Dislocation Density of FCC Metals Processed by ARB

Accumulative roll bonding (ARB) was applied to three FCC metals, such as Al, Cu and Ni. Differential scanning calorimetry (DSC) and X-ray diffraction (XRD) were made to evaluate dislocation density ρ of the ARB processed FCC metals. The values of ρ of ARB processed Cu and Ni increased rapidly after the first ARB cycle, and then, tend to saturate after the following cycles. The evaluated values of ρ of both ARB 8-cycled Cu and Ni using DSC were around 2×1015 m−2. Whereas, those using XRD were around 5×1014m−2 (for Cu) and 3×1014m−2 (for Ni). Although the ρ values depend on the measurement methods, the trends that DSC values are about an order of magnitude higher than XRD values seem to be common. In the case of Al, dislocation density evaluated using XRD increased to about 1×1013m−2 at the first ARB cycle, and then gradually decreased to about 1×1012m−2 with increasing number of ARB cycles.


Introduction
Metals having ultrafine grains (UFG), of which grain size less than one micro meter, can be produced by severe plastic deformation (SPD) processes from metals having coarse grains (CG). The strength of UFG metals is several times higher than that of CG counterparts, which is associated with the smaller grain size and higher dislocation density introduced by SPD. Thus, it is important to measure and of UFG.
However, it is relatively difficult to measure compared with the measurement of , since the number of applicable measurement methods are limited. In general, all the measurements have their own errors and uncertainties, and therefore, evaluated values rarely coincide. For instance, transmission electron microscopy / scanning transmission electron microscopy (TEM/STEM) can directly observe dislocations, but, there are always some dislocations satisfying the invisible condition and close to the surface may be reduced due to the image force [1,2]. Electrical resistivity measurement can detect the change in the amount of lattice defects, but, the contribution of dislocations must be separated from the contribution of grain boundaries and vacancies [3]. X-ray diffraction (XRD) can be also used to evaluate , but, suitable models are requested for the analysis. Differential scanning calorimetry (DSC) can measure the released energy during heating which is stored as lattice defects, but, the contribution of dislocation must be separated from the contribution of the others. Thus, several measurement methods should be adopted for one UFG sample to determine its .
Accumulative roll bonding (ARB) is one of the SPD processes, which can provide plateshape metals having ultrafine grains (UFGs) [4]. However, of ARB processed FCC metals are rarely reported using TEM/STEM [1,2,5] and electrical resistivity [3]. In the present study, we measured of three FCC metals; Al, Cu, and Ni, using XRD and DSC in order to determine as certain as possible.

Experimental procedure
The chemical composition of pure Al, Cu, and Ni are shown in Tables 1, 2, and 3, respectively. Al, Cu, and Ni were subjected for the ARB process after annealing at 673K for 7.2 ks,   The ARB process was carried out at room temperature with lubrication up to 8 cycles. The detail of the ARB process can be found elsewhere [4,6]. A sheet of metal ARB processed with cycles is denoted as c. For instance, a sheet of Ni ARB processed with 8c is expressed as Ni ARB 8c. The annealed sheets before ARB will be denoted as 0c for convenience. The rolling direction, transverse direction, and normal direction are denoted as RD, TD, and ND, respectively. The planes normal to RD, TD, and ND are denoted as RD, TD, and ND planes, respectively.
All ARB sheets with the thickness of 1 mm were cut by a wire arc discharge machine to 5 mm disks for DSC and 10 mm × 10 mm squares for XRD. The damage layer due to arc discharge on the specimens for DSC was removed using acid. The surface of the ND plane of the specimens for XRD was mechanically polished by SiC paper.
DSC measurements were performed using X-DSC7000T (SII nanotechnology) with Al sample holders in Ar atmosphere. The temperature range was between 293 K and 773 K with the heating rate of 5 K/min. The scan was performed twice for each sample in order to check whether a peak can be associated with the stored energy or not. In fact, an exothermic peak was observed only at the first heating process and the entire second scan showed no peaks apart from the peak associated with the magnetic transition.
XRD measurements were performed using SmartLab (Rigaku) with a Cu tube. The parameters for measurements were the applied voltage for the tube of 45 kV, the tube current of 200 mA, the step angle of 0.01 degree, and the scan time of 0.03 s. Bragg peak position and the full width-half maximum, and the wavelength of incident X-ray were used to evaluate lattice micro strain with the Williamson-Hall method [7]. In this study, six peaks; ( ), ( ), ( ), ( ), ( ), and ( ), were used. was converted to using the following equation proposed by Williamson and Smallman [8]. b (1) Here, is the magnitude of the Burgers vector. Grain boundary (GB) maps were constructed using a field emission type scanning electron microscope / electron backscattering diffraction (FE-SEM/EBSD) in JSM7001F (JEOL). The acceleration voltage was 15 kV. Orientation imaging microscopy (OIM) data collection and OIM data analysis (TLS) were used for the measurements and the analysis. The mean grain separation along ND , TD and RD were measured using GB maps on TD and RD planes. The shape of grains was assumed to be rectangular parallelepiped and the grain boundary density [m -1 ] is defined as the total area of GB within a unit volume. was evaluated using the following equation [3].
= + + (2) In this study, the densities of both total GB and high-angle grain boundary (HAGB) H were evaluated using equation 2. Then, the density of low-angle grain boundary (LAGB) was obtained as the subtraction of from . Here, GB having the misorientation angle less than 15 o is defined as LAGB, whereas, GB having the misorientation angle more than 15 o is defined as HAGB. Figure 1 (a)-(c) show DSC curves for Al, Cu, and Ni ARB1c-8c, respectively. These curves were from the first scan, and there were no peaks for the second scan. Because, these first peaks are associated with released-stored energy. The broad peaks were measured for most of specimens apart from Al ARB1c-2c. Here, a small spike at around 631 K in each Ni curve is due to the magnetic transition.

Results and discussions
For Al, ARB1c and ARB 2c show no specific peaks. Though some humps in the DSC curves start to appear with increasing , they are still near the lower detection limit of the DSC apparatus. ARB processed Al with 7c-8c show characteristic three broad peaks. For Cu and Ni, only one peak was observed at each specimen, and, the peak height seems to increase with increasing . The peak temperature defined as the centre value of temperature for the peaks decreases with increasing for all the ARB specimens. Figure 1 (d) shows dependence of released-stored energy density measured by estimating the area under the peak of the DSC curves for Al, Cu, and Ni. Since well annealed specimens were used as a reference for DSC, of ARB 0c for Al, Cu, and Ni are assumed be zero. Thus, strictly speaking, the released is defined as increase in the stored energy from that of ARB 0c specimens.
For Al, remains zero up to ARB 2c since there are no peaks on DSC curves. of ARB Al increases from zero to around 1 MJm -3 with increasing to seven. After Al ARB 7c, saturates at about 1 MJm -3 . For Cu, increases from zero to around 8 MJm -3 with increasing . For Ni, increases from zero to around 9.5 MJm -3 with increasing up to five, and then, seems to saturate.
Let us first consider the contribution of GB. The GB energy density can be written as follows [13].
Here, is the energy density of GB [Jm -2 ]. We now consider that is a function of misorientation angle of the two abutting grains and is written as [14,15], Here, average γ for HAGBγ is 0.32 Jm -2 , 0.64 Jm -2 , and 0.87 Jm -2 for, Al Cu, and Ni, respectively [16]. In this study, EBSD was used to evaluate so that GB having misorientation angle less than 2 o could not be detected. The average for LAGB γ was evaluated from the misorientation distribution chart constructed from the EBSD data.
The contribution of GB for is expressed as equation 5.
Thus, it is necessary to evaluate and in order to evaluate . Figure 2 (a)-(c) shows dependence on and for Al, Cu, and Ni, respectively. The of ARB0c for all metals is nearly zero since there are almost no LAGBs on GB maps. For Al ARB1c and Cu ARB1c, there are too many LAGBs on GB maps so that was impossible to evaluate. However, is expected to be in the order of Mm -1 since of other specimens is between 2 Mm -1 and 5 Mm -1 . Since and are now known for all the ARB specimens, it is possible to estimate from equation 5. Figure 3 shows the measured and estimated . For most Cu and Ni specimens, is larger than so that the difference between and is expressed as white bars in Fig. 3. On the other hand, and estimated are comparable for Al and both are rather small. Thus, it is concluded that measured mainly comes from for Al, and the other contributions such as by dislocations and vacancies must be small.
Secondly, the contribution of vacancies for will be considered. This contribution is expressed as follows.  Here, e , , A , and V M are the formation energy of a vacancy, vacancy concentration, Avogadro's number, and molar volume, respectively. Even a situation well above recrystallization temperature is considered, is much less than measured for Cu and Ni. Thus, is assumed to be zero in this study. Furthermore, there is a report that is negligible compared with the measured of rolled pure metals [13]. This is also supported by electrical resistivity measurements indicating that C is almost constant before and after the ARB process [3].
Thirdly, the contribution of dislocations l has to be considered. The evaluation of from l is one of the purposes of this study. l is expressed as equation 7, with considering the elastic strain energy of dislocation per unit length and . l =aμb (7) Here, a is the coefficient with the value of about 0.5 and μ is the shear modulus. μ = 79 GPa and b = 0.249 nm are used for Ni, and, μ = 48 GPa and b = 0.256 nm are used for Cu. By assuming a = 0.5, we can estimate from equation 7 Figure 4 shows dependence of the increment of dislocation density from ARB 0c for Cu and Ni.
for both Cu and Ni increase from zero m -2 to 2×10 15 m -2 with increasing from zero to two, and then, saturate. This trend agrees with the reported change in for 2N-Al with ARB process   measured by TEM/STEM [2]. It should be noted that of annealed pure metals are normally about 10 11~1 0 13 m -2 . Thus, when is more than 10 14 m -2 , can be regarded as for all practical purposes. Figure 5 shows dependence of for Al, Cu, and Ni evaluated using XRD peak broadening. All ARB 0c specimens have small compared with their ARB processed specimens. For Al, rapidly increases at = 1, and then gradually decreases with increasing . For Cu and Ni, significantly increases at the first ARB cycle, and then remains similar as values.
The saturation values of for Cu and Ni ARB1c-8c is about one order of magnitude different between XRD and DSC. Thus, it is important to know that there are uncertainties for the measurements of .

Conclusions
Evaluation of dislocation density of ARB processed FCC pure metals; Al, Cu, and Ni, were performed using DSC and XRD. Stored energy was measured using DSC, and then, the contribution of GB for stored energy was subtracted. Although the stored energy of Al could be explained as being composed of GB energy, that of Cu and Ni contains other contributions. The difference of the energy between the measured stored energy and the contribution of the GB energy was identified to be due to the accumulation of dislocations. The dislocation density of Cu and Ni was evaluated. Peak broadening of XRD was also converted to dislocation density of Al, Cu, and Ni. As a result, it was found that dislocation density significantly increased after the first cycle of ARB for all metals. Then, dislocation density of Al slightly decreased with increasing the ARB cycle number whereas,