Tangled Dislocation Structures inside Dislocation Channels of Rapid-Cooled and Tensile-Deformed Aluminum Single Crystals

Kazushige Tokuno; Masatoshi Mitsuhara; Shinnosuke Tsuchida; Ryo Tsuboi; Junji Miyamoto; Masahiro Hagino; Takashi Inoue; Kouki Nishidate

doi:10.2320/matertrans.MT-M2021230

Abstract

Tangled dislocation structures inside the dislocation channels of rapid-cooled and tensile deformed aluminum single crystals were investigated by using BF-STEM. Inside the dislocation channels, arrays of the prismatic dislocation loops belonging to the primary slip system, i.e., $(1\ 1\ 1)[\bar{1}\ 0\ 1]$, were mainly formed. Dislocations of the primary coplanar slip systems such as $(1\ 1\ 1)[0\ 1\ \bar{1}]$ and $(1\ 1\ 1)[\bar{1}\ 1\ 0]$ were activated due to the internal stresses caused by the primary dislocations pile-up inside the cleared channels. The activated primary coplanar dislocations leave the dislocation loops elongated along the edge dislocation directions behind them. Inter-dislocation-loop interactions take place especially at the arrays of the prismatic dislocation loops of the primary slip systems and produce “butterfly shape” dislocation loops. Since the “butterfly shape” dislocation loops have “sessile” junctions, they should act as “obstacles” against the following multiplications and glides of the dislocations. As the interactions proceed, the arrays are stabilized and grow as “tangles”.

Fig. 3 BF-STEM images of the dislocation structures inside a cleared dislocation channel of a foil taken from the specimen elongated to 3% macroscopic tensile strain. (a) z ≅ 0 1 1, $\boldsymbol{g} = 1\ 1\ \bar{1}$, (b) z ≅ 0 1 1, g = 2 0 0 and (c) z ≅ 0 1 1, $\boldsymbol{g} = 1\ \bar{1}\ 1$. Magnified views of the enclosed areas of (a), (b) and (c) are posted each right. Arrows with solid lines show $[0\ \bar{1}\ 1]$ and with dotted lines show projected traces of $[\bar{1}\ 0\ 1]$, $[1\ \bar{2}\ 1]$, $[\bar{2}\ 1\ 1]$, $[1\ \bar{1}\ 0]$, $[\bar{1}\ \bar{1}\ 2]$ on the photo surface. In (a) and (b), an array of the prismatic loops “T”, isolated prismatic loops “P” and individual dislocations “d” belonging to the primary slip system, i.e., “$\textbf{B4}(1\ 1\ 1)[\bar{1}\ 0\ 1]$” are mainly observed. Other than the primary dislocations, isolated prismatic loops “P_{_B2}” and “P_{_B5}” which are considered to be belonging to “$\textbf{B2}(1\ 1\ 1)[0\ 1\ \bar{1}]$” and “$\textbf{B5}(1\ 1\ 1)[\bar{1}\ 1\ 0]$”, respectively, are observed. In (c) where the primary dislocations are invisible, “butterfly shape” dislocation loops, “B_{_B2}” and “B_{_B5}”, which are belonging to “$\textbf{B2}(1\ 1\ 1)[0\ 1\ \bar{1}]$” and “$\textbf{B5}(1\ 1\ 1)[\bar{1}\ 1\ 0]$”, respectively, are observed. These “butterfly shape” dislocation loops are connected by a short dislocation “J” which is considered to be belonging to “$\textbf{B4}(1\ 1\ 1)[\bar{1}\ 0\ 1]$”.

1. Introduction

Plastic deformation of metals which are including highly dense point defect clusters such as dislocation loops or stacking fault tetrahedra proceeds with the formation of the dislocation channels.¹^–⁷⁾ Point defects forming the clusters can be introduced in metals through high-energy-particle irradiations or rapid-cooling from elevated temperatures. Dislocation channels are formed at the area where the point defect clusters are swept out by glide dislocations. Mechanisms of the sweeping processes of the point defect clusters by glide dislocations in face-centered-cubic metals were discussed by e.g., Foreman et al.,⁸⁾ Strudel et al.,⁹⁾ and Matsukawa et al.¹⁰^,¹¹⁾

Fukuoka et al.⁶⁾ compared the early-stage tensile stress-tensile strain curves of a rapid-cooled aluminum single crystal and an air cooled one. According to them, the 0.2% proof tensile stress, i.e., yield stress, was 9.0 MPa for a rapid-cooled specimen and 5.4 MPa for an air-cooled one. Due to the dislocation loop distribution, yield stresses of the rapid-cooled specimens were increased. On the other hand, macroscopic work hardening rate after the yielding of the rapid-cooled specimens were low compared to the air-cooled ones. Figure 1 shows transmission electron microscope (TEM) images of the dislocation channel formed in a rapid-cooled and tensile deformed aluminum single crystal taken by Fukuoka et al.⁶⁾ Since the dislocation channel is “highway-like” area where multiplications and glides of dislocations are concentrated, plastic deformation process may occur with “compact scale” inside the channels. Therefore, systematic TEM observation of the dislocation structures focusing inside the channels may contribute to an understanding regarding the plastic deformation process of metals. Figure 1(b) shows a detailed dislocation structures of Fig. 1(a). Fukuoka et al.⁶⁾ revealed that the arrays of prismatic dislocation loops of the primary slip system, i.e., $(1\ 1\ 1)[\bar{1}\ 0\ 1]$, were essentially formed by elongating along $[\bar{1}\ 2\ \bar{1}]$ direction and each prismatic loop stacked to $[\bar{1}\ 0\ 1]$ inside the dislocation channels. With the progress of plastic deformation, number of the prismatic loops composing the array increased and tangled structures consisting of the prismatic loops and dislocations of the primary coplanar slip system, i.e., $(1\ 1\ 1)[0\ 1\ \bar{1}]$ are produced. “T₁” and “T₂” in Fig. 1 are the examples of the tangled structures. They suggest that those structure would become the “embryo” of the cell structures which can be seen in deeply deformed crystals. However, despite their expected important roles, structures of the dislocation tangles had not been made clear by the observation of Fukuoka et al.⁶⁾ As Erel et al.¹²⁾ and Veyssière et al.¹³^–¹⁶⁾ investigated, the early stages of plastic deformation of the face-centered-cubic metals are characterized by the appearance of the prismatic loops. The tangled structures, “T₁” and “T₂”, observed by Fukuoka et al.⁶⁾ were obviously composed by dislocation loops.

Fig. 1

TEM images of dislocation structures inside a cleared dislocation channel of the primary slip system in a thick area of a foil taken from the specimen elongated to 12.1% macroscopic tensile strain.⁶⁾ (a) $\boldsymbol{z} \cong \bar{1}\ \bar{1}\ 2$ and g = 1 1 1, (b) z ≅ 0 1 1 and $\boldsymbol{g} = \bar{1}\ \bar{1}\ 1$. In (b), arrows with dotted lines show projected traces of $[\bar{1}\ 0\ 1]$, $[\bar{1}\ 2\ \bar{1}]$, $[0\ 1\ \bar{1}]$ and $[\bar{2}\ 1\ \bar{1}]$ on the photo surface. Thicker “band-shaped” weak contrasts “T_₁” and “T_₂” in (a) were tangled structures “T_₁” and “T_₂” consisting of arrays of prismatic loops of the primary and the primary coplanar slip systems in (b). In (b), “P” were isolated prismatic loops (primary slip system), “P_{_B2}” isolated prismatic loops (primary coplanar slip system) and “S_{_B2}” screw dislocations with cusps (primary coplanar slip system).

In this study, we conducted characterizations of the dislocation tangles produced inside the dislocation channels of a rapid-cooled and tensile-deformed aluminum single crystal by using BF-STEM (Bright Field – Scanning Transmission Electron Microscopy) and discussed their structures.

2. Experimental Procedure

Specimens used for the present study were prepared by the same procedures adopted by Fukuoka et al.⁶⁾ and Tsuchida et al.⁷⁾ 2 mm thick aluminum single crystal was grown by a Bridgman method from 99.999% purity raw materials. From the grown crystal, 10 mm width and 50 mm length sheet-shaped tensile specimen was cut by wire-spark sawing. Since tensile axis of the specimen was $[\bar{6}\ 13\ 17]$ which was inside the crystallographic stereo triangle of which vertices were [0 0 1], [0 1 1] and $[\bar{1}\ 1\ 1]$ spots each, primary slip plane was (1 1 1) and Burgers vectors of the primary slip system was parallel to $[\bar{1}\ 0\ 1]$. Crystallographic orientations were determined by using EBSP (Electron Back Scatter Pattern) with fixing the tensile direction as the longitudinal axis of the patterning. Table 1 shows all the 12 slip systems of the specimen and their Schmid factors. The notation of the slip systems corresponds to the Boas-Schmid notation adopted by Tiba et al.,¹⁷⁾ Fukuoka et al.⁶⁾ and Tsuchida et al.⁷⁾

Table 1 Slip systems and Schmid factors of the specimens used for the present experiments. System notation corresponds to the Boas-Schmid notation adopted by Tiba et al.,¹⁹⁾ Fukuoka et al.⁶⁾ and Tsuchida et al.⁷⁾

In order to produce the point-defect-clusters, the specimen was heated to 893 K and kept for 3.6 ks and vertically dropped to salt water of which temperature was 253 K. After electro-polishing for removing oxidized films of surfaces, the specimen was uniaxially tensile deformed with a speed of 0.1 mm/min at room temperature. Tensile strain rate was equivalent to 5.6 × 10⁻⁵/s. Since the present specimen was elongated to 3% tensile strain which was much lower than that of Fig. 1,⁶⁾ i.e., 12.1%, early stages of the dislocation tangle formation can be expected. The deformed specimen was chemically polished with NaOH solution (NaOH: 20 g and H₂O: 100 cm³) to 0.2 mm thickness. From the thinned specimen, disc-shaped foils of 3 mm diameter were carefully cut out by wire-spark sawing and jet-polished to produce wedge-shaped foils which have a small hole at their center for BF-STEM observations.

Regarding the dislocation characterizations of the BF-STEM observations, we utilized Tecnai-F20 with 200 kV acceleration voltage. For the observations, in order to keep good comparisons between the images of Fukuoka et al.⁶⁾ and the present observations, we adopted the electron beam direction (z direction) as z ≅ 0 1 1 which was the same condition with that of Fukuoka et al.⁶⁾ Table 2 shows the visibility of each dislocation of the face-centered-cubic metals due to the g · b ≠ 0 conditions under the adopted g vectors of the present investigation. “V” means “visible” and “I.V” means “invisible”. This table also shows the possible slip systems and the prismatic loop directions (parallel with edge dislocations) to which each slip directions are belonging. Slip systems notations in Table 2 are based on Table 1. Since slip planes of the conjugate slip systems (C1, C5, C3) and the cross slip systems (D4, D1, D6) are perpendicular to the photo surface, i.e., edge-on, under the observations with z ≅ 0 1 1, contrasts of the dislocations belonging to these systems should be weak or invisible for the present investigation.

Table 2 Visibility of each dislocations of the face-centered-cubic metals due to the g · b ≠ 0 conditions under the adopted g vectors of the present investigation. “V” means “visible” and “I.V” means “invisible”. This table also shows the possible slip systems and the prismatic loop directions (parallel with edge dislocations) to which each slip directions are belonging. Slip systems notations are based on Table 1. Since slip planes of the conjugate slip systems (C1, C5, C3) and the cross slip systems (D4, D1, D6) are perpendicular to the photo surface, i.e., edge-on, under the observations with z ≅ 0 1 1, contrasts of the dislocations belonging to these systems should be weak or invisible.

3. Experimental Results

3.1 Stress-strain curves

Figure 2 shows the nominal tensile stress-tensile strain curves of the rapid-cooled specimen for the present investigation. For a comparison, tensile stress-tensile strain curve of an air-cooled specimen obtained by Fukuoka et al.⁶⁾ was posted on this figure. The 0.2% proof tensile stress, i.e., yield stress, is higher than 9.0 MPa for a rapid-cooled specimen and 5.4 MPa for an air-cooled one. On the other hand, macroscopic work hardening rate at the beginning stage plastic deformation of the rapid-cooled specimens is low compared to the air-cooled one as revealed by Fukuoka et al.⁶⁾

Fig. 2

The tensile stress-tensile strain curve of the rapid-cooled specimen for the present investigation. For a comparison, tensile stress-tensile strain curve of an air-cooled specimen obtained by Fukuoka et al.⁶⁾ was posted on this figure.

3.2 Tangled dislocations inside the dislocation channels

Figure 3 shows BF-STEM images of the dislocation structures inside a dislocation channel of a rapid-cooled aluminum single crystal deformed to 3% macroscopic tensile strain. These images were taken under the conditions of (a) z ≅ 0 1 1 and $\boldsymbol{g} = 1\ 1\ \bar{1}$, (b) z ≅ 0 1 1 and g = 2 0 0 and (c) z ≅ 0 1 1 and $\boldsymbol{g} = 1\ \bar{1}\ 1$, respectively. Magnified views of the enclosed areas of Figs. 3(a), 3(b) and 3(c) are posted each right. Arrows with solid lines show $[0\ \bar{1}\ 1]$ and those with dotted lines show projected traces of $[\bar{1}\ 0\ 1]$, $[1\ \bar{2}\ 1]$, $[\bar{2}\ 1\ 1]$, $[1\ \bar{1}\ 0]$, $[\bar{1}\ \bar{1}\ 2]$ on the photo surface, respectively. As shown in Table 1 and Table 2, $[1\ \bar{2}\ 1]$, $[\bar{2}\ 1\ 1]$ and $[\bar{1}\ \bar{1}\ 2]$ are elongation directions of the prismatic loops belonging to “$\textbf{B4}(1\ 1\ 1)[\bar{1}\ 0\ 1]$”, “$\textbf{B2}(1\ 1\ 1)[0\ 1\ \bar{1}]$” and “$\textbf{B5}(1\ 1\ 1)[\bar{1}\ 1\ 0]$”, respectively. In Fig. 3(a), an of the array prismatic dislocation loops elongating along $[1\ \bar{2}\ 1]$, “T”, is observed. This is a dominant structure inside the dislocation channels. Besides the array of the prismatic dislocation loops, isolated prismatic loops elongating along $[1\ \bar{2}\ 1]$, “P”, and individual dislocations, “d”, are also observed. Since those three types of dislocation structures are also visible in Fig. 3(b), those may be belonging to the primary slip system, i.e., “$\textbf{B4}(1\ 1\ 1)[\bar{1}\ 0\ 1]$” and matching with the structures Fukuoka et al.⁶⁾ reported. In Fig. 3(a), individual dislocation loops “P_B2” elongating along $[\bar{2}\ 1\ 1]$ are also visible. Since these loops are invisible in Fig. 3(b) but visible in Fig. 3(c), dislocation loops “P_B2” are considered to be belonging to a primary coplanar slip system, i.e., “$\textbf{B2}(1\ 1\ 1)[0\ 1\ \bar{1}]$”. In Fig. 3(b), an individual dislocation loop “P_B5” elongating along $[\bar{1}\ \bar{1}\ 2]$ is visible. Since this loop is invisible in Fig. 3(a) but visible in Fig. 3(c), this dislocation loop “P_B5” is considered to be belonging to another primary coplanar slip system, i.e., “$\textbf{B5}(1\ 1\ 1)[\bar{1}\ 1\ 0]$”. On the other hand, since the images of dislocations belonging to the primary slip system, i.e., “$\textbf{B4}(1\ 1\ 1)[\bar{1}\ 0\ 1]$”, are invisible in Fig. 3(c), all visible dislocations in Fig. 3(c) are the secondary dislocations. In Fig. 3(c), peculiar shape dislocation loops are observed. By characterizing the enlarged views of Figs. 3(a), 3(b) and 3(c), we identified “butterfly shape” dislocation loops which have two wings (“B_B2” and “B_B5”). Since one of the two wings is visible in Figs. 3(a) and 3(c) and the other one is visible in Figs. 3(b) and 3(c), these wings are considered to be belonging to the primary coplanar slip systems, i.e., “$\textbf{B2}(1\ 1\ 1)[0\ 1\ \bar{1}]$” and “$\textbf{B5}(1\ 1\ 1)[\bar{1}\ 1\ 0]$”, respectively. And we recognize a short dislocation “J” which seems to be “connecting” the two loops (“B_B2” and “B_B5”). Since this short dislocation is visible in Figs. 3(a) and 3(b) and invisible in Fig. 3(c), this may be belonging to “$\textbf{B4}(1\ 1\ 1)[\bar{1}\ 0\ 1]$”.

Fig. 3

BF-STEM images of the dislocation structures inside a cleared dislocation channel of a foil taken from the specimen elongated to 3% macroscopic tensile strain. (a) z ≅ 0 1 1, $\boldsymbol{g} = 1\ 1\ \bar{1}$, (b) z ≅ 0 1 1, g = 2 0 0 and (c) z ≅ 0 1 1, $\boldsymbol{g} = 1\ \bar{1}\ 1$. Magnified views of the enclosed areas of (a), (b) and (c) are posted each right. Arrows with solid lines show $[0\ \bar{1}\ 1]$ and with dotted lines show projected traces of $[\bar{1}\ 0\ 1]$, $[1\ \bar{2}\ 1]$, $[\bar{2}\ 1\ 1]$, $[1\ \bar{1}\ 0]$, $[\bar{1}\ \bar{1}\ 2]$ on the photo surface. In (a) and (b), an array of the prismatic loops “T”, isolated prismatic loops “P” and individual dislocations “d” belonging to the primary slip system, i.e., “$\textbf{B4}(1\ 1\ 1)[\bar{1}\ 0\ 1]$” are mainly observed. Other than the primary dislocations, isolated prismatic loops “P_{_B2}” and “P_{_B5}” which are considered to be belonging to “$\textbf{B2}(1\ 1\ 1)[0\ 1\ \bar{1}]$” and “$\textbf{B5}(1\ 1\ 1)[\bar{1}\ 1\ 0]$”, respectively, are observed. In (c) where the primary dislocations are invisible, “butterfly shape” dislocation loops, “B_{_B2}” and “B_{_B5}”, which are belonging to “$\textbf{B2}(1\ 1\ 1)[0\ 1\ \bar{1}]$” and “$\textbf{B5}(1\ 1\ 1)[\bar{1}\ 1\ 0]$”, respectively, are observed. These “butterfly shape” dislocation loops are connected by a short dislocation “J” which is considered to be belonging to “$\textbf{B4}(1\ 1\ 1)[\bar{1}\ 0\ 1]$”.

Figure 4 shows BF-STEM images of the dislocation structures inside a different channel of Fig. 3. Since the dislocation channels are heterogeneously formed in deformed specimens, we can observe different stage channels in one TEM foil. Because of its dislocation density, dislocation structure observed in Fig. 4 seems to be more developed one compared to that in Fig. 3. The images of Figs. 4(a), 4(b) and 4(c) were taken under the same conditions of Figs. 3(a), 3(b) and 3(c), respectively. Figure 4(d) is the magnified view of the enclosed area of Fig. 4(c). In this channel, we observed another array of the prismatic dislocation loops elongating along $[1\ \bar{2}\ 1]$, “T”, isolated prismatic loops elongating along $[1\ \bar{2}\ 1]$, “P”, and individual dislocations “d” which are considered to be belonging to the primary slip system, i.e., “$\textbf{B4}(1\ 1\ 1)[\bar{1}\ 0\ 1]$”. Other than the primary dislocations, isolated prismatic loops “P_B2” and “P_B5” which are elongating along $[\bar{2}\ 1\ 1]$ and $[\bar{1}\ \bar{1}\ 2]$ are observed. These are considered to be belonging to “$\textbf{B2}(1\ 1\ 1)[0\ 1\ \bar{1}]$” and “$\textbf{B5}(1\ 1\ 1)[\bar{1}\ 1\ 0]$”, respectively. In Figs. 4(c) and 4(d) where the primary dislocations are invisible, we observed several “butterfly shape” dislocation loops (encircled in Fig. 4(d)) and secondary dislocations which are making tangles. Since majority of those secondary dislocations are locating at the arrays of the prismatic loops “T”, precise characterizations of all secondary dislocations of which TEM images are covered by the primary dislocations are difficult. Among them, since a dislocation with cusp, “d_B5”, in Fig. 4(b) can be observed in Fig. 4(c), this is identified as a dislocation belonging to “$\textbf{B5}(1\ 1\ 1)[\bar{1}\ 1\ 0]$” of which cusp is elongating along $[\bar{1}\ \bar{1}\ 2]$. We observe similar secondary dislocations (indicated as “d_B2”) of which cusps are elongating along $[\bar{2}\ 1\ 1]$, i.e., prismatic loop elongation direction of “$\textbf{B2}(1\ 1\ 1)[0\ 1\ \bar{1}]$”. From those results, we speculate that majority of the secondary dislocations making tangles at the array of the prismatic loops “T” are belonging to “$\textbf{B2}(1\ 1\ 1)[0\ 1\ \bar{1}]$” and “$\textbf{B5}(1\ 1\ 1)[\bar{1}\ 1\ 0]$”.

Fig. 4

BF-STEM images of the dislocation structures inside a cleared dislocation channel (different channel of Fig. 3) of a foil taken from the specimen elongated to 3% macroscopic tensile strain. (a) z ≅ 0 1 1, $\boldsymbol{g} = 1\ 1\ \bar{1}$, (b) z ≅ 0 1 1, g = 2 0 0 and (c) z ≅ 0 1 1, $\boldsymbol{g} = 1\ \bar{1}\ 1$. Arrows with solid lines show $[0\ \bar{1}\ 1]$ and with dotted lines show projected traces of $[\bar{1}\ 0\ 1]$, $[1\ \bar{2}\ 1]$, $[\bar{2}\ 1\ 1]$, $[1\ \bar{1}\ 0]$, $[\bar{1}\ \bar{1}\ 2]$ on the photo surface. In (a) and (b), array of the prismatic loops “T”, isolated prismatic loops “P” and individual dislocations “d” belonging to the primary slip system, i.e., “$\textbf{B4}(1\ 1\ 1)[\bar{1}\ 0\ 1]$” are mainly observed. Other than the primary dislocations, isolated prismatic loops “P_{_B2}” and “P_{_B5}” which are considered to be belonging to “$\textbf{B2}(1\ 1\ 1)[0\ 1\ \bar{1}]$” and “$\textbf{B5}(1\ 1\ 1)[\bar{1}\ 1\ 0]$”, respectively, are observed. In (c) and (d) where the primary dislocations are invisible, several “butterfly shape” dislocation loops (encircled in (d)) and dislocations with cusps are also observed. Since a dislocation “d_{_B5}” with cusp is visible in (b) and (c), this is considered to be belonging to “$\textbf{B5}(1\ 1\ 1)[\bar{1}\ 1\ 0]$”. Similar dislocations with cusps, “d_{_B2}”, are considered to be belonging to “$\textbf{B2}(1\ 1\ 1)[0\ 1\ \bar{1}]$”.

Figure 5 shows BF-STEM images of the dislocation structures inside a different channel of Figs. 3 and 4. In Fig. 5, a well-developed array of the prismatic dislocation loops elongating along $[1\ \bar{2}\ 1]$, “T”, is observed inside the dislocation channel. Other than the array of the prismatic dislocation loops “T”, many isolated prismatic loops elongating along $[1\ \bar{2}\ 1]$, $[\bar{2}\ 1\ 1]$ and $[\bar{1}\ \bar{1}\ 2]$ which are indicated by, e.g., “P”, “P_B2” and “P_B5”, respectively, are observed. These three types of the prismatic loops are considered to be belonging to “$\textbf{B4}(1\ 1\ 1)[\bar{1}\ 0\ 1]$”, “$\textbf{B2}(1\ 1\ 1)[0\ 1\ \bar{1}]$” and “$\textbf{B5}(1\ 1\ 1)[\bar{1}\ 1\ 0]$”, respectively. In Figs. 5(c) and 5(d) where the primary dislocations invisible, several “butterfly shape” dislocation loops (encircled loops in Fig. 5(d)) and dislocations which are complexly tangling are also observed.

Fig. 5

BF-STEM images of the dislocation structures inside a cleared dislocation channel (different channel of Figs. 3 and 4) of a foil taken from the specimen elongated to 3% macroscopic tensile strain. (a) z ≅ 0 1 1, $\boldsymbol{g} = 1\ 1\ \bar{1}$, (b) z ≅ 0 1 1, g = 2 0 0 and (c) z ≅ 0 1 1, $\boldsymbol{g} = 1\ \bar{1}\ 1$. Arrows with solid lines show $[0\ \bar{1}\ 1]$ and with dotted lines show projected traces of $[\bar{1}\ 0\ 1]$, $[1\ \bar{2}\ 1]$, $[\bar{2}\ 1\ 1]$, $[1\ \bar{1}\ 0]$, $[\bar{1}\ \bar{1}\ 2]$ on the photo surface. In (a) and (b), well-developed array of the prismatic loops “T” is observed. Other than the array of the prismatic dislocation loops “T”, many isolated prismatic loops elongating along $[\bar{1}\ 2\ \bar{1}]$, $[\bar{2}\ 1\ 1]$ and $[\bar{1}\ \bar{1}\ 2]$ which are indicated by, e.g., “P”, “P_{_B2}” and “P_{_B5}” are observed. These three types of the prismatic loops are considered to be belonging to “$\textbf{B4}(1\ 1\ 1)[\bar{1}\ 0\ 1]$”, “$\textbf{B2}(1\ 1\ 1)[0\ 1\ \bar{1}]$” and “$\textbf{B5}(1\ 1\ 1)[\bar{1}\ 1\ 0]$”, respectively. In (c) and (d) where the primary dislocations are invisible, several “butterfly shape” dislocation loops (encircled loops in (d)) and dislocations which are complexly tangling are also observed.

4. Discussions: Formation Mechanisms of the Dislocation Structures Inside the Dislocation Channels

4.1 Array of the prismatic dislocation loops of the primary slip system

We observed the arrays of the prismatic dislocation loops belonging to the primary slip system, i.e., “$\textbf{B4}(1\ 1\ 1)[\bar{1}\ 0\ 1]$”, inside the dislocation channels. Regarding the formation process of the arrays of prismatic dislocation loops in face-centered-cubic metals during plastic deformation, Fukuoka et al.⁶⁾ described a schematic process which was based on a computational model proposed by Erel et al.¹²⁾ who utilized “Discrete Dislocation Dynamics (DDD)” developed by Ghoniem et al.¹⁸^–²⁰⁾ The formation process of the arrays of the prismatic dislocation loop “T” proposed by Fukuoka et al.⁶⁾ were as follows.

(a) During deformation, two opposite signs’ screw dislocations on different but sufficient close primary slip planes meet and attract one another, resulting in cross-slipped configurations at multiple locations.
(b) The two segments pinch-off at cross-slipped locations and make a loop, leaving two pinched-off hair-pin dislocations which have super jogs.
(c) Two arms of one of the hair-pin dislocations meet and make another pinch-off.
(d) The pinch-off makes another loop and the pinched-off loop is straighten-up to the $[1\ \bar{2}\ 1]$ direction. By the sequence of (c) to (d), arrays of the prismatic loops could be created.

Although the proposals by Fukuoka et al.⁶⁾ may not be the perfect mechanism which can explain the total structures of the arrays of prismatic dislocation loops observed in the present investigation, the model proposed by them is currently one of the most likely events. We consider that the so-called “bundles of the edge dislocation dipoles” belonging to the primary slip system which had been recognized during the last several decades as the essential structures at the stage I, i.e., early stage of the plastic deformation in the well-annealed face-centered-cubic single crystals,²¹^–²⁶⁾ could be the arrays of the prismatic dislocation loops. As Steeds²¹⁾ mentioned, with progress of the plastic deformation, bundles of the edge dislocation dipoles were connected by dislocations of the secondary slip systems at the beginning of the stage II and the cell structures consisting of the primary and the secondary dislocations were produced with the progress of the stage II. Therefore, the arrays of prismatic dislocation loops observed in the present investigation could be one of the key structures which play an important role on the work hardening of the face-centered-cubic metals.

4.2 Isolated prismatic dislocation loops

Other than the arrays of the prismatic dislocation loops, we frequently observed isolated dislocation loops which are belonging to several slip systems, i.e., dislocation loops elongating along $[1\ \bar{2}\ 1]$, $[\bar{2}\ 1\ 1]$ and $[\bar{1}\ \bar{1}\ 2]$ which are edge dislocation directions of “$\textbf{B4}(1\ 1\ 1)[\bar{1}\ 0\ 1]$”, “$\textbf{B2}(1\ 1\ 1)[0\ 1\ \bar{1}]$” and “$\textbf{B5}(1\ 1\ 1)[\bar{1}\ 1\ 0]$”, respectively. We consider that those isolated dislocation loops are formed through the glides of screw dislocations which had super-jogs as parts of them. This process was basically proposed by Fukuoka et al.⁶⁾ who explained the formation mechanism of the isolated dislocation loops which are belonging to the primary slip systems. We believe that this basic idea should be applicable for all slip systems and can be described as follows.

(a) Through cutting processes with dislocations with other slip systems during plastic deformation, several jogs created on a screw dislocation are integrated into a super jog which is unable to glide with the screw dislocation.
(b) The super jog is left behind the screw dislocation.
(c) An isolated prismatic dislocation loop elongated along the edge dislocation direction is pinched off.

Since the existence of the isolated prismatic dislocation loops indicates the “trace” of the dislocation glides, we can recognize that dislocations belonging to at least the three types of slip systems, i.e., “$\textbf{B4}(1\ 1\ 1)[\bar{1}\ 0\ 1]$”, “$\textbf{B2}(1\ 1\ 1)[0\ 1\ \bar{1}]$” and “$\textbf{B5}(1\ 1\ 1)[\bar{1}\ 1\ 0]$”, are activated inside the dislocation channels of the present single crystal. However, according to Table 1, Schmid factor of one of the primary coplanar slip systems, “$\textbf{B2}(1\ 1\ 1)[0\ 1\ \bar{1}]$”, is too small (0.079) for the activation of dislocations. Therefore, we should draw out a consistency for the activation of “$\textbf{B2}(1\ 1\ 1)[0\ 1\ \bar{1}]$”. Mitchell²⁷⁾ proposed the calculation results showing the stress-fields on 11 slip systems created by pile-ups of the primary dislocations of face-centered-cubic crystals. In his calculation,

\begin{equation} \boldsymbol{\tau}_{\boldsymbol{y}\boldsymbol{z}} \end{equation}

(1)

means the created shear stress on the primary slip plane’s normal (y plane) and the primary dislocation’s slip direction (z direction). This shear stress was resolved on other 11 slip systems and described as,

\begin{equation} \boldsymbol{\tau}_{\boldsymbol{y}'\boldsymbol{z}'} \end{equation}

(2)

where y′ and z′ were the slip plane normal direction and the slip direction of each slip system. According to his calculation, the resolved shear stress on the dislocations belonging to “$\textbf{B2}(1\ 1\ 1)[0\ 1\ \bar{1}]$” and “$\textbf{B5}(1\ 1\ 1)[\bar{1}\ 1\ 0]$” were obtained as follows.

\begin{equation} \boldsymbol{\tau}_{\boldsymbol{y}'\boldsymbol{z}'} = \frac{\textbf{1}}{\textbf{2}}\boldsymbol{\tau}_{\boldsymbol{y}\boldsymbol{z}} \end{equation}

(3)

Since $\boldsymbol{\tau}_{\boldsymbol{yz}}$ is increased with the number of primary dislocations in the pile-up, $\boldsymbol{\tau}_{\boldsymbol{y'z'}}$ may easily reach a threshold magnitude for the activation of the dislocation sources belonging to “$\textbf{B2}(1\ 1\ 1)[0\ 1\ \bar{1}]$” and “$\textbf{B5}(1\ 1\ 1)[\bar{1}\ 1\ 0]$” inside the dislocation channels. Therefore, we consider that the activation of the primary coplanar dislocations shall be strongly depending on the concentration of the primary dislocations’ glides inside the dislocation channels.

4.3 Inter-dislocation-loop interactions

Other than the arrays of the prismatic dislocation loops belonging to “$\textbf{B4}(1\ 1\ 1)[\bar{1}\ 0\ 1]$” and the isolated dislocation loops belonging to “$\textbf{B4}(1\ 1\ 1)[\bar{1}\ 0\ 1]$”, “$\textbf{B2}(1\ 1\ 1)[0\ 1\ \bar{1}]$” and “$\textbf{B5}(1\ 1\ 1)[\bar{1}\ 1\ 0]$”, we have found the several peculiar shaped dislocation loops such as “butterfly shape” dislocation loops. As observed in Fig. 3, we identified “butterfly shape” dislocation loops with two wings which are considered to be belonging to the primary coplanar slip systems, i.e., “$\textbf{B2}(1\ 1\ 1)[0\ 1\ \bar{1}]$” and “$\textbf{B5}(1\ 1\ 1)[\bar{1}\ 1\ 0]$”, respectively. And through the further observation, we recognized a short dislocation “J” belonging to “$\textbf{B4}(1\ 1\ 1)[\bar{1}\ 0\ 1]$” connecting the two loops. Regarding the formation mechanism of the “butterfly shape” dislocation loops, although several mechanisms could be possible, we may be able to propose a sessile junction reaction based on another computational proposal of Erel et al.¹²⁾ Figure 6 shows brief and simplified schematics of a junction reaction between the two prismatic dislocation loops belonging to the primary coplanar slip system, i.e., “$\textbf{B2}(1\ 1\ 1)[0\ 1\ \bar{1}]$” and “$\textbf{B5}(1\ 1\ 1)[\bar{1}\ 1\ 0]$”, respectively. In Fig. 6, a prismatic dislocation loop “ABCD” is belonging to the primary coplanar slip system, i.e., “$\textbf{B2}(1\ 1\ 1)[0\ 1\ \bar{1}]$”, and another primary coplanar dislocation loop “EFGH” is belonging to “$\textbf{B5}(1\ 1\ 1)[\bar{1}\ 1\ 0]$”. In Fig. 6,

(a) Primary coplanar dislocation loops belonging to “$\textbf{B2}(1\ 1\ 1)[0\ 1\ \bar{1}]$” and “$\textbf{B5}(1\ 1\ 1)[\bar{1}\ 1\ 0]$” which are produced through the process described in 4.2 locates sufficiently close to each other.
(b) Because of the attractive force between the side “CD” of the loop belonging to “$\textbf{B2}(1\ 1\ 1)[0\ 1\ \bar{1}]$” and the side “EF” of the loop belonging to “$\textbf{B5}(1\ 1\ 1)[\bar{1}\ 1\ 0]$”, both loops glide on their glide cylinders and contact one another.
(c) A junction reaction between “CD” and “EF” makes a new segment “J”. Because of the newly created sessile segment “J”, both loops are not able to separate and would act as an obstacle for the following dislocation glides. Erel et al.¹²⁾ called the joined loops “pinned butterfly”.

The junction reaction of Fig. 6(c) is described as follows.

\begin{equation} \frac{\boldsymbol{a}}{\textbf{2}}[\textbf{0}\ \bar{\textbf{1}}\ \textbf{1}] + \frac{\boldsymbol{a}}{\textbf{2}}[\bar{\textbf{1}}\ \textbf{1}\ \textbf{0}] = \frac{\boldsymbol{a}}{\textbf{2}}[\bar{\textbf{1}}\ \textbf{0}\ \textbf{1}] \end{equation}

(4)

Here, a is the lattice constant of the face-centered-cubic metal. The above-mentioned inter-dislocation-loop interaction could also happen between the dislocation loops belonging to the primary slip system “$\textbf{B4}(1\ 1\ 1)[\bar{1}\ 0\ 1]$” and one of the two primary coplanar slip systems, “$\textbf{B2}(1\ 1\ 1)[0\ 1\ \bar{1}]$” or “$\textbf{B5}(1\ 1\ 1)[\bar{1}\ 1\ 0]$”. Those reactions are described as follows, respectively.

\begin{equation} \frac{\boldsymbol{a}}{\textbf{2}}[\bar{\textbf{1}}\ \textbf{0}\ \textbf{1}] + \frac{\boldsymbol{a}}{\textbf{2}}[\textbf{0}\ \textbf{1}\ \bar{\textbf{1}}] = \frac{\boldsymbol{a}}{\textbf{2}}[\bar{\textbf{1}}\ \textbf{1}\ \textbf{0}] \end{equation}

(5)

\begin{equation} \frac{\boldsymbol{a}}{\textbf{2}}[\bar{\textbf{1}}\ \textbf{0}\ \textbf{1}] + \frac{\boldsymbol{a}}{\textbf{2}}[\textbf{1}\ \bar{\textbf{1}}\ \textbf{0}] = \frac{\boldsymbol{a}}{\textbf{2}}[\textbf{0}\ \bar{\textbf{1}}\ \textbf{1}] \end{equation}

(6)

Since the newly created dislocations through the above reactions cannot glide on the cross slip planes of the original dislocations, the original parts of the dislocation loops are pinned like “butterfly shape”. Therefore, the “butterfly shape” dislocation loops should act as “obstacles” against the following dislocation glides of the secondary dislocations such as “$\textbf{B2}(1\ 1\ 1)[0\ 1\ \bar{1}]$” or “$\textbf{B5}(1\ 1\ 1)[\bar{1}\ 1\ 0]$” and the interrupted dislocations are considered to make “tangles”. The arrays of the prismatic dislocation loops of the primary slip system are considered to be the place where those reactions frequently take place.

Fig. 6

Brief and simplified schematics of a junction reaction between two prismatic dislocation loops which are belonging to the two primary coplanar slip systems. This process was based on the computational model of Erel et al.¹²⁾ This figure shows a case between a prismatic dislocation loop “ABCD” belonging to a primary coplanar slip system, i.e., “$\textbf{B2}(1\ 1\ 1)[0\ \bar{1}\ 1]$”, and another primary coplanar dislocation loop “EFGH” belonging to “$\textbf{B5}(1\ 1\ 1)[\bar{1}\ 1\ 0]$”. (a) Primary coplanar dislocation loops belonging to “$\textbf{B2}(1\ 1\ 1)[0\ 1\ \bar{1}]$” and “$\textbf{B5}(1\ 1\ 1)[\bar{1}\ 1\ 0]$” which are produced through the process described in 4.2 locates sufficiently close to each other. (b) Because of the attractive force between the side “CD” of the loop belonging to “$\textbf{B2}(1\ 1\ 1)[0\ 1\ \bar{1}]$” and the side “EF” of the loop belonging to “$\textbf{B5}(1\ 1\ 1)[\bar{1}\ 1\ 0]$”, both loops glide on their glide cylinders and contact one another. (c) A junction reaction between “CD” and “EF” makes a new segment “J”. Because of the newly created sessile segment “J”, the both loops are not able to separate and would act as an obstacle for the following dislocation glides. Erel et al.²⁰⁾ called the joined loops “pinned butterfly”.

4.4 Formation process of the tangled dislocations inside the dislocation channels

Through the present observation results and discussions, we are able to assume the formation process of the tangled dislocations inside the dislocation channels as follows.

Stage A: Once a cleared dislocation channel is produced during deformation, multiplications and glides of the dislocations belonging to the primary slip system are concentrated inside the channel.
Stage B: As the deformation proceeds, the arrays of the prismatic dislocation loops belonging to “$\textbf{B4}(1\ 1\ 1)[\bar{1}\ 0\ 1]$” are produced.
Stage C: As the concentration of the glides of the primary dislocations proceeds, multiplications and glides of the dislocations belonging to the primary coplanar slip system, i.e., “$\textbf{B2}(1\ 1\ 1)[0\ 1\ \bar{1}]$” and “$\textbf{B5}(1\ 1\ 1)[\bar{1}\ 1\ 0]$”, are activated due to the internal stress enhanced by the primary dislocations pile-up. The activated primary coplanar dislocations produce their dislocation loops elongated along $[\bar{2}\ 1\ 1]$ and $[\bar{1}\ \bar{1}\ 2]$ as the remaining of their glides.
Stage D: The inter-dislocation-loop interactions take place especially at the arrays of the prismatic dislocation loops of the primary slip systems. Since “butterfly shape” dislocation loops which are produced through the inter-dislocation-loop interactions have “sessile” junctions, they should act as “obstacles” against the following multiplications and glides of the dislocations. As the interactions proceed, the arrays are stabilized and grow as “tangles”.

The so-called “cell structure” could be a developed structure of the “tangles” observed in the present investigation. As Fukuoka et al.⁶⁾ mentioned based on the calculations by Basinski et al.,²⁸⁾ with the further progress of the deformation, other secondary dislocations such as “$\textbf{C1}(1\ 1\ \bar{1})[0\ \bar{1}\ \bar{1}]$” and “$\textbf{A6}(1\ \bar{1}\ \bar{1})[1\ 1\ 0]$” could be activated. Those newly activated secondary dislocations shall react with the former structures in the similar manner of Fig. 6 and create the more developed “cell structure”. Tsuchida et al.⁷⁾ examined the dislocations composing the boundaries of “cell structure” formed inside the dislocation channels of rapid-cooled and tensile deformed aluminum single crystals and categorized them as energetically driven structures rather than the geometrically necessary boundaries, “GNB”.²⁹^–³⁵⁾

5. Conclusion

Tangled dislocation structures inside the dislocation channels of rapid-cooled and tensile deformed aluminum single crystals were investigated by using BF-STEM. Main results are as follows.

(1) Inside the dislocation channels, arrays of the prismatic dislocation loops belonging to the primary slip system, i.e., $(1\ 1\ 1)[\bar{1}\ 0\ 1]$, were mainly formed. These were not the simple bundle of the edge dislocation dipoles.
(2) Dislocations of the primary coplanar slip systems such as $(1\ 1\ 1)[0\ 1\ \bar{1}]$ and $(1\ 1\ 1)[\bar{1}\ 1\ 0]$ were activated due to the internal stresses caused by the primary dislocations pile-up. The activated primary coplanar dislocations leave the dislocation loops elongated along the edge dislocation directions behind them.
(3) Inter-dislocation-loop interactions take place especially at the arrays of the prismatic dislocation loops of the primary slip systems “T”. Since “butterfly shape” dislocation loops which are produced through the inter-dislocation-loop interactions have “sessile” junctions, they should act as “obstacles” against the following multiplications and glides of the dislocations. As the interactions proceed, the arrays are stabilized and grow as “tangles”. The so-called “cell structure” could be a developed structure of the “tangles” observed in the present investigation.

REFERENCES

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