The hexaborides MB₆ of the rare earth elements and the alkaline earth elements, such as YB₆, CeB₆, SrB₆, and BaB₆, have long been popular topics of theoretical and experimental studies.^[1–4] These hexaborides crystallize in a CsCl-type structure with the alkaline earth element or rare earth atom and the octahedral B₆ molecules. Among these hexaborides, the trivalent rare earth hexaborides show novel physical properties, such as YB₆ with superconductivity, CeB₆ with dense Kondo behavior, and SmB₆ with intermediate valence state.^[5–7] The divalent alkaline-earth hexaborides are renowned for having properties of high melting point and hardness, low density and coefficient of thermal expansion, and excellent chemical stability.^[8–11]

At present, semiconductor CaB₆ with high Curie temperature has received much attention.^[12–14] CaB₆ doped with small quantities of La contains no magnetic ions with an electron density of 7 × 10¹⁹ cm⁻³. At the magnetic ordering temperature about 600 K, its ground state is ferromagnetically polarized with a saturation moment of per electron. Considerable experimental and theoretical work is carried out for CaB₆ towards understanding this unexpected phenomenon. The theoretical calculations have given some explanations including ferromagnetic phase of the conventional itinerant magnetism, dilute electron gas, and the doped excitonic insulator.^[15] Furthermore, Cho et al. have studied CaB₆ with 99.9999% (6N) purity boron and 99.9% (3N) purity boron by electrical measurements, and reported that CaB₆ with higher purity boron exhibited semiconducting features and another one exhibited metal properties.^[16] Therefore, it can be concluded that the dramatic change in the electrical properties of CaB₆ is affected by the boron purity and the preparing conditions.

Pressure is an efficient method for changing the structures and properties of materials. Metal hexaborides such as LaB₆ and EuB₆ have been the focus in high-pressure study.^[17,18] The LaB₆ structure was indexed as Pban but was not observed in subsequent experiments. Several studies on CaB₆ under extreme conditions have recently been reported. The earliest high pressure study of CaB₆ was fulfilled by in situ resistance measurement and energy dispersive x-ray diffraction (XRD) with the sample loaded in the diamond anvil cell (DAC).^[19] Two phase transitions under high pressure were discovered: an electronic transition occurs at 3.7 GPa, and a structural phase transition occurs at 12 GPa with the CsCl-type structure transformed to orthogonal structure. Subsequently, an unexpectedly complex crystal structure of CaB₆ (space group: I4/mmm) was reported under high pressure and temperatures.^[20] In theory, density functional theory (DFT) calculations predicted several structural transitions based on the dynamically stability.^[21] However, the inconsistency between theory and experiment still exists, which needs further studies.

In this work, we report a joint of synchrotron XRD and Raman spectra study of CaB₆ up to 40 GPa to explore its crystal structures and vibrational properties. Synchrotron XRD and Raman spectroscopy have proven to be powerful tools to investigate the structural properties under high pressure. The present work will also provide new insights into the structural stability of other metal hexaborides.

The powder sample was purchased from the Alfa Aesar Products, and loaded in the DAC with . The sample chamber was made on a T-301 stainless steel gasket by laser beam drilling machine. Its diameter was and the thick was . The methanol–ethanol mixture with a volume ratio of 4:1 was used for pressure-transmitting media.^[22] The pressure was determined by ruby fluorescence R1 peaks inside the sample chamber.^[23]

The Raman spectra were measured by an ActonSpetraPro500i spectrograph with a liquid-nitrogen-cooled charge-coupled device (CCD) detector. The excitation laser wavelength was 532 nm and laser power was 10 mW. The acquisition time for each experiment was 200 s, and the experimental data was analysed by OriginPro 8.5 software.

In situ high-pressure angle-dispersive XRD experiments were carried out at the 16-BM-D station of High Pressure Collaborative Access Team (HPCAT), Advanced Photon Source, Argonne National Laboratory. A focused monochromatic x-ray beam was used for measurement. Its diameter was and the wavelength was 0.4122 Å. The acquisition time was adjusted as 300 s in order to get clear XRD data. The geometric parameters were calibrated by CeO₂ standard. The image plate area detector (Mar345) was used to record the Bragg diffraction rings, and Fit2D software was used to convert the Bragg diffraction rings into plots of intensity.^[24] The XRD patterns were fitted by Rietveld profile matching of the Materials Studio program.^[25]

As one of the divalent alkaline-earth hexaborides, CaB₆ crystallizes into a CsCl-type structure with the space group of Pm- under ambient pressure.^[26] There is one molecule in the unit cell. The crystal structure of CaB₆ under ambient conditions is shown in the inset of Fig. 1. A boron octahedral cage is located at the cubic center and metal ions (Ca) are located at the cubic corners. In Fig. 1, the refinement of CaB₆ carried out on an XRD pattern is shown at about 1.9 GPa. The refined lattice constant a is 4.148 (2) Å, and unit cell volume V is 71.35 (9) ų which matches well with previous report.^[27]

Fig. 1.

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	Fig. 1. Full profile Rietveld structural refinement of CaB6 under high pressure. The fit has an Rwp of 2.0% and the calculated intensities are in good agreement with the observed intensities. The pattern is collected at 1.9 GPa with the incident x-ray wavelength of 0.4122 Å. The crystal structure of CaB6 is shown in the illustration.

Synchrotron XRD experiments are carried out to trigger the structural changes of CaB₆ under high pressure. The representative XRD patterns of CaB₆ with pressure uploading are shown in Fig. 2. The pressure is compressed up to 35 GPa in this experiment. As pressure increases, all diffraction peaks shift to higher angles, showing the crystalline interplanar spacing decreases gradually. In addition, the Bragg peaks are broadened. However, no new peaks are observed up to 35.2 GPa, indicating that no phase transition occurs with pressure uploading. So the cubic structure of CaB₆ appears to be quite stable with pressure up to 35 GPa. Meanwhile, as pressure decreases to ambient pressure, the cubic structure of CaB₆ is obtained. As for the work of Li Ming et al., an electronic transition occurs at 3.7 GPa, and a structural phase transition occurs at 12 GPa, with the CsCl-type structure transformed to orthogonal structure.^[19] And the study of Kolmogorov et al. showed that Cmcm is the lowest enthalpy structure for 13 GP-32 GPa pressures, and I4/mmm is a new ground state candidate above 32 GPa.^[20] A different result has been obtained in our experiment—up to 35.2 GPa, no new peaks are observed, which means that the structure of CaB₆ remains stable up to 35 GPa. All the XRD patterns are refined by Rietveld full profile structure. The refined lattice constants and volume of CaB₆ as a function of pressure are shown in Fig. 3, which are obtained by Rietveld refinements using Materials Studio software. All the relative unit-cell volumes with pressure changes are fitted to a third-order Birch-Murnaghan equation of state (EOS)^[28] In the formula, B represents the isothermal bulk modulus, represents the first derivative of the bulk modulus versus pressure, V represents the volume per formula unit under ambient pressure, and V represents the volume per formula unit at given pressure P. The lattice parameter monotonically decreases with pressure uploading, which indicates the preservation of the original structure. We have used V = 71.6 ų from experiments to constrain the equation of state.^[29] By fitting, as shown in Fig. 3, results are obtained as with fixed at 4.

Fig. 2.

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	Fig. 2. Selected angle dispersive x-ray diffraction patterns of CaB6 with pressure range from 1.9 GPa to 35.0 GPa. The top dotted line represents the pattern upon decompression to ambient pressure.

Fig. 3.

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	Fig. 3. The volume of CaB6 at different pressures. The square symbols represent experiment data, and solid-black lines are the results after fitting. The pressure-volume data is fitted by third-order Birch–Murnaghan equation of state.

Raman spectroscopy has proven to be useful to study the vibrational properties and structural changes under high pressure.^[30–32] We also have performed high-pressure Raman spectra to confirm the results from XRD patterns. The representation for the optical vibration modes of q = 0 (center of Brillouin zone) with point group O_h for CaB₆ was predicted with group theory as follows:^[33] where A_1g, E_g, and T_2g represent Raman-active modes, one of three modes is acoustic mode, the other two represent infrared-active mode, and and are optically inactive.

Figure 44 shows the measured Raman spectra of CaB₆ under ambient pressure. This shows that there are four peaks centered at 777 cm⁻¹, 1137 cm⁻¹, 1147 cm⁻¹, and 1279 cm⁻¹, and the results are in agreement with previous report.^[16] These vibration modes are related with the boron octahedron. For the three vibration modes, T_2g is triply degenerate symmetric bending vibration mode, E_g is double degenerate symmetric stretch vibration mode, and A_1g is nondegenerate symmetric stretch vibration mode. Besides, it is known that E_g mode is a broad single peak for the trivalent hexaborides case but a doublet for divalent.^[33] figure 4(b)–4(d) specifically show T_2g, E_g, and A_1g vibration modes, respectively.

Fig. 4.

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	Fig. 4. (a) The Raman spectra of CaB6 measured under ambient pressure, and panels (b), (c), and (d) represent T2g, Eg, and A1g vibration modes, respectively.

Table 1.

Table 1.

Table 1. The volume and corresponding errors of CaB6 at different pressures. . Pressure/GPa Volume/Å3 Errors/Å3 1.9 71.35 0.09 4. 71.00 0.03 7.5 70.26 0.24 10.3 69.12 0.15 12.4 68.41 0.08 15. 68.14 0.11 18. 67.63 0.15 21.3 66.99 0.21 24.1 65.74 0.19 27.3 65.15 0.07 32. 64.63 0.17 35.2 63.1 0.14

Table 1. The volume and corresponding errors of CaB6 at different pressures. .

High-pressure Raman spectra are measured up to 40 GPa. The selected Raman spectra with pressure increasing are shown in Fig. 5(a). The corresponding Raman frequency shifts with pressure are shown in Fig. 5(b). In the whole pressure range, in Fig. 5(a), it is noticed that the wavenumber of the T_2g and A_1g vibration modes blueshifts with pressure uploading. The two Raman peaks of the E_g mode shift towards high frequency with pressure uploading until 18.9 GPa. However, E_g mode is invisible above 18.9 GPa, which is covered by the intense first-order Raman peak of diamond. Up to 40 GPa, no new Raman peaks appears, indicating the original structure is stable. As shown in Fig. 5(b), the pressure dependence of each vibration mode is linearly fitted, which means each vibration mode has smooth monotonic pressure dependence. The T_2g, E_g, and A_1g vibration modes depending on the structure are shown in Figs. 4(b)–4(d). As shown in Fig. 5, Raman peaks of T_2g, A_1g, and E_g modes exist stable up to 40 GPa and shift to high frequency with pressure as normal. This indicates that the structure of CaB₆ remains stable up to 40 GPa. This is in good agreement with the XRD results. The fitted results are listed in Table 2. Furthermore, the pressure dependence of vibration mode can be represented as the mode-Grüneisen parameter , where represents the phonon frequency, B represents the bulk modulus at ambient conditions, V represents the molar volume, and P represents the pressure. As shown in Table 2, the Grüneisen parameter of E_g mode is the largest one. The Grüneisen parameter describes the vibration mode dependence on the volume of a crystal lattice.

Fig. 5.

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	Fig. 5. (a) Selected Raman spectra of CaB6 measured with pressure uploading, and (b) Raman shift with pressure for main vibrational of CaB6; the open symbols represent the results of the first run compression while filled symbols represent the second run compression. The lineally fitted data is marked by dotted lines.

Table 2.

Table 2.

Table 2. Assignment, frequencies, pressure coefficients, and mode-Grüneisen parameters of the Raman vibrational modes of CaB6. . Vibration mode /cm−1 /(cm−1/GPa) T2g 777 3.5 0.9 Eg 1137 8.5 1.5 1147 9.7 1.7 A1g 1279 9.1 1.4

Table 2. Assignment, frequencies, pressure coefficients, and mode-Grüneisen parameters of the Raman vibrational modes of CaB6. .

The Raman frequency shift of the vibration modes with pressure is related to the change of bond length or bond angle. We have calculated the bond length in boron octahedron and bond length of the neighbouring boron octahedron under high pressure with the Material Studio program. Figure 6 shows B–B_inter bond and B–B_intra bond length change with pressure. The data is linearly fitted: k_intra = −0.00231 Å/GPa, k_inter = −0.00309 Å/GPa. For CaB₆, six boron atoms form an octahedron connected by covalent bonds in the simple cubic crystal structure. Furthermore, covalent bonds connect the octahedron with other six closest octahedrons, and they form a three-dimensional network together. Due to this strong covalent network, the framework of the Pm-3m structure is very stable. This also explains that the ambient cage structure (Pm-3m) with a basic covalent network remains stable during the whole experimental pressure run. The bond length in boron octahedron and bond length of the neighbouring boron octahedron change linearly and steadily with pressure, indicating that the structure remains stable and is compressed evenly with pressure. Based on these results, no phase transitions occur in CaB₆ with pressure increasing up to 40 GPa.

Fig. 6.

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	Fig. 6. The B–B distances of CaB6 at different pressures.

In this work, we have successfully studied the structural stability and vibrational characteristics of CaB₆ by means of in situ high pressure Raman spectra and synchrotron x-ray diffraction. As pressure increases up to 40 GPa, no phase transitions occur and the lattice constant decreases linearly with pressure. Upon compression, all the vibration modes have smooth monotonic pressure dependence. The Grüneisen parameter of E_g modes is the largest, indicating its largest dependence on the volume of a crystal lattice. Our experimental results reveal that the covalent network of CaB₆ is difficult to break only under pressure conditions. To promote the occurrence of phase transition, it must be supplied with an alternative pathway to break the energy barrier and further studies are required.