American Mineralogist; April 2008; v. 93; no. 4;
p. 558-564; DOI: 10.2138/am.2008.2591
© 2008 Mineralogical Society of America
Temperature derivatives of elastic wave velocities in plagioclase (An51±1) above and below the order-disorder transition temperature
Yoshio Kono1,*,
Akira Miyake2,
Masahiro Ishikawa1 and
Makoto Arima1
1 Graduate School of Environment and Information Sciences, Yokohama National University, Yokohama 2408501, Japan
2 Department of Geology and Mineralogy, Kyoto University, Kyoto 6068502, Japan
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ABSTRACT
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Compressional (vp) and shear (vs) wave velocities of plagioclase (An51±1) were measured up to 900 °C at 1 GPa. The temperature derivatives of vp (
vp/T) and vs (vp/T) show a discontinuous change at ~400 °C. The vp/T is –0.9 x 10–4 km/s/°C below 400 °C and –4.4 x 10–4 km/s/°C above 400 °C. The vp/T also increases from –0.7 x 10–4 to –4.1 x 10–4 km/s/°C. These vp and vs show reversible changes between 25 and 700 °C. In contrast, both vp and vs increase (0.08 and 0.08 km/s, respectively) at 700–800 °C, and show irreversible changes after heating to 800 and 900 °C. The X-ray powder diffraction analysis shows that the run product heated to 900 °C shows a higher lattice angle 
than the run products obtained on heating up to 700 °C, which is comparable to the lattice angle of high and low plagioclase, respectively. We ascribe the discontinuous change in vp, vs, vp/T, and vs/T to the order-disorder transition of plagioclase at high temperatures.
Key Words: Elastic wave velocity • plagioclase • phase transition • high temperature
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INTRODUCTION
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Plagioclase is one of the most predominant constituents of the Earth’s crust, and therefore defining the elastic wave velocities of plagioclase contributes to our understanding of seismic velocity structures within the crust. Ryzhova (1964) was the first to determine the elastic properties of plagioclase of differing compositions at atmospheric pressure. Subsequent investigations of the elastic wave velocities of plagioclase under high-pressure conditions include those of Birch (1960, 1961), Liebermann and Ringwood (1976), Seront et al. (1993), and Wang et al. (1973), who examined the effect of composition and pressure on the elastic wave velocities of plagioclase. In particular, Angel (2004) demonstrated a discontinuous change in the bulk modulus of plagioclase with varying anorthite contents compared to that predicted by the pressure-volume equation of state. This change was attributed to a phase transition of plagioclase.
Plagioclase has several crystal structures depending on chemical composition and temperature (e.g., Carpenter 1985; Smith and Brown 1988). Phase transitions at high temperatures that involve order-disorder transitions may cause a discontinuous change in the elastic wave velocities of plagioclase, in a similar manner to that producing the discontinuous change in bulk modulus observed for varying compositions in Angel’s (2004) study. Since the Al, Si order-disorder transition of intermediate plagioclase (An30–70) takes place above 600–800 °C at 0.06–0.12 GPa (Carpenter 1986; 1994), disordered plagioclase will be stable at mid-to-lower crustal depths in relatively high geothermal regions (e.g., arc-subduction system). Hence, an understanding of the elastic wave velocities of disordered plagioclase is necessary to elucidate seismic wave velocity structures in the mid-to-lower crust. As previous studies have investigated the elastic properties of plagioclase at room temperatures only, the elastic wave velocities of plagioclase at high temperatures are not well understood.
Recently, Kono et al. (2004, 2006) found a discontinuous change in the temperature derivative of vp and vs in polycrystalline plagioclase and plagioclase-rich lower crustal rocks at high temperatures. This discontinuous change in the temperature derivative of vp and vs may arise from a phase transition in plagioclase at high temperatures. To investigate the behavior of temperature derivatives of vp and vs of plagioclase above and below the order-disorder transition, we measured vp and vs in a polycrystalline plagioclase (An51±1) in the temperature range from 25 to 900 °C at 1 GPa. X-ray powder diffraction analysis was used to determine the lattice parameters of both the initial plagioclase sample and the run products.
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EXPERIMENTAL METHODS AND SAMPLE DESCRIPTIONS
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These vp and vs measurements at high pressure and high temperatures were carried out in a piston-cylinder apparatus having a 34 mm inner diameter at Yokohama National University. Pressures were calibrated using vp measurements of the high–low quartz transition (Groos and Heege 1973) with ±0.03 GPa uncertainty (cf. Kono et al. 2007). Figure 1a
shows a schematic illustration of the cell assemblage and electrical circuit for vp and vs measurements. We used a cylindrical rock sample with 5.7 mm in diameter and ~5.0–5.5 mm long. Both ends of the sample were polished with 1 µm diamond paste and the sample length was measured under atmospheric condition, with 1 µm accuracy. The cylindrical rock sample was loaded into a sealed Pt capsule of 0.15 mm wall thickness that effectively prevented infiltration of H2O into the sample from any of pressure transmitting mediums. The temperature was monitored with a Pt-PtRh13 thermocouple. The uncertainty of the sample temperature was estimated to be less than ±7 °C at 400 °C, ±14 °C at 700 °C, and ±27 °C at 1000 °C (cf. Kono et al. 2007).
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FIGURE 1. (a) Schematic illustration of the cell assembly and electrical circuit used for vp and vs measurements. (b) An example of P- and S-wave signals reflected at the lower (R1) and upper (R2) ends of the sample.
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Measurements of vp and vs were conducted using pulse reflection method (Fig. 1
). An electrical signal with a 4 MHz frequency was generated by waveform generator (Tektronix AWG2021). We used a 10° Y-cut LiNbO3 transducer (5.7 mm diameter and 0.5 mm thickness) that generates both compressional and shear waves. A Pt buffer rod (16 mm long and 6 mm diameter) was placed between the rock sample and the LiNbO3 transducer to provide a long delay line, enabling the compressional and shear wave signals to be clearly separated in time (Fig. 1b). The elastic wave is partly reflected from the interface between the bottom of the rock sample and the Pt capsule (R1) and is partly transmitted to the rock sample. The component of the elastic wave that passes through the rock sample is also reflected at the interface between the top of the rock sample and the Pt capsule (R2). The travel time can be determined directly by comparing the arrival times of each peak, R1 and R2, in phase, because no glue has been used at the interfaces between the transducer, Pt buffer rod, and rock sample. The sample length (LP, 25°C) under highpressure (P) conditions was estimated from LP, 25°C/L0 = (1 – P/K)1/3, where L0 is the sample length under atmospheric condition and K is bulk modulus of 74 (Angel et al. 2004). The sample length (LP,T) at high temperature (T) was determined as LP,T/LP, 25°C = {exp[
0(T – 25)]}1/3 using a thermal expansion coefficient (0) of 10.6 x 10–6 (Fei 1995). The uncertainty in vp and vs is within ±0.35%, and hence, the uncertainty in Poisson’s ratio calculated using vp and vs is ±1.1%. In contrast, thermal expansion and bulk modulus change across the order-disorder transition might affect the sample length. However, these parameters of disordered plagioclase have not been measured and published as of yet, and we cannot make a relevant estimation for a change in sample length across the order-disorder transition. Hence, we test the effect of thermal expansion and bulk modulus change of 5% on the sample length and resultant vp and vs. The estimation shows 5% change leads to less than ~0.04 km/s difference in vp and vs, and therefore the thermal expansion and bulk modulus change across the order-disorder transition would not significantly affect on our vp and vs determination.
The sample of polycrystalline plagioclase was collected from Betioky, Tulear Province, Madagascar. It consists predominantly of plagioclase with an anorthite content of 51 ± 1 (99.3 vol%) and contains minor chlorite (0.2 vol%) and opaque minerals (0.5 vol%). The average chemical compositions of the major elements in the plagioclase determined by SEM-EDS are given in Table 1. The crossed-polar photomicrograph in Figure 2 shows the plagioclase to possess an equigranular texture with no recognizable foliation or lineation. Crystals are ~0.5 mm in grain size. If the wavelength of the elastic wave becomes less than about three times the grain size in the specimen, the energy will be scattered (Mason and McSkimin 1947). The wavelength used in this study was ~1.75 mm (vp = ~7 km/s and frequency = 4 MHz), ~3.5x the diameter of the plagioclase grains. Hence, our sample satisfies the requirement of wavelength/diameter >3. The sample was preheated to 700 °C at 1 atmospheric pressure for 3 h before undertaking vp and vs measurements, and we consider the sample to be anhydrous, although a small amount of water (ppm H2O by weight) might exist in the plagioclase. The bulk density of the initial polycrystalline plagioclase was determined as 2.609 g/cm3 by Archimedes’ method. The X-ray density of the plagioclase was calculated as 2.696 g/cm3 from the unit-cell volume (Table 2) and implies the initial sample had a porosity of ~3.2%.
We carried out three experiments at 1 GPa: Run LPS7 up to 700 °C, Run LPS8 up to 800 °C, and Run LPS9 up to 900 °C. The sample was first pressurized to 1 GPa, and then vp and vs measurements were carried out at 100 °C increments/decrements during heating and cooling in all runs. The sample was kept at each measurement temperature for ~2 h to ensure a steady value of vp and vs.
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RESULTS
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These vp and vs measurement in Run LPS9 were carried out under a constant pressure of 1 GPa in the first (up to 700 °C), second (up to 800 °C), and third heating and cooling cycles (up to 900 °C). In a fourth cycle, we also measured vp and vs up to 900 °C. The original sample length, travel time, vp, vs, vp/vs, and Poisson’s ratio observed in the second and fourth heating cycles of Run LPS9 are shown in Table 3. Discontinuous change in the temperature derivatives of vp and vs were observed during the four heating and cooling cycles (Fig. 3 and Table 4). In the first heating and cooling cycle up to 700 °C, a slight and linear decrease occurred in vp and vs below 400 °C, but above 400 °C vp and vs showed a significant decrease with increasing temperature (Figs. 3a and 3b). The temperature derivative of vp (vp/T) and vs (vs/T) is –0.9 x 10–4 and –0.7 x 10–4 km/s °C–1, respectively, below 400 °C, but increased to –4.4 x 10–4 and –4.1 x 10–4 km/s/°C, respectively, above 400 °C (Table 4). During cooling we observed comparable vp and vs values to those found in the heating run. In the second cycle up to 800 °C, vp and vs slightly decreased during heating below 400 °C but showed significant decreases from 400 to 700 °C as seen in the first cycle (Figs. 3d and 3e). In contrast, a sudden increase occurred in both vp and vs, at 700–800 °C, of 0.08 and 0.08 km/s, respectively. In the cooling run, both vp and vs showed irreversible changes and had higher values than those measured during heating. In the third cycle up to 900 °C, vp and vs also exhibited irreversible changes (Figs. 3g and 3h) with vp and vs returning higher values in the cooling run than during heating. In the fourth cycle, vp and vs had comparable values to those measured in the cooling run of the third cycle with the results showing reversible changes occurring during both heating and cooling cycles (Figs. 3j and 3k).
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TABLE 3. Sample length, travel time for P- (tvp) and S-wave (tvs), vp, vs, vp/vs, and Poisson’s ratio ( ) of the second and fourth heating cycle in the run LPS9
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FIGURE 3. Variations in vp (a, d, g, j), vs (b, e, h, k), and Poisson’s ratio (c, f, i, l) as a function of temperature in the first (a–c), second (d–f), third (g–i), and fourth (j–l) cycles of Run LPS9. The solid and open symbols represent the data in the heating and cooling runs, respectively. The lines in the graphs represent the first heating and cooling and second heating cycles (dashed line), second cooling and third heating cycles (thin broken line), and third cooling and fourth heating and cooling cycles (dotted line). The vp/T and vs/T values for each of these lines are shown in Table 4.
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Poisson’s ratio in Run LPS9 remained more or less constant below 400 °C but increased with increasing temperature between 400 and 700 °C in the first heating cycle (Fig. 3c). On cooling, the Poisson’s ratio showed the same reversibility seen with vp and vs. In contrast, after heating to 800 °C in the second cycle, Poisson’s ratio changed irreversibly with decreasing temperature to 25 °C (Fig. 3f). We also observed positive temperature dependence in Poisson’s ratio in the third and fourth cycles (Figs. 3i and 3l) that changed reversibly during both heating and cooling. The change in Poisson’s ratio was from ~0.295 at 25 °C to ~0.315 at 900 °C.
The pronounced reversible change in vp, vs, and Poisson’s ratio observed in the first cycle of Run LPS9 were confirmed by measuring vp and vs during three heating and cooling cycles up to 700 °C at 1 GPa (Run LPS7; Fig. 4). Both vp and vs had relatively lower vp/T and vs/T below 400 °C, and significantly decreased between 400 and 700 °C. The Poisson’s ratio remained nearly constant between 25 and 400 °C but increased with increasing temperature above 400 °C.
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FIGURE 4. vp (a), vs (b), and Poisson’s ratio (c) of Run LPS7 up to 700 °C at 1 GPa for each of the three heating and cooling cycles.
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In Run LPS8, vp and vs measurements were carried out up to 700 °C in the first cycle and up to 800 °C in the second cycle. The results confirmed a discontinuous change in the temperature derivative of vp and vs at ~400 °C, and a sudden increase in vp and vs between 700 and 800 °C, the results being similar to those observed in the first and second cycles of Run LPS9 (Figs. 3a, 3b, 3d, and 3e).
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DISCUSSION
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In this study, we observed discontinuous change in vp/T and vs/T at 400 °C and sudden increase in vp and vs at 700–800 °C. Measurements of vp and vs up to 700 °C in Run LPS7 and in the first cycle of Run LPS8 and LPS9 showed excellent reversibility in the change in vp and vs with varying temperature. In contrast, after heating to 800 and 900 °C in the second cycle of Run LPS8 and in the second and third cycles of Run LPS9, we observed irreversible changes in vp and vs, with the results showing relatively higher vp and vs values than those observed in the run up to 700 °C.
Some studies have suggested that thermally induced stresses may cause cracking (thermal cracking), and consequently, a significant decrease in vp and vs (e.g., Kern and Richter 1981). However, the thermal cracking field is limited to pressures less than ~0.5 GPa and temperatures less than 700 °C (Khazanehdari et al. 2000; Kono et al. 2004) because of a linear pressure dependence of the thermal cracking temperature of ~1 °C/MPa (Fredrich and Wong 1986). Consequently, thermal cracking would be suppressed by the high confining pressure of 1 GPa used in this study. Alternatively, differential stress due to friction may provide a cause of the discontinuous change observed in vp and vs. However, the BN, talc, and pyrophyllite used as pressure mediums in this study become soft at high temperatures and transmit pressure plastically as a quasi-fluid medium. Hence, friction is unlikely to arise and generate any discontinuous change in vp/T and vs/T through microcracking.
It is known that an order-disorder transition occurs with increasing temperature in intermediate plagioclase (An30–70). Such an order-disorder transition might cause the discontinuous changes in vp, vs, vp/T, and vs/T observed in the plagioclase. The effect of cation ordering on elasticity has been discussed in spinel (e.g., Liebermann et al. 1977) with a recent experimental study by Hazen and Yang (1999) pointing to significant effects of the order-disorder transition in spinel on its bulk modulus and thermal expansion coefficient. In the same way, the Al, Si order-disorder transition in plagioclase could affect the elastic wave velocities. To investigate this possibility, we analyzed the initial sample and the run products using X-ray powder diffraction analysis.
Smith and Yoder (1956) introduced the 
131 method to distinguish low (ordered) and high (disordered) plagioclase based on a simple measurement of the difference between the 2
angle of the 131 and 131 peaks [.131 = 2 (131)–2 (131) for CuK radiation]. The .131 values of plagioclase with an anorthite content of 52 are 1.827 °(2) for low plagioclase and 1.998 °(2) for high plagioclase (Kroll and Ribbe 1980). Our XRD results also show the product of Run LPS7 to have a relatively low 131 value of 1.79 corresponding to low plagioclase. In contrast, the products of Runs LPS9 and LPS8 show a markedly higher 131 value of 1.92 comparable to that of the high plagioclase. However, the 131 method is prone to being influenced by the orthoclase content of plagioclase, and Kroll and Ribbe (1980) showed that the method provides more precise results. Consequently, we calculated the lattice parameters of the initial sample and the run products of LPS7, LPS8, and LPS9 using the "CellCalc" software (Miura 2003). The results are shown in Table 2, and the lattice angle of the initial sample and the run products are plotted in the determinative diagram for Al, Si ordering in plagioclase (Fig. 5) (cf. Kroll and Ribbe 1980; Carpenter 1994). The comparatively low value of lattice angle of LPS7 corresponds to low plagioclase. In contrast, the results of LPS8 and LPS9 are markedly higher, with the lattice angle of LPS9 being comparable to that of high plagioclase and that of LPS8 being intermediate between those of LPS9 and LPS7.
Furthermore, the diagram can be contoured in terms of t1O – <t1m> values calculated from the regression data of Kroll and Ribbe (1980) (Fig. 5). The parameter t1O corresponds to an average aluminum content in the T1O site with the <t1m> representing the average aluminum content in T1m, T2O, and T2m sites, i.e., <t1m> = 1/3(t1m + t2O + t2m). Values of t1O and <t1m> are calculated as t1O = 0.25(1 + nAn) + 0.75(t1O – <t1m>) and <t1m> = 0.25(1 + nAn) – 0.25(t1O – <t1m>), in which nAn is the anorthite content. Figure 6 shows the t1O and <t1m> plot as a function of anorthite content. The fully disordered structures are shown as the dashed line between t1O = t1m = t2O = t2m = 0.25 for albite and t1O = t1m = t2O = t2m = 0.50 for anorthite. The dash-dot lines represent the t1O and <t1m> values expected if plagioclases are completely ordered. The t1O and <t1m> values for the high and low plagioclase of Kroll and Ribbe (1980) are also given. The t1O and <t1m> values of the initial sample and run product of LPS7 show good agreement with those of low plagioclase. The t1O and <t1m> values of the run products of LPS9 have values comparable to high plagioclase and the run product of LPS8 has intermediate values between LPS9 and LPS7.
These data confirm that the initial sample and run product LPS7 consist of low plagioclase, while run product LPS9 has a structure comparable to high plagioclase. Run product LPS8 is likely to be composed of plagioclase with a structure intermediate between run products LPS7 and LPS9. Consequently, the discontinuous change in vp, vs, vp/T, and vs/T at high temperatures is consistent with an order-disorder transition in plagioclase. For a plagioclase with an anorthite content of ~51, the order-disorder transition takes place at ~700–800 °C under 0.06–0.12 GPa (Carpenter 1986; 1994). To the best of our knowledge, no experimental or calculated transition temperatures of the order-disorder transition above 0.12 GPa have been published. Our experimental results at 1 GPa show marked increase in vp and vs between 700 and 800 °C, and could correspond to the order-disorder transition temperature. In addition, Goldsmith and Jenkins (1985) showed that 131 values of albite decrease rapidly at 300 °C less than the order-disorder temperature and vary reversibly as a function of temperature below the stability temperature of high albite. They exhibit a transitional temperature range of ~300 °C between low and high temperature states. These results are comparable to our results showing a discontinuous change in vp/T and vs/T at ~400 °C that occurs below the order-disorder transition temperature of ~700–800 °C. Our data also show that the reversal in variations of vp and vs occurs well below the order-disorder transition temperature. We therefore consider the transitional state between low and high plagioclase to be responsible for the pronounced variations in vp/T and vs/T in the temperature range between 400 and 700 °C.
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CONCLUDING REMARKS
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Measurements of vp and vs of a polycrystalline plagioclase (An51±1) show a discontinuous change in temperature dependence of vp and vs, which can be attributed to the order-disorder transition of plagioclase. The vp/T and vs/T values of both high plagioclase and a transitional state are significantly higher than those of low plagioclase. Since plagioclase is one of the most common mineral constituents of crustal rocks, the marked increase in its vp/T and vs/T at 400–700 °C would result in significant effects on seismic velocity structures within the crust. A discontinuous change in vp/T and vs/T at ~400 °C has also been observed at 0.6 and 0.8 GPa (Kono et al. 2006). The vp and vs significantly decrease above 400 °C at 0.6–1.0 GPa. The results of Kono et al. (2006) showed that anomalous decreases in vp and vs at high heat flow regions correspond to low velocity anomalies at lower crustal depths. Furthermore, the sudden increase in vp and vs that occurs at 700–800 °C observed in run LPS8 and LPS9 could allow for recovery from a low velocity anomaly to normal velocity. The sudden decrease at 400–700 °C and the subsequent recovery at 700–800 °C that can be attributed to phase transition in plagioclase would account for low velocity anomalies at mid-to-lower crustal depths in high heat flow regions (e.g., Wang and Zhao 2005, 2006).
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ACKNOWLEDGMENTS
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We thank anonymous reviewers, and the editor for constructive comments and suggestions, which helped improve this manuscript. We thank M. Kitamura for his helpful comments. This study was supported by Grants-in-Aid for Scientific Research provided by the Japan Society for the Promotion of Science to M.A. (16340167) and M.I. (15540457) and by the Sasakawa Scientific Research Grant from the Japan Science Society to Y.K. (17-257).
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Footnotes
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* Present address: Geodynamics Research Center, Ehime University, Matsuyama 7908577, Japan. E-mail: kono{at}sci.ehime-u.ac.jp 
MANUSCRIPT HANDLED BY MARTIN KUNZ
MANUSCRIPT RECEIVED February 1, 2007;
MANUSCRIPT ACCEPTED October 9, 2007
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REFERENCES CITED
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Abstract
Introduction
