Bcc Fe Lattice Research Articles

Fundamental insights on ductile to brittle transition phenomenon in ferritic steel

Ductile to brittle transition (DBT) is a well-known phenomenon responsible for deteriorating the low temperature fracture toughness of ferritic steels. It is unambiguous to state that the transition phenomenon is a direct consequence of the strong temperature and strain rate sensitivity of flow stress, which in turn is regulated by the thermally activated motion of screw dislocation at the atomic scale. Due to very high Peierls stress, screw dislocation motion is accompanied by the nucleation and propagation of kink-pairs along the dislocation line. Thus, the activation energy required for kink-pair nucleation is an essential ingredient for correctly predicting the flow stress sensitivity and hence the ductile to brittle transition temperature (DBTT) of ferritic steel. However, experimental determination of kink-pair activation energy is rather tedious and there exists a strong discrepancy between atomistic simulation results (using Density Functional Theory and empirical potentials). Therefore, the present review is aimed at understanding the mechanism of screw dislocation motion in BCC Fe lattice and comparing the results obtained for kink-pair activation energy through experiments and simulations. The effect of different alloying elements on the overall flow stress sensitivity of Fe is also discussed with reference to the interaction of screw dislocation with solute atoms or clusters. Finally, the importance of screw dislocation on predicting the DBTT is explored to identify the present knowledge gaps and the future research directions.

Research on the Lattice Matching of Different Solute Atoms in BCC Fe: A Molecular Dynamics Simulation

AbstractIn this article, molecular dynamics simulation is used to primarily explore the lattice matching problem of solute atoms in different configurations after entering the Fe lattice at 0 K temperature. It reveals that by changing the initial configurations, metal solute atoms (Cr, Cu, Ti, Al) are more stable in the <110> configuration while C atom tends to stay in the octahedral gap of the BCC lattice. In addition, the matching mechanisms of different solute atoms in BCC Fe lattice in different configurations are elaborated in detail. The relaxation of metal solute atoms in different configurations eventually forms different stable structures while C atoms only exist in the nearest‐neighbor octahedral gap of the BCC Fe lattice in each configuration.

A new interatomic potential describing Fe-H and H-H interactions in bcc iron

We present a new many-body interatomic potential for H in body-centered cubic (bcc) Fe. The potential is developed based on extensive energetics and atomic configurations of an H atom and H-H interactions in Fe from density functional theory calculations. In detail, the potential is parameterized by fitting not only to a single H atom in the perfect bcc Fe lattice and to the properties of H trap binding to a vacancy and surfaces as being done by previous studies, but also to multiple H trapping to a vacancy and H-H interaction in Fe lattice. With such a fitting strategy, the developed potential outperforms existing potentials in its ability not only describing the behaviors of a single H atom in Fe, but also capturing the features of H-H interaction reliably, which is of key importance in revealing H behaviors in local H accumulation around dislocation cores, grain boundaries and crack tips.

Distortion energy-electronic energy compensation determines the nature of solute interactions with irradiation induced vacancies in ferritic steel

Fundamental knowledge of vacancy-solute atom (in particular, Cu and Ni) interactions at the electronic level is of utmost importance to understand experimentally observed Cu-precipitation in reactor pressure vessel (RPV) steel. In the present investigation, using first-principles electronic structure calculations within the framework of density functional theory (DFT), we unravel the nature of such interactions between a vacancy (V) or di-vacancy and solute atoms (mainly Cu and Ni) in the bcc-Fe lattice. One of the very novel features of the present investigation is that we demonstrate the importance of distortion energy-electronic energy compensation in stabilizing the formation of vacancy-Cu and vacancy-Ni clusters in ferritic steel. Further decomposition of the electronic energy contribution into different bonding contributions in conjugation with differential charge density analyses clearly reveals the origin of stability as a consequence of mutual compensation of different energy modes. For both Cu-Cu and Ni-Ni interactions, the presence of a vacancy leads to a more attractive interaction, implying that such vacancies generated due to irradiation make solute aggregation easier compared with the case of model steel with no defects. We have also demonstrated that the formation of CumNin clusters (m, n = 1, 5) is energetically favorable in addition to demonstrating that the stability increases with an increasing number of Cu or Ni atoms. The rate of increase of stability with the addition of solute atoms is higher in the case of the addition of Cu atoms into a Ni cluster than it is for adding Ni atoms into a Cu cluster. The present investigation thus provides a deeper electronic level understanding of solute-point defect interaction and cluster formation probability for Cu and Ni atoms in the ferritic steel.

Efficient approach to calculating radial distribution function in bcc Fe lattice

Many properties of condensed matter systems can be described by means of pair correlation functions that makes them an important structural characteristic. The shortest-graph interpolation method allows us to calculate pair correlation functions of classical crystals with pairwise interactions between particles. However, there is still no just so simple and practical approach to predict correlation functions in crystals with many-body interactions that are ubiquitous in nature. In this work, a simple modification of the interpolation method is suggested allowing to describe pair correlations bcc Fe lattice, considered as a classical crystal with many-body interactions of embedded atom model type. It is shown that the radial distribution function of the crystal can be calculated with high accuracy if mean square displacements are known. The obtained results would be useful in various fields of condensed matter physics, materials science, and crystallography.

First-principle investigation of electronic structures and interactions of foreign interstitial atoms (C, N, B, O) and intrinsic point defects in body- and face-centered cubic iron lattice: A comparative analysis

Carbon, Nitrogen, Boron and Oxygen are common alloying elements in ferritic as well as in austenitic steels and their small concentration of only few parts per million significantly influence the materials mechanical properties. In this report, a detailed comparative analyses of electronic structures and interactions of foreign solute atoms (C, N, B, and O) with point defects (vacancy/interstitial) in bcc- and fcc-iron lattices as obtained from density functional theory calculations are presented. It is found that the energetically favourable configurational site for B atom is the substitutional site in bcc-Fe whereas it is the octahedral interstitial site in fcc-Fe. For all other solute (C, N, O) atoms octahedral interstitial position is energetically favourable in both Fe lattices. The stability of all solute atoms is discussed from view point of their chemical nature as well as geometrical factor. In addition, the interaction of B atom with the point defects in the two Fe-lattices is found to be quite different as compared to any other solute atoms. We found that B atom strongly binds the point defects in bcc-Fe, in contrast, repels in fcc-Fe lattice. Furthermore, strong resemblance is observed between B atom and vacancy regarding their nature of interaction with other point defects in bcc-Fe lattice. Although vacancy always exhibit strong attraction with solute atoms in both Fe-lattices, the trapping ability of the vacancy in bcc-Fe is found to be stronger than that in fcc-Fe. The interaction among V-SAm cluster is also calculated for m upto 5 in order to investigate the trapping ability of a vacancy and covalent bond formation is observed in case of C atoms only in bcc-Fe lattice. Further insights into electronic structure and interaction of the point defects in the two Fe lattices have been obtained from density of states and differential charge density calculations.

Effect of hydrogen on Fe and Pd alloying and physical properties

Metastable Fe–Pd powder samples were synthesized by mechanically activated solid-state diffusion using high-energy ball milling. The Fe and Pd alloying and the hydrogen effect on this process were followed by preparation of two samples: the A-sample was a mixture of Fe powder and of Pd powder pre-charged with hydrogen (PdH) and milled under Ar atmosphere, the B-sample was a mixture of the Fe and Pd powders milled under hydrogen atmosphere.The fundamental properties, i.e., chemical and phase composition, lattice parameters, microstructure, morphology, grain size, defect structure, and macro- and micro-magnetic properties, were monitored after several steps of the alloying at room and appropriately at elevated temperatures.The alloying of Fe and Pd in both samples begins already after 5 h of milling and two phases are formed, the dominating bcc-Fe(Pd) phase and a minor fraction of the fcc-Pd(Fe) phase. The occurrence of the fcc phase, not observed previously by solid-state diffusion under argon atmosphere, is ascribed to mainly a positive effect of hydrogen reducing the formation energy of lattice defects and facilitating their formation. Consequently, the moving defects during mechanical alloying make the solid-state diffusion of Pd into bcc-Fe lattice and Fe into fcc-Pd lattice easier. On the other hand, hydrogen used as atmosphere in the milling procedure is adsorbed on the particle surfaces and after the vial opening hydrogen atoms form water molecules with oxygen from air. This exothermic reaction causes a removal of hydrogen atoms from the particle surface which thus becomes more sensitive to oxidation. Nothing similar was observed after mechanical alloying under argon atmosphere having positive impact on the particle surface stability.

Surface orientation dependence of the activation energy of S diffusion in bcc Fe

The formation of vacancies in the low-index orientations of bcc Fe was studied by a combined computational modelling and experimental investigation by making use of density functional theory (DFT), Auger electron spectroscopy (AES), time-of-flight secondary ion mass spectrometry (TOF-SIMS) and X-ray diffraction (XRD). Vacancies were considered to occur as a result of a Schottky defect forming in the bcc Fe lattice. This predicted a surface orientation dependence on the vacancy formation energy and consequently also on the activation energy of diffusion. Activation energies for the segregation of S in the Fe(100), Fe(110) and Fe(111) surface orientations were calculated by DFT modelling as 2.75eV, 2.86eV and 1.94eV respectively. Simulations furthermore revealed a variation in the segregation kinetics of S as a result of the activation energy dependence on the surface orientation. Experimental data obtained by AES, TOF-SIMS and XRD confirmed this variation in the segregation kinetics of S segregation in different Fe orientations. This article provides compelling evidence for the formation of vacancies in bcc Fe to occur via the Schottky defect mechanism, which results in the orientation dependence for the activation energy of diffusion.

On the surface properties and baric fragmentation of iron

The dependence of the specific surface energy (σ) on the normalized volume (V/V 0) and temperature (T) for the body-centered cubic (BCC) lattice of iron has been studied on the basis of the Mie-Lennard-Jones potential of interatomic interaction. It is shown that below the definite value of the normalized volume (V/V 0)fr the specific surface energy of the BCC-Fe lattice passes to the negative range of values: σ(V/V 0)fr = 0, and the (V/V 0)fr value increases almost linearly with temperature. In the case of compression, when (V/V 0) < (V/V 0)fr, the exothermal process of crystal fragmentation into dendritic domains with the maximum possible specific intercrystalline surface takes place. In the case of nanofragmentation, surface pressure (P sf) emerges, leading to self-packing of the formed nanocrystals. The dependence of the σ(V/V 0) and P sf (V/V 0) functions on the size and shape of the BCC-Fe nanocrystals has been studied at different temperature values T = 1500–3500 K. It has been shown that the P sf function increases with a decrease in the size; this occurs more strongly, the more the nanocrystal deviates from the most thermodynamically stable cubic shape. The dimensional compression of the lattice parameter of BCC-Fe nanocrystals has been studied. The specific (per volume unit) amount of heat released during fragmentation of the BCC-Fe lattice at high pressures and temperatures has been estimated.

Formation of Y-Ti-O nanoclusters in nanostructured ferritic alloys: A first-principles study

Density-functional theory (DFT) calculations have been performed to study the atomic scale energies, structures, and formation mechanisms of dissolved Y, Ti, and O solutes and small Y-Ti-O nanoclusters (NCs) in a bcc Fe lattice. Key results include the following observations. The Y and O are dissolved during mechanical alloying of ${\text{Y}}_{2}{\text{O}}_{3}$ with metal powders by ball milling, which provides the large requisite solution energy of about 4 eV per yttria atom. The solution energies of substitutional Y as well as interstitial O, which are referenced to elemental Y and solid FeO, respectively, are also high. Bound O-O, Y-O, and Ti-O pairs decrease the system energy relative to the isolated solutes and constitute the basic building blocks for NCs. The lowest energy configuration for a ${\text{Y}}_{2}{\text{TiO}}_{3}$ NC is 5.11 eV less than the total energy of the dissolved solutes. Our DFT calculations show that Y-Ti-O NC formation can take place without the energetic assistance of pre-existing vacancies. This conclusion is significant since excess vacancies are not a persistent thermodynamic-energetic constituent of the Fe-Y-Ti-O system and will quickly annihilate at dislocations during high-temperature powder consolidation.

The structural response of BCC Fe lattice loaded in [110] direction

AbstractThe structural response of BCC Fe lattice loaded in [110] direction has been investigated with MAEAM. The results show that, even if an orthorhombic path (b2≠b3) is applied, the deformation is spontaneous along the tetragonal path (b2≡b3) while b1 is less than 0.3449nm in compressive region. In addition to the initial BCC phase, a BCT phase and the other BCC phase appear also at stress‐free states. The BCT phase with the local maximum internal energy of ‐4.227eV is unstable and would slip spontaneously into the appeared BCC phase with the same minimum internal energy of ‐4.280eV as the initial BCC phase. The stable region ranges from ‐43.87eV/nm3 to 44.06eV/nm3 in the theoretical strength or from ‐7.34% to 6.49% in the strain correspondingly. Furthermore, the relations B11=B22, B13=B23 and B44=B55 occur at the initial state. (© 2009 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Atomistic modeling of nanosized Cr precipitate contribution to hardening in an Fe–Cr alloy

Molecular dynamics simulations of the interaction between an edge dislocation and nanosized Cr precipitates in bcc Fe have been performed to investigate the hardening effect of α′ phases in high Cr ferritic/martensitic steels. The critical resolved shear stress needed for an edge dislocation to overcome Cr precipitates of diameter between 3 and 6 nm is larger than for dislocation glide in the bcc Fe lattice containing 10% Cr solute atoms. This indicates that the precipitation of α′ phases leads to hardening in high Cr ferritic/martensitic steels. The MD simulations reveal that the interspacing of Cr precipitates plays a more crucial role in the hardening of Fe–Cr alloys than the precipitate size. An attractive interaction exists between an edge dislocation and nanosized Cr precipitates, which is evident as a decrease in total energy when an edge dislocation is placed within in a Cr precipitate.

Metastable phase formation and magnetic properties of the Fe–Nb system studied by atomistic modeling and ion beam mixing

With the aid of ab initio calculations, an n-body Fe–Nb embedded-atom potential is first constructed and then applied to study the crystal-to-amorphous phase transition through molecular dynamic simulations. The simulations determine that the glass-forming range of the Fe–Nb system is 18–83 at. % of Nb. In ion beam mixing experiments, five Fe–Nb multilayered films with overall compositions of Fe85Nb15, Fe75Nb25, Fe55Nb45, Fe25Nb75, and Fe15Nb85, respectively, are irradiated by 200 keV xenon ions to doses in the range of (1–7)×1015Xe+/cm2. The result shows that the Fe–Nb metallic glasses can be synthesized within a composition range of 25–75 at. % of Nb, matching reasonably well the theoretical prediction. Moreover, in the Fe55Nb45 sample, a fcc-structured alloy phase with a large lattice constant of a≈0.408 nm was obtained at a dose of 3×1015 Xe+/cm2 and the associated magnetic moment per Fe atom was measured to be 2.41μB. The observed magnetic moment is much greater than the initial value of 1.42μB in the bcc-Fe lattice and can thus serve as evidence confirming the high-spin ferromagnetic state of fcc Fe predicted by ab initio calculations. Interestingly, further irradiation induced phase separation in the Fe55Nb45 sample, i.e., irradiation to a dose of 5×1015 Xe+/cm2 results in the growth of a fractal pattern consisting of Fe72Nb28 nanoclusters embedded in Fe35Nb65 matrix. The formation mechanism of the metastable phases as well as that of the fractal pattern observed in the Fe–Nb system was discussed in terms of the atomic collision theory and the well-known cluster-diffusion-limited-aggregation model.

Structural evolution during deposition of epitaxial Fe/Pt(001) multilayers

We have investigated the structure of epitaxial Fe/Pt(001) multilayers deposited by direct current magnetron sputtering. In these multilayers, the structure of the Fe layers depends on their thickness: Thick (tFe&amp;gt;22 Å) Fe layers are body-centered cubic (bcc), while thin (tFe&amp;lt;12 Å) Fe layers are face-centered cubic (fcc). Ex situ x-ray diffraction reveals that the unstrained lattice parameter of bcc Fe in epitaxial multilayers is significantly greater than that of bulk bcc Fe, possibly due to alloying with Pt. This suggests that the observed “fcc Fe” is actually an intermixed fcc Fe–Pt interfacial layer. To investigate this possibility, we have performed grazing-incidence x-ray scattering in situ during deposition of epitaxial Fe/Pt(001) multilayers. The structure of Fe(001) layers as thin as 10 Å is bcc, strained due to epitaxial mismatch with the Pt(001) underlayer. Additional Fe deposition results in relaxation of the bcc Fe lattice parameter toward its bulk value. Deposition of Pt onto a 50 Å thick bcc Fe(001) layer has little effect on the Fe, other than to increase its lattice parameter slightly. In contrast, deposition of Pt onto a 20-Å-thick bcc Fe(001) layer results in a partial transformation of the Fe to a fcc structure. We propose that this transformation is the result of intermixing of Pt into the previously deposited Fe layer, resulting in the formation of a fcc Fe-Pt alloy layer.

Magnetic domain imaging with low energy electron microscopy (abstract)

Photoelectron microscopy has recently been developed into a strong tool for the investigation of surfaces of solids. The use of electron energy analyzers or synchrotron radiation tunable to particular electron excitation edges provides high element sensitivity of the method. In addition, when circularly polarized soft x rays are used, the magnetic circular dichroism effect offers the possibility of imaging magnetic domain structures in an element specific way.1234 The low energy electron microscope (LEEM) in combination with the PM 3 monochomator at BESSY which supplies circularly polarized soft x rays has been used for this purpose. The LEEM was equipped with an electrostatic energy analyzer providing an energy resolution of the photon-excited electrons of better than 500 meV. The lateral resolution of the LEEM instrument was shown earlier to reach down to 10 nm in the electron excitation mode. In the case of synchrotron radiation excitation the resolution depends largely on the brightness of the photon beam. At the BESSY TGM 5 undulator beamline which supplies linearly polarized light we have achieved a resolution of 30–40 nm in chemically sensitive photoelectron microscopy. At the PM 3 beamline using circularly polarized soft x rays at about 700 eV photon energy the resolution was 200–300 nm. In the chemically and magnetically sensitive mode we have studied a stainless steel sample that showed locally ordered grains with interesting magnetic domain structures. On the basis of LEEM in the electron impact low energy electron diffraction (LEED) mode (= LEED microprobe) it was possible to correlate the domain structures to the underlying bcc Fe lattice orientation. Exposure to external magnetic fields and heat treatment had a strong influence on the magnetic structure.

Stress and magnetic properties in high moment FeN thin films

Single layer FeN films with low coercivity and low residual stress were prepared on Corning 0211 glass and Si substrates using rf diode sputtering without postannealing. Substrates and a small amount of nitrogen in the film had a significant effect on the magnetic properties and residual stress of FeN films. The residual stress in the pure Fe films showed tensile characteristics due to thermal stress. The stress decreased with increasing N2/Ar flow ratio and passed a zero point at a flow rate ratio of ∼3.5%, accompanied with a low coercivity. The stress changed to compressive with further increasing nitrogen in the lattice. The tensile-to-compressive transition in residual stress can be explained by the increase in lattice constant in FeN films. The lattice constant increased with increasing nitrogen flow during deposition, which was probably due to more nitrogen incorporation in the bcc Fe lattice.

Magnetic Properties of Tetragonally Distorted Fe3Pt and the Hybrid Structure Fe3Pt/Fe

To investigate the magnetic performance of a hybrid structure of transition metals, we consider the Fe 3 Pt/Fe system and examine the effects both of the tetragonal distortion of L1 2 type Fe 3 Pt and the hybridization with bcc-Fe on the magnetic properties, using LMTO-ASA method in the framework of LSD. The magnetic moment of Fe 3 Pt has a maximum stationary value of 8.85 µ B / cell at \(c/a=1/\sqrt {2}\). The hypothetical struc- ture of Fe 20 Pt 4 is supposed by combining Fe 3 Pt of \(c/a=1/\sqrt {2}\) and bcc-Fe lattice. It is predicted that the magnetization reaches 2.27 T with the magnetic anisotropy constant of 11× 10 5 J/ m 3 . With using the coherent rotation model for magnetization reversal process, we get maximum energy product ( B H ) max =10.2 MJ/ m 3 .

Structural analysis of nanocrystalline FeCuSiB alloys by Mössbauer spectroscopy

The distribution of metalloid atoms, Si and B, in α-Fe(Si) and Fe 2B nanophases of nanostructured FeCuSiB alloys, as well as its variation with grain growth by means of Mössbauer spectroscopy are the concerns of this paper. Results show that B atoms exhibit two states in the nanocrystalline alloys studied. Si atoms are totally dissolved in α-Fe phase and show short range order. With grain size refinement the distribution of Si and B atoms was found to change, especially for short range order of Si atoms in bcc Fe lattice points.

Binary And Ternary Amorphous Alloys of Ion-Implanted Fe-Ti-C

ABSTRACTThe microstructure of Fe implanted with up to 50 at.% C was found to consist of hexagonal iron carbide precipitates oriented with respect to the Fe matrix. For higher C concentrations, an amorphous phase forms. This concentration dependence is explained in terms of the lattice structure of the iron carbide. In Ti-implanted Fe, substitutional Ti was found in the bcc Fe lattice for concentrations ≤ 15 at.% Ti. The work of others suggests that amorphous phases form for ≥ 33 at.% Ti. These results are discussed in terms of concentration boundaries of the ternary Fe(Ti,C) amorphous phase.Ion beam alloying methods are currently being used to form metastable alloys [1], both for fundamental investigations of such alloys as well as for potential use to improve physical properties of components [2]. An important consideration in metal alloys is what phase will form upon implantation; one aspect of this question is to determine when amorphous phases will form. Rules are currently being advanced to predict alloy systems which will yield amorphous phases. By using ion irradiation and ion beam mixing as well as ion implantation, such rules can be evaluated over entire composition ranges.To gain insight into amorphous phase formation, we have studied Fe alloys implanted with C, Ti and Ti + C. The Fe(C) alloys exhibit compound precipitation and amorphous phase formation; the precipitation and the concentrations at which the amorphous phase appears can be accounted for by considerations of the structure of the hexagonal carbide which forms. Based on conventional uses of the Fe(C) system, such alloys may be useful for improving mechanical properties by implanting C into ferrous components. Iron implanted with Ti is examined to a limited extent here, but by including ion irradiation studies by others [3], a more complete characterization of Fe(Ti) alloys is obtained. The microstructures of Fe(C) and Fe(Ti) are examined along with the known composition limits of amorphous Fe(Ti,C) alloys, which are important for their improved mechanical properties [2]. Taken together, a more complete determination of amorphous phase formation in this ternary system is obtained.