Change in Electrical Resistivity in Nickel Processed by Accumulative Roll Bonding

Abstract

Pure nickel was processed by accumulative roll bonding (ARB), and the change in electrical resistivity measured at 77 K was about 2.2 nΩm after 8 ARB cycles. The change in electrical resistivity was estimated based on the microstructural parameters, such as, dislocation density of about 3 × 10¹⁴ m⁻² and density of grain boundaries of about 8 Mm⁻¹ after 8 ARB cycles. Those values were evaluated using X-ray diffraction and electron backscattering diffraction in a field emission-scanning electron microscope, respectively. The change in the electrical resistivity was associated with the above-mentioned microstructural parameters.

Fig. 3 Change in electrical resistivity at 77 K with increasing number of ARB cycle. Increment of electrical resistivity at 77 K from ARB 0c is displayed as right axis. The dashed line is the guide of eyes.

1. Introduction

Lately, change in electrical resistivity ρ of pure metals caused by the severe plastic deformation (SPD) process has been reported, such as, aluminium (Al)^1–3) and copper (Cu).⁴⁾ SPD allows to fabricate ultrafine grained (UFG) metals of which grain size is less than a few micrometres, since the SPD process can give much higher effective strain than the conventional plastic deformation process.⁵⁾ As the SPD processes, high pressure torsion (HPT), equal-channel angular pressing and accumulative roll bonding process have been widely used.^5,6) Furthermore, the UFG metals show abnormal mechanical properties compared with coarse grained (CG) metals. For instance, the strength of the UFG metals is several times higher than that of CG metals and inverse temperature dependence of thermal activation volume is seen.^7–9)

Bhattacharjee et al. showed that the recrystallized ARB processed nickel (Ni) is highly cube oriented,¹⁰⁾ which is useful as substrates of superconductor since cube texture is required growing the epitaxial buffer layer on it.¹¹⁾ However, the electrical properties of the ARB processed Ni has not been systematically reported yet. Thus, it is important to measure the change in ρ, δρ, of Ni during the ARB process from the electrical application point of view. ρ of metals is associated with the mean free path of free electron in metals. Thus, any scattering centres affecting the mean free path result in the increase of ρ, for instance, impurity atoms, lattice defects such as vacancies, dislocations and grain boundaries (GB).^1–4) Furthermore, free surface also works as the scattering centre of electrons, and thus, ρ increases when the thickness of metal foil or diameter of metal wire is effectively small.^12,13) The effect of surface can be ignored for the ARB processed metals since thickness is maintained to be almost the same before and after the ARB process. In the present study, the change in ρ of the ARB processed Ni is measured and discussed with the microstructural evolution.

2. Experimental Procedures

2 mm thick pure Ni sheets with a purity of 99.9 mass% (three nine nickel: 3N-Ni) were subjected for this study. The chemical composition of the 3N-Ni is shown in Table 1. The Ni sheets were annealed at 873 K for 3.6 ks in a vacuum furnace prior to the ARB process. The ARB process consists of four steps; (1) cutting a metal sheet into two along longitudinal direction, (2) surface treatment of two sheets (degreasing with acetone and applying wire blushing in order to remove the oil and oxide layers on the surface of the sheets), (3) stacking the two sheets and fixing the four corners using metallic wires, and (4) roll bonding with a rolling reduction of 50% at room temperature (R.T.).^6,14,15) The rolling speed was 2.0 m/min. Water quenching was performed immediately after the roll bonding to reduce the effect of the temperature increase during the rolling caused by processing heat generation which is normally less than 353 K. ARB Nc denotes the Ni sheet ARB processed N times, and the starting material is treated as ARB 0c. It is noted that the ARB 1c corresponds to the cold rolling with the thickness reduction of 50%. The sample coordinates are defined as rolling direction (RD), transverse direction (TD) and normal direction (ND), respectively. A plane normal to RD, TD and ND are also defined as RD, TD and ND planes, respectively.

Table 1 Chemical composition (mass%) of provided Ni.

The detail of the electrical resistivity measurement can be found elsewhere.^1,2) The four terminal resistivity measurements were carried out with the bar-shaped specimen with the length of about 50 mm and the cross-sectional area of about 1 mm² in a liquid nitrogen bath (77 K). The passing constant current of 100 mA was provided by a constant DC current supply (Keithley 6221), and the voltage drop was measured by a nanovoltmeter (Keithley 2182A). The delta mode, in other words, reversing the polarity of the current source and averaging values,⁴⁾ was used to cancel the thermoelectromotive force generated at contacts between two different metals. The accuracy of the measurement is at least three digits.

The microstructure observation of ARB-processed Ni was carried out using electron back scattering diffraction (EBSD) in a field emission type-scanning electron microscope (FE-SEM, JSM-6500FK and JSM-7001F, JEOL) with an acceleration voltage of 15 kV. A TSL orientation imaging microscopy (OIM) data collection system was used for EBSD measurements. The surface of the specimens for EBSD was mechanically polished by SiC paper, and finally, electrolytically polished in the mixture of nitric acid and methanol 1:2 in volume. The electrolytic polishing was performed at 233 K with the applied voltage of 14 V for 10 s, and then, 6 V for 45 s. OIM data analysis (TSL) was used to construct GB, high angle grain boundary (HAGB) and inverse pole figure (IPF) maps. GBs with the misorientaion angles θ < 15° is defined as low angle grain boundaries (LAGBs), and, GBs with θ ≥ 15° are defined as high angle grain boundaries (HAGBs). In this study, the GBs having misorientations less than 2° were excluded due to the limitation of the EBSD analysis.

The powder method of X-ray diffraction (XRD) was performed using a SmartLab (Rigaku) diffractometer with a Cu tube. The applied voltage and the tube current were 45 kV and 200 mA, respectively. The step angle and the scan time were set to be 0.01° and 0.03 s, respectively. From the XRD spectra, lattice microstrain ε was evaluated using the Williamson-Hall method¹⁶⁾ via Bragg peak position and the full width-half maximum (FWHM) of 111, 200, 310, 222 and 400 peaks. Finally, dislocation density L_V was converted from ε following equation.¹⁷⁾   

\begin{equation} L_{\text{V}} = \frac{16.1 \varepsilon^{2}}{b^{2}} \end{equation} (1)

Here, b is the magnitude of the Burgers vector of dislocation.

3. Results and Discussions

According to Matthiessen’s rule, ρ of an alloy measured at a temperature T (K), ρ_T (Ωm), is the summation of each contribution of alloying elements and lattice defects. Here, the subscript indicates T. It is emphasized that the contribution of lattice defect, such as vacancies, dislocations and GBs, can be treated like alloying element as expressed by eq. (2):^1–4)   

\begin{equation} \left. \begin{array}{l} \rho_{T} = \rho_{T}^{\text{alloy}} + \varDelta \rho^{\text{vac}} \cdot N_{\text{V}} + \varDelta \rho^{\text{disl}}\cdot L_{\text{V}} + \varDelta\rho^{\text{GB}}\cdot S_{\text{V}}\\ \rho_{T}^{\text{alloy}} = \rho_{T}^{\text{pure}} + \displaystyle\sum\nolimits_{i}^{n} \varDelta\rho^{i}\cdot C^{i} \end{array} \right\} . \end{equation} (2)

$\rho _{T}^{\text{alloy}}$ (Ωm) is the resistivity of a single crystalline alloy without any lattice defects. N_V is the atomic fraction of vacancies and S_V (m⁻¹) is the density of GBs. The coefficients related with vacancies, dislocations and GBs are Δρ^vac (Ωm/at. fr.), Δρ^disl (Ωm³), and Δρ^GB (Ωm²), respectively. $\rho _{T}^{\text{pure}}$ (Ωm) is the resistivity of a single crystalline metal without any impurity and lattice defects. For ‘i’-th solute atom, Cⁱ (at%) and Δρⁱ (Ωm/at%) are the concentration and coefficient, respectively. It was also assumed that the coefficients of the lattice defects and solute atoms do not have temperature dependence.

In this study, $\rho _{T}^{\text{alloy}}$ is treated as a constant before and after the ARB process like former reports^1,2) since 3N-Ni is used in this study. In such a case, the change in ρ at T compared with that of ARB 0c, δρ_T, can be expressed by following equation.   

\begin{equation} \delta \rho_{T} = \varDelta \rho^{\text{disl}}\cdot \delta L_{\text{V}} + \varDelta \rho^{\text{GB}}\cdot \delta S_{\text{V}} \end{equation} (3)

Here, δL_V and δS_V are the changes in L_V and S_V compared with that of ARB 0c, respectively.

It is also assumed that N_V is same before and after the ARB process.^1,2) It is because, the excess vacancies formed during the roll bonding were reduced due to the processing heat reaching to about 353 K immediately after each roll bonding. Furthermore, N_V decreases down to the equilibrium at R.T. when the resistivity was measured, at least a few days after the ARB process.

Figure 1 shows the RD IPF maps of TD plane on ARB processed Ni with (a) 0c, (b) 2c, (c) 4c, (d) 6c and (d) 8c. The ARB 0c consists of equiaxed and coarse grains due to the initial annealing. The initial grains are compressed along ND, and elongated along RD with increasing N, which is associated with the grain subdivision.¹⁸⁾ The grain thickness seems to decrease continuously with increasing N. It is noted that shear bands are also observed in N > 4.

Fig. 1

RD IPF maps of TD plane on ARB (a) 0c, (b) 2c, (c) 4c, (d) 6c and (e) 8c.

Figure 2 shows N dependence of two types of mean grain separation d evaluated from EBSD data; one is mean grain separation of GB, d_GB, and the other is mean grain separation of HAGB, d_HAGB. The superscript indicates the sample coordinates. d^ND was evaluated using interception method, whereas d^TD and d^RD are the average of actually measured grains with the number more than one hundred. It should be noted that the data is the same as literature.¹⁹⁾

Fig. 2

Change in mean separation of grain boundary along ND, RD and TD with increasing number of ARB cycle. The same data was used in the literature.¹⁹⁾

As can be seen from Fig. 2, d_HAGB is always larger than d_GB. Both $d_{\text{HAGB}}^{\text{ND}}$ and $d_{\text{GB}}^{\text{ND}}$ decreases with increasing N, and finally, seems to saturate at N > 6. $d_{\text{HAGB}}^{\text{TD}}$ are almost constant until N = 2, and then, start decreasing with increasing N. On the other hand, $d_{\text{GB}}^{\text{TD}}$ decreases with increasing N from the initial stage of the ARB process. $d_{\text{HAGB}}^{\text{RD}}$ initially increases with increasing N, and then starts to decrease with increasing N. On the other hand, $d_{\text{GB}}^{\text{TD}}$ continuously decreases with increasing N. Finally, the initial grain size of 20 µm was reduced to be $d_{\text{HAGB}}^{\text{ND}} = 260$ nm, $d_{\text{HAGB}}^{\text{TD}} = 1.2$ µm, $d_{\text{HAGB}}^{\text{RD}} = 1.6$ µm, $d_{\text{GB}}^{\text{ND}} = 160$ nm, $d_{\text{GB}}^{\text{TD}} = 430$ nm and $d_{\text{GB}}^{\text{RD}} = 1.1$ µm.

The deformation along TD and RD after roll bonding are almost constant and twice compared with the original size, respectively, since the ARB process uses rolling bonding with the rolling reduction of 50%. It explains the change of $d_{\text{HAGB}}^{\text{TD}}$ and $d_{\text{HAGB}}^{\text{RD}}$ during the initial stage of the ARB process. However, grain subdivision also occurs at the same time, and therefore LAGBs are continuously introduced. The grain subdivision is also associated with the trend of $d_{\text{GB}}^{\text{TD}}$ and $d_{\text{GB}}^{\text{RD}}$. The misorientation of introduced LAGBs continuously increases and changed to be HAGBs, which explains the change of the fraction of d_HAGB at later stage.

Figure 3 shows the change in the electrical resistivity of ARB processed Ni measured at 77 K, ρ₇₇, with increasing N. ρ₇₇ increases from 6.1 nΩm at N = 0 to 8.3 nΩm at N = 6. For N > 6, ρ₇₇ seems to be almost constant, and δρ₇₇ is about 2.2 nΩm at N = 8. It should be also pointed out that the wire brushing was used just before the roll bonding in the case of the ARB process, a small (invisible for naked eyes) debris of wire rush may remain on the interface as contaminants. In addition, the surface oxide films must have been formed immediately after wire brushing, and fragmented during the roll bonding on the interfaces. Such interfaces were folded at every roll bonding process, and therefore, such included contaminants/oxide debris can be thought to be a scattering centre of electrons. However, it was also indicated that such debris at interface has higher electrical resistivity, and therefore, such debris is thought to work as the reduction of effective cross-sectional area, which is not like the case for the ARB processed sheets.¹⁾ Thus, such δρ₇₇ is associated with the increase in δL_V and δS_V through eq. (3). In order to discuss the contribution of δL_V and δS_V on δρ₇₇, microstructure observations and XRD measurements were performed, respectively.

Fig. 3

Change in electrical resistivity at 77 K with increasing number of ARB cycle. Increment of electrical resistivity at 77 K from ARB 0c is displayed as right axis. The dashed line is the guide of eyes.

First, S_V was evaluated using d^ND, d^TD and d^RD via eq. (4). Here, the grain shape is simply assumed to be a rectangular parallelepiped.   

\begin{equation} S_{\text{V}} = \frac{1}{d^{\text{ND}}} + \frac{1}{d^{\text{TD}}} + \frac{1}{d^{\text{RD}}} \end{equation} (4)

Figure 4 shows the N dependence of S_V. Initially, S_V is about 0.2 Mm⁻¹ at N = 0, and then drastically increases to about 2 Mm⁻¹ at N = 1. The increase is mainly due to the increase of LAGB, which is reasonable as ARB 1c is the initial stage of grain subdivision.^18,20) Then, S_V continuously increases up to about 8 Mm⁻¹, at N = 6.¹⁹⁾ Then S_V seems to be almost constant at about 8 Mm⁻¹. It can be seen that the fraction of HAGB seems more than 50% at N > 4.

Fig. 4

Change in density of grain boundaries with increasing number of ARB cycle. The data are taken from the literature.¹⁹⁾

Figure 5 shows the N dependence of L_V evaluated using XRD. It is noted that the data is taken from the literature.¹⁹⁾ L_V is at about 1 × 10¹³ m⁻² at N = 0 since it is recrystallized microstructure. Then, L_V drastically increases up to about 3 × 10¹⁴ m⁻² at N = 1, and then, remains almost unchanged at N > 1.

Fig. 5

Change in dislocation density evaluated from XRD with increasing number of ARB cycle. The data are taken from the literature.¹⁹⁾

Such trend of ARB processed Ni is similar to the ARB processed Cu,⁴⁾ but, different from the case of Al.¹⁾ In the case of Al, L_V increases drastically and then gradually decreases with increasing N. The difference can be attributed with the difference of stacking fault energy (SFE) since that of Cu, Ni and Al are in decreasing order. In general, recovery easily occurs in higher SFE material, so that L_V of Al drastically increases at N = 1, but then, even gradually decreases since dynamic recovery during roll bonding occurs.¹⁾ Whereas, L_V of Ni at N > 1 does not seem to decrease compared with the case of Al since SFE of Ni is lower than that of Al. Furthermore, the purity of Ni used in this study is 99.9%, and thus, the relatively higher concentration of impurity compared with Al of 99.99%¹⁾ may prevent the movement of dislocations, so dynamic recovery due to the annihilation of dislocations during roll bonding may be prevented.

Metals having high SFE, such as Al, leads smaller width of an extended dislocation, and thus, the cross slip becomes easier. On the other hand, if the width of an extended dislocation is wider like Cu or Ni cases, the slip becomes more planar compared with the case of Al, and therefore, the cross slip becomes more difficult. Then, the recovery becomes more difficult since the frequency of the extinction of dislocations becomes lower. Thus, L_V in the ARB processed Ni is higher than that in Al, since the SFE of Ni is lower than that of Al. Furthermore, recovery in Ni is expected less than the case in Al, since Ni has a higher melting point than that of Al.

Karolik and Luhvich calculated theoretical value of the coefficients, i.e. $\varDelta \rho _{T}^{\text{disl}}$ and $\varDelta \rho _{T}^{\text{GB}}$ as shown in Table 2.²¹⁾ It should be pointed out that the theoretically calculated coefficients were based on the CG metals and compared with the experimental results of GB metals. However, such coefficients have been used for some UFG pure metals/dilute alloys for explaining microstructural change.^1–4) Thus, it is possible to estimate δρ_77K based on the microstructural parameters such as δL_V and δS_V, as shown in Fig. 6. Here, the actually measured ρ_77K are represented as symbols and estimated ρ₇₇ based on microstructure observations/measurements are represented as bars. Here superscript of S_V indicates the contribution of the type of GB, i.e. LAGB and HAGB.

Table 2 Theoretically calculated value of coefficient for lattice defects of Ni against electrical resistivity.

Fig. 6

Change in increment of electrical resistivity at 77 K with increasing the number of ARB cycle. Filled circles represent the actually measured value, and bars are the estimated values based on the microstructure observations and XRD measurements.

It should be emphasized that the calculated values of ρ₇₇ based on the microstructural parameters are the same order of magnitude compared with the actually measured ρ₇₇. Strictly speaking, the calculated ρ₇₇ are underestimate at N < 4, and the calculated ρ₇₇ are overestimate at N > 6. Although there is not such difference between actually measured and estimated ρ₇₇ for the ARB processed 2N-Al,¹²⁾ such underestimate and overestimate within the same order of magnitude was also observed in ARB processed Cu.⁴⁾

First, the difference between actually measured and estimated ρ₇₇ can be associated with the error of evaluation of S_V. Especially, the underestimate at N < 4 could be the effect of excluded LAGBs having misorientation angle less than 2 degrees due to the EBSD analysis. On the other hand, the overestimate at N > 6 may be associated with the simple assumption for the grain shape to be a rectangular parallelepiped. For instance, 3D-EBSD using FIB serial sectioning may provide more accurate S_V, but, the calculated values are thought to be reasonable for current stage since such large difference cannot be found in the case of 2N-Al.¹⁾

Second possibility is that the difference of the GB character introduced by the SPD process compared with the normal GBs appears in CG metals.^22,23) Such GBs in UFG metals introduced by SPD processes are sometimes called non-equilibrium GBs.^20,21) According to Orlova et al., there is a possibility that the coefficient Δρ^GB is different depending on the character of GBs; normally Δρ^GB for non-equilibrium GBs are higher than that for equilibrium GBs.²²⁾ It should be pointed out that the SPD process used by Orlova et al. is HPT which can give much higher effective strain compared with the ARB process of 8c. Thus, Δρ^GB for non-equilibrium GBs formed in the ARB processed Ni could be similar to Δρ^GB for equilibrium GBs formed in CG Ni.

Thus, the underestimation of ρ₇₇ at N < 4 can be explained by Δρ^GB, since non-equilibrium GB introduced by the SPD process may have higher Δρ^GB compared by the theoretically calculated Δρ^GB assuming equilibrium GBs normally formed in CG metals. On the other hand, there is another possibility for the over estimation of ρ₇₇ at N > 6, which can be associated with the change of Δρ^GB. The overestimation occurs in the saturation region of the ARB process, where dynamic recrystallization may occur.²⁴⁾ In such a region, the degree of non-equilibrium can be lower and Δρ^GB may decrease compared with lower N.

The third possibility is the presence of shear bands as shown in Fig. 1. It is reported that there are relatively small grains in the shear bands, compared with the lamellar microstructure.^25,26) Thus, there may be smaller grains within the shear bands which can increase ρ₇₇ at N > 6. Nevertheless, it should be emphasized that the actually measured ρ₇₇ and calculated ρ₇₇ based on the microstructural parameters are the same order of magnitude, and it is a good agreement in the case of ρ of the SPD processed metals.

If the estimation of ρ₇₇ based on the microstructural parameter in Fig. 6 is carefully seen, the contribution of dislocation density is almost 70% of all contributions at N = 1. It can be said that the contribution of LAGBs and dislocations are much smaller than that of HAGBs at N > 1, in Ni case, and the contribution of dislocation is higher than that of LAGB. At N = 8, the contribution of dislocations and LAGB are about 1% and about 6%, respectively. These are obviously understood by the coefficients (Table 2), the maximum L_V of 3 × 10¹⁴ m⁻² (Fig. 5) and maximum S_V of 8 Mm⁻¹ (Fig. 4).

In the case of the ARB processed Cu, the contribution of dislocations and LAGBs are also smaller than that of HAGBs.⁴⁾ For instance, the fraction of contribution of dislocations at N = 1 is about 80% of all contributions, in the case of Cu. However, the contribution of LAGB for Cu is larger than that for Ni. For instance, the contribution of dislocations and LAGB are about 9% and about 6%, respectively, in the case of Cu ARB 8c.

In the case of the ARB processed 2N-Al (A1100 alloy),¹⁾ δρ₇₇ due to the ARB process is about 1.1 nΩm as maximum, after ARB 8c. The contribution of dislocation is only 0.03 nΩm (less than 3% of δρ₇₇) based on $\varDelta \rho _{T}^{\text{disl}}$ of about 2.7 × 10⁻¹⁶ nΩm^3,21) and δL_V of about 1 × 10¹⁴ m⁻². The value is between the case of Cu and Ni.

Consequently, the change in ρ₇₇ is also associated with both δS_V and δL_V caused by the ARB process in the case of Ni. Nevertheless, the estimation of the change in the electrical resistivity based on the microstructure observations/measurements is possible. In other words, it is possible to estimate the microstructure parameters using electrical resistivity measurements in future. It means if two out of three parameters related to lattice defects are measured, the last parameter can be evaluated.

4. Summary and Conclusions

ARB process was applied to 3N-Ni up to 8 cycle. The electrical resistivity of 3N-Ni was measured at 77 K, and the increase in the electrical resistivity about 2.2 nΩm due to the ARB process with 8 cycles was found. XRD and FE-SEM/EBSD measurements gave change in dislocation density and density of grain boundaries due to the ARB processed 3N-Ni with 8 cycles to be about 3 × 10¹⁴ m⁻² and about 8 Mm⁻¹, respectively. The change in the electrical resistivity at 77 K was associated with both the change in dislocation density and the density of GBs, which is similar to the case of Cu and Al. According to the analysis, the contribution of dislocations for the electrical resistivity of Ni is about 70% at ARB 1c, whereas the contribution of dislocations and LAGB are about 1% and about 6%, respectively, at ARB 8 cycles. Thus, the contribution of GBs for the electrical resistivity becomes dominant at higher ARB cycle numbers, and that of dislocations is almost constant after ARB 1c.

Acknowledgements

Y.M. would like to posthumously thank Emeritus Professor M. Kato for his support and detailed discussions. Y.M. would like to appreciate Prof. Numakura at Osaka metropolitan university for his advice about electrical resistivity measurements. The authors would like to thank Prof. S. Onaka for the discussion in Tokyo Institute of Technology and Prof. N. Tsuji for the ARB process in his laboratory, Kyoto University. This study was financially supported by the Grand-in-aid (No. 22102002, 22102006, 19H05168 and 19K05056) through the Japan Society for the Promotion of Science (JSPS) and the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan.

REFERENCES

• 1)   Y.  Miyajima,  S.Y.  Komatsu,  M.  Mitsuhara,  S.  Hata,  H.  Nakashima and  N.  Tsuji: Philos. Mag. 90 (2010) 4475–4488.
• 2)   Y.  Miyajima,  S.  Komatsu,  M.  Mitsuhara,  S.  Hata,  H.  Nakashima and  N.  Tsuji: Philos. Mag. 95 (2015) 1139–1149.
• 3)   Y.  Miyajima,  K.  Fukuda,  H.  Adachi,  T.  Fujii and  M.  Kato: Mater. Trans. 61 (2020) 305–310.
• 4)   Y.  Miyajima,  T.  Shinohara,  H.  Adachi,  T.  Fujii,  S.  Onaka and  M.  Kato: Mater. Trans. 59 (2018) 393–398.
• 5)   M.A.  Meyers,  A.  Mishra and  D.J.  Benson: Prog. Mater. Sci. 51 (2006) 427–556.
• 6)   A.  Azushima,  R.  Kopp,  A.  Korhonen,  D.Y.  Yang,  F.  Micari,  G.D.  Lahoti,  P.  Groche,  J.  Yanagimoto,  N.  Tsuji,  A.  Rosochowski and  A.  Yanagida: CIRP Annu.-Manuf. Technol. 57 (2008) 716–735.
• 7)   T.  Kunimine,  N.  Takata,  N.  Tsuji,  T.  Fujii,  M.  Kato and  S.  Onaka: Mater. Trans. 50 (2009) 64–69.
• 8)   T.  Kunimine,  T.  Aragaki,  T.  Fujii,  S.  Onaka and  M.  Kato: J. Mater. Sci. 46 (2011) 4302–4307.
• 9)   S.  Okubo,  H.  Abe,  Y.  Miyajima,  T.  Fujii,  S.  Onaka and  M.  Kato: Mater. Trans. 55 (2014) 1525–1530.
• 10)   P.P.  Bhattacharjee and  N.  Tsuji: Int. J. Mater. Res. 102 (2011) 173–182.
• 11)   P.P.  Bhattacharjee,  R.K.  Ray and  A.  Upadhyaya: J. Mater. Sci. 42 (2007) 1984–2001.
• 12)   E.H.  Sondheimer: Adv. Phys. 1 (1952) 1–42.
• 13)   A.F.  Mayadas and  M.  Shatzkes: Phys. Rev. B 1 (1970) 1382–1389.
• 14)   Y.  Saito,  H.  Utsunomiya,  N.  Tsuji and  T.  Sakai: Acta Mater. 47 (1999) 579–583.
• 15)   Y.  Miyajima,  M.  Mitsuhara,  S.  Hata,  H.  Nakashima and  N.  Tsuji: Mater. Sci. Eng. A 528 (2010) 776–779.
• 16)   G.K.  Williamson and  R.E.  Smallman: Proc. Phys. Soc. London Sect. B 68 (1955) 577–585.
• 17)   G.K.  Williamson and  R.E.  Smallman: Philos. Mag. 1 (1956) 34–46.
• 18)   N.  Hansen and  D.J.  Jensen: Philos. Trans. R. Soc. A 357 (1999) 1447–1469.
• 19)  Y. Miyajima, T. Ueda, H. Adachi, T. Fujii, S. Onaka and M. Kato: 6th International Conference on Nanomaterials by Severe Plastic Deformation, (IOP Publishing, Metz, 2014) p. 012138.
• 20)   N.  Hansen: Metall. Mater. Trans. A 32 (2001) 2917–2935.
• 21)   A.S.  Karolik and  A.A.  Luhvich: J. Phys. Condens. Matter 6 (1994) 873–886.
• 22)   T.S.  Orlova,  A.M.  Mavlyutov,  A.S.  Bondarenko,  I.A.  Kasatkin,  M.Y.  Murashkin and  R.Z.  Valiev: Philos. Mag. 96 (2016) 2429–2444.
• 23)   R.Z.  Valiev,  R.K.  Islamgaliev and  I.V.  Alexandrov: Prog. Mater. Sci. 45 (2000) 103–189.
• 24)   Y.  Miyajima,  M.  Uchiyama,  H.  Adachi,  T.  Fujii,  S.  Onaka and  M.  Kato: Mater. Trans. 57 (2016) 1411–1417.
• 25)   H.  Miura,  M.  Kobayashi,  Y.  Todaka,  C.  Watanabe and  Y.  Aoyagi: J. Japan Inst. Met. Mater. 81 (2017) 536–541.
• 26)   C.  Watanabe,  S.  Kobayashi,  Y.  Aoyagi,  Y.  Todaka,  M.  Kobayashi,  N.  Sugiura,  N.  Yoshinaga and  H.  Miura: ISIJ Int. 60 (2020) 582–589.