Fractal model for dielectric relaxation in deuteron pseudospin glass DRADP

Abstract

Proton and deuteron glasses such as Rb1−x(ND4)xD2PO4 (DRADP) are ideal systems for investigating dynamics of spin‐glass‐type systems because the basic mechanism for their dynamics is well understood. This mechanism consists of three processes; creation, effective diffusion, and annihilation of DPO4 and D3PO4 “Takagi groups.” Each process involves a deuteron transfer from one side of an O–D⋯O bond to the other. The effective diffusion changes the configurational energies of the D2PO4 “Slater groups” traversed by the Takagi groups. Each diffusion step changes this energy by a random amount with magnitude of order εd. This εd is comparable to the basic energy ε0 of the Slater model for RbD2PO4, and considerably smaller than the Takagi DPO4‐D3PO4 pair creation energy 2εc. The Takagi group diffusion path between creation and annihilation on average does not change the configurational energy. Thus the energy landscape along the path has an unbiased fractal nature, with small energy barriers superimposed on larger ones. The Takagi group diffusion path has side branches that are retraced, and loops of six or more steps. We approximate this path by a deterministic fractal path, having shorter side branches superimposed on longer ones, attached to a trunk running from the creation to the annihilation site. The longest dielectric relaxation time constant is governed by the Boltzmann factor for the highest barrier on the entire trunk. Shorter time constants correspond to the highest barriers on shorter trunk or branch segments. The relaxation strength distribution over these time constants depends on the basic fractal path unit, namely the number m of forward steps per side step. It depends also on temperature T and on εc and εd. This model predicts with good qualitative accuracy the T and f (frequency) dependences of the real (ε’) and imaginary (ε”) parts of the dielectric permittivity measured by Courtens in x=0.62 DRADP over wide T and f ranges. No adjustable parameters were used except for m. The static and high‐f permittivities εs, and ε∞f were chosen to fit Courtens’ data, while εc and εd were set at the values εc/k=940 K and εd/k=140 K chosen by the Blinc/Kind groups to fit DRADP NMR data. This consideration of diffusion path topology and prediction of dielectric permittivity are major extensions of our previous work.