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Phase boundaries and molar volumes of high-temperature and high-pressure phase V of LiBH4
Journal of Physics and Chemistry of Solids 76 (2015) 40–44
Contents lists available at ScienceDirect
Journal of Physics and Chemistry of Solids journal homepage: www.elsevier.com/locate/jpcs
Phase boundaries and molar volumes of high-temperature and high-pressure phase V of LiBH4 Hiroshi Yamawaki a,n, Hiroshi Fujihisa a, Yoshito Gotoh a, Satoshi Nakano b a b
National Institute of Advanced Industrial Science and Technology (AIST), AIST Tsukuba Central 5, 1-1-1 Higashi, Tsukuba, Ibaraki 305-8565, Japan National Institute for Materials Science (NIMS), Tsukuba, Ibaraki 305-0044, Japan
art ic l e i nf o
a b s t r a c t
Article history: Received 25 October 2013 Received in revised form 25 April 2014 Accepted 17 July 2014 Available online 4 August 2014
Raman measurements up to 14 GPa and 570 K and powder x-ray diffraction measurement from 4 to 28 GPa at 510 K were used to investigate the high-temperature and high-pressure phases of LiBH4. The B–H stretching Raman bands in high-temperature and high-pressure phase V were observed as one broad peak, which would arise from the disordered structure. The rotation of BH4 ions has also been observed by a quantum MD calculation. The results are consistent with the reported structure of phase V that is known to be an orientationally disordered structure. The Raman measurements indicated that the phase boundary between phases I and V and that between phases III and V have a negative slope against pressure. The negative slope could be explained by the Clausius–Clapeyron equation, assuming that the entropy of phase V is larger than that of phase I or III for the disordered structure of phase V. The molar volume of phase V, despite being a high-temperature phase, is smaller than that of phase III at the same pressure from powder x-ray diffraction measurement; therefore, the thermal expansion would be small compared to the volume change at the phase transition from phase III to V. & 2014 Elsevier Ltd. All rights reserved.
Keywords: A. Inorganic compounds C. High pressure C. Raman spectroscopy C. X-ray diffraction D. Phase transitions
1. Introduction Lithium-ion conductors have been widely investigated to satisfy the high requirements for a secondary battery. Fast Li þ ion conduction of LiBH4 was recently reported in a hightemperature phase [1]. Many complex hydrides including LiBH4 have been studied as solid ionic conductors [2–9]. Furthermore, many researchers have studied the complex hydrides as hydrogen storage materials [10]. The polymorphs of these substances with the same chemical composition can cause the appearance of different properties. The polymorphs of LiBH4 have been studied at various pressures and temperatures. Ambient pressure phase II of LiBH4 at room temperature is known to be an orthorhombic lattice with the Pnma space group [11]. It transforms to high-temperature phase I at 381 K. Phase I is an orientationally disordered structure that is accompanied by the rotation of the BH4 tetrahedron [12,13]. Many studies have reported the rotational motion of the BH4 ion in the crystal lattice [14–17]. The rotational motion has been reported to be associated with the fast-ion conduction in phase I [18–20]. In the past, the pressure–temperature phase diagram in
n
Corresponding author. E-mail address: [email protected] (H. Yamawaki).
http://dx.doi.org/10.1016/j.jpcs.2014.07.015 0022-3697/& 2014 Elsevier Ltd. All rights reserved.
LiBH4 was studied by a differential thermal analysis (DTA) measurement [21]. High-pressure phase III and high-temperature and high-pressure phase V were found, and the existence of phase IV has also been mentioned. The phase boundary from phase I to V was speculated from the connection between the anomaly points on the melting curve and by the kink of the phase boundary between phase III and the high-temperature phases (I and V). The slope of the phase boundary between phases I and V was estimated to be negative. However, the transition from phase I to V has not been confirmed directly, and the structures for some crystalline phases remain unresolved. Raman and x-ray diffraction measurements have been used to determine the pressure-induced phase transition to high-pressure phase III of LiBH4 at around 1 GPa [22]. Filinchuk et al. performed the x-ray diffraction measurement under high pressure at room temperature [23], and found a transition from phase III to another high-pressure phase (phase V denoted by Pistorius) above 10 GPa. They claimed that the structure models are Ama2 for phase III and Fm3m for phase V. Then, Dmitriev et al. reported the pressure–temperature phase diagram using these structural models [24]. On the other hand, we have reported that the I41/ acd structural model is appropriate for phase III by our powder x-ray diffraction measurement and the DFT calculation [25,26]. The I41/acd model can be verified by a theoretical study [27]. In addition, further compression of phase III caused a metastable phase V' at room temperature [25,26]. Phase V is thermodynamically stable around
H. Yamawaki et al. / Journal of Physics and Chemistry of Solids 76 (2015) 40–44
20 GPa. Takamura et al. reported ionic conductivity for these phases at high pressures [28]. Phases I and V have a higher conductivity than phase III. However, the ionic conductivity in both phases I and V decreased with increasing pressure. Our purpose is to clarify the high-pressure behaviors in phase V that was caused by the disordered structure. In this study, we examine the phase boundaries by the Raman measurement, and obtain the molar volumes of phase V by a powder x-ray measurement in a high-pressure and high-temperature region. The pressure–temperature phase diagram obtained by the Raman measurement has already been reported [25]; however, the details have not been described yet. This report discusses the negative slope of the phase boundary and the comparison of the molar volumes of phases III and V.
2. Material and methods A LiBH4 sample (purity 495%, Alfa-Aesar) was commercially obtained. Several diamond-anvil cells (DAC) were used to generate high pressure for the Raman, powder x-ray diffraction, and AC impedance measurements. A type-K thermocouple probe was fixed on one side of the anvil using an adhesive (Stycast 2850 GT), to monitor the temperature of the sample. About 10 disc-spring washers were inserted in each clamp screw to maintain the load during the temperature changes. The applied pressure was determined by measuring the fluorescence of the ruby balls, which were packed with the sample in the DAC [29]. The pressure resolution was 0.1 GPa. The procedure of sample preparation was carried out under an Ar atmosphere in a glove box due to the sensitivity of LiBH4 to moisture. High pressure was generated for the Raman measurement using a small DAC with a 30-mm diameter and a 20-mm height. The sample was sandwiched between diamond anvils with a culet diameter of 0.5 mm and a thickness of 1.2 mm. A sample chamber, 0.15 mm in diameter and 0.16 mm in thickness, was made by drilling a hole into an SUS301 or Rhenium metal plate. The Raman spectra were measured using a SPEX1877 triple polychromator with a liquid-nitrogen cooled CCD detector. The spectral resolution was 1.4 cm 1. An incident beam of 488 nm was produced by an Ar ion laser with a power of 10 mW. A 30-mm working distance 20 objective (Mitutoyo) was used to focus the beam on the sample in the DAC. The DAC was heated up to 570 K with a cartridge heater (160 W) in the atmosphere. Raman peaks for the lower frequency region cannot be observed clearly at high temperatures. Thus, we only measured the Raman spectra in the region from 2000 to 2500 cm 1. For the powder x-ray diffraction measurement, high pressure was generated using a DAC (a culet diameter of 0.4 mm) with a 48 mm diameter and a 25 mm height. The diamond anvil where the x-ray diffraction lines pass through was mounted onto a Be backing-plate to collect whole Debye–Scherrer rings up to 451 in 2θ. A sample chamber, 0.12 mm in diameter and 0.10 mm in thickness, was made by drilling a hole into a rhenium metal plate. The powdered sample was put inside this sample chamber without a pressure-medium. A pressure-medium could not be used due to the high reactivity of the sample. According to a previous paper [23], the quasi-hydrostatic condition was retained without a pressure-medium up to about 10 GPa at room temperature, which was indicated by the narrow ruby fluorescence bands. Furthermore, an inhomogeneous pressure distribution would be reduced at the high temperature of 510 K. The measurements of the samples were carried out on the beamline 18C at the Photon Factory of the High Energy Accelerator Research Organization (KEK) with the DAC. The x-ray beam was monochromatized to 20 keV and introduced to the sample through a pinhole collimator
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with a 60-μm diameter. The typical exposure time was 30 min. The x-ray diffraction patterns were recorded on an image-plate and converted into conventional 2θ-intensity data by the x-ray analysis software IPAnalizer [30] and the pattern-integration software PIP [31]. For the AC impedance measurements, high pressure was generated using a DAC with a 30 mm diameter and a 20 mm height. A sample piece was placed on the NaCl (a pressure medium) and bridged between the electrodes (thin platinum foil with a 5 μm thickness). The AC impedance data were collected using an impedance analyzer (Agilent 4294A) over a frequency range of 100 Hz to 10 MHz and were fitted by a semicircle in the Nyquist plot. We examined the relative change in the conductivity because of the unknown form factor. The detailed procedures for these Raman, powder x-ray diffraction, and AC impedance measurements are described elsewhere [32,33]. Quantum molecular dynamics (MD) calculations were made using the density functional theory (DFT) methods with the program Materials Studio CASTEP of Accelrys, Inc. [34]. The generalized gradient approximation using the Perdew–Burke– Ernzerhof for solids (GGA–PBEsol) exchange-correlation functional [35] and ultrasoft pseudopotentials [36] were employed. The energy cut-off for the plane wave basis set was 300.0 eV. The 2 2 2 supercell was simulated with the NVT ensemble at a specific temperature. The Monkhorst–Pack grid separation [37] was set to approximately 0.07 Å 1. The lattice parameters were set to the experimental values, and the atomic positions were optimized to minimize the total energy. The maximum force tolerance, maximum atomic displacement and total energy convergence tolerance were less than 0.01 eV/Å, 5.0 10 4 Å and 5.0 10 6 eV/atom, respectively.
3. Results and discussion Fig. 1 shows the pressure dependence of the Raman frequencies of the B–H stretching peaks in LiBH4 at 510 K. A discontinuous change with a frequency gap of 37 cm 1 caused by the transition from phase I to V appears at 3.8 GPa. The frequency shifts upward with increasing pressure at rates of 15.5 cm 1/GPa in phase I, and 12.4 cm 1/GPa in phase V. Raman peaks for the lower frequency
Fig. 1. Variation of Raman frequencies of the B–H stretching peak in LiBH4 against pressure at 510 K. Discontinuous change due to the transition from phase I to V was observed at 3.8 GPa. The inset shows Raman B–H stretching peaks in phases I and V.
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regions cannot be observed clearly due to the broadenings caused by thermal heating and/or compression. The inset in the figure shows the Raman peaks in the B–H stretching region of phases I and V. They have similar peak profiles and a broad peak for the B–H stretching bands. The ν1 and ν3 stretching modes of the BH4 ion exist in the 2200–2500 cm 1 region, and the very broad peaks for these modes were observed at 384 K and ambient pressure due to the transition to high-temperature phase I [13]. The Raman peak was reported not to separate into ν1 and ν3 peaks by the curvefitting due to the large broadening that originated from the ν3 peak [13]. The broadening was caused by the disordered structure due to the reorientation motion of the BH4 ion in the crystal lattice of phase I [12–17]. Phase V is a cubic lattice with the Fm3m space group and an orientationally disordered structure [23]. This structure has also been confirmed with a powder x-ray diffraction measurement as described later. Thus, the broad B–H stretching peak for phase V, which is similar to that for phase I, can be explained by the orientationally disordered structure of phase V. We performed a quantum MD calculation for phase V by the CASTEP code [34]. The MD calculation at 8 GPa and 450 K showed frequent rotations of BH4 ions within a period of 6 ps in phase V. The phase transitions from phase I to V at temperatures of 530, 550, and 570 K were also detected by the changes in the Raman frequencies of the B–H stretching peaks with a frequency gap of about 40 cm 1. Thus, the phase boundary between phases I and V could be obtained by Raman measurements. A reverse transition took place from phase V to phase I on decompression at the higher temperatures. The change in grain boundaries due to the transition was observed in-situ by a microscope. The I–V transition at 570 K occurred at a pressure of 3.6 GPa which is slightly lower than that at 510 K. The observed transition pressures decreased with increasing temperature with some variation. Fig. 2 shows that the slope of the phase boundary between phases I and V is inclined slightly from the perpendicular toward the negative side indicating a gradient of 1.5 102 K/GPa. In a previous DTA measurement, the I–V phase boundary was speculated by connecting two anomalous points of the phase boundaries with a straight line, and the slope of the phase boundary was suggested to be negative [21]. Our result is consistent with this report. The slope of the phase boundary in the pressure–temperature phase diagram can be described by the Clausius–Clapeyron equation, dT/dP ¼ΔV/ΔS. The ΔV is usually negative in the pressure-induced
Fig. 2. Pressure–temperature phase diagram for LiBH4 in the high-temperature region above 400 K. The phase boundary between phases I and V was slightly inclined from the perpendicular toward the negative slope side.
transition which indicates that the entropy change ΔS in the transition from phase I to V is positive. Namely, the entropy for phase V is larger than that for phase I. However, the slope of the phase boundary is approximately perpendicular; therefore, the difference in entropy for phases I and V would be quite small since both phases are orientationally disordered structures. The variation of Raman frequencies of the B–H stretching peaks at 473 K against pressure is plotted in Fig. 3. The B–H stretching bands split into four peaks at the transition from phase I to III, and become a single peak again at the transition from phase III to V. The high frequency region in phase III has been reported to exhibit more than four peaks due to B–H stretching peaks and some combination bands in the Raman measurement at room temperature under high pressure [22]. However, the correspondence relation between the observed peaks and the detailed vibrational modes has not been clarified yet. The phase transition from phase I to III and the subsequent transition to phase V were observed in the temperature range of 400–500 K. The phase boundaries that were obtained by Raman measurements in this temperature range are shown in Fig. 2. Phase transitions between phases I and III and between phases III and V were reversible for the compression and decompression processes. The phase boundary between phases III and V also has a negative slope as in the phase boundary between phases I and V. The pressure–temperature phase diagram agreed with the one in the previous report [24] with the exception of the structure of phase III. We believe that the I41/acd structural model is appropriate for phase III, which we suggested in our previous work [25,26]. The negative slope of the III–V phase boundary indicates that the entropy of phase V is larger than that of phase III. The orientation of the BH4 ions in the I41/acd structure of phase III is ordered. (In terms of an ordered structure, it is also the same for the Ama2 structure that Filinchuk et al. have claimed [23].) Therefore, the phase boundary between the ordered phase III and the disordered phase V would have a negative slope. A powder x-ray diffraction measurement was performed at 510 K. The inset in Fig. 4 shows a representative powder x-ray pattern of phase V at 510 K. However, the powder x-ray pattern of phase I did not have the sufficient quality for analysis due to the rapid grain growth. Meanwhile, the x-ray pattern of phase V could be fitted to the structural model with the cubic space group—Fm3m, which Filinchuk et al. have reported [23]. Thus, the BH4
Fig. 3. Variation of Raman frequencies of the B–H stretching peak in LiBH4 against pressure at 473 K. Phase I transformed to phase III, and subsequently to phase V on compression. The inset shows Raman B–H stretching peaks in phase III at 4.8 GPa and 473 K.
H. Yamawaki et al. / Journal of Physics and Chemistry of Solids 76 (2015) 40–44
Fig. 4. Pressure dependence of the molar volume in LiBH4 at room temperature and 510 K. The molar volumes of phase V (closed circles) as a function were fitted with a Vinet-type equation-of-state. The molar volumes of phase V, despite being a high-temperature phase are slightly smaller than those of phase III (open diamonds, lit. [25,26]) at the same pressure. The inset shows a powder x-ray pattern in phases V at 8.4 GPa and 510 K. The tick marks represent the calculated positions of the Bragg peaks for Fm3m cubic lattice.
Fig. 5. Single logarithmic plot of the inverse of the sample's resistances R against pressure on compression process at 510 K. No discontinuous change was observed on the compression path from phase I to V. The inset shows a Nyquist plot for LiBH4 at 2.7 GPa and 510 K.
tetrahedron would rotate almost isotropically. The pressure dependence of the molar volume of phase V at 510 K is shown in Fig. 4. We found the molar volume of phase V to be smaller than that of phase III at room temperature [25,26] despite the thermal expansion. Since phase III is an ordered structure and phase V is a disordered structure, the phase boundary is shown to have a negative slope against pressure as in Fig. 2. Therefore, the molar volume should shrink at the transition from phase III to V by the heating process. Phase V would have a higher density than phase III with this volume decrease. The thermal expansion would be small compared to the volume change at the phase transition. The molar volume versus pressure of phase V was fitted with the Vinet-type equation-of-state [38] by fixing a pressure derivative B0' to 4.0 as shown in Fig. 4. We
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obtained the molar volume of phase V at ambient pressure V0 ¼28.5 (3) cm3/mol, a bulk modulus B0 ¼ 25(2) GPa. The B0 of phase V at 510 K is larger than that of phase III (B0 ¼20.7(6) GPa by Nakano et al. [26], B0 ¼ 23.23(9) GPa by Filinchuk et al. [23]) at room temperature. The compressibility of phase V would be lower than that of phase III since phase V is a higher density phase than phase III. The molar volumes of phase V are larger than that of phase V' that appeared above 16 GPa. The difference in the volume would mainly be attributed to the thermal expansion since phase V' is a disordered structure distorted from phase V. Phase V was stable up to 28 GPa at 510 K. However, the rotation of the BH4 ion would be suppressed by the pressure increase. According to the MD calculation at 300 K, the rotation was observed frequently at 8 GPa. However, the rotation could not be observed at 25 GPa and BH4 ions only vibrated within 10 ps. If the rotation stopped, a transition to a new phase would occur due to the change in the symmetry of the crystal lattice. Fast-ion conduction of Li þ ions was reported in phase I at ambient pressure [1]. Ikeshoji et al. suggested that the hopping of Li ions occurs in conjunction with the rotation of the BH4 ion by a theoretical calculation [18,19]. The rotation of BH4 ions might also contribute to the ionic conduction in phase V. Therefore, we carried out an AC impedance measurement during the compression process from phase I to V (see the Supplementary data for details). First, a discontinuous change in conductivity was observed at around 400 K on heating at 1.2 GPa due to the transition from phase III to I. Subsequently a relative change of ionic conductivity was measured during the compression process from 2.7 GPa to 4.4 GPa at 510 K. The relative conductivity decreased as the pressure increased monotonically as shown in Fig. 5. The activation volume of ionic conduction was estimated to be 6.4 cm3/mol for phase I in the region of 2.7–3.5 GPa. No discontinuous change was observed on the compression path from phase I to V. The difference of ionic conductivity between phases I and V would be small in the pressure–temperature region around the phase boundary at 510 K. Takamura et al. have already reported the ionic conductivity of LiBH4 on heating at various pressures [28]. Their data shows that the conductivity in phase V is lower than that in phase I, which roughly agrees with our results. Takamura et al. [28] and Sundqvist et al. [39] have reported the activation volume for phase I to be near 3 cm3/mol at 2–3 GPa, while we obtained a value of 6.4 cm3/mol. The larger value may be due to the large deformation that occurred in our sample during the compression process. In this study, we also performed the Raman measurement around the phase boundary between phases I and III. Pistorius has reported the existence of phase IV in this region [21]. In our measurement, the Raman spectrum of the central part in the sample corresponds to that of phase III at 2.5 GPa and 442 K, while that of the surrounding part shows an overlapped spectrum of phases I and III. The pressure gradient in the sample would cause the coexistence of phases I and III. Thus, our data does not show any existence of phase IV. Dmitriev et al. reported that the anomaly of the DTA measurement could be explained on the basis of the mechanism of a two-stage transformation process [24]. Phase IV would not exist in the intermediate region between phases I and III.
4. Summary A pressure–temperature phase diagram of LiBH4 was examined in the high-temperature and high-pressure region. The phase transitions among phases I, III, and V were mutually reversible for the compression and decompression processes at high temperatures. Raman measurements indicated that the phase
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boundary between phases I and V and that between phases III and V have negative slopes against pressure. The negative slope could be explained by the Clausius–Clapeyron equation, assuming that the entropy of phase V is larger than that of phase I or III for the disordered structure of phase V. The rotationally disordered structure of phase V was confirmed by the quantum MD calculation. The molar volume of phase V, despite being a hightemperature phase, is smaller than that of phase III at the same pressure. The molar volume should shrink at the phase transition from phase III to V on heating due to the order–disorder transition. The thermal expansion would be small compared to the volume change at the phase transition. Acknowledgments This study was supported by JSPS KAKENHI [17550067, 20045019 and 22550185]. The synchrotron radiation x-ray experiments were performed at BL-18C of KEK-PF under the approval of Proposal nos. 2006G275, 2008G614 and 2010G516. Appendix A. Supplementary material Supplementary data associated with this paper can be found in the online version at http://dx.doi.org/10.1016/j.conengprac.2014. 04.004. References [1] M. Matsuo, Y. Nakamori, S. Orimo, H. Maekawa, H. Takamura, Appl. Phys. Lett. 91 (2007) 224103. [2] H. Maekawa, M. Matsuo, H. Takamura, M. Ando, Y. Noda, T. Karahashi, S. Orimo, J. Am. Chem. Soc. 131 (2009) 894–895. [3] H. Oguchi, M. Matsuo, J.S. Hummelshoj, T. Vegge, J.K. Norskov, T. Sato, Y. Miura, H. Takamura, H. Maekawa, S. Orimo, Appl. Phys. Lett. 94 (2009) 141912. [4] M. Matsuo, H. Takamura, H. Maekawa, H. Li, S. Orimo, Appl. Phys. Lett. 94 (2009) 084103. [5] M. Matsuo, A. Remhof, P. Martelli, R. Caputo, M. Ernst, Y. Miura, T. Sato, H. Oguchi, H. Maekawa, H. Takamura, A. Borgschulte, A. Züttel, S. Orimo, J. Am. Chem. Soc. 131 (2009) 16389–16391. [6] H. Oguchi, M. Matsuo, T. Sato, H. Takamura, H. Maekawa, H. Kuwano, S. Orimo, J. Appl. Phys. 107 (2010) 096104. [7] R. Miyazaki, T. Karahashi, N. Kumatani, Y. Noda, M. Ando, H. Takamura, M. Matsuo, S. Orimo, H. Maekawa, Solid State Ion. 192 (2011) 143–147.
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Contents lists available at ScienceDirect
Journal of Physics and Chemistry of Solids journal homepage: www.elsevier.com/locate/jpcs
Phase boundaries and molar volumes of high-temperature and high-pressure phase V of LiBH4 Hiroshi Yamawaki a,n, Hiroshi Fujihisa a, Yoshito Gotoh a, Satoshi Nakano b a b
National Institute of Advanced Industrial Science and Technology (AIST), AIST Tsukuba Central 5, 1-1-1 Higashi, Tsukuba, Ibaraki 305-8565, Japan National Institute for Materials Science (NIMS), Tsukuba, Ibaraki 305-0044, Japan
art ic l e i nf o
a b s t r a c t
Article history: Received 25 October 2013 Received in revised form 25 April 2014 Accepted 17 July 2014 Available online 4 August 2014
Raman measurements up to 14 GPa and 570 K and powder x-ray diffraction measurement from 4 to 28 GPa at 510 K were used to investigate the high-temperature and high-pressure phases of LiBH4. The B–H stretching Raman bands in high-temperature and high-pressure phase V were observed as one broad peak, which would arise from the disordered structure. The rotation of BH4 ions has also been observed by a quantum MD calculation. The results are consistent with the reported structure of phase V that is known to be an orientationally disordered structure. The Raman measurements indicated that the phase boundary between phases I and V and that between phases III and V have a negative slope against pressure. The negative slope could be explained by the Clausius–Clapeyron equation, assuming that the entropy of phase V is larger than that of phase I or III for the disordered structure of phase V. The molar volume of phase V, despite being a high-temperature phase, is smaller than that of phase III at the same pressure from powder x-ray diffraction measurement; therefore, the thermal expansion would be small compared to the volume change at the phase transition from phase III to V. & 2014 Elsevier Ltd. All rights reserved.
Keywords: A. Inorganic compounds C. High pressure C. Raman spectroscopy C. X-ray diffraction D. Phase transitions
1. Introduction Lithium-ion conductors have been widely investigated to satisfy the high requirements for a secondary battery. Fast Li þ ion conduction of LiBH4 was recently reported in a hightemperature phase [1]. Many complex hydrides including LiBH4 have been studied as solid ionic conductors [2–9]. Furthermore, many researchers have studied the complex hydrides as hydrogen storage materials [10]. The polymorphs of these substances with the same chemical composition can cause the appearance of different properties. The polymorphs of LiBH4 have been studied at various pressures and temperatures. Ambient pressure phase II of LiBH4 at room temperature is known to be an orthorhombic lattice with the Pnma space group [11]. It transforms to high-temperature phase I at 381 K. Phase I is an orientationally disordered structure that is accompanied by the rotation of the BH4 tetrahedron [12,13]. Many studies have reported the rotational motion of the BH4 ion in the crystal lattice [14–17]. The rotational motion has been reported to be associated with the fast-ion conduction in phase I [18–20]. In the past, the pressure–temperature phase diagram in
n
Corresponding author. E-mail address: [email protected] (H. Yamawaki).
http://dx.doi.org/10.1016/j.jpcs.2014.07.015 0022-3697/& 2014 Elsevier Ltd. All rights reserved.
LiBH4 was studied by a differential thermal analysis (DTA) measurement [21]. High-pressure phase III and high-temperature and high-pressure phase V were found, and the existence of phase IV has also been mentioned. The phase boundary from phase I to V was speculated from the connection between the anomaly points on the melting curve and by the kink of the phase boundary between phase III and the high-temperature phases (I and V). The slope of the phase boundary between phases I and V was estimated to be negative. However, the transition from phase I to V has not been confirmed directly, and the structures for some crystalline phases remain unresolved. Raman and x-ray diffraction measurements have been used to determine the pressure-induced phase transition to high-pressure phase III of LiBH4 at around 1 GPa [22]. Filinchuk et al. performed the x-ray diffraction measurement under high pressure at room temperature [23], and found a transition from phase III to another high-pressure phase (phase V denoted by Pistorius) above 10 GPa. They claimed that the structure models are Ama2 for phase III and Fm3m for phase V. Then, Dmitriev et al. reported the pressure–temperature phase diagram using these structural models [24]. On the other hand, we have reported that the I41/ acd structural model is appropriate for phase III by our powder x-ray diffraction measurement and the DFT calculation [25,26]. The I41/acd model can be verified by a theoretical study [27]. In addition, further compression of phase III caused a metastable phase V' at room temperature [25,26]. Phase V is thermodynamically stable around
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20 GPa. Takamura et al. reported ionic conductivity for these phases at high pressures [28]. Phases I and V have a higher conductivity than phase III. However, the ionic conductivity in both phases I and V decreased with increasing pressure. Our purpose is to clarify the high-pressure behaviors in phase V that was caused by the disordered structure. In this study, we examine the phase boundaries by the Raman measurement, and obtain the molar volumes of phase V by a powder x-ray measurement in a high-pressure and high-temperature region. The pressure–temperature phase diagram obtained by the Raman measurement has already been reported [25]; however, the details have not been described yet. This report discusses the negative slope of the phase boundary and the comparison of the molar volumes of phases III and V.
2. Material and methods A LiBH4 sample (purity 495%, Alfa-Aesar) was commercially obtained. Several diamond-anvil cells (DAC) were used to generate high pressure for the Raman, powder x-ray diffraction, and AC impedance measurements. A type-K thermocouple probe was fixed on one side of the anvil using an adhesive (Stycast 2850 GT), to monitor the temperature of the sample. About 10 disc-spring washers were inserted in each clamp screw to maintain the load during the temperature changes. The applied pressure was determined by measuring the fluorescence of the ruby balls, which were packed with the sample in the DAC [29]. The pressure resolution was 0.1 GPa. The procedure of sample preparation was carried out under an Ar atmosphere in a glove box due to the sensitivity of LiBH4 to moisture. High pressure was generated for the Raman measurement using a small DAC with a 30-mm diameter and a 20-mm height. The sample was sandwiched between diamond anvils with a culet diameter of 0.5 mm and a thickness of 1.2 mm. A sample chamber, 0.15 mm in diameter and 0.16 mm in thickness, was made by drilling a hole into an SUS301 or Rhenium metal plate. The Raman spectra were measured using a SPEX1877 triple polychromator with a liquid-nitrogen cooled CCD detector. The spectral resolution was 1.4 cm 1. An incident beam of 488 nm was produced by an Ar ion laser with a power of 10 mW. A 30-mm working distance 20 objective (Mitutoyo) was used to focus the beam on the sample in the DAC. The DAC was heated up to 570 K with a cartridge heater (160 W) in the atmosphere. Raman peaks for the lower frequency region cannot be observed clearly at high temperatures. Thus, we only measured the Raman spectra in the region from 2000 to 2500 cm 1. For the powder x-ray diffraction measurement, high pressure was generated using a DAC (a culet diameter of 0.4 mm) with a 48 mm diameter and a 25 mm height. The diamond anvil where the x-ray diffraction lines pass through was mounted onto a Be backing-plate to collect whole Debye–Scherrer rings up to 451 in 2θ. A sample chamber, 0.12 mm in diameter and 0.10 mm in thickness, was made by drilling a hole into a rhenium metal plate. The powdered sample was put inside this sample chamber without a pressure-medium. A pressure-medium could not be used due to the high reactivity of the sample. According to a previous paper [23], the quasi-hydrostatic condition was retained without a pressure-medium up to about 10 GPa at room temperature, which was indicated by the narrow ruby fluorescence bands. Furthermore, an inhomogeneous pressure distribution would be reduced at the high temperature of 510 K. The measurements of the samples were carried out on the beamline 18C at the Photon Factory of the High Energy Accelerator Research Organization (KEK) with the DAC. The x-ray beam was monochromatized to 20 keV and introduced to the sample through a pinhole collimator
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with a 60-μm diameter. The typical exposure time was 30 min. The x-ray diffraction patterns were recorded on an image-plate and converted into conventional 2θ-intensity data by the x-ray analysis software IPAnalizer [30] and the pattern-integration software PIP [31]. For the AC impedance measurements, high pressure was generated using a DAC with a 30 mm diameter and a 20 mm height. A sample piece was placed on the NaCl (a pressure medium) and bridged between the electrodes (thin platinum foil with a 5 μm thickness). The AC impedance data were collected using an impedance analyzer (Agilent 4294A) over a frequency range of 100 Hz to 10 MHz and were fitted by a semicircle in the Nyquist plot. We examined the relative change in the conductivity because of the unknown form factor. The detailed procedures for these Raman, powder x-ray diffraction, and AC impedance measurements are described elsewhere [32,33]. Quantum molecular dynamics (MD) calculations were made using the density functional theory (DFT) methods with the program Materials Studio CASTEP of Accelrys, Inc. [34]. The generalized gradient approximation using the Perdew–Burke– Ernzerhof for solids (GGA–PBEsol) exchange-correlation functional [35] and ultrasoft pseudopotentials [36] were employed. The energy cut-off for the plane wave basis set was 300.0 eV. The 2 2 2 supercell was simulated with the NVT ensemble at a specific temperature. The Monkhorst–Pack grid separation [37] was set to approximately 0.07 Å 1. The lattice parameters were set to the experimental values, and the atomic positions were optimized to minimize the total energy. The maximum force tolerance, maximum atomic displacement and total energy convergence tolerance were less than 0.01 eV/Å, 5.0 10 4 Å and 5.0 10 6 eV/atom, respectively.
3. Results and discussion Fig. 1 shows the pressure dependence of the Raman frequencies of the B–H stretching peaks in LiBH4 at 510 K. A discontinuous change with a frequency gap of 37 cm 1 caused by the transition from phase I to V appears at 3.8 GPa. The frequency shifts upward with increasing pressure at rates of 15.5 cm 1/GPa in phase I, and 12.4 cm 1/GPa in phase V. Raman peaks for the lower frequency
Fig. 1. Variation of Raman frequencies of the B–H stretching peak in LiBH4 against pressure at 510 K. Discontinuous change due to the transition from phase I to V was observed at 3.8 GPa. The inset shows Raman B–H stretching peaks in phases I and V.
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regions cannot be observed clearly due to the broadenings caused by thermal heating and/or compression. The inset in the figure shows the Raman peaks in the B–H stretching region of phases I and V. They have similar peak profiles and a broad peak for the B–H stretching bands. The ν1 and ν3 stretching modes of the BH4 ion exist in the 2200–2500 cm 1 region, and the very broad peaks for these modes were observed at 384 K and ambient pressure due to the transition to high-temperature phase I [13]. The Raman peak was reported not to separate into ν1 and ν3 peaks by the curvefitting due to the large broadening that originated from the ν3 peak [13]. The broadening was caused by the disordered structure due to the reorientation motion of the BH4 ion in the crystal lattice of phase I [12–17]. Phase V is a cubic lattice with the Fm3m space group and an orientationally disordered structure [23]. This structure has also been confirmed with a powder x-ray diffraction measurement as described later. Thus, the broad B–H stretching peak for phase V, which is similar to that for phase I, can be explained by the orientationally disordered structure of phase V. We performed a quantum MD calculation for phase V by the CASTEP code [34]. The MD calculation at 8 GPa and 450 K showed frequent rotations of BH4 ions within a period of 6 ps in phase V. The phase transitions from phase I to V at temperatures of 530, 550, and 570 K were also detected by the changes in the Raman frequencies of the B–H stretching peaks with a frequency gap of about 40 cm 1. Thus, the phase boundary between phases I and V could be obtained by Raman measurements. A reverse transition took place from phase V to phase I on decompression at the higher temperatures. The change in grain boundaries due to the transition was observed in-situ by a microscope. The I–V transition at 570 K occurred at a pressure of 3.6 GPa which is slightly lower than that at 510 K. The observed transition pressures decreased with increasing temperature with some variation. Fig. 2 shows that the slope of the phase boundary between phases I and V is inclined slightly from the perpendicular toward the negative side indicating a gradient of 1.5 102 K/GPa. In a previous DTA measurement, the I–V phase boundary was speculated by connecting two anomalous points of the phase boundaries with a straight line, and the slope of the phase boundary was suggested to be negative [21]. Our result is consistent with this report. The slope of the phase boundary in the pressure–temperature phase diagram can be described by the Clausius–Clapeyron equation, dT/dP ¼ΔV/ΔS. The ΔV is usually negative in the pressure-induced
Fig. 2. Pressure–temperature phase diagram for LiBH4 in the high-temperature region above 400 K. The phase boundary between phases I and V was slightly inclined from the perpendicular toward the negative slope side.
transition which indicates that the entropy change ΔS in the transition from phase I to V is positive. Namely, the entropy for phase V is larger than that for phase I. However, the slope of the phase boundary is approximately perpendicular; therefore, the difference in entropy for phases I and V would be quite small since both phases are orientationally disordered structures. The variation of Raman frequencies of the B–H stretching peaks at 473 K against pressure is plotted in Fig. 3. The B–H stretching bands split into four peaks at the transition from phase I to III, and become a single peak again at the transition from phase III to V. The high frequency region in phase III has been reported to exhibit more than four peaks due to B–H stretching peaks and some combination bands in the Raman measurement at room temperature under high pressure [22]. However, the correspondence relation between the observed peaks and the detailed vibrational modes has not been clarified yet. The phase transition from phase I to III and the subsequent transition to phase V were observed in the temperature range of 400–500 K. The phase boundaries that were obtained by Raman measurements in this temperature range are shown in Fig. 2. Phase transitions between phases I and III and between phases III and V were reversible for the compression and decompression processes. The phase boundary between phases III and V also has a negative slope as in the phase boundary between phases I and V. The pressure–temperature phase diagram agreed with the one in the previous report [24] with the exception of the structure of phase III. We believe that the I41/acd structural model is appropriate for phase III, which we suggested in our previous work [25,26]. The negative slope of the III–V phase boundary indicates that the entropy of phase V is larger than that of phase III. The orientation of the BH4 ions in the I41/acd structure of phase III is ordered. (In terms of an ordered structure, it is also the same for the Ama2 structure that Filinchuk et al. have claimed [23].) Therefore, the phase boundary between the ordered phase III and the disordered phase V would have a negative slope. A powder x-ray diffraction measurement was performed at 510 K. The inset in Fig. 4 shows a representative powder x-ray pattern of phase V at 510 K. However, the powder x-ray pattern of phase I did not have the sufficient quality for analysis due to the rapid grain growth. Meanwhile, the x-ray pattern of phase V could be fitted to the structural model with the cubic space group—Fm3m, which Filinchuk et al. have reported [23]. Thus, the BH4
Fig. 3. Variation of Raman frequencies of the B–H stretching peak in LiBH4 against pressure at 473 K. Phase I transformed to phase III, and subsequently to phase V on compression. The inset shows Raman B–H stretching peaks in phase III at 4.8 GPa and 473 K.
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Fig. 4. Pressure dependence of the molar volume in LiBH4 at room temperature and 510 K. The molar volumes of phase V (closed circles) as a function were fitted with a Vinet-type equation-of-state. The molar volumes of phase V, despite being a high-temperature phase are slightly smaller than those of phase III (open diamonds, lit. [25,26]) at the same pressure. The inset shows a powder x-ray pattern in phases V at 8.4 GPa and 510 K. The tick marks represent the calculated positions of the Bragg peaks for Fm3m cubic lattice.
Fig. 5. Single logarithmic plot of the inverse of the sample's resistances R against pressure on compression process at 510 K. No discontinuous change was observed on the compression path from phase I to V. The inset shows a Nyquist plot for LiBH4 at 2.7 GPa and 510 K.
tetrahedron would rotate almost isotropically. The pressure dependence of the molar volume of phase V at 510 K is shown in Fig. 4. We found the molar volume of phase V to be smaller than that of phase III at room temperature [25,26] despite the thermal expansion. Since phase III is an ordered structure and phase V is a disordered structure, the phase boundary is shown to have a negative slope against pressure as in Fig. 2. Therefore, the molar volume should shrink at the transition from phase III to V by the heating process. Phase V would have a higher density than phase III with this volume decrease. The thermal expansion would be small compared to the volume change at the phase transition. The molar volume versus pressure of phase V was fitted with the Vinet-type equation-of-state [38] by fixing a pressure derivative B0' to 4.0 as shown in Fig. 4. We
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obtained the molar volume of phase V at ambient pressure V0 ¼28.5 (3) cm3/mol, a bulk modulus B0 ¼ 25(2) GPa. The B0 of phase V at 510 K is larger than that of phase III (B0 ¼20.7(6) GPa by Nakano et al. [26], B0 ¼ 23.23(9) GPa by Filinchuk et al. [23]) at room temperature. The compressibility of phase V would be lower than that of phase III since phase V is a higher density phase than phase III. The molar volumes of phase V are larger than that of phase V' that appeared above 16 GPa. The difference in the volume would mainly be attributed to the thermal expansion since phase V' is a disordered structure distorted from phase V. Phase V was stable up to 28 GPa at 510 K. However, the rotation of the BH4 ion would be suppressed by the pressure increase. According to the MD calculation at 300 K, the rotation was observed frequently at 8 GPa. However, the rotation could not be observed at 25 GPa and BH4 ions only vibrated within 10 ps. If the rotation stopped, a transition to a new phase would occur due to the change in the symmetry of the crystal lattice. Fast-ion conduction of Li þ ions was reported in phase I at ambient pressure [1]. Ikeshoji et al. suggested that the hopping of Li ions occurs in conjunction with the rotation of the BH4 ion by a theoretical calculation [18,19]. The rotation of BH4 ions might also contribute to the ionic conduction in phase V. Therefore, we carried out an AC impedance measurement during the compression process from phase I to V (see the Supplementary data for details). First, a discontinuous change in conductivity was observed at around 400 K on heating at 1.2 GPa due to the transition from phase III to I. Subsequently a relative change of ionic conductivity was measured during the compression process from 2.7 GPa to 4.4 GPa at 510 K. The relative conductivity decreased as the pressure increased monotonically as shown in Fig. 5. The activation volume of ionic conduction was estimated to be 6.4 cm3/mol for phase I in the region of 2.7–3.5 GPa. No discontinuous change was observed on the compression path from phase I to V. The difference of ionic conductivity between phases I and V would be small in the pressure–temperature region around the phase boundary at 510 K. Takamura et al. have already reported the ionic conductivity of LiBH4 on heating at various pressures [28]. Their data shows that the conductivity in phase V is lower than that in phase I, which roughly agrees with our results. Takamura et al. [28] and Sundqvist et al. [39] have reported the activation volume for phase I to be near 3 cm3/mol at 2–3 GPa, while we obtained a value of 6.4 cm3/mol. The larger value may be due to the large deformation that occurred in our sample during the compression process. In this study, we also performed the Raman measurement around the phase boundary between phases I and III. Pistorius has reported the existence of phase IV in this region [21]. In our measurement, the Raman spectrum of the central part in the sample corresponds to that of phase III at 2.5 GPa and 442 K, while that of the surrounding part shows an overlapped spectrum of phases I and III. The pressure gradient in the sample would cause the coexistence of phases I and III. Thus, our data does not show any existence of phase IV. Dmitriev et al. reported that the anomaly of the DTA measurement could be explained on the basis of the mechanism of a two-stage transformation process [24]. Phase IV would not exist in the intermediate region between phases I and III.
4. Summary A pressure–temperature phase diagram of LiBH4 was examined in the high-temperature and high-pressure region. The phase transitions among phases I, III, and V were mutually reversible for the compression and decompression processes at high temperatures. Raman measurements indicated that the phase
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boundary between phases I and V and that between phases III and V have negative slopes against pressure. The negative slope could be explained by the Clausius–Clapeyron equation, assuming that the entropy of phase V is larger than that of phase I or III for the disordered structure of phase V. The rotationally disordered structure of phase V was confirmed by the quantum MD calculation. The molar volume of phase V, despite being a hightemperature phase, is smaller than that of phase III at the same pressure. The molar volume should shrink at the phase transition from phase III to V on heating due to the order–disorder transition. The thermal expansion would be small compared to the volume change at the phase transition. Acknowledgments This study was supported by JSPS KAKENHI [17550067, 20045019 and 22550185]. The synchrotron radiation x-ray experiments were performed at BL-18C of KEK-PF under the approval of Proposal nos. 2006G275, 2008G614 and 2010G516. Appendix A. Supplementary material Supplementary data associated with this paper can be found in the online version at http://dx.doi.org/10.1016/j.conengprac.2014. 04.004. References [1] M. Matsuo, Y. Nakamori, S. Orimo, H. Maekawa, H. Takamura, Appl. Phys. Lett. 91 (2007) 224103. [2] H. Maekawa, M. Matsuo, H. Takamura, M. Ando, Y. Noda, T. Karahashi, S. Orimo, J. Am. Chem. Soc. 131 (2009) 894–895. [3] H. Oguchi, M. Matsuo, J.S. Hummelshoj, T. Vegge, J.K. Norskov, T. Sato, Y. Miura, H. Takamura, H. Maekawa, S. Orimo, Appl. Phys. Lett. 94 (2009) 141912. [4] M. Matsuo, H. Takamura, H. Maekawa, H. Li, S. Orimo, Appl. Phys. Lett. 94 (2009) 084103. [5] M. Matsuo, A. Remhof, P. Martelli, R. Caputo, M. Ernst, Y. Miura, T. Sato, H. Oguchi, H. Maekawa, H. Takamura, A. Borgschulte, A. Züttel, S. Orimo, J. Am. Chem. Soc. 131 (2009) 16389–16391. [6] H. Oguchi, M. Matsuo, T. Sato, H. Takamura, H. Maekawa, H. Kuwano, S. Orimo, J. Appl. Phys. 107 (2010) 096104. [7] R. Miyazaki, T. Karahashi, N. Kumatani, Y. Noda, M. Ando, H. Takamura, M. Matsuo, S. Orimo, H. Maekawa, Solid State Ion. 192 (2011) 143–147.
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