Interaction of Elastic Strain with the Structural Transition of Strontium Titanate
IBM1
TL;DR: In this article, a phenomenological model employing optical soft-mode and elastic-strain coordinates is proposed for second-order displacive transitions of a type often observed in crystals of perovskite structure.
Abstract: Second-order displacive transitions of a type often observed in crystals of perovskite structure are analyzed by means of a phenomenological model employing optical soft-mode and elastic-strain coordinates. Relations connecting spontaneous distortion, soft-mode vibrational frequencies, and elastic constants of a tetragonal low-temperature phase are derived. These relations are found to be consistent with existing x-ray, neutron, EPR, Raman, Brillouin, and ultrasonic data for SrTi${\mathrm{O}}_{3}$. From these data, it is inferred that properties of SrTi${\mathrm{O}}_{3}$ are isotropic to a considerable degree and that, of the small anisotropy which determines the symmetry of the low-temperature phase, interaction with strain contributes a large portion. Under certain assumptions, the soft-mode force constant inferred from the data appears to vary fairly smoothly through the transition temperature. Discontinuities in the specific heat and the temperature-derivative of the restoring-force coefficient amounting to 1.3% in SrTi${\mathrm{O}}_{3}$ and about 8% in LaAl${\mathrm{O}}_{3}$ are predicted.
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TL;DR: In this article, the tetragonal to orthorhombic ferroelastic phase transition between rutile- and CaCl-type phonon modes at high pressures is studied using first-principles calculations and the Landau free-energy expansion.
Abstract: The tetragonal to orthorhombic ferroelastic phase transition between rutile- and ${\text{CaCl}}_{2}$-type ${\text{SiO}}_{2}$ at high pressures is studied using first-principles calculations and the Landau free-energy expansion. The phase transition is systematically investigated in terms of characteristic phonon modes with ${\text{B}}_{1g}$ and ${\text{A}}_{g}$ symmetries, shear moduli, transverse-acoustic mode, rotation angle of the ${\text{SiO}}_{6}$ octahedra, spontaneous symmetry-breaking and volume strains, and enthalpy. The results show that these physical behaviors at the transition are well described using the Landau free-energy expansion parametrized by the first-principles calculations.
4,196 citations
TL;DR: In this article, the experimental studies of displacive phase transitions in solids are summarized, focusing on inelastic light scattering and neutron scattering; related infrared reflectivity measurements, as well as x-ray and EPR analyses are also summarized.
Abstract: This paper reviews the experimental studies of displacive phase transitions in solids. Primary emphasis is upon inelastic light scattering and neutron scattering; related infrared reflectivity measurements, as well as x-ray and EPR analyses are also summarized. Several prototype structures are considered in detail: (1) the rocksalt IV-VI semiconductors PbTe, SnTe, and GeTe; (2) the ferroelectric perovskites exemplified by PbTi${\mathrm{O}}_{3}$ and BaTi${\mathrm{O}}_{3}$; (3) perovskites which exhibit cell-doubling transitions, such as LaAl${\mathrm{O}}_{3}$, SrTi${\mathrm{O}}_{3}$, and KMn${\mathrm{F}}_{3}$; (4) crystals having the $\ensuremath{\alpha}$-quartz structure, including Ge${\mathrm{O}}_{2}$, Si${\mathrm{O}}_{2}$, and AlP${\mathrm{O}}_{4}$; (5) the "improper ferroelectrics" ${\mathrm{Gd}}_{2}$${(\mathrm{M}\mathrm{o}{\mathrm{O}}_{4})}_{3}$ and ${\mathrm{Tb}}_{2}$${(\mathrm{M}\mathrm{o}{\mathrm{O}}_{4})}_{3}$; (6) the V-VI-VII semiconductors typified by SbSI; (7) the hydrogen-bonded ferroelectrics of the K${\mathrm{H}}_{2}$P${\mathrm{O}}_{4}$ family; (8) Jahn-Teller systems such as DyV${\mathrm{O}}_{4}$ and RbCo${\mathrm{F}}_{3}$, in which structural distortions occur as secondary effects; (9) order-disorder systems such as NaN${\mathrm{O}}_{2}$ and the ammonium halides (N${\mathrm{H}}_{4}$Cl, N${\mathrm{H}}_{4}$Br), in which no "soft mode" occurs in the spectral region ($\ensuremath{\omega}g{10}^{11}$ Hz) probed by ir, Raman, and neutron spectroscopy; (10) $\ensuremath{\beta}$-tungsten ($A\ensuremath{-}15$) structures such as ${\mathrm{V}}_{3}$Si and ${\mathrm{Nb}}_{3}$Sn, which exhibit high-temperature superconductivity. These crystal categories are used to illustrate several phenomena of current physical interest: Specifically, we discuss harmonic and anharmonic mode coupling; "critical exponents" $\ensuremath{\beta}$ differing from one-half in the temperature dependences of the order parameter $\ensuremath{\phi}(T)={\ensuremath{\phi}}_{0}{(T\ensuremath{-}{T}_{0})}^{\ensuremath{\beta}}$ and of the soft-mode frequency $\ensuremath{\omega}(T)={\ensuremath{\omega}}_{0}{(T\ensuremath{-}{T}_{0})}^{\ensuremath{\beta}}$; and the recently discovered "central" modes centered at zero frequency, which grow in intensity as the transition temperature ${T}_{0}$ is approached from above or below. The review covers the period 1940-1972. A few 1973 works are mentioned for which the author had preprints in 1972 or very early 1973. This review is in no sense a comprehensive survey of ferroelectricity. Readers are referred to the following earlier reviews on that subject: Silverman (1966, 1969), Cochran and Cowley (1967), Blinc (1968), Murzin et al. (1968), Nettleton (1970), and Blinc and Zaks (1972).
639 citations
TL;DR: In this article, the authors describe instrumentation and computational methods for acquiring and analyzing the resonant ultrasound spectrum of very small (0.001 cm3) samples as a function of temperature, and provide examples to demonstrate the power of the technique.
Abstract: The mechanical resonant response of a solid depends on its shape, density, elastic moduli and dissipation. We describe here instrumentation and computational methods for acquiring and analyzing the resonant ultrasound spectrum of very small (0.001 cm3) samples as a function of temperature, and provide examples to demonstrate the power of the technique. The information acquired is in some cases comparable to that obtained from other more conventional ultrasonic measurement techniques, but one unique feature of resonant ultrasound spectroscopy (RUS) is that all moduli are determined simultaneously to very high accuracy. Thus in circumstances where high relative or absolute accuracy is required for very small crystalline or other anisotropic samples RUS can provide unique information. RUS is also sensitive to the fundamental symmetry of the object under test so that certain symmetry breaking effects are uniquely observable, and because transducers require neither couplant nor a flat surface, broken fragments of a material can be quickly screened for phase transitions and other temperature-dependent responses.
513 citations
TL;DR: It is demonstrated that the phase transition was in fact first-order, although still very close to tricritical, according to the variation of the order parameter Q for this transition scaled with temperature T as Q ∼ (Tc−T)β.
Abstract: We have examined the crystal structures and structural phase transitions of the deuterated, partially deuterated and hydrogenous organic-inorganic hybrid perovskite methyl ammonium lead iodide (MAPbI3) using time-of-flight neutron and synchrotron X-ray powder diffraction. Near 330 K the high temperature cubic phases transformed to a body-centered tetragonal phase. The variation of the order parameter Q for this transition scaled with temperature T as Q ∼ (Tc−T)β, where Tc is the critical temperature and the exponent β was close to ¼, as predicted for a tricritical phase transition. However, we also observed coexistence of the cubic and tetragonal phases over a range of temperature in all cases, demonstrating that the phase transition was in fact first-order, although still very close to tricritical. Upon cooling further, all the tetragonal phases transformed into a low temperature orthorhombic phase around 160 K, again via a first-order phase transition. Based upon these results, we discuss the impact of the structural phase transitions upon photovoltaic performance of MAPbI3 based solar cells.
433 citations
01 Dec 2008
TL;DR: In this article, the authors presented a detailed analysis of Piezoelectric Transducers for Sonar Applications. And they proposed a method to construct a three-dimensional piezelectric fiber composite material for medical transducers, which can be used for medical diagnosis and NDE.
Abstract: Fundamentals of Piezoelectricity- Thermodynamics of Ferroelectricity- Piezoelectricity and Crystal Symmetry- Crystal Chemistry of Piezoelectric Materials- Piezoelectric and Acoustic Materials for Transducer Technology- Lead-Based Piezoelectric Materials- KNN-Based Piezoelectric Ceramics- Bismuth-based Piezoelectric Ceramics- Electropolymers for Mechatronics and Artificial Muscles- Low-Attenuation Acoustic Silicone Lens for Medical Ultrasonic Array Probes- Carbon-Fiber Composite Materials for Medical Transducers- Transducer Design and Principles- Piezoelectric Transducer Design for Medical Diagnosis and NDE- Piezoelectric Transducer Designs for Sonar Applications- Finite Element Analysis of Piezoelectric Transducers- Piezoelectric Transducer Fabrication Methods- Piezoelectric Fiber Composite Fabrication- Composition Gradient Actuators- Robocasting of Three-Dimensional Piezoelectric Structures- Micropositioning- Piezoelectric Actuator Designs- Piezoelectric Energy Harvesting using Bulk Transducers- Piezocomposite Ultrasonic Transducers for High-Frequency Wire Bonding of Semiconductor Packages- Piezoelectric MEMS: Materials and Devices- High-Frequency Ultrasonic Transducers and Arrays- Micromachined Ultrasonic Transducers
421 citations
Cites background from "Interaction of Elastic Strain with ..."
...Additional terms may arise if there are structural variations due to the tilting or rotation of the oxygen octahedron as it is the case for the “incipient” ferroelectric SrTiO3 (Slonczewski and Thomas 1970; Pertsev et al. 2000)....
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