Effect of copper content, initial structure, and scheme of treatment on magnetic properties of ultra-thin grain oriented electrical steel

The effect of the copper content, initial structure, and scheme of treatment on the magnetic properties of an ultra-thin grain oriented electrical steel has been investigated. In the material with copper and an initial sharp texture, the nucleation of new grains upon primary recrystallization is connected with deformation twins; in the samples without copper and with copper and diffuse texture, it is connected predominantly with shear bands and transition bands. Upon heating at a rate of ∼0.004 K/s, the temperature of primary recrystallization in the copper-bearing samples is considerably higher than in the copper-free material. Upon heating at a rate of ∼4 K/s the appearance of new grains occurs almost simultaneously for all of the studied samples. In the samples with copper and initial sharp texture after annealing at 1050 C, a significant part of the volume is occupied by grains that had undergone normal grain growth; in the samples without copper and with copper and diffuse texture, anomalous growth is hardly observed at all. To obtain high final magnetic properties of the ultra-thin grain oriented electrical steel produced by the Littmann method, it has been suggested to use an grain oriented electrical steel with 0.5% Cu that exhibits the diffuse orientation of grains as the workpiece. © 2013 Pleiades Publishing, Ltd

A quantum group version of quantum gauge theories in two dimensions

For the special case of the quantum group $SL_q (2,{\bf C})\ (q= \exp \pi i/r,\ r\ge 3)$ we present an alternative approach to quantum gauge theories in two dimensions. We exhibit the similarities to Witten's combinatorial approach which is based on ideas of Migdal. The main ingredient is the Turaev-Viro combinatorial construction of topological invariants of closed, compact 3-manifolds and its extension to arbitrary compact 3-manifolds as given by the authors in collaboration with W. Mueller.Comment: 6 pages (plain TeX

Secondary recrystallization in Fe-3% Si alloy with (110)[001] single-component texture

After the primary recrystallization of a preliminarily deformed (110)[001] single crystal, the texture also has the preferred (110)[001] orientation. Furthermore, the texture contains weak orientations, a major part of which is formed at the sample surface and can be described by a spectrum of scattered orientations 120вЊ©210вЊ.351 вЊ©103вЊ. A further heating leads to two concurrent processes taking place in the samples, i.e., the normal growth of Goss grains and secondary recrystallization. Abnormally grown crystals are represented by a quartet of orientations related with the initial Goss orientation by a rotation around [011], [011̄], [101], and [101̄] axes at an angle of ∼30. The crystallographic relationship between the initial and final grain orientations can be explained by their closeness to special misorientations as follows: Σ9, Σ19a, Σ27a, and Σ33a (rotation around 〈110⌠axes to close angles). © 2013 Pleiades Publishing, Ltd

Formation of special misorientations related to transition bands in structure of deformed and annealed single crystal (110)[001] of Fe-3% Si alloy

A transition band between two deformation bands retains for the most part the orientation (110)[001] and shrinks to a thin interlayer or boundary with increasing degree of deformation. At a certain stage of deformation, the microvolumes that are arranged along the interface of the bands become adjusted to special misorientations. During primary recrystallization, cube-on-edge (Goss) grains, which grow from the transition band, have portions of special boundaries common with the deformed matrix; these boundaries were found earlier between the deformation bands. This indicates that the local domains with special misorientations formed at the stage of cold deformation transform during annealing into the corresponding primary-recrystallization nuclei. © 2013 Pleiades Publishing, Ltd

The String Calculation of QCD Wilson Loops on Arbitrary Surfaces

Compact string expressions are found for non-intersecting Wilson loops in SU(N) Yang-Mills theory on any surface (orientable or nonorientable) as a weighted sum over covers of the surface. All terms from the coupled chiral sectors of the 1/N expansion of the Wilson loop expectation values are included.Comment: 10 pages, LaTeX, no figure

Evaluation of the Free Energy of Two-Dimensional Yang-Mills Theory

The free energy in the weak-coupling phase of two-dimensional Yang-Mills theory on a sphere for SO(N) and Sp(N) is evaluated in the 1/N expansion using the techniques of Gross and Matytsin. Many features of Yang-Mills theory are universal among different gauge groups in the large N limit, but significant differences arise in subleading order in 1/N.Comment: 10 pages; no figures; LaTe

Two dimensional lattice gauge theory based on a quantum group

In this article we analyze a two dimensional lattice gauge theory based on a quantum group.The algebra generated by gauge fields is the lattice algebra introduced recently by A.Yu.Alekseev,H.Grosse and V.Schomerus we define and study wilson loops and compute explicitely the partition function on any Riemann surface. This theory appears to be related to Chern-Simons Theory.Comment: 35 pages LaTex file,CPTH A302-05.94 (we have corrected some misprints and added more material to be complete

Solid state amorphization in a thin Fe-Si-Mg-O surface film triggered by the reduction of elements from oxides in the temperature range of the α-γ transformation

The study of the processes occurring in the surface layer of the MgO coated commercial alloy Fe-3%Si-0.5%Cu (grain oriented electrical steel) demonstrated that the amorphous phase in the form of a Fe-based solid solution is formed during continuous heating in the 95%N2 + 5%H2 atmosphere. For the purposes of this study, the following methods were used: non-ambient XRD at 20 –1060°C with heating and cooling at a rate of 0.5 dps, layer-by-layer chemical analysis performed by a glow discharge analyzer, scanning electron microscopy and energy dispersive X-ray spectroscopy. ThermoCalc software was used to calculate the potential phase equilibrium states. The amorphous phase was formed in the α → γ transformation temperature range, when the heating rates were altered in the surface layer of 1 µm initially consisted of a solid α-Fe-based solution with ~1– 2 wt.% Si with (MgFe)2 SiO4, (MgFe)O, SiO2 oxide inclusions. We suppose that (MgFe)2 SiO4 oxides are partly reduced by H2 to Mg2 Si molecular complexes, which become solid solutions in the temperature range of the metastability of the α-Fe crystal lattice with subsequent amorphization as an alternative to the α → γ transition. The amorphous state is obtained at 920 – 960°C and is retained both at subsequent heating (to 1060°C) and cooling (to 20°С), which is super-stable compared to the established metallic glasses. The composition of the amorphous phase can be described by the formula Fe89.5 Si6 Mg4 Cu0.5. © 2020, Institute for Metals Superplasticity Problems of Russian Academy of Sciences. All rights reserved.Russian Foundation for Basic Research, RFBR: 20‑08‑00332Ministry of Education and Science of the Russian Federation, Minobrnauka: 11.1465.2014/K.Acknowledgements. This study was conducted using equipment provided by the Laboratory of Structural Analysis Techniques and Materials and Nanomaterials Properties of CKP Ural Federal University. The study was financially supported by Government Decree No. 211 of the Russian Federation, Contract No. 02. A03.21.0006 and within the framework of the state task issued by the Ministry of Education and Science of the Russian Federation, project No. 11.1465.2014/K. The reported study was funded by RFBR, project number 20‑08‑00332