Crystal defects produced by α to β phase transformation during ECP in Cu-40%Zn alloy

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Bcc to hexagonal structure transition

In addition, the bcc to two kinds of hexagonal structure transition mechanism have been widely and deeply studied on many alloys systems, such as Ti-based alloys [143-162], Zr-based alloys [163, 164] and Cu-based alloys [166-172]. Of the two hexagonal structures, the one possesses a crystal structure resembling that of the equilibrium α phase with the Burges orientation relation (BOR) with the β matrix [163], and the other have a crystal structure resembling that of the metastable ω phase with the Blackburn OR with the β matrix [159]. Due to the two kinds of structure distortions in the β matrix, additional weak reflections are produced at the approximate 1/2 β reflection positions in the TEM Selected Area Electron Diffraction (SAED) patterns for the former and at the approximate 1/3 and 2/3 β reflection positions for the latter [145-148]. Furthermore, it is reported that characteristic atomic shuffles or displacements on certain shear systems of the bcc phase commonly result in the formation of hexagonal structures in a form of nano-sized atomic clusters. Many experimental investigations have shown that the atomic shuffles or displacements are associated with the {110}<1̅10> and {1̅12}<1̅11̅> shear systems [147, 165]. Further studies revealed that the softening of the two shear systems corresponds to the lower energy or soft phonon modes of the β phase [165]. It should be noted that the {110}<1̅10> and {1̅12}<1̅11̅> shear systems are coincidence with the typical dislocations of the bcc structure.
To summarized above, the dislocations of the parent phase played an important role to ensure the typical phase transformation. However, the impact of the dislocations on the phase transformation from fcc to bcc and the cooresponding mechanism on the dislocation evolution with the new phase are still not clear. So, it needs further studying.

Crystal defect type associated transformation OR selection

As we known, to ensure that the structure change is energetically economical, a specific orientation relationship (OR) is respected by the two end phases to minimize the lattice distortion energy. Depending on the crystal system of the two end phases, different ORs are present, such as the Kurdjumov-Sachs OR (K-S), i.e., {111}α //{110}β, <1̅10>α //<1̅11>β, observed in steels [173-176], Fe–based alloys [177-179] and Cu-Zn alloys [180]; the Nishiyama-Wasserman OR (N-W), i.e., {111}α //{110}β, <112̅> α //<1̅10> β in steels [173, 175, 176], Fe‐Ni‐Co‐Ti shape memory alloy [181] and in Gibeon meteorites [182], the Burgers OR (BOR), i.e., {110}β //{0001}α, <1̅11̅>β //<112̅0>α, in Ti based alloys [183-186], the Pitsch OR, i.e., {101}α //{12̅1̅}β, <101̅>α //<1̅1̅1>β, in Ni–Mn based intermetallic compounds [187] and other special OR, i.e., {001}7M //{112}NM, <100>7M //<111̅>NM, in Ni–Mn–Ga alloys [188]. According to the above results, the structure change is always realized by the existing dislocations of the parent crystal structure. Moreover, the nucleation of a new phase occurs heterogeneously at some preferential nucleation sites in the parent phase such as grain boundaries, dislocations and second phase during most phase transformation processes. Thus, the phase transformation OR should be related to the different type defects. The relation between the observed transformation ORs and the possible perfect or partial dislocations to facilitate certain OR variants produced by phase transformation in some materials have been an interest of study since last century and continues to attract attention [182, 189-195] to date.
Bogers et al. observed different orientation relationships regarding to the transition of austenite into martensite and suggested that a certain orientation relation be realized depending on the action of the dislocations present or created by external stress [116]. Later, Luo and Weatherly further studied the crystallography of bcc precipitates nucleated on various kinds of defects in the fcc matrix of a Ni–Cr alloy [193]. They found that the bcc precipitates nucleated on dislocation hold the variant of the K–S relationship, for which the maximum misfit direction calculated by the surface dislocation theory [194] is nearly parallel to the Burgers vector of the dislocation. Ameyama and Maki further found that a fcc γ precipitate holds the K–S relationship with respect to both the bcc α matrix and the twin at the {112}<111> deformation twin boundary in a duplex stainless steel [195]. Furthermore, the correspondence relations between the OR plane and the glide plane and between the OR direction and the Burgers vectors of the dislocations (perfect or partial) have been phenomenologically studied for the K-S and N-W relations [190, 191]. With such an approach of correspondence relations, the association of each plane/ burgers vector combination with a particular variant is established and the presence of both “positive slip” and “negative slip” variants within individual grains, a puzzling phenomenon, have been successfully interpreted [190]. The approach explains well the differences in the proportions of the K-S and the N-W variants observed experimentally in relation with the stacking fault energy of the parent phase [190, 192].

Phase transformations in Cu-Zn alloys

The Cu-Zn alloys are widely used in many applications such as lead frames, connectors, pipes, valves, and in fittings in potable water systems due to their superior electrical and thermal conductivities, excellent corrosion resistance, ease of fabrication, and good strength and fatigue resistance [196]. The development of high-performance brasses is necessary to satisfy new demands posed by the electronics industry, automotive, and aerospace applications and household appliance development. It is well known that their mechanical properties are strongly dependent on the microstructural characteristics, especially the size, the volume fraction, the morphology and distribution of the precipitates [197-200], therefore the phase transformation process has been extensively studied to obtain an appropriate microstructure.
From the last century on, many studies have focused on the phase transformation during cooling course in the Cu-Zn alloys. It was reported that the phase transformation usually follows specific orientation relationships [201-209], such as the K-S OR, i.e., {111} α //{110} β, <1̅10> α //<1̅11> β [203-208] or N-W OR, i.e., {111} α //{110} β, <112̅> α //<1̅10> β [209] and displays different occurrences of the variant following the different ORs under different treatments [202-205]. At the same time, the precipitates also show different morphology such as the widmanstatten typed under heat treatment [206], the needle shape under dezincification [207, 210], the fine globular shape under extrusion [209] and the plate shape [211, 212] and so on.
In the recent years, the heating phase transformation from the fcc structure to the bcc structure was realized by the ECP treatment [52, 54-57, 213]. It is evidenced that the high temperature β phase could be retained to the ambient temperature and the ECP could enhance the nucleation resulting from the electric current itself. It is worth noting that, by the ECP treatments, the high temperature β phase nucleated from the α phase obeyed the orientation relation of 44.3°/<114> [56], which is close to the K-S relationship, during the heating phase transformation in the Cu-Zn alloys.

Microstructural characterization

The microstructural examinations and crystallographic orientation investigations were performed in a field emission gun scanning electron microscope (SEM, Jeol JSM 6500 F) with an EBSD acquisition camera and the Aztec online acquisition software package (Oxford Instruments). During the EBSD measurements, the “beam-control” mode was applied with a step size of 0.15 μm under an accelerating voltage of 15 kV. The EBSD data were analyzed with the Oxford Channel 5 software and the Atex software [221]. The EBSD samples were first mechanically ground using the emery/ SiC grinding paper up to 4000 # and then polished using diamond paste (1 μm), and then electrolytically polished with a solution of 20 % (volume fraction) nitride acid in methanol at 18 V for 3 seconds at room temperature.
The nano scaled microstructural and crystallographic features of the constituent phases were analyzed using a Philips CM 200 transmission electron microscope (TEM) operated at 200 kV. The TEM is equipped with a LaB6 cathode, a Gatan Orius 833 CCD camera, and homemade automatic orientation analysis software – Euclid’s Phantasies (EP) [214, 215]. The atomic scaled microstructures were analyzed by high-resolution scanning transmission electron microscopy (STEM), using a JEOL JEM-ARM200F TEM operated at 200 kV. High-angular dark-field (HAADF) images were acquired with an inner and outer collecting angle of 68 and 280 mrad, respectively. TEM thin films were prepared first by mechanical thinning to 80 μm and then by electrolytic polishing to perforation at -30°C in a solution of 20 % (in volume) nitride acid in methanol at 20 V, using a Struers Tenupol-5 twin-jet electropolisher.
During the TEM examination, the crystallographic orientation of the microstructural constituents was determined by indexing the TEM Kikuchi line patterns using the software EP and expressed in a triplet of Euler angles in Bunge’s notation [216, 217]. Orientation relationships (OR) between the microstructural constituents were analyzed by misorientation calculation. The dislocation types and the dislocation Burgers vectors were analyzed using invisibility criterion and by matching the observed dislocation line orientation with the theoretical ones as described in [218]. The atomic correspondences and the electron diffraction patterns for the structure transformation from the parent phase to the product phase were analyzed using the Crystal Maker® [219] software.

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Chemical composition analysis

The chemical composition distribution characteristics were examined by the electron probe microanalysis (EPMA). X-ray line profiles and energy scans were obtained using an FEG-EPMA instrument (JEOL JXA-8530 F). In each measurement, the working distance was approximately 11 mm, the take-off angle was 40° and the In-Lα X-rays (critical excitation voltage: 3.73 keV) were employed. The radius of the Rowland circle was 100 mm (an H-type spectrometer with a JEOL microprobe) and the analyzing crystal was made of pentaerythritol (PETH). The probe current (Iprob) was in the range of 10-12 – 5 * 10-7 A and the sampling time was 1 second per point. The electron beam was focused.

Basic crystallographic calculations

During the crystallographic calculation processes, two kinds of coordinate systems were used in the present work. The one is the orthonormal coordinate system ‘x- y- z’ or ‘i-j-k’ which is either set to the sample frame or to the crystal bases as shown in Fig. 2.3. The other is the Bravais lattice basis of the cubic crystal (α and β structure) and the hexagonal crystals (ε and ω structure), i.e. ‘a- b- c’ of the cubic crystal structure in Fig. 2.3 (b) and the hexagonal structure in Fig. 2.3 (c). When the orthonormal coordinate system is set to the Bravais lattice basis, the geometrical relation between the orthonormal coordinate system and the Bravais lattice basis conforms to the convention defined by the Channel 5 software package. All coordinate systems are of right-handedness.

Phase transformation orientation relationship

In general, the crystallographic transformation orientation relationship (OR) between the parent crystal (P) and the product crystal (D) could be defined by a pair of parallel crystalline planes and a pair of in-plane parallel directions, as described in Equation (2-12): (ℎ𝑘𝑙)𝑃//(ℎ𝑘𝑙)𝐷 [𝑢𝑣𝑤]𝑃//[𝑢𝑣𝑤]𝐷 (2-12).
During the crystallographic calculations, the coordinate transformation matrix is often used to describe the orientation relation between the two crystal systems (parent and product phases). The geometrical relation between the two crystal systems (ap-bp-cp and aD-bD-cD) under the OR is illustrated in Fig. 2.7. The orthonormal or Cartesian coordinate system ‘i- j- k’ is set on the OR system of the two phases. k is parallel to the normal of the OR plane, j is parallel to the OR direction and i is parallel to the vector cross product of the OR direction and the OR plane normal direction. MP and MD are the coordinate transformation matrix from the Bravais lattice basis ‘a-b-c’ of the parent crystal or the product crystal to the Cartesian coordinate system ‘i-j-k’. Thus the coordinate transformation matrix between the two Bravais lattice bases of the two phase MOR can be deduced as follows.

Hexagonal coordinates

The Bravais lattice basis of hexagonal crystals are always expressed in two ways. The one uses a three-axis coordinate system, where the (H K L) represents an arbitrary plane and the <U V W> represents an arbitrary direction in the hexagonal basis. The other way uses a four-axis basis, where the (h k i l) represents an arbitrary plane and the <u v t w> represents an arbitrary direction in the hexagonal structure. The relation between the three Miller indices of the three-axis coordinate system and the four Miller indices of the four-axis coordinate system can be obtained by the following Equations.

Chemical composition distribution characteristics

As the transformation from α to β phase is normally diffusional and the ECP induced transformation happened in a very short time from 118 μs to 150 μs depending on the electric current density, the composition of the ECP induced β phase was analyzed with respect to its parent phase α. Table 3.2 shows the contents (the Cu and Zn) of the ECP induced β phase on the α grain boundaries and in the α grain interiors and the surrounding α matrix in the annealed and ECPed Cu-40%Zn samples. For reference, those of the residual β phase in the initial as-annealed sample were also measured and given in Table 3.2. Some example measurement positions indicated with the cross are displayed in Fig. 3.6. It can be found that the compositions of the ECP induced β phase on the α grain boundaries (βGB) and in the α grain interiors (βGI) are quite close to those of the initial β phase of the annealed sample but different from those of the parent α phase, demonstrating that atom repartition happened during the ECP induced phase transformation although the transformation time was very short.

Orientation relationship (OR) between α ̸ β

In consideration of the crystal structure features of the α phase (FCC) and the β phase (BCC), the Bain, the Nishiyama-Wassermann (N-W), the Kurdjumov-Sachs (K-S) and the Pitsch relations (as listed in Table 3.3) might be possible for the phase transformation in the investigated material. To evaluate the possibility of these orientation relationships (ORs), a large number of α and β grains were selected for the crystallographic analysis, using the measured orientations of the parent α phase and the β precipitates. It is found that one part of β precipitates respects the N-W with the surrounding α phase, whereas the other part respects the K-S ORs with the neighboring α phase, both with certain angular deviations (up to 5°), as shown in Fig. 3.7 (a) and (b). Fig. 3.7 (a) and (b) displayed the βGB along α grain boundaries and the βGI in the α grain interiors where the α grains are in gray contrasted with the EBSD band quality indices and the β ones are in white. The colored contour lines around the β precipitates indicate the angular deviations from the exact ORs (K-S and N-W) where the red lines represented the K-S OR and the green line the N-W OR. The plane and direction parallelisms of the respective K-S and the N-W ORs are illustrated in the corresponding plane and direction pole figures in Fig. 3.7 (c) and (d), using the example orientation data of the two phase measured by EBSD i.e. the {111} of the α phase and the <011> of the β phase. From those maps it can be observed that the {111} poles of the α phase roughly coincide with the {011} poles of the βGI. For the pole figures of ORs directions, there are two kinds of situations. One is the [11̅0] poles of the α phase almost coincide with the [11̅1] poles of the βGB, and the other is the [112̅] poles of the α phase coincide with the [11̅0] poles of the βGI. Thus, there are two kinds of ORs between the α phase and the βGI: the K-S and the N-W OR for the ECP induced phase transformation. Due to the existence of the angular deviations, the actual transformation ORs deviate from the theoretical ORs, indicating that lattice strains are produced during the structure transition from the α phase to β phase.

Table of contents :

Chapter 1 Literature review
1.1 General introduction
1.2 The Electric Current Pulses (ECP) technology
1.2.1 Introduction
1.2.2 The phase transformation induced by ECP
1.3 Crystal defect associated solid-state phase transformation
1.3.1 Basic crystal defects of metallic materials
1.3.2 The effect of the defects on the phase transformation
1.3.3 The dislocation mechanism on the phase transformation
1.3.4 Crystal defect type associated transformation OR selection
1.4 Phase transformations in Cu-Zn alloys
1.5 Content of the present work
Chapter 2 Experimental and calculation methods
2.1 Experimental details
2.1.1 Alloy preparation and heat treatment
2.1.2 ECP treatments
2.1.3 X-ray diffraction measurement
2.1.4 Microstructural characterization
2.1.5 Chemical composition analysis
2.2 Basic crystallographic calculations
2.2.1 Coordinate system
2.2.2 Coordinate transformation and orientation relation
2.2.3 Stereographic projection
2.2.4 Deformation gradient tensor
2.2.5 Trace analysis method
2.2.6 Twinning elements
2.2.7 Hexagonal coordinates
Chapter 3 Microstructure and crystallographic characteristics of Cu-40%Zn alloy after the ECP treatments
3.1 Introduction
3.2 Experimental
3.3 Results
3.3.1 Phase constituents and lattice constants
3.3.2 Microstructure characteristics
3.3.3 Chemical composition distribution characteristics
3.3.4 Orientation relationship (OR) between α ̸ β
3.3.5 Morphology of intragranular β (βGI)
3.4 Discussion
3.4.1 The thermal effect of the ECP
3.4.2 The electrical effect of the ECP
3.4.3 The lattice strain effect
3.5 Summary
Chapter 4 Crystal defects produced by α to β phase transformation during ECP in Cu-40%Zn alloy
4.1 Introduction
4.2 Experimental
4.3 Results
4.3.1 Microstructural characteristics
4.3.2 Crystal defect characteristics
4.4 Discussion
4.5 Summary
Chapter 5 Sub-structure of β precipitates formed by ECP treatment in Cu-40%Zn alloy
5.1 Introduction
5.2 Experimental
5.3 Results
5.3.1 Microstructural characteristics
5.3.2 Identification of sub structures in β precipitates
5.3.3 Identification of atomic shuffling and displacement system to realize the structure change
5.3.4 Origin of concomitant formation of the two hexagonal structures
5.4 Summary
Chapter 6 Conclusions and Perspectives
6.1 Conclusions
6.2 Perspectives


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