Composition Dependence of Elastic Moduli of Mixed Cobalt-Zinc Ferrites Prepared by Citrate Precursor Method

CoxZn1-xFe2O4 nanoparticles were prepared by chemical citrate precursor synthesis method. The Young’s modulus ‘E’ and the rigidity modulus ‘n’ of mixed cobalt-zinc ferrites have been determined by the ultrasonic pulse transmission technique at 1 MHz. The elastic modules of the ferrites were corrected to zero porosity using the formulae of Harselman and Fulrath. The observed variation of the elastic module with composition has been interpreted on the basis of binding forces between the atoms of the spinal lattice. A linear relationship between Debye temperature ØD and average sound velocity Vm has also been observed.

Experimental identification of the transition from elasticity to inelasticity from ultrasonic attenuation analyses

The transition from recoverable elastic to permanent inelastic deformation is marked by the onset of fracturing in the brittle field. Detection of this transition in materials is crucial to predict imminent failure/fracturing. We have used an ultrasonic pulse transmission method to record the change in waveform across this transition during fracturing experiments. The transition from elastic to inelastic deformation coincides with a minimum in ultrasonic attenuation (i.e., maximum wave amplitude). Prior to this attenuation minimum, the existing microfractures close. After this minimum, new microfractures form and attenuation increases until peak stress conditions, at which point, larger fractures form leading to complete sample failure. In our experiments, velocity changes are not sensitive enough to be indicative for the transition from elastic to inelastic deformation. Analysis of attenuation, not velocity, may thus detect imminent failure in materials. Our results may help detect fracturing in borehole casings or the near-wellbore area, or they may help predict imminent release of energy by seismic rupture.

Ultrasonic velocity measurements on thin rock samples: Experiment and numerical modeling

The ultrasonic pulse transmission (UPT) method has been the gold standard for laboratory measurements of rock elastic properties for decades, and it is used by oil and gas industry and service companies routinely. In spite of the wide acceptance and use of the UPT method, experimentalists are still looking for ways to further extend the limits of its applicability and to improve its state-of-the-art practices. One of the problems that limits wider application of the method is the length of the standard samples used (approximately 40–100 mm). This is a crucial limitation either in the case of a damaged core when preparation of a standard size sample is impossible or in the case when an ultrasonic experiment is combined with saturation or desiccation processes that might be extremely time-consuming on the long samples. On the other hand, thinner samples are not typically used due to the implication of inhomogeneity of stress fields inside and whereas few results of the measurements on thin disc samples have been reported in the literature, detailed justifications of the procedures have not been done yet. To fill this gap, we compare ultrasonic velocities measured at confining stresses up to 50 MPa done on standard and thin samples with lengths of 60 and 15 mm, respectively. First, we evaluate a new developed experimental setup for ultrasonic measurements on thin discs and develop a detailed experimental procedure. Then, we use finite-element modeling to numerically simulate stress fields in both types of samples. Finally, we compare the ultrasonic velocities measured on the thin discs and on standard samples and determine how to obtain reliable elastic properties on thin samples.

On the Relationship between Structural-Elastic Properties of Co-Zn Ferrites at 300 K

The structural - elastic properties correlations have been studied for polycrystalline spinel ferrite system, ZnxCo1-xFe2O4, x = 0.0-0.6, at 300 K. The cation distribution formulae determined from X-ray diffraction line intensity calculations are used to calculate bulk modulus (Ko) in particular and Young′s modulus (E0), rigidity modulus (G0), longitudinal modulus (L0) and Lame′s constant (λL0) in general. The longitudinal wave velocity (Vl0) and transverse wave velocity (Vso) computed from empirical relation based on X-ray density and mean atomic weight is used to calculate L0 and G0 respectively. The applicability of the heterogeneous metal mixture rule for theoretical estimation of elastic constants has been tested. The results are compared with elastic moduli determined from conventional ultrasonic pulse transmission technique and causes for the observed difference between the two have been discussed.