Supporting Data for “All-temperature barocaloric effects at pressure-induced phase transitions”

<b>Sample preparation and characterization. </b>Sample preparation and characterization. Polycrystalline KPF6 (purity 99.98%) was purchased from Aladdin. Heat flow data of the samples were obtained using differential scanning calorimetry (TA, Q1000) at a rate of 20 K min-1 in the temperature range from 173 to 313 K. Specific heat capacity measurements were performed on a sample weighted 2.5 mg using a Quantum Design Physical Property Measurement System (PPMS-14 T, Quantum Design). For the dielectric measurements, a plate-like sample with a thickness of ~0.9 mm were prepared, and silver conductive paste deposited on the plate surfaces were used as top and bottom electrodes. The dielectric constants (εʹ) was measured using the two-probe AC impedance method with an Impedance Analyzer (Tonghui, TH2838)9,30. The thermal conductivity at room temperature was measured using the laser flash method with a NETZSCH LFA 467HT instrument. Similar to other plastic crystals, the thermal conductivity of KPF6 is very low, about 0.368 W m-1 K-1, but it can be significantly improved by compositing with highly-conductive materials like graphene26.<b>Adiabatic temperature change measurements. </b>We utilized a homemade instrument to measure the temperature of samples pressurized in a piston-cylinder unit, which is powered by an oil pump. Powder samples of approximately 1 gram were pelletized and inserted into a Teflon cell. A Teflon cap embedded with a type-E thermocouple was mounted onto the pellet in the cell. Subsequently, the cell containing the sample was fixed in a beryllium copper pressurized mold, placed in a stainless steel container, and put on a hydraulic press for the experiment. The low-temperature environment was realized in a liquid nitrogen flow. The temperature of the samples was recorded using a high-precision cryogenic temperature controller (Lakeshore 336). This system was well-calibrated using NaCl. The applied pressures were determined by converting the pressure of the oil pump, whose error bars were estimated to be smaller than 10 MPa. Pressure ramping up time was as short as 7 s from 0 to 100 MPa and 9 s from 0 to 250 MPa, while the pressure ramping down time was set to 1 s. The response time of the thermocouple is about 0.5 s. Such time structures guarantee the adiabatic conditions. Another measurement using a PE cell is also given in Supplementary Fig. 8. Note that the profile of adiabatic temperature change is sensitive to the microstructures of the samples and sometimes a peak appears with a shoulder.<b>Raman spectroscopy. </b>Temperature- and pressure-dependent Raman spectra were obtained using an in-situ Raman spectrometer (LabRAM HR Evolution, Horiba) equipped with a 4He cryostat (S-300, Physike) and a diamond anvil cell (CryoDAC Tesla, ALmax easylab). The wavelength of the laser was 532 nm. At a constant temperature, of 4, 30, 50, 70, 100, 130, 150, 180, 200, 220, 240, 250, 260, 280, 300, 310, 330, and 350 K, the diamond anvil cell was used to apply pressure to the sample. The pressure applied to the sample was determined using the ruby fluorescence method, whose error bars were usually regarded to be about 50 MPa at the current pressure region³1. To access a stable temperature, we waited for a least 20 minutes before measurements. The Raman data were processed using LabSpec6 software.<b>Neutron Powder Diffraction. </b>Temperature- and pressure-dependent neutron diffraction experiments were carried out using a high-pressure neutron diffraction spectrometer, PLANET³², J-PARC, at selected temperatures of 10, 50, 100, 150, 200, and 300 K and pressures of about 0.1, 100, 400, and 700 MPa. The pelletized samples, about 5 grams, were inserted into a piston-cylinder sample cell. The applied pressures were determined using the Pb reference, which gives rise to error bar of about 50 MPa. The neutron diffraction data obtained were refined using the GSAS Ⅰ software³³. At a lower temperature of 3.5 K, the crystal structure was checked using the ECHIDNA³⁴ at ACNS of ANSTO. The neutron wavelength was 2.4395 Å. The Rietveld refinements were used to analyze crystal structures by the Fullprof Suite program³⁵.<b>Computational details.</b> The first-principles density functional theory (DFT) calculations were performed using the Vienna ab initio simulation package (VASP)^36,37. The interactions between nuclei and valence electrons were described by the VASP recommended PAW pseudopotentials^38,39. The PBEsol⁴⁰ exchange-correlation functional was used, which yields a better description of the equilibrium properties of solids⁴⁰. The plane wave energy cutoff was set to 700 eV, and a G-centered k-point grid with a reciprocal-space resolution of 0.21 Å-1 was used for sampling the Brillouin zone. The convergence criteria for the total energy and ionic forces were set to 10-6 eV and 5 meV/Å, respectively. The phonon dispersions and density of states were calculated by finite displacements using the Phonopy code⁴¹. The variable cell nudged elastic band method18 was employed to obtain the energy barrier of phase transition. The structure search for the low-temperature phase was conducted using the generic evolutionary algorithm implemented in the USPEX code^42–44. The structures of the first generation were created based on the information available from experiments, including the space groups, lattice parameters, and the number of formula units in the unit cell. The structures of the following generations were produced by using heredity (45%), random symmetric structure generator (15%), soft mutation (15%), transmutation (15%), and lattice mutations (15%). Five-step DFT calculations with increasing precision were used for each structure to compromise the search speed and accuracy. The structure search was terminated until the structures with the simulated X-ray diffraction pattern matching the experimental one were obtained. The electronic band structures of the monoclinic I and rhombohedral phases of KPF6 were computed and displayed in Supplementary Fig. 9, showing the insulating states for both phases.