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Post-spinel transition in Mg2SiO4 determined by high P–T in situ X-ray diffractometry
Physics of the Earth and Planetary Interiors 136 (2003) 11–24
Post-spinel transition in Mg2 SiO4 determined by high P–T in situ X-ray diffractometry Tomoo Katsura a,∗ , Hitoshi Yamada a , Toru Shinmei a,1 , Atsushi Kubo a , Shigeaki Ono a,2 , Masami Kanzaki a , Akira Yoneda a , Michael J. Walter a , Eiji Ito a , Satoru Urakawa a,b , Kenichi Funakoshi a,c , Wataru Utsumi a,d a
c
Institute for Study of the Earth’s Interior, Okayama University, Misasa, Tottori-ken 682-0193, Japan b Department of Earth and Planetary Sciences, Okayama University, Okayama 700-0082, Japan Japan Synchrotron Radiation Research Institute, Kouto 1-1-1, Mikazuki-cho, Sayo-gun, Hyogo 678-5198, Japan d Japan Atomic Energy Research Institute, Kouto 1-1-1, Mikazuki-cho, Sayo-gun, Hyogo 678-5148, Japan Received 3 October 2001; received in revised form 16 June 2002; accepted 29 July 2002
Abstract The phase boundary of the post-spinel transition in Mg2 SiO4 was re-investigated by means of high P–T in situ X-ray diffractometry with a gold pressure marker in a Kawai-type apparatus. Rapid and continuous temperature changes were conducted to initiate dissociation of spinel, which tends to be inert after long annealing. Isothermal decompression at high temperature was conducted to form spinel from perovskite plus periclase. The phase boundary is located at ca. 22 GPa in the temperature range from 1550 to 2100 K, which is 1–1.5 GPa lower than the 660 km discontinuity. This discrepancy might be explained in terms of the pressure effect of thermocouple emf and inaccurate equation of state (EOS) for the pressure maker. The transition is found to be less sensitive to temperature than reported previously, with a Clapeyron slope ranging from −2 to −0.4 MPa/K. This small Clapeyron slope implies that the post-spinel transition would not be an effective barrier to mantle convection. © 2003 Elsevier Science B.V. All rights reserved. Keywords: Post-spinel transition; Mg2 SiO4 ; 660 km discontinuity; Mantle; High pressures and temperatures; In situ X-ray diffractometry
1. Introduction The 660 km seismic discontinuity is one of the most important structural boundaries in the Earth’s mantle, and is usually attributed to the dissociation of ∗ Corresponding author. Fax: +81-858-43-2184. E-mail address: [email protected] (T. Katsura). 1 Present address: Department of Geology and Geophysics, Yale University, New Haven, CT, USA. 2 Present address: Institute for Frontier Research on Earth Evolution, Japan Marine Science and Technology Center, Showa-machi, Kanazawa-ku, Yokohama 236-0001, Japan.
(Mg, Fe)2 SiO4 spinel to (Mg, Fe)SiO3 perovskite and (Mg, Fe)O ferropericlase (post-spinel transition). For this reason, many workers have studied the phase relations of the post-spinel transition in the end-member Mg2 SiO4 system (Ito and Yamada, 1982; Ito and Takahashi, 1989; Akaogi and Ito, 1993b; Irifune et al., 1998; Chudinovskikh and Boehler, 2001; Shim et al., 2001). Ito and Takahashi (1989) studied the post-spinel transition in the system Mg2 SiO4 –Fe2 SiO4 by means of the quench method in a Kawai-type apparatus. They found that the phase boundary is located at
0031-9201/03/$ – see front matter © 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0031-9201(03)00019-0
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23 GPa at 1900 K, corresponding to 660 km depth, and has a steep negative Clapeyron slope of −3 MPa/K. However, they were not able to determine pressure accurately and precisely because generated pressures were estimated by calibration against press load. Pressure measurements by in situ X-ray diffractometry suggest that generated pressures in multi-anvil presses vary due to different heating efficiency, heating path and run duration even if temperature and press load are the same. Further, we will show that the phase relations determined by normal quench-type experiments may have uncertainty due to the kinetic effects. Irifune et al. (1998) studied the post-spinel transition in Mg2 SiO4 using in situ X-ray diffractometry in a Kawai-type apparatus. Although they found essentially the same steep negative Clapeyron slope as Ito and Takahashi (1989), they located the phase boundary at about 2 GPa lower pressure. This result, if correct, has serious implications for our understanding of mantle structure because it suggests that the post-spinel transition should occur at ca. 600 km depth in the Earth at 1900 K. Therefore, the 660 km discontinuity cannot be explained by the post-spinel transition, and must be a result of a different phase transition and/or a change in bulk mantle chemistry. Recently, the post-spinel transition in Mg2 SiO4 was studied by means of the laser-heated diamond anvil cell (Chudinovskikh and Boehler, 2001; Shim et al., 2001). Although the boundary was not precisely determined in these two studies, it was concluded that the post-spinel transition occurs at a pressure that is generally consistent with the depth of 660 km discontinuity, contrary to Irifune et al.’s (1998) results. In this study, we re-investigated the phase relations of the post-spinel transition in Mg2 SiO4 by means of in situ X-ray diffractometry in a Kawai-type apparatus to examine the discrepancy of the transition pressure given by Irifune et al. (1998) with the depth of 660 km discontinuity. Although we adopted cell designs and reaction paths different from those of Irifune et al. (1998), the main principles of our experimental method are essentially the same. Therefore, if we would obtain similar results to Irifune et al. (1998), the discrepancy should result from the uncertainties associated with high P–T in situ X-ray diffraction study using a multi-anvil press, or the transition cannot be the cause of the 660 km discontinuity.
2. Experimental 2.1. Starting material Starting material for most runs was a mixture of synthetic forsterite (Mg2 SiO4 ) and gold with a 5:1 weight ratio. Mg metal was put into pure water, and HNO3 was added to make a Mg(NO3 )2 solution. Tetraethylorthosilicate ((CH3 CH2 O)4 Si) was weighed to produce a 2:1 molar Mg:Si ratio, and was added to the Mg(NO3 )2 solution. Ethanol was added to make a homogeneous solution. Ammonia was added to make gel. The gel was heated at 390 K to remove water and ethanol. Temperature was increased to 410 K, and then to 650 K to remove NH4 NO3 . The sample was baked at 1700 K for several hours to make pure crystalline forsterite. Fine gold powder with 0.1 m grain size obtained from Nilaco Corp was weighed, and mechanically mixed with the forsterite. An exception is run 161, in which a mixture of forsterite, enstatite, periclase and gold with weight ratio of 7:5:10:1 was used. The enstatite was synthesized in a similar way to forsterite. Periclase was reagent-grade MgO baked at 1300 K. As mentioned later, this mixture was finely pulverized, and may have absorbed a certain amount of water. 2.2. X-ray diffractometry Experiments were conducted at the third generation synchrotron radiation facility ‘SPring-8’ at Hyogo prefecture, Japan. We used a Kawai-type3 apparatus, ‘SPEED-1500’, installed at a bending magnet beam line BL04B1 (Utsumi et al., 1998). Energy-dispersive X-ray diffractometry was conducted with a horizontal goniometer using white X-rays. The vertical and horizontal widths of incident slits were 0.1 and 0.05 mm, respectively. The horizontal width of the collimator was 0.05 mm. The vertical and horizontal widths of receiving slits varied, but were usually 0.4 mm and 3 “Kawai-type apparatus” is a general name used for a doublestage multi-anvil apparatus that compresses an octahedral pressure medium with eight truncated cubes. So far, this apparatus has been called by many ways like “6–8 type apparatus”, “MA8 type apparatus”, “cubic-octahedral anvil press”, “split-sphere apparatus” or “Walker-type apparatus”. This name was proposed by Yagi (2001) after late professor N. Kawai, who originally developed this apparatus.
T. Katsura et al. / Physics of the Earth and Planetary Interiors 136 (2003) 11–24
0.2–0.3 mm, respectively. A Ge solid-state detector was used and connected to a multi-channel analyzer with 4096 channels, which was calibrated using characteristic X-rays of Cu, Mo, Ag, Ta, Pt, Au and Pb. Exposure times were usually 200–300 s. The energy range available for analyzing the sample was ca. 40–150 keV. The diffraction angle (2θ ) was ca. 4.9◦ . The diffraction angles were calibrated before compression of each run by matching the observed unit cell parameter of the pressure standard to the one at ambient conditions (a0 = 4.0786 A). Uncertainty in determination of the diffraction angle is ca. 0.001◦ , which produces 0.15 GPa uncertainty in pressure calculation. The generated pressure at high temperature was calculated from the unit cell volume of gold using the equation of state (EOS) of gold proposed by Anderson et al. (1989). At least three diffraction lines (1 1 1), (2 0 0) and (2 2 0) or (2 0 0), (2 2 0) and (3 1 1) were used to calculate pressure. In many cases, five diffraction lines (1 1 1), (2 0 0), (2 2 0), (3 1 1) and (2 2 2) were used. In the best case, seven lines were used, when the (4 0 0) and (4 2 0) lines were also sufficiently intense. Uncertainty of unit cell volume of
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gold determined by least squares calculation usually gives 0.1–0.2 GPa uncertainty in pressure. Unfortunately, however, the SSD was in a bad condition during runs 289 and 291, and the errors are much larger in these experiments (Table 1). 2.3. Sample assembly We used WC anvils with 2.5 mm (run 239, 240, 285, 289, 291 and 666) and 3.0 mm (run 161 and 241) truncations. A horizontal cross-section of the sample assembly used with 2.5 mm truncations is shown in Fig. 1. The assembly used with 3.0 mm truncation is essentially the same. The incident X-rays followed a path from edge to edge of the octahedral pressure medium in a horizontal direction, and the cylindrical furnace system was placed with its axis almost parallel to the incident X-rays. The heater was a LaCrO3 cylinder with a length of 3.9 mm and outer and inner diameters of 2.2 and 1.5 mm, respectively. The heater was surrounded by a ZrO2 thermal insulator with a 5.0 mm outer diameter. A sample about 1.0 mm in length was loaded into a gold tube with a length of 2.0 mm, and outer and inner diameters of 0.8 and 0.75 mm. The
Fig. 1. A cross-section of the sample assembly in the horizontal plain parallel to the incident X-ray beam.
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Table 1 Experimental results Number Previous temperature (K)
Previous pressure (GPa)
Previous phases
Reaction temperature (K)
Reaction pressure (GPa)
Load Resultant (tonnes) phases
Comment
161028
RT
18.8 ± 0.5
Sp
2000
22.5 ± 0.1
1500
Pv
239013
1200
25.0 ± 0.1
Sp
1200
25.0 ± 0.1
1300
Pv + Sp
239015
1200
24.8 ± 0.1
Pv + Sp
1250
25.0 ± 0.1
1300
Pv
240024
1300
24.4 ± 0.1
Sp
1350
24.4 ± 0.1
1300
Pv + Sp
240029
1200
23.8 ± 0.1
Pv + Sp
1600
24.3 ± 0.1
1300
Pv
240088 241014
1700 1300
21.9 ± 0.1 23.0 ± 0.1
Pv Sp
1700 1700
21.8 ± 0.2 22.5 ± 0.2
870 1150
Sp Pv
285014
1300
23.5 ± 0.3
Sp
1550
23.2 ± 0.2
1300
Pv
285060 285061 285066
1800 1800 1800
21.0 ± 0.2 20.7 ± 0.2 20.9 ± 0.1
Pv Pv + Sp Pv + Sp
1800 1800 1850
20.7 ± 0.1 20.4 ± 0.1 20.9 ± 0.1
630 612 1000
Sp Sp Sp
285069 285071
1300 1800
ND 23.0 ± 0.1
Sp + Pv Sp + Pv
1800 1800
23.0 ± 0.1 22.6 ± 0.3
1350 1350
Sp + Pv Pv
285072
1800
22.6 ± 0.3
Pv + Sp
1900
22.8 ± 0.1
1350
Pv
285078 285082
1900 1900
21.8 ± 0.2 21.5 ± 0.1
Pv Pv + Sp
1900 1650
21.8 ± 0.2 21.1 ± 0.5
700 700
Sp Sp
285087
1400
20.2 ± 0.1
Pv + Sp
1900
21.1 ± 0.1
650
Sp
285095
Ambient temperature
ND
Sp + Pv
1900
23.1 ± 0.1
1400
Pv + Sp
285097
1900
22.8 ± 0.1
Sp + Pv
1900
23.0 ± 0.3
1400
Pv
285102 285103 285105 285110 285117 289013 291021 291023
1900 1900 RT 2000 2050 1300 RT 2050
22.3 21.9 ND 21.8 21.0 23.4 20.7 22.7
± 0.2 ± 0.2 0.1 0.1 0.1 0.5 0.1
Pv Pv + Sp Pv + Sp Pv Pv + Sp Sp Sp Pv
1900 1900 2000 2000 2050 1660 2050 1900
21.9 21.4 23.6 21.6 20.9 22.1 22.2 20.8
± ± ± ± ± ± ± ±
0.2 0.1 0.1 0.2 0.1 0.5 0.1 0.7
700 680 1500 725 600 1100 1170 704
Pv + Sp Sp Pv Pv + Sp Sp Pv Pv Sp
291025 291038
1300 1400
ND 21.5 ± 0.4
Pv + Sp Pv
2000 1750
23.2 ± 0.3 21.8 ± 0.3
1174 1194
Pv Sp
Normal heating at constant press load Temperature was kept constant for 20 min Temperature was gradually increased for 2 min Temperature was increased for 5 min Temperature was increased for 10 min Isothermal decompression Temperature was increased continuously by ca. 100 K/min Rapid heating at constant press load Isothermal decompression Isothermal decompression Temperature was slowly increased at constant press load. Continuous temperature increase The temperature and press load kept constant for 12 min Gradual temperature increase at constant press load Isothermal decompression Temperature gradually decreased at constant load. Growth of spinel peak is subtle Temperature gradually increased at constant load after decompression from 700 to 650 tonnes Continuous temperature increase. Growth and diminishing of perovskite and spinel, respectively, were subtle but continuing Temperature and load were kept constant for 30 min Isothermal decompression Isothermal decompression Rapid temperature increase Isothermal decompression Isothermal decompression Continuous temperature increase Continuous temperature increase Temperature decreased, and then isothermal decompression Continuous temperature increase Temperature was gradually increased at constant load
± ± ± ± ±
T. Katsura et al. / Physics of the Earth and Planetary Interiors 136 (2003) 11–24
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Table 1 (Continued ) Number
Previous temperature (K)
Previous pressure (GPa)
Previous phases
Reaction temperature (K)
Reaction pressure (GPa)
Load Resultant (tonnes) phases
291043
1750
22.0 ± 0.5
Pv
1800
20.6 ± 0.2
710
Sp
291046
1800
ND
Sp + Pv
1550
22.8 ± 0.1
1300
Pv
291050
2000
ND
Sp + Pv
1600
22.1 ± 0.2
1150
Pv
666008
1140
22.9 ± 0.1
Sp
1557
22.9 ± 0.1
1000
Pv + Sp
666009
1557
22.9 ± 0.1
Pv + Sp
1557
22.7 ± 0.1
1000
Pv
666017 666026
1550 560
21.6 ± 0.1 ND
Pv Pv + Sp
1550 1607
21.4 ± 0.2 22.3 ± 0.1
700 900
Pv + Sp Pv + Sp
666028
1607
22.4 ± 0.1
Pv + Sp
1607
22.3 ± 0.1
900
Pv
666032 666034
1600 1600
21.9 ± 0.1 21.9 ± 0.1
Pv Pv + Sp
1600 1600
21.8 ± 0.1 21.9 ± 0.1
735 735
Pv + Sp Sp + Pv
666042 666044 666044
RT 579 1650
ND 20.0 ± 0.1 22.3 ± 0.1
Sp + Pv Pv + Sp Pv + Sp
1550 1650 1650
22.2 ± 0.1 22.3 ± 0.1 22.1 ± 0.1
903 900 900
Pv + Sp Pv + Sp Pv
666048 666050
1650 1650
22.1 ± 0.1 22.8 ± 0.1
Pv Pv + Sp
1650 1650
21.8 ± 0.1 21.5 ± 0.1
750 700
Pv + Sp Sp + Pv
666054
1196
21.6 ± 0.2
Sp + Pv
1800
22.4 ± 0.1
900
Py
666058 666059
1800 1800
21.9 ± 0.1 21.6 ± 0.1
Pv Pv + Sp
1800 1800
21.6 ± 0.1 21.5 ± 0.1
700 700
Pv + Sp Pv + Sp
666060
1647
ND
Pv + Sp
1784
22.2 ± 0.1
900
Pv + Sp
666061
1784
22.2 ± 0.1
Pv + Sp
1784
22.2 ± 0.1
900
Pv
666068
2100
21.4 ± 0.1
Pv
2100
21.1 ± 0.1
600
Pv + Sp
Comment
Isothermal decompression at 1800 K Temperature was rapidly decreased Temperature was rapidly decreased Continuous temperature increase by 100 K/min Temperature and press load kept constant Isothermal decompression Quick temperature increase. Sp largely decreased Temperature and press load kept constant Isothermal decompression Temperature and press load kept constant. Sp clearly grew Quick temperature increase Quick temperature increase Temperature and press load kept constant Isothermal decompression Isothermal decompression. Pv largely decreased. Continuous temperature increase by 200 K/min Isothermal decompression Temperature and press load kept constant. Spinel increased Continuous teinperature increase by 100 K/min Temperature and press load kept constant Isothermal decompression
ND: not determined; RT: room temperature; Pv: perovskite; Sp: spinel. In this table, only data points where an irreversible proceeding of the dissociation and formation of spinel was observed are shown. Other data points, where no clear proceeding of reactions was observed, are omitted. Diffraction peaks of periclase were always observed because of the X-ray window of the sample assembly, and therefore, periclase is omitted in the description of the phases.
gold tube was surrounded by an MgO spacer loaded into the heater. The temperature of the sample was measured by a W97Re3–W75Re25 thermocouple, which was inserted perpendicular to the sample through 0.6 mm diameter holes that were electrically insulated from the heater by MgO sleeves with outer and inner diameters of 0.6 and 0.2 mm. The electrical junction of the thermocouple was made with the gold tube, and thus the temperature of the gold tube was measured.
In the present cell assembly, we did not measure temperature exactly at the sample. However, we took a diffraction pattern of the sample in an area near the thermocouple in order to minimize uncertainty in sample temperature. In addition, we examined temperature variation in the sample in the horizontal direction by observing the cell parameter variation of gold while shifting the diffraction area, assuming constant pressure. We observed no systematic variation of the cell, which suggests the variation is
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probably <20 K. Therefore, we consider that the temperature measurement at the thermocouple is likely to be within 20 of the sample temperature. 2.4. Run procedure At the beginning of each run, the 2θ angle was calibrated by measuring the unit cell volume of the gold pressure marker at ambient conditions. The sample was then compressed to the desired press load at ambient temperature, and heated gradually. At 1100–1300 K, starting material of forsterite first transformed to spinel at pressures of 23–26 GPa. After that, while continuously taking diffraction patters, temperature and press load were increased and decreased, following complex P–T paths as described later. Generally, in the first heating cycles, sample pressure decreased with increasing temperature at a rate of −1 MPa/K at constant press load, probably due to stress relaxation of the pressure medium and gasket. In successive heating cycles, sample pressures increased upon temperature increase and decreased upon temperature decrease, at a rate of 1–3 MPa/K, as a consequence of thermal pressure. Decreasing press load can decrease sample pressure, although the first 10–15% decrease of load did not decrease samples pressures effectively due to considerable hysteresis. Note that the main problem in accurately determining the phase boundary of the post-spinel transition in Mg2 SiO4 was difficulty in initiating the dissociation of spinel to perovskite plus periclase. Spinel formed at high P–T conditions is very inert, which was also reported by Irifune et al. (1998). To eliminate this difficulty, temperature was changed rapidly (100–1000 K/min) and continuously, a procedure that we found promoted spinel dissociation. In contrast, formation of spinel from perovskite plus periclase occurred easier than dissociation. Although formation of spinel could be caused by cooling at constant press load as adopted by Irifune et al. (1998), we observed that spinel formation was more easily promoted by decreasing pressure isothermally at high temperature. Based on these observations, we adopted the P–T path illustrated in Fig. 2 in the later runs (285, 291, and 666). From ambient temperature, we increased temperature gradually to 1300–1500 K at constant press load. Then we continuously and rapidly (100–
Fig. 2. The general pattern of the P–T paths followed in typical experiments.
1000 K/min) increased temperature. We closely monitored the diffraction patterns, and when spinel peaks began to diminish noticeably, we stopped increasing temperature. Upon completion of spinel dissociation, the press load was decreased at constant temperature (>1550 K) until we recognized that some spinel peaks appeared and some perovskite peaks diminished in the diffraction pattern. Then we cooled the sample to ambient temperature, and compressed it to desired press load. After that, this heating cycle was repeated. 2.5. Detection of the phase transitions In principle, it should be possible to determine the reaction from one phase to another by observing the weakening of peaks of a consumed phase and growth of those of a forming phase. However, the intensity ratios are usually not ideal because of the limited number of grains in the diffraction area. Therefore, unless the intensity changes of peaks are extremely clear, directions of a reaction cannot be reliably determined. For this reason, we adopted strict criteria to judge whether a reaction was proceeding or not. In the case of the dissociation of spinel to perovskite plus periclase, almost all peaks of spinel should disappear, and the main perovskite peaks should appear and grow large. Although it is difficult to initiate the dissociation as mentioned previously, once initiated, the reaction usually proceeded very fast, and was completed within
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Fig. 3. Examples of changes in diffraction patters associated with the phase transition. (a) Change of the diffraction patterns associated with the dissociation of spinel to perovskite plus periclase by rapid continuous temperature increase. All spinel peaks have disappeared. (b) Change of the diffraction patterns associated with the formation of spinel from perovskite plus periclase by isothermal decompression. New spinel peaks (e.g. (2 2 0)) merge. Some perovskite peaks (e.g. (0 2 0)) diminish or disappear, but others (e.g. (0 0 2)) still remain.
several minutes at temperatures above 1600 K. It was easy to judge the occurrence of the dissociation reaction in this case. A typical example of the change in the diffraction pattern associated with the dissociation of spinel to perovskite plus periclase is shown in Fig. 3a. In the case of formation of spinel from perovskite plus periclase, the reaction rate is much slower than that of dissociation. Usually, spinel formation did not
become complete within our experimental duration (a few tens of minutes). Hence, our criterion for spinel formation is that at least two spinel peaks should be observed, and some perovskite peaks should disappear or diminish. Spinel peaks should be weak or absent before the reaction. An example of a typical change in diffraction pattern associated with the formation of spinel from perovskite plus periclase is shown in Fig. 3b.
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3. Results We conducted nine runs (090, 161, 239, 240, 241, 285, 289, 291 and 666) in which compression, heating, temperature monitoring and acquiring of diffractions were successful. In all runs in which the starting material was forsterite + gold, forsterite first transformed to spinel at 1100–1300 K in any investigated pressure. In run number 090, we gradually increased temperature in 50 K steps up to 2000 K. Pressure was relatively constant, ranging from 22.0 to 22.4 GPa. It took 15 min for one temperature step in total. Spinel never dissociated to perovskite plus periclase in this run. In runs 239 and 240, spinel dissociated to perovskite plus periclase at the relatively low temperature of 1300 K and high pressure of 25.0 and 24.4 GPa, respectively, by normal temperature increase. In the later runs (241, 285, 289 and 666), the spinel that formed directly from forsterite dissociated at temperatures of 1550–1760 K and lower pressures of 22.1–23.2 GPa, by rapid temperature increase. In runs 285, 291 and 666, formation and dissociation of spinel were observed by isothermal decompression and rapid temperature increase, respectively. In these three runs, the formation and dissociation of spinel were repeated until the beam time was expired. Note that, in the run in which the starting material was a fine-grained mixture of forsterite + enstatite + periclase +gold, phase C (Kanzaki, 1993) was formed at 1050 K and 22.6 GPa because of absorbed water. This phase C began to decompose to form spinel from 1750 K and 22.6 GPa to higher temperatures. Table 1 summarizes the experimental conditions where an irreversible proceeding of the dissociation and formation of spinel was observed. Although we have numerous data points in which we did not observe a clear proceeding of the reactions, all such points are omitted because of kinetic problems. 4. Discussion 4.1. Phase relations The experimental results are plotted in Fig. 4. Spinel dissociation was observed above 22 GPa, whereas spinel formation was observed below 22 GPa.
Thus, we locate the phase boundary at 22 GPa in the temperature range of 1500–2100 K. Based on our parentheses, the post-spinel phase boundary in Mg2 SiO4 is constrained to have a gentle Clapeyron slope. The critical data points that define the Clapeyron slope are spinel formation at 1600 K and 21.9 GPa (666034), spinel dissociation at 2050 K and 22.2 GPa (291029), spinel formation at 2000 K and 21.6 GPa (285110) and spinel dissociation at 1550 K and 22.2 GPa (666042). Uncertainty in the slope arise from errors in calculating the pressure of spinel dissociation and formation (σ d and σ f , respectively) and from the 2θ calibration (σ a ). Considering the total error, σt2 = σd2 +σf2 +σa2 , the most positive and negative Clapeyron slopes are found to be 1.2 and −2.0 MPa/K, respectively. The central value is −0.4 MPa/K. Thus, the Clapeyron slope obtained here is less negative than previously obtained (−2.8 MPa/K, Ito and Takahashi, 1989), and could even be slightly positive. However, as mentioned previously and discussed in Section 4.2, the dissociation of spinel is more difficult to initiate than formation. The phase boundary should be located near the highest-pressure points in which spinel formation was detected rather than the lowest-pressure points in which spinel dissociation was detected. The Clapeyron slope should be close to the most negative bound. Therefore, we consider that the real phase boundary will have the Clapeyron slope of −0.4 to −2.0 MPa/K. 4.2. Reaction kinetics As mentioned above, spinel formed at high P–T is very inert. At temperatures around 1600 K, more than 2 GPa over-pressure is required to initiate the dissociation of spinel by gradual heating (240024). Even at temperatures around 2000 K, spinel survived outside its stability filed (22.4 GPa), when the sample was annealed for more than 10 h (run 090). In general, phase transitions should start from defects in crystals. Starting materials compressed at ambient temperature should have a high defect density in high-pressure experiments. This is the reason why phase transitions occur easily from starting materials in many high-pressure experiments. However, new phases that are formed at high pressure and temperature conditions should have a very low defect density because softening of the pressure media at
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Fig. 4. The phase relations of the post-spinel transition in Mg2 SiO4 . The solid circles denote the P–T conditions where growth of perovskite and diminishing of spinel were clearly observed. The open diamonds denote the P–T conditions where growth of spinel and diminishing of perovskite were clearly observed. The solid lines are possible locations of the phase boundary. The slope of the boundary can be from 1.2 to −2.0 MPa/K, and the middle value is −0.4 MPa/K. The probable slope will be between −0.4 and −2.0 MPa/K. Dotted and dashed lines are phase boundaries reported by Ito and Takahashi (1989) and Irifune et al. (1998), respectively. The gray triangles and squares denote the P–T conditions where the stability of spinel was reported by laser-heated diamond anvil studies, Shim et al. (2001) and Chudinovskikh and Boehler (2001), respectively.
high temperatures generates quasi-hydrostatic conditions in the sample. If the new phases are annealed at higher temperatures, their defect density will decrease further, and the sample will become more inert. To avoid this situation in our experiments, temperature was raised rapidly and continuously in order to generate uniaxial stresses on the sample by anisotropic thermal expansion in the cylindrical furnace system. Uniaxial stresses will create dislocations in the spinel crystals. Note that although rapid temperature increase is effective for initiating the transition, it should not have a significant affect on the pressure of the main part of the phase transition. It might also be postulated that upon rapid heating, the total pressure is increased by rapid temperature increase, leading to an underestimation in pressure once materials have relaxed. While this is a concern, we observed that after the reaction was initiated it proceeded even after temperature was held constant for tens of minutes. During that time we
observed no meaningful pressure variation (e.g. numbers 666026 and 666028). Formation of spinel is easier to initiate than dissociation. This is because the formation of spinel begins on the grain boundaries between perovskite and periclase, which are effective regions of crystal defects (Fig. 5). However, spinel formation is not reproducible and various amounts of under-pressures were required as seen in Fig. 4. One reason for the irreproducibility is the difficulty of detecting the beginning of spinel formation due to the limited number of grains in the diffraction area. Another is that high-temperature annealing is effective for preventing not only spinel dissociation but also spinel formation. The amount of under-pressure required to initiate the transition may vary depending on the experimental P–T time path due to variation in the extent of annealing in the sample. Once initiated, the formation of spinel did not proceed to completion in a few tens minutes. This is
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Fig. 5. Back-scattered electron images of the sample quenched from 2050 K and 20.8 GPa. Bright, light, gray, and dark parts should be gold, perovskite, spinel and periclase. Spinel is growing at the interfaces between perovskite and periclase.
probably because newly formed spinel grains effectively separate the perovskite and periclase grains, impeding further reaction (Fig. 5). 4.3. Comparison with previous works Irifune et al. (1998) located the post-spinel phase boundary in the temperature range of 1500–1700 K at nearly the same pressure (22 GPa) as in the present study. On the other hand, at 2000 K they located the boundary at 20.6 GPa, which is 1–1.5 GPa lower than our boundary. Although we constrain the Clapeyron slope between 1.2 and −2.0 MPa/K, they found a Clapeyron slope of −3 MPa/K. One possible explanation for this discrepancy is temperature variation in the sample. Irifune et al. (1998) adopted a sheet heater system, which should have a steeper temperature gradient than the cylindrical heater system in our assembly. If, for example, the sample was observed at a position close to the sheet heater but away from the thermocouple to remove diffractions of W–Re from their profiles, actual sample temperature could have been considerably higher than that indicated by the thermocouple. A 1–1.5 GPa pressure difference can be explained by 200 K deviation of temperature
because thermal pressure of gold is 0.6 MPa/K (Anderson et al., 1989). Another possible difference between studies is the criteria used to determine when a reaction is proceeding. Although the criteria used by Irifune et al. (1998) were not entirely clear, they did rely on change in the intensity of diffraction lines to judge when a reaction occurred. However, the small diffraction area relative to grain size makes it difficult, and dangerous, to estimate mineral proportions from the intensities of diffraction lines. As discussed above, we have adopted a strict criteria to judge when a reaction occurs, and did not rely on changes in relative peak intensities. Chudinovskikh and Boehler (2001) located the post-spinel transition in Mg2 SiO4 near 23 GPa at temperatures of 1800–2400 K using a laser-heated diamond anvil cell. However, they analyzed quenched samples, so strictly speaking, the direction of the reaction between spinel and perovskite plus periclase were not directly observed in their experiments. They used a very soft pressure media of either Ar or CsCl, and therefore, their spinel could have become very inert. Thus, although spinel or modified spinel was found in quenched samples, these observations do not directly indicate stability of these phases. However,
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these authors claimed that spinel and modified spinel were formed at 1800 K and 23.4 GPa and at 2300 K and 20.8 GPa, respectively, from perovskite plus periclase by pressure decrease. Although formation of modified spinel at 2300 K and 20.8 GPa agrees with our results, the formation of spinel at 1800 K and 23.4 GPa is in clear disagreement (Fig. 4). Shim et al. (2001) also located the post-spinel phase boundary in Mg2 SiO4 at 23–25 GPa by means of the laser-heated diamond anvil cell, but with in situ X-ray diffractometry. They estimated pressures using Pt for a pressure marker, which was mixed with sample and also served as a laser absorber. Some of the data points they reported are discrepant with our study: the disappearance of periclase at 1942 K and 22.3 GPa and formation of spinel at 1756 K and 22.7 GPa, and 1969 K and 22.8 GPa (Fig. 4) with errors of temperature and pressure of 50–150 K and 0.3–0.9 K, respectively. It is possible that stable phases could have been missed due to the limited number of grains in the diffraction area in their sample. They showed 2 GPa wide area of coexistence of spinel, perovskite, and periclase. In our study, once dissociation of spinel occurred, it was usually completed within several minutes and almost all spinel was consumed. This may indicate that the P–T condition of Shim et al.’s (2001) sample could be less uniform than considered by the authors. Ito and Takahashi (1989) placed the post-spinel phase boundary in Mg2 SiO4 with 1–2 GPa higher than found here, and with a steeper negative Clapeyron slope (−3 MPa/K). This discrepancy might be explained in terms of kinetic effects. Previous experiments have shown that, even when well within the perovskite stability field, forsterite starting material transforms into a metastable spinel phase at relatively low temperatures (<1500 K), but subsequently transforms into perovskite plus periclase at higher temperatures (Wang et al., 1997; Irifune et al., 1998). These results, combined with our own observations of the sluggish kinetics of the spinel transition at low temperatures (e.g. <1700 K) and especially in annealed samples, suggest that considerable excess pressures are needed to produce spinel dissociation at relatively lower temperatures. These effects could result in a steep negative Clapeyron slope for the dissociation reaction. This would also provide a reason why spinel and perovskite plus perilcase are formed
21
in lower and higher temperature regions, respectively, in a single sample (Ito and Takahashi, 1989). Calorimetric studies have also indicated a steep negative Clapeyron slope for the post-spinel transition (−3±1 MPa/K, i.e. Akaogi and Ito, 1993b). However, the entropy change associate with the transition is difficult to estimate because the thermochemical measurements are conducted at P–T conditions far from those of the phase boundary. For example, Mg and Si in spinel might be disordered at high temperatures, and in this case, spinel might have higher entropy than estimated from calorimetric measurements at relatively lower temperatures. If this were the case, the Clapeyron slope would be less steep than estimated thermochemically in the previous studies. Heat capacities at constant pressure, Cp at high temperatures are also difficult to estimate. MgSiO3 perovskite is easily altered at ambient pressure by slight heating and, therefore, Cp measurements have been conducted only in the temperature range of 140–295 K (Akaogi and Ito, 1993a), well below the Debye temperature of 1000 K. Reliable thermal expansion data are lacking for the same reason and, therefore, Cp at high temperatures is also difficult to estimate from heat capacity at constant volume, Cv . Taking into account these uncertainties, the thermochemically calculated Clapeyron slope could be less steep than −2 MPa/K (Akaogi, personal communication). 4.4. Accuracy of in situ X-ray diffraction study with multi-anvil press Although there are some discrepancies between our and Irifune et al.’s (1998) results, both studies showed 1–2 GPa lower pressure than that expected from the 660 km discontinuity (23 GPa). Garnet–perovskite transition in Mg3 Al2 Si3 O12 was also observed at by lower pressures by 1–2 GPa than expected (Hirose et al., 2001). Assuming that the 660 km discontinuity is definitely a consequence of the post-spinel transition, this would indicate that high P–T in situ X-ray diffraction studies in a multi-anvil press have some essential errors, as pointed out by Chudinovskikh and Boehler (2001) and Shim et al. (2001). One possible source of error is the unknown effect of pressure on thermocouple emf Getting and Kennedy (1970) studied the pressure effects on the emf of chromel–almel and Pt–Pt10Rh thermocouples.
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They suggested that Pt–Pt10Rh thermocouple underestimates temperature by 28 K at 5 GPa and 2273 K. Walter et al. (1995) compared temperatures indicated by W3Re–W25Re and Pt–Pt13Rh thermocouples. They showed that W3Re–W25Re thermocouple indicates 30 K higher temperature than Pt–Pt13Rh thermocouple at 7 GPa and 1573 K, and that this difference decreases with increasing temperature and pressure. We can use these findings to estimate the effect of pressure on thermocouple emf in this study. If we assume that the pressure dependencies of emf are similar between Pt–Pt10Rh and Pt–Pt13Rh thermocouples and that the temperatures indicated by W3Re–W25Re and Pt–Pt13Rh thermocouples are similar at 20–25 GPa and near 2000 K, we might have underestimated temperatures by 100–120 K at these P–T conditions. Underestimation of temperature by 100–120 K results in 0.6–0.7 GPa underestimation of pressure when using the gold pressure scale. Therefore, we suggest that pressure effects on thermocouple emf can partially explain the lower transition pressure, but may not be sufficient to explain the 2 GPa difference. Another source of uncertainty is the EOS for the gold pressure marker. For example, pressures calculated using the gold EOS proposed by Jamieson et al. (1982) are ca. 2 GPa higher than those calculated from Anderson et al.’s (1989) EOS at 22–25 GPa and 1200–1700 K (Ono et al., 2001). A similar uncertainty in pressure is also evident in the various proposed forms of the EOS for MgO (periclase) even though the state properties of this material have been extensively studied at high P and T. For example, the EOSs proposed by Matsui et al. (2000) and Speziale et al. (2001), respectively, give 2 and 1.5 GPa higher pressures at 1900 K and 25 GPa than that proposed by Jamieson et al. (1982). The point is, that in order to compare the pressure of the post-spinel transition to the depth of the seismic discontinuity, we must first establish a pressure marker with an equation of state that is reliable at simultaneously high pressure and high temperature. 4.5. Geophysical implications The absolute pressure of the post-spinel transition obtained in this study cannot be used to precisely elucidate the structure of the Earth’s interior due to the errors in the high P–T diifractometry in a multi-anvil
press as discussed earlier. However, our observation of a small Clapeyron slope is pertinent for discussing the dynamics in Earth’s mantle. Indeed, if we obtained transition pressures lower than the real ones due to inaccurate high P–T equation of state and pressure effect on emf, the Clapeyron slope would be less negative than that proposed here. Thus, we consider a Clapeyron slope of −2 MPa/K as a well constrained-lower bound. Flanagan and Shearer (1998) observed 20 km depressions in the 660 km discontinuity beneath Japan and Kuril island arcs, west of the Izu–Bonin arc, and west of the Tonga arc and under South America. A depression of 20 km corresponds to 0.86 GPa, as calculated from PREM (Dzievonski and Anderson, 1981). If these depressions are due to a temperature effect, then using the most negative Clapeyron slope of −2 MPa/K obtained in this study, temperatures at these regions are calculated to be at least 400 K lower than the surrounding mantle. However, based on our preliminary results on the water-bearing system (run 161), the presence of water may expand the stability field of spinel by at least 0.6 GPa at 1800 K. Therefore, an alternate explanation for topography at the 660 km discontinuity is water storage at the boundary between the upper and lower mantles. This hypothesis is not dependent on the Clapeyron slope of the post-spinel transition. A geophysically important controversy is whether the 660 km discontinuity can work as a barrier to mantle convection. In this debate, the Clapeyron slope of the post-spinel transition is usually considered to be −2 to −3 MPa/K (Davis, 1998). Our experimental results, however, indicate that the Clapeyron slope is less steep than −2 MPa/K. Therefore, it could be difficult for the post-spinel transition to act as an effective barrier to convective material transport between the upper and lower mantle. Recent seismological observations show that some subducted slabs, like those at Kurile and Izu–Bonin, do not penetrate into the lower mantle and stagnate at the upper and lower mantle boundary (Fukao, 2001). Such observations are usually explained by negative buoyancy caused by the steep negative Clapeyron slope of the post-spinel transition because the temperature of the subducted slab may be lower than the surrounding mantle. However, some subducted slabs, like those at Central and North America do penerate into the lower mantle (Fukao, 2001). These observations suggests that, if the floatation
T. Katsura et al. / Physics of the Earth and Planetary Interiors 136 (2003) 11–24
of the subducted slab is caused by the negative Clapeyron slope of the post-spinel transition, the Clapeyron slope may be close to the critical value that causes stagnancy of the subducted slab. This explanation is consistent with the present experimental results.
5. Summary 1. The phase relations of the post-spinel transition in Mg2 SiO4 were re-investigated by means of high P–T in situ X-ray diffractometry. The method used here is similar to that of Irifune et al. (1998), that is, we used energy-dispersive X-ray diffractometry, a Kawai-type apparatus, a gold pressure maker, a resistive furnace, and a W–Re thermocouple. 2. Spinel becomes very inert during long annealing at high temperatures, and it is difficult to initiate its dissociation. Continuous and fast temperature changes were conducted to overcome this difficulty. 3. Contrary to dissociation, formation of spinel from perovskite and periclase is easy to initiate by isothermal decompression. However, various amount of under-pressures were required to observe the spinel formation. 4. The phase boundary is located at 22 GPa, which is substantially lower than that expected from the depth of 660 km discontinuity. This result is similar to that of Irifune et al.’s (1998). If the 660 km discontinuity is attributed to the post-spinel transition, this discrepancy is possibly due to uncertainty in the equation of state of gold and/or pressure effect on emf of W–Re thermocouple. 5. It is found that the post-spinel transition has a smaller temperature dependence on pressure than found previously. From the present data set, the Clapeyron slope can be in the range of −2.0 to 1.2 MPa/K. Taking into account of the difficulty to initiate the dissociation of spinel, the Clapeyron slope will be in the range of −0.4 to −2.0 MPa/K. 6. The 20 km depressions observed at the 660 km discontinuity under subduction zones indicates at least 400 K lower temperature in these regions than in the surrounding mantle, if it is attributed to the temperature effect on the transition pressure. 7. The post-spinel transition would not be an effective barrier to mantle convection because the Clapey-
23
ron slope is not very steep. The reason why some slabs penetrate into the lower mantle and others do not could be the Clapeyron slope of the post-spinel transition is close to the critical value for which an effective buoyancy is achieved by the cold subducted slab.
Acknowledgements We thank C. Oka and Y. Shimizu for their technical assistances. The following people helped the X-ray operation at SPring-8: N. Mayama, R. Tanaka, K. Ozawa, M. Takano, M. Matsui, S. Koito, C. Takata and H. Kojitani. This study was conducted in the beam times of SPring-8 (Proposal no. 1997B0099-NODnp, 1998A0163-ND-np, 1999A0293-CD-np, and 1999B0276-CD-np). References Akaogi, M., Ito, B., 1993a. Heat capacity of MgSiO3 perovskite. Geophys. Res. Lett. 20, 105–108. Akaogi, M., Ito, E., 1993b. Refinement of enthalpy measurement of MgSiO3 perovskite and negative pressure–temperature slopes for perovskite-forming reactions. Geophys. Res. Lett. 20, 1839– 1842. Anderson, O.L., Isaak, D.G., Yamamoto, S., 1989. Anharmonicity and the equation of state for gold. J. Appl. Phys. 65, 1534–1543. Chudinovskikh, L., Boehler, R., 2001. High-pressure polymorphs of olivine arid the 660 km seismic discontinuity. Nature 411, 574–577. Davis, G.F., 1998. Plates, plumes, mantle convection, and mantle evolution. In: Jackson, I. (Ed.), The Earth’s Mantle. Cambridge University Press, New York, pp. 228–258. Dzievonski, A.M., Anderson, D.L., 1981. Preliminary reference Earth model. Phys. Earth Planet. Int. 25, 297–356. Flanagan, M.P., Shearer, P.M., 1998. Global mapping of topography on transition zone velocity discontinuities by stacking SS precursors. J. Geophys. Res. 103, 2673–2692. Getting, I.C., Kennedy, G.C., 1970. Effect of pressure on the emf of chromel–almel and platinum–platinum 10% rhodium thermocouples. J. Appl. Phys. 41, 4552–4563. Hirose, K., Fei, Y.-W., Ono, S., Yagi, T., Funakoshi, K., 2001. In situ measurements of the phase transition boundary in Mg3 Al2 Si3 O12 : implications for the nature of the seismic discontinuities in the Earth’s mantle. Earth Planet. Sci. Lett. 184, 567–573. Irifune, T., Nishiyama, N., Kuroda, K., Inoue, T., Isshiki, M., Utsumi, W., Funakoshi, K., Urakawa, S., Uchida, T., Katsura, T., Ohtaka, O., 1998. The postspinel phase boundary in Mg2 SiO4 determined by in situ X-ray diffraction. Science 279, 1693– 1700.
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Ito, E., Yamada, H., 1982. Stability relations of silicate spinels, ilmenites and perovskites, advances in earth and planetary sciences. In: Akimoto, S., Manghnani, M.H. (Eds.), High Pressure Research in Geophysics, vol. 12. Center for Academic Publications Japan, Tokyo, pp. 405–419. Ito, E., Takahashi, E., 1989. Post-spinel transformations in the system Mg2 SiO4 –Fe2 SiO4 and some geophysical implications. J. Geophys. Res. 94, 10637–10646. Jamieson, J.C., Fritz, J.N., Manghnani, M.H., 1982. Pressure measurement at high temperatures in X-ray diffraction studies: gold as a primary standard. In: Akimoto, S., Manghnani, M.H. (Eds.), High-Pressure Research in Geophysics. Center for Academic Publications Japan, Tokyo, pp. 27–48. Kanzaki, M., 1993. Calculated powder X-ray patterns of phase B, anhydrous B and superhydrous B: re-assessment of previous studies. Mineral. J. 16, 278–285. Matsui, M., Parker, S.C., Leslie, M., 2000. The MD simulation of the equation of state of MgO: application as a pressure calibration standard at high temperature and high pressure. Am. Mineral. 85, 312–316. Ono, S., Katsura, T., Ito, E., Kanzaki, M., Yoneda, A., Walter, M.J., Urakawa, S., Utsumi, W., Funakoshi, K., 2001. In situ
observation of ilmenite –perovskite phase transition in MgSiO3 using synchrotron radiation. Geophys. Res. Lett. 28, 835–838. Shim, S.-H., Duffy, T.S., Shen, G.-Y., 2001. The post-spinel transformation in Mg2 SiO4 and its relation to the 660 km seismic discontinuity. Nature 411, 571–574. Speziale, S., Zha, C.-S., Duffy, T.S., Hemley, R.J., Mao, H.-K., 2001. Quasi-hydrostatic compression of magnesium oxide to 52 GPa: implications for the pressure–volume–temperature equation of state. J. Geophys. Res. 106, 515–518. Utsumi, U., Funakoshi, K., Urakawa, S., Yamakata, M., Tsuji, K., Konishi, H., Shimomura, O., 1998. SPring-8 beamlines for high pressure science with multi-anvil apparatus. Rev. High Press. Sci. Technol. 7, 1484–1486. Walter, M.J., Thibault, Y., Wei, K., Luth, R.W., 1995. Characterizing experimental pressure and temperature conditions in multi-anvil apparatus. Can. J. Phys. 73., 273–296. Wang, Y.-B., Martinez, I., Guyot, F., Liebermann, R.C., 1997. The breakdown of olivine to perovskite and magnesiowustite. Science 275, 510–512. Yagi, T., 2001. “Kawai-type” apparatus. Foreword Rev. High Press. Sci. Tech. 11, 171 (in Japanese).
Post-spinel transition in Mg2 SiO4 determined by high P–T in situ X-ray diffractometry Tomoo Katsura a,∗ , Hitoshi Yamada a , Toru Shinmei a,1 , Atsushi Kubo a , Shigeaki Ono a,2 , Masami Kanzaki a , Akira Yoneda a , Michael J. Walter a , Eiji Ito a , Satoru Urakawa a,b , Kenichi Funakoshi a,c , Wataru Utsumi a,d a
c
Institute for Study of the Earth’s Interior, Okayama University, Misasa, Tottori-ken 682-0193, Japan b Department of Earth and Planetary Sciences, Okayama University, Okayama 700-0082, Japan Japan Synchrotron Radiation Research Institute, Kouto 1-1-1, Mikazuki-cho, Sayo-gun, Hyogo 678-5198, Japan d Japan Atomic Energy Research Institute, Kouto 1-1-1, Mikazuki-cho, Sayo-gun, Hyogo 678-5148, Japan Received 3 October 2001; received in revised form 16 June 2002; accepted 29 July 2002
Abstract The phase boundary of the post-spinel transition in Mg2 SiO4 was re-investigated by means of high P–T in situ X-ray diffractometry with a gold pressure marker in a Kawai-type apparatus. Rapid and continuous temperature changes were conducted to initiate dissociation of spinel, which tends to be inert after long annealing. Isothermal decompression at high temperature was conducted to form spinel from perovskite plus periclase. The phase boundary is located at ca. 22 GPa in the temperature range from 1550 to 2100 K, which is 1–1.5 GPa lower than the 660 km discontinuity. This discrepancy might be explained in terms of the pressure effect of thermocouple emf and inaccurate equation of state (EOS) for the pressure maker. The transition is found to be less sensitive to temperature than reported previously, with a Clapeyron slope ranging from −2 to −0.4 MPa/K. This small Clapeyron slope implies that the post-spinel transition would not be an effective barrier to mantle convection. © 2003 Elsevier Science B.V. All rights reserved. Keywords: Post-spinel transition; Mg2 SiO4 ; 660 km discontinuity; Mantle; High pressures and temperatures; In situ X-ray diffractometry
1. Introduction The 660 km seismic discontinuity is one of the most important structural boundaries in the Earth’s mantle, and is usually attributed to the dissociation of ∗ Corresponding author. Fax: +81-858-43-2184. E-mail address: [email protected] (T. Katsura). 1 Present address: Department of Geology and Geophysics, Yale University, New Haven, CT, USA. 2 Present address: Institute for Frontier Research on Earth Evolution, Japan Marine Science and Technology Center, Showa-machi, Kanazawa-ku, Yokohama 236-0001, Japan.
(Mg, Fe)2 SiO4 spinel to (Mg, Fe)SiO3 perovskite and (Mg, Fe)O ferropericlase (post-spinel transition). For this reason, many workers have studied the phase relations of the post-spinel transition in the end-member Mg2 SiO4 system (Ito and Yamada, 1982; Ito and Takahashi, 1989; Akaogi and Ito, 1993b; Irifune et al., 1998; Chudinovskikh and Boehler, 2001; Shim et al., 2001). Ito and Takahashi (1989) studied the post-spinel transition in the system Mg2 SiO4 –Fe2 SiO4 by means of the quench method in a Kawai-type apparatus. They found that the phase boundary is located at
0031-9201/03/$ – see front matter © 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0031-9201(03)00019-0
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23 GPa at 1900 K, corresponding to 660 km depth, and has a steep negative Clapeyron slope of −3 MPa/K. However, they were not able to determine pressure accurately and precisely because generated pressures were estimated by calibration against press load. Pressure measurements by in situ X-ray diffractometry suggest that generated pressures in multi-anvil presses vary due to different heating efficiency, heating path and run duration even if temperature and press load are the same. Further, we will show that the phase relations determined by normal quench-type experiments may have uncertainty due to the kinetic effects. Irifune et al. (1998) studied the post-spinel transition in Mg2 SiO4 using in situ X-ray diffractometry in a Kawai-type apparatus. Although they found essentially the same steep negative Clapeyron slope as Ito and Takahashi (1989), they located the phase boundary at about 2 GPa lower pressure. This result, if correct, has serious implications for our understanding of mantle structure because it suggests that the post-spinel transition should occur at ca. 600 km depth in the Earth at 1900 K. Therefore, the 660 km discontinuity cannot be explained by the post-spinel transition, and must be a result of a different phase transition and/or a change in bulk mantle chemistry. Recently, the post-spinel transition in Mg2 SiO4 was studied by means of the laser-heated diamond anvil cell (Chudinovskikh and Boehler, 2001; Shim et al., 2001). Although the boundary was not precisely determined in these two studies, it was concluded that the post-spinel transition occurs at a pressure that is generally consistent with the depth of 660 km discontinuity, contrary to Irifune et al.’s (1998) results. In this study, we re-investigated the phase relations of the post-spinel transition in Mg2 SiO4 by means of in situ X-ray diffractometry in a Kawai-type apparatus to examine the discrepancy of the transition pressure given by Irifune et al. (1998) with the depth of 660 km discontinuity. Although we adopted cell designs and reaction paths different from those of Irifune et al. (1998), the main principles of our experimental method are essentially the same. Therefore, if we would obtain similar results to Irifune et al. (1998), the discrepancy should result from the uncertainties associated with high P–T in situ X-ray diffraction study using a multi-anvil press, or the transition cannot be the cause of the 660 km discontinuity.
2. Experimental 2.1. Starting material Starting material for most runs was a mixture of synthetic forsterite (Mg2 SiO4 ) and gold with a 5:1 weight ratio. Mg metal was put into pure water, and HNO3 was added to make a Mg(NO3 )2 solution. Tetraethylorthosilicate ((CH3 CH2 O)4 Si) was weighed to produce a 2:1 molar Mg:Si ratio, and was added to the Mg(NO3 )2 solution. Ethanol was added to make a homogeneous solution. Ammonia was added to make gel. The gel was heated at 390 K to remove water and ethanol. Temperature was increased to 410 K, and then to 650 K to remove NH4 NO3 . The sample was baked at 1700 K for several hours to make pure crystalline forsterite. Fine gold powder with 0.1 m grain size obtained from Nilaco Corp was weighed, and mechanically mixed with the forsterite. An exception is run 161, in which a mixture of forsterite, enstatite, periclase and gold with weight ratio of 7:5:10:1 was used. The enstatite was synthesized in a similar way to forsterite. Periclase was reagent-grade MgO baked at 1300 K. As mentioned later, this mixture was finely pulverized, and may have absorbed a certain amount of water. 2.2. X-ray diffractometry Experiments were conducted at the third generation synchrotron radiation facility ‘SPring-8’ at Hyogo prefecture, Japan. We used a Kawai-type3 apparatus, ‘SPEED-1500’, installed at a bending magnet beam line BL04B1 (Utsumi et al., 1998). Energy-dispersive X-ray diffractometry was conducted with a horizontal goniometer using white X-rays. The vertical and horizontal widths of incident slits were 0.1 and 0.05 mm, respectively. The horizontal width of the collimator was 0.05 mm. The vertical and horizontal widths of receiving slits varied, but were usually 0.4 mm and 3 “Kawai-type apparatus” is a general name used for a doublestage multi-anvil apparatus that compresses an octahedral pressure medium with eight truncated cubes. So far, this apparatus has been called by many ways like “6–8 type apparatus”, “MA8 type apparatus”, “cubic-octahedral anvil press”, “split-sphere apparatus” or “Walker-type apparatus”. This name was proposed by Yagi (2001) after late professor N. Kawai, who originally developed this apparatus.
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0.2–0.3 mm, respectively. A Ge solid-state detector was used and connected to a multi-channel analyzer with 4096 channels, which was calibrated using characteristic X-rays of Cu, Mo, Ag, Ta, Pt, Au and Pb. Exposure times were usually 200–300 s. The energy range available for analyzing the sample was ca. 40–150 keV. The diffraction angle (2θ ) was ca. 4.9◦ . The diffraction angles were calibrated before compression of each run by matching the observed unit cell parameter of the pressure standard to the one at ambient conditions (a0 = 4.0786 A). Uncertainty in determination of the diffraction angle is ca. 0.001◦ , which produces 0.15 GPa uncertainty in pressure calculation. The generated pressure at high temperature was calculated from the unit cell volume of gold using the equation of state (EOS) of gold proposed by Anderson et al. (1989). At least three diffraction lines (1 1 1), (2 0 0) and (2 2 0) or (2 0 0), (2 2 0) and (3 1 1) were used to calculate pressure. In many cases, five diffraction lines (1 1 1), (2 0 0), (2 2 0), (3 1 1) and (2 2 2) were used. In the best case, seven lines were used, when the (4 0 0) and (4 2 0) lines were also sufficiently intense. Uncertainty of unit cell volume of
13
gold determined by least squares calculation usually gives 0.1–0.2 GPa uncertainty in pressure. Unfortunately, however, the SSD was in a bad condition during runs 289 and 291, and the errors are much larger in these experiments (Table 1). 2.3. Sample assembly We used WC anvils with 2.5 mm (run 239, 240, 285, 289, 291 and 666) and 3.0 mm (run 161 and 241) truncations. A horizontal cross-section of the sample assembly used with 2.5 mm truncations is shown in Fig. 1. The assembly used with 3.0 mm truncation is essentially the same. The incident X-rays followed a path from edge to edge of the octahedral pressure medium in a horizontal direction, and the cylindrical furnace system was placed with its axis almost parallel to the incident X-rays. The heater was a LaCrO3 cylinder with a length of 3.9 mm and outer and inner diameters of 2.2 and 1.5 mm, respectively. The heater was surrounded by a ZrO2 thermal insulator with a 5.0 mm outer diameter. A sample about 1.0 mm in length was loaded into a gold tube with a length of 2.0 mm, and outer and inner diameters of 0.8 and 0.75 mm. The
Fig. 1. A cross-section of the sample assembly in the horizontal plain parallel to the incident X-ray beam.
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Table 1 Experimental results Number Previous temperature (K)
Previous pressure (GPa)
Previous phases
Reaction temperature (K)
Reaction pressure (GPa)
Load Resultant (tonnes) phases
Comment
161028
RT
18.8 ± 0.5
Sp
2000
22.5 ± 0.1
1500
Pv
239013
1200
25.0 ± 0.1
Sp
1200
25.0 ± 0.1
1300
Pv + Sp
239015
1200
24.8 ± 0.1
Pv + Sp
1250
25.0 ± 0.1
1300
Pv
240024
1300
24.4 ± 0.1
Sp
1350
24.4 ± 0.1
1300
Pv + Sp
240029
1200
23.8 ± 0.1
Pv + Sp
1600
24.3 ± 0.1
1300
Pv
240088 241014
1700 1300
21.9 ± 0.1 23.0 ± 0.1
Pv Sp
1700 1700
21.8 ± 0.2 22.5 ± 0.2
870 1150
Sp Pv
285014
1300
23.5 ± 0.3
Sp
1550
23.2 ± 0.2
1300
Pv
285060 285061 285066
1800 1800 1800
21.0 ± 0.2 20.7 ± 0.2 20.9 ± 0.1
Pv Pv + Sp Pv + Sp
1800 1800 1850
20.7 ± 0.1 20.4 ± 0.1 20.9 ± 0.1
630 612 1000
Sp Sp Sp
285069 285071
1300 1800
ND 23.0 ± 0.1
Sp + Pv Sp + Pv
1800 1800
23.0 ± 0.1 22.6 ± 0.3
1350 1350
Sp + Pv Pv
285072
1800
22.6 ± 0.3
Pv + Sp
1900
22.8 ± 0.1
1350
Pv
285078 285082
1900 1900
21.8 ± 0.2 21.5 ± 0.1
Pv Pv + Sp
1900 1650
21.8 ± 0.2 21.1 ± 0.5
700 700
Sp Sp
285087
1400
20.2 ± 0.1
Pv + Sp
1900
21.1 ± 0.1
650
Sp
285095
Ambient temperature
ND
Sp + Pv
1900
23.1 ± 0.1
1400
Pv + Sp
285097
1900
22.8 ± 0.1
Sp + Pv
1900
23.0 ± 0.3
1400
Pv
285102 285103 285105 285110 285117 289013 291021 291023
1900 1900 RT 2000 2050 1300 RT 2050
22.3 21.9 ND 21.8 21.0 23.4 20.7 22.7
± 0.2 ± 0.2 0.1 0.1 0.1 0.5 0.1
Pv Pv + Sp Pv + Sp Pv Pv + Sp Sp Sp Pv
1900 1900 2000 2000 2050 1660 2050 1900
21.9 21.4 23.6 21.6 20.9 22.1 22.2 20.8
± ± ± ± ± ± ± ±
0.2 0.1 0.1 0.2 0.1 0.5 0.1 0.7
700 680 1500 725 600 1100 1170 704
Pv + Sp Sp Pv Pv + Sp Sp Pv Pv Sp
291025 291038
1300 1400
ND 21.5 ± 0.4
Pv + Sp Pv
2000 1750
23.2 ± 0.3 21.8 ± 0.3
1174 1194
Pv Sp
Normal heating at constant press load Temperature was kept constant for 20 min Temperature was gradually increased for 2 min Temperature was increased for 5 min Temperature was increased for 10 min Isothermal decompression Temperature was increased continuously by ca. 100 K/min Rapid heating at constant press load Isothermal decompression Isothermal decompression Temperature was slowly increased at constant press load. Continuous temperature increase The temperature and press load kept constant for 12 min Gradual temperature increase at constant press load Isothermal decompression Temperature gradually decreased at constant load. Growth of spinel peak is subtle Temperature gradually increased at constant load after decompression from 700 to 650 tonnes Continuous temperature increase. Growth and diminishing of perovskite and spinel, respectively, were subtle but continuing Temperature and load were kept constant for 30 min Isothermal decompression Isothermal decompression Rapid temperature increase Isothermal decompression Isothermal decompression Continuous temperature increase Continuous temperature increase Temperature decreased, and then isothermal decompression Continuous temperature increase Temperature was gradually increased at constant load
± ± ± ± ±
T. Katsura et al. / Physics of the Earth and Planetary Interiors 136 (2003) 11–24
15
Table 1 (Continued ) Number
Previous temperature (K)
Previous pressure (GPa)
Previous phases
Reaction temperature (K)
Reaction pressure (GPa)
Load Resultant (tonnes) phases
291043
1750
22.0 ± 0.5
Pv
1800
20.6 ± 0.2
710
Sp
291046
1800
ND
Sp + Pv
1550
22.8 ± 0.1
1300
Pv
291050
2000
ND
Sp + Pv
1600
22.1 ± 0.2
1150
Pv
666008
1140
22.9 ± 0.1
Sp
1557
22.9 ± 0.1
1000
Pv + Sp
666009
1557
22.9 ± 0.1
Pv + Sp
1557
22.7 ± 0.1
1000
Pv
666017 666026
1550 560
21.6 ± 0.1 ND
Pv Pv + Sp
1550 1607
21.4 ± 0.2 22.3 ± 0.1
700 900
Pv + Sp Pv + Sp
666028
1607
22.4 ± 0.1
Pv + Sp
1607
22.3 ± 0.1
900
Pv
666032 666034
1600 1600
21.9 ± 0.1 21.9 ± 0.1
Pv Pv + Sp
1600 1600
21.8 ± 0.1 21.9 ± 0.1
735 735
Pv + Sp Sp + Pv
666042 666044 666044
RT 579 1650
ND 20.0 ± 0.1 22.3 ± 0.1
Sp + Pv Pv + Sp Pv + Sp
1550 1650 1650
22.2 ± 0.1 22.3 ± 0.1 22.1 ± 0.1
903 900 900
Pv + Sp Pv + Sp Pv
666048 666050
1650 1650
22.1 ± 0.1 22.8 ± 0.1
Pv Pv + Sp
1650 1650
21.8 ± 0.1 21.5 ± 0.1
750 700
Pv + Sp Sp + Pv
666054
1196
21.6 ± 0.2
Sp + Pv
1800
22.4 ± 0.1
900
Py
666058 666059
1800 1800
21.9 ± 0.1 21.6 ± 0.1
Pv Pv + Sp
1800 1800
21.6 ± 0.1 21.5 ± 0.1
700 700
Pv + Sp Pv + Sp
666060
1647
ND
Pv + Sp
1784
22.2 ± 0.1
900
Pv + Sp
666061
1784
22.2 ± 0.1
Pv + Sp
1784
22.2 ± 0.1
900
Pv
666068
2100
21.4 ± 0.1
Pv
2100
21.1 ± 0.1
600
Pv + Sp
Comment
Isothermal decompression at 1800 K Temperature was rapidly decreased Temperature was rapidly decreased Continuous temperature increase by 100 K/min Temperature and press load kept constant Isothermal decompression Quick temperature increase. Sp largely decreased Temperature and press load kept constant Isothermal decompression Temperature and press load kept constant. Sp clearly grew Quick temperature increase Quick temperature increase Temperature and press load kept constant Isothermal decompression Isothermal decompression. Pv largely decreased. Continuous temperature increase by 200 K/min Isothermal decompression Temperature and press load kept constant. Spinel increased Continuous teinperature increase by 100 K/min Temperature and press load kept constant Isothermal decompression
ND: not determined; RT: room temperature; Pv: perovskite; Sp: spinel. In this table, only data points where an irreversible proceeding of the dissociation and formation of spinel was observed are shown. Other data points, where no clear proceeding of reactions was observed, are omitted. Diffraction peaks of periclase were always observed because of the X-ray window of the sample assembly, and therefore, periclase is omitted in the description of the phases.
gold tube was surrounded by an MgO spacer loaded into the heater. The temperature of the sample was measured by a W97Re3–W75Re25 thermocouple, which was inserted perpendicular to the sample through 0.6 mm diameter holes that were electrically insulated from the heater by MgO sleeves with outer and inner diameters of 0.6 and 0.2 mm. The electrical junction of the thermocouple was made with the gold tube, and thus the temperature of the gold tube was measured.
In the present cell assembly, we did not measure temperature exactly at the sample. However, we took a diffraction pattern of the sample in an area near the thermocouple in order to minimize uncertainty in sample temperature. In addition, we examined temperature variation in the sample in the horizontal direction by observing the cell parameter variation of gold while shifting the diffraction area, assuming constant pressure. We observed no systematic variation of the cell, which suggests the variation is
16
T. Katsura et al. / Physics of the Earth and Planetary Interiors 136 (2003) 11–24
probably <20 K. Therefore, we consider that the temperature measurement at the thermocouple is likely to be within 20 of the sample temperature. 2.4. Run procedure At the beginning of each run, the 2θ angle was calibrated by measuring the unit cell volume of the gold pressure marker at ambient conditions. The sample was then compressed to the desired press load at ambient temperature, and heated gradually. At 1100–1300 K, starting material of forsterite first transformed to spinel at pressures of 23–26 GPa. After that, while continuously taking diffraction patters, temperature and press load were increased and decreased, following complex P–T paths as described later. Generally, in the first heating cycles, sample pressure decreased with increasing temperature at a rate of −1 MPa/K at constant press load, probably due to stress relaxation of the pressure medium and gasket. In successive heating cycles, sample pressures increased upon temperature increase and decreased upon temperature decrease, at a rate of 1–3 MPa/K, as a consequence of thermal pressure. Decreasing press load can decrease sample pressure, although the first 10–15% decrease of load did not decrease samples pressures effectively due to considerable hysteresis. Note that the main problem in accurately determining the phase boundary of the post-spinel transition in Mg2 SiO4 was difficulty in initiating the dissociation of spinel to perovskite plus periclase. Spinel formed at high P–T conditions is very inert, which was also reported by Irifune et al. (1998). To eliminate this difficulty, temperature was changed rapidly (100–1000 K/min) and continuously, a procedure that we found promoted spinel dissociation. In contrast, formation of spinel from perovskite plus periclase occurred easier than dissociation. Although formation of spinel could be caused by cooling at constant press load as adopted by Irifune et al. (1998), we observed that spinel formation was more easily promoted by decreasing pressure isothermally at high temperature. Based on these observations, we adopted the P–T path illustrated in Fig. 2 in the later runs (285, 291, and 666). From ambient temperature, we increased temperature gradually to 1300–1500 K at constant press load. Then we continuously and rapidly (100–
Fig. 2. The general pattern of the P–T paths followed in typical experiments.
1000 K/min) increased temperature. We closely monitored the diffraction patterns, and when spinel peaks began to diminish noticeably, we stopped increasing temperature. Upon completion of spinel dissociation, the press load was decreased at constant temperature (>1550 K) until we recognized that some spinel peaks appeared and some perovskite peaks diminished in the diffraction pattern. Then we cooled the sample to ambient temperature, and compressed it to desired press load. After that, this heating cycle was repeated. 2.5. Detection of the phase transitions In principle, it should be possible to determine the reaction from one phase to another by observing the weakening of peaks of a consumed phase and growth of those of a forming phase. However, the intensity ratios are usually not ideal because of the limited number of grains in the diffraction area. Therefore, unless the intensity changes of peaks are extremely clear, directions of a reaction cannot be reliably determined. For this reason, we adopted strict criteria to judge whether a reaction was proceeding or not. In the case of the dissociation of spinel to perovskite plus periclase, almost all peaks of spinel should disappear, and the main perovskite peaks should appear and grow large. Although it is difficult to initiate the dissociation as mentioned previously, once initiated, the reaction usually proceeded very fast, and was completed within
T. Katsura et al. / Physics of the Earth and Planetary Interiors 136 (2003) 11–24
17
Fig. 3. Examples of changes in diffraction patters associated with the phase transition. (a) Change of the diffraction patterns associated with the dissociation of spinel to perovskite plus periclase by rapid continuous temperature increase. All spinel peaks have disappeared. (b) Change of the diffraction patterns associated with the formation of spinel from perovskite plus periclase by isothermal decompression. New spinel peaks (e.g. (2 2 0)) merge. Some perovskite peaks (e.g. (0 2 0)) diminish or disappear, but others (e.g. (0 0 2)) still remain.
several minutes at temperatures above 1600 K. It was easy to judge the occurrence of the dissociation reaction in this case. A typical example of the change in the diffraction pattern associated with the dissociation of spinel to perovskite plus periclase is shown in Fig. 3a. In the case of formation of spinel from perovskite plus periclase, the reaction rate is much slower than that of dissociation. Usually, spinel formation did not
become complete within our experimental duration (a few tens of minutes). Hence, our criterion for spinel formation is that at least two spinel peaks should be observed, and some perovskite peaks should disappear or diminish. Spinel peaks should be weak or absent before the reaction. An example of a typical change in diffraction pattern associated with the formation of spinel from perovskite plus periclase is shown in Fig. 3b.
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T. Katsura et al. / Physics of the Earth and Planetary Interiors 136 (2003) 11–24
3. Results We conducted nine runs (090, 161, 239, 240, 241, 285, 289, 291 and 666) in which compression, heating, temperature monitoring and acquiring of diffractions were successful. In all runs in which the starting material was forsterite + gold, forsterite first transformed to spinel at 1100–1300 K in any investigated pressure. In run number 090, we gradually increased temperature in 50 K steps up to 2000 K. Pressure was relatively constant, ranging from 22.0 to 22.4 GPa. It took 15 min for one temperature step in total. Spinel never dissociated to perovskite plus periclase in this run. In runs 239 and 240, spinel dissociated to perovskite plus periclase at the relatively low temperature of 1300 K and high pressure of 25.0 and 24.4 GPa, respectively, by normal temperature increase. In the later runs (241, 285, 289 and 666), the spinel that formed directly from forsterite dissociated at temperatures of 1550–1760 K and lower pressures of 22.1–23.2 GPa, by rapid temperature increase. In runs 285, 291 and 666, formation and dissociation of spinel were observed by isothermal decompression and rapid temperature increase, respectively. In these three runs, the formation and dissociation of spinel were repeated until the beam time was expired. Note that, in the run in which the starting material was a fine-grained mixture of forsterite + enstatite + periclase +gold, phase C (Kanzaki, 1993) was formed at 1050 K and 22.6 GPa because of absorbed water. This phase C began to decompose to form spinel from 1750 K and 22.6 GPa to higher temperatures. Table 1 summarizes the experimental conditions where an irreversible proceeding of the dissociation and formation of spinel was observed. Although we have numerous data points in which we did not observe a clear proceeding of the reactions, all such points are omitted because of kinetic problems. 4. Discussion 4.1. Phase relations The experimental results are plotted in Fig. 4. Spinel dissociation was observed above 22 GPa, whereas spinel formation was observed below 22 GPa.
Thus, we locate the phase boundary at 22 GPa in the temperature range of 1500–2100 K. Based on our parentheses, the post-spinel phase boundary in Mg2 SiO4 is constrained to have a gentle Clapeyron slope. The critical data points that define the Clapeyron slope are spinel formation at 1600 K and 21.9 GPa (666034), spinel dissociation at 2050 K and 22.2 GPa (291029), spinel formation at 2000 K and 21.6 GPa (285110) and spinel dissociation at 1550 K and 22.2 GPa (666042). Uncertainty in the slope arise from errors in calculating the pressure of spinel dissociation and formation (σ d and σ f , respectively) and from the 2θ calibration (σ a ). Considering the total error, σt2 = σd2 +σf2 +σa2 , the most positive and negative Clapeyron slopes are found to be 1.2 and −2.0 MPa/K, respectively. The central value is −0.4 MPa/K. Thus, the Clapeyron slope obtained here is less negative than previously obtained (−2.8 MPa/K, Ito and Takahashi, 1989), and could even be slightly positive. However, as mentioned previously and discussed in Section 4.2, the dissociation of spinel is more difficult to initiate than formation. The phase boundary should be located near the highest-pressure points in which spinel formation was detected rather than the lowest-pressure points in which spinel dissociation was detected. The Clapeyron slope should be close to the most negative bound. Therefore, we consider that the real phase boundary will have the Clapeyron slope of −0.4 to −2.0 MPa/K. 4.2. Reaction kinetics As mentioned above, spinel formed at high P–T is very inert. At temperatures around 1600 K, more than 2 GPa over-pressure is required to initiate the dissociation of spinel by gradual heating (240024). Even at temperatures around 2000 K, spinel survived outside its stability filed (22.4 GPa), when the sample was annealed for more than 10 h (run 090). In general, phase transitions should start from defects in crystals. Starting materials compressed at ambient temperature should have a high defect density in high-pressure experiments. This is the reason why phase transitions occur easily from starting materials in many high-pressure experiments. However, new phases that are formed at high pressure and temperature conditions should have a very low defect density because softening of the pressure media at
T. Katsura et al. / Physics of the Earth and Planetary Interiors 136 (2003) 11–24
19
Fig. 4. The phase relations of the post-spinel transition in Mg2 SiO4 . The solid circles denote the P–T conditions where growth of perovskite and diminishing of spinel were clearly observed. The open diamonds denote the P–T conditions where growth of spinel and diminishing of perovskite were clearly observed. The solid lines are possible locations of the phase boundary. The slope of the boundary can be from 1.2 to −2.0 MPa/K, and the middle value is −0.4 MPa/K. The probable slope will be between −0.4 and −2.0 MPa/K. Dotted and dashed lines are phase boundaries reported by Ito and Takahashi (1989) and Irifune et al. (1998), respectively. The gray triangles and squares denote the P–T conditions where the stability of spinel was reported by laser-heated diamond anvil studies, Shim et al. (2001) and Chudinovskikh and Boehler (2001), respectively.
high temperatures generates quasi-hydrostatic conditions in the sample. If the new phases are annealed at higher temperatures, their defect density will decrease further, and the sample will become more inert. To avoid this situation in our experiments, temperature was raised rapidly and continuously in order to generate uniaxial stresses on the sample by anisotropic thermal expansion in the cylindrical furnace system. Uniaxial stresses will create dislocations in the spinel crystals. Note that although rapid temperature increase is effective for initiating the transition, it should not have a significant affect on the pressure of the main part of the phase transition. It might also be postulated that upon rapid heating, the total pressure is increased by rapid temperature increase, leading to an underestimation in pressure once materials have relaxed. While this is a concern, we observed that after the reaction was initiated it proceeded even after temperature was held constant for tens of minutes. During that time we
observed no meaningful pressure variation (e.g. numbers 666026 and 666028). Formation of spinel is easier to initiate than dissociation. This is because the formation of spinel begins on the grain boundaries between perovskite and periclase, which are effective regions of crystal defects (Fig. 5). However, spinel formation is not reproducible and various amounts of under-pressures were required as seen in Fig. 4. One reason for the irreproducibility is the difficulty of detecting the beginning of spinel formation due to the limited number of grains in the diffraction area. Another is that high-temperature annealing is effective for preventing not only spinel dissociation but also spinel formation. The amount of under-pressure required to initiate the transition may vary depending on the experimental P–T time path due to variation in the extent of annealing in the sample. Once initiated, the formation of spinel did not proceed to completion in a few tens minutes. This is
20
T. Katsura et al. / Physics of the Earth and Planetary Interiors 136 (2003) 11–24
Fig. 5. Back-scattered electron images of the sample quenched from 2050 K and 20.8 GPa. Bright, light, gray, and dark parts should be gold, perovskite, spinel and periclase. Spinel is growing at the interfaces between perovskite and periclase.
probably because newly formed spinel grains effectively separate the perovskite and periclase grains, impeding further reaction (Fig. 5). 4.3. Comparison with previous works Irifune et al. (1998) located the post-spinel phase boundary in the temperature range of 1500–1700 K at nearly the same pressure (22 GPa) as in the present study. On the other hand, at 2000 K they located the boundary at 20.6 GPa, which is 1–1.5 GPa lower than our boundary. Although we constrain the Clapeyron slope between 1.2 and −2.0 MPa/K, they found a Clapeyron slope of −3 MPa/K. One possible explanation for this discrepancy is temperature variation in the sample. Irifune et al. (1998) adopted a sheet heater system, which should have a steeper temperature gradient than the cylindrical heater system in our assembly. If, for example, the sample was observed at a position close to the sheet heater but away from the thermocouple to remove diffractions of W–Re from their profiles, actual sample temperature could have been considerably higher than that indicated by the thermocouple. A 1–1.5 GPa pressure difference can be explained by 200 K deviation of temperature
because thermal pressure of gold is 0.6 MPa/K (Anderson et al., 1989). Another possible difference between studies is the criteria used to determine when a reaction is proceeding. Although the criteria used by Irifune et al. (1998) were not entirely clear, they did rely on change in the intensity of diffraction lines to judge when a reaction occurred. However, the small diffraction area relative to grain size makes it difficult, and dangerous, to estimate mineral proportions from the intensities of diffraction lines. As discussed above, we have adopted a strict criteria to judge when a reaction occurs, and did not rely on changes in relative peak intensities. Chudinovskikh and Boehler (2001) located the post-spinel transition in Mg2 SiO4 near 23 GPa at temperatures of 1800–2400 K using a laser-heated diamond anvil cell. However, they analyzed quenched samples, so strictly speaking, the direction of the reaction between spinel and perovskite plus periclase were not directly observed in their experiments. They used a very soft pressure media of either Ar or CsCl, and therefore, their spinel could have become very inert. Thus, although spinel or modified spinel was found in quenched samples, these observations do not directly indicate stability of these phases. However,
T. Katsura et al. / Physics of the Earth and Planetary Interiors 136 (2003) 11–24
these authors claimed that spinel and modified spinel were formed at 1800 K and 23.4 GPa and at 2300 K and 20.8 GPa, respectively, from perovskite plus periclase by pressure decrease. Although formation of modified spinel at 2300 K and 20.8 GPa agrees with our results, the formation of spinel at 1800 K and 23.4 GPa is in clear disagreement (Fig. 4). Shim et al. (2001) also located the post-spinel phase boundary in Mg2 SiO4 at 23–25 GPa by means of the laser-heated diamond anvil cell, but with in situ X-ray diffractometry. They estimated pressures using Pt for a pressure marker, which was mixed with sample and also served as a laser absorber. Some of the data points they reported are discrepant with our study: the disappearance of periclase at 1942 K and 22.3 GPa and formation of spinel at 1756 K and 22.7 GPa, and 1969 K and 22.8 GPa (Fig. 4) with errors of temperature and pressure of 50–150 K and 0.3–0.9 K, respectively. It is possible that stable phases could have been missed due to the limited number of grains in the diffraction area in their sample. They showed 2 GPa wide area of coexistence of spinel, perovskite, and periclase. In our study, once dissociation of spinel occurred, it was usually completed within several minutes and almost all spinel was consumed. This may indicate that the P–T condition of Shim et al.’s (2001) sample could be less uniform than considered by the authors. Ito and Takahashi (1989) placed the post-spinel phase boundary in Mg2 SiO4 with 1–2 GPa higher than found here, and with a steeper negative Clapeyron slope (−3 MPa/K). This discrepancy might be explained in terms of kinetic effects. Previous experiments have shown that, even when well within the perovskite stability field, forsterite starting material transforms into a metastable spinel phase at relatively low temperatures (<1500 K), but subsequently transforms into perovskite plus periclase at higher temperatures (Wang et al., 1997; Irifune et al., 1998). These results, combined with our own observations of the sluggish kinetics of the spinel transition at low temperatures (e.g. <1700 K) and especially in annealed samples, suggest that considerable excess pressures are needed to produce spinel dissociation at relatively lower temperatures. These effects could result in a steep negative Clapeyron slope for the dissociation reaction. This would also provide a reason why spinel and perovskite plus perilcase are formed
21
in lower and higher temperature regions, respectively, in a single sample (Ito and Takahashi, 1989). Calorimetric studies have also indicated a steep negative Clapeyron slope for the post-spinel transition (−3±1 MPa/K, i.e. Akaogi and Ito, 1993b). However, the entropy change associate with the transition is difficult to estimate because the thermochemical measurements are conducted at P–T conditions far from those of the phase boundary. For example, Mg and Si in spinel might be disordered at high temperatures, and in this case, spinel might have higher entropy than estimated from calorimetric measurements at relatively lower temperatures. If this were the case, the Clapeyron slope would be less steep than estimated thermochemically in the previous studies. Heat capacities at constant pressure, Cp at high temperatures are also difficult to estimate. MgSiO3 perovskite is easily altered at ambient pressure by slight heating and, therefore, Cp measurements have been conducted only in the temperature range of 140–295 K (Akaogi and Ito, 1993a), well below the Debye temperature of 1000 K. Reliable thermal expansion data are lacking for the same reason and, therefore, Cp at high temperatures is also difficult to estimate from heat capacity at constant volume, Cv . Taking into account these uncertainties, the thermochemically calculated Clapeyron slope could be less steep than −2 MPa/K (Akaogi, personal communication). 4.4. Accuracy of in situ X-ray diffraction study with multi-anvil press Although there are some discrepancies between our and Irifune et al.’s (1998) results, both studies showed 1–2 GPa lower pressure than that expected from the 660 km discontinuity (23 GPa). Garnet–perovskite transition in Mg3 Al2 Si3 O12 was also observed at by lower pressures by 1–2 GPa than expected (Hirose et al., 2001). Assuming that the 660 km discontinuity is definitely a consequence of the post-spinel transition, this would indicate that high P–T in situ X-ray diffraction studies in a multi-anvil press have some essential errors, as pointed out by Chudinovskikh and Boehler (2001) and Shim et al. (2001). One possible source of error is the unknown effect of pressure on thermocouple emf Getting and Kennedy (1970) studied the pressure effects on the emf of chromel–almel and Pt–Pt10Rh thermocouples.
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T. Katsura et al. / Physics of the Earth and Planetary Interiors 136 (2003) 11–24
They suggested that Pt–Pt10Rh thermocouple underestimates temperature by 28 K at 5 GPa and 2273 K. Walter et al. (1995) compared temperatures indicated by W3Re–W25Re and Pt–Pt13Rh thermocouples. They showed that W3Re–W25Re thermocouple indicates 30 K higher temperature than Pt–Pt13Rh thermocouple at 7 GPa and 1573 K, and that this difference decreases with increasing temperature and pressure. We can use these findings to estimate the effect of pressure on thermocouple emf in this study. If we assume that the pressure dependencies of emf are similar between Pt–Pt10Rh and Pt–Pt13Rh thermocouples and that the temperatures indicated by W3Re–W25Re and Pt–Pt13Rh thermocouples are similar at 20–25 GPa and near 2000 K, we might have underestimated temperatures by 100–120 K at these P–T conditions. Underestimation of temperature by 100–120 K results in 0.6–0.7 GPa underestimation of pressure when using the gold pressure scale. Therefore, we suggest that pressure effects on thermocouple emf can partially explain the lower transition pressure, but may not be sufficient to explain the 2 GPa difference. Another source of uncertainty is the EOS for the gold pressure marker. For example, pressures calculated using the gold EOS proposed by Jamieson et al. (1982) are ca. 2 GPa higher than those calculated from Anderson et al.’s (1989) EOS at 22–25 GPa and 1200–1700 K (Ono et al., 2001). A similar uncertainty in pressure is also evident in the various proposed forms of the EOS for MgO (periclase) even though the state properties of this material have been extensively studied at high P and T. For example, the EOSs proposed by Matsui et al. (2000) and Speziale et al. (2001), respectively, give 2 and 1.5 GPa higher pressures at 1900 K and 25 GPa than that proposed by Jamieson et al. (1982). The point is, that in order to compare the pressure of the post-spinel transition to the depth of the seismic discontinuity, we must first establish a pressure marker with an equation of state that is reliable at simultaneously high pressure and high temperature. 4.5. Geophysical implications The absolute pressure of the post-spinel transition obtained in this study cannot be used to precisely elucidate the structure of the Earth’s interior due to the errors in the high P–T diifractometry in a multi-anvil
press as discussed earlier. However, our observation of a small Clapeyron slope is pertinent for discussing the dynamics in Earth’s mantle. Indeed, if we obtained transition pressures lower than the real ones due to inaccurate high P–T equation of state and pressure effect on emf, the Clapeyron slope would be less negative than that proposed here. Thus, we consider a Clapeyron slope of −2 MPa/K as a well constrained-lower bound. Flanagan and Shearer (1998) observed 20 km depressions in the 660 km discontinuity beneath Japan and Kuril island arcs, west of the Izu–Bonin arc, and west of the Tonga arc and under South America. A depression of 20 km corresponds to 0.86 GPa, as calculated from PREM (Dzievonski and Anderson, 1981). If these depressions are due to a temperature effect, then using the most negative Clapeyron slope of −2 MPa/K obtained in this study, temperatures at these regions are calculated to be at least 400 K lower than the surrounding mantle. However, based on our preliminary results on the water-bearing system (run 161), the presence of water may expand the stability field of spinel by at least 0.6 GPa at 1800 K. Therefore, an alternate explanation for topography at the 660 km discontinuity is water storage at the boundary between the upper and lower mantles. This hypothesis is not dependent on the Clapeyron slope of the post-spinel transition. A geophysically important controversy is whether the 660 km discontinuity can work as a barrier to mantle convection. In this debate, the Clapeyron slope of the post-spinel transition is usually considered to be −2 to −3 MPa/K (Davis, 1998). Our experimental results, however, indicate that the Clapeyron slope is less steep than −2 MPa/K. Therefore, it could be difficult for the post-spinel transition to act as an effective barrier to convective material transport between the upper and lower mantle. Recent seismological observations show that some subducted slabs, like those at Kurile and Izu–Bonin, do not penetrate into the lower mantle and stagnate at the upper and lower mantle boundary (Fukao, 2001). Such observations are usually explained by negative buoyancy caused by the steep negative Clapeyron slope of the post-spinel transition because the temperature of the subducted slab may be lower than the surrounding mantle. However, some subducted slabs, like those at Central and North America do penerate into the lower mantle (Fukao, 2001). These observations suggests that, if the floatation
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of the subducted slab is caused by the negative Clapeyron slope of the post-spinel transition, the Clapeyron slope may be close to the critical value that causes stagnancy of the subducted slab. This explanation is consistent with the present experimental results.
5. Summary 1. The phase relations of the post-spinel transition in Mg2 SiO4 were re-investigated by means of high P–T in situ X-ray diffractometry. The method used here is similar to that of Irifune et al. (1998), that is, we used energy-dispersive X-ray diffractometry, a Kawai-type apparatus, a gold pressure maker, a resistive furnace, and a W–Re thermocouple. 2. Spinel becomes very inert during long annealing at high temperatures, and it is difficult to initiate its dissociation. Continuous and fast temperature changes were conducted to overcome this difficulty. 3. Contrary to dissociation, formation of spinel from perovskite and periclase is easy to initiate by isothermal decompression. However, various amount of under-pressures were required to observe the spinel formation. 4. The phase boundary is located at 22 GPa, which is substantially lower than that expected from the depth of 660 km discontinuity. This result is similar to that of Irifune et al.’s (1998). If the 660 km discontinuity is attributed to the post-spinel transition, this discrepancy is possibly due to uncertainty in the equation of state of gold and/or pressure effect on emf of W–Re thermocouple. 5. It is found that the post-spinel transition has a smaller temperature dependence on pressure than found previously. From the present data set, the Clapeyron slope can be in the range of −2.0 to 1.2 MPa/K. Taking into account of the difficulty to initiate the dissociation of spinel, the Clapeyron slope will be in the range of −0.4 to −2.0 MPa/K. 6. The 20 km depressions observed at the 660 km discontinuity under subduction zones indicates at least 400 K lower temperature in these regions than in the surrounding mantle, if it is attributed to the temperature effect on the transition pressure. 7. The post-spinel transition would not be an effective barrier to mantle convection because the Clapey-
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ron slope is not very steep. The reason why some slabs penetrate into the lower mantle and others do not could be the Clapeyron slope of the post-spinel transition is close to the critical value for which an effective buoyancy is achieved by the cold subducted slab.
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