Correlation between milling parameters and microstructure characteristics of nanocrystalline copper powder prepared via a high energy planetary ball mill

Journal of Alloys and Compounds 432 (2007) 103–110

Correlation between milling parameters and microstructure characteristics of nanocrystalline copper powder prepared via a high energy planetary ball mill O. Boytsov a,c , A.I. Ustinov a,∗ , E. Gaffet b , F. Bernard c a

G.V. Kurdyumov Institute for Metal Physics, 36, Vernadsky Str., Kiev-142 03142, Ukraine b NRG, UMR 5060 CNRS/UTBM, F90010 Belfort, France c LRRS, UMR 5613 CNRS, Universit´ e de Bourgogne, BP 47870, F21078 Dijon, France

Received 3 February 2006; received in revised form 24 May 2006; accepted 26 May 2006 Available online 10 July 2006

Abstract The microstructure evolution of Cu-nanostructured powders versus the ball milling conditions was investigated by whole peak profile powder pattern modeling method. This method allows defining in some approach the characteristics of as-milled Cu powder microstructure in terms of crystallite size, type and density of dislocations and twin faults density. It is shown that the change of microstructure characteristics of as-milled Cu powder versus the ball milling conditions (under constant time of the ball milling) depend on only some energy parameters of the milling, for example, average size of crystallite is uniquely defined by energy of the shock, whereas the portion of edge and screw components of dislocation structures depend on a ratio between normal and tangential components of shock. © 2006 Elsevier B.V. All rights reserved. Keywords: Nanostructured materials; Ball-milling; Whole peak profile powder pattern modeling; Crystallite size; Dislocations; Twin faults

1. Introduction The ball milling of metallic powders using a high planetary mill in inert atmosphere leads to many modifications of particle microstructure. Indeed, during the ball milling which can be performed in various types of high energy mills, powders are trapped between colliding balls and/or balls and vials are subjected to high stresses. Consequently, powders are subjected to a severe plastic deformation which exceeds their mechanical strength accompanied by a temperature. However, the characteristics of as-milled powders depend mainly on the mechanical behavior (ductile or brittle) of the powder. A balance between coalescence and fragmentation is achieved during milling, which leads to a rather stable average particle size. Indeed, in most cases, the rate of particle refinement (i.e. particle size and/or crystallite size) is roughly logarithmic with the processing time or with ball-to-powder ratio. In addition, many crystal defects

∗

Corresponding author. E-mail addresses: [email protected], [email protected] (A.I. Ustinov). 0925-8388/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2006.05.101

such as dislocations, stacking faults, twin faults may be introduced during mechanical alloying (MA). Consequently, the investigation of as-milled powder microstructure by XRD and TEM experiments show clearly that the crystallite size decreases to nano-scale [1–17], the dislocation density increases [9–12] and, in the same time twin faults can be formed [13–16] during the process. In addition, microstructure characteristics depend on the ball milling conditions especially the power of shocks, itself depends on the type of mill, the rotation velocity of the disk and vials, ball to powder ratio (BPR) and, the ball milling duration [18,19]. Many articles reported the existence of correlation between the milling conditions and the microstructure of as-milled powders using a modeling of XRD patterns coupled to TEM and SEM observations [20]. It was determined that the crystallite size and the dislocation density had the interval of time for which such parameters do not depend on the time (i.e. saturation period) whereas in the same time the twin faults density (twin density) increased proportionally to milling duration. The calculations of the additive energy which can be accumulated in the powder in different milling stages show that this change versus time is not monotonous. The maximum of

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this additive energy reached after 24 h of process decreases after. The authors explained this phenomenon as follows: at the beginning of the milling the small-angle boundary predominates whereas at the end of this process, the formation of low-energy twin boundaries is promoted. It seems that the creation of twin faults can be attributed to the plastic deformation inside the nanoparticles. Moreover a modeling of such processes using a molecular dynamics method confirms this suggestion [21,22]. On the contrary, the microstructure parameters depended on the energy of shocks and the shock mode (normal and/or friction). The determination of the dependency type versus the ball milling energy is complicated because the change of one of the milling energy parameters which are correlated with the rotation speed of disk or vials leads to another change. Therefore, the study of such dependencies of microstructure characteristics versus the energy parameters of the milling is a multiple-factors problem. Thereby, for a development of the physical model taking into account the evolutions of ball-milling powder microstructure, it is essential to determine the correlations between the powder microstructure and ball milling processing parameters. Consequently, it is necessary to identify clearly parameters characterizing of powder microstructure, and to calculate the shock power (more precisely the energy and the frequency of shocks) of the ball milling process. From a kinematic model developed by Abdellaoui and Gaffet [23] on G5 machine [24], the change of speed rotations of disc and vials can be led to the injected power during the ball milling process which can be expressed as energy of shocks (E) and the frequency of shocks (F). In addition, in the ball milling process, the total kinetic energy during the shock can be decomposed in two components [25]: (i) the friction kinetic energy (Et ) which is proportional to the tangential velocity and (ii) normal kinetic energy (En ) which is proportional to the normal velocity. On the other hand to characterize the microstructure of materials, the TEM and XRD techniques can be used. However, the TEM can only provide a high validity of local information on the occurrence of structural defects such as planar defects and dislocations. Besides, TEM technique is not particularly suitable method for investigating agglomerated powders. The XRD analysis can provide the high degree of average information but the interpretation of XRD patterns are not unambiguously. As a consequence, the combination of complementary characterization methods (such as TEM, Raman) is achieved for a better description of experimental XRD patterns. In particular, a previous works [20,24] described the use of this approach for determining microstructure characteristics, namely the crystallites size, the dislocations density and the density of the planar defects (essentially the twin boundaries) in as-milled powder by whole powder pattern modeling method [20] and whole peak profile powder pattern modeling method [26]. Thereupon the main objectives of this paper is to establish a correlation between ball milling characteristics such as frequency of shocks, energy of shocks and the ratio between normal and tangential components of kinetic energy and the

Table 1 Energy parameters of ball milling at different Ω/ω ratio Ω (rpm)

ω (rpm)

F (Hz)

E (J)

En /Et

150 150 250 250 350 350 350

50 200 50 400 50 200 400

6 4 9 8 13 15 17

0.030 0.030 0.080 0.095 0.160 0.170 0.170

0.06 0.17 0.02 0.32 0.01 0.19 1.50

microstructure parameters such as the crystallite size (D), the type of dislocations and their density and twin faults density. 2. Experimental procedure Pure elemental copper powder was milled using a planetary ball-mill referred to as G5 milling machine [24]. One hundred and twenty-five mL powders and 5 stainless steel balls (15 mm in diameter, 14 g in weight) were sealed under in air, into the stainless steel vials. The ball to powder weight ratio is 7/1. The rotation speed of the vials (ω) which are fixed onto a rotating disc (Ω) can be set independently. Each milling condition is characterized by three essential parameters: the speed of the disc rotation (Ω, rpm), the speed of the vial rotation (ω, rpm) and the duration of the process (t, h). The selection of the copper and the ball milling conditions have been motivated by the fact that particularities of the mechanical behavior (elastic and plastic deformations) of massive copper was already investigated for different pulsed loads using mechanical [27,28] and radio frequency [29]. The magnitude of ball milling parameters is provided in Table 1. In Fig. 1, it was shown the ball milling conditions for different equipments in comparison with experiments using G5 machine [18]. This figure exhibit, that from such ball milling conditions, only crystallized phases will be formed. Consequently, the presence of amorphous phases does not take into account in this work. To identify the as-milled Cu powders and determine their microstructure parameters, X-ray diffraction analyses were performed with a high resolution diffractometer (D5000 Siemens) using a monochromatic Cu K␤ beam focused with a secondary curved graphite monochromator. We have chosen Cu K␤ radiation in order to decrease the broadening of peak due to K␣1,2 doublet. The distribution of intensities was measured by discrete mode (step-interval 0.02◦ of arc). The time of the measurement of intensities in point for each peak

Fig. 1. Experimental conditions of the milling and the different experiments which are performed using the planetary mill G5.

O. Boytsov et al. / Journal of Alloys and Compounds 432 (2007) 103–110 was determined in accordance with its intensity. For example, the time of the measurement of intensities for peak 111 was 30–40 s per point, but the time of the measurement of intensities for peak 222 was 75 s per point.1

3. Modeling procedure The method of whole peak profile powder pattern modeling was used for determining the microstructure characteristics of ball-milling powders in order to better understand the influence of ball milling processing parameters [26]. By analogy with WPPM (Whole Powder Pattern Modeling) [20], the determination of the parameters of microstructure consists in simultaneous modeling of all profiles peak of XRD pattern without the use of a function describing profiles peak. Such a model is established assuming (in first approximation) that the influence of each parameter as the dislocation density, the correlation between screw and edge components of dislocation, the twin density and the average of crystallite size are independent. Based on theses assumptions, all components of XRD peaks can be calculated as a convolution of functions describing XRD peak when stacking faults, the finite size of the coherently diffracting domains (size factor), types of dislocations, elastic properties of the crystal (microdistortion factor) were taken into account. Consequently, considering a previous paper [26] in which all terms have been clearly explained, the XRD intensity may be expressed as follows:  I(ϑ) = Is (Hsϑ , Ksϑ , Lϑs ) ⊗ S(ϑ) ⊗ D(ϑ) ⊗ A(ϑ), (1) s

where - ⊗ is the means a convolution procedure. - Is (Hsθ Ksθ Lθi ) is the intensity distribution of the sth-component due to the presence of planar defects. Because the investigation of as-milled copper microstructure by TEM [26] showed that the dominant type of the planar defects is twin faults, only twins faults will be considered in this work. Assuming that twin faults arrangement in a crystal chaotically their density (ρt ) one can defined as ρt = 1/¯lt , where ¯lt is mean number of atomic layers between nearest twin boundaries. On the other hand, ρt -probability to find the twin boundaries may be determined in percent. Thereby, the density of the twin borders expressed in the percent is the number of the twin borders in 100 atomic layers. - S(ϑ) hereafter referred to as the size factor, is the function describing the XRD peak broadening due to the finite size of crystallites (coherently diffracting domain). As is customary in many works (see for example [30]), we assume that size factor can be described by symmetrical functions for which the integral breadth, Bs at the angle ϑ is defined by Scherrer’s equation [30], Bs = 0.9λ/Dcos ϑ, where λ is the wavelength of 1

Since the experimental profiles of peak was compared to theoretically calculated, for achievement more pinpoint accuracy of this comparison, measurement to intensities advisable to conduct in condition, which provide equal accuracy of the experimental determination to intensities for each point all interval locations of diffraction peaks.

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the X-ray radiation and D is the mean size2 of the coherently diffracting domains. - D(ϑ) hereafter referred to as the microdistorsion factor, is a function describing the XRD peak broadening due to the presence of dislocation in the crystal lattice and as in the event of [31] we shall suppose, that the change of XRD peak profile can be described by a function close to the Lorentzian function. From results reported by Ung´ar et al. [31], the integral breadth, Bd , of the XRD peak at the angle ϑ can be presented, in first approximation, as Bd = 2ECh k l tgϑ, where E = ρ1/2 (πA2 b2 /2)1/2 . A is a parameter which depends on the effective outer cut-off radius of dislocations and it was taken equal to 10 [33], b the Burgers vector, Ch k l the mean factor of the dislocation contrast of the h k l peak, ρd is the dislocation density. Taking into account that the dislocation contrast depends on the type of dislocations (edge or screw) as reported in [31], the dislocation contrast coefficient has a edg value ranged from the value (Ch k l ) when only edge dislocations are present and the value when only screw dislocations (Chscrk l ) are present. From a linear approach, the coefficient of the dislocation contrast for a crystal in which the portion of edge dislocations is P can be described as follows: edg Ch k l = Chscrk l + (Ch k l − Chscrk l )P. So, if we specify the values of E and P a priori then one can calculate the profile of h k l XRD peaks. - A(ϑ) describes the XRD peak broadening caused by the instrumental factors. Parameters of this instrumental function for each peak has been extracted from the resolution curve obtained from the broadening of BaF2 3 XRD powder peaks (as reference materials) at different scattering angles. The XRD peak profiles of this powder have been also described by a symmetric pseudo-Voigt function in which parameters vary in a monotonous way versus the scattering angle. The magnitudes of these parameters were used to model the instrumental function at a given interval of the scattering angles.4 All calculated XRD powder patterns were compared to experimental ones in order to obtain the best correspondence between experimental and modeling profiles peaks [26]. Thereby, in accordance with offered by way of modeling of the full profiles of diffraction peak, it is necessary a priori to select four parameters crystallite size, dislocation density, twins density, ratio between the number of edge and screw dislocations. For each combination of parameter to calculate simultaneously all profiles and 2 The increasing of accuracy of the determination of the average crystallite size can be reached by account of more exact modeling of dimensioned factor. Consequently, it is necessary to take into account that profile peaks is defined not only by average size, but also by the distribution of sizes [20] provided that they is equiaxial. Otherwise, it is necessary to take into account as well as factor of the form of crystallite size [32]. 3 The choice of powder BaF , was accepted in attention that peaks powdered 2 diffractogram BaF2 are evenly located in all interval angles of Cu powdered diffractogram, but the halfwidth of BaF2 peaks greatly less of experimental observed Cu peaks. 4 Actually the instrumental function is more exactly described using asymmetric p-Voigt functions. Since inexactnesses of the description instrumental functions carry the systematic nature, that their influence upon change the values characterizing of microstructure of powder greatly does not influence.

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Fig. 2. Comparison between the experimental peak breadths (black point) obtained in the case of the ball milling condition (250/50/24 h) and those obtained from the simulated powder X-ray diagram.

compare them with experimental observed. This approach is liked of WPPM [20] procedure and differs only the method of searching for parameter, under which is reached best correspondence between experimental and calculated profile of peaks. Fig. 2 shows the comparison between the calculated intensity and experimental measured profiles of diffraction peaks. As measures for estimation of their divergence in work is used  i i , where n is number of peaks, value R = (1/n) i |Iexp − Isi |/Iexp

i − I i | an average deflection in point for experimental and |Iexp s

i simulated i-profile, Iexp is the average intensity in point on iprofile.

4. Experimental results and discussion Microstructure data obtained from a whole XRD peak profile analysis of as-milled copper powders are presented in Table 2. In order to correlate the milling conditions (i.e. frequency of shocks (F), energy of shocks (E), mode of shocks (En /Et , where En is the normal energy and Et is the friction energy)) and the microstructure characteristics (i.e. crystallite size (D), dislocation density (ρd ), twins density (ρt ), correlation between the number of edge and screw dislocations (P)), it is essential to determine a correlation between different couples such as for example (E) and (ρd ) or (E) and (D) or (F) and (D), etc. . .. This correlation analysis was performed using the method of Spirmen grade correlation [34] in which each ball milling

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Table 2 Microstructure characteristics of Cu powder after ball milling Ω (rpm)

ω (rpm)

D (nm)

ρd × 1016 (m−2 )

ρt (%)

P

R

150 150 250 250 350 350 350

50 200 50 400 50 200 400

102 67 55 45 35 36 45

1.2 1.8 3.3 4.5 7.4 4.7 5.4

1.83 3.01 3.21 4.19 3.11 4.35 4.42

0.1 0.2 0.1 0.7 0.1 0.5 0.6

0.04 0.07 0.05 0.06 0.06 0.07 0.08

parameter {Fi }, {Ei } and {Eni /Eti } should be associated with each microstructure parameter {Di }, {ρdi }, {ρti }, {Pi }. Then, if between these variables a dependency exists, a coupling function can be used and a correlation factor can be evaluated from the Spirmen formula presented as follows:  6 i (ri − si )2 Rs = 1 − (2) n3 − n ri , si is the ranks factors, which are compared (for example frequency of shocks (ri ) dislocation density (si ) and etc.), n is the number of experimental conditions. The value of the ranks correlation for different number of the experimental conditions is tabulated in special table. The existence of intercoupling function between pair variables (for example frequency of shocks and dislocation density) is postulated, if calculated value r is more tabular. The calculations of correlation factor for different pair of variables are provided in Table 3. The critical value of the Spirmen factor is 0.89 corresponding to a confidence probability of 99%. Then, it is more convenient, from this table to obtain a qualitative information relative to the milling/microstructure dependency. From Table 3, it appears that the frequency of shocks practically does not modify the microstructure parameters whereas the microstructure parameters are strongly dependent on the energy of shocks. In addition, the ratio En /Et does not modify the microstructure parameters but it can change the ratio between screw and edge dislocations. As two ball milling parameters can be varied simultaneously during this experiment, a well description of the influence of ball milling parameters on the microstructure characteristics (crystallite size, dislocation density and twin density) is more complicated. At the same time due to the significant non-linearity dependence of milling parameters on the rotation velocities of Table 3 Spirmen correlation factors

F (Hz) E (J) En /Et D (nm) ρd × 1016 (m−2 ) ρt (%) P

D (nm)

ρd × 1016 (m−2 )

ρt (%)

P

−0.66 −0.89 −0.03 1

0.83 0.94 −0.09 0.94 1

0.60 0.89 0.54 −0.83 0.77 1

−0.14 0.23 0.97 −0.02 −0.09 0.54 1

Fig. 3. The topogram of the crystallite size dependency vs. the rotation speed of the disk (Ω) and the vials (ω).

the disk and vials, it is rather difficult to select one set of rotation velocities allowing to fix independently one of these parameters (e.g. energy effect) without the influence of the another ones (e.g. frequency effect) and reciprocity. In addition, a response surface can be established to adjust a set of experimental data. Thus, points of this surface will allow forecasting what’s happen in an unexplored domain. Then, it will be possible to plot a surface cross-sections using one of the contour parameters and to establish a bivariate dependence with the help of the obtained results. As an example, the topogram of crystallite size dependency on the rotation speed of the disk (Ω) and that of the vials (ω) is shown in Fig. 3. Large points represent the experimental data; the number onearea of validity, the number two-area of forecast. The domain in grey corresponds to a domain in which the crystallite size may be obtained with a good reliability. In order to determine the admissible domain for establishing cross-sections and to minimize the forecasted error, a series of surfaces having the following form Z = Xn + Yn + 1 and Z = sin(X) × Yn have been constructed. In addition, several different cross-sections within the reliable system and outside have been determined. From theses constructions the obtained values were compared with the calculated ones. It was determined that the average value of the maximum error between theoretical and experimental is equal to 15%. The cross-section method cannot be considered as universal, i.e. this method does not allow calculating exactly values of unknown parameters using the known data, but it allows to determine the dependence type with a sufficient reliability and to modify the strategy of further research. All constructions have been made within the reliable domain only. From Table 2, it appears that the frequency of shocks (in range of 6–17 Hz) does not affect the microstructure parameters. Therefore, we decided to plot the cross-sections for a constant frequency of shocks in order to determine the influence of the energy of shocks on the crystallite size (Fig. 4), on the dislocation density (Fig. 5) and the twin density (Fig. 6). These figures show that when E is increasing, the decrease of the crystallite size is monotonous whereas the evolution of the dislocation and

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Fig. 4. Evolution of the crystallite size when the energy of shock is modified.

Fig. 5. Evolution of the dislocation density when the energy of shock is modified.

Fig. 6. Evolution of the twin density when the energy of shock is modified.

twin densities is not monotonous. Non-monotonic change of the crystallite size and dislocation density was observed also at study of the kinetics of the change of these values under constant energy of the ball milling [17,20]. However, from influences of the energy features of the milling on microstructure parameters usually, it is supposed that these dependencies are monotonous [12,20]. The dependency of twins density from shock energy has three anomalous domains: (a) 40–110 mJ, (b) 110–160 mJ and (c) >160 mJ in which three different behaviors of microstructure characteristics may be observed. For a-domain it is characteristic that a decreasing of the crystallite size and a linear increasing of the dislocation and twin densities are observed. It is necessary to note that the dependence of dislocation density practically linear but the dependence of crystallite size and twins density have the inflection point that can be indicative of intercoupling the change of these values result from particularity of the mechanism to deformation of nano-size crystallite. For b-domain, the decrease of the crystallite size is maintained, the dislocation density continues to increase whereas in the same time the twin density reached a maximum before decreasing. In c-domain the decreasing of crystallite size is very low (from 35 to 25 nm), the density of dislocations reached a maximum then decreases. In the same time, the twin density reached a minimum (corresponds to dislocation density maximum) before increasing again. This latter domain seems to be connected to a specific plastic deformation of nanocrystallites. In the domains (a) and (b) in which the modification of the dislocation density is correlated with the crystallite size evolution, an expected situation is observed. Indeed, the decreasing −1/2 of the crystallite size is proportional to ρd . Concerning the increasing of twin density, it may be attributed to the twin formation by recrystallization which is occurred at the beginning of the ball milling process. On the contrary, in the domain (b), the evolution in opposite direction of dislocation density (increases) and twin density (decreases after reaching a maximum concentration) is interesting. Indeed, we can imagine that during the ball milling process, a twin can cross the crystal resulting from a generation and a motion of dislocations in the crystal and, when the concentration of twins is large beside a dislocation, the modification of dislocation structure may be occurred. Concerning the last part (from domain (b) to domain (c)) in which the concentration of dislocations versus the energy of shocks is maximal, it can be expected that during the plastic deformation caused by milling, a motion of dislocation begins. In addition, it is well known that for generating dislocations via a reconstruction mechanism a volume activation of the order of 200 Burgers vector is necessary [35]. Consequently, it is normal to expect the maximum dependency of dislocation density as a function of energy of shocks when the crystallite size of Cu is approximately equal to 35 nm [36]. Then, from smaller crystallite size, such a generation mechanism of dislocation seems more difficult. Indeed, in the same period, a decreasing of dislocation density is observed; it can be

O. Boytsov et al. / Journal of Alloys and Compounds 432 (2007) 103–110

Fig. 7. Dependency of the crystallite size vs. dislocation density.

explained by a modification of plastic deformation mechanism from dislocation motion to twinning. Nevertheless, a modeling of plastic deformation mechanism of nanomaterials using dynamic molecular approach also predicted a possible crystallite deformation by twinning [21,22] in relation with a dimensional effect. Unfortunately, from this model, it appears that a critical size, in the case of a copper powder, for producing such a deformation by twinning is close to 8 nm [22]. However, further investigations will be necessary to have a well description of such mechanisms. In addition, a complete analysis of the dependency between the dislocation density and crystallite size was performed. Such a dependency is represented in Fig. 7. The break of the dependence in the interval of 5.5 × 1016 to 5.8 × 1016 dislocation density is a result of deficiency of experimental conditions at which Cupowder was prepared. From this figure, it appears that up to the critical size of 35 nm, the dependence between the dislocation density and the crystallite size is proportional to ρ−1/2 . On the contrary, from crystallite size close to 35 nm, an ambiguity exists. Namely for one dislocation density, two crystallite sizes can be obtained. Such type of dependency is probably connected to a realignment of dislocations. It can correspond to the coexistence of two dislocation structures. In this convergent area, a transformation between two different dislocation structures may be occurred. Then, from this observation, it was interesting to identify the dominant type of dislocations (edge or screw dislocations) versus the ratio En /Et (shock mode) as be shown in Fig. 8. This figure exhibits clearly that the dislocation type edge or screw depends on the shock mode (friction or direct shocks). This suggestion was also reported by Vives et al. [12] in the case of iron ball milled powders. Such an evolution can explain the dislocation density/crystallite size dependency described above because the modification of the dislocation structures is occurred from screw

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Fig. 8. Dependency of the P parameter vs. En /Et .

dislocations (high mobility) to edge dislocation (low mobility). Such results confirm the modification of the generation and the motion of dislocations (resulting from dislocation structure change) when the crystallite size decreases. 5. Conclusion On the basis of the microstructure evolution of Cunanostructured powders versus ball-milling conditions, one can conclude that: - the frequency of shocks in range of 6–17 Hz does not affect the microstructure characteristics; - crystallites size, dislocation and twin density are function of the energy of shocks, however the energy of shock does not change the dislocation structure, i.e. the ratio between edge and screw dislocations; - the ratio between normal and tangential components of shock is dominant factor which determines the ratio between edge and screw of dislocations. When the energy of shocks increases, the change of dislocation and twin densities is non-monotonous. Indeed, it exists an area of energy in which the dependency of dislocation density has a maximum. At the same time the dependency of twin density have both a minimum and, a maximum. This dependency defined the change of the plastic deformation mechanism in the case of nanocrystallites. The mode of shocks is dominant on the type of dislocations. Indeed, the dominant type of dislocations is edge dislocations when the correlation between normal and tangential component of shocks achieve the threshold value. The coupling between the dislocation density and the crystallite size has an area of functional ambiguity that it is determined by the conversion of the dislocation structure.

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