Characteristic Twin Formation in Body-centered Cubic Fe–Ga Alloy Single Crystals with Different Orientations

Abstract

Tensile tests and electron backscatter diffraction (EBSD) measurements were performed to understand the microscopic processes in the plastic deformation of Fe–17-at%-Ga alloy single crystals with a body-centered cubic (BCC) structure. Samples close to the [001], [012], and [011] orientations for the tensile directions were cut from the alloy single crystal grown by the Czochralski method. They were plastically deformed at room temperature. The surface morphologies and microstructures of the deformed samples were characterized using an EBSD instrument attached to a scanning electron microscope. The mechanical properties such as elasticity and flow stress depended on the crystal orientation. Slip by dislocation glide was dominant in the tensile deformation in the [011]-oriented sample. Coarse planar deformation twins were observed in the [001]-oriented sample by plastic deformation. Thin deformation twins and slips were observed in the [012]-oriented sample. This implies that deformation twins have an important role in the plastic deformation of alloys. Although the addition of Ga induces solid solution hardening of iron-based alloys, the characteristic microscopic processes in the plastic deformations of the present alloys are similar to those in the plastic deformations of BCC iron and its alloys.

1. Introduction

Fe–13–23-at%-Ga alloy single crystals undergo a large magnetostriction under a relatively low magnetic field, which strongly depends on the orientation.^1,2) The magnetostrictive properties of the Fe–Ga alloys are considered to be related to the elastic and magnetoelastic anisotropy in body-centered cubic (BCC) iron alloys. The properties are degraded by stress fields in the alloys upon an external loading.³⁾ It has been considered that such stress fields easily change the magnetic domains in Fe–Ga alloys, as the magnetostrictive and elastic properties of Fe–Ga alloys are correlated with magnetic domains.⁴⁾ Regarding the mechanical properties of the Fe–Ga alloys, their slip systems, critical resolved shear stresses, elastic moduli, and Poisson’s ratios were investigated by tensile deformation.⁵⁾ A sample with a [011] tensile axis orientation exhibited a {110}<111> slip, whereas a sample with a [001] tensile axis orientation exhibited a {211}<111> slip and discontinuous yielding. The former sample exhibited an ultimate tensile strength of approximately 580 MPa through an elongation of 1.6%, while the latter sample exhibited a maximum tensile strength of approximately 515 MPa with fracture upon an elongation of 2%. The levels of yield and flow stress of the Fe–Ga alloys are higher than those of high-purity iron because the high flow stresses are attributed to a large solid solution hardening by the addition of gallium.^4,6) Related to the mechanical properties of these BCC alloys, the physical properties of the Fe–Ga alloys at room temperature have been recently investigated.^7,8,9)

The plastic deformation of pure BCC metals depends on the crystal orientation and test temperature. The deformation mechanism has been discussed based on the characteristic mobility of screw dislocation motions etc.^{10,11,12,13,14,15,16,17,18)} In addition, the roles of substitutional alloying elements on the plastic deformations of BCC iron-based alloys have been extensively investigated.^{19,20,21,22,23,24,25,26)} These investigations demonstrated that alloying elements such as silicon and aluminum induce solid solution hardening of iron and that the plastic deformation of iron alloy single crystals depends on the crystal orientation. Models of the formation of deformation twins (mechanical twins) were proposed for {112} planes in BCC metals, which suggested an orientation dependence of the twinning formation.^27,28,29,30)

This inspired us to study the microscopic processes of deformation in Fe–Ga alloy single crystals with different orientations and analyze the deformation mechanism of plastic deformation of BCC metals and alloys. The objective of this study was to investigate the characteristics of plastic deformations of Fe–Ga alloy single crystals with different orientations using electron backscatter diffraction (EBSD) observations coupled with tensile tests. In particular, the occurrence of deformation twins in Fe–Ga alloys by deformation was the focus of this study. The microstructures observed in the deformed alloys are discussed by comparing to the previous results on BCC iron-based alloys.

2. Experimental Procedures

2.1. Sample Preparation

A starting Fe₈₃Ga₁₇ alloy for single-crystal growth was prepared using pure 4N Fe and 5N Ga under an Ar atmosphere. The single-crystal alloy ingot was grown in an alumina crucible using the Czochralski technique.⁴⁾ Samples with tensile axes close to the [001], [012], and [011] orientations were cut from the ingot into tensile test samples using a multi-wire saw. These three samples are referred to as Samples A, B, and C, respectively. The tensile test sample dimensions were designed to be 4 mm (length) × 3 mm (width) × 1 mm (thickness) in the gauge portion. After spark erosion machining and electrochemical polishing, the orientation of each specimen was determined by a Laue X-ray back-reflection analysis. Figure 1 shows a stereographic representation of the slip and twinning geometry in the BCC structure, in which the initial orientations of Samples A, B, and C to the tensile direction were determined by EBSD. The Schmid factors of the {011}<111> and {112}<111> slips are large in Samples B and C, respectively. The Schmid factor of {211}<111> twinning is large in Sample A and intermediate in Sample B.

Fig. 1.

Slip and twining geometry in the BCC structure shown in the stereographic projection. The initial orientations of Samples A, B, and C before tensile tests are denoted as small circles in the triangle.

2.2. Measurements

As expected, in Fig. 1, the deformation modes in the present samples are different. Tensile tests of Samples A, B, and C were carefully performed. They were deformed at strain rates of 1 × 10⁻⁴ s⁻¹ and 0.5 × 10⁻⁴ s⁻¹ by a tensile machine (A&D RTF-1310) at room temperature; the rates were used as crosshead speeds.

Scanning electron microscopy (SEM) images and EBSD patterns were obtained using a scanning electron microscope (Hitachi SU5000). The observed area was fundamentally 400 × 400 μm², and horizontal and vertical pixel sizes were 1 μm. The orientation analysis of the samples was carried out using an EBSD software (TSL OIM Analysis). To estimate the density of geometrically necessary dislocations (GNDs) formed in tensile-deformed samples, kernel average misorientation (KAM) values were estimated by EBSD data.^31,32) The GND density (ρ_GND) obtained by the average value in the observed area is   

$${\rho }_{GND}= a{\varphi }_{av}/bs,$$(1)

where α is a constant on the grain boundary character, ϕ_av is the average value, b is the Burgers vector, and s is the unit of the observed area. The αvalue was assumed to be three in this analysis.³²⁾ In the experiment, the practical GND density was obtained by   

$${\rho }_{GND}=\frac{a}{b} \times \frac{d{\varphi }_{av}}{ds}.$$(2)

The inhomogeneity of GNDs in the KAM maps was utilized to characterize the plastic deformations among the different samples.

3. Results and Discussion

3.1. Orientation Dependence of the Tensile Deformation

Figures 2 and 3 show the nominal stress–strain curves of Samples A, B, and C at strain rates of 1 × 10⁻⁴ s⁻¹ and 0.5 × 10⁻⁴ s⁻¹, respectively. These results suggest that the Young’s moduli of the crystals decrease in the crystal orientation order of <001>, <012>, and < 011>. Although more precise methods should be applied to obtain accurate values,³²⁾ the present results may be fundamentally consistent with the results of elasticity obtained by the strain gauge method.⁵⁾ Notably, abrupt drops in flow stress occur in the stress–strain curve of Sample A close to [001] in the tensile test at a strain rate of 1 × 10⁻⁴ s⁻¹, although they are unclear in the tensile test at a strain rate of 0.5 × 10⁻⁴ s⁻¹. Such abrupt drops in flow stress were observed in BCC iron alloy single crystals during deformation at low temperatures and relatively high strain rate, which is concerned with a thermally activated deformation process of the BCC iron alloy crystals.^29,30) This phenomenon seems to arise from the formation of deformation twins.^29,30,33) The formation of deformation twins in BCC structures is sensitive to the tensile orientation and easily occurs in the tensile direction close to the [001] orientation in the case of Sample A, as demonstrated in Fig. 1. The stress drops during tensile tests were also observed in bamboo-structured iron crystals,³⁴⁾ which were also thought to be strictly related to the initial orientation of preferably oriented crystals close to [001] in the bamboo structure.

Fig. 2.

Nominal stress–strain curves of Samples A, B, and C at a strain rate of 1 × 10⁻⁴ s⁻¹. (Online version in color.)

Fig. 3.

Nominal stress–strain curves of Samples A, B, and C at a strain rate of 0.5 × 10⁻⁴ s⁻¹. (Online version in color.)

The flow stress of Sample B close to [012] is lower than those of the other samples. This tendency was also observed in Fe–Si alloy single crystals,²⁰⁾ which was interpreted by characteristic motions of screw dislocations with the Burgers vector of [111] on the slip plane of (101). Even if the Schmid factor of slip is not considered, this is thought to be mainly due to the primary slip on (101) in the deformation of the sample close to the [012] orientation, as shown in Fig. 1.

The plastic flow and elongation to fracture were different among the three samples. It is considered that the total tensile elongation of single crystals is influenced by the deformation mode and microscopic processes in plastic deformation, which depend on the crystal orientation. To understand the microscopic processes in the plastic deformation of the present samples, an EBSD analysis is useful to characterize the microstructures of the deformed samples.

3.2. Microstructures in Deformed Samples

Figure 3 shows inverse pole figure (IPF) maps of the microstructures of Samples A, B, and C after fracture by tensile deformation at the strain rate of 1 × 10⁻⁴ s⁻¹. The map of Sample A reveals that approximately 10 μm thick planar microstructures in the matrix were formed by deformation. The planar microstructure corresponds to deformation twins for which the orientation is characterized later. If such planar microstructures are abruptly formed by shear deformation, the stress drops may appear in the stress–strain curve due to strains. This behavior was observed, as shown in Fig. 2.

Very thin planar microstructures were observed in Sample B, as shown in Fig. 4(b), although their contrast was low in the image. The orientation relationship between the matrix and planar structure will be analyzed later. In this case, abrupt stress changes were not observed in the stress–strain curve, likely owing to the very thin microstructure and plastic deformation of the slip system of (101)[111]. However, twins in microstructures were not observed in the IPF map of sample C. This indicates that slips by dislocation glide on the (211) plane are predominant in this tensile orientation.

Fig. 4.

IPF maps near fractured areas in Samples (a) A, (b) B, and (c) C. M and T denote the matrix and twin in the microstructure, respectively. An enlarged IPF map is inset in the map of Sample B to easily observe thin twins. These maps are represented as orientation with respective to tensile direction, together with stereo-triangle showing crystal orientation in pseudo-color. The tensile direction is the upper and lower direction in these images. (Online version in color.)

To investigate the local plastic strains formed during the tensile tests, EBSD was used to characterize the misorientations in the microstructures of the deformed samples. KAM maps obtained by EBSD provide information about microscopically inhomogeneous strain distribution by plastic deformation and are useful to compare the deformation mode. Figures 5(a)–5(c) show KAM maps near the fractured areas in Samples A, B, and C, respectively. The areas of these KAM maps are the same as those of the IPF maps shown in Fig. 4. The green contrasts correspond to the dense portions of the GNDs formed in the deformed samples. Microscopic plastic strains were observed in the deformation twins and at the interface between matrix and twins of Sample A. The densities of GNDs were estimated by the KAM maps. The dislocation densities in Samples A, B, and C were 1.9 × 10¹³, 2.5 × 10¹³, and 2.3 × 10¹³ m⁻², respectively, at a strain rate of 1 × 10⁻⁴ s⁻¹. These values seem to be related to the total elongations of the samples, although the deformation mode depends on the orientation. Notably, local plastic strains are concentrated near the twin boundaries in Sample A. This implies that twin formation may be accompanied by the generation of dislocations in the twins.

Fig. 5.

KAM maps near fractured areas in Samples A, B, and C, which are the same areas shown in Fig. 4. (Online version in color.)

3.3. Orientation Relationships in the Microstructures in the Deformed Samples

To consider the orientation relationship between the BCC matrix and deformation twin as a planar microstructure, the atomic arrangement in twin formation in the BCC matrix by tensile deformation is illustrated in Fig. 6. The arrangement is shown as a stacking of {110} planes; the twin boundary is on the {112} plane. The Burgers vector of twin dislocations is a/6[111] (a: lattice constant). This orientation relationship is typically expressed by the rotation axis of [110] and rotation angle of 70.6°. A stereographic projection of the experimental results was utilized to represent such a twin relationship.

Fig. 6.

Atomic arrangement in the twin formation in the matrix of the BCC structure observed from the [110] direction. The twin boundary is on the {112} plane, while the Burgers vector of twin dislocations is a/6[111], where a is the lattice constant. (Online version in color.)

Using stereographic projection, the orientation relationship between the matrix (red color) and planar microstructure or deformation twin (blue color) in Sample A is shown in Fig. 7. The results were obtained by the EBSD data. The tensile axis rotated slightly owing to tensile deformation. The tensile axis is the center of the projection, which is close to [001] (solid circle) and comparable to that in Fig. 1. The rotation axis of twinning is denoted as a large open circle. Twinning occurs by a rotation of 70.6° around the axis. A typical rotation is shown as a rotation of [111] in the matrix to [111] in the twin. These plots indicate that twinning occurs in the matrix during the tensile test, although the small misorientation between the matrix and twins may arise from slips caused by dislocation glides.

Fig. 7.

Orientation relationship between the matrix (red color) and deformation twin (blue color) in Sample A after plastic deformation obtained using a stereographic projection. The tensile axis is the center of the circle, which is close to [001] (open square). The rotation axis of the twin relation is denoted as an open circle. The twinning occurred by a rotation of 70.6° around the axis, which is two <111> orientation. (Online version in color.)

It is remarked that secondary twins may be observed together with the primary deformation twins, as the orientation is close to the secondary twin geometry in Sample A, as shown in Fig. 1. This occurs because the tensile axis is rotated to the [111] orientation by the plastic deformation of the sample. Thus, secondary twins can be formed, although the slip line is not clearly observed. Multiple slips, such as primary and secondary slips, may contribute to the deformations in these samples. A small content of such secondary twins was observed, as shown in Fig. 5(a).

In Sample B, the thinner planar microstructure revealed a twin relationship against the matrix, which almost corresponds to the secondary twin relationship in Sample A. However, the EBSD results for Sample C showed no formation of deformation twins, which implies that slip by dislocation glides is dominant in the tensile deformation of the [011]-oriented sample. Therefore, the present results suggest that the initial orientation of the samples is an important factor determining the deformation mode of the Fe–Ga alloys, although other factors such as temperature and strain rate during deformation may influence the deformation mode. The gallium content in the iron alloy is another factor that affects the deformation mode because it causes solid solution hardening. These deformation characteristics seem to be common in BCC metals and alloys, as twin formation has been observed in studies on plastic deformation of iron alloy single crystals.^35,36,37)

4. Summary

Tensile tests and EBSD measurements were performed to characterize the plastic deformation and microstructure of BCC Fe–17-at%-Ga alloy single crystals oriented close to [001], [012], and [011] orientations. Slip by dislocation glides was dominant in the tensile deformation in the [011]-oriented sample, while coarse planer deformation twins were formed in the [001]-oriented sample. In the deformed sample with the [012] orientation, thin deformation twins were observed with slip lines. The characteristics of the Fe–Ga alloys by plastic deformation are analogous to the previous results on the plastic deformation of BCC iron alloys. The addition of gallium to iron induced solid solution hardening. The increase in the flow stress by the addition of Ga enhanced the formation of deformation of twins.

Acknowledgements

The authors acknowledge the support from Grant-in-Aid for Scientific Research by the Japan Society for the Promotion of Science (17H03422, 20H02474) and Global Institute for Materials Research of Tohoku University and sincerely thank Assoc. Prof. K. Shinoda, Assoc. Prof. R. Simura and Prof. K. Sugiyama for their help with the experiments.

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