We present a new methodology that enables a significant sensitivity improvement for transverse magneto-optical Kerr effect (T-MOKE) detection. For this purpose, we developed a novel measurement ...scheme, in which the polarization detection conditions are changed during the measurement sequence in a pre-defined way. An analytical expression of the associated T-MOKE signal pattern was derived, which allowed us to analyze and classify our experimental data in a straightforward way. Furthermore, this new measurement approach enables the identification of noise and false background signals that might be generated by the sample under investigation, the environment or the detection system itself and it provides a pathway to unambiguously separate all these effects from true T-MOKE signals. These capabilities significantly increase the sensitivity and robustness of T-MOKE detection. The method enabled us to measure magneto-optical signals for samples that are paramagnetic at room temperature or exhibit really small magneto-optical responses, even in the presence of false signals that were far larger in size. Our new methodology was integrated into a scanning wafer tool, which allows for nondestructive, laterally resolved surface characterization measurements and even has the capability of measuring optical and magneto-optical properties simultaneously.
The experimental magnetic susceptibility curves of several soft steel grades, like interstitial free (IF) or low carbon (LC) steels, can be interpreted within the framework of universal scaling ...functions obtained for systems with quenched disorder, such as the one described by the random field Ising model with supercritical disorder. Mean-field theory (both scalar and site-dependent) is used to explore the behaviour at the proximity of the coercive field, and explicit expressions are derived. As a result, the susceptibility values close to the coercive field can be approximated to a good extend by a Lorentzian function. Theoretical results are compared against a number of experimental curves obtained from interstitial free (IF) and extra low carbon (ELC) steels subjected to isothermal annealing.
•Experimental curves of magnetic susceptibility of soft steels demonstrate common trends.•Susceptibility profiles can be used to monitor steel microstructure.•Interpretation from first-principles using a simple statistical physics model.
Annealing after cold rolling brings about the activation of recovery and recrystallization in microalloyed steels. The importance of recovery has been most often associated with its effects on the ...recrystallization kinetics. However, recovery has gained particular importance as an alternative heat treatment under the name “back annealing” or “recovery annealing”. In the present work, various annealing treatments were applied to a Nb-microalloyed steel in the range of temperatures and times where recrystallization is not complete. As a consequence, a large set of tensile strength-ductility pairs was obtained, even for conditions in which recrystallization was avoided. Through non-destructive magnetic coercive field measurements, recovery and partial recrystallization were monitored for each annealing treatment. Magnetic softening is significantly greater than mechanical softening. The variation in recovery in terms of temperature and time is highly affected by the presence of Nb in solution in the hot band (before cold rolling). At low recovery annealing temperatures, 350–450°C, Nb solute drag on dislocations is the main mechanism that controls recovery, whereas at 550°C, Nb strain induced precipitation leads to a recovery plateau in terms of coercive field.
We perform a detailed comparative study of conventional transverse magneto-optical Kerr effect (T-MOKE) measurements and a methodology that utilizes an effective polarization detection scheme for ...mixed s- and p-polarized incoming light. To test the ultimate sensitivity of both methods, we also design a series of specialized samples in which the T-MOKE signal of a Co-film is artificially reduced by means of a Ag overcoat of varying thickness. We find that the effective polarization detection scheme leads to a more than 30-fold increase of the T-MOKE signal and signal-to-noise ratio, even under general operation conditions which were not individually optimized. This allowed for the observation of T-MOKE hysteresis loops of Co-films that were buried under 80 nm of Ag, for which the MOKE signal was only 1/600 of that for an uncoated Co-film. In comparison, conventional T-MOKE measurements did not succeed for Ag overcoats thicker than 40 nm.
The evolution of recrystallization kinetics of a cold rolled low carbon steel with an initial coarse grain size and heterogeneous microstructure is studied by means of nucleation and ...interface-averaged grain boundary migration rate. Recrystallization is governed by two annealing time ranges, characterized by two Avrami exponents. Range 1 is associated to the recrystallization of high stored energy regions mostly belonging to the γ-fiber and Range 2 to the progression of recrystallization mainly through low stored energy α-fiber grains. The transition from Range 1 to Range 2 is consistent with the decrease of high stored energy regions. Afterwards, recrystallization is very sluggish due to the low stored energy regions remaining in the material and leads to incomplete recrystallization for annealing times of practical significance. Additionally, coercive field measurements are used to infer the evolution of concurrent recovery with recrystallization. Recovery only accounts for a small part of the decrease of the total stored energy, the rest being due to the heterogeneous distribution of the stored energy.
In this work, two different parametric hysteresis models, the Jiles-Atherton model and the Mel'gui relation, have been combined to form a more general hysteresis operator, suitable for the ...description of families of experimental B(H) curves obtained for low carbon (LC) steel specimens after isothermal annealing at different temperatures and times. As it has been demonstrated in a number of previous studies, characteristic values of steel hysteresis curves can be used as very efficient identifiers for the monitoring of the different metallurgical transformations that take place during the annealing, such as recovery and recrystallisation processes. It is thus important from a practical point to be able to reproduce the experimental curves obtained under different conditions, as precisely as possible, in order to proceed to the samples characterisation. Hybridisation of the two aforementioned models demonstrated satisfactory results for the reproduction of all considered curves obtained under the different considered annealing conditions.
The meta-modelling approach based on an adaptive sparse grid interpolator is proposed for tackling the identification problem of parametric hysteresis models for steels with different ...microstructures. Parametric models of Jiles-Atherton and Mel'gui, respectively, have been considered in this work. The main advantage of the present approach is the separation of the calculation procedure in a computationally demanding off-line phase, which has to be carried out only once, and a very fast on-line evaluation. This decomposition is particularly interesting when a large amount of successive evaluations has to be carried out. Especially in the case that we are interested in a particular family of ferromagnetic materials (e.g. steels subjected to different treatments), where the sought parameters are lying in a specific interval, a single meta-model may be sufficient to be used for the study of a wide range of specimens. The steel samples considered in this study have been obtained from industrially produced low carbon steel, 84% cold rolled, and isothermally annealed in laboratory.
How structure sensitive parameters derived from hysteresis loops can provide nondestructive information about the evolution of the microstructure of cold rolled low carbon steel as a result of ...recovery and recrystallization processes during the annealing is shown. The coercive field, remanent induction and hysteresis losses can be used to monitor the decrease in the dislocation density during recovery. These parameters are also influenced by the average grain refinement that takes place during recrystallization, which compensates the variation produced by the annihilation of dislocations during recrystallization. The maximum of the induction and of the relative differential permeability are shown to be very sensitive to the onset and to the monitoring of the recrystallization, respectively. The correlations between coercive field and remanent induction and hysteresis losses can also be used to distinguish between recovery and recrystallization.
A cold rolled low carbon steel has been annealed at low temperatures (300–500 °C) in order to promote recovery without interaction with recrystallization. It has been shown that the recovery process ...can be monitored by means of non-destructive magnetic techniques using coercive field (
H
c) measurements. Transmission electron microscopy and electron backscattering diffraction (EBSD) observations were carried out in order to investigate the microstructural changes associated with the measured decrease in
H
c produced by the recovery. The EBSD image quality maps show that on a microstructural scale, the cold work stored energy is distributed heterogeneously among different texture components, in agreement with previous studies. Recovery mainly affects the {1
1
1} γ-fibre orientations, leading to the formation of well defined subgrains.
The recovery kinetics of a cold-rolled (84% cold reduction) extra-low carbon steel were studied during isothermal annealing at low temperatures (300–500 °C). The recovery process has been monitored ...by magnetic coercive field measurements. The experimental data were satisfactorily modelled using a logarithmic time dependence law. The activation energy for the recovery process has been found to increase with the fraction of recovery. The existing relationship between the coercive field and the internal stress was obtained experimentally as both variables are directly related to the total dislocation density. By applying this correlation the kinetics of the dislocation hardening part of the yield stress was derived from the kinetics of the coercive field.
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