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Stable phase with the α-PbO2 type structure in MgF2 under high pressure and high temperature
Solid State Communications 148 (2008) 440–443
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Solid State Communications journal homepage: www.elsevier.com/locate/ssc
Stable phase with the α -PbO2 type structure in MgF2 under high pressure and high temperature Keiji Kusaba a,∗ , Takumi Kikegawa b a
Institute for Materials Research, Tohoku University, Katahira 2-1-1, Sendai 980-8577, Japan
b
Institute of Materials Structure Science, High Energy Accelerator Research Organization, Tsukuba 305-0801, Japan
article
info
Article history: Received 25 February 2008 Received in revised form 20 June 2008 Accepted 7 September 2008 by J.A. Brum Available online 11 September 2008 PACS: 61.10.NZ 61.50.Ks
a b s t r a c t High-pressure and high-temperature behavior of MgF2 was observed up to 15 GPa and 750 ◦ C by an insitu X-ray diffraction method. The single phase with the α -PbO2 type structure was obtained at 12.7 GPa and 750 ◦ C. The phase was almost quenchable to ambient condition. Its orthorhombic cell parameters were a0 = 4.590(1) Å, b0 = 5.555(1) Å and c0 = 5.048(1) Å and its volume per chemical formula was 1.1% smaller than that of the rutile phase at ambient condition. MgF2 was confirmed to have a stable region for the phase at around 13 GPa and 600 ◦ C and to have the rutile–CaCl2 –α -PbO2 –PdF2 type phase transition series under high pressure and high temperature, as predicted by a previous theoretical calculation method. The bulk modulus of the α -PbO2 type phase was determined to be K0 = 98.0(7) GPa. © 2008 Elsevier Ltd. All rights reserved.
Keywords: C. Crystal structure and symmetry D. Phase transition E. High pressure E. Synchrotron radiation
1. Introduction There have been many investigations of post-rutile type structures under high pressure in the field of earth science, crystallography, and solid state physics and chemistry since synthesis of rutile type SiO2 [1]. For example, MO2 -type oxides (M = Si, Ge, Sn and Pb) with the rutile structure (P42 /mnm) were examined for their high-pressure behavior using an in-situ Xray diffraction method [2–7]. These dioxides of 14th atomic group elements were generally reported to have three high-pressure phases, i.e. the CaCl2 -, the α -PbO2 - and the PdF2 -type phases. The thermodynamic stability fields of the three phases were confirmed under high pressure and high temperature. On the other hand, previous results about difluoride compounds with the rutile structure [8–12] were slightly different from those of the dioxides; however the sequence of the pressure-induced transitions itself was similar to that in oxides. The thermodynamic stability fields of the high-pressure phases were not determined yet. Especially, the α -PbO2 type phase was observed only in the decompression process of the PdF2 -type phase at room temperature [11,12]. Haines et al. [11] demonstrated that the α -PbO2 type MgF2 was stable in the pressure range between 11 GPa and 15 GPa
∗
Corresponding author. Tel.: +81 22 215 2089; fax: +81 22 215 2086. E-mail address: [email protected] (K. Kusaba).
0038-1098/$ – see front matter © 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.ssc.2008.09.017
using a theoretical calculation method. However, they could not experimentally observe the α -PbO2 type phase in the calculated pressure region. They only observed a metastable α -PbO2 type phase below 9 GPa in a decompression process. They proposed that the α -PbO2 type polymorph was a possible candidate for an intermediate phase between the rutile-type or the CaCl2 -type phases and the PdF2 -type phase. The aim of the present study is to find the stable α -PbO2 type MgF2 in the predicted pressure region, and to examine high-pressure behavior of the phase. Our final goal is to discuss the transition to the α -PbO2 type phase by comparing the experimental result of MgF2 with the theoretical calculation result. 2. Experimental In-situ X-ray observation was carried out using a large volume cubic press apparatus ‘‘MAX80’’ at AR-NE5C in Institute of Materials Structure Science, High Energy Accelerator Research Organization (KEK) [13]. Energy-dispersive type X-ray powder diffraction patterns were collected using a germanium solid state detector at 2θ = 6.99◦ . After each high-pressure experiment, an effective 2θ value was exactly determined from X-ray data of NaCl in a pressure medium at ambient condition. The fluctuation of the effective values in the present study was less than ±0.003◦ . The useful energy range was between 20 keV and 100 keV. Details
K. Kusaba, T. Kikegawa / Solid State Communications 148 (2008) 440–443
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Fig. 2. Energy-dispersive type X-ray powder diffraction patterns of recovered specimens at 0.1 MPa and 27 ◦ C. Escape peaks and diffraction lines of the rutiletype phase are shown by italic small characters, ‘‘e’’ and ‘‘r’’, respectively. (a) The α -PbO2 type phase with a small amount of the rutile-type phase quenched from the α -PbO2 type phase at 12.7 GPa and 750 ◦ C, as shown in Fig. 1(c). (b) A mixture of a metastable phase with the α -PbO2 type structure and the rutile-type phase quenched from the PdF2 -type phase at 14.7 GPa and 650 ◦ C, as shown in Fig. 1(d).
Fig. 1. Typical energy-dispersive type X-ray powder diffraction patterns of MgF2 . Escape peaks of a Ge-solid state detector are indicated by an italic small character, ‘‘e’’. (a) The rutile-type phase as a starting material. Diffraction lines lower than 70 keV are indexed on a tetragonal cell. (b) The CaCl2 -type phase after annealing at 500 ◦ C. Diffraction lines lower than 70 keV are indexed on an orthorhombic cell. (c) The α -PbO2 type phase. Major diffraction lines of the α -PbO2 type phase are only indexed on an orthorhombic cell in this figure. All diffraction lines can be indexed on an orthorhombic cell, as listed in Table 1. (d) The PdF2 -type phase. Diffraction lines lower than 80 keV are indexed on a cubic cell.
of the MAX80 system and the X-ray diffraction method were described in our report about high-pressure behavior of ZnF2 [12]. Single crystal of MgF2 provided by Union Materials Inc. was powdered for staring materials. The tetragonal cell parameters of MgF2 with the rutile structure at ambient condition were determined to be a0 = 4.620 ± 0.001 Å and c0 = 3.050 ± 0.001 Å by the X-ray powder diffraction method, as shown in Fig. 1(a). The volume per chemical formula was calculated to be V0 = 32.55 ± 3
0.01 Å , which was consistent with reported values [11,14–16]. The powdered MgF2 , and a mixture of NaCl as a pressure marker and MgO, were separately encased in a boron-epoxy pressure medium. A couple of carbon disk heaters for elevating temperature were also enclosed in the pressure medium. Temperatures of the specimen were directly measured using a K -type thermocouple, which was put in the center of the pressure medium. The internal heating system can hold the specimen under stable temperature condition. Pressures were calculated from X-ray diffraction data of NaCl on the basis of the Decker scale [17]. An error of pressure determination was estimated to be less than ±0.1 GPa. 3. Result and discussion 3.1. High-pressure phases of MgF2 Fig. 1 shows typical X-ray powder diffraction patterns of MgF2 , collected by energy-dispersive method. The X-ray diffraction pattern of the ambient-pressure phase with the rutile structure (P42 /mnm, Z = 2), as shown in Fig. 1(a), was broadened
by increasing pressure under solid state compression at room temperature. A typical preferential broadening phenomenon was observed at higher than ca. 9 GPa: the hkl (h 6= k) reflections were much broader than the hhl reflections. The 211 reflection was clearly split to 121 and 211 reflections at 12 GPa in the first high-pressure experiment. These results indicated that the rutile–CaCl2 type transition was induced under solid state compression condition. Fig. 1(b) shows the X-ray diffraction pattern of the high-pressure phase with the CaCl2 -type structure (Pnnm, Z = 2) at 11.1 GPa and 27 ◦ C, collected after annealing at 500 ◦ C in the first highpressure and high-temperature experiment. The orthorhombic cell parameters of the CaCl2 -type phase were calculated to be a = 4.407 ± 0.001 Å, b = 4.518 ± 0.001 Å and c = 2.971 ± 0.001 Å by least square method. The present result of the CaCl2 -type phase is consistent with the previous report using the diamond anvil cell [11]. Some new diffraction lines except for those of the CaCl2 type phase emerged by elevating temperature at 13 GPa in the second experiment. All diffraction lines from the CaCl2 -type phase vanished and the new diffraction lines were only observed at 12.7 GPa and 750 ◦ C, as shown in Fig. 1(c). All observed diffraction lines could be indexed on an orthorhombic cell, as listed in Table 1, and its cell parameters were calculated to be a = 4.456 ± 0.001 Å, b = 5.385 ± 0.001 Å and c = 4.908 ± 0.001 Å by a least-square method. The indices and relative intensities of the diffraction lines (Fig. 1(c)) indicated that the high-pressure phase has the α -PbO2 type structure (Pbcn, Z = 4). The α -PbO2 type phase remained at room temperature under the high-pressure condition after a cooling process, and the single phase was observed above 0.4 GPa in a pressure-release process at room temperature. The α -PbO2 type phase with a trace of the rutile-type phase was finally recovered at ambient condition, as shown in Fig. 2(a). The diffraction lines of the α -PbO2 type phase were still sharp, and its cell parameters at ambient condition were determined to be a0 = 4.590 ± 0.001 Å, b0 = 5.555 ± 0.001 Å and c0 = 5.048 ± 0.001 Å, as listed in Table 1. The volume per chemical formula of the α -PbO2 type phase was 1.1% smaller than that of the rutile-type phase. New diffraction lines of a cubic phase with the PdF2 type structure (Pa − 3, Z = 4) appeared in a diffraction pattern of the CaCl2 type phase, by elevating temperature at 15 GPa in the third experiment. The single phase of the PdF2 type phase was obtained at 14.7 GPa and 650 ◦ C, as shown in Fig. 1(d). Its cubic cell parameter was determined to be a = 4.797 ± 0.001 Å, based
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K. Kusaba, T. Kikegawa / Solid State Communications 148 (2008) 440–443
Table 1 Observed and calculated d-values of MgF2 with the α -PbO2 type structure hkl
110 111 002 021 200 102 121 112 211 022 220 130 202 221 113 023 041 302 321 312
P = 11.7 GPa and T = 750 ◦ C
P = 0.1 MPa and T = 27 ◦ C
dobs ./Å
dcalc . a /Å
dobs. /Å
dcalc . b /Å
3.433 2.813 2.452 2.361 2.228 2.150 2.085 1.997 1.897 1.814 1.717 1.665 1.650 1.620 1.477 1.399 1.299 – 1.258 –
3.433 2.813 2.454 2.361 2.228 2.150 2.086 1.996 1.899 1.814 1.717 1.665 1.650 1.620 1.477 1.398 1.298 – 1.257 –
3.537 2.896 2.779 2.433 2.297 2.213 2.150 2.056 1.955 1.868 1.769 1.717 1.698 1.669 1.519 1.440 1.340 1.308 1.295 1.274
3.538 2.898 2.778 2.434 2.295 2.212 2.150 2.055 1.956 1.868 1.769 1.717 1.698 1.670 1.520 1.439 1.339 1.308 1.295 1.274
a Values were calculated from cell parameters (a = 4.456 Å, b = 5.385 Å and c = 4.908 Å). b Values were also from cell parameters (a = 4.590 Å, b = 5.555 Å and c = 5.048 Å).
Fig. 4. Volume fraction change in a mixture of α -PbO2 type phase and the PdF2 type phase at 13.3 GPa and 500 ◦ C. (a) Initial state and (b) after 10 min. Circles and squares indicate major diffraction lines of the α -PbO2 type phase and the PdF2 -type phase, respectively. This change of the volume fraction shows that the α -PbO2 type phase is stabler than the PdF2 -type phase in this P–T condition.
also kinetic effects. A mixture of the phases was kept under a given pressure and temperature condition in an interval. Figs. 3 and 4 show changes of X-ray diffraction patterns in intervals. A partial transition from the rutile- or CaCl2 -type phase to the α -PbO2 type phase was clearly observed at 13.0 GPa and 600 ◦ C, as shown in Fig. 3. A partial transition from the PdF2 -type phase to the α -PbO2 type phase was also observed at 13.3 GPa and 500 ◦ C, as shown in Fig. 4. These two results demonstrated that the α -PbO2 type phase had a stable region nearby 13 GPa and 600 ◦ C. In other words, MgF2 has the rutile–CaCl2 –α -PbO2 –PdF2 type phase transition series under high pressure and high temperature as similar to SiO2 [6] and GeO2 [4,5]. 3.3. High-pressure behavior of the α -PbO2 type phase
Fig. 3. Volume fraction change in a mixture of α -PbO2 type phase and the rutileor CaCl2 -type phase at 13.0 GPa and 600 ◦ C. (a) Initial state and (b) after 20 min. Circles and triangles indicate major diffraction lines of the α -PbO2 type phase and the rutile- or CaCl2 -type phase, respectively. This change of the volume fraction shows that the α -PbO2 type phase is stabler than the rutile- or CaCl2 -type phase in this P–T condition.
on eleven observed d-values data. The cubic phase remained at room temperature after a cooling process under the high-pressure condition, and the single phase was observed above 11.5 GPa in a pressure-release process at room temperature. X-ray diffraction patterns became complicated below 11.5 GPa. The complicated pattern at ambient condition demonstrated that the PdF2 -type phase completely reverted to a mixture of the rutile-type phase and the α -PbO2 type phase, as shown in Fig. 2(b). It is remarkable that the X-ray diffraction pattern of the α -PbO2 type phase in Fig. 2(b) was broader than that in Fig. 2(a). The broad pattern suggests that the α -PbO2 type phase be metastably formed from the PdF2 -type phase at room temperature condition. 3.2. Stable region for the α -PbO2 type phase As mentioned in the above section, MgF2 had three highpressure phases in a narrow pressure range between 11 and 15 GPa. The phase relation among the three high-pressure phases was examined with a mind to not only thermodynamic effects but
Fig. 5 shows P–V data of the α -PbO2 type phase at 27 ◦ C, which observed in the decompression process of the single phase as shown in Fig. 1(c) anf Fig. 2(a). The bulk modulus of the α -PbO2 type phase was determined to be K0 = 98.0 ± 0.7 GPa by fitting the P–V data to the third-order Birch–Murnaghan equation of state with K 0 = 4 [18]. The present value was larger than that of a metastable phase (K0 = 69 GPa) [11]. The difference is probably attributed to a determination error of the volume in the previous study because the metastable phase with an orthorhombic cell was always observed with the rutile-type phase [11]: the volume of the orthorhombic cell was determined based on only four diffraction lines (110, 111, 102 and 121) and the 102 diffraction line overlapped to the 111 diffraction line of the rutile-type phase (see Fig. 2). On the other hand, the predicted value by the theoretical calculation (K0 = 78 GPa) [11] was relatively consistent with the present experimental value (K0 = 98.0 ± 0.7 GPa). Volume data of the rutile-type phase (Fig. 1(a)), the CaCl2 -type phase (Fig. 1(b)) and the PdF2 -type phase were also plotted in Fig. 5. The α -PbO2 type phase was slightly denser than the rutile type phase and the CaCl2 -type phase, and the FdF2 -type phase was much denser than the α -PbO2 -type phase. The volume change between the CaCl2 - and α -PbO2 type phases was calculated to be –0.6% at 11.1 GPa, and that between the α -PbO2 and PdF2 -type phases was –4.9% at 11.5 GPa. These results supported that MgF2 has the rutile–CaCl2 -α -PbO2 –PdF2 type phase transition series under high pressure as similar to the result about the stable region of the α -PbO2 type phase, as mentioned in Section 3.2. By linear fit of the pressure-cell parameter data of the α -PbO2 type phase in Fig. 6, the axial compressibilities of a, b and c axes were calculated to be 3.19 ± 0.05, 2.83 ± 0.03 and 2.64 ± 0.02 × 10−3 GPa−1 , respectively. The a-axis was more compressive than b-axis and c-axis, slightly.
K. Kusaba, T. Kikegawa / Solid State Communications 148 (2008) 440–443
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Table 2 Summary of α -PbO2 type MgF2
Thermodynamic Stable region V0 /Vrutile,0 K0 /GPa K0 β a /10−3 GPa−1 β b /10−3 GPa−1 β c /10−3 GPa−1
Present study
Previous study [11]
Experiment
Theory
Experimenta
Around 13 GPa and 600 ◦ C 0.989 ±0.001 98.0 ±0.7 4 (fixed) 3.19 ± 0.05 2.83 ± 0.03 2.64 ± 0.02
11–15 GPa
Not found
1.005 78 3.4 –b –b –b
0.984 69 4 (fixed) –b –b –b
a Data of a metastable phase, which formed from the PdF2 -type in a decompression process at room temperature. b An anisotropic property (βa > βb , βc ) was reported. However, these values were not reported.
the α -PbO2 type phase was not observed in compression experiments at room temperature, and the other is that the phase transition to α -PbO2 type phase was incomplete in 20 min at 13.0 GPa and 600 ◦ C, as shown in Fig. 3. Fig. 5. Volume per chemical formula of MgF2 as a function of pressure at 27 ◦ C. Diamonds, triangles, circles and squares show the rutile-, CaCl2 -, α -PbO2 - and PdF2 -type phases, respectively. Larger-open symbols and smaller-solid symbols indicate the present result and a previous study [11], respectively. The solid line shows a Birch–Murnaghan equation of state for the α -PbO2 type phase with K0 = 3
98 GPa, K = 4 and V0 = 32.18 Å . 0
4. Conclusion High-pressure and high-temperature behavior of MgF2 was investigated using a large volume press apparatus, ‘‘MAX80’’ with an internal heating system. We found a high-pressure phase with the α -PbO2 type structure based on a previous theoretical calculation. The present investigation is the first discovery of the stable α -PbO2 type phase in fluoride compounds. The property of the α -PbO2 type phase was agreement with the calculation. The present result shows an advantage of a large volume press apparatus with an internal heater system for an investigation about a transition controlled by kinetics. This discovery also suggests that high-pressure behavior of difluoride compounds with the rutile structure is similar to that of dioxides and that the stable α -PbO2 type phase of other difluoride compounds will be found under high pressure and high temperature. Acknowledgements We thank Dr. Shiro Sakuragi, the president of Union Materials Inc., who donated us single crystal specimens. This study was performed under the approval of the Photon Factory Program Advisory Committee (Proposal No. 06G257). References
Fig. 6. The axial compressibilities of α -PbO2 type phase at 27 ◦ C. Triangles, squares and diamonds show a/a0 , b/b0 and c /c0 , respectively.
3.4. Comparison with the theoretical calculation We found the stable α -PbO2 type MgF2 under high pressure in the present study, based on the previous theoretical calculation [11]. The observed properties of the phase are listed and compared to the predictions in Table 2. The experimental values of a metastable α -PbO2 type phase [11] are also listed in Table 2. The present result was consistent with the calculation. Especially, the present result and the calculation were in agreement on the thermodynamic stable region of the α -PbO2 type phase. The result demonstrates that the transition from the CaCl2 -type phase to the α -PbO2 type phase is not controlled only thermodynamically but also kinetically. In other words, the phase transition is a typical first-order transition, which is accelerated by a thermal effect. It is consistent with two experimental results, as follows. One is that
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18]
S.M. Stishov, S.V. Popova, Geochimiya 10 (1961) 837. T. Yagi, S. Akimoto, J. Geophys. Res. 85 (1980) 6991. J. Haines, J.M. Léger, O. Schulte, Science 271 (1996) 629. S. One, T. Tsuchiya, K. Hirose, Y. Ohishi, Phys. Rev. B 68 (2003) 014103. S. One, T. Tsuchiya, K. Hirose, Y. Ohishi, Phys. Rev. B 68 (2003) 134108. Y. Kuwayama, K. Hirose, N. Sata, Y. Ohishi, Science 309 (2005) 923. S. One, K. Funakoshi, A. Nozawa, T. Kikegawa, J. Appl. Phys. 97 (2005) 073523. L.-C. Ming, M.H. Manghnani, Geophys. Res. Lett. 6 (1973) 13. A. Tressaud, J.L. Soubeyroux, H. Touhara, G. Demazeau, F. Langlais, Mater. Res. Bull. 16 (1981) 207. A. Tressaud, G. Demazeau, High Temp. High Press. 16 (1984) 303. J. Haines, J.M. Léger, F. Gorelli, D.D. Klug, J.S. Tse, Z.Q. Li, Phys. Rev. B 64 (2001) 134110. K. Kusaba, T. Kikegawa, Solid State Commun. 145 (2008) 279. K. Kusaba, T. Kikegawa, J. Phys. Chem. Solids 63 (2002) 651. R.W.G. Wyckoff, Crystal Structures, vol. 1, 2nd ed., Robert E. Krieger Publishing, Malabar, 1982, p. 251. Baur W H, Acta Cryst. B 32 (1976) 2200. G. Vidal-Valat, J.P. Vidal, C.M.E. Zeyen, K. Kurki-Suonio, Acta Cryst. B 35 (1979) 1584. D.L. Decker, J. Appl. Phys. 42 (1971) 3239. F. Birch, Phys. Rev. 71 (1947) 809.
Contents lists available at ScienceDirect
Solid State Communications journal homepage: www.elsevier.com/locate/ssc
Stable phase with the α -PbO2 type structure in MgF2 under high pressure and high temperature Keiji Kusaba a,∗ , Takumi Kikegawa b a
Institute for Materials Research, Tohoku University, Katahira 2-1-1, Sendai 980-8577, Japan
b
Institute of Materials Structure Science, High Energy Accelerator Research Organization, Tsukuba 305-0801, Japan
article
info
Article history: Received 25 February 2008 Received in revised form 20 June 2008 Accepted 7 September 2008 by J.A. Brum Available online 11 September 2008 PACS: 61.10.NZ 61.50.Ks
a b s t r a c t High-pressure and high-temperature behavior of MgF2 was observed up to 15 GPa and 750 ◦ C by an insitu X-ray diffraction method. The single phase with the α -PbO2 type structure was obtained at 12.7 GPa and 750 ◦ C. The phase was almost quenchable to ambient condition. Its orthorhombic cell parameters were a0 = 4.590(1) Å, b0 = 5.555(1) Å and c0 = 5.048(1) Å and its volume per chemical formula was 1.1% smaller than that of the rutile phase at ambient condition. MgF2 was confirmed to have a stable region for the phase at around 13 GPa and 600 ◦ C and to have the rutile–CaCl2 –α -PbO2 –PdF2 type phase transition series under high pressure and high temperature, as predicted by a previous theoretical calculation method. The bulk modulus of the α -PbO2 type phase was determined to be K0 = 98.0(7) GPa. © 2008 Elsevier Ltd. All rights reserved.
Keywords: C. Crystal structure and symmetry D. Phase transition E. High pressure E. Synchrotron radiation
1. Introduction There have been many investigations of post-rutile type structures under high pressure in the field of earth science, crystallography, and solid state physics and chemistry since synthesis of rutile type SiO2 [1]. For example, MO2 -type oxides (M = Si, Ge, Sn and Pb) with the rutile structure (P42 /mnm) were examined for their high-pressure behavior using an in-situ Xray diffraction method [2–7]. These dioxides of 14th atomic group elements were generally reported to have three high-pressure phases, i.e. the CaCl2 -, the α -PbO2 - and the PdF2 -type phases. The thermodynamic stability fields of the three phases were confirmed under high pressure and high temperature. On the other hand, previous results about difluoride compounds with the rutile structure [8–12] were slightly different from those of the dioxides; however the sequence of the pressure-induced transitions itself was similar to that in oxides. The thermodynamic stability fields of the high-pressure phases were not determined yet. Especially, the α -PbO2 type phase was observed only in the decompression process of the PdF2 -type phase at room temperature [11,12]. Haines et al. [11] demonstrated that the α -PbO2 type MgF2 was stable in the pressure range between 11 GPa and 15 GPa
∗
Corresponding author. Tel.: +81 22 215 2089; fax: +81 22 215 2086. E-mail address: [email protected] (K. Kusaba).
0038-1098/$ – see front matter © 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.ssc.2008.09.017
using a theoretical calculation method. However, they could not experimentally observe the α -PbO2 type phase in the calculated pressure region. They only observed a metastable α -PbO2 type phase below 9 GPa in a decompression process. They proposed that the α -PbO2 type polymorph was a possible candidate for an intermediate phase between the rutile-type or the CaCl2 -type phases and the PdF2 -type phase. The aim of the present study is to find the stable α -PbO2 type MgF2 in the predicted pressure region, and to examine high-pressure behavior of the phase. Our final goal is to discuss the transition to the α -PbO2 type phase by comparing the experimental result of MgF2 with the theoretical calculation result. 2. Experimental In-situ X-ray observation was carried out using a large volume cubic press apparatus ‘‘MAX80’’ at AR-NE5C in Institute of Materials Structure Science, High Energy Accelerator Research Organization (KEK) [13]. Energy-dispersive type X-ray powder diffraction patterns were collected using a germanium solid state detector at 2θ = 6.99◦ . After each high-pressure experiment, an effective 2θ value was exactly determined from X-ray data of NaCl in a pressure medium at ambient condition. The fluctuation of the effective values in the present study was less than ±0.003◦ . The useful energy range was between 20 keV and 100 keV. Details
K. Kusaba, T. Kikegawa / Solid State Communications 148 (2008) 440–443
441
Fig. 2. Energy-dispersive type X-ray powder diffraction patterns of recovered specimens at 0.1 MPa and 27 ◦ C. Escape peaks and diffraction lines of the rutiletype phase are shown by italic small characters, ‘‘e’’ and ‘‘r’’, respectively. (a) The α -PbO2 type phase with a small amount of the rutile-type phase quenched from the α -PbO2 type phase at 12.7 GPa and 750 ◦ C, as shown in Fig. 1(c). (b) A mixture of a metastable phase with the α -PbO2 type structure and the rutile-type phase quenched from the PdF2 -type phase at 14.7 GPa and 650 ◦ C, as shown in Fig. 1(d).
Fig. 1. Typical energy-dispersive type X-ray powder diffraction patterns of MgF2 . Escape peaks of a Ge-solid state detector are indicated by an italic small character, ‘‘e’’. (a) The rutile-type phase as a starting material. Diffraction lines lower than 70 keV are indexed on a tetragonal cell. (b) The CaCl2 -type phase after annealing at 500 ◦ C. Diffraction lines lower than 70 keV are indexed on an orthorhombic cell. (c) The α -PbO2 type phase. Major diffraction lines of the α -PbO2 type phase are only indexed on an orthorhombic cell in this figure. All diffraction lines can be indexed on an orthorhombic cell, as listed in Table 1. (d) The PdF2 -type phase. Diffraction lines lower than 80 keV are indexed on a cubic cell.
of the MAX80 system and the X-ray diffraction method were described in our report about high-pressure behavior of ZnF2 [12]. Single crystal of MgF2 provided by Union Materials Inc. was powdered for staring materials. The tetragonal cell parameters of MgF2 with the rutile structure at ambient condition were determined to be a0 = 4.620 ± 0.001 Å and c0 = 3.050 ± 0.001 Å by the X-ray powder diffraction method, as shown in Fig. 1(a). The volume per chemical formula was calculated to be V0 = 32.55 ± 3
0.01 Å , which was consistent with reported values [11,14–16]. The powdered MgF2 , and a mixture of NaCl as a pressure marker and MgO, were separately encased in a boron-epoxy pressure medium. A couple of carbon disk heaters for elevating temperature were also enclosed in the pressure medium. Temperatures of the specimen were directly measured using a K -type thermocouple, which was put in the center of the pressure medium. The internal heating system can hold the specimen under stable temperature condition. Pressures were calculated from X-ray diffraction data of NaCl on the basis of the Decker scale [17]. An error of pressure determination was estimated to be less than ±0.1 GPa. 3. Result and discussion 3.1. High-pressure phases of MgF2 Fig. 1 shows typical X-ray powder diffraction patterns of MgF2 , collected by energy-dispersive method. The X-ray diffraction pattern of the ambient-pressure phase with the rutile structure (P42 /mnm, Z = 2), as shown in Fig. 1(a), was broadened
by increasing pressure under solid state compression at room temperature. A typical preferential broadening phenomenon was observed at higher than ca. 9 GPa: the hkl (h 6= k) reflections were much broader than the hhl reflections. The 211 reflection was clearly split to 121 and 211 reflections at 12 GPa in the first high-pressure experiment. These results indicated that the rutile–CaCl2 type transition was induced under solid state compression condition. Fig. 1(b) shows the X-ray diffraction pattern of the high-pressure phase with the CaCl2 -type structure (Pnnm, Z = 2) at 11.1 GPa and 27 ◦ C, collected after annealing at 500 ◦ C in the first highpressure and high-temperature experiment. The orthorhombic cell parameters of the CaCl2 -type phase were calculated to be a = 4.407 ± 0.001 Å, b = 4.518 ± 0.001 Å and c = 2.971 ± 0.001 Å by least square method. The present result of the CaCl2 -type phase is consistent with the previous report using the diamond anvil cell [11]. Some new diffraction lines except for those of the CaCl2 type phase emerged by elevating temperature at 13 GPa in the second experiment. All diffraction lines from the CaCl2 -type phase vanished and the new diffraction lines were only observed at 12.7 GPa and 750 ◦ C, as shown in Fig. 1(c). All observed diffraction lines could be indexed on an orthorhombic cell, as listed in Table 1, and its cell parameters were calculated to be a = 4.456 ± 0.001 Å, b = 5.385 ± 0.001 Å and c = 4.908 ± 0.001 Å by a least-square method. The indices and relative intensities of the diffraction lines (Fig. 1(c)) indicated that the high-pressure phase has the α -PbO2 type structure (Pbcn, Z = 4). The α -PbO2 type phase remained at room temperature under the high-pressure condition after a cooling process, and the single phase was observed above 0.4 GPa in a pressure-release process at room temperature. The α -PbO2 type phase with a trace of the rutile-type phase was finally recovered at ambient condition, as shown in Fig. 2(a). The diffraction lines of the α -PbO2 type phase were still sharp, and its cell parameters at ambient condition were determined to be a0 = 4.590 ± 0.001 Å, b0 = 5.555 ± 0.001 Å and c0 = 5.048 ± 0.001 Å, as listed in Table 1. The volume per chemical formula of the α -PbO2 type phase was 1.1% smaller than that of the rutile-type phase. New diffraction lines of a cubic phase with the PdF2 type structure (Pa − 3, Z = 4) appeared in a diffraction pattern of the CaCl2 type phase, by elevating temperature at 15 GPa in the third experiment. The single phase of the PdF2 type phase was obtained at 14.7 GPa and 650 ◦ C, as shown in Fig. 1(d). Its cubic cell parameter was determined to be a = 4.797 ± 0.001 Å, based
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K. Kusaba, T. Kikegawa / Solid State Communications 148 (2008) 440–443
Table 1 Observed and calculated d-values of MgF2 with the α -PbO2 type structure hkl
110 111 002 021 200 102 121 112 211 022 220 130 202 221 113 023 041 302 321 312
P = 11.7 GPa and T = 750 ◦ C
P = 0.1 MPa and T = 27 ◦ C
dobs ./Å
dcalc . a /Å
dobs. /Å
dcalc . b /Å
3.433 2.813 2.452 2.361 2.228 2.150 2.085 1.997 1.897 1.814 1.717 1.665 1.650 1.620 1.477 1.399 1.299 – 1.258 –
3.433 2.813 2.454 2.361 2.228 2.150 2.086 1.996 1.899 1.814 1.717 1.665 1.650 1.620 1.477 1.398 1.298 – 1.257 –
3.537 2.896 2.779 2.433 2.297 2.213 2.150 2.056 1.955 1.868 1.769 1.717 1.698 1.669 1.519 1.440 1.340 1.308 1.295 1.274
3.538 2.898 2.778 2.434 2.295 2.212 2.150 2.055 1.956 1.868 1.769 1.717 1.698 1.670 1.520 1.439 1.339 1.308 1.295 1.274
a Values were calculated from cell parameters (a = 4.456 Å, b = 5.385 Å and c = 4.908 Å). b Values were also from cell parameters (a = 4.590 Å, b = 5.555 Å and c = 5.048 Å).
Fig. 4. Volume fraction change in a mixture of α -PbO2 type phase and the PdF2 type phase at 13.3 GPa and 500 ◦ C. (a) Initial state and (b) after 10 min. Circles and squares indicate major diffraction lines of the α -PbO2 type phase and the PdF2 -type phase, respectively. This change of the volume fraction shows that the α -PbO2 type phase is stabler than the PdF2 -type phase in this P–T condition.
also kinetic effects. A mixture of the phases was kept under a given pressure and temperature condition in an interval. Figs. 3 and 4 show changes of X-ray diffraction patterns in intervals. A partial transition from the rutile- or CaCl2 -type phase to the α -PbO2 type phase was clearly observed at 13.0 GPa and 600 ◦ C, as shown in Fig. 3. A partial transition from the PdF2 -type phase to the α -PbO2 type phase was also observed at 13.3 GPa and 500 ◦ C, as shown in Fig. 4. These two results demonstrated that the α -PbO2 type phase had a stable region nearby 13 GPa and 600 ◦ C. In other words, MgF2 has the rutile–CaCl2 –α -PbO2 –PdF2 type phase transition series under high pressure and high temperature as similar to SiO2 [6] and GeO2 [4,5]. 3.3. High-pressure behavior of the α -PbO2 type phase
Fig. 3. Volume fraction change in a mixture of α -PbO2 type phase and the rutileor CaCl2 -type phase at 13.0 GPa and 600 ◦ C. (a) Initial state and (b) after 20 min. Circles and triangles indicate major diffraction lines of the α -PbO2 type phase and the rutile- or CaCl2 -type phase, respectively. This change of the volume fraction shows that the α -PbO2 type phase is stabler than the rutile- or CaCl2 -type phase in this P–T condition.
on eleven observed d-values data. The cubic phase remained at room temperature after a cooling process under the high-pressure condition, and the single phase was observed above 11.5 GPa in a pressure-release process at room temperature. X-ray diffraction patterns became complicated below 11.5 GPa. The complicated pattern at ambient condition demonstrated that the PdF2 -type phase completely reverted to a mixture of the rutile-type phase and the α -PbO2 type phase, as shown in Fig. 2(b). It is remarkable that the X-ray diffraction pattern of the α -PbO2 type phase in Fig. 2(b) was broader than that in Fig. 2(a). The broad pattern suggests that the α -PbO2 type phase be metastably formed from the PdF2 -type phase at room temperature condition. 3.2. Stable region for the α -PbO2 type phase As mentioned in the above section, MgF2 had three highpressure phases in a narrow pressure range between 11 and 15 GPa. The phase relation among the three high-pressure phases was examined with a mind to not only thermodynamic effects but
Fig. 5 shows P–V data of the α -PbO2 type phase at 27 ◦ C, which observed in the decompression process of the single phase as shown in Fig. 1(c) anf Fig. 2(a). The bulk modulus of the α -PbO2 type phase was determined to be K0 = 98.0 ± 0.7 GPa by fitting the P–V data to the third-order Birch–Murnaghan equation of state with K 0 = 4 [18]. The present value was larger than that of a metastable phase (K0 = 69 GPa) [11]. The difference is probably attributed to a determination error of the volume in the previous study because the metastable phase with an orthorhombic cell was always observed with the rutile-type phase [11]: the volume of the orthorhombic cell was determined based on only four diffraction lines (110, 111, 102 and 121) and the 102 diffraction line overlapped to the 111 diffraction line of the rutile-type phase (see Fig. 2). On the other hand, the predicted value by the theoretical calculation (K0 = 78 GPa) [11] was relatively consistent with the present experimental value (K0 = 98.0 ± 0.7 GPa). Volume data of the rutile-type phase (Fig. 1(a)), the CaCl2 -type phase (Fig. 1(b)) and the PdF2 -type phase were also plotted in Fig. 5. The α -PbO2 type phase was slightly denser than the rutile type phase and the CaCl2 -type phase, and the FdF2 -type phase was much denser than the α -PbO2 -type phase. The volume change between the CaCl2 - and α -PbO2 type phases was calculated to be –0.6% at 11.1 GPa, and that between the α -PbO2 and PdF2 -type phases was –4.9% at 11.5 GPa. These results supported that MgF2 has the rutile–CaCl2 -α -PbO2 –PdF2 type phase transition series under high pressure as similar to the result about the stable region of the α -PbO2 type phase, as mentioned in Section 3.2. By linear fit of the pressure-cell parameter data of the α -PbO2 type phase in Fig. 6, the axial compressibilities of a, b and c axes were calculated to be 3.19 ± 0.05, 2.83 ± 0.03 and 2.64 ± 0.02 × 10−3 GPa−1 , respectively. The a-axis was more compressive than b-axis and c-axis, slightly.
K. Kusaba, T. Kikegawa / Solid State Communications 148 (2008) 440–443
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Table 2 Summary of α -PbO2 type MgF2
Thermodynamic Stable region V0 /Vrutile,0 K0 /GPa K0 β a /10−3 GPa−1 β b /10−3 GPa−1 β c /10−3 GPa−1
Present study
Previous study [11]
Experiment
Theory
Experimenta
Around 13 GPa and 600 ◦ C 0.989 ±0.001 98.0 ±0.7 4 (fixed) 3.19 ± 0.05 2.83 ± 0.03 2.64 ± 0.02
11–15 GPa
Not found
1.005 78 3.4 –b –b –b
0.984 69 4 (fixed) –b –b –b
a Data of a metastable phase, which formed from the PdF2 -type in a decompression process at room temperature. b An anisotropic property (βa > βb , βc ) was reported. However, these values were not reported.
the α -PbO2 type phase was not observed in compression experiments at room temperature, and the other is that the phase transition to α -PbO2 type phase was incomplete in 20 min at 13.0 GPa and 600 ◦ C, as shown in Fig. 3. Fig. 5. Volume per chemical formula of MgF2 as a function of pressure at 27 ◦ C. Diamonds, triangles, circles and squares show the rutile-, CaCl2 -, α -PbO2 - and PdF2 -type phases, respectively. Larger-open symbols and smaller-solid symbols indicate the present result and a previous study [11], respectively. The solid line shows a Birch–Murnaghan equation of state for the α -PbO2 type phase with K0 = 3
98 GPa, K = 4 and V0 = 32.18 Å . 0
4. Conclusion High-pressure and high-temperature behavior of MgF2 was investigated using a large volume press apparatus, ‘‘MAX80’’ with an internal heating system. We found a high-pressure phase with the α -PbO2 type structure based on a previous theoretical calculation. The present investigation is the first discovery of the stable α -PbO2 type phase in fluoride compounds. The property of the α -PbO2 type phase was agreement with the calculation. The present result shows an advantage of a large volume press apparatus with an internal heater system for an investigation about a transition controlled by kinetics. This discovery also suggests that high-pressure behavior of difluoride compounds with the rutile structure is similar to that of dioxides and that the stable α -PbO2 type phase of other difluoride compounds will be found under high pressure and high temperature. Acknowledgements We thank Dr. Shiro Sakuragi, the president of Union Materials Inc., who donated us single crystal specimens. This study was performed under the approval of the Photon Factory Program Advisory Committee (Proposal No. 06G257). References
Fig. 6. The axial compressibilities of α -PbO2 type phase at 27 ◦ C. Triangles, squares and diamonds show a/a0 , b/b0 and c /c0 , respectively.
3.4. Comparison with the theoretical calculation We found the stable α -PbO2 type MgF2 under high pressure in the present study, based on the previous theoretical calculation [11]. The observed properties of the phase are listed and compared to the predictions in Table 2. The experimental values of a metastable α -PbO2 type phase [11] are also listed in Table 2. The present result was consistent with the calculation. Especially, the present result and the calculation were in agreement on the thermodynamic stable region of the α -PbO2 type phase. The result demonstrates that the transition from the CaCl2 -type phase to the α -PbO2 type phase is not controlled only thermodynamically but also kinetically. In other words, the phase transition is a typical first-order transition, which is accelerated by a thermal effect. It is consistent with two experimental results, as follows. One is that
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