Hard Lattice Research Articles

Phase transition and temperature stability of piezoelectric properties in Mn-modified Pb(Mg1/3Nb2/3)O3-PbZrO3-PbTiO3 ceramics

This study investigates the effect of two different Mn modifiers [MnO2 and Pb(Mn1/3Nb2/3)O3(PMnN)] on the of phase transitions in Pb(Mg1/3Nb2/3)O3-PbZrO3-PbTiO3 ceramics. The temperature dependence of polarization derived from measured pyroelectric current indicated change in nature of phase transition with MnO2 doping. This phenomenon was supported by the temperature evolution of the linear softening of low lying hard lattice mode as revealed by Raman analysis. The grain size was found to increase with MnO2 doping (5X) while decrease with PMnN modification (0.5X). Interestingly, the piezoelectric constant of MnO2 modified composition showed negligible degradation (<1%) even after heat treatment very close to the ferroelectric-paraelectric transition temperature.

Residual Stresses in Austenitic Stainless Steel due to High Strain Rate

Austenitic stainless steel (SUS316L) was used as specimen material, and the plate specimens were deformed plastically with a wide range of strain rates (6.67×10-5~ 6.70×102/s). The residual micro-stress for each lattice plane was measured with hard synchrotron X-rays. The residual macro-stress due to tensile deformation depended on strain rate. The residual micro-stresses varied from tension to compression, depending on the diffraction elastic constant. The soft lattice plane had tensile residual stress, and the hard lattice plane had compressive residual stress. The higher the strain rate, the smaller the difference in residual micro-stresses. The residual micro-stresses of the surfaces peened with the laser-peening or water-jet-peening were examined. Both surfaces had exhibited large compressive residual stress. The residual micro-stress on the peened surfaces showed a tendency opposite to residual micro-stress due to tensile deformation.

Erratum: Nonlinear envelope-function equation and strongly localized vibrational modes in anharmonic lattices

A nonlinear envelope-function equation and matching conditions for the short-wavelength vibrational excitations in monatomic anharmonic lattices are derived. This equation coincides with the nonlinear Klein-Gordon or Schrodinger equation only in the limit of relatively small oscillation amplitudes. Strongly localized soliton and soliton-kink solutions of this equation are found within the rotating-wave approximation. High-frequency intrinsic localized and propagating modes in one-, two-, and threedimensional homogeneous hard anharmonic lattices, previously obtained by Sievers and Takeno in a discrete-lattice theory, are described within the framework of the contineous envelope-function approach

Distribution of activation energies for impurity hopping in amorphous metals

The distribution of activation energies $\ensuremath{\Delta}$ for classical over-the-barrier hopping is computed for a model amorphous metal. The spread in $\ensuremath{\Delta}$ is determined by the variation in equilibrium-site and saddle-point sizes for the assumed model of dense random packing (DRP) of soft spheres. The size distribution is related to the radial distribution function in a manner which reproduces recent numerical results for the interstitials in DRP models. Size (distance) variation in general is related to energy variation by the form of the potential energy $V(r)$. We show, however, that the distribution of equilibrium-site energies can be related directly to the impurity-induced lattice expansion and bulk modulus without detailed knowledge of $V(r)$. The form of $V(r)$ is necessary for the saddle-point distribution, and we estimate this using simple analytic expressions which fit the observed lattice expansion and impurity (hydrogen) vibrational frequency. The effects of a hard core plus lattice relaxation at the saddle point are also considered. Specific account is taken of the correlation between saddle-point and equilibrium-site configurations in the computation of the distribution of $\ensuremath{\Delta}$. Results are compared with recent data on hydrogen internal friction in amorphous ${\mathrm{Pd}}_{80}$${\mathrm{Si}}_{20}$ and good agreement is found between our first-principles distribution and that used to fit the data.

Phase transitions in the square well and hard ramrod lattice gases

A numerical investigation of the two-dimensional square well lattice gas and a gas of hard ramrods has been carried out using the scaling transformation. Both models appear to exhibit a single Ising-model-like second-order phase transition over the whole temperature range.

Refractive indices and electro-optics at ferroelectric and structural phase

Changes δn of refractive indices induced by structural phase transitions are considered. Two main categories of transitions are pointed out. In proper ferroelastics, morphic birefringence or the angle of indicatrix rotation are proportional to the order parameter η through a coefficient measurable by light scattering in the parent phase, while at most other transitions these are proportional to η2. Roles of η, deformation and hard lattice modes are treated separately and these are shown to give competitive contributions to δn in the latter case. Data on materials representing different categories of transitions are discussed.Changes of electro-optic coefficients, z, caused by structural transitions are treated either macroscopically or on the basis of a mode approach. In the latter, contributions to z of lattice vibrational modes are connected with changes of their Raman and infrared strengths. Both methods are used to discuss z in proper ferroelectric, improper ferroelectric and nonferroelectric phase transitions.