Grain growth of camphor as a rock analogue: microstructural development and grain growth law

Abstract

Grain growth experiments were performed on rhombohedral camphor as a rock analogue at 24 °C [i.e., room temperature (RT)] and higher temperatures of 31, 35, 43, and 50 °C. The experiments were very simple compared with those on rocks, which require special apparatuses. The ground sample of camphor was pressed on a glass slide, and a thermometer was set next to the sample. The two-dimensional see-through experiment was performed at RT under a polarizing microscope. The evolving microstructures were clearly observable and showed real-time grain boundary migration by grain growth and the consumption of smaller grains by neighboring larger grains. The result was a consistent increase in grain size from ∼ 10 to ∼ 40 µm in 2 h. The higher-temperature experiments were performed on a hot plate. A glass slide and a weight that had been preheated on the hot plate were placed on top of the glass slide that contained the pressed sample and thermometer. The increase in grain size was controlled by increasing the temperature, with the temperature being held for the same durations. The grain size data in the case of grain growth were analyzed with the grain growth law of dⁿ − d₀ⁿ = k₀ exp(−Q/RT)t, where d (µm) is the grain size at time t (s), d₀ (µm) is the initial grain size, n is the grain growth exponent, k₀ (µmⁿ/s) is a constant, Q (kJ/mol) is the activation energy, R is the gas constant, and T is the temperature in Kelvin. The determined parameters were n = 3.7 ± 0.2, k₀ = 10^−12.7±0.1, and Q = 60.4 ± 6.1.

INTRODUCTION

Grain growth is an important process that has the potential to change the behavior of rock deformation and reactions controlled by grain size. For example, grain growth in nature may change the states of stress and strain rate of grain-size-sensitive creep (e.g., diffusion creep and grain boundary sliding), and it may also explain the transition at a certain grain size from grain-size-sensitive creep to grain-size-insensitive creep such as dislocation creep (e.g., Wightman et al., 2006; Campbell and Menegon, 2019). In addition, grain growth caused by intrusion of an igneous body as a heat source may change the original texture of pre-existing rock, and the changing grain size may therefore record the history of the thermal event (e.g., Joesten, 1983; Okudaira et al., 2013; Mori et al., 2015).

Many experimental studies have investigated the behavior of grain growth in monomineralic aggregates with a focus on quartz (Tullis and Yund, 1982; Michibayashi and Imoto, 2012; Fukuda et al., 2019; Tokle and Hirth, 2021), calcite, dolomite, and/or magnesite (Tullis and Yund, 1982; Olgaard and Evans, 1988; Covey-Crump, 1997; Davis et al., 2011), anorthite (Dresen et al., 1996), and olivine (Karato, 1989). Karato (2008) provided data on other minerals and a review of the topic. However, experiments on mineral aggregates require special large apparatuses such as solid-pressure-medium and gas-pressure-medium apparatuses. In addition, such experiments need to be performed under very high pressures and temperatures (e.g., ∼ 1 GPa and ∼ 1000 °C) to accelerate grain growth processes that take much longer in nature (e.g., thousands or millions of years). In such experimental setups, samples are enclosed in a metal jacket, and many other experimental pieces are assembled. The sample needs to be removed from the assembly after each experiment to observe the frozen microstructure. This approach has the benefit of providing information on actual rocks, but limited information on temporal evolution of the microstructures is obtained relative to the effort and cost required to run the experiment.

Experiments using rock analogues such as ice, salt, and organic matter are more easily performed than those using rocks, as they require simpler equipment and can be performed under lower pressures and temperatures. Note that these materials are crystalline, which means that their basic physics is applicable to rocks, although their crystal systems may need to be considered. Previous grain growth and deformation experiments on rock analogues (for a review, see Piazolo et al., 2019) have revealed microstructural processes similar to those reported in rocks. Rhombohedral camphor, C₁₀H₁₆O, which was used in this study, is stable at <92 °C, becomes cubic at ≥92 °C, and melts at 179 °C. It has been used for see-through grain growth and deformation experiments (Urai et al., 1980; Urai and Humphreys, 1981; Bons and Urai, 1996; Urai and Humphreys, 2000; Schmatz and Urai, 2010; Schmatz et al., 2011). Another major organic material used for rock analogue experiments is octachloropropane, C₃Cl₈, which is hexagonal with a melting temperature of 160 °C (McCrone, 1949; Jessell, 1986; Means and Ree, 1988; Bons and Urai, 1992, 1996; Nam et al., 1999; Urai and Humphreys, 2000). Otoh (1994) and Urai and Humphreys (2000) provide a summary of the materials that can be used as rock analogues.

Previous studies on rock analogues have focused mainly on deformation and grain size was increased by grain growth to the scale of hundreds of micrometers. Then, local processes involving a few neighboring grains were directly observed under a microscope in see-through experiments. However, the microstructural evolution during the growth of a larger number of grains (e.g., hundreds) has not been sufficiently reported. In addition, only limited amounts of quantitative data on grain growth have been obtained in previous experiments, although the initial grain size before subsequent deformation experiments is important; e.g., experiments on octachloropropane by McCrone (1949) and Nam et al. (1999). Nam et al. (1999) performed grain growth experiments at room temperature (RT) and higher temperatures up to 60 °C for durations of up to ∼ 47 days. All the above earlier experiments using rock analogues were performed with specially made apparatus that had been designed mainly for deformation experiments.

In the present study, camphor was used as a rock analogue, and grain growth experiments were performed with a very simple technique. See-through experiments were performed under an optical polarizing microscope at RT, and this paper describes how microstructures were developed by grain growth within just 2 h. A hot plate was used for experiments at higher temperatures of 31-50 °C. Qualitative grain growth data are presented for camphor and a grain growth law is established.

EXPERIMENTAL PROCEDURES

Sample preparation

Natural camphor was ground in an alumina mortar, and ∼ 5 mg of the ground powder was placed on a glass slide and pressed under another glass slide. In this way, a dense area of camphor with a thickness of 100-200 µm was prepared. Photomicrographs were taken at RT under a polarizing microscope before experiments at RT or higher temperatures. These photomicrographs were used to determine the initial grain sizes. Image acquisition at RT before each experiment was completed within 1 min because the grain size increases by a few micrometers, especially within a few minutes of the beginning of the experiment as a result of grain growth.

Experiment at RT

A see-through experiment at RT was performed under a polarizing microscope. A digital microscope camera with a CMOS sensor (Flexacam C3, Leica Microsystems) was placed on top of the microscope and connected to a monitor (Fig. 1a). A thin thermometer with a flexible cable (MonotaRO, order code 68283793) was placed next to the pressed sample on the glass slide and a cover glass slide was set on top (Fig. 1b). The sensor part of the thermometer is 1.0 mm long × 0.5 mm wide × 0.5 mm thick (The schematic image is shown in Fig. 2a). The sample is 100-200 µm thick, as stated above. Therefore, the cover glass slide over the pressed sample is supported by the sensor of the thermometer and does not disturb the sample surface. The temperature displayed on the thermometer increased from the atmospheric temperature by a few °C due to light irradiation, but RT became stable at 24 °C during the experiment. Immediately after taking the first photomicrograph under the 10× objective lens, the microstructural changes due to grain growth were recorded. The recording stopped every 30 min due to the specifications of the equipment. Photomicrographs were taken under the 4× objective lens to ensure enough grains were included for counting, especially when the grain size increased. This was done within ∼ 30 s so it did not affect the grain growth recording. Then, a new video was started immediately after the image acquisition, and 30-min recordings were repeated. The 30-min videos were later spliced together. A count-up timer and a scale were added in the spliced video.

Figure 1. Setup of the see-through experiment at RT (24 °C). (a) The entire setup. (b) Sample stage including the pressed sample on a glass slide (inset), the thermometer placed adjacent to the sample, and the cover glass slide.

Figure 2. Schematic diagram (a) and photograph (b) of the higher-temperature experiments (up to 50 °C). In (b), the weight is a piece of granite, and the thermometer is set next to the assembly shown in (a). The sensor part of the thermometer shown as a black tip in (a) is 1.0 mm long × 0.5 mm wide × 0.5 mm thick and the sample thickness is 100-200 µm. Therefore, the upper glass slide and weight over the pressed sample are supported by the sensor of the thermometer and do not disturb the sample surface. (c) and (d) Optical photomicrographs of two experiments under plane-polarized, cross-polarized, or reflected light, as indicated on each photomicrograph along with the experiment temperature and duration. The scale shown on Figure 2c-1 applies to all four photomicrographs. Note that the clearest microstructures are observable under plane-polarized light. The photomicrographs taken under plane-polarized light during the higher-temperature experiments are shown in Supplementary Figures S1-S6 (Supplementary Figs. S1-S6 are available online from https://doi.org/10.2465/jmps.240229).

Experiments at higher temperatures

Grain growth experiments were performed at 31, 35, 43, and 50 °C on a hot plate (EHP-170N, AS ONE) (Fig. 2). The pressed sample and thermometer were placed on the glass slides in the same way as for the experiment at RT. In the higher-temperature experiments, another glass slide and a weight made of granite were preheated to the desired temperature on a hot plate and then placed on top of the sample (Fig. 2a). The upper glass slide and weight helped to maintain the sample temperature. The upper glass slide is supported by the sensor part of the thermometer, which is slightly thicker than the sample (see the previous section). The experimental temperatures of 31-50 °C were measured from the thermometer set next to the sample and were 1-3 °C lower than the values from a surface thermometer set directly on the hot plate (Fig. 2b). The temperature adjustment dial on the hot plate was checked in advance to set the desired temperature. The temperature fluctuations recorded by the thermometer next to the sample were less than ±1 °C. The temperature displayed on the thermometer reached ∼ 90% of the desired temperature from RT within ∼ 15 s and reached the desired temperature within 60 s. The lower the set temperature, the faster the desired temperature was reached from RT. Heating above 50 °C led to evaporation of the sample and the glass slides became dusty. Furthermore, the grain growth rates at such high temperatures became too fast to follow the process under the microscope. Therefore, the maximum temperature of the experiments was 50 °C.

After heating for 5-10 min, the bottom glass slide with the sample was removed from the hot plate and photomicrographs were taken at RT. The components of the experiment, including the thermometer, upper glass slide and weight block, were then re-assembled as shown in Figures 2a and 2b. This entire process of taking photomicrographs was done within 1 min to minimize the grain growth occurring after taking the glass slide from the hot plate. Approximately the same area of the sample was observed after each period of heating. With any period of heating at each temperature, the grain size data show consistent grain growth. The durations of the higher-temperature experiments mentioned hereafter refer to the total time on the hot plate.

Observations under plane-polarized light show the clearest microstructures. Figure 2c shows examples of observations under plane-polarized and cross-polarized light for the same area at an arbitrary temperature and heating duration. Similarly, Figure 2d shows observations under plane-polarized and reflected light. Under cross-polarized light, the interference colors are the result of multiple grains overlapping (compare Fig. 2c-1 and 2c-2). Under reflected light, the light appears to be scattered among the grain boundaries (compare Fig. 2d-1 and 2d-2). Therefore, this paper only considers the microstructures observable under plane-polarized light.

Data analysis

For each image obtained, the number of grains was manually counted within one or two set circles with diameters of 200-800 µm to obtain enough grain numbers (mostly >300 grains). In the case that >50% of the area of a grain was included in the circle, it was counted. Then, the average grain size (d_av) for each image was obtained with the radius r₁ of a circle (or r₁ and r₂ if two circles were employed for counting) and the numbers of counted grains N₁ (or N₁ + N₂) as $d_{\text{av}} = 2\sqrt{(r_{1}^{2} + r_{2}^{2})/(N_{1} + N_{2})} $.

The grain size data were analyzed based on the following conventional grain growth law (e.g., Karato, 2008):

  

\begin{equation} d^{n} - d_{0}^{n} = k_{0}\exp(-Q/RT)t \end{equation} (1),

where d is the grain size at time t (= durations in the experiments), d₀ is the initial grain size, n is the grain growth exponent, k₀ is a constant, Q is the activation energy, R is the gas constant, and T is the temperature in Kelvin. The grain growth laws for silicate rocks can include a term for water fugacity (e.g., Fukuda et al., 2019). Although water does not seem to have a significant effect on camphor, at least under the experimental conditions, ethanol does, which means it can be used as a fluid phase that simulates the water in silicates (Schmatz and Urai, 2010; Schmatz et al., 2011).

RESULTS

Grain growth at RT

Grain boundary migration by grain growth was clearly observed in the see-through experiment at RT (Supplementary Video S1; Videos S1 and S2 are available online from https://doi.org/10.2465/jmps.240229). Smaller grains were consumed by larger neighboring grains. Snap shots at arbitrary durations from 0 to 2 h were used to determine the average grain sizes (Fig. 3). Grain boundary migration by grain growth occurred at all times and on all scales, and the most stable angle of grain boundaries (120°) was maintained. Figure 4 shows close-up images from a specific area in Figure 3 at the beginning of the experiment from 0 to ∼ 13 min (see also Video S2). One or a few neighboring smaller grains (outlined by red dashed lines in Fig. 4) were consumed by larger neighboring grains. This is consistent with the see-through observations for octachloropropane reported by Nam et al. (1999) and computer simulations such as those of Fan and Chen (1997) and Kim et al. (2006), where the driving force is to reduce the total energy. In addition to grain growth, pores with sizes of a few micrometers that make up a small proportion of the slide are rapidly closed within ∼ 1 min during the grain boundary migration caused by grain growth, which would have partly taken place in the direction of specimen thickness. Fukuda et al. (2019) also observed grain growth and pore closures in a quartz aggregate prepared from compacted quartz powder. They used a piston cylinder and experimental conditions up to 2.5 GPa and 1100 °C. The real-time process was not observed in their study, but it was clearly observed in our experiment, as described here.

Figure 3. See-through observations at RT. The duration (h, min, and s) is shown on each image. The images taken at time points of 5-40 min are snapshots from Video S1 in the supplementary material, and the other images were taken manually. The images taken at time points of 0-40 min were taken under a 10× lens and the rest under a 4× lens. The red circles indicate the areas where grains were counted (as indicated by blue lines). In the case that >50% of the area of a grain was included in the circle, it was counted. The diameters of circles (Φ), the numbers of counted grains (N), and the average grain sizes (d_av) are shown. The white rectangle in the first image indicates the area shown in Figure 4.

Figure 4. See-through observations at RT. The images are snapshots from Video S2 in the supplementary material, which is an enlarged view of an area in Video S1. The area that was enlarged is shown in Figure 3. The duration (h, min, and s) is shown on each image. Grain growth is clearly observable on a smaller scale and in a shorter time than in Figure 3. Pores as indicated by white arrows in the first image, had disappeared by ∼ 1 min. Some grains (outlined by red dashed lines) showed a reduction in size.

Grain size data at RT and higher temperatures

Higher-temperature experiments were performed at 31, 35, 43, and 50 °C on a hot plate, and photomicrographs were taken after arbitrary durations of heating. The grain growth processes were the same as those at RT, and photomicrographs are shown in Figures S1-S6.

The average grain sizes are provided in Table 1. The data show grain growth with time, and all plotted datasets (from RT to 50 °C) show clear straight lines on log-log plots of duration versus average grain size (Fig. 5a). Two replicate experiments were conducted at both 31 and 43 °C, and show good reproducibility. Each trend line in Figure 5a shifts upward with increasing temperature. Based on the grain growth law of Eq. (1), the slopes of $\Delta \log (d^{n} - d_{0}^{n})$ should be unity for specific n values, which were determined in Figure 5b. The n values vary from 3.3 to 3.9 (Table 1), with all errors within <0.1. The average value of n from all experiments with the standard deviation is 3.7 ± 0.2.

Table 1. Experimental conditions and the determined grain sizes for different durations of heating that give the n values in Figure 5b

24 °C n = 3.9		31 °C-1 n = 3.6		31 °C-2 n = 3.4		35 °C n = 3.5		43 °C-1 n = 3.7		43 °C-2 n = 3.6		50 °C n = 3.9
t (sec)	d (µm)	t (sec)	d (µm)	t (sec)	d (µm)	t (sec)	d (µm)	t (sec)	d (µm)	t (sec)	d (µm)	t (sec)	d (µm)
0	9.5	0	8.5	0	9.4	0	11.8	0	9.1	0	8.8	0	10.7
300	17.8	300	17.9	300	17.4	300	21.4	300	25.1	300	24.2	120	23.5
600	20.9	600	21.6	600	22.3	600	27.2	600	29.6	600	27.7	300	32.3
900	22.7	900	24.9	900	25.7	1200	32.1	900	31.6	1200	34.2	600	36.1
1200	24.5	1200	27.3	1200	28.6	1800	36.7	1200	35.1	1800	38.7	900	41.3
1800	26.8	1800	29.9	1800	32.2	2400	37.6	1500	38.3	2400	42.9	1200	43.9
2400	28.6	2400	33.0	2400	34.5	3000	40.6	1800	40.8			1500	46.3
3600	32.6	3600	35.5	3600	37.9	3600	43.5					1800	47.4
5400	36.3	4800	38.5	4800	40.0	4200	44.9
7200	39.2	7200	42.8	7200	42.6

Figure 5. Grain size versus duration for different temperatures. The data are given in Table 1. (a) logd as a simple expression. (b) $\text{log}d^{n} - d_{0}^{n}$ based on the grain growth law. The n values giving the slope of unity are shown. Because the errors are <0.1, they are not shown.

Figure 6 shows the relation of $\Delta \ln (d^{n} - d_{0}^{n})$ versus 1/T with the average n value of 3.7 at durations of 10, 20, 30, and 40 min, showing relatively consistent trends. The average activation energy is Q = 60.4 ± 6.1 kJ/mol and the pre-exponential factor is k₀ = 10^−12.7±0.1.

Figure 6. Dependence of temperature on grain size for four durations of heating. The data are from Table 1 and were fitted with the average n value of 3.7 to determine the activation energies (Q in kJ/mol).

DISCUSSION

Normal grain growth was observed in the see-through experiment at RT involving hundreds of grains (snapshots in Figs. 3 and 4 from Videos S1 and S2, respectively), where smaller grains are consistently consumed by larger neighboring grains due to grain boundary migration. This is an interesting observation for a crystalline material, compared with previous studies that focused on local processes of grain growth and subsequent deformation involving only a few grains of camphor (e.g., Urai et al., 1980; Urai and Humphreys, 1981; Bons and Urai, 1996; Urai and Humphreys, 2000; Schmatz and Urai, 2010; Schmatz et al., 2011). Although real-time grain boundary migration was not observed in the experiments at higher temperatures on the hot plate, the same process would have occurred. Thus, the grain growth data at any temperature show consistent trends (Fig. 5a), giving the n value of 3.7 ± 0.2. The ideal theoretical derivation for normal grain growth in a pure single-phase system gives n = 2 (e.g., Atkinson, 1988; Karato, 2008). On the other hand, in theory, n values can vary from 1 to 4, depending on controlling factors such as pores, impurities, and diffusion through the surface, the crystal lattice, solution, etc. (Atkinson, 1988). In real materials including camphor, these factors would act in combination. In silicates and carbonates, the reported n values are mostly from 3 to 4. The data for quartz are given by Michibayashi and Imoto (2012), Fukuda et al. (2019), and Tokle and Hirth (2021); for calcite, dolomite, and magnesite by Olgaard and Evans (1988), Covey-Crump (1997), and Davis et al. (2011); for anorthite by Dresen et al. (1996); and for olivine by Karato (1989). For other minerals, see the review by Karato (2008). Therefore, the value obtained in the present study is consistent with those obtained for silicates and carbonates, although there might be some difference between the essentially two-dimensional grain growth in the present experiments and the three-dimensional grain growth in experiments with rocks that were enclosed in a metal jacket. Nevertheless, in those previous experiments with rocks, it was two-dimensional samples that were examined in polished thin sections under an optical and/or electron microscope. Nam et al. (1999) determined a grain growth law for octachloropropane using two-dimensional see-through observations. However, they assumed a grain growth law of d ∝ t^1/n, so their values can not be compared with those of the present study. The activation energy of ∼ 60 kJ/mol for camphor is also consistent with the values for silicates in the experiments referenced above, even though those values have a wider range of 60-700 kJ/mol.

The results of conventional grain growth experiments on rocks are observed as frozen microstructures, and each experiment must be conducted under specific conditions of temperature, pressure, and duration. This means that limited information can be obtained on microscale processes, evolving grain size data, and so on. The see-through experiment at RT reported here allowed clear observations to be made on the processes of grain boundary migration by grain growth, and the same sample area could be observed throughout, even in the higher-temperature experiments. Therefore, the grain size data of this study provide very clear and consistent trends for different durations and temperatures. The grain growth law for camphor can be used in future studies, and these could include, for example, deformation experiments on rock analogues with any desired grain size.

CONCLUDING REMARKS

Grain growth experiments on camphor as a rock analogue were performed with a simple technique at RT (24 °C) and higher temperatures up to 50 °C. Approximately 5 mg of the ground sample powder was pressed on a glass slide, thus producing a transparent and densely compacted aggregate of grains of ∼ 10 µm in size with an aggregate thickness of 100-200 µm. Observations were made during the experiments with a polarizing microscope. In the RT experiment, grain boundary migration and the consumption of smaller grains by larger neighboring grains were clearly observed. The higher-temperature experiments were performed on a hot plate. The experiments were completed within periods that ranged from 2 h at RT to 0.5 h at 50 °C. The data for grain sizes up to ∼ 47 µm at different temperatures were consistently analyzed. Grain growth occurred at all times and on all scales, involving hundreds of grains. A grain size exponent of ∼ 3.7 and an activation energy of ∼ 60 kJ/mol were determined during the experiments, and these values are consistent with those previously reported for aggregates of silicates and carbonates.

ACKNOWLEDGMENTS

The author thanks Yusuke Seto, Takamoto Okudaira, and Keiji Shinoda for discussions on the experimental setup and data interpretation. Positive and constructive reviews by Keishi Okazaki and anonymous reviewer are greatly acknowledged. This study was supported by JSPS KAKENHI Grant Number JP23K03531.

SUPPLEMENTARY MATERIALS

Supplementary Figures S1-S6 and Videos S1 and S2 are available online from https://doi.org/10.2465/jmps.240229.

REFERENCES

•  Atkinson,  H.V. (1988) Overview no. 65: Theories of normal grain growth in pure single phase systems. Acta Metallurgica, 36, 469-491.
•  Bons,  P.D. and  Urai,  J.L. (1992) Syndeformational grain growth: microstructures and kinetics. Journal of Structural Geology, 14, 1101-1109.
•  Bons,  P.D. and  Urai,  J.L. (1996) An apparatus to experimentally model the dynamics of ductile shear zones. Tectonophysics, 256, 145-164.
•  Campbell,  L.R. and  Menegon,  L. (2019) Transient high strain rate during localized viscous creep in the dry lower continental crust (Lofoten, Norway). Journal of Geophysical Research: Solid Earth, 124, 10240-10260.
•  Covey-Crump,  S.J. (1997) The normal grain growth behavior of nominally pure calcite aggregates. Contributions to Mineralogy and Petrology, 129, 239-254.
•  Davis,  N.E.,  Newman,  J.,  Wheelock,  P.B. and  Kronenberg,  A.K. (2011) Grain growth kinetics of dolomite, magnesite and calcite: a comparative study. Physics and Chemistry of Minerals, 38, 123-138.
•  Dresen,  G.,  Wang,  G. and  Bai,  Q. (1996) Kinetics of grain growth in anorthite. Tectonophysics, 258, 251-262.
•  Fan,  D. and  Chen,  L.-Q. (1997) Computer simulation of grain growth using a continuum field model. Acta Materialia, 43, 611-622.
•  Fukuda,  J.,  Raimbourg,  H.,  Shimizu,  I.,  Neufeld,  K. and  Stünitz,  H. (2019) Experimental grain growth of quartz aggregates under wet conditions and its application to deformation to nature. Solid Earth, 10, 621-636.
•  Jessell,  M.W. (1986) Grain boundary migration and fabric development in experimentally deformed octachloropropane. Journal of Structural Geology, 8, 527-542.
•  Joesten,  R. (1983) Grain growth and grain boundary diffusion in quartz from the Christmas Mountains (Texas) contact aureole. American Journal of Science, 283A, 233-254.
•  Karato,  S. (1989) Grain growth kinetics in olivine aggregates. Tectonophysics, 168, 255-273.
• Karato, S. (2008) Deformation of Earth Materials. Cambridge Univ. Press, New York.
•  Kim,  S.G.,  Kim,  D.I.,  Kim,  W.T. and  Park,  Y.B. (2006) Computer simulations of two-dimensional and three-dimensional ideal grain growth. Physical Review, E74, 061605.
•  McCrone,  W.C. (1949) Boundary migration and grain growth. Discussions of the Faraday Society, 5, 158-166.
•  Means,  W.D. and  Ree,  J.H. (1988) Seven types of subgrain boundaries in octachloropropane. Journal of Structural Geology, 10, 765-770.
•  Michibayashi,  K. and  Imoto,  H. (2012) Grain growth kinetics and the effect of crystallographic anisotropy on normal grain growth of quartz. Physics and Chemistry of Minerals, 39, 213-218.
•  Mori,  N.,  Wallis,  S. and  Mori,  H. (2015) Graphitization of carbonaceous material in sedimentary rocks on short geologic time-scales: An example from the Kinsho-zan area, central Japan. Island Arc, 24, 119-130.
•  Nam,  T.N.,  Otoh,  S. and  Masuda,  T. (1999) In-situ annealing experiments of octachloropropane as a rock analogue: kinetics and energetics of grain growth. Tectonophysics, 304, 57-70.
•  Okudaira,  T.,  Bando,  H. and  Yoshida,  K. (2013) Grain-boundary diffusion rates inferred from grain-size variations of quartz in metacherts from a contact aureole. American Mineralogist, 98, 680-688.
•  Olgaard,  D.L. and  Evans,  B. (1988) Grain growth in synthetic marbles with added mica and water. Contributions to Mineralogy and Petrology, 100, 246-260.
•  Otoh,  S. (1994) See-through deformation experiments of rock analogues. Structural Geology, 39, 173-183 (in Japanese with English abstract).
•  Piazolo,  S.,  Bons,  P.D.,  Griera,  A.,  Llorens,  M.-G., et al (2019) A review of numerical modelling of the dynamics of microstructural development in rocks and ice: Past, present and future. Journal of Structural Geology, 125, 111-123.
•  Schmatz,  J. and  Urai,  J.L. (2010) The interaction of fluid inclusions and migrating grain boundaries in a rock analogue: deformation and annealing of polycrystalline camphor-ethanol mixtures. Journal of Metamorphic Geology, 28, 1-18.
•  Schmatz,  J.,  Schenk,  O. and  Urai,  J.L. (2011) The interaction of migrating grain boundaries with fluid inclusions in rock analogues: the effect of wetting angle and fluid inclusion velocity. Contributions to Mineralogy and Petrology, 162, 193-208.
•  Tokle,  L. and  Hirth,  G. (2021) Assesment of quartz grain growth and the application of the wattmeter to predict quartz recrystallized grain sies. Journal of Geophysical Research: Solid Earth, 162, e2020JB021475.
•  Tullis,  J. and  Yund,  R.A. (1982) Grain growth kinetics of quartz and calcite aggregates. The Journal of Geology, 90, 301-318.
•  Urai,  J.L.,  Humphreys,  F.J. and  Burrows,  S.E. (1980) In-situ studies of the deformation and dynamic recrystallization of rhombohedral camphor. Journal of Materials Science, 15, 1231-1240.
•  Urai,  J.L. and  Humphreys,  F.J. (1981) The development of shear zones in polycrystalline camphor. Tectonophysics, 78, 677-685.
• Urai, J.L. and Humphreys, F.J. (2000) A collection of time-lapse movies from transmitted light deformation experiments. In Stress, Strain and Structure, A volume in honour of Win Means (Jessell, M.W. and Urai, J.L. Eds.). Journal of the Virtual Explorer, Vol. 2.
•  Wightman,  R.H.,  Prior,  D.J. and  Little,  T.A. (2006) Quartz veins deformed by diffusion creep-accommodated grain boundary sliding during a transient, high strain-rate event in the Southern Alps, New Zealand. Journal of Structural Geology, 28, 902-918.