain boundary density (the average grain boundary length per unit area) defined as: X 1X Li= Ai (6) BD 2 The values of B were plotted on log.B/ log.t/ diagram (Fig. 12), and a linear relationship between them was revealed. Hence, B can be expressed by a power function of the annealing time as: B D Ct m
6. The relationship between grain growth rate and the driving force We want to derive the relationship between the average grain growth rate and the driving force. The 0 grain growth rate (D ) is calculated by differentiating Eq. 2:
where C is the constant and m is the time exponent. The value of C ranges from 0.03 to 0.14, whereas that of m ranges from 0.22 to 0.09 (Table 1). 0 The relationship between D and B is obtained from Eqs. 5 and 7 as: 0
D D K nC dD D K nt n D D dt 0
1
(5)
(7)
.n 1/=m
B .n
1/=m
(8) 0
Thus, the relationship between D and P can be
T.N. Nam et al. / Tectonophysics 304 (1999) 57–70
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Fig. 9. Coalescence and amalgamation (ANO4). Dashed line D subgrain boundary. t D annealing time in hours. Coalescence of grains 11 and 21 was accomplished in (d) where the two intervening grains (16 and 17) were consumed. The impingement boundary between grains 11 and 21 was a subgrain boundary because the crystallographic axes of the grains were similarly oriented. Grains 11 and 8 also coalesced with each other. Amalgamation can be seen in (d) where grain boundaries between grains 21 and 22, 15 and 19, 19 and 23 in (a)–(c) became subgrain boundaries by progressive reduction of misorientation between them. Grains 7, 10, 14, 24, 25, 16 and 17 shrunk and disappeared by t D 35.25 (d). Grain 20 was stable in size. (Based on 20 color images between (a) and (d).)
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Fig. 10. Sketches showing dissection of large grains (ANO4). Dashed lines show subgrain boundaries. t D annealing time in hours. Scale bar D 0.5 mm. Grain B was dissected into two grains (B1 and B2) by invasion of grains 4a and 5 by t D 74 h (c), whereas grain A was dissected into three separate grains (A1, A2 and A3) by t D 170 h. Dissected grains were sooner or later consumed.
T.N. Nam et al. / Tectonophysics 304 (1999) 57–70
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7. Evaluation of theory The theory of normal grain growth by Hillert (1965) assumes an equation giving the grain growth rate of individual grains .d Di =d t/ as: d Di =d t D M.1=D
Fig. 11. The mean diameter (D) with respect to the annealing time .t/. D was not measured at the first few hours during the annealing experiment, because grain boundaries were not clear. The data of ANO6 can be fitted by two straight lines, indicating that the grain growth occurred in two stages: the first (t < 103:3 s) rapid growth stage and the subsequent one (t > 103:3 s). Judging from the microstructural development, the rapid growth stage can be assigned to the primary recrystallization stage, and the second one to the normal grain growth stage. The straight line of other experiments is assigned to normal grain growth.
expressed as: 0
D D K n. C/
.n 1/=m
P .n
1/=m
(9)
The driving force exponent, .n 1/=m, ranges from 3.7 to 9.9 (Table 1). Such a power law relationship is the same as previously reported in the metallurgical literature (e.g., Hu and Rath, 1970; Simpson et al., 1976) and for quartz (Masuda et al., 1997).
1=Di /
(10)
where M is the constant. Quantitatively, most grains do not obey this equation. Here, we restrict our consideration using the sign of d Di =d t, where Di > D, d Di =d t > 0 is obtained from Eq. 10; this means that grains larger than the mean diameter are growing. On the contrary, where Di < D, d Di =d t < 0; this means that the grains smaller than the mean diameter are shrinking. We examine the applicability of this sign rule to our data. In the distributions of the diameter (Fig. 4), we classified grains into three categories: growing, shrinking and ‘others’. The average diameter of the growing grains is larger than that of shrinking grains. However, approximately 1=3–1=2 of the number of grains disobey the sign rule. The theory of Hillert (1965) results in a normal-like distribution of the diameter. The theoretical distribution differs from our measured, log-normallike distribution. The theory predicts that the time exponent in Eq. 2 is 0.5. This is not equal to our data (n D 0:1–0:2). Considering these differences, we judged that the Hillert theory is not acceptable for OCP.
8. Summary
Fig. 12. Grain boundary density .B/ with respect to the annealing time .t/. A linear relationship between log.B/ and log.t/ was revealed.
The microstructural development of OCP aggregates during quasi-static annealing after initial plastic deformation was analyzed; the results are summarized as follows: (1) Deformation microstructures of the starting material such as undulatory extinction within grains and unclear grain boundaries can be completely destroyed by primary recrystallization a few hours after annealing started. (2) After primary recrystallization was completed, grain growth occurred in the aggregates. (3) Microstructural change involving grain growth is principally proceeded by grain boundary migration. New grain formation, dissection, coalescence,
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amalgamation, cyclic growth–shrinkage and grain migration occur. (4) The average grain size is represented by a power function of time as D / t n where the time exponent n D 0.1–0.2, being temperature independent. (5) The relationship between grain growth rate 0 (D ) and the driving force (P: reduction of surface energy stored at grain boundaries) is expressed as 0 D / P .n 1/=m where the exponent .n 1/=m ranges from 4 to 15. (6) The theory of normal grain growth proposed by Hillert (1965) is not applicable for OCP.
Acknowledgements We thank Ei Horikoshi for supporting our experiments in Toyama, Mark Jessell for giving permission to build the apparatus, the workshop at Monash University for building it, and Tim Bell for giving stimulative comments and correcting the English of the manuscript. We also thank Terry Engelder, W.D. Means and two anonymous reviewers for constructive comments which improved the text. References Bons, P.D., 1993. Experimental deformation of polyphase rock analogues. Geol. Ultraject. 110, Mededelingen van de Faculteit Aardwetenschappen der Universiteit Utrecht, 207 pp. Bons, P.D., Urai, J.L., 1992. Syndeformational grain growth: microstructures and kinetics. J. Struct. Geol. 14, 1101–1109. Bons, P.D., Jessell, M.W., Passchier, C.W., 1993. The analysis of progressive deformation in rock analogues. J. Struct. Geol. 15, 403–411. Buntebarth, G., Voll, G., 1991. Quartz grain coarsening by collective crystallization in contact quartzites. In: Voll, G., Topel, J., Pattison, D.R.M., Seifert, F. (Eds.), Equilibrium and Kinetics in Contact Metamorphism. Springer-Verlag, pp. 251– 265. Hillert, M., 1965. On the theory of normal and abnormal grain growth. Acta Metall. 13, 227–238. Hobbs, B.E., Means, W.D., Williams, P.F., 1976. An Outline of Structural Geology. Wiley, New York, 571 pp. Hu, H., Rath, B.B., 1970. On the time exponent in isothermal
grain growth. Metall. Trans. 1, 3181–3184. Jessell, M.W., 1986. Grain boundary migration and fabric development in experimentally deformed octachloropropane. J. Struct. Geol. 8, 527–542. Jessell, M.W., Lister, G.S., 1991. Strain localization behaviour in experimental shear zones. Pure Appl. Geophys. 137, 421–438. Joesten, R.L., 1983. Grain growth and grain-boundary diffusion in quartz from the Christmas Mountains (Texas) contact aureole. Am. J. Sci. 283A, 233–254. Joesten, R.L., 1991. Kinetics of coarsening and diffusion-controlled mineral growth. In: Kerrick, D.M. (Ed.), Contact Metamorphism. Mineral. Soc. Am. Rev. Mineral. 26, 507–582. Karato, S., 1989. Grain growth kinetics in olivine aggregates. Tectonophysics 168, 255–273. Masuda, T., Mizuno, N., Kobayashi, M., Nam, T.N., Otoh, S., 1995. Stress and strain estimates for Newtonian and non-Newtonian materials in a rotational shear zone. J. Struct. Geol. 17, 451–454. Masuda, T., Morikawa, T., Nakayama, Y., Suzuki, S., 1997. Grain-boundary migration of quartz during annealing experiments at high temperatures and pressures, with implications for metamorphic geology. J. Metamorph. Geol. 15, 311–322. McCrone, W.C., Cheng, P.T., 1949. Grain growth in octachloropropane. J. Appl. Phys. 20, 230–231. Means, W.D., 1983. Microstructure and micromotion in recrystallization flow of octachloropropane: a first look. Geol. Rundsch. 72, 511–528. Means, W.D., 1989. Synkinematic microscopy of transparent polycrystals. J. Struct. Geol. 11, 163–174. Means, W.D., 1995. Shear zones and rock history. Tectonophysics 247, 157–160. Means, W.D., Ree, J.H., 1988. Seven types of subgrain boundaries in octachloropropane. J. Struct. Geol. 10, 765–770. Ree, J.-H., Park, Y., 1997. Static recovery and recrystallization microstructures in sheared octachloropropane. J. Struct. Geol. 19, 1521–1526. Simpson, C.J., Winegard, W.C., Aust, K.T., 1976. Grain boundary mobility and boundary–solute interactions. In: Chadwick, G.A., Smith, D.A. (Eds.), Grain Boundary Structure and Properties. Academic Press, New York, pp. 201–234. ten Brink, C.E., Passchier, C.W., 1995. Modelling of mantled porphyroclasts using non-Newtonian rock analogue materials. J. Struct. Geol. 17, 131–146. Urai, J.L., Means, W.D., Lister, J.S., 1986. Dynamic recrystallization of minerals. Am. Geophys. Union, Geophys. Monogr. 39, 161–199. Urai, J.L., 1987. Development of microstructure during deformation of carnallite and bischofite in transmitted light. Tectonophysics 135, 251–263. Wilson, C.J.L., 1982. Texture and grain growth during the annealing of ice. Texture Microstruct. 5, 19–31.
Tectonophysics 304 (1999) 57–70
In-situ annealing experiments of octachloropropane as a rock analogue: kinetics and energetics of grain growth Tran Ngoc Nam a,1 , Shigeru Otoh b , Toshiaki Masuda a,* a
Institute of Geosciences, Faculty of Science, Shizuoka University, Ohya 836, Shizuoka 422-8529, Japan b Department of Earth Sciences, Faculty of Science, Toyama University, Toyama 930-8555, Japan Received 3 March 1998; accepted 9 December 1998
Abstract Two-dimensional in-situ observation of the change of size of individual grains of octachloropropane (OCP) during post-deformation annealing revealed that grain boundary migration occurred to reduce the grain boundary energy. Within the polycrystalline aggregate studied some grains show a cyclic change in grain size, others have a stable grain size, while most grains were consumed and disappeared in order that the mean grain size could increase. During grain coarsening, some grains were dissected, then coalesced, amalgamated with others and their centers migrated across the aggregate. The average grain size (D) can be expressed by D D k0 exp. Q=RT /t n , where k0 is a constant, Q is the activation energy, R is the gas constant, T is the temperature, t is the annealing time and n is a constant. We obtained n D 0.1–0.2 and Q D 6.2 kcal=mol. The driving force .P/ is the surface energy stored at grain boundaries. The driving force can be expressed as 0 0 P / t m , where m is the constant, and hence the grain growth rate (D ) can be expressed as D / P .n 1/=m . The value of .n 1/=m ranges from 4 to 10. 1999 Elsevier Science B.V. All rights reserved. Keywords: annealing experiments; energetics; kinetics; normal grain growth; octachloropropane; rock analogue
1. Introduction Octachloropropane (OCP) is an analogue material for quartz, and the microstructures of OCP are very similar to those of metamorphosed and deformed quartz aggregates (e.g., Means, 1989 and references therein). The study of microstructural development using OCP may greatly help our understanding of natural processes under metamorphic conditions, beŁ Corresponding
author. Tel.: C81 (54) 2384794; Fax: C81 (54) 2379895; E-mail: [email protected] 1 Present address: Geological Institute, Faculty of Science, University of Tokyo, Tokyo 113-0033, Japan.
cause OCP enables us to obtain two-dimensional in-situ observations using an optical microscope. This allows us to monitor how each grain changes its shape and size with time at specific conditions (e.g., Means, 1983; Jessell, 1986; Bons and Urai, 1992; Ree and Park, 1997). Although we can only observe frozen natural quartz microstructures which do not change under the microscope, we will speculate on predecessor microstructures and even successor microstructures by the knowledge of the in-situ observations of OCP so that we can understand their real microstructural history (cf. Means, 1995). Most in-situ experiments of OCP have been performed to trace microstructural changes during plas-
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tic deformation, and many processes such as new grain formation and grain boundary migration have been described (e.g., McCrone and Cheng, 1949; Means, 1983, 1989 and references therein; Bons and Urai, 1992; Bons et al., 1993). These studies, however, have been mostly qualitative with no consideration given to the energetics of the processes studied. Since use of in-situ observation provides us with quantitative data, this technique can produce much more quantitative analyses of microstructural development. This paper deals with the energetics of normal grain growth of OCP under static conditions, aiming at (1) precisely describing grain growth processes, and (2) quantifying the grain growth rate as a function of the driving force. Normal grain growth is a thermally activated process by which the average grain size of a polycrystalline aggregate increases with the annealing time, its driving force being the reduction of surface energy stored at grain boundaries (e.g., Hobbs et al., 1976; Joesten, 1991). As the surface energy can be evaluated by measuring the length of grain boundaries of all the grains, in-situ observation is suitable for a quantitative study. Hillert (1965) proposed a theory for normal grain growth. Assuming the grain growth rate of each grain to be a function of its size, he derived a relationship between the average grain size and time. This paper also compares our data with the results derived using his theory. The results of our experiments will help considering coarsening processes of quartz in contact aureoles where static recrystallization took place. Such examples are the evolution of the microstructure of quartz aggregates in the Ballachulish contact aureole (Buntebarth and Voll, 1991; Joesten, 1991) and the kinetic analysis of grain growth of quartz in nodular chert in the Christmas Mountains contact aureole (Joesten, 1983).
2. Experiments 2.1. Apparatus We used a torsional ring shear apparatus designed by Mark Jessell. The apparatus, similar to that described by Jessell and Lister (1991) and ten Brink
and Passchier (1995), was mounted on a microscope and allowed us to make in situ observations of microstructural development that took place in rockanalogue materials at room temperatures. A specimen was placed between two frosted glass plates. The rotation of the upper plate around a central axis with respect to the lower plate induced an in-plate torsional deformation geometry, and produced a 1.7 mm wide annular shear zone in the sample. The sample was heated using an electric heater. The temperature of the sample was monitored with a copper–constantan thermocouple and kept constant to within š2ºC. The microstructures were recorded as digitized images on a computer using a video microscopy system and a RasterOps 24STV video card. 2.2. Procedure A specimen of OCP was mixed with 0.1 weight percent of silicon carbide grit of about 9–10 µm in diameter. The grit acted as marker particles, allowing the motion of material points and grain boundaries to be traced. When the sample was placed between two glass plates, a very thin film of silicone oil was coated on the plates to reduce the friction of the interface between the plates and the sample. The thickness of the sample was kept at approximately 0.1 mm, but could not be controlled exactly during deformation and annealing. The sample was first deformed by switching on an electric motor. The start of the annealing experiment was defined as the time when the electric motor stopped driving the deformation. Digitized images of a selected area of 6 mm2 were taken at certain time intervals during the annealing. Hundreds of digitized images for each experiment allowed us to trace the progressive microstructural development. 2.3. Conditions Six annealing experiments were performed at atmospheric pressure, temperatures .T / of 20 and 60ºC and an annealing time .t/ up to 1127.5 h (Table 1). Pre-annealing deformation was done at the same temperature for each experiment. The conditions of the deformation can be represented by the angular velocity and the rotated angle of the inner wall (Table 1). The shear strain rate in the annular shear zone is pro-
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Table 1 Experimental conditions and results Run no.
ANO4 ANO5 ANO6 ANO1 ANO8 ANO7
Pre-annealing deformation a (º=h)
b (º)
165 165 870 870 870 870
205 270 270 200 360 360
Temperature (ºC)
Time (hours)
60 60 60 20 22 20
230.5 192.0 144.0 1127.5 336.4 196.0
D D K tn
B D Ct m
K
n
C
39 40 39 12 37 64
0.20 0.21 0.20 0.19 0.16 0.10
0.06 0.05 0.05 0.14 0.05 0.03
.n
m 0.21 0.22 0.20 0.19 0.16 0.09
1/=m
3.7 3.7 4.0 4.3 5.1 9.9
a: Angular velocity of the inner wall of the annular shear zone. b: Rotation angle of the inner wall.
Fig. 1. Photomicrographs (digitized images) of OCP aggregates (crossed polarizers). Scale bar D 1 mm. (a) Starting microstructure (t D 0) of ANO1. Most of the grains were not clear with unclear grain boundaries. Microstructures of the sample annealed for t D 10 h (b), t D 107:5 h (c) and t D 1007:5 h (d). Primary recrystallization took place more rapidly in the inner part of the annular shear zone. (b) and (c) show the co-existence of two processes: normal grain growth in the inner part and primary recrystallization in the outer part. These processes took place diachronously.
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portional to r 2n s where r is the distance from the center of the rotation and n s is the stress exponent for power-law creep (Masuda et al., 1995): it maximizes at the inner wall of the shear zone and decreases with increasing distance from the inner wall. At n s D 4:5 (Bons, 1993) or n s D 5 (ten Brink and Passchier, 1995), the shear strain rate at the inner wall of the shear zone is about 5 ð 102 –103 times larger than that at the outer wall. Strain rate during the annealing experiments is not exactly zero. Our brief estimation using the marker particles is about 10 7 =s for the first 100 h and less than that for the next hours.
3. General observations Fig. 1 shows the microstructural development of ANO1 during the annealing. The starting microstruc-
ture at t D 0 is shown in Fig. 1a. Grains commonly show undulatory extinction, and since most grain boundaries were not clear, it was difficult to measure the grain size, although we can perceive that grains situated in the inner half of the shear zone appeared larger than those in the outer half. A foliation could not be detected, although some grains were elongated. Microstructures in the frosted-glass area looked less clear, and were not the site for further observations. Analogous to the metallurgical and ceramic sciences, the annealing process of OCP can be explained by two mechanisms: primary recrystallization and normal grain growth (e.g., Hobbs et al., 1976; Urai et al., 1986). The deformation microstructures changed rapidly in the inner half of the shear zone in the first few hours of annealing. Grains showing no signs of undulatory extinction devel-
Fig. 2. Grain boundary angles at triple junctions (ANO1). N D number of measured angles. t D annealing time in hours. The distributions are symmetric and centered at 120º. The range narrowed and the peak sharpened with increasing t.
T.N. Nam et al. / Tectonophysics 304 (1999) 57–70
oped, their grain boundaries being clear and straight or only slightly curved. A similar change took place much slower in the outer half. This stage is called primary recrystallization. The driving force is the strain energy stored at dislocations plus surface energy stored at grain boundaries. After the microstructures resulting from deformation have been completely replaced by clear (strain-free) ‘two-dimensional’ equigranular polygonal grains through primary recrystallization, the mean grain size still increases gradually with increasing annealing time (Fig. 1b–d). This process results from normal grain growth (e.g., Hobbs et al., 1976; Urai et al., 1986) for which the driving force is the surface energy. Since an increase in mean grain size is accomplished by a decrease in the number of grains in a certain area, many grains disappear during annealing. The transition of mechanisms from primary recrystallization to normal grain growth took place earlier in the inner half of the shear zone than
61
in the outer half. Fig. 1b and c shows that the domain of primary recrystallization, characterized by unclear grains, diminished with annealing time. This transition took place earlier for the 60ºC than the 20ºC experiments. The following description deals with the normal grain growth stage unless stated otherwise. Fig. 2 shows the typical distribution of angles at triple junctions during normal grain growth. The angle gradually converges to 120º with increasing annealing time.
4. Observation of individual grains Two-dimensional in situ observation enables us to trace the change of size and shape of individual grains during annealing. The change was mostly accomplished by grain boundary migration. There was an exception that we describe later involving amalgamation of grains. We document the change in terms
Fig. 3. Sketch of typical shrinking grains (shaded) of ANO1. The same number refers to the same grain from sketch to sketch. t D annealing time in hours. See text for explanation.
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of diameter (Di ), area (Ai ) and perimeter (L i ) of individual grains, the latter two of which were measured using a computerized image processor from a video camera p with an accuracy of š3%. Di is defined as Di D 2 Ai =³ where ³ is the ratio of a circle’s
circumference to its diameter. Di is the diameter of a circle which has the same area as the grain. Most grains were short-lived and consumed by surrounding grains (Figs. 3–5). Typically, five- or six-sided grains developed less sides as they became
Fig. 4. Grain size distributions with respect to annealing time for ANO1. For N and t, see Fig. 2. SD D standard deviation. The mean grain diameters are indicated by arrows. ∆t D time interval between two photomicrographs used for identifying whether grains were growing, shrinking or others. This classification was based on a comparison of grain sizes and grain growth histories of two photomicrographs taken at a different interval of time ∆t.
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Fig. 5. Sketches of grains (ANO1). Height of each sketch D 1 mm. t in hours. We used 105 images to prepare (a) to (i). Shaded grains were shrinking and disappeared. The same label refers to the same grain from sketch to sketch. New grains p* and 6* formed by progressive misorientation of grains p and 6, respectively. A small grain (7) survived for 1127 h, while larger grains such as f, p and q disappeared earlier.
smaller. Ultimately, after they became three-sided, they rapidly disappeared (Fig. 3). As a result, other grains became larger. Fig. 4 shows typical distributions of the diameter. Obviously, the average diameter of growing grains was larger than that of shrinking ones. However, no critical diameter exists
separating growing grains from shrinking ones (cf. theory by Hillert, 1965). Fig. 5 shows sketches of microstructures demonstrating how grains changed their diameter and shape. Fig. 6 shows how the diameter of typical long-lived grains changed with increasing annealing
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Fig. 6. Change of the diameter with increasing the annealing time .t/ in seconds. Only data of typical long-lived grains are plotted. (a) ANO1; (b) ANO5.
time. The two figures show a slow increase and a rather rapid decrease in diameter. The history of the diameter looks unique for each grain. Several grains are characterized by a cyclic change in the diameter. The timing of growth and shrinkage differs from grain to grain. Fig. 7 shows one such grain. This grain rapidly grew from a nucleus at t D 0 to Di D 480 µm at t D 9 h. This stage is related to primary recrystallization. Then it shrank to Di D 150 µm at t D 36 h. However, then it enlarged causing an increase in surface energy. This behavior is ‘irrational’. Some relatively small grains surrounded by larger grains were ‘stable’ in size as exemplified in Fig. 5: one grain survived for 1127 h, while surrounding larger grains completely disappeared.
New grain formation preceded by progressive misorientation were recognized as shown in Fig. 5. The new grain formation caused a temporal decrease in the local mean diameter. An exceptional new grain appeared at a quadruple junction at 1:33 < t < 2:08 h in ANO1 (Fig. 8). It grew as large as Di D 70 µm at t D 6 h and disappeared by t D 20 h (Fig. 8). Such a new grain formation in the course of normal grain growth has not been theoretically predicted. An example of coalescence (Means, 1989) is shown in Fig. 9. New subgrain boundaries (type IV of Means and Ree, 1988) are usually straight. Fig. 9 also shows examples of amalgamation (Means, 1989). Progressive reduction of misorientation in crystallographic axes between neighboring grains changes the grain boundary between them into a subgrain boundary (type III of Means and Ree, 1988) leaving one amalgamated grain. No effective grain boundary migration occurred in this case. The subgrain boundaries were usually straight. Coalescence and amalgamation contributed to the grain growth of OCP after the grain size exceeded 400 µm. Fig. 10 shows an example of dissection (Urai et al., 1986; Means, 1989). Dissection was locally observed when the grains became large (>500 µm). It is related to the non-homogeneous migration rate of a grain boundary. Fig. 7 and 10 show examples of grain migration (Urai et al., 1986; Urai, 1987). Grain migration can be seen when a grain shifts its position in relation to marker particles. In these figures the marked grains have migrated so far that they did not contain any former material inside.
5. Grain growth traced with statistical parameters 5.1. Grain size Fig. 4 shows typical distributions of the diameter. Each distribution is approximately log-normal. The mean diameter (D) is defined as: 1 X log.Di / log.D/ D (1) N where N is the number of grains. D increases with increasing the annealing time .t/. The relationship between log.D/ and log.t/ can be fitted by a straight
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Fig. 7. An example of cyclic change in grain size and grain migration (ANO5). Solid squares (A and B) D marker particles. t in hours.
line (Fig. 11), which indicates the following form of equation: D D K tn
(2)
where K is a constant and n is the time exponent. In a strict sense, we should use the form: D
1=n
1=n
D0
D kt
(3)
where D 0 is the initial mean grain diameter at t D 0. However, as we cannot measure D 0 , due to unclear microstructures, we prefer to use Eq. 2 to Eq. 3. We have until now used an hour as the unit of time to
describe the microstructural development. From now on we will use a second to show the quantitative relationship between the mean diameter and time. Eq. 2 is the same as the empirically established formula for normal grain growth of metals, ceramics, silicates and ice (Hu and Rath, 1970; Wilson, 1982; Karato, 1989). K varies from experiment to experiment in the range from 12 to 64, while n is between 0.1 and 0.2 irrespective of the temperature (Table 1). K can be expressed as: K D K 0 exp. Q=RT /
(4)
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Fig. 8. Sketches of a new grain formation (black grain) by grain boundary migration in ANO1. t in hours.
where K 0 is a constant, Q is the activation energy, R is the gas constant and T is the absolute temperature (e.g., Hu and Rath, 1970). The value of Q D 6:2 kcal=mol was obtained using ANO1 at 20ºC and ANO4–6 at 60ºC assuming n D 0:2. The standard deviation of the diameter does not change greatly during annealing, mostly ranging from 0.18 to 0.26. The magnitudes show that sizes of the individual grains are relatively uniform during normal grain growth. The skewness is also stable, mostly between 0.8 and 0.
As the driving force .P/ for normal grain growth is the surface energy of grain boundaries, P D B where is the specific surface energy and B is the grain boundary density (the average grain boundary length per unit area) defined as: X 1X Li= Ai (6) BD 2 The values of B were plotted on log.B/ log.t/ diagram (Fig. 12), and a linear relationship between them was revealed. Hence, B can be expressed by a power function of the annealing time as: B D Ct m
6. The relationship between grain growth rate and the driving force We want to derive the relationship between the average grain growth rate and the driving force. The 0 grain growth rate (D ) is calculated by differentiating Eq. 2:
where C is the constant and m is the time exponent. The value of C ranges from 0.03 to 0.14, whereas that of m ranges from 0.22 to 0.09 (Table 1). 0 The relationship between D and B is obtained from Eqs. 5 and 7 as: 0
D D K nC dD D K nt n D D dt 0
1
(5)
(7)
.n 1/=m
B .n
1/=m
(8) 0
Thus, the relationship between D and P can be
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Fig. 9. Coalescence and amalgamation (ANO4). Dashed line D subgrain boundary. t D annealing time in hours. Coalescence of grains 11 and 21 was accomplished in (d) where the two intervening grains (16 and 17) were consumed. The impingement boundary between grains 11 and 21 was a subgrain boundary because the crystallographic axes of the grains were similarly oriented. Grains 11 and 8 also coalesced with each other. Amalgamation can be seen in (d) where grain boundaries between grains 21 and 22, 15 and 19, 19 and 23 in (a)–(c) became subgrain boundaries by progressive reduction of misorientation between them. Grains 7, 10, 14, 24, 25, 16 and 17 shrunk and disappeared by t D 35.25 (d). Grain 20 was stable in size. (Based on 20 color images between (a) and (d).)
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Fig. 10. Sketches showing dissection of large grains (ANO4). Dashed lines show subgrain boundaries. t D annealing time in hours. Scale bar D 0.5 mm. Grain B was dissected into two grains (B1 and B2) by invasion of grains 4a and 5 by t D 74 h (c), whereas grain A was dissected into three separate grains (A1, A2 and A3) by t D 170 h. Dissected grains were sooner or later consumed.
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7. Evaluation of theory The theory of normal grain growth by Hillert (1965) assumes an equation giving the grain growth rate of individual grains .d Di =d t/ as: d Di =d t D M.1=D
Fig. 11. The mean diameter (D) with respect to the annealing time .t/. D was not measured at the first few hours during the annealing experiment, because grain boundaries were not clear. The data of ANO6 can be fitted by two straight lines, indicating that the grain growth occurred in two stages: the first (t < 103:3 s) rapid growth stage and the subsequent one (t > 103:3 s). Judging from the microstructural development, the rapid growth stage can be assigned to the primary recrystallization stage, and the second one to the normal grain growth stage. The straight line of other experiments is assigned to normal grain growth.
expressed as: 0
D D K n. C/
.n 1/=m
P .n
1/=m
(9)
The driving force exponent, .n 1/=m, ranges from 3.7 to 9.9 (Table 1). Such a power law relationship is the same as previously reported in the metallurgical literature (e.g., Hu and Rath, 1970; Simpson et al., 1976) and for quartz (Masuda et al., 1997).
1=Di /
(10)
where M is the constant. Quantitatively, most grains do not obey this equation. Here, we restrict our consideration using the sign of d Di =d t, where Di > D, d Di =d t > 0 is obtained from Eq. 10; this means that grains larger than the mean diameter are growing. On the contrary, where Di < D, d Di =d t < 0; this means that the grains smaller than the mean diameter are shrinking. We examine the applicability of this sign rule to our data. In the distributions of the diameter (Fig. 4), we classified grains into three categories: growing, shrinking and ‘others’. The average diameter of the growing grains is larger than that of shrinking grains. However, approximately 1=3–1=2 of the number of grains disobey the sign rule. The theory of Hillert (1965) results in a normal-like distribution of the diameter. The theoretical distribution differs from our measured, log-normallike distribution. The theory predicts that the time exponent in Eq. 2 is 0.5. This is not equal to our data (n D 0:1–0:2). Considering these differences, we judged that the Hillert theory is not acceptable for OCP.
8. Summary
Fig. 12. Grain boundary density .B/ with respect to the annealing time .t/. A linear relationship between log.B/ and log.t/ was revealed.
The microstructural development of OCP aggregates during quasi-static annealing after initial plastic deformation was analyzed; the results are summarized as follows: (1) Deformation microstructures of the starting material such as undulatory extinction within grains and unclear grain boundaries can be completely destroyed by primary recrystallization a few hours after annealing started. (2) After primary recrystallization was completed, grain growth occurred in the aggregates. (3) Microstructural change involving grain growth is principally proceeded by grain boundary migration. New grain formation, dissection, coalescence,
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amalgamation, cyclic growth–shrinkage and grain migration occur. (4) The average grain size is represented by a power function of time as D / t n where the time exponent n D 0.1–0.2, being temperature independent. (5) The relationship between grain growth rate 0 (D ) and the driving force (P: reduction of surface energy stored at grain boundaries) is expressed as 0 D / P .n 1/=m where the exponent .n 1/=m ranges from 4 to 15. (6) The theory of normal grain growth proposed by Hillert (1965) is not applicable for OCP.
Acknowledgements We thank Ei Horikoshi for supporting our experiments in Toyama, Mark Jessell for giving permission to build the apparatus, the workshop at Monash University for building it, and Tim Bell for giving stimulative comments and correcting the English of the manuscript. We also thank Terry Engelder, W.D. Means and two anonymous reviewers for constructive comments which improved the text. References Bons, P.D., 1993. Experimental deformation of polyphase rock analogues. Geol. Ultraject. 110, Mededelingen van de Faculteit Aardwetenschappen der Universiteit Utrecht, 207 pp. Bons, P.D., Urai, J.L., 1992. Syndeformational grain growth: microstructures and kinetics. J. Struct. Geol. 14, 1101–1109. Bons, P.D., Jessell, M.W., Passchier, C.W., 1993. The analysis of progressive deformation in rock analogues. J. Struct. Geol. 15, 403–411. Buntebarth, G., Voll, G., 1991. Quartz grain coarsening by collective crystallization in contact quartzites. In: Voll, G., Topel, J., Pattison, D.R.M., Seifert, F. (Eds.), Equilibrium and Kinetics in Contact Metamorphism. Springer-Verlag, pp. 251– 265. Hillert, M., 1965. On the theory of normal and abnormal grain growth. Acta Metall. 13, 227–238. Hobbs, B.E., Means, W.D., Williams, P.F., 1976. An Outline of Structural Geology. Wiley, New York, 571 pp. Hu, H., Rath, B.B., 1970. On the time exponent in isothermal
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