Line-Profile Analysis Combined with Texture Analysis for Characterizing Dislocation Distribution in Texture Components of Cold-Rolled Copper Sheets

Sample

Commercial copper sheets (99.99 mass%) with 1-mm thickness were used for a sample in this study. The copper sheets were annealed at 773 K for 3 h in vacuum. The average grain size of the annealed sheets was about 50 μm. The sheets were rolled at room temperature at rolling reductions of 20, 30, 40, 50, 70, 75, and 85%. The Vickers hardness was measured on the chemically polished surface of the samples. A load of 0.98 N was applied for a dwell time of 5 s. Hardness values were the average of five different indentations. Figure 1 shows a variation in the Vickers hardness with the rolling reductions. The hardness rose up to the 20% rolling reduction and then increased gradually with further rolling reduction. When analyzing the recovery and recrystallization for individual texture components, the rolled samples were heated in an oil bath bubbled with N₂ gas at 473 K.

Figure 1:

Vickers hardness of cold-rolled pure copper sheets at different deformation levels.

Microstructural observation

The microstructures of the cold-rolled copper samples were observed with EBSD using a field-emission scanning electron microscope (FE-SEM) (FEI XL30S-FEG) operated at 20 kV. The EBSD data were accumulated and analyzed on an orientation imaging microscopy (OIM; TexSEM Laboratories, Inc.) system. The samples for the EBSD measurements were polished to a mirror surface using colloidal silica solution.

Microstructural characterization in texture components

The XRD measurements were conducted by using an X-ray diffractometer (SmartLab, Rigaku Co.). Incident X-ray of Cu Kα was monochromated with a Göbel mirror, and diffraction profiles were measured in a parallel beam geometry. 111, 200, and 220 reflections from the copper samples were measured for the pole-figure analysis. The orientation distribution function (ODF) was analyzed using MTEX software to identify texture components [10]. The texture components such as cube, brass, and copper were confirmed on a complete {100} pole figure. The {100}-plane directions for individual texture components were aligned to the scattering vector, so that the line-profile analysis using 200 and 400 reflections could be performed for each texture component. In the line-profile analysis procedure, Cu Kα₂ lines were eliminated from the measured profiles by Ladell’s method [11]. It should be mentioned that diffraction intensity derived from fiber components is also included in the profiles for the line-profile analysis. However, especially for strongly textured samples, the contribution of a texture-dependent component could be dominantly larger than that of the fiber component. Diffraction profiles of LaB₆ (SRM-660b, NIST) were measured for obtaining instrumental profiles at the same tilt angles as measured the individual texture components of samples. Using the instrumental profiles, structural profiles were extracted from the measured profiles with the Stokes method [12]. Mean square of microstrain, ε(L)2, and size part of Fourier coefficient, A^S(L), were evaluated using the Warren–Averbach procedure [13]:

where A, L, and d are the real part of Fourier coefficient, the column length, and the lattice spacing, respectively. Figure 2(a) shows an example of A^S(L) obtained from the copper at a cold rolling of 75% reduction. A straight part of the A^S(L) was approximated by a linear function, and the intercept of the linear function at A^S(L)=0 indicates the crystallite size. The mean-square strain is related to dislocation density, ρ [14]:

where b and R_e are the size of Burgers vector (0.2556 nm) and the outer cut-off radius of dislocations. Cˉh00 is the average contrast factor for the {100} plane. The plot of ε(L)2 versus ln L can be fitted with a linear function at small L region as shown in Figure 2(b). The slope of the fitted function is the coefficient of ln L in eq. (2). The dislocation density can be estimated by employing Cˉh00 of 0.304, which assumes an equal population of the edge and screw dislocations in an approximate manner [15].

Figure 2:

(a) Size component of Fourier coefficient A^s(L) and (b) mean-square strain ε(L)2 of the copper at a cold rolling of 75% reduction.

Microstructure of cold-rolled copper observed by EBSD

Figure 3 shows normal-direction (ND) inverse pole figure (IPF) maps of microstructures for the samples at rolling reductions of 30, 50, and 75%. The {110} plane became dominant in the ND-IPF maps with an increase in the rolling reduction. The crystallographic orientation changed locally within a grain due to GN dislocations. Figure 4 shows the image quality map, the ND-IPF map, and the kernel average misorientation (KAM) map of an arbitrary {110} grain at a rolling reduction of 50%. The maps in Figure 4 were observed at a step size of 80 nm. The KAM value was calculated up to the second neighboring point with a maximum misorientation angle of 2°, in accordance with the procedure reported by Herrera et al. [16]. While the microstructure in Figure 4 is built up by partial domains of a single grain, we can divide two regions with low and high KAM values. The KAM values of the upper and lower regions in Figure 4(c) were 0.40°±0.17° and 0.68°±0.28°, respectively, which are related to GN dislocations [17]. The average density of the GN dislocations, ρ_gnd, in the observed area can be calculated with the KAM value (misorientation angle), θ, by using the relational expression [18]:

where u and b are the unit length and the size of Burgers vector. The calculated ρ_gnd values of the upper and lower regions in Figure 4(c) were estimated to be (3.4±1.5)×10¹⁴ and (5.8±2.3)×10¹⁴ m⁻², respectively. These values by the EBSD technique could provide the inhomogeneous distribution of the dislocation density in the local region; however, it could give no information on the average dislocation density, which can be determined with an XRD line-profile analysis.

Figure 3:

ND-IPF maps of cold-rolled pure copper at rolling reductions of (a) 30, (b) 50, and (c) 75%.

Figure 4:

Magnification of a {110} grain of pure copper cold rolled at 50% reduction: (a) image quality map, (b) ND-IPF map, (c) KAM map.

Distribution of dislocations between texture components

Texture evolution of a copper sheet with an increase in a rolling reduction was evaluated using pole figures of the 111, 200, and 220 reflections. The ODFs in φ₂=45° section of the samples at different reductions are shown in Figure 5(a). The ODFs are characterized by three distinct texture components: {001}<100>, {112}<111>, and {110}<112>, which are generally called as cube, copper, and brass, respectively. The texture evolution in Figure 5(a) is almost similar to the texture evolution of cold-rolled copper sheets obtained in a previous work [19]. These texture components were individually assigned on a {100} complete pole figure, as shown in Figure 5(b). The brass component developed at first, and subsequently the copper component appeared with an increase in rolling reduction. On the other hand, the cube component appeared thinly. Figure 6 shows a {100} complete pole figure at a rolling reduction of 75%. The symbols of X, Y, and Z designate the cube, copper, and brass components, respectively, and the point A with a low diffraction intensity corresponds to a non-texture component. For determination of the dislocation density and crystallite size in these components, line profiles of the 200 and 400 reflections were measured at the orientations of the encircled X, Y, Z, and A in Figure 6. As an example of the measured line profiles, Figure 7 shows the 200 reflections of the copper component of the cold-rolled sheets at reductions of 30, 50, and 75%. With an increase in the rolling reduction, the line broadening was enhanced by introducing dislocations. The diffraction profiles of LaB₆ powder were also measured at the equivalent geometry of the X, Y, Z, and A positions for estimating each instrumental broadening. The 200 and 421 reflections of LaB₆ were used as instrumental profiles for the 200 and 400 reflections of the copper samples, respectively. The full width at half maximum (FWHM) values of the instrumental profiles at the encircled X, Y, Z, and A positions were 0.12°, 0.12°, 0.12°, and 0.11° for the 200 reflection, respectively, and they were 0.32°, 0.33°, 0.32°, and 0.34° for the 400 reflection, respectively. On the other hand, the FWHMs of rolled samples were typically more than 0.18° and 0.77° for the 200 and 400 reflections, respectively. Thus, the FWHMs of the instrumental profiles were sufficiently small to carry out the line-profile analysis so that the dislocation density and the crystallite size can be evaluated with high accuracy. Figure 8 shows a comparison between measured and instrumental profiles of 200 reflections of the copper component of the 75% cold-rolled sample. Since the difference in the peak width between the measured and instrumental profiles was clear, the structural profile containing essential information on crystalline structure of metal was successfully deconvoluted as shown in Figure 8.

Figure 5:

(a) ODFs in φ₂ = 45° section and (b) {100} complete pole figures of cold-rolled pure copper at different reduction levels. The directions of the texture and non-texture components in the pole figures are described in Figure 6.

Figure 6:

A {100} complete pole figure of pure copper at a cold rolling of 75% reduction. The symbols X, Y, Z, and A designate the cube, copper, brass, and non-texture components, respectively.

Figure 7:

200 reflections of the copper component of the cold-rolled sheets at reductions of 30, 50, and 75%.

Figure 8:

Measured, instrumental, and deconvoluted profiles of 200 reflections of the copper component of the 75% cold-rolled sample.

Figure 9 shows the dislocation density and the crystallite size for the cube, copper, brass texture components, with the non-texture component of the cold-rolled copper sheets at rolling reductions of 30, 50, and 75%. The dislocation density increased with an increase in the rolling reduction in all the components. Correspondingly, the crystallite size decreased with an increase in the rolling reduction. This is consistent with the variation of the Vickers hardness in Figure 1 which shows that the hardness increased gradually with an increase in the rolling reduction. The dislocation density at a rolling reduction of 50% was higher than that estimated by the EBSD in Section 3.1. This is because the XRD line-profile analysis could estimate the total density of the GN and the statistically stored dislocations in a large area of a sample, whereas the EBSD only evaluated the GN dislocations in a local area; in addition, the KAM map (Figure 4(c)) shows the formation of dislocation cell structure, suggesting that the density of the statistically stored dislocations would be relatively high. The difference in the dislocation density was small between the cube, copper, and brass components, irrespective of the rolling reductions. This is probably because the generation and annihilation of dislocations would be independent of the slip paths during the formation of the distinct texture components. On the other hand, with an increase in the rolling reduction, the dislocation density of the non-texture component became higher than those of the other texture components. The similar phenomenon was also confirmed for tensile-deformed austenitic steels in our previous study [6]. The non-texture grains would originate from a microband, which generally appears in largely deformed metals and contains high-density dislocations. The microband was observed in plastically deformed copper in previous works [20, 21]. Thus, in the case of the cold-rolled copper sheet, the recovery and recrystallization in the components were expected to exhibit different behavior at elevated temperatures, because of their non-uniform dislocation distribution.

Figure 9:

(a)–(c) Dislocation density and (d)–(f) crystallite size for texture and non-texture components of the cold-rolled copper sheets at rolling reductions of (a) and (d) 30, (b) and (e) 50, and (c) and (f) 75%.

Effect of dislocation density on dislocation recovery and recrystallization

The dislocation density of the texture components of the cube, copper, and brass were almost comparable at a rolling reduction of 75% as shown in Figure 9(c). The thermal relaxation process on the dislocation densities would occur in a similar manner in these texture components at the rolling reduction. Therefore, the recovery and recrystallization were characterized for the individual texture components of cold-rolled copper at 75% reduction. Figure 10 shows a variation in the Vickers hardness of the 75%-rolled copper sheets at 473 K as a function of annealing time. The hardness almost remained unchanged until 150 s and then decreased along with the annealing up to 600 s. The ODFs in φ₂=45° section and complete {100} pole figures of the 75%-rolled samples at different annealing times of 0, 150, 300, and 1,200 s are shown in Figure 11. The copper and brass components tended to disappear after the annealing time of 150 s, suggesting the onset of the recrystallization. On the contrary, the cube component evolved with the recrystallization. The decrease in the Vickers hardness can be explained by the recrystallization process.

Figure 10:

Variation in the Vickers hardness of the annealed 75% cold-rolled copper sheets at 473 K as a function of the annealing time.

Figure 11:

(a) ODFs in φ₂ = 45° section and (b) {100} complete pole figures of the annealed 75% cold-rolled copper sheets at 473 K for different holding times. The directions of the texture and non-texture components in the pole figures are described in Figure 6.

The 200-reflection profiles for the individual components were measured at the same position as depicted in Figure 6 to evaluate the recovery and recrystallization. Figure 12 shows variations in FWHMs of the 200-reflection profiles for the individual components of the 75%-rolled samples as a function of annealing time at 473 K. A decrease in the FWHMs is derived from the recovery and/or recrystallization. Whereas the FWHMs for the cube, copper, and brass components remained unchanged until 150 s, the FWHM for the non-texture component decreased from the start of the annealing, suggesting that the recovery proceeded initially in the non-texture component, probably because the higher dislocation density of the non-texture component could prompt the recovery. In accordance with a variation in the Vickers hardness in Figure 10, the large decrease in the FWHMs, which may originate from the recrystallization, occurred at around 200 s in all the components. It is noteworthy that the decrease in the FWHMs for the cube component at around 200 s was more distinct than those for the copper and brass components. The difference in the variations in the FWHMs between the three texture components could not be explained from their dislocation densities, because the initial dislocation density of these components was almost comparable. The {100} pole figures in Figure 11(b) seem to indicate that the cube component developed from 150 s to 300 s as a recrystallization texture, whereas the copper and brass components became disappeared. Therefore, the larger decrease in the FWHM for the cube component would originate from the formation of new cube grains emerged by the recrystallization and having a small slight strain.

Figure 12:

Variation in FWHMs of the 200-reflection profiles for texture and non-texture components of the annealed 75% cold-rolled copper sheets as a function of the annealing time.