The paper is dedicated to the 60th anniversary of the Urbach rule. The Urbach edge behaviour, measured by optical absorption spectroscopy, is analysed for different solids. The general regularities of the Urbach rule revealed in crystalline and amorphous solids as well as the temperature behaviour of its main parameters are discussed. The main attention is paid to the studies of the possibilities of the Urbach rule parameters to be used for studying disordering processes in solids, short- and medium-range order in amorphous materials, specific features of the Urbach "bundle" in nanosystems and its variation in the vicinity of phase transitions. It is shown that the parameters obtained from the Urbach rule give an important information about dynamic properties of elementary excitations in condensed matter as well as about the interaction of electronic excitations with phonons.

/pdf/urbach-rule-in-solid-state-physics-2z1bog9lpf.pdf

Urbach Rule in Solid State Physics

The fundamental absorption edge and optical constants of some charge transfer compounds

The crystal structures of 12 argyrodite type copper compounds with the general formula Cu (12-n) B n+ Q 2- 6-y X - y (B=P, As, Si, Ge; Q = S, Se; X = Cl, Br, I) were refined. The positions of the copper atoms were refined by using a non-harmonic approach. All polymorphic argyrodites were investigated in their cubic high temperature modification crystallizing in spacegroup F43m (No. 216). A comprehensible way to describe the complex structures was developed based on a topological description of the rigid anion- and B-cation substructure as an arrangement of Frank-Kasper polyhedra. An analysis of the joint probability density function and of the one particle potentials for the copper atoms was performed to get a detailed insight in the copper distribution in these argyrodites. They can be divided into four types based on their different distribution of copper. This classification corresponds to the physical properties of the argyrodites, especially to their ionic conductivities, which show a significant dependence on the composition.

/pdf/a-structural-differentiation-of-quaternary-copper-lx2ok7i9q1.pdf

A structural differentiation of quaternary copper argyrodites: Structure — property relations of high temperature ion conductors

Temperature dependent diffuse reflectance spectroscopy measurements were carried out on polycrystalline samples of BaTiO3 across the tetragonal to cubic structural phase transition temperature (TP). The values of various optical parameters such as band gap (Eg), Urbach energy (Eu), and Urbach focus (E0) were estimated in the temperature range of 300 K to 480 K. It was observed that with increasing temperature, Eg decreases and shows a sharp anomaly at TP. First principle studies were employed in order to understand the observed change in Eg due to the structural phase transition. Near TP, there exist two values of E0, suggesting the presence of electronic heterogeneity. Further, near TP, Eu shows metastability, i.e., the value of Eu at temperature T is not constant but is a function of time (t). Interestingly, it is observed that the ratio of Eu (t=0)/Eu (t = tm), almost remains constant at 300 K (pure tetragonal phase) and at 450 K (pure cubic phase), whereas this ratio decreases close to the transition temperature, which confirms the presence of electronic metastability in the pure BaTiO3. The time dependence of Eu, which also shows an influence of the observed metastability can be fitted with the stretched exponential function, suggesting the presence of a dynamic heterogeneous electronic disorder in the sample across TP. First principle studies suggest that the observed phase coexistence may be due to a very small difference between the total cohesive energy of the tetragonal and the cubic structure of BaTiO3. The present work implies that the optical studies may be a sensitive probe of disorder/heterogeneity in the sample.

Electronic and optical properties of BaTiO3 across tetragonal to cubic phase transition: An experimental and theoretical investigation

Urbach rule and disordering processes in Cu6P(S1−xSex)5Br1−yIy superionic conductors

The effect of temperature and pressure on the optical absorption edge in Cu6PS5X crystals

The fundamental absorption edge of Cu6P(S0.6Se0.4)5I and Cu6P(S0.4Se0.6)5I crystals was studied in the 77–320 K temperature range where no phase transitions were revealed by optical techniques. The temperature behavior of the exponential Urbach absorption edge in Cu6P(S0.6Se0.4)5I and Cu6P(S0.4Se0.6)5I crystals was analyzed. The effect of compositional disorder upon the Urbach edge parameters, parameters of exciton-phonon interaction, and lattice parameters in Cu6P(S1−xSex)5I, 0 ≤ x ≤ 1, crystals was studied. The effect of various types of disordering upon the optical absorption processes in Cu6P(S1−xSex)5I crystals is discussed.

Influence of compositional disorder on optical absorption processes in Cu 6 P(S 1− x Se x ) 5 I crystals

Electrical and optical absorption studies of Cu7GeS5I fast-ion conductor

The absorption edge of monocrystalline Cu 6 PS 5 Br was studied in the 4.2–505 K temperature range. At low temperatures ( T T >200 K were analyzed and interpreted in the framework of the Dow–Redfield theory. Two types of structural disorder affecting the optical absorption tail were studied.

V. V. Pan'ko

Papers

The effect of temperature and pressure on the optical absorption edge in Cu6PS5X crystals

Influence of compositional disorder on optical absorption processes in Cu 6 P(S 1− x Se x ) 5 I crystals

Electrical and optical absorption studies of Cu7GeS5I fast-ion conductor

Fundamental optical absorption edge and exciton–phonon interaction in Cu6PS5Br superionic ferroelastic

Preparation, electric conductivity and dielectrical properties of Cu6PS5I-based superionic composites