First-principles study on the dilute Si in bcc Fe: Electronic and elastic properties up to 12.5 at.%Si
Highlights
► Calculate elastic properties of Si-doped bcc-Fe at different Si concentrations using first-principles calculations. ► Significantly change in elastic properties above 8.3 at.%Si. ► Different bond properties between 8.3 and 10.9 at.%Si structures.
Introduction
Silicon steel (Si dilute Fe–Si alloys) has excellent magnetic and mechanical properties. Depending on compositions and manufacturing processes, wide range of properties can be achieved such as small hysteresis, high permeability, or nearly zero magnetostriction constant [1], [2], [3], [4]. Thus, it is widely used in transformers, motors, magnetic coils, and structural materials due to better corrosion resistance than carbon steel. Phase diagram of Fe–Si system [5] shows that, as Si content increases, there are three bcc-based structures from a disordered bcc (A2) to two ordered bcc (B2 and D03). At high temperature and low Si contents, A2 structure is presented. As the Si contents increase B2 becomes stable and D03 appears. Typical silicon steel has silicon content from 2 up to 6.5 wt.%. Increasing the Si content from 2–3 to 5–6 wt.% improves yield stress without decreasing ductility. However, at Si concentration beyond 4.5 wt.%, the ductility decreases significantly [6]. It is become more difficult to form, i.e. cold roll into thin sheet, for the high Si content steel. Several processing techniques have been investigated [7], [8], [9], [10], [11], [12] to produce higher Si content for Fe–Si alloys but mostly are not suitable for industrial scale. Poor ductility at higher Si concentration inhibits further development for this alloy for an industrial applications. Understanding the behavior, mechanism, or origin of the decreasing ductility might be enabling a further development of higher Si content steel.
The present work aims at investigating the behavior of dilute bcc Fe as the Si concentrations increase up to 12.5 at.% through the first-principles calculations. The goal is to explain the Si concentration dependence of the ductility and figure out the main factors which dominant the phenomenon. Section 2 details the first-principles calculations used in this work. Elastic constants and force constants procedures are also provided. In Section 3, we present the results of our calculations from elastic, electronic, and force constant data for different Si concentration of dilute bcc Fe up to 12.5 at.%Si. The concentrations dependent elastic properties such as elastic stiffness, bulk modulus, shear modulus, and Young’s modulus will be discussed. The effect of Si to the ground state electronic properties of dilute bcc Fe will be investigated. Force constants between different types of atoms will also presented. From various properties discussed in Section 3, we try to figure out the main reason behind the lower ductility in silicon steel at higher silicon concentration.
Section snippets
First-principles calculations
All the calculations in this study are based on density functional theory (DFT) which implemented in the Vienna Ab-initio Simulation Package (VASP) [13], [14]. Projector augmented wave (PAW) method is used to describe the electron–ion interactions [15]. The exchange and correlation are treated using generalized gradient approximation (GGA) of Perdew–Burke–Ernzerhof (PBE) [16]. The PAW potential set comprised of a 3d74s1 valence configurations for Fe and 3s23p2 for Si. Spin polarized
Results and discussions
Different concentrations of Si in the bcc lattice are achieved through supercells of standard bcc primitive cell [22]. By changing supercell size and substituting one Si atoms in the supercell, different Si concentrations from 2.7 up to 8.3 at.%Si can be achieved. Fig. 1a–c illustrates the supercell represented different Si concentrations from 2.7 up to 8.3 at.%Si. For the Si concentration higher than 8.3%, 64 atoms supercell that also based on the bcc primitive cell was used which 7 and 8 Fe
Conclusion
Elastic and electronic investigations on dilute Si in bcc Fe have been performed through first-principles calculations. The non-monotonous behavior of bulk modulus, as well as other elastic properties as a function of Si concentrations are observed and agreed with experimental data. It is found that elastic properties significantly decrease when Si concentrations increase beyond 8.3 at.%, and this revealed a ductile to brittle transition according to an empirical principle at 10.9 at.% Si
Acknowledgements
This research was supported by Japan Science and Technology Agency (JST) under Collaborative Research Based on Industrial Demand “Heterogeneous Structure Control: Towards Innovative Development of Metallic Structural Materials. The authors would like to express their sincere thanks to the crew of Center for Computational Materials Science of the Institute for Materials Research, Tohoku University for their continuous support of the SR11000/SR16000 supercomputing facilities.
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