Yutaka Aikawa

Theory of Instability Phenomena in Crystals

The crystal instability due to anharmonic lattice vibrations is discussed by applying the self-consistent Einstein theory to three dimentional crystal systems. It is shown that there exist a mode connected with the crystal instability which depends on the crystal structure and symmetry. The Lindemann parameter is obtained on the basis of this model, and the results are compared with the experimental data for BCC and FCC metals.

Self-Consistent Anharmonic Theory and Its Application to Ferroelectric Crystal

The dielectric properties of barium titanate near the Curie temperature are studied using the variational principle method on a self-consistent anharmonic model. A trial Hamiltonian was devised using the terms of the anharmonic oscillator and asymmetric potential energy, which was adopted as the inter-atomic potential of the ferroelectric crystal. The temperature dependence of the dielectric property of barium titanate that was derived from this theory is in good agreement with the experimental result of the inter-atomic potential determined from first-principles ultrasoft pseudo potential calculations.

Instability of the order-disorder ferroelectrics

An instability of the order–disorder ferroelectrics is studied in the variationl method at finite temperature. A double-well potential based on the unfied oscillator model is adopted as a trial pot...

Theoretical Consideration of Size Effect for Barium Titanate

The dielectric property of the ferroelectric crystal was studied in the variational method on the basis of the self-consistent model. The anharmonic oscillator was used as a trial Hamiltonian, and a double-well potential which was formed by superposing the back-to back Morse potentials was adopted as an inter atomic potential in the ferroelectric crystal. On the basis of the self-consistent model, a theoretical treatment for the temperature dependence of dielectric constant and the size dependence thereof is presented.

Isotope-Induced Ferroelectric Phase Transition in Strontium Titanate Only by a Decrease in Zero-Point Vibration Frequency

The possibility of the ferroelectric phase transition in SrTi 18 O 3 only by decreasing the frequency of zero-point vibration due to the substitution of 18 O for 16 O is investigated by the self-consistent phonon approximation (SCPA) of an anharmonic lattice vibration system. The SC equation for the soft-mode frequency is shown to be described by only two parameters; the paraelectric Curie–Weiss temperature T 0 in SrTi 16 O 3 and the quantum factor T 1 inversely proportional to the square root of the effective mass M . The experimental finding that T c =0 in the mixed crystal SrTi( 18 O x 16 O 1- x ) 3 at x =0.33 is used to determine T 1 at this concentration and that at another x using only the ratio of M . The transition temperature T c in SrTi 18 O 3 is numerically calculated for comparison with the experimental value. Several factors determining T c are discussed on the basis of numerical results.

Self-Consistent Anharmonic Theory and Its Application to the Soft Mode of BaTiO3

The phase transition with soft mode caused by the anharmonic lattice vibration is studied by applying the variational principle at finite temperature. The normal coordinates are introduced in order to reflect the crystal symmetry to the softening. It is found how the appearance condition for the soft mode depends on the interactions between atoms and the crystal symmetry. An equation to determine the soft mode is derived, and is substantiated by applying to the phase transition from cubic phase to tetragonal phase in the BaTiO3 crystal.

Theoretical Investigation of the Isotope-Induced Ferroelectric Phase Transition in Quantum Paraelectric Strontium Titanate

The isotope-induced ferroelectric phase transition is theoretically investigated in terms of a compact formula based on the self-consistent phonon approximation (SCA) on the anharmonic lattice vibration system. The T c − T 1 phase diagram, where T c and T 1 are the transition temperature T c and the quantum fluctuation parameter T 1, respectively, is numerically calculated to demonstrate the nonlinear dependence of T c on T 1 sensitive to the increase of the oxygen mass. Experimental results of the small transition entropy and the perfect softening are discussed from the viewpoint of the ideal displacive type phase transition.

Theory of instability phenomena in crystals

Abstract Crystal instability due to anharmonic lattice vibrations is discussed by applying the self-consistent Einstein theory to three-dimensional crystals. It is shown that there exists a mode connected with the crystal instability which depends on the crystal structure and symmetry. Using this theory, the structure of amorphous metals has been studied. It is found that the structural unit in an amorphous state prepared from a face-centered cubic crystal forms an icosahedron with 13 atoms.

On the instability phenomena in FCC structure

The structure of amorphous metals has been studied by applying the theory of instability phenomena in crystals. As the results, it has been found that the structural unit in amorphous state prepared from face centered cubic crystal forms the icosahedron with 13 atoms.