The influence of adding Fe₂O₃ at the expense of Na₂O in sodium lead borate glasses on the structural, physical and electrical properties have been investigated. Results obtained from Fourier transform infrared (FTIR) spectra indicated that Fe₂O₃ plays an important role in converting three coordinated boron atoms [BO₃] to four coordinated boron atoms [BO₄]. The physical properties such as density and molar volume helped to evaluate the compact structure of the prepared glass samples due to presence of [BO₄] groups. The increase of Fe₂O₃/Na₂O replacements led to increasing the microhardness values and decreasing the thermal expansion coefficients of the studied glasses. The increase of Fe₂O₃/Na₂O replacements generally decreased the AC conductivity. That decrease might be due to converting of the three coordinated boron atoms [BO₃] to four coordinated boron atoms [BO₄]. Dielectric constants of the samples might be an indication of the distortion in the coordinated boron atoms. The obtained experimental data indicated the internal structure of glass network and the change of the structure of the samples from three [BO₃] to four coordinated boron atoms [BO₄].

There has been increasing interest in the electrical properties of rocks at different temperatures. Studies of the electrical properties under high temperatures became important to understand the materials within the earth's interior. This paper reports on the development of forward and inverse modelling of the electrical properties of the samples considering their internal texture. Sediments in Hammamat area, Egypt, containing magnetite, were extensively heated by intruded magma. As a result, magnetite was altered to hematite with different degrees according to the distance from the intrusion. Complex impedance measurements in the frequency range from 10 Hz to 100 kHz were performed on samples taken at different distances from the magmatic intrusion. It is supposed that the conductivity will decrease with increasing distance from the intrusion due to the decrease of the conductive magnetite and increase of the much less conductive hematite, but our results show the opposite trend. Conventional mixture laws cannot interpret this abnormal behaviour. A new pseudo-random renormalization group method was developed to model the samples properties with four supposed constituents to match the experimental results. The four constituents are magnetite blocked by air, hematite blocked by air, sand covered by hematite and magnetite covered by hematite. The fitting results with the experimental data show that as the samples are more heated, volume of the air pores, blocking the hematite and magnetite, decreases due to partial or complete melting, causing an increase in the sample conductivity in spite of the decrease of the magnetite content. This shows that the pseudo-random renormalization group method can model the abnormal properties of the samples. The texture represented mainly by blocking air has a larger effect on the samples conductivity than the concentration of the conductive magnetite.