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Kinetics of grain growth in anorthite
TECTONOPHYSICS ELSEVIER
Tectonophysics 258 (1996) 251-262
Kinetics of grain growth in anorthite G.
Dresen *, Z. Wang, Q. Bai
~
GeoForschungsZentrum Potsdam, 14473 Potsdam. Germany
Received 22 May 1995; accepted 29 November 1995
Abstract
We investigated the grain growth kinetics of synthetic pure anorthite aggregates. The starting material was prepared from glass and has a homogeneous starting grain size of 3-4/xm. Porosity was less than 1% and the dislocation density was less than 2 X 10 ~ cm -'. The samples were subsequently annealed at temperatures between l l00°C and 1350°C in air from 10 min to 480 h. Grain size was determined optically. We observed normal grain growth for anneals less than 24 h. The grain growth exponent n varied between 2.5-2.7 for different temperatures. We determined the activation energy for grain growth to be 365 + 25 kJ/mol. Microstructural observations show a decrease in aspect ratio of the grains from 2.8 to 1.7 with increasing annealing temperatures and duration.
1. Introduction
Grain size influences many physical and chemical properties of polycrystalline rocks and ceramics; for instance, the chemical diffusion process and the mechanical strength of rocks in different deformation regimes may be affected. Grain size reduction due to dynamic recrystallization may lead to a transition from dislocation creep to diffusion creep (Schmid et al., 1977: Tullis and Yund, 1991; Karato and Wu, 1993) and may promote strain localization (Olgaard, 1990; Drury et al., 1991). In a mylonite shear zone, dynamic equilibrium may be established between grain size reduction related to recrystallization and grain growth (Karato, 1989). Estimates of flow stress
• Corresponding author. Fax: 49-331 288-1302. E-mail: [email protected]. IGPP, University of California at Riverside, Riverside, CA 92521, USA.
in shear zones may be based on the size of recrystallized grains (Twiss, 1977; Ross et al.. 1980: Derby, 1990). Post-tectonic annealing and grain growth can introduce substantial errors in the stress estimates. In frictional faulting, grain size reduction due to fracturing may be compensated by grain growth from Ostwald ripening (Sleep, 1994). Thus, investigating the kinetics of grain growth processes is important in evaluating microstructural development of deformed rocks. The evolution of the average grain size (G) in a polycrystalline aggregate is assumed to be proportional to the average grain boundary velocity, ~, ~ d G / d t , i' depends on the mobility of the grain boundary and the driving force (F). For grain growth the driving force is the grain boundary interracial free energy: a pressure gradient across a curved grain boundary will move the boundary towards its center of curvature. This will reduce the total grain boundary area and the associated free energy of a polycrystalline material. For normal grain growth (Brook,
0040-1951/96/$15.00 © 1996 Elsevier Science B.V. All rights reserved SSDI 0040- 1951 (95)00203-0
G. Dresen et al. / Tectonophysics 258 (1996) 251-262
252
1976), a growth law can be derived on integration of the boundary velocity:
G"-G~=Kt
(1)
where G represents the average grain size after annealing time t, G O is the starting grain size, n is the growth exponent and K is a rate constant. Since grain growth is a thermally activated process, the temperature dependence of K can be expressed as: K = K 0 exp( -
Q/RT)
(2)
where Q is the activation energy for grain growth, K 0 is a constant, R is the gas constant and T is the temperature. The mobility of a grain boundary may be controlled by different mechanisms (Yan et al., 1977; Nichols and Mackwell, 1991). In intrinsic grain growth the mobility of a grain boundary will be limited by the slowest ionic species transferred from the shrinking grain across the boundary to its grow-
ing neighbor. Interaction of the mobile boundary with impurities may result in a drag force. Residual pores, second phase particles or liquid inclusions attached to the grain boundary may reduce mobility and effectively stabilize grain size (Kingery and Francois, 1965: Nichols, 1966; Olgaard and Evans, 1986, 1988). If the grains are wetted by a liquid film the slowest diffusing species across the boundary between neighboring grains may control grain boundary mobility (Kingery et al., 1976). Depending on the rate-limiting mechanism different exponents n in (1) ranging from 2 to 5 are predicted (Brook, 1976). Recently many experimental and field studies of grain growth have been performed on calcite (Tullis and Yund, 1982; Olgaard and Evans, 1986, 1988: Covey-Crump and Rutter, 1989; Olgaard, 1990), quartz (Tullis and Yund, 1982; Karato and Masuda, 1989; Masuda et al., 1991) and olivine (Cooper and
1.00Absorbance Units
0.750.50 0.25 0.00-
Wavenumber cm-1
-0.25 4000
38'00
3600
3400
3200
30'00
2800
2600
A 0.075 0.050
Absorbance Units
0.025 0.000 Wavenumber cm-1 4400
4200
4000
3800
3600
3400
3200
3000
2800
2600
B Fig. 1. (A) Fourier transformed infrared spectrum of the starting glass. A large broad-band absorbency extending from 3700 cm i to 3000 cm -I was observed. It represents a continuum of O - H bond energies in molecular H20 inferred to be present as boundary films, fluid inclusions a n d / o r small domains of molecular H20. The sharp peaks at 2910 cm ~ and 2850 cm t, may result from carbon-hydrogen stretching motions (G.R. Rossman, pers. commun.). (B) Lower spectrum is from a sample annealed at 1200°C for 10 h. Both, large broad-band and sharp absorbencies decreased with annealing time of samples.
G. Dresen et al. / Tectonophysics 258 (19961 251-262
253
Table l Chemical composition of starting material (ICP-MS analysis)
Kohlstedt, 1984; Karato et al., 1986; Karato, 1989; Nichols and Mackwell, 1991; Fisler and Mackwell, 1994). However, we are not aware of a study concerned with the grain growth of feldspar, which is one of the most abundant mineral phases in the middle and lower crust. The goals of this study were to determine the kinetics of grain growth in anorthite and elucidate the physical processes that may govern the grain size of anorthite in nature.
Items
Concentration a
Standard deviation
Ca Al Si Sr Mg Fe Ti K
19.4655 34.9833 46.2104 0.3271 0.1196 0.0641 0.0132 0.0118
0.0625 0.2240 0.1618 0.0261 4.149× 8.773 X 3.922 X 5.159X
I0 :~ 10 10 l0 ~
" -wt.% oxide.
2. Experimental procedures 2.1. Starting material
sistently show a prominent broad-band absorbency at wavelengths from 3700 cm ~ to 3000 cm-~ representing a continuum of O - H bond energies in hydroxyl a n d / o r molecular H20 (Fig. 11, which may be present as fluid inclusions or small domains of H 2 0 in the starting glass monolith. The sharp peaks at 2910 cm -~ and 2850 cm -~, may result from carbon-hydrogen stretching motions due to contamination by organic materials (G.R Rossman, pers. commun.).
For our experiments we used CAS-monolith glass (Calcium-Aluminosilicate Glass from Coming Inc., provided by D. Kohlstedt). Chemical composition of the glass was determined by ICP-MS (InductiveCoupled Plasma Mass Spectrometry) to be anorthite An98 with Sr, Mg, K and Ti as major impurities, with concentrations of 0.33, 0.12, 0.06 and 0.01 wt.%, respectively (see Table 1). FT-IR spectra (Fourier Transformed Infra-Red Spectroscopy) con30
An 100 ( 16 - 32 p,m ) Wt: 94.90 m g Atmosphere: AIR
£3
Scan Rate: 20counts/min 40 cc/min
Peak from : 995 to : 1050.3 O n s e t : 1024.7 Peak Height : 16.45 Peak : 1045.7
15 Peak from : 864.8 to : 920' O n s e t : 871 P e a k Height : -.23 Peak : 889.8
30
i 150
i 270
1 390
i 510
i 630
i 750
i 870
i 990
~
i
Temperature ( C )
Fig. 2. A DTA-spectrum shows the onset temperature of crystallization for An98. The first peak at 871°C indicates the glass transition. The sharp peak at 1024°C indicates the nucleation temperature of anorthite. The heating rate was 20°C/rain.
G. Dresen et al. / Tectonophysics 258 (1996) 251-262
254
The starting material is a fine-grained polycrystalline aggregate of anorthite produced from the CAS-glass monolith. To prepare a desirable starting material, crystallization kinetics of the CAS-glass were investigated with a DTA (Differential Thermal Analysis) technique. Glass samples were heated to maximum temperatures of 1130°C to 1180°C at heating rates from 5 ° to 2 0 ° C / m i n to determine the onset temperature for crystal nucleation in the CAS-glass. The resultant DTA-spectra show generally two peaks (Fig. 2) indicating the sequence of crystallization of CAS-glass. The first peak occurs at 871°C and represents the glass transition, and the second sharp peak occurs at 1024°C and represents the nucleation temperature of anorthite. Higher heating rate will slightly increase the onset temperatures of the glass transition and of nucleation (Ping Li, pers. commun.). Usually, a heating rate of 100°C/min. was applied to fabricate completely crystallized fine-grained (G 0 < 3 /xm) anorthite polycrystals with a homogeneous microstructure. We investigated both the CAS-glass and the starting polycrystalline aggregate by X-ray powder diffraction (Fig. 3). The CAS-glass showed no diffraction peak indicating that only glass was present. The X-ray powder diffraction spectrum showed a number of peaks in the starting polycrystalline aggregate with strong peaks at 2 0 = 2 4 . 1 ° , 27.828.1 ° and 36.6 °, which are characteristic of anorthite. No extra peaks were detected. Transmission electron microscopy (TEM) did not indicate any residual glass or melt in triple junctions or on the grain boundaries to a resolution of less than 5 nm (Fig. 4).
5000. 4000' 204 r o c_)
3000" 2000"
1301040141L004
242
1000" 0
S
20
25
30
35
40
Fig. 4. Transmission electron micrograph(bright field) taken from a sample annealed at temperature T = 1290°C for 13.5 h. No melt or glassy phase was observed on the grain boundaries or at triple junctions. Growth twins are common. Curved grain boundaries can still be seen. Both X-ray and TEM observations showed anorthite as the only major crystalline phase in the starting material. Samples annealed at temperatures higher than 1350°C show very few submicron sized A I 2 0 3 inclusions. The density of the starting polycrystalline aggregate, measured by immersion in ethanol, is 2.75 _+ 0.01 g / c m 3. Porosity, which was evaluated by comparison of measured density of samples with X-ray density of pure anorthite (taken as 2.76 g / c m 3 ) , is less than 1%. The average dislocation density of the starting material measured under TEM was estimated to be smaller than 2 × 1 0 7 c m 2
45
2 Theta
Fig. 3. X-ray diffraction pattern of a synthetic anorthite polycrystal annealed at 1200°C for 1.0 h. Numbers are [hkl}-values of dominant reflections from crystal faces.
2.2. Annealing experiments Subsequent to nucleation and initial crystallization samples of 2 × 2 × 1 mm 3 in size were annealed at
G. Dresen et al. / Tectonophysics 258 (1996) 251-262 Table 2 Grain-sizes of starting anorthite polycrystal, G 0, range from 1.54.0 /zm with average grain size about 2.0 p,m. The grain size of an individual sample listed here is the average of over 400 measurements Sample
T (°C)
t (hours)
G (/~m)
FG -01 FG-02a FG -02b FG-03 FG-04 FG-19 FG-05 FG -06 FG -07 FG-08 FG-09 FG-18 FG-10 FG-II FG-12 FG-13 FG-14 FG-15 FG-20 FG-21 FG-22 FG-23 FG-24 FG-17 FG-16
1093 1093 1093 1093 1093 1093 193 193 193 193 193 193 1291 1291 1291 1291 1291 1291 1291 1350 1350 1350 1350 1275 1384
0.5 2.5 4.5 1.0 13.4 168 4.5 1.1) 2.5 0.3 13.4 168 1.0 2.5 4.5 0.2 13.4 120 480 1.0 2.5 4.5 13.4 48.0 5.0
3.00 6.33 8.52 4.25 10.88 20.02 10.13 4.72 7.83 3.00 15.00 24.90 5.801 11.05 14.56 3.0 21.36 28.60 31.24 9.05 t4.56 22.36 30.12 23.12 27.45
/l 2.7 ~0.1
255
3. Results
3.1. Grain growth The kinetics of grain growth in anorthite were studied at various temperatures and annealing times and the results are summarized in Table 2. Fig. 5 shows the grain size development of anorthite as a function of annealing time at 1093 ° (Fig. 5a), 1193 ° (Fig. 5b) and 1291°C (Fig. 5c). The data measured at
! O0
2.6_+0.1
~..
-I
ncrmal gram growt:q
0
10 o
.E
o
o
2.5+0.1
o '093 ........
i 1
C
........
= ........ J ........ j !0 100 !000 time (hours)
2.5___0.1 100
B F
normal grain - - I growth I
o
10
o o
o
o o o 1193 'C
temperatures between l O00°C and 1400°C in a l-atm. furnace in air. The temperature was controlled to within _+ I°C with two Pt/Pt-13%Rh thermocouples located within 5 mm of the sample. The thermal gradient between sample and thermocouple is less than I°C and the temperature was continuously recorded during the experiments. Annealing times ranged from 10 rain to 480 h. After annealing, samples were quenched to 800°C in 5 rain and then further cooled down to room temperature at a constant rate of 100°C/h. Grain growth was examined in detail at 1100 °, 1200 °, 1290 ° and 1350°C. Average grain size was measured optically in transmission from ultra thin sections (10-30 /zm) to avoid overlap of multiple grains and evaluated using the line intercept method
(Exner, 1972).
1
10
time
10ClO
1C0
(hours)
i O0
~.
normal grain .-~ growth
o
0
o 10.
o o
.E
o 12~1
I
I0
time
IO0
C
~,0 0 0
(hours)
Fig. 5. Grain sizes versus time for samples annealed at temperatures of 1093°C (A), 1193°C (B) and 1291°C (C). The grain size was measured optically using the line intercept method (Exner, 1972). Error bars are smaller than drawing symbols. Grain growth rate decreased after 24 h annealing.
G. Dresen et al. / Tectonophysics 258 (1996) 251-262
256
A
3.5 1093°C 3.0'
2.5'
2.0'
1.5"
,
1.0 -0.5
.
.
.
.
i
.
.
.
i . . . . 0.5
.
0.0 Log
t
, . . . . 1.0
1.5
(hours)
3.51193
°C
3.0 A
plot of log (G" - G~) versus log t until a slope of ~ 1.0 was obtained (Fig. 6). Growth exponents (n) vary from 2.5 at 1291°C to 2.7 at 1093°C (Table 2). With n, the rate constant K for different temperatures can be determined. Fig. 7 shows a plot of log K versus inverse temperature. A linear least squares fit to the data gives an estimate of the activation energy, Q, of 365 +_ 25 kJ/mol. An average of n = 2.6 _+ 0.1 and the constant K 0 is 2.59 + 0.52 × 10-4 (m26_+ 0.1 s 1). The resulting grain growth law obtained for synthetic anorthite polycrystals is: G 2 . 6 + o.1 __ Go.~_+ o.1
_+ 25(kJ/mol)/RT)
Xexp( - 3 6 5
2.0 t~
X 10-4(m26+0ls 1)
= ( 2 . 5 9 _+ 0 . 5 2 )
2 . 5
(3)
1.5
3.2. Microstructure deuelopment 1.0 -0.5
.
.
.
.
i
.
.
.
.
i
0.0
.
.
.
0.5 log
A m
.
i
.
.
.
.
1.0
t
1.5
(hours)
3.5" 1291
cJ
3.0"
m
2.5-
°
~
n
=
l,O
2.0N 1.5-
o~ --
1,0 . . . . -0,5
i . . . . 0.0 log
i . . . . 0.5 t
i . . . . 10
1.5
(hours)
Fig. 6. The data obtained for normal grain growth were used to estimate the growth exponent (n); it varied from 2.5 at 1291°C and 1193°C to 2.7 at 1093°C. In order to determine values of the growth exponent n for each set of experiments at a given temperature, n was varied in a plot of log (G ~ - G~) vs. log t until a slope of 1.0 was obtained.
The grain size of the starting material (G o) is relatively homogeneous and ranges from 1.5-4.0 /zm with an average grain size of ca. 2.5 /zm. Most of the grains are needle-like in shape with a large aspect ratio of about 3 (Figs. 8 and 11). The grain boundaries are highly serrated, curved, and show no equilibrium geometry. Grain growth is fast in the first 24 h with the grain size increasing up to 2 0 - 6 0 /zm depending on annealing temperature. Grains with a more regular prism shape are formed during grain growth. The grain size stays relatively uniform (Figs. 9 A - D and Fig. 10), indicating normal grain growth. 1300 [
.15
1200 I
1100 I
CC)
10 Q = 3 6 5
k J / m o l
t6 10
different annealing temperatures show that increase in grain size (G) follows a growth law (Eq. 1). Normal grain growth is observed for annealing time (t) < 24 h. Grain sizes ranging from 15-50 /xm were obtained at different annealing temperatures. Grain growth slows down for t > 24 h and a stable grain size of 30 to 60 /xm is obtained after 160 h annealing. In order to determine a growth law, exponent n was first evaluated for each set of experiments at constant annealing temperature, n was varied in a
1017
g 18 10 -19 10 6,0
•
i
6,2
,
i
6,4
•
i
6,6
,
i
6,8
,
i
7,0
,
i
7,2
7,4
IO00O/T(K)
Fig. 7. Log of the rate constant K versus inverse temperature for a given growth exponent of n = 2.6. The linear least squares fit to the data gives an estimate of the apparent activation energy of grain growth, Q = 3 6 5 + 2 5 k J / m o l and K o = 2 . 5 9 ( _ + 0 . 5 2 ) × 10 - 4 m 2 6 s - I . The error in K o was estimated from the errors in temperature, annealing time and grain size measurements.
257
G. Dresen et al. / Tectonophysies 258 (1996) 251 262
We noticed four distinct features of the microstructural development associated with grain growth. (1) The boundaries of individual grains became less serrated with time (Fig. 9). During the first 24 h of annealing curvature of the boundaries decreased considerably and at grain junctions angles close to 120 ° are commonly observed optically and in TEM (Fig. 4). (2) The grains became more equant during growth and aspect ratios ( c / a ) decreased from ~ 3 at t = 0.5 h to ~ 1.5 at t = 24 h (Fig. 11). (3) The amount of twinning increases with annealing time. Both the numbers of grains containing twins and the intensity of twinning inside individual grains increase with annealing time. After longer anneals most grains show growth twins with variable width. (4) The dislocation density remains relatively constant during grain growth and is ~ 1.4 × 10 7 c m 2 Voids with a diameter of ~ 50 nm were occasionally observed at the TEM scale in annealed samples, even at T = 1290°C for t > 13.5 h (Fig. 4). Most of the voids were located on the grain boundary a n d / o r triple-junctions. They may have formed during preparation of TEM foils from residual fluid phases in the samples. Spherical intragranular pores
are relatively common. The pores are generally small
(_< 1 ~m). 4. Discussion In general, the velocity of a grain boundary is proportional to the mobility ( M ) and the driving force (F). In the case of normal grain growth, it can be expressed as: z'=M.F=M.o-.
(~7 + ~ ')
(4)
in which p~ and P2 are the principle radii of curvature (Hillert, 1965). Eq. (4) assumes that the grain boundary interfacial free energy is the driving force in normal grain growth. The mobility, M, depends on the specific growth mechanism, which can be evaluated through the grain growth law (Eq. 1), and the rate constant K (Eq. 2). Although the activation energy and the growth exponent n do not indicate unambiguously the specific growth mechanism and the rate-limiting ionic species (Brook, 1976; Yan et al.. 1977), different physical mechanisms of grain
Fig. 8. Optical micrographof the starting material, Nichols crossed. The horizontal scale bar is 20/~m long. The grain size (G0) is relatively homogeneous and ranges from 1.5-4.0 /~m with an average grain size of ca. 2.5 /zm. Most of the grains are needle-like in shape with a large aspect ratio.
258
G. Dresen et al. / Tectonophysics 258 (1996) 251 262
z .6
2 c. ttq C
27 -~-
5
~.z
z
z~
,~_
0
~~ ~.~.~..-
.~ E
0
-
G. Dresen et al. / Tectonophysics 258 (1996) 251-262
259
-fi
rv
G. Dresen et al. / Tectonophysics 258 (1996) 251 262
260 7O
FG-05 T=II93~C,
60o o m
t=4.5
hours
50' 40" 3o j
20. 10" 0
,
125
32
100
200
gr01n size (p m)
A 70
FG-12 T=1291oC,
60" '~
t=4.5
hours
50" 40.
"~ m
;o.
~m
20. !o. o 13
32
B
lOO
20.0
grain size ( u m )
Fig. 10. H i s t o g r a m s of grain size distribution o f samples annealed for 4.5 hours at (A) 1193°C and (B) 1291°C.
growth may show a difference in Q and n. For instance, intrinsic grain growth, in which the mobility of the grain boundary is commonly correlated with the grain boundary diffusivity of the slowest ionic species, is typically characterized by a parabolic growth law with n = 2 (Brook, 1976). Cubic growth (n = 3) can be indicative of pore or second phase control, diffusion through a continuous second phase or impurity drag. However growth exponents be-
4,0 1100
~C
3,5 e~
3,0
.9
2,5
2,0 t 1,0
....
t i ....
i ....
50
100
time
i .... 150
200
(hours)
Fig. I I. Aspect ratio of grains ( c / a ) versus time for samples annealed at T = I100°C. The vertical error bar s h o w s standard deviation o f the average value at a given annealing time.
tween 2 and 3 are often found in pure systems (Kingery et al., 1976; Vandermeer and Hsun, 1994). The synthetic anorthite polycrystals investigated in our study show grain growth with an average growth exponent n = 2.6 +_ 0.1 and an activation energy Q = 365 -I- 25 kJ/mol, values which are relatively constant over the investigated range of temperatures. TEM analysis and X-ray diffraction of the annealed samples show anorthite as the only major phase. Therefore grain boundary mobility is not controlled by dispersed second-phase particles. No melt or glass residues are found even in very fine-grained samples at the TEM scale. Migrating pores attached to grain boundaries frequently control boundary movement (Hsueh and Evans, 1983) and depending on their size, pores may pin the boundary. A stabilized grain size will be reached during the heat treatment when the retarding pressure of the second phase equals the driving pressure for grain boundary migration (Olgaard and Evans, 1986; Nichols and Mackwell, 1991; Liu and Patterson, 1993). Olgaard and Evans (1988) found a qualitative correlation between porosity and grain size for grain growth in pure calcite. Brook (1976) predicts growth exponents n between 2 and 4 for pore controlled kinetics of grain growth. Porosity of the synthetic anorthite aggregates is generally very low ( < 1%) and the observed pores are mostly smaller than 1 p,m. The pores mostly represent fluid inclusions filled with water, which is probably released from the glass phase during crystallization (Fig. 1). Pores migrating with the grain boundaries may coalesce and increase along with the grain size (Brook, 1976). Only anorthite samples subjected to longer anneals ( > 10 h) show optically visible pores, both intragranular and decorating the grain boundaries. Although the porosity of the anorthite aggregates is very low, we suggest, that the dispersed pores may effectively slow down grain growth and lead to the observed stable grain size of 30-60 /zm. Grain boundary diffusion data from experimental and field studies for various oxide and silicate minerals were recently compiled by Joesten (1991). Farver and Yund (1995) found Ca grain boundary diffusion in feldspar aggregates slower than oxygen diffusion along grain boundaries. Thus, oxygen is unlikely to be the rate controlling species for grain growth in
G. Dresen et al./Tectonophysics 258 (1996) 251-262
anorthite. The activation energy for Ca grain boundary diffusion in anorthite was determined as 291 k J / m o l (Farver and Yund, 1995). This is lower than the activation energy for grain growth. To our knowledge no data exists on grain boundary diffusion of AI and Si in feldspar. The activation energies for AI-Si interdiffusion in albite range from 360 k J/tool at room pressure to 280 k J/tool at 200 MPa confining pressure with water added. (Yund and Tullis, 1980). Tullis and Yund (1982) also found that the A1-Si interdiffusion rate is increased by both, on increase in water content at constant pressure and on increase in pressure at constant water content. Thus it is likely, that the presence of water will enhance grain growth kinetics in anorthite, as was observed in olivine (Karato, 1989). Carpenter (1991) found an activation energy of 500-630 k J / m o l for AI-Si interdiffusion in anorthite under dry conditions at room pressure. The diffusion data can be compared to data from creep experiments of synthetic anorthite in the diffusion creep regime. The measured activation energies for diffusion creep are higher and range from 660 _+ 60 k J / m o l (Meyer et al., 1993), 650 ± 40 k J / m o l (Mercer and Chokshi, 1993) to 740 +_ 40 k J / m o l (Montardi, 1987). These are even higher than the activation energies measured so far for cation lattice diffusion in feldspars (Behrens et al., 1990). When considered together the existing data on grain boundary diffusion does not yet permit a conclusion about the identity of the rate-limiting species controlling grain boundary mobility in anorthite. The chemical composition of the glass includes > 0.5 wt.C~ of mostly bivalent impurity cations including St. Fe and Mg. Small amounts of impurities ( < 1%) may affect significantly grain boundary mobility by solute drag through the lattice (Chen and Chen. 1994). If the boundary cannot break away from the impurities its mobility depends on the diffusion of the solute ions near the boundary. The activation energy for Sr diffusion in anorthite was determined by Giletti and Casserly (1994) as 267 kJ/mol. Behrens et al. (1990) measured Fe diffusivity in An~ 6 as a function of oxygen activity, and it appears to be an order of magnitude slower than Sr. It is possible, that the grain boundary mobility of synthetic anorthite is also affected by impurity drag, which could not be separated from the pore drag mechanism.
261
Crystal growth of anorthite polycrystals from a melt is very anisotropic. Growth was found to take place along the c direction preferentially (Klein and Uhlmann, 1974). In their experiments interface morphology was always faceted. The high aspect ratio of the grains in the initial stages of growth after nucleation may be due to anisotropic surface energy varying with orientation of the boundaries. This is supported by faceted grain boundaries, which were observed in some of the annealed samples. It remains unclear, however, why the grains become more equant with a decrease of grain aspect ratio of anorthite during grain growth from about 2.6 to 1.7 (Fig. 11). This observation suggests changes in the mobility of the boundaries during grain growth.
5. Summary We studied grain growth of pure synthetic anorthite and observed normal grain growth for annealing times less than 24 h. The increase in grain size with time follows a growth law with exponent n = 2.6 ± 0.1. We determined the activation energy Q to be 365 _+ 25 kJ/mol. After annealing for more than 24 h, grain growth kinetics become slow due to the reduction of free surface energy and presumably pore drag. A saturated grain size of 30-60 /xm can be reached depending on the annealing temperature. Grain growth in synthetic anorthite is accompanied by changes in the microstructure. Needle-shaped grains become increasingly equant with time and aspect ratios of the grains change from 2.6 to 1.7 after 16 h. The mobility of the grain boundaries may be affected by impurities present in the starting material.
Acknowledgements D. Kohlstedt is gratefully acknowledged for providing the CAS glass sample. We thank Ping Li for the DTA data, R.Wirth for TEM observation and B. Evans and D. Olgaard for helpful discussions, S.Germann for preparing the optical thin sections and TEM foils and G. Rossman for commenting on the FTIR data. Constructive reviews by J. Tullis and S. Mackwell improved the manuscript.
262
G. Dresen et al. / Tectonophysics 258 (1996) 251 262
References Behrens, H., Johannes, W. and Schmalzried, H., 1990. On the mechanism of cation diffusion processes in ternary feldspars. Phys. Chem. Minerals, 17: 62-78. Brook, R.J., 1976. Controlled grain growth. In: F.F.Y. Wang (Editor), Treatise on Materials Science and Technology, 9. Academic Press, London, pp. 331-364. Carpenter, M.A., 199I. Mechanisms and kinetics of AI-Si ordering in anorthite: I. Incommensurate structure and domain coarsening. Am. Mineral., 76:1 110-1119. Chen, P.L. and Chen, 1.W., 1994. Role of defect interaction in boundary mobility and cation diffusivity of CeO,. J. Am. Ceram. Soc., 77: 2289-2297. Cooper, R.F. and Kohlstedt, D.E., 1984. Sintering of olivine and olivine-basalt aggregates. Phys. Chem. Minerals, 11: 5-16. Covey-Crump, S.J. and Rutter, E.H., 1989. Thermally induced grain growth of calcite marbles on Naxos Island, Greece. Contrib. Mineral. Petrol., 101:69 86. Derby, B., 1990. Dynamic recrystallization and grain size. In: D.J. Barber and P.G. Meredith (Editors), Deformation Processes in Minerals, Ceramics and Rocks. Unwin, London, pp. 354-364. Drury, M.R., Vissers, R.L.M., Van der Wal, D. and Strating, E.H.H., 1991. Shear Iocatisation in upper mantle peridotites. Pure Appl. Geophys., 137: 439-460. Exner, H.E., 1972. Analysis of grain and particle size distributions in metallic materials. Int. Metall. Rev., 17: 25-42. Farver, J.R. and Yund, R.A., 1995. Grain boundary diffusion of oxygen, potassium and calcium in natural and hot-pressed feldspar aggregates. Contrib. Mineral. Petrol., 118: 340-355. Fisler, D.K. and Mackwell, S.J., 1994. Kinetics of diffusion-controlled growth of fayalite. Phys. Chem. Minerals, 21 : 156-165. Giletti, B.J. and Casserly, LED., 1994. Strontium diffusion kinetics in plagioclase feldspars. Geochim. Cosmochim. Acta, 58: 3785-3793. Hillert, M., 1965. On the theory of normal and abnormal grain growth. Acta Metall., 13: 227-238. Hsueh, C.H. and Evans, A.G., 1983. Microstructure evolution during sintering: the role of evaporation/condensation. Acta Metall., 31: 189-198. Joesten, R.L., 1991. Kinetics of coarsening and diffusion-controlled mineral growth. In: D.M. Kerrick (Editor), Contact Metamorphism. Rev. Min., 26: 507-582. Karato, S., 1989. Grain growth kinetics in olivine aggregates. Tectonophysics, 168: 255-273. Karato, S. and Wu, P., 1993. Rheology of upper mantle: a synthesis. Science, 260: 771-778. Karato, S. and Masuda, T., 1989. Anisotropic grain growth in quartz aggregates under stress and its implication for foliation development. Geology, 17: 695-698. Karato, S., Paterson, M.S. and FitzGerald, J., 1986. Rheology of synthetic olivine aggregates: influence of grain size and water. J. Geophys. Res., 91: 8151-8176. Kingery, W.D., Bowen, H.K. and Uhlmann, D.R., 1976. Introduction to Ceramics, 2nd ed. Wiley, New York, 1032 pp. Kingery, W.D. and Francois, B., 1965. Grain growth in porous compacts. J. Am. Ceram. Soc., 48: 546-547.
Klein, L. and Uhhnann, D.R., 1974. Crystallization behavior of anorthite. J. Geophys. Res., 79: 4869-4874. Liu, Y. and Patterson, B.R., 1993. Grain growth inhibition by porosity. Acta Metall. Mater., 41: 2651-2656. Masuda, T., Koike, T., Yuko, T. and Morikawa, T., 1991. Discontinuous grain growth of quartz in metacherts: the influence of mica on a microstructural transition. J. Metamorph. Geol., 9: 389-402. Mercer, R.F. and Chokshi, A.H., 1993. The elevated temperature compression creep behavior of a calcium-aluminositicate (Anorthite) glass ceramic. Metall. Mater., 28:1177-1182. Meyer, D.W.. Cooper, R.F. and Plesha, M.E., 1993. High-temperature creep and the interfacial mechanical response of a ceramic matrix composite. Acta Metall. Mater., 41:3157-3170. Montardi, Y.. 1987. Etude du Frittage et de la Deformation Plastique Experimentale de Plagioclases. PhD Thesis Univ. Montpellier II, 249 pp. Nichols, F.A.. 1966. Theory of grain growth in porous compacts. J. Appl. Phys., 37: 4599-4602. Nichols, S.J. and Mackwell, S.J., 199l. Grain growth in porous olivine aggregates. Phys. Chem. Minerals, 18: 269-278. Olgaard, D.L. and Evans, B.. 1986. Effect of second-phase particles on grain growth in calcite. J. Am. Ceram. Sot., 69: C272-C277. Olgaard, D.L. and Evans, B., 1988. Grain growth in synthetic marbles with added mica and water. Contrib. Mineral. Petrol.. 100: 246-260. Olgaard. D.L., 1990. The role of second phases in localizing deformation. In: R.J. Knipe and E.H. Rutter (Editors), Deformation Mechanisms, Rheology and Tectonics. Geol. Soc. Spec. Publ.. 54: 175-181. Ross, J.V., Ave Lallement, H.G. and Carter, N., 1980. Stress dependence of recrystallized-grain and subgrain size in olivine. Tectonophysics, 70: 39-61. Sleep, N.H., 1994. Grain size and chemical controls on the ductile properties of mostly frictional faults at low-temperature hydrothermal conditions. Pure Appl. Geophys., 143: 41-60. Schmid, S.M., Boland, J.N. and Paterson, M.S., 1977. Superplas tic flow in finegrained limestone. Tectonophysics, 4 3 : 2 5 7 291. Tullis, J. and Yund, R.A., 1982. Grain growth kinetics of quartz and calcite aggregates. J. Geol., 90: 301-318. Tullis, J. and Yund, R.A., 1991. Diffusion creep in leldspar aggregates: experimental evidence. J. Struct. Geol., 13: 9871000. Twiss, R.J., 1977. Theory and applicability of a recrystallized grain size paleopiezometer. Pure Appl. Geophys., 115: 227244. Yan, M.F.. Cannon, R.M. and Bowen, H.K., 1977. Grain boundary migration in ceramics. In: R.M. Fulrath and J.A. Pask (Editors), Ceramic Microstructures '76. Westview Press, Boulder, pp. 276-307. Yund. R.A. and Tutlis, J., 1980. The effect of water, pressure and strain on AI/Si order-disorder kinetics in feldspar. Contrib. Mineral. Petrol.. 72: 297-302. Vandermeer, R.A. and Hsun H., 1994. On the grain growth exponent of pure iron. Acta Metall. Mater.. 42:3071-3075.
Tectonophysics 258 (1996) 251-262
Kinetics of grain growth in anorthite G.
Dresen *, Z. Wang, Q. Bai
~
GeoForschungsZentrum Potsdam, 14473 Potsdam. Germany
Received 22 May 1995; accepted 29 November 1995
Abstract
We investigated the grain growth kinetics of synthetic pure anorthite aggregates. The starting material was prepared from glass and has a homogeneous starting grain size of 3-4/xm. Porosity was less than 1% and the dislocation density was less than 2 X 10 ~ cm -'. The samples were subsequently annealed at temperatures between l l00°C and 1350°C in air from 10 min to 480 h. Grain size was determined optically. We observed normal grain growth for anneals less than 24 h. The grain growth exponent n varied between 2.5-2.7 for different temperatures. We determined the activation energy for grain growth to be 365 + 25 kJ/mol. Microstructural observations show a decrease in aspect ratio of the grains from 2.8 to 1.7 with increasing annealing temperatures and duration.
1. Introduction
Grain size influences many physical and chemical properties of polycrystalline rocks and ceramics; for instance, the chemical diffusion process and the mechanical strength of rocks in different deformation regimes may be affected. Grain size reduction due to dynamic recrystallization may lead to a transition from dislocation creep to diffusion creep (Schmid et al., 1977: Tullis and Yund, 1991; Karato and Wu, 1993) and may promote strain localization (Olgaard, 1990; Drury et al., 1991). In a mylonite shear zone, dynamic equilibrium may be established between grain size reduction related to recrystallization and grain growth (Karato, 1989). Estimates of flow stress
• Corresponding author. Fax: 49-331 288-1302. E-mail: [email protected]. IGPP, University of California at Riverside, Riverside, CA 92521, USA.
in shear zones may be based on the size of recrystallized grains (Twiss, 1977; Ross et al.. 1980: Derby, 1990). Post-tectonic annealing and grain growth can introduce substantial errors in the stress estimates. In frictional faulting, grain size reduction due to fracturing may be compensated by grain growth from Ostwald ripening (Sleep, 1994). Thus, investigating the kinetics of grain growth processes is important in evaluating microstructural development of deformed rocks. The evolution of the average grain size (G) in a polycrystalline aggregate is assumed to be proportional to the average grain boundary velocity, ~, ~ d G / d t , i' depends on the mobility of the grain boundary and the driving force (F). For grain growth the driving force is the grain boundary interracial free energy: a pressure gradient across a curved grain boundary will move the boundary towards its center of curvature. This will reduce the total grain boundary area and the associated free energy of a polycrystalline material. For normal grain growth (Brook,
0040-1951/96/$15.00 © 1996 Elsevier Science B.V. All rights reserved SSDI 0040- 1951 (95)00203-0
G. Dresen et al. / Tectonophysics 258 (1996) 251-262
252
1976), a growth law can be derived on integration of the boundary velocity:
G"-G~=Kt
(1)
where G represents the average grain size after annealing time t, G O is the starting grain size, n is the growth exponent and K is a rate constant. Since grain growth is a thermally activated process, the temperature dependence of K can be expressed as: K = K 0 exp( -
Q/RT)
(2)
where Q is the activation energy for grain growth, K 0 is a constant, R is the gas constant and T is the temperature. The mobility of a grain boundary may be controlled by different mechanisms (Yan et al., 1977; Nichols and Mackwell, 1991). In intrinsic grain growth the mobility of a grain boundary will be limited by the slowest ionic species transferred from the shrinking grain across the boundary to its grow-
ing neighbor. Interaction of the mobile boundary with impurities may result in a drag force. Residual pores, second phase particles or liquid inclusions attached to the grain boundary may reduce mobility and effectively stabilize grain size (Kingery and Francois, 1965: Nichols, 1966; Olgaard and Evans, 1986, 1988). If the grains are wetted by a liquid film the slowest diffusing species across the boundary between neighboring grains may control grain boundary mobility (Kingery et al., 1976). Depending on the rate-limiting mechanism different exponents n in (1) ranging from 2 to 5 are predicted (Brook, 1976). Recently many experimental and field studies of grain growth have been performed on calcite (Tullis and Yund, 1982; Olgaard and Evans, 1986, 1988: Covey-Crump and Rutter, 1989; Olgaard, 1990), quartz (Tullis and Yund, 1982; Karato and Masuda, 1989; Masuda et al., 1991) and olivine (Cooper and
1.00Absorbance Units
0.750.50 0.25 0.00-
Wavenumber cm-1
-0.25 4000
38'00
3600
3400
3200
30'00
2800
2600
A 0.075 0.050
Absorbance Units
0.025 0.000 Wavenumber cm-1 4400
4200
4000
3800
3600
3400
3200
3000
2800
2600
B Fig. 1. (A) Fourier transformed infrared spectrum of the starting glass. A large broad-band absorbency extending from 3700 cm i to 3000 cm -I was observed. It represents a continuum of O - H bond energies in molecular H20 inferred to be present as boundary films, fluid inclusions a n d / o r small domains of molecular H20. The sharp peaks at 2910 cm ~ and 2850 cm t, may result from carbon-hydrogen stretching motions (G.R. Rossman, pers. commun.). (B) Lower spectrum is from a sample annealed at 1200°C for 10 h. Both, large broad-band and sharp absorbencies decreased with annealing time of samples.
G. Dresen et al. / Tectonophysics 258 (19961 251-262
253
Table l Chemical composition of starting material (ICP-MS analysis)
Kohlstedt, 1984; Karato et al., 1986; Karato, 1989; Nichols and Mackwell, 1991; Fisler and Mackwell, 1994). However, we are not aware of a study concerned with the grain growth of feldspar, which is one of the most abundant mineral phases in the middle and lower crust. The goals of this study were to determine the kinetics of grain growth in anorthite and elucidate the physical processes that may govern the grain size of anorthite in nature.
Items
Concentration a
Standard deviation
Ca Al Si Sr Mg Fe Ti K
19.4655 34.9833 46.2104 0.3271 0.1196 0.0641 0.0132 0.0118
0.0625 0.2240 0.1618 0.0261 4.149× 8.773 X 3.922 X 5.159X
I0 :~ 10 10 l0 ~
" -wt.% oxide.
2. Experimental procedures 2.1. Starting material
sistently show a prominent broad-band absorbency at wavelengths from 3700 cm ~ to 3000 cm-~ representing a continuum of O - H bond energies in hydroxyl a n d / o r molecular H20 (Fig. 11, which may be present as fluid inclusions or small domains of H 2 0 in the starting glass monolith. The sharp peaks at 2910 cm -~ and 2850 cm -~, may result from carbon-hydrogen stretching motions due to contamination by organic materials (G.R Rossman, pers. commun.).
For our experiments we used CAS-monolith glass (Calcium-Aluminosilicate Glass from Coming Inc., provided by D. Kohlstedt). Chemical composition of the glass was determined by ICP-MS (InductiveCoupled Plasma Mass Spectrometry) to be anorthite An98 with Sr, Mg, K and Ti as major impurities, with concentrations of 0.33, 0.12, 0.06 and 0.01 wt.%, respectively (see Table 1). FT-IR spectra (Fourier Transformed Infra-Red Spectroscopy) con30
An 100 ( 16 - 32 p,m ) Wt: 94.90 m g Atmosphere: AIR
£3
Scan Rate: 20counts/min 40 cc/min
Peak from : 995 to : 1050.3 O n s e t : 1024.7 Peak Height : 16.45 Peak : 1045.7
15 Peak from : 864.8 to : 920' O n s e t : 871 P e a k Height : -.23 Peak : 889.8
30
i 150
i 270
1 390
i 510
i 630
i 750
i 870
i 990
~
i
Temperature ( C )
Fig. 2. A DTA-spectrum shows the onset temperature of crystallization for An98. The first peak at 871°C indicates the glass transition. The sharp peak at 1024°C indicates the nucleation temperature of anorthite. The heating rate was 20°C/rain.
G. Dresen et al. / Tectonophysics 258 (1996) 251-262
254
The starting material is a fine-grained polycrystalline aggregate of anorthite produced from the CAS-glass monolith. To prepare a desirable starting material, crystallization kinetics of the CAS-glass were investigated with a DTA (Differential Thermal Analysis) technique. Glass samples were heated to maximum temperatures of 1130°C to 1180°C at heating rates from 5 ° to 2 0 ° C / m i n to determine the onset temperature for crystal nucleation in the CAS-glass. The resultant DTA-spectra show generally two peaks (Fig. 2) indicating the sequence of crystallization of CAS-glass. The first peak occurs at 871°C and represents the glass transition, and the second sharp peak occurs at 1024°C and represents the nucleation temperature of anorthite. Higher heating rate will slightly increase the onset temperatures of the glass transition and of nucleation (Ping Li, pers. commun.). Usually, a heating rate of 100°C/min. was applied to fabricate completely crystallized fine-grained (G 0 < 3 /xm) anorthite polycrystals with a homogeneous microstructure. We investigated both the CAS-glass and the starting polycrystalline aggregate by X-ray powder diffraction (Fig. 3). The CAS-glass showed no diffraction peak indicating that only glass was present. The X-ray powder diffraction spectrum showed a number of peaks in the starting polycrystalline aggregate with strong peaks at 2 0 = 2 4 . 1 ° , 27.828.1 ° and 36.6 °, which are characteristic of anorthite. No extra peaks were detected. Transmission electron microscopy (TEM) did not indicate any residual glass or melt in triple junctions or on the grain boundaries to a resolution of less than 5 nm (Fig. 4).
5000. 4000' 204 r o c_)
3000" 2000"
1301040141L004
242
1000" 0
S
20
25
30
35
40
Fig. 4. Transmission electron micrograph(bright field) taken from a sample annealed at temperature T = 1290°C for 13.5 h. No melt or glassy phase was observed on the grain boundaries or at triple junctions. Growth twins are common. Curved grain boundaries can still be seen. Both X-ray and TEM observations showed anorthite as the only major crystalline phase in the starting material. Samples annealed at temperatures higher than 1350°C show very few submicron sized A I 2 0 3 inclusions. The density of the starting polycrystalline aggregate, measured by immersion in ethanol, is 2.75 _+ 0.01 g / c m 3. Porosity, which was evaluated by comparison of measured density of samples with X-ray density of pure anorthite (taken as 2.76 g / c m 3 ) , is less than 1%. The average dislocation density of the starting material measured under TEM was estimated to be smaller than 2 × 1 0 7 c m 2
45
2 Theta
Fig. 3. X-ray diffraction pattern of a synthetic anorthite polycrystal annealed at 1200°C for 1.0 h. Numbers are [hkl}-values of dominant reflections from crystal faces.
2.2. Annealing experiments Subsequent to nucleation and initial crystallization samples of 2 × 2 × 1 mm 3 in size were annealed at
G. Dresen et al. / Tectonophysics 258 (1996) 251-262 Table 2 Grain-sizes of starting anorthite polycrystal, G 0, range from 1.54.0 /zm with average grain size about 2.0 p,m. The grain size of an individual sample listed here is the average of over 400 measurements Sample
T (°C)
t (hours)
G (/~m)
FG -01 FG-02a FG -02b FG-03 FG-04 FG-19 FG-05 FG -06 FG -07 FG-08 FG-09 FG-18 FG-10 FG-II FG-12 FG-13 FG-14 FG-15 FG-20 FG-21 FG-22 FG-23 FG-24 FG-17 FG-16
1093 1093 1093 1093 1093 1093 193 193 193 193 193 193 1291 1291 1291 1291 1291 1291 1291 1350 1350 1350 1350 1275 1384
0.5 2.5 4.5 1.0 13.4 168 4.5 1.1) 2.5 0.3 13.4 168 1.0 2.5 4.5 0.2 13.4 120 480 1.0 2.5 4.5 13.4 48.0 5.0
3.00 6.33 8.52 4.25 10.88 20.02 10.13 4.72 7.83 3.00 15.00 24.90 5.801 11.05 14.56 3.0 21.36 28.60 31.24 9.05 t4.56 22.36 30.12 23.12 27.45
/l 2.7 ~0.1
255
3. Results
3.1. Grain growth The kinetics of grain growth in anorthite were studied at various temperatures and annealing times and the results are summarized in Table 2. Fig. 5 shows the grain size development of anorthite as a function of annealing time at 1093 ° (Fig. 5a), 1193 ° (Fig. 5b) and 1291°C (Fig. 5c). The data measured at
! O0
2.6_+0.1
~..
-I
ncrmal gram growt:q
0
10 o
.E
o
o
2.5+0.1
o '093 ........
i 1
C
........
= ........ J ........ j !0 100 !000 time (hours)
2.5___0.1 100
B F
normal grain - - I growth I
o
10
o o
o
o o o 1193 'C
temperatures between l O00°C and 1400°C in a l-atm. furnace in air. The temperature was controlled to within _+ I°C with two Pt/Pt-13%Rh thermocouples located within 5 mm of the sample. The thermal gradient between sample and thermocouple is less than I°C and the temperature was continuously recorded during the experiments. Annealing times ranged from 10 rain to 480 h. After annealing, samples were quenched to 800°C in 5 rain and then further cooled down to room temperature at a constant rate of 100°C/h. Grain growth was examined in detail at 1100 °, 1200 °, 1290 ° and 1350°C. Average grain size was measured optically in transmission from ultra thin sections (10-30 /zm) to avoid overlap of multiple grains and evaluated using the line intercept method
(Exner, 1972).
1
10
time
10ClO
1C0
(hours)
i O0
~.
normal grain .-~ growth
o
0
o 10.
o o
.E
o 12~1
I
I0
time
IO0
C
~,0 0 0
(hours)
Fig. 5. Grain sizes versus time for samples annealed at temperatures of 1093°C (A), 1193°C (B) and 1291°C (C). The grain size was measured optically using the line intercept method (Exner, 1972). Error bars are smaller than drawing symbols. Grain growth rate decreased after 24 h annealing.
G. Dresen et al. / Tectonophysics 258 (1996) 251-262
256
A
3.5 1093°C 3.0'
2.5'
2.0'
1.5"
,
1.0 -0.5
.
.
.
.
i
.
.
.
i . . . . 0.5
.
0.0 Log
t
, . . . . 1.0
1.5
(hours)
3.51193
°C
3.0 A
plot of log (G" - G~) versus log t until a slope of ~ 1.0 was obtained (Fig. 6). Growth exponents (n) vary from 2.5 at 1291°C to 2.7 at 1093°C (Table 2). With n, the rate constant K for different temperatures can be determined. Fig. 7 shows a plot of log K versus inverse temperature. A linear least squares fit to the data gives an estimate of the activation energy, Q, of 365 +_ 25 kJ/mol. An average of n = 2.6 _+ 0.1 and the constant K 0 is 2.59 + 0.52 × 10-4 (m26_+ 0.1 s 1). The resulting grain growth law obtained for synthetic anorthite polycrystals is: G 2 . 6 + o.1 __ Go.~_+ o.1
_+ 25(kJ/mol)/RT)
Xexp( - 3 6 5
2.0 t~
X 10-4(m26+0ls 1)
= ( 2 . 5 9 _+ 0 . 5 2 )
2 . 5
(3)
1.5
3.2. Microstructure deuelopment 1.0 -0.5
.
.
.
.
i
.
.
.
.
i
0.0
.
.
.
0.5 log
A m
.
i
.
.
.
.
1.0
t
1.5
(hours)
3.5" 1291
cJ
3.0"
m
2.5-
°
~
n
=
l,O
2.0N 1.5-
o~ --
1,0 . . . . -0,5
i . . . . 0.0 log
i . . . . 0.5 t
i . . . . 10
1.5
(hours)
Fig. 6. The data obtained for normal grain growth were used to estimate the growth exponent (n); it varied from 2.5 at 1291°C and 1193°C to 2.7 at 1093°C. In order to determine values of the growth exponent n for each set of experiments at a given temperature, n was varied in a plot of log (G ~ - G~) vs. log t until a slope of 1.0 was obtained.
The grain size of the starting material (G o) is relatively homogeneous and ranges from 1.5-4.0 /zm with an average grain size of ca. 2.5 /zm. Most of the grains are needle-like in shape with a large aspect ratio of about 3 (Figs. 8 and 11). The grain boundaries are highly serrated, curved, and show no equilibrium geometry. Grain growth is fast in the first 24 h with the grain size increasing up to 2 0 - 6 0 /zm depending on annealing temperature. Grains with a more regular prism shape are formed during grain growth. The grain size stays relatively uniform (Figs. 9 A - D and Fig. 10), indicating normal grain growth. 1300 [
.15
1200 I
1100 I
CC)
10 Q = 3 6 5
k J / m o l
t6 10
different annealing temperatures show that increase in grain size (G) follows a growth law (Eq. 1). Normal grain growth is observed for annealing time (t) < 24 h. Grain sizes ranging from 15-50 /xm were obtained at different annealing temperatures. Grain growth slows down for t > 24 h and a stable grain size of 30 to 60 /xm is obtained after 160 h annealing. In order to determine a growth law, exponent n was first evaluated for each set of experiments at constant annealing temperature, n was varied in a
1017
g 18 10 -19 10 6,0
•
i
6,2
,
i
6,4
•
i
6,6
,
i
6,8
,
i
7,0
,
i
7,2
7,4
IO00O/T(K)
Fig. 7. Log of the rate constant K versus inverse temperature for a given growth exponent of n = 2.6. The linear least squares fit to the data gives an estimate of the apparent activation energy of grain growth, Q = 3 6 5 + 2 5 k J / m o l and K o = 2 . 5 9 ( _ + 0 . 5 2 ) × 10 - 4 m 2 6 s - I . The error in K o was estimated from the errors in temperature, annealing time and grain size measurements.
257
G. Dresen et al. / Tectonophysies 258 (1996) 251 262
We noticed four distinct features of the microstructural development associated with grain growth. (1) The boundaries of individual grains became less serrated with time (Fig. 9). During the first 24 h of annealing curvature of the boundaries decreased considerably and at grain junctions angles close to 120 ° are commonly observed optically and in TEM (Fig. 4). (2) The grains became more equant during growth and aspect ratios ( c / a ) decreased from ~ 3 at t = 0.5 h to ~ 1.5 at t = 24 h (Fig. 11). (3) The amount of twinning increases with annealing time. Both the numbers of grains containing twins and the intensity of twinning inside individual grains increase with annealing time. After longer anneals most grains show growth twins with variable width. (4) The dislocation density remains relatively constant during grain growth and is ~ 1.4 × 10 7 c m 2 Voids with a diameter of ~ 50 nm were occasionally observed at the TEM scale in annealed samples, even at T = 1290°C for t > 13.5 h (Fig. 4). Most of the voids were located on the grain boundary a n d / o r triple-junctions. They may have formed during preparation of TEM foils from residual fluid phases in the samples. Spherical intragranular pores
are relatively common. The pores are generally small
(_< 1 ~m). 4. Discussion In general, the velocity of a grain boundary is proportional to the mobility ( M ) and the driving force (F). In the case of normal grain growth, it can be expressed as: z'=M.F=M.o-.
(~7 + ~ ')
(4)
in which p~ and P2 are the principle radii of curvature (Hillert, 1965). Eq. (4) assumes that the grain boundary interfacial free energy is the driving force in normal grain growth. The mobility, M, depends on the specific growth mechanism, which can be evaluated through the grain growth law (Eq. 1), and the rate constant K (Eq. 2). Although the activation energy and the growth exponent n do not indicate unambiguously the specific growth mechanism and the rate-limiting ionic species (Brook, 1976; Yan et al.. 1977), different physical mechanisms of grain
Fig. 8. Optical micrographof the starting material, Nichols crossed. The horizontal scale bar is 20/~m long. The grain size (G0) is relatively homogeneous and ranges from 1.5-4.0 /~m with an average grain size of ca. 2.5 /zm. Most of the grains are needle-like in shape with a large aspect ratio.
258
G. Dresen et al. / Tectonophysics 258 (1996) 251 262
z .6
2 c. ttq C
27 -~-
5
~.z
z
z~
,~_
0
~~ ~.~.~..-
.~ E
0
-
G. Dresen et al. / Tectonophysics 258 (1996) 251-262
259
-fi
rv
G. Dresen et al. / Tectonophysics 258 (1996) 251 262
260 7O
FG-05 T=II93~C,
60o o m
t=4.5
hours
50' 40" 3o j
20. 10" 0
,
125
32
100
200
gr01n size (p m)
A 70
FG-12 T=1291oC,
60" '~
t=4.5
hours
50" 40.
"~ m
;o.
~m
20. !o. o 13
32
B
lOO
20.0
grain size ( u m )
Fig. 10. H i s t o g r a m s of grain size distribution o f samples annealed for 4.5 hours at (A) 1193°C and (B) 1291°C.
growth may show a difference in Q and n. For instance, intrinsic grain growth, in which the mobility of the grain boundary is commonly correlated with the grain boundary diffusivity of the slowest ionic species, is typically characterized by a parabolic growth law with n = 2 (Brook, 1976). Cubic growth (n = 3) can be indicative of pore or second phase control, diffusion through a continuous second phase or impurity drag. However growth exponents be-
4,0 1100
~C
3,5 e~
3,0
.9
2,5
2,0 t 1,0
....
t i ....
i ....
50
100
time
i .... 150
200
(hours)
Fig. I I. Aspect ratio of grains ( c / a ) versus time for samples annealed at T = I100°C. The vertical error bar s h o w s standard deviation o f the average value at a given annealing time.
tween 2 and 3 are often found in pure systems (Kingery et al., 1976; Vandermeer and Hsun, 1994). The synthetic anorthite polycrystals investigated in our study show grain growth with an average growth exponent n = 2.6 +_ 0.1 and an activation energy Q = 365 -I- 25 kJ/mol, values which are relatively constant over the investigated range of temperatures. TEM analysis and X-ray diffraction of the annealed samples show anorthite as the only major phase. Therefore grain boundary mobility is not controlled by dispersed second-phase particles. No melt or glass residues are found even in very fine-grained samples at the TEM scale. Migrating pores attached to grain boundaries frequently control boundary movement (Hsueh and Evans, 1983) and depending on their size, pores may pin the boundary. A stabilized grain size will be reached during the heat treatment when the retarding pressure of the second phase equals the driving pressure for grain boundary migration (Olgaard and Evans, 1986; Nichols and Mackwell, 1991; Liu and Patterson, 1993). Olgaard and Evans (1988) found a qualitative correlation between porosity and grain size for grain growth in pure calcite. Brook (1976) predicts growth exponents n between 2 and 4 for pore controlled kinetics of grain growth. Porosity of the synthetic anorthite aggregates is generally very low ( < 1%) and the observed pores are mostly smaller than 1 p,m. The pores mostly represent fluid inclusions filled with water, which is probably released from the glass phase during crystallization (Fig. 1). Pores migrating with the grain boundaries may coalesce and increase along with the grain size (Brook, 1976). Only anorthite samples subjected to longer anneals ( > 10 h) show optically visible pores, both intragranular and decorating the grain boundaries. Although the porosity of the anorthite aggregates is very low, we suggest, that the dispersed pores may effectively slow down grain growth and lead to the observed stable grain size of 30-60 /zm. Grain boundary diffusion data from experimental and field studies for various oxide and silicate minerals were recently compiled by Joesten (1991). Farver and Yund (1995) found Ca grain boundary diffusion in feldspar aggregates slower than oxygen diffusion along grain boundaries. Thus, oxygen is unlikely to be the rate controlling species for grain growth in
G. Dresen et al./Tectonophysics 258 (1996) 251-262
anorthite. The activation energy for Ca grain boundary diffusion in anorthite was determined as 291 k J / m o l (Farver and Yund, 1995). This is lower than the activation energy for grain growth. To our knowledge no data exists on grain boundary diffusion of AI and Si in feldspar. The activation energies for AI-Si interdiffusion in albite range from 360 k J/tool at room pressure to 280 k J/tool at 200 MPa confining pressure with water added. (Yund and Tullis, 1980). Tullis and Yund (1982) also found that the A1-Si interdiffusion rate is increased by both, on increase in water content at constant pressure and on increase in pressure at constant water content. Thus it is likely, that the presence of water will enhance grain growth kinetics in anorthite, as was observed in olivine (Karato, 1989). Carpenter (1991) found an activation energy of 500-630 k J / m o l for AI-Si interdiffusion in anorthite under dry conditions at room pressure. The diffusion data can be compared to data from creep experiments of synthetic anorthite in the diffusion creep regime. The measured activation energies for diffusion creep are higher and range from 660 _+ 60 k J / m o l (Meyer et al., 1993), 650 ± 40 k J / m o l (Mercer and Chokshi, 1993) to 740 +_ 40 k J / m o l (Montardi, 1987). These are even higher than the activation energies measured so far for cation lattice diffusion in feldspars (Behrens et al., 1990). When considered together the existing data on grain boundary diffusion does not yet permit a conclusion about the identity of the rate-limiting species controlling grain boundary mobility in anorthite. The chemical composition of the glass includes > 0.5 wt.C~ of mostly bivalent impurity cations including St. Fe and Mg. Small amounts of impurities ( < 1%) may affect significantly grain boundary mobility by solute drag through the lattice (Chen and Chen. 1994). If the boundary cannot break away from the impurities its mobility depends on the diffusion of the solute ions near the boundary. The activation energy for Sr diffusion in anorthite was determined by Giletti and Casserly (1994) as 267 kJ/mol. Behrens et al. (1990) measured Fe diffusivity in An~ 6 as a function of oxygen activity, and it appears to be an order of magnitude slower than Sr. It is possible, that the grain boundary mobility of synthetic anorthite is also affected by impurity drag, which could not be separated from the pore drag mechanism.
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Crystal growth of anorthite polycrystals from a melt is very anisotropic. Growth was found to take place along the c direction preferentially (Klein and Uhlmann, 1974). In their experiments interface morphology was always faceted. The high aspect ratio of the grains in the initial stages of growth after nucleation may be due to anisotropic surface energy varying with orientation of the boundaries. This is supported by faceted grain boundaries, which were observed in some of the annealed samples. It remains unclear, however, why the grains become more equant with a decrease of grain aspect ratio of anorthite during grain growth from about 2.6 to 1.7 (Fig. 11). This observation suggests changes in the mobility of the boundaries during grain growth.
5. Summary We studied grain growth of pure synthetic anorthite and observed normal grain growth for annealing times less than 24 h. The increase in grain size with time follows a growth law with exponent n = 2.6 ± 0.1. We determined the activation energy Q to be 365 _+ 25 kJ/mol. After annealing for more than 24 h, grain growth kinetics become slow due to the reduction of free surface energy and presumably pore drag. A saturated grain size of 30-60 /xm can be reached depending on the annealing temperature. Grain growth in synthetic anorthite is accompanied by changes in the microstructure. Needle-shaped grains become increasingly equant with time and aspect ratios of the grains change from 2.6 to 1.7 after 16 h. The mobility of the grain boundaries may be affected by impurities present in the starting material.
Acknowledgements D. Kohlstedt is gratefully acknowledged for providing the CAS glass sample. We thank Ping Li for the DTA data, R.Wirth for TEM observation and B. Evans and D. Olgaard for helpful discussions, S.Germann for preparing the optical thin sections and TEM foils and G. Rossman for commenting on the FTIR data. Constructive reviews by J. Tullis and S. Mackwell improved the manuscript.
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