Polarization echo in type-II superconductor powders

Properties of polarization echoes in piezoelectric powders

“…The existence of the memory echoes in piezoelectric powders was attributed to the motion of dislocations [8][9][10][11][12][13][14][15]. Here we mean the mobile dislocations created during the preparation of powder samples.…”

“…As a result, the dislocation motion causes a change in the modulus, G = G 0 − G d , and an additional internal friction, = 0 + d , where G 0 and 0 are related to the dislocationless crystal. The qualitative model and phenomenological theory of dislocation losses described below present the natural development of our previous work [11][12][13] on the subject.…”

“…At new equilibrium positions, they will oscillate under the influence of σ (x, t). Their contributions to d and G d are again described by equations (3) [13,20]. However, now the total length ir (or number N ir ) of the irreversibly displaced dislocation segments with length L ir is a function of the stress amplitude σ j at the end of j th rf pulse: ir (σ j ) = N ir (σ j )L ir (σ j ).…”

“…When the dislocation moves with respect to the cloud, an electric dipole is formed. An irreversible displacement of dislocation line leads to quasistatic polarization and it can give contributions both to the two-pulse echoes and the three-pulse memory echoes through electrostriction [13,14]. This 'field-mode interaction' is operative during the applied pulses.…”

“…From equation (10) one sees that a 12 (ωτ ) as well as the contained expressions for s2 , ω s2 (11) and ψ re(im) 2 ( 14) are periodic in ωτ . Therefore, we may perform the Fourier expansion of a(t, τ, ω, ϕ, φ) with the Bessel functions as the Fourier coefficients [2,6,9,13]. The insertion of this expansion into V (t) (17) gives, after the integration over ω, the echoes at times t ≈ mτ (m = 2, 3, 4, .…”