1500 HUANG et al:NANOSTRUCTURED Cu dislocation is referred as a 60 dislocation.In many subgrain boundary as non-equilibrium subgrain cases,such a dislocation is dissociated or extended to boundary. more than 10 atomic planes. Figure 6(a)shows a Fourier filtered HRTEM image Figure 5(a)shows another example of subgrain of a low-angle GB,which is delineated by periodic generation from larger grains.The parallelogram- dislocations and Moire Fringes.The GB plane is shaped subgrain with a size of about 250 nm is delin- curved and changes from the (55 12)plane to the eated clearly by the dense-dislocation walls (DDWs) (002)plane.The corresponding EDP (Fig.6(b)) [18,19],which are almost parallel to the two sets of shows that the two grains are misoriented for about (111)planes.This subgrain is clearly inside a larger 9.HRTEM images from the upper-left and lower- grain and is isolated from other subgrains.We shall right part of the low-angle GB(see the framed areas) call it isolated subgrains since its boundary does not are shown in Fig.6(c)and (e),respectively.Figure meet with other subgrain boundaries.The dislocation 6(d)is a structural model corresponding to the low- density is higher inside the subgrain than outside it.angle GB in Fig.6(c).From this model,it is seen that Some of the dislocations are forming cell structures two types of dislocations with Burgers vectors inside the subgrain.Figure 5(b)is a Fourier filtered b=1/2[1011 and b2 1/2[1011.hereafter referred as HRTEM image of the dislocation wall at the point type 1 and type 2 dislocations,respectively,are marked by an arrowhead in Fig.5(a).The dislocation needed to accommodate the geometrical misorien- density is estimated as 3x1017 m-2 at the DDW tation.In other words,these dislocations are geo- subgrain boundary.The estimation is based on the metrically necessary.Valiev et al.[28]referred these Fourier filtered HREM image shown in Fig.5(b).The geometrically necessary dislocations as intrinsic dis- number of dislocations was counted,and divided by locations.According to Fig.6(d),the spacing of type the area in this figure.Such an estimation assumes I dislocations is about 18 A,which is consistent with that the dislocation line goes straight from the top of that measured from Fig.6(c).However,there are the grain through the bottom of it,which may not be three more type 2 dislocations in Fig.6(c)than in(d), the case for most dislocations,since most of them are which indicates that three extrinsic (or non-geometri- curved,or they may terminate in the grain interior. cally necessary)dislocations exist at the GB shown Therefore such estimation is only qualitative but not in Fig.6(c).Therefore,this segment of low-angle GB quantitative.Interstitial loops (marked by black is in a high energy configuration and should be called circles)and vacancy loops (marked by white circles) non-equilibrium grain boundary also exist.The dislocations are again mostly 60 type In Fig.6(e),dislocations are periodically spaced. ones.In addition,the lattice planes near the cell walls The Burgers vector is determined as 1/2[101].The are heavily distorted.The width of the subgrain dislocation spacing in a low-angle GB can be calcu- boundary is about 10 nm.The misorientation across lated using the formula:D b/e,where b is the Burg- the subgrain boundary is measured as about 5.There ers vector of the GB dislocation and 6 the rotation are significantly more dislocations than required to angle of the two grains.The calculated dislocation accommodate the misorientation.These dislocations spacing is 20 A,which is in reasonable agreement are not arranged in the lowest-energy dislocation with experimentally measured values of 22 A in Fig. structure (LEDS)[17,19,36],which makes the 6(e).No extrinsic dislocation is found in Fig.6(e). subgrain boundary unstable.We shall refer such This segment GB is equilibrium GB. Besides the 60 dislocations,other dislocations such as screw dislocations and Frank dislocations were also frequently observed.Figure 7(a)shows a number of dislocations in a grain.The Fourier filtered HRTEM image shown in Fig 7(b)reveals that these dislocations are Frank dislocations.The Burgers vec- tor was determined as 1/2[110].which is in (110) plane.Therefore,they are immobile or sessile dislo- cations. 20m 3.2.Deformation microstructures at intermediate plastic strain Fig.5.(a)A TEM micrograph of a subgrain;inset is an To investigate the microstructural evolutions and HRTEM image from the subgrain showing the crystalline planes.Note that the subgrain is delineated by DDWs which grain-refinement mechanisms,deformation structures are almost parallel to two sets of (111)planes.(b)A Fourier at an intermediate deformation strain (6 RCS passes) filtered HRTEM image from the DDW as pointed out by an were studied.Shown in Fig.8 is a TEM micrograph arrowhead in (a).The electron beam and the dislocation line that depicts many microstructural features.The is parallel to [1fo],and the Burgers vector b 1/2[011]or description of deformation microstructures is contro- 1/2[101].The dislocations are all 60 type.The longer arrow points out the grain boundary orientation.The black circles versial and is confusing in the literature [37].In a mark interstitial loops and the white circles mark vacancy series of recent papers [16-27].Hansen and cowork- loops. ers systematically studied the evolution of microstruc-1500 HUANG et al.: NANOSTRUCTURED Cu dislocation is referred as a 60° dislocation. In many cases, such a dislocation is dissociated or extended to more than 10 atomic planes. Figure 5(a) shows another example of subgrain generation from larger grains. The parallelogram￾shaped subgrain with a size of about 250 nm is delin￾eated clearly by the dense-dislocation walls (DDWs) [18,19], which are almost parallel to the two sets of {111} planes. This subgrain is clearly inside a larger grain and is isolated from other subgrains. We shall call it isolated subgrains since its boundary does not meet with other subgrain boundaries. The dislocation density is higher inside the subgrain than outside it. Some of the dislocations are forming cell structures inside the subgrain. Figure 5(b) is a Fourier filtered HRTEM image of the dislocation wall at the point marked by an arrowhead in Fig. 5(a). The dislocation density is estimated as 3×1017 m2 at the DDW subgrain boundary. The estimation is based on the Fourier filtered HREM image shown in Fig. 5(b). The number of dislocations was counted, and divided by the area in this figure. Such an estimation assumes that the dislocation line goes straight from the top of the grain through the bottom of it, which may not be the case for most dislocations, since most of them are curved, or they may terminate in the grain interior. Therefore such estimation is only qualitative but not quantitative. Interstitial loops (marked by black circles) and vacancy loops (marked by white circles) also exist. The dislocations are again mostly 60° type ones. In addition, the lattice planes near the cell walls are heavily distorted. The width of the subgrain boundary is about 10 nm. The misorientation across the subgrain boundary is measured as about 5°. There are significantly more dislocations than required to accommodate the misorientation. These dislocations are not arranged in the lowest-energy dislocation structure (LEDS) [17, 19, 36], which makes the subgrain boundary unstable. We shall refer such Fig. 5. (a) A TEM micrograph of a subgrain; inset is an HRTEM image from the subgrain showing the crystalline planes. Note that the subgrain is delineated by DDWs which are almost parallel to two sets of {111} planes. (b) A Fourier filtered HRTEM image from the DDW as pointed out by an arrowhead in (a). The electron beam and the dislocation line is parallel to [11¯0], and the Burgers vector b = 1/2[011] or 1/2[101]. The dislocations are all 60° type. The longer arrow points out the grain boundary orientation. The black circles mark interstitial loops and the white circles mark vacancy loops. subgrain boundary as non-equilibrium subgrain boundary. Figure 6(a) shows a Fourier filtered HRTEM image of a low-angle GB, which is delineated by periodic dislocations and Moire´ Fringes. The GB plane is curved and changes from the (5 5 12) plane to the (002) plane. The corresponding EDP (Fig. 6(b)) shows that the two grains are misoriented for about 9°. HRTEM images from the upper-left and lower￾right part of the low-angle GB (see the framed areas) are shown in Fig. 6(c) and (e), respectively. Figure 6(d) is a structural model corresponding to the low￾angle GB in Fig. 6(c). From this model, it is seen that two types of dislocations with Burgers vectors b1 = 1/2[101] and b2 = 1/2[101], hereafter referred as type 1 and type 2 dislocations, respectively, are needed to accommodate the geometrical misorien￾tation. In other words, these dislocations are geo￾metrically necessary. Valiev et al. [28] referred these geometrically necessary dislocations as intrinsic dis￾locations. According to Fig. 6(d), the spacing of type 1 dislocations is about 18 A˚ , which is consistent with that measured from Fig. 6(c). However, there are three more type 2 dislocations in Fig. 6(c) than in (d), which indicates that three extrinsic (or non-geometri￾cally necessary) dislocations exist at the GB shown in Fig. 6(c). Therefore, this segment of low-angle GB is in a high energy configuration and should be called non-equilibrium grain boundary. In Fig. 6(e), dislocations are periodically spaced. The Burgers vector is determined as 1/2[101]. The dislocation spacing in a low-angle GB can be calcu￾lated using the formula: D = b/q, where b is the Burg￾ers vector of the GB dislocation and q the rotation angle of the two grains. The calculated dislocation spacing is 20 A˚ , which is in reasonable agreement with experimentally measured values of 22 A˚ in Fig. 6(e). No extrinsic dislocation is found in Fig. 6(e). This segment GB is equilibrium GB. Besides the 60° dislocations, other dislocations such as screw dislocations and Frank dislocations were also frequently observed. Figure 7(a) shows a number of dislocations in a grain. The Fourier filtered HRTEM image shown in Fig 7(b) reveals that these dislocations are Frank dislocations. The Burgers vec￾tor was determined as 1/2[1¯10], which is in (11¯0) plane. Therefore, they are immobile or sessile dislo￾cations. 3.2. Deformation microstructures at intermediate plastic strain To investigate the microstructural evolutions and grain-refinement mechanisms, deformation structures at an intermediate deformation strain (6 RCS passes) were studied. Shown in Fig. 8 is a TEM micrograph that depicts many microstructural features. The description of deformation microstructures is contro￾versial and is confusing in the literature [37]. In a series of recent papers [16–27], Hansen and cowork￾ers systematically studied the evolution of microstruc-