Strain dependence of deformation and recrystallization microstructure homogeneity in clock-rolled tantalum sheets

Materials Characterization 161 (2020) 110165

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Strain dependence of deformation and recrystallization microstructure homogeneity in clock-rolled tantalum sheets

T

Jialin Zhua, Shifeng Liua,b, , Shuai Yanga, Doudou Longa, Yahui Liua, Xiaoli Yuanc, Dmytro Orlovd ⁎

a

College of Materials Science and Engineering, Chongqing University, Chongqing 400044, China Electron Microscopy Center of Chongqing University, Chongqing University, Chongqing 400044, China c School of Metallurgy and Material Engineering, Chongqing University of Science and Technology, Chongqing 401331, China d Division of Materials Engineering, Department of Mechanical Engineering, LTH, Lund University, Lund 22363, Sweden b

ARTICLE INFO

ABSTRACT

Keywords: Strain Microstructure Taylor model Schmid factor Texture

Microstructure and crystallographic texture are the key factors that determine the sputtering target properties. Clock rolling plays an important role in improving the microstructure homogeneity, but the effect of strain during rolling on deformation and recrystallization behavior is not clear. Thus, high-purity tantalum (Ta) plates were 135° clock rolled to 70% and 87% reduction and then annealed at various temperatures to observe the microstructure evolution. Texture and microstructure in the center layer of the rolled and annealed Ta sheets were characterized via optical microscope (OM), X-ray diffraction (XRD), electron backscatter diffracting (EBSD) and transmission electron microscope (TEM). The results displayed that significant microstructure difference existed between 70% and 87% sample. Grain average misorientation value of {111} grains {〈111〉//normal direction (ND)} in the 70% sample was considerably higher than that in the 87% sample, suggesting a more heterogeneous grain fragmentation. Schmid factor (SFrolling) and Taylor model analysis of {111} grains in the 70% sample demonstrated that the slip was easier, and the system with higher SFrolling could alone accommodate the majority of plastic strain, contributing to the formation of micoshear bands. Upon annealing, the sample rolled 70% recrystallized more quickly, owing to strong {111} deformed texture, and severe microstructure subdivision and great stored energy within {111} grains. The {111} texture is very strong and grain size distribution was not uniform after the completion of recrystallization. However, after annealing of sample rolled 87%, smaller average grain size and variation, and relatively homogeneous texture distribution can be obtained.

1. Introduction Electronic components such as wires and substrates are prone to atomic diffusion owing to high-intensity current state in the integrated circuits [1] resulting in damage to the wires and the substrate. To prevent the occurrence of interconnected electro-migration, it is necessary to attach a coating layer between the wires and the substrate to ensure the normal operation of a circuit. As copper gradually replaces aluminum as a material for wire processing and manufacturing, Ta has been widely used as a sputtering target for anti-diffusion coating layer [2–4]. Previous studies [5–7] demonstrated that the homogeneity of a coating layer mainly depends on the crystallographic orientation and the grain size of a target. That is, homogeneous microstructure in the target can significantly improve the uniformity of the coating layer obtained by magnetron sputtering. Manufacturing method of initial Ta ingot, and subsequent rolling

⁎

and annealing treatments play a key role in obtaining a high-quality sputtering target in industry. Powder metallurgy and electron beam melting are two main preparation methods for Ta ingots [8,9]. Voids can be formed by powder metallurgy preparation since impurities such as oxygen can be introduced easily into Ta ingot and cannot be removed simply during subsequent processing [8]. This extremely limits the applications of Ta in special fields, although the average grain size is finer. Nowadays, Ta as sputtering targets used in industry requires low impurity content, good compactness and no porosity. Original Ta ingots are more preferentially prepared via electron beam melting (EBM), which has an excellent impurity removal capacity, and the purity can reach not only 5 N (99.999 at.%) but even 6 N (99.9999 at.%) [9]. However, coarse columnar grains with dimensions up to centimeters exist in high-purity Ta EBM ingots, which cannot be used directly [10]. Deformation processing such as forging and rolling combined with heat treatment is typically adopted in industry to break the coarse columnar

Corresponding author at: College of Materials Science and Engineering, Chongqing University, Chongqing 400044, China. E-mail address: [email protected] (S. Liu).

https://doi.org/10.1016/j.matchar.2020.110165 Received 14 December 2019; Received in revised form 22 January 2020; Accepted 22 January 2020 Available online 23 January 2020 1044-5803/ © 2020 Elsevier Inc. All rights reserved.

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Fig. 1. Schematic diagram of 135° clock rolling. 1, 2, 3…, in turn, represent the first rolling pass, the second rolling pass and the third rolling pass, etc.

more rolling passes in each cycle, which is beneficial for obtaining more homogeneous textures and microstructures. Recently, Liu et al. [12,13] reported that 135° clock rolling was efficient in mitigating orientation dependence and through-thickness texture gradients typically observed in cold-rolled Ta plates. In such processing, the rolling direction (RD) is rotated by 135° around normal direction sequentially, and one processing cycle consists of eight passes in 135° clock rolling. However, the dependence of microstructure homogeneity (crystallographic orientation and grain size) on strain in Ta plates during 135° clock rolling, has not been investigated sufficiently yet. The aim in this study is to explore the effect of strain on deformation microstructure and texture as well as subsequent recrystallization microstructure in clock-rolled Ta sheets.

Table 1 Detailed annealing temperatures and time in the two samples.

70% sample 87% sample

Temperature

Annealing times

950 °C 1050 °C 1100 °C 950 °C 1050 °C 1250 °C

5 min, 10 min, 30 min, 60 min 5 min, 10 min, 30 min, 60 min 2 min, 5 min, 10 min, 30 min 5 min, 10 min, 60 min 60 min, 90 min, 120 min 10 min, 20 min, 30 min

grains and to refine the grain size. Unfortunately, severe throughthickness texture gradient is generated in Ta sheets during conventional unidirectional rolling and is retained after annealing [11]. Furthermore, the textures with γ fiber {〈111〉//ND} and θ fiber {〈100〉//ND} show different subdivision behaviors during conventional rolling, which results in orientation-dependent stored energy distribution [12,13]. This orientation-dependent stored energy, which then becomes a driving force for recrystallization [13] can lead to severe through-thickness texture gradient, texture clusters, and residual deformation bands after annealing, which adversely affects the performance of Ta targets and causes unevenness of coating layer during sputtering [5,7]. Several new rolling technologies are proposed to alleviate the defects resulting from traditional rolling. Kim et al. [14] applied cross-roll rolling to produce AZ31 Mg sheets with homogeneous through-thickness texture intensity. Lin et al. [15] used asymmetric rolling combined with 90° cross rolling to improve the homogeneity of microstructure and texture in Ta sheets from surface to center layers. Oertel et al. [16] adopted 90° cross rolling to manufacture Mo plates with enhanced formability thanks to more uniform texture and microstructure refinement. Clearly, strain path change during rolling plays a key role in improving the uniformity of texture and microstructure. Rotation angle is an important parameter in the change of strain path, and 90° rotation angle is employed in cross rolling. A proper rotation angle can allow

2. Experimental procedures Ta plates (99.95 wt% purity) with fully recrystallized microstructure were 135° clock rolled to 70% and 87% total reduction in thickness in 8 and 16 passes, respectively, as illustrated schematically in Fig. 1. Hereafter the samples will be simply referred as 70% and 87% samples. Detailed chemical composition of the initial Ta plates and rolling parameters can be found in Ref. [17]. Samples (12 mmL × 10 mmW) cut from the plates were then annealed at different temperatures and times to capture the pattern of microstructure evolution during recrystallization. Respective annealing parameter is summarized in Table 1. Note that heat treatment process can effectively eliminate the hardening of metal sheets after plastic deformation and homogenize the microstructure. Considering that the annealing temperature has an important influence on the microstructure and properties of the Ta sheets during the heat treatment process, 70% and 87% samples were then annealed according to the parameters listed in Table 1, to explore the effect of strain on the final recrystallization microstructure and properties. Metallographic observations were carried out with an Axio Lab.A1 2

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Fig. 2. (a) Inverse pole figure (IPF) map of as-received Ta plate before rolling, (b) corresponding grain size distribution, and (c) pole figures.

3.2. Deformation microstructure

Pol optical microscope (OM). {200} and {222} line profiles were recorded using X-ray diffractometer (XRD, Rigaku D/max-2500 PC) to semi-quantitatively compare macroscopic textures. The relative diffraction peaks were fitted by JADE 7.0 software after background subtraction and instrumental broadening correction. Electron backscatter diffraction (EBSD, TESCAN MIRA 3 field emission gun-scanning electron microscope) technique was adopted to examine local crystallographic orientations. Dislocation boundaries were analyzed using transmission electron microscopy (TEM, JEOL JEM-2100 operated at an accelerating voltage 200 kV). Sample preparation was in accordance with a method suggested by Zhu et al. in [18]. Microhardness (MH, MH5L model) testing was conducted to evaluate the degree of deformation and recrystallization.

Fig. 3(a)–(d) displays the deformation microstructure of clock-rolled Ta sheets at various rolling strains. Clearly, many parallel bands, approximately inclined at 30° with RD, appear in the 70% rolled sample. Grains are “stretched” into much slender microstructure with the increase of deformation, and more layered grain structure can be observed in the 87% sample. IPF maps in Fig. 3(c)–(d) show that the deformed grains with {111} {〈111〉//ND} and {100} orientation {〈100〉//ND} are primary texture components after clock rolling. It is also worth noting that {110}〈uvw〉 {〈110〉//ND} sheared grains (green) appear in the 70% sample, as displayed in Fig. 3(c). Many parallel microshear bands (MSBs), which typically appear with the {110} {〈110〉//ND} orientation [19], exist within the {111} deformed grains in the 70% sample, while there are no clear MSBs in the 87% sample. The occurrence of sheared grains and MSBs in the 70% sample suggests the heterogeneous deformation behavior. Fig. 3(e) and (f) shows the misorientation distribution corresponding to Fig. 3(c) and (d), respectively. Note that misorientation angle higher than 10° is defined as high-angle boundaries (HABs), and misorientation angle between 2° and 10° is defined as low-angle boundaries (LABs) [17]. The fraction of LABs in the 70% sample is higher than that in the 87% sample. The formation of low-angle misorientations is primarily the result of dislocation activity. The higher fraction of low-angle misorientations is supposed to indicate a higher activity of dislocations. The “slender” grains in the 87% sample with misorientation angle distribution shifting to higher values suggest that the increase of clock-rolling passes promotes the recovery of dislocations within deformed grains and their rearrangement into a more stable deformation structure with the strain increase.

3. Results 3.1. As-received microstructure As-received microstructure of a Ta plate before rolling is illustrated by an inverse pole figure (IPF) map in Fig. 2(a). Grains are colored according to their crystallographic orientations with the sample's ND in a standard triangle of crystal-stereographic projection. It can be clearly seen that the grains are nearly equiaxed with virtually no color gradient inside the grains, i.e. no substructure, indicating that the as-received Ta plate is in a fully recrystallized state. Strong {111} {〈111〉//ND} texture bands exist in the initial Ta plate. Note, the texture bands refer to the aggregation of grains with similar crystallographic orientation in a local region, as in the area indicated by a yellow ellipse in Fig. 2(a). The distribution of grain sizes in the as-received Ta plate (Fig. 2(b)) is lognormal. The fraction of grains with size > 100 μm approaches 17.9%, and grains as large as 334 μm are found. The pole figure in Fig. 2(c) further indicates that strong {111} texture {〈111〉//ND} exists in the starting Ta plates, and the volume fraction of {111} oriented grains accounts for 65%.

3.3. Grain subdivision Fig. 4 displays discrete {111} pole figures of crystallographic orientations in region “R1” to “R4” in Fig. 3(c) and (d). The projection of 3

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Fig. 3. Optical micrographs (a, b) and IPF maps (c, d) of clock-rolled Ta sheets at the strain levels of 70% (a, c) and 87% (b, d); diagrams (e) and (f) are misorientation angle distributions in the IPF maps (c) and (d), respectively. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)

the crystallographic orientations in the pole figure reflects the degree of grain subdivision. The more dispersed the crystallographic orientation in the pole figure, the more severe the grain fragmentation. The subdivision in {111} grains, Fig. 4(a, b), is significantly greater than that in {100} grains, Fig. 4(c, d), in both the samples. At the same time, the grains with {111} orientation in the 70% sample are more dispersed than those in the 87% sample, while the difference in the fragmentation of {100} grains in the two samples is minor. To further clarify the difference between the 70% and 87% samples in the degree of

subdivision within the {111} and {100} grains, we employ calculations using a more quantitative method, the grain average misorientation (GAM) [20]. For a pixel i, the Kernel Average Misorientation is given by

KAM (i ) =

1 K

ik k

(1)

where K is the number of pixels around the pixel number i (8 in our case) and ωik means the misorientation angle between pixel couples (i, k). 4

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Fig. 4. Discrete {111} pole figures of orientations in regions (a) “R1” (b) “R3” (c) “R2” and (d) “R4” in Fig. 3(c, d).

For a grain j, the grain average misorientation (GAM) is

GAM (j ) =

1 I (j )

KAM (i) i

1050 °C, the sample becomes fully recrystallized after 120 min; and recrystallization is virtually complete after annealing at 1250 °C for 10 min. The average recrystallized grain size is calculated roughly via intercept method to better compare the recrystallization microstructure difference between the 70% and 87% samples. The statistical results are listed in Table 2. It can be clearly observed that the average recrystallized grain size in the 70% sample is significantly higher than that in the 87% sample, and the size increases gradually with the increasing annealing temperatures both in the two samples. Besides, the completely recrystallized grain size is heterogeneous in the 70% sample when annealed at different temperatures. In contrast, the recrystallized grain size in the 87% sample is more homogeneous and finer than that in the 70% sample.

(2)

with I(j) the number of pixels of grain j. And, for a set of J grains (30 in this study), the global grain average misorientation becomes

GAM =

1 J

GAM (j) j

(3)

The material deformation leads to grain distortion, which results in a high GAM value. More specifically, the greater the degree of deformation within a grain, the greater the GAM values. The results of calculation show that the GAM values of the {111} grains (GAM{111}) in the 70% and 87% sample are 1.148° and 0.670°, respectively. However, the GAM values of the {100} grains (GAM{100}) in the 70% and 87% sample were 0.296° and 0.287°, respectively. The higher GAM{111} values in the 70% sample indicate a more heterogeneous grain-scale plastic deformation. However, the difference of GAM{100} values in the two samples is small, and the GAM{100} values in the two samples are much lower compared to GAM{111}, suggesting that {100} oriented grains deform more homogeneously. Indeed, the deformed microstructure in grains with {111} orientation differs in the two samples.

3.4.2. Texture The integrated intensity of X-ray diffraction peaks can reflect semiquantitatively the texture intensity of metals [21]. More accurately, the texture intensity can be analyzed by observing diffraction peaks difference under different conditions. Since the {100} and {111} orientations are main texture components in Ta plates, we only observed the variation of {200} and {222} diffraction peaks, as displayed in Fig. 7. Note that {200} and {222} line profiles are the second-order diffractions of {100} and {111} grains. To facilitate the analysis and to compare the texture intensity in different samples, a new parameter R is introduced as follows:

3.4. Recrystallization microstructure and texture

R=

3.4.1. Microstructure evolution Figs. 5 and 6 display optical micrographs illustrating the evolution of microstructure during annealing at various temperatures in the 70% and 87% clock-rolled Ta sheets, respectively. It can be observed that a few recrystallized grains emerge from the deformed matrix in the 70% sample when annealed at 950 °C for 5 min. With increasing annealing time, the deformed matrix is consumed continuously. When annealing time extends to 60 min, the deformed matrix disappears completely indicating a fully recrystallized state. The sample recrystallized at a faster and faster rate with the increasing annealing temperatures. Numerous defect-free grains appear in the deformed grains when annealed at 1050 °C for 5 min, and recrystallization completes when annealing time increases to 10 min. The deformed matrix is fully consumed while the grains are recrystallized when annealed at 1100 °C for 2 min. Afterwards, the recrystallized grains continue to grow rapidly with the extension of annealing time. In contrast to the 70% sample, in the 87% sample the grains are still in the deformed state when annealed at 950 °C for 5 min, while a few fine recrystallized grains emerge from the deformed matrix when the time increase to 10 min. As the time further extends to 60 min, the sample is still in partially recrystallized condition, as many deformed grains can still be found. The rate of recrystallization in the 87% sample is significantly lower than that in the 70% sample. When annealed at

o I{222} / I{222} o I{200} / I{200} o

(4) o

where I{222} and I{200} are the standard X-ray integrated intensity of Ta powder; I{222} and I{200} are the integrated intensity of our samples. When the parameter R is close to one, there is no preferential {111} or {100} texture in a sample; when R ≫ 1 or R ≪ 1, there is a strong {111} or {100} texture, respectively. The results of calculations displayed in Table 3 reveal that R for the 70% sample is greater than one, indicating that strong {111} textures form. However, R for the 87% sample is closer to one, indicating relatively random textures. Annealing at low temperature leads to a decrease of R, whereas at high temperature it results in R increase. More accurately, high-temperature annealing can significantly enhance the {111} texture, while more homogeneous texture distribution can be obtained when annealed at low temperature. 3.4.3. Microstructure by EBSD EBSD was adopted to observe in more details the difference of recrystallization microstructure in clock-rolled samples with different strains, as displayed in Fig. 8. The distribution of fully recrystallized grain sizes in the 70% sample is extremely inhomogeneous (variance = 37.4), with an average grain size of 39.0 μm. Conversely, the distribution of fully recrystallized grain sizes in the 87% sample is relatively homogeneous (variance = 18.1). The size of most grains is

5

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Fig. 5. Optical micrographs (100×) of the 70% clock-rolled Ta sheets annealed at different temperatures: 950 °C (a1) 5 min, (a2) 10 min, (a3) 30 min, (a4) 60 min; 1050 °C (b1) 5 min, (b2) 10 min, (b3) 30 min, (b4) 60 min; 1100 °C (c1) 2 min, (c2) 5 min, (c3) 10 min, (c4) 30 min.

lower than 100 μm and the average grain size is 26.8 μm. It can be observed that numerous {111} grains in the 70% samples grow abnormally, and the maximum grain size reaches 204 μm. The average grain size in the 70% sample displays a significant orientation-dependence, i.e. {111} grains are apparently larger than the others, particularly the smallest {100} grains. Such orientation dependence in the average grain size is prominently weakened in the 87% sample (see Fig. 8(e) and (f)). The analysis of pole figure indicates that a strong

{111} recrystallization texture is generated in the 70% sample, while a more random recrystallization texture can be observed in the 87% sample. These results are consistent with the XRD result in Table 3. 3.5. Hardness Hardness value can reflect indirectly the degree of deformation and recrystallization in metal [22,23]. In general, greater hardness value 6

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Fig. 6. Optical micrographs (100×) of the 87% clock-rolled Ta sheets annealed at different temperatures: 950 °C (a1) 5 min, (a2) 10 min, (a3) 60 min; 1050 °C (b1) 60 min, (b2) 90 min, (b3) 120 min; 1250 °C (c1) 10 min, (c2) 20 min, (c3) 30 min.

There is an obvious drop in hardness curve during the initial period of annealing suggesting the occurrence of recovery or the onset of recrystallization. Afterwards, hardness decreases slowly with increasing annealing time, and the variation of hardness slightly fluctuates at later stages of annealing. Hardness values decrease more rapidly with increasing annealing temperatures, owing to the higher recrystallization rate.

Table 2 The average recrystallized grain size of the 70% and 87% samples when annealed at different annealing conditions.

70% sample 87% sample

Annealing conditions

Average recrystallized grain size

950 °C + 60 min 1050 °C + 10 min 1100 °C + 2 min 950 °C + 60 min 1050 °C + 120 min 1250 °C + 10 min

52.0 55.3 59.7 / 38.1 46.2

4. Discussion 4.1. Density of geometrically necessary dislocations

indicates higher dislocation density stored in materials, and thus a high fraction of deformed grains. Fig. 9 depicts the evolution of hardness in clock-rolled samples annealed at different temperatures. Average hardness value in the clock-rolled Ta sheets after 70% strain is significantly greater than that after 87% strain. The difference in hardness seems to further indicate that the increase of strain promotes the recovery of dislocations within deformed grains during clock rolling.

The 70% and 87% samples exhibit significantly different deformation microstructure. The quantification of dislocation density is important in the analysis of microstructure differences since dislocations are closely related to deformation behavior. Statistically stored dislocations (SSDs) and geometrically necessary dislocations (GNDs) can be distinguished in metals [24]. The mutual trapping of SSDs results in the formation of ordinary cell boundaries, with a relatively small

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Fig. 7. Intensity of {200} and {222} diffraction peaks in Ta sheets under various conditions: (a) 70% sample, (b) 87% sample. Table 3 The variation of R with different annealing temperatures and times in the two samples.

70% sample

87% sample

Rolled 950 °C + 60 min 1050 °C + 10 min 1100 °C + 2 min Rolled 950 °C + 60 min 1050 °C + 120 min 1250 °C + 2 min

I{222}o

I{200}o

I{222}

I{200}

R

17% 17% 17% 17% 17% 17% 17% 17%

30% 30% 30% 30% 30% 30% 30% 30%

262,574 28,188 97,021 46,915 86,613 70,146 117,168 35,059

24,206 8687 8792 2671 354,435 359,728 188,280 37,276

19.1 5.73 19.5 31.0 0.43 0.34 1.10 1.66

GND

24

= i=1

I(

i < )/

I( i=1

i < )

(6)

where ρ means the resulting GND density in one pixel; θ0 is corresponding KAM value of the pixel; b is the Burgers vector, estimated to be 0.286 nm for Ta; d is the unit length (step size: 100 nm) of the pixel. A Matlab program was used to calculate GND densities. Reconstructed GND distribution map is displayed in Fig. 10. It can be clearly observed that the distribution of GNDs is inhomogeneous, and GND density in {111} grains is significantly greater than that in {100} grains for both the 70% and 87% samples, suggesting that the GND density is orientation dependent. Fig. 11 displays corresponding histograms for each map of Fig. 10 along with average values. It can be found that the difference of average GND density within {111} grains between the 70% and 87% samples is high reaching 3.71 × 1014 m/m3; while the difference of average GND density within {100} grains is only 0.2 × 1014 m/m3. Clearly, the GND density within the {111} grains is significantly reduced with the increase of strain. 4.2. Deformation mechanisms As demonstrated in the discussion above, the effect of increasing number of passes and total strain on deformation microstructure is mainly reflected in {111} grains. Therefore, deformation microstructure within {111} grains is further analyzed, as displayed in Fig. 12(a) and (b). It can be observed that numerous parallel and clearly visible microshear bands (MSBs) are inclined at an angle of 26° to RD in {111} grain (G1) in the 70% sample. By contrast, similarly oriented {111} grain (G2) in the 87% sample reveals two sets of parallel MSBs that are less distinct (slightly misoriented) and have opposing inclination angles with respect to RD. One set is inclined at +25° angle to RD, and the other at −31°. The analysis of these MSB traces in oriented stereographic projections and EBSD data shows that their habit planes in the 70% sample are mainly aligned with {110} slip planes, while in the 87% sample they are parallel to {110} and {112}. This suggests that both the {110}〈111〉 and {112}〈111〉 slip modes become activated in the 87% sample, while only {110}〈111〉 mode is activate in the 70% sample. The Schmid factors (SFrolling) of each slip system in rolling were computed based on the following equation [35]:

24 i

2 0 bd GND

misorientation gradient and a narrow spread, while misorientation angles across GNDs are large with a wide spread [25]. On a grain scale, any net geometric effect of SSDs is offset by adjacent dislocations with Burgers vectors of opposite signs. The existence of GNDs, however, is characterized by a net Burgers vector, which leads to the gradual increase of lattice curvature and the occurrence of an orientation difference [26,27]. Thus, GND density may be elucidated by the heterogeneity of local strain tensor and its development as a function of imposed strain. It is possible to visualize dislocation lines and quantify dislocation density at the nanoscale by TEM owing to its high spatial resolution, but the detection region is indeed limited [28–30]. Highresolution EBSD technique allows indexing relatively larger areas and thus can be adopted to measure GND densities when the probe size is limited to approximately 100 nm [30–32]. In this study, GND density is calculated from the kernel average misorientation (KAM) values that can be obtained directly from EBSD data [30,33]. KAM values are average orientation differences between pixels considered on the measurement grid and its adjacent neighbor pixels. The limit of grain boundary misorientation in this calculation was set as 3°, so misorientations between considered and adjacent pixels above 3° are excluded. The KAM values of a point with respect to neighboring 24 points (5 × 5 pixels) were quantified based on the following equation [33]: 0

=

(5)

where θ0 is the calculated KAM value of one pixel and θi is a difference in orientation between this and adjacent neighboring pixels i. I(θi < α) is an indicator function, and α is the critical misorientation angle (here α = 3°). Then a simple method from the strain gradient theory was applied to quantify the GND density [30,33,34]:

SFrolling = (cos

× cos

cos × cos )/2

(7)

where α or β are the angles between rolling direction and slip plane normal or slip direction, and γ or δ are the angles between normal direction and slip plane normal or slip direction. It should be noted that

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Fig. 8. IPF maps of completely recrystallized microstructure of clock-rolled Ta sheets with different strains. (a) 70% clock-rolling sample annealed at 1100 °C for 2 min (b) 87% clock-rolled sample annealed at 1050 °C for 120 min. (c) and (d) are corresponding grain size distribution in Fig. 3(a) and (b), respectively. (e) Average grain size of grains with different orientations. (f) is corresponding pole figure in Fig. 3(a) and (b), respectively. 9

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Fig. 9. Hardness curve distribution of clock-rolling Ta sheets with different strains annealed at different temperatures: (a) 70% sample, (b) 87% sample.

Fig. 10. GND density map based on local misorientation results in two samples. 70% sample (a) {111} grains (b) {100} grains; 87% sample (c) {111} grains (d) {100} grains.

the effective activated slip systems (out of 12 possible in each mode) were considered in the calculation of Schmid factors. The maximum Schmid factor (SFmax) for {111} grains (50 × 2 grains in total) in the two samples was calculated and counted in Fig. 13. It can be found that in the 70% sample SFmax is mainly between 0.4500 and 0.4875, while in the 87% one it is in a range from 0.4000 to 0.4500. The greater SFmax values of {111} grains in the 70% sample indicate that slip is easier, and

the system with higher SFrolling can alone accommodate the majority of plastic strain. Furthermore, Taylor model simulations were utilized to quantify the shear strain of activated slip systems in the {111} grains of the two samples under investigation. The deviation angle within {111} grains was < 15°. A rate insensitive Taylor model, considering {110}〈111〉 slip mode in the 70% sample and {110}〈111〉 and {112}〈111〉 slip

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Fig. 11. Histograms of GND density distribution for each map in Fig. 10. The mean value of GND density and standard deviation (ρGND std) are shown in inserts in each histogram.

modes in the 87% sample and plane strain compression condition (with extension along the last rolling pass direction) were applied to the {111} grains extracted from Fig. 12. We also assumed that the final orientation is equal to the initial orientation of the last rolling pass since strain per pass and crystal rotation were small. The calculation results indicate that the amount of shear strain of the most activate systems in {111} grains of the 70% and 87% samples are 3.383 and 1.294, respectively. These mean the fewer slip systems operating in a specific region lead to the accumulation of higher density of dislocations and intensive shear localized on a certain slip plane (primary slip system) that contribute to the formation of MSBs within {111} grains in the 70% sample [36,37]. As clearly displayed in Fig. 14(a), these regularly arranged MSBs, tiny band-like structures, are surrounded by straight and sharp dislocation walls that are approximately 100–300 nm in width. By contrast, relatively lower SFmax values in the {111} grains of the 87% sample suggest that multiple slip is activated, and a shear strain in each the system is relatively small. The generation of dislocations in more active slip systems may enhance the probability of dislocation rearrangement and annihilation contributing to the formation of cell blocks (CBs) and reduced dislocation stacks [12,36,37], as shown in Fig. 14(b). According to the low-energy theory, the stored energy of dislocations within different deformation structures (i.e. MSBs and CBs) can be evaluated as [38,39]:

SEMSBs =

SECBs =

MSBs

CBs

µb 2 ln 4

µb 2 ln 4

MSBs

b

SEMSBs =

µb2 ln f (1/2) 4

(10)

where f is the volume fraction of CB boundaries. The energy stored in the MSBs is greater than that in CBs since f is always less than one. Therefore, the stored energy within {111} grains in the 70% sample is higher than that in the 87% sample owing to the high-energy MSBs structure. 4.3. Homogeneity of recrystallization microstructure The elevated-temperature recrystallization behavior of Ta sheets with ultrahigh stacking fault energy is strongly dominated by recovery processes since cross slip can operate easily [40–42]. During recovery, annihilation and rearrangement of dislocations can greatly reduce the magnitude of stored energy and thus affect the process of nucleation. In a deformed material, recovery and recrystallization take place simultaneously during annealing. They are driven by stored energy within each grain. Upon low-temperature annealing, recovery and recrystallization occur preferentially in the 70% sample since the deformed matrix possess high-misoriented regions and high stored energy as driving force as compared with the 87% sample. Nucleation in subsequent static recrystallization occurs via coalescence and growth of numerous sub-grains formed during the process of recovery. The growth rate of nuclei with {111} orientation generated from respective deformed matrix tends to be fast because of the rapid migration of {111} grain boundaries [43] and the high stored energy within the matrix. However, {100} deformed grains are low-misoriented regions that have low stored energy. The intensity of {100} texture is also very low in the 70% sample. Hence, {100} grains have a very weak tendency to form potential nuclei, and are more likely to be consumed by the nuclei growing from {111} deformed matrix during recrystallization. After the completion of recrystallization, {111} grains are coarse and respective texture component is relatively strong (see Fig. 8). With the increase of annealing temperature, the sample has less time to recovery,

( 1/2)

b

( 1/2) b

SECBs

(8)

(9)

where MSBs and CBs are the average density of dislocations in MSBs and CBs, respectively; μ is the shear modulus of a material; b is the Burgers vector; ρb(−1/2) is the outer cut-off radius of CBs. If c = m = ρ, 11

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Fig. 12. High-magnification EBSD maps showing deformation microstructure within {111} grains in the 70% (a) and 87% (b) samples. (c) and (d) show the trace analysis of microshear bands in stereographic projection figures for G1 (c) and G2 (d) that are close to {111}〈uvw〉 orientations (maximum deviation < 15°). Red lines show the trace of {110}, and blue lines show the trace of {112}. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

and more energy would then store in the {111} deformed matrix at the initiation of recrystallization. Thus, the growth speed of nuclei with {111} orientation would be further improved owing to the increased recrystallized driving force, intensifying the {111} recrystallized texture and increasing the average recrystallized grain size (see Tables 2 and 3). The sample clock-rolled to 87% strain has a weaker {111} texture and a much lower stored energy in the deformed {111} grains than in its 70% counterpart. The microstructure evolution of the low-temperature annealing (see Fig. 6) and the corresponding R (< 1) in Table 3 indicate the presence of {100} deformed grain that need higher

temperature to finish recrystallization, because the driving force in the deformed {100} grains is significantly lower than that in the deformed {111} grains [44,45]. The {100} texture intensity is very strong thus making it more likely to generate nuclei in the deformed {100} grains with the increase of annealing temperature. During intermediate-temperature annealing, a part of the energy stored in the deformed {111} grains is released due to long-time recovery and the stored energy difference between {111} and {100} grains decreases. Meanwhile, numerous immobile low-angle boundaries, i.e. in {100} grains, act as obstacles to moving grain boundaries and consequently pin them, which can be classified as “orientation pinning” [46,47]. The growth 12

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Fig. 13. Distribution of maximum Schmid factor within {111} grains (deviation angle < 15°) in the 70% (a) and 87% (b) samples.

Fig. 14. TEM micrographs of dislocation structure within {111} grains in the 70% (a) and 87% (b) samples.

rate of nuclei with {111} orientation is significantly reduced, and nuclei with other orientations are more likely to nucleate and grow. More nuclei with random orientations combined with a slow rate of grain growth result in finer grain size and a fairly uniform orientation distribution. While high-temperature annealing can significantly increase the migration rate of the grain boundary, especially the {111} grain boundary [43], contributing to the increase of {111} texture intensity and average recrystallized grain size. More in-depth nucleation and growth mechanisms leading to the formation of relatively random texture after intermediate-temperature annealing in the clock-rolled 87% sample demand further investigation, which will be reported in a follow-up paper.

model simulations suggest that in the 70% sample only one slip system {110}〈111〉 dominates plastic deformation leading to the formation of micro-shear bands. The analysis of the 87% sample reveals activities of two slip modes, i.e. {110}〈111〉 and {112} 〈111〉, which explains the occurrence of cell blocks. 3. Smaller grain sizes with more uniform distribution and relatively homogeneous texture are obtained in the 87% sample after annealing. However, the 70% sample demonstrates the strong {111} recrystallization texture, and grain size distribution is inhomogeneous. Declaration of competing interest

5. Conclusions

No conflict of interest exits in the submission of this manuscript, and manuscript is approved by all authors for publication. The authors declare that the work described was original research that has not been published previously, and not under consideration for publication elsewhere, in whole or in part.

The effects of accumulated strain during 135° clock-rolling and following annealing on microstructure homogeneity in high purity Ta sheets are investigated in the present study. 1. Grain average misorientation and distribution of geometrically necessary dislocations suggest that stored energy within grains having {111} orientation is higher in 70% deformed sample than that in the 87% one. Therefore, the 70% sample recrystallizes at lower temperature and faster than its 87% counterpart. 2. The calculation of Schmid factor values SFmax along with Taylor-

Acknowledgements The present work was co-supported by the National Natural Science Foundation of China (Grants 51421001, 51701032 and 51504051), the Chongqing Research Program of Basic Research and Frontier Technology (No. cstc2017jcyjAX0094 and cstc2019jcyj-msxmX013), 13

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the Scientific and Technological Research Program of Chongqing Municipal Education Commission (Grant No. KJQN201801507), and the Major “Scientific and Technological Innovation 2025” Project of Ningbo (No. 2018B10066).

[23] [24]

Data availability statement

[25]

The raw/processed data required to reproduce these findings cannot be shared at this time as the data also forms part of an ongoing study.

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