Lowering Of Crystal Symmetry Research Articles

Brittle-to-ductile transition in Ti–Pt intermetallic compounds

Phase transformation changes numerous properties of materials. Ti–Pt alloys have received much interest because of high martensitic transformation temperature. However, the intrinsic brittleness of these intermetallic compounds with low crystal symmetry and complicated phase structure limit their applications, especially when composition deviates from stoichiometry ratio. By performing in situ heating high-resolution scanning transmission electron microscopy experiment and micro-mechanical testing on Ti-35 at% Pt that contained majorly Ti3Pt and αTiPt phases, it was found that precipitating herringbone twinned αTiPt islands within Ti3Pt could occur upon heating, significantly refining mixed-phase structure. The refinement of multi-intermetallic mixed-phase structure endowed brittle material with remarkable capacity for plastic deformation and strain hardening. The plastic deformation mechanisms include phase transformation upon yielding and dislocation slips during hardening, which rarely occurs in intermetallic compounds with low symmetry. The strong interaction between different deformation modes even caused nano-crystallization along slip bands. The results demonstrate that brittle-to-ductile transition in intermetallic compounds can be achieved by tuning mixed-phase structure through phase transformations.

Spin orbit torques in Pt-based heterostructures with van der Waals interface* *Project supported by the National Natural Science Foundation of China (Grant Nos. 51732010, 51802341, and 12004415), the China Postdoctoral Science Foundation (Grant Nos. 2020M671592, 2019M661965), and the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20200255).

Spin orbit torques (SOTs) in ferromagnet/heavy-metal heterostructures have provided great opportunities for efficient manipulation of spintronic devices. However, deterministically field-free switching of perpendicular magnetization with SOTs is forbidden because of the global two-fold rotational symmetry in conventional heavy-metal such as Pt. Here, we engineer the interface of Pt/Ni heterostructures by inserting a monolayer MoTe2 with low crystal symmetry. It is demonstrated that the spin orbit efficiency, as well as the out-of-plane magnetic anisotropy and the Gilbert damping of Ni are enhanced, due to the effect of orbital hybridization and the increased spin scatting at the interface induced by MoTe2. Particularly, an out-of-plane damping-like torque is observed when the current is applied perpendicular to the mirror plane of the MoTe2 crystal, which is attributed to the interfacial inversion symmetry breaking of the system. Our work provides an effective route for engineering the SOT in Pt-based heterostructures, and offers potential opportunities for van der Waals interfaces in spintronic devices.

About the ground state structure and superconductivity of the [formula omitted] compound

In the present investigation, based on density functional theory computational approach, we show how the experimentally accepted AlB2-like structure of the SrAlGe compound is suggested to be dynamically unstable at 0 K. We propose a stable configuration that is deduced from the detailed analysis of the phonon spectrum with a doubled unit cell and buckled AlGe layers. It allows to closely reproduce the experimental critical superconducting temperature assuming a phonon mediated superconductivity as described within BCS theory. A soft puckering mode is identified both as the cause for the structural instability and as the main contributor in the electron-phonon coupling constant. From the detailed study of the electronic structure, we show how a peierls-like distortion with the crystal symmetry lowering, affecting mainly the Al-pz orbitals, is correlated with the puckering and with the electron-phonon coupling mechanism.

Record Enhancement of Curie Temperature in Host-Guest Inclusion Ferroelectrics.

Solid-state molecular rotor-type materials such as host-guest inclusion compounds are very desirable for the construction of molecular ferroelectrics. However, they usually have a low Curie temperature (Tc) and uniaxial nature, severely hindering their practical applications. Herein, by regulating the anion to control "momentum matching" in the crystal structure, we successfully designed a high-temperature multiaxial host-guest inclusion ferroelectric [(MeO-C6H4-NH3)(18-crown-6)][TFSA] (MeO-C6H4-NH3 = 4-methoxyanilinium, TFSA = bis(trifluoromethanesulfonyl)ammonium) with the Aizu notation of mmmFm. Compared to the parent uniaxial ferroelectric [(MeO-C6H4-NH3)(18-crown-6)][BF4] with a Tc of 127 K, the introduction of larger TFSA anions brings a lower crystal symmetry at room temperature and a higher energy barrier of molecular motions in phase transition, giving [(MeO-C6H4-NH3)(18-crown-6)][TFSA] multiaxial ferroelectricity and a high Tc up to 415 K (above that of BaTiO3). To our knowledge, such a record temperature enhancement of 288 K makes its Tc the highest among the reported crown-ether-based ferroelectrics, giving a wide working temperature range for applications in data storage, temperature sensing, actuation, and so on. This work will provide guidance and inspiration for designing high-Tc host-guest inclusion ferroelectrics.

Electronic, mechanical, optical and photocatalytic properties of perovskite RbSr2Nb3O10 compound

Development of suitable photocatalyst materials is a major challenge for applications in photocatalytic water splitting and degradation of pollutants. In this respect, the triple-layered perovskite RbSr2Nb3O10 shows promising photocatalytic properties and have the potential to be used in photocatalytic water splitting and degradation of pollutants. Herein, we have investigated the mechanical stability, electronic and optical properties, and redox potential of RbSr2Nb3O10 by using a first-principles density functional theory (DFT) calculations. The investigated elastic properties reveal that the perovskite RbSr2Nb3O10 is mechanically stable and elastically anisotropic. The studied electronic band structure confirms that the material RbSr2Nb3O10 is a semiconductor with indirect bandgap energy having the band gap value of 2.37 eV. The calculated low values of electron and hole effective masses suggest that the considered material have better electrical conductivity compared to other conventional semiconductors. The narrow bandgap and the small carrier effective mass of hole support the strong oxidation ability, which is favourable for the migration of charge carriers to the surface to facilitate the photocatalytic reaction. The suitable band edge potential indicates that electron-hole pairs are created upon photon absorption suggesting the material has the ability to split water into hydrogen and oxygen. The optical property investigation indicates the directional variation of the bandgap and other properties. Furthermore, the significant optical anisotropy along different polarization directions ascribed the lowering of crystal symmetry. Therefore, it is expected that our findings can be useful to develop high-performance photocatalytic device for water splitting and decompose of environmental pollutants.

In-plane anisotropic 2D Ge-based binary materials for optoelectronic applications.

In-plane anisotropic two-dimensional (2D) materials possess unique in-plane anisotropic physical properties arising from their low crystal lattice symmetry. Among these low-symmetry 2D materials, anisotropic Ge-based binary materials have the advantages of simple binary and earth-abundant compositions, good stability, highly anisotropic physical properties along two principle axes, and wide coverage of bandgaps, enabling use in broadband photodetection from the infrared to ultraviolet region. Here, we review recent progress in in-plane anisotropic 2D Ge-based binary materials, focusing on their anisotropic structural, electrical and optical properties. We then discuss demonstrations of optoelectronic applications related to those anisotropic properties including polarization-sensitive photodetection and polarization-based all-optical switches. Finally, we provide further possible opportunities for this relatively new, but quickly expanding family of materials.

Emergence of large exchange anisotropy in Pr doped nanocrystalline spinel ferrites

This paper reports the influence of rare earth Pr3+ doping on microstructural and magnetic properties in soft nickel nanoferrites. All the samples were prepared by soft chemical co-precipitation route with the generic formula NiPrxFe2-xO4 (x = 0.00, 0.04, 0.08 and 0.12). The prepared nanoparticles were single-phase as verified by x-ray diffractograms. Mean crystallite sizes of all the samples were found in the range of 4 nm–15 nm from the Williamson-Hall plot. Raman spectra signalled the lowering of crystal symmetry of octahedral co-ordinated sites due to the doping of large size Pr3+ ions. Field cooled M(H) loops registered at 5 K detected the existence of significant exchange bias field and large coercivity in the samples. The superparamagnetic behavior of prepared nanoferrites at room temperature became more prominent for higher Pr concentration as confirmed by both hysteresis loops and M(T) curves.

Elastic3rd: A tool for calculating third-order elastic constants from first-principles calculations

The third-order elastic constants (TOECs) are fundamental to describe crystal’s nonlinear response to stress, and can be applied to explore anharmonic properties of crystals such as Grüneisen parameters, thermal expansion coefficient, and the effect of pressure on second-order elastic constants (SOECs). Here, we report an open-source python package, Elastic3rd, which is able to calculate the SOECs and TOECs using the strain–energy method for crystals with any symmetry from first-principles calculations. An algorithm to generate necessary strain modes and the corresponding coefficients for a given symmetry is proposed. These strain modes are then applied to the fully relaxed structure to generate the deformed structures. The total energies of the strained structures are calculated by a chosen first-principles code, and the SOECs and TOECs are determined by fitting the resulted strain–energy data. The present code has been validated by several case studies of C, Si and Mg, and the case of MnP4 shows the ability for low-symmetry crystals. Program summaryProgram title: Elastic3rdCPC Library link to program files:https://doi.org/10.17632/n54vr2kwx8.1Developer’s repository link:https://github.com/hitliaomq/ELASTIC3rdLicensing provisions: GNU General Public License 3Programming language: Python 2.7.X and Python 3.X.External routines/libraries: Numpy [1], Scipy [2], and Matplotlib [3].Nature of problem: To automatically calculate the third-order elastic constants for crystals with any symmetry from first-principles calculations.Solution method: Firstly, the deformed patterns and the corresponding coefficients for the second- and third-order elastic constants are automatically generated according to the symmetry. Secondly, the deformed patterns are applied to the initial lattice and the corresponding input files for first-principles calculations are generated. Thirdly, the energies of the deformed structures are calculated by first-principles software such as CASTEP [4] and VASP [5]. Then, the parameters of strain–energy functions are obtained by fitting the strain and energy relationships. Finally, the third-order elastic constants are determined by solving the linear-independent equations, and the second-order elastic constants are calculated by solving the overdetermined equation using the least squares method.Addition comments including restrictions and unusual features: This code is well modularized. Thus, the energy can be calculated using energy-generated first-principles or other packages only by writing few functions.[1] S. Van Der Walt, S.C. Colbert, G. Varoquaux, Comput. Sci. Eng. 13(2011):22–30[2] P. Virtanen, R. Gommers, T.E. Oliphant, et al., ArXiv:1907.10121 (2019).[3] J.D. Hunter, Comput. Sci. Eng. 9(2007):99–104.[4] S.J. Clark, M. D. Segall, C.J. Pickard, et al. Z. Kristallogr. 220(2005):567-570.[5] G. Kresse, J. Furthmüller, Phys. Rev. B 54 (1996) 11169.

Phonon-driven ultrafast symmetry lowering in a Bi2Se3 crystal

Selective excitation of coherent high-amplitude vibrations of atoms in a solid can induce exotic nonequilibrium states, in which the character of interactions between electronic, magnetic and lattice degrees of freedom is considerably altered and the underlying symmetries are broken. Here we use intense single-cycle terahertz pulses to drive coherently the dipole-active $E_u^1$ phonon mode of a Bi$_2$Se$_3$ crystal. As a result, several Raman-active modes are simultaneously excited in a nonlinear process, while one of them, having the $E_g^2$ symmetry, experiences dynamical splitting during the first two picoseconds after excitation. The corresponding angular scattering pattern is modified indicating coexistence of two phonon modes characteristic of a nonequilibrium state with a lower crystal symmetry. We observe also a short-lived frequency splitting of the original $E_g^2$ mode that immediately after excitation amounts to $\sim 25\%$ of the unperturbed value. This transient state relaxes with a characteristic time of $\sim$ 1 ps, that is close to the decay time of the squared amplitude of the resonantly excited infrared-active $E_u^1$ mode. We discuss possible mechanisms of the dynamical splitting: nonlinear lattice deformation caused by the intense $E_u^1$ vibrations and excitation of anisotropic electronic distribution due to nonlinear electron-phonon interaction. Our data also contain an evidence in favor of the sum-frequency Raman mechanism of generation of the coherent $E_g^2$ phonons in Bi$_2$Se$_3$ excited by terahertz pulses.

Controlling the Lithium Intercalation Voltage in the Li(Mn1-x Ni x )2O4 Spinel Via Tuning of the Ni Concentration: A Density Functional Theory Study.

LiMn2O4 spinel is a promising cathode material for secondary lithium-ion batteries. However, although showing a high average voltage of lithium intercalation, the material is structurally unstable, suffering lowering of the crystal symmetry lowering due to Jahn-Teller distortion of the six-fold Mn3+ cations. Although Ni has been proposed as a suitable substitutional dopant to improve the structural stability of LiMn2O4 and enhance the average lithium intercalation voltage, the thermodynamics of the Ni incorporation and its effect on the electrochemical properties of this spinel material are not yet known. In this work, we have employed density functional theory calculations with a Hubbard Hamiltonian (DFT+U) to investigate the thermodynamics of mixing of the Li(Mn1-x Ni x )2O4 solid solution. Our results suggest that LiMn1.5Ni0.5O4 is the most stable composition from room temperature up to at least 1000K, which is in excellent agreement with experiment. We also found that the configurational entropy is much lower than the maximum entropy at 1000K, indicating that higher temperatures are required to reach a fully disordered solid solution. A maximum average lithium intercalation voltage of 4.8 eV was calculated for the LiMn1.5Ni0.5O4 composition, which is very close to the experimental value. The temperature was found to have a negligible effect on the Li intercalation voltage of the most stable composition. The findings reported here support the application of LiMn1.5Ni0.5O4 as a suitable cathode material for lithium-ion batteries with a highly stable voltage of intercalation under a wide range of temperatures.

High-temperature creep of magnetite and ilmenite single crystals

We performed deformation experiments on dry natural single crystals of magnetite and ilmenite to determine the rheological behavior of these oxide minerals as a function of temperature, orientation, and oxygen fugacity. Samples were deformed at temperatures of 825–1150 ,^{circ }C to axial strains of up to 15–24% under approximately constant stress conditions up to 120 MPa in a dead-load-type creep rig at ambient pressure in a controlled gas atmosphere. Oxygen fugacity ranged from 10^{-9.4} to 10^{-4} atm. Ilmenite creep was insensitive to oxygen fugacity, while magnetite displayed a strong, non-monotonic oxygen fugacity dependence, with creep rates varying as f_{O_{2}}^{-0.7} and f_{O_{2}}^{0.4} at more reducing and more oxidizing conditions, respectively. Dislocation creep rates of magnetite single crystals were weakly dependent on crystallographic orientation with stress exponents that varied between 2.8 and 4.3 (mean 3.5 ± 0.4). Magnetite compressed parallel to <100>, <110>, and <111> axes exhibited apparent activation energies of 315±5, 345±30, and 290±5 kJ/mol, respectively. We estimated {f_O}_2-independent magnetite activation energies of 715 ± 150, 725 ± 145, and 690 ± 150 kJ/mol for <100>, <110>, and <111> orientations, respectively, in the region of negative {f_O}_2-dependence. Ilmenite single crystals were compressed parallel, normal, and inclined to the c-axis. Stress exponents of 3.4, 4.3, and 3.9 indicate dislocation creep with activation energies of 420 ± 35, 345 ± 30, and 360 ± 40 kJ/mol, respectively, for these orientations. Mechanical anisotropy in ilmenite is notably higher than in magnetite, as expected from its lower crystal symmetry. Constitutive equations were formulated for ilmenite and magnetite creep.

Three-Dimensional Lead Bromide Hybrid Ferroelectric Realized by Lattice Expansion.

Three-dimensional (3D) organic-inorganic lead halide hybrids have become a hot academic topic because of their various functional properties. However, 3D lead halide hybrid ferroelectrics are still very rare until now. Here, we report a new 3D lead halide perovskite-related ferroelectric, (EATMP)Pb2Br6 [EATMP = (2-aminoethyl)trimethylphosphanium]. Based on nonferroelectric CH3NH3PbBr3, by replacing PbBr6 octahedra with a Pb2Br10 dimer of edge-sharing octahedra as the basic building unit, the expanded 3D lead bromide perovskite analog was formed with the large [EATMP]2+ cations occupying the voids of framework. Notably, (EATMP)Pb2Br6 displays a direct bandgap of 2.81 eV, four polarization directions, and a high Curie temperature (Tc) of 518 K (much beyond that of BaTiO3, 393 K), which is the highest among all reported 3D organic-inorganic hybrid ferroelectrics. Such a high Tc may result from the high rotational energy barrier of cations induced by a larger molecular volume and relatively low crystal symmetry. Our work provides an efficient avenue to construct new 3D organic-inorganic lead halide hybrids and would inspire the further exploration of 3D lead halide ferroelectrics.

Copper doped nickel ferrite nanoparticles: Jahn-Teller distortion and its effect on microstructural, magnetic and electronic properties

Samples with empirical formula Ni1-xCuxFe2O4 (x = 0.00, 0.25, 0.50, and 1.00) were prepared using chemical route. All the samples showed single spinel phase without any impurity. Average crystallite sizes were observed in the range of 12 nm to 39 nm as calculated by using Williamson-Hall (W-H) graphs. Raman spectra of all samples confirmed the lowering of crystal symmetry of octahedral sublattices with increasing Cu content. Signature of Jahn-Teller distortion due to substitution of Cu2+ (3d9) ions was detected using Raman spectroscopy. Absorption spectra of all the samples were recorded using UV–Vis spectroscopy, which confirmed the opaque character near red and infrared (IR) region. Onset of superparamagnetic behaviour has been observed by incorporating Cu2+ in the nickel ferrite with the mean blocking temperatures for all samples well below 300 K. Dielectric studies revealed that the grain boundaries played a major role in controlling the properties with increase in Cu2+ percentage.

Multi-crystal data collection using synchrotron radiation as exemplified with low-symmetry crystals of Dps.

Multi-crystal data collection using synchrotron radiation was successfully applied to determine the three-dimensional structure of a triclinic crystal form of Dps from Escherichia coli at 2.0 Å resolution. The final data set was obtained by combining 261 partial diffraction data sets measured from crystals with an average size of approximately 5 µm. The most important features of diffraction data measurement and processing for low-symmetry crystals are discussed.

Attraction between Permanent Dipoles and London Dispersion Forces Dominate the Thermodynamics of Organic Crystallization

Organic crystallization controls natural and pathological processes and technologies to produce pharmaceuticals, fine chemicals, and electronic and optical devices. In contrast to water-based crystallization, the interactions and structures that govern crystallization from organic solvents remain elusive. We characterize the thermodynamics of crystallization of etioporphyrin I from five solvents selected to highlight the roles of several solute–solvent interactions; etioporphyrin I represents a class of molecules that arrange in low-symmetry crystals suitable for semiconductors and solar panels. To understand solvent structuring at the crystal interface and solvent–solute interactions in the solution, we employ as molecular probes the crystallization enthalpy and entropy, complemented by UV–vis absorption spectra of the solutions and electron microscopy and X-ray characterization of the crystal phases. The enthalpy and entropy trends reveal that solvent structuring insignificantly affects the solution thermodynamics owing to the weak solvent–solvent bonds. London dispersion forces between nonpolar groups of the solute and solvent take the place of the hydrophobic interactions common in aqueous solutions and, directed by attraction between permanent dipoles, dominate the solute–solvent interactions. Surprisingly, both hydrogen bonds and salt bridges contribute little to the solution thermodynamics. The emerging insight into the fundamental interactions in organic solutions illuminates the search for crystallization solvents that optimize the numbers, morphologies, and sizes of crystals of organic materials with appealing properties.

Multiplicative suppression of decoherence.

Combining different protocols extends the life of a quantum system

Experimental observation of magnetic dimers in dilutedYb:YAlO3

We present a comprehensive experimental investigation of Yb magnetic dimers in Yb$_{0.04}$Y$_{0.96}$AlO$_3$, an Yb-doped Yttrium Aluminum Perovskite (YAP) YAlO$_3$ by means of specific heat, magnetization and high-resolution inelastic neutron scattering (INS) measurements. In our sample, the Yb ions are randomly distributed over the lattice and $\sim 7$\% of Yb ions form quantum dimers due to nearest-neighbor antiferromagnetic coupling along the $c$-axis. At zero field, the dimer formation manifests itself in an appearance of an inelastic peak at $\Delta \approx 0.2$~meV in the INS spectrum and a Schottky-like anomaly in the specific heat. The structure factor of the INS peak exhibits a cosine modulation along the $L$ direction, in agreement with the $c$-axis nearest-neighbor intra-dimer coupling. A careful fitting of the low-temperature specific heat shows that the excited state is a degenerate triplet, which indicates a surprisingly small anisotropy of the effective Yb-Yb exchange interaction despite the low crystal symmetry and anisotropic magnetic dipole contribution, in agreement with previous reports for the Yb parent compound, YbAlO$_3$ [arXiv:1904.11513, arXiv:1902.04112], and in contrast to Yb$_2$Pt$_2$Pb [arXiv:1606.01309, arXiv:1907.01067]. The obtained results are precisely reproduced by analytical calculations for the Yb dimers.

Symmetry of linear dielectric response tensors: Dispersion models fulfilling three fundamental conditions

Physically correct dispersion models must fulfill three fundamental conditions (time-reversal symmetry, Kramers–Kronig consistency, and conformity with sum rules). The application of these conditions on systems exhibiting low crystal symmetry, spatial dispersion, and/or magneto-optic effects is a non-trivial task. The aim of this contribution is to present an approach using decomposition of dielectric tensors into a set of independent spectral functions. For the derivation, the most general case of anisotropic dielectric response with optical activity is considered. The contribution discusses both the natural optical activity exhibiting spatial dispersion and the local magneto-optic effect of rotation of the plane of polarization induced by the external magnetic field. If the response tensor is expressed up to the term linear in the direction of the wave vector, then its symmetry can be classified into 16 types. Formulas expressing each type of the dielectric tensor using independent spectral functions are presented (the most complex case with the lowest symmetry requires 15 spectral functions). The symmetry for different internal and external conditions is demonstrated with the help of several simple models based on solving the classical equations of motion. It is shown that interpreting free particles in the magnetic field as bound particles is not correct. Instead, the Landau levels in a non-dissipative system must be interpreted as splitting of diamagnetic part of the dielectric response, rather than energy of bound states.

The seismically fastest chemical heterogeneity in the Earth's deep upper mantle—implications from the single-crystal thermoelastic properties of jadeite

Jadeite is a major mineral phase (up to 50 vol%) in the subducted sediments/crust with continental origin, which are one of the major heterogeneities and important enriched geochemical reservoirs (such as EM-1 and EM-2) for incompatible elements in the Earth's interior. Identifying and locating the enriched geochemical heterogeneities requires knowledge of the elastic properties of relevant mineral phases at high pressure-temperature conditions. Unfortunately, the single-crystal elastic properties of jadeite have never been measured at high-pressure conditions, partially due to its low crystal symmetry. In this study, we have experimentally determined the single-crystal elastic moduli of jadeite at high pressures for the first time up to 18 GPa at the ambient temperature condition using Brillouin spectroscopy. Fitting the third-order finite strain equation of state to the velocity-pressure data yields KS0′=3.9(1), G0′=1.09(4) with ρ0=3.302(5) g/cm3, KS0=138(3) GPa, and G0=84(2) GPa. In addition, we have also conducted synchrotron single-crystal X-ray diffraction experiments up to 25 GPa and 700 K. The fitting of a Holland-Powell type thermal-pressure Birch-Murnaghan equation of state yields KT0′=3.8(2) and α0=3.4(5) ×10−5 K−1. Based on the obtained thermoelastic parameters of jadeite, the density and seismic velocities of continent-derived sediments/crust are modeled at the depth range from 200 to 500 km. The seismic velocities of the subducted continental sediments/crust become extremely fast at depths greater than ∼300 km, up to 11.8% and 14.7% faster than the Vp and Vs of the ambient mantle, and 5.6% and 7.3% faster than the Vp and Vs of the subducted oceanic crust. The existence of even a small amount of the subducted continental sediments/crust can result in strong seismic anomalies in the Earth's interior.

(Invited) Ferroelectric Materials Study Using First-Principles Calculations and Materials Informatics

In the past a couples of decades, first-principles calculation has become powerful tool for materials study. In our group, ferroelectric material is one of important research target.Softmodes and the structural phase transitions associated with them are is one of most important research topic in the field of ferroelectric materials. In the 2000s, a technique for calculating phonon using first-principles calculations was developed. Since then, softmode in ferroelectric materials have been extensively studied by many groups. More reentry, an automated method for comprehensive softmode analysis using simple algorithm for automated searching of phase-transition pathways based upon first-principles phonon calculations has been developed by Togo and Tanaka.[1] Figuer1(a) shows how the procedure is composed of multiple calculation “units.” Each calculation takes a crystal structure as its input. The initial structure is relaxed under the constraints of its crystal symmetry, i.e., during relaxation no lowering of crystal symmetry is allowed. However, increase in symmetry is allowed and often occurs. In such higher symmetry cases, the space group of the crystal structure may not be a subgroup of the space group of the initial structure, but it is a subgroup of the space group of the relaxed (final) structure. The dynamical stability of the final structure is then examined by calculate supercell force constant. If any instabilities are found, the structure is deformed along the relevant direction. These calculations are repeated until all of softmodes are eliminated.Using this procedure, we can examine the mechanisms of softmode related structural phase transitions. Another advantage of this method is that it allows phase transition pathway via metastable structures to be proved, which may enable. Possible phase transition pathways are difficult to determine to be discovered experimentally. Fluorite structured hafnia (HfO2) is used as a high-k gate dielectric material in Si semiconductor devices. Recently, the ferroelectric behavior of thin film HfO2 has been reported. However, the origin and mechanism of this ferroelectric phase transition are still not well understood. Identifying the origin of this ferroelectricity would allow hafnia-based materials to be developed for application in nonvolatile memories and ferroelectric field effect transistors. Hence, in this study, we have attempted to elucidate the mechanism of the ferroelectric phase transition in thin-film HfO2 by performing comprehensive softmode analysis.Our results are summarized in Fig.1(b). Under ambient pressure, no softmode is observed for the tetragonal P42/nmc phase. However, under slight negative (tensile) pressure (-3 GPa), a softmode leading resulting in a transition to the experimentally observed ferroelectric Pca21 phase was found. This softmode path is sensitive to pressure, as it vanished we applying positive (compressive) pressure, or zero pressure. In thin film form, the volume change HfO2 need to undergo during the first-order phase transition from tetragonal to monoclinic is suppressed by the constraining substrate. Under these condition, a ferroelectric phase transition through this softmode path can occur.[2] References [1] A. Togo and I. Tanaka, Phys. Rev. B, 87, 184104 (2013).[2] H. Moriwake, A. Taguchi, C.A.J. Fisher, A. Togo, T. Shimizu, H. Funakubo, in preparation. Figure 1