Al coating deposited by mechanochemical technique

Applied Surface Science 222 (2004) 43–64

Deformations, subgrain structure, dislocation arrangement and transition layer formation in Cu/Al coating deposited by mechanochemical technique V.S. Harutyunyana,*, A.R. Torossyanb, A.P. Aivazyana a

Department of Solid State Physics, Yerevan State University, A. Manukian 1, 375025 Yerevan, Armenia Institute of General and Inorganic Chemistry NAS of Armenia, Argutyan 10, 2-tup., Yerevan 375051, Armenia

b

Received 15 January 2002; received in revised form 1 August 2003; accepted 1 August 2003

Abstract The deformed state, dimensions and mosaicity of subgrains, arrangement and density of excess dislocations in Cu/Al coating deposited by mechanochemical technique are investigated by X-ray diffraction method. For Cu coating the estimates 10 nm, 6:4
1011 cm2 and 0.24 GPa are evaluated for average size of subgrains, excess dislocation density and shear strength, respectively. The strain-hardening mechanism of constraint on dislocation motion is proposed to be a dominant channel for the coating strengthening. A model is proposed for interdiffusion process of the Cu and the Al atoms at the Cu/Al interface. It is assumed that this interdiffusion is activated by the impact temperature oscillations due to repeated ‘‘ball–coating’’ collisions over the deposition process. On the basis of analysis of X-ray diffraction data and the obtained estimate for diffusive run of the Cu atoms into the Al substrate, formation of a Al1xCux transition layer with compound parameter x  0:02 and thickness 5.1 mm is predicted. # 2003 Published by Elsevier B.V. PACS: 61.10.-i; 61.72; 62.20; 67.80.Mg; 68.55 Keywords: Coating; Subgrain; Deformation; Dislocation; Vacancy; Diffusion; X-ray diffraction

1. Introduction Coatings are widely applied in various fields of technology thanks to their ability to give an improved quality to the surfaces that had to be coated. In many cases, the mechanical, chemical, physical and structural properties of coatings and thin films are sharply different from the properties of the bulk material, *

Corresponding author. Tel.: þ374-1-58-69-32; fax: þ374-1-55-46-41. E-mail address: [email protected] (V.S. Harutyunyan). 0169-4332/$ – see front matter # 2003 Published by Elsevier B.V. doi:10.1016/S0169-4332(03)00965-6

forming the basis of specific areas of their applications. Nowadays, numerous techniques, such as CVD, PVD, electrochemical, thermal spray processes, sol– gel technology, etc. have been developed for the deposition of coatings and thin films. The choice of the process and the processing conditions directly affect the microstructure of coatings, while the properties of coatings depend on their microstructure. An exact knowledge of the microstructure, therefore, is essential in order to understand the basic mechanism of the formation and structure–property relationships of the coatings [1,2].

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In order to produce coatings with novel physical, chemical and mechanical properties, a combination of different coating technologies with new deposition methods are being developed [3]. From this point of view the method described below offers a novel approach to obtain coatings with specific mechanical and physical properties. Extensive experimental analysis of the behavior of powders under mechanical impact conditions has demonstrated that mechanical activation initiates and accelerates both physical (origination and motion of dislocations, local melting, considerable increase of solid phase diffusion, electronic and ionic emission, etc.) and chemical interactions in the solid phase [4]. In particular, the intensification of the reduction of some metal oxides by a more active metal and the formation of metal alloys and composites has been reported in our earlier publications [5–7] as well as in works of other authors engaged in mechanochemistry [8,9]. Starting from the experience with processing powders, a novel mechanochemical route was developed for metal surface modification and finishing under the action of repeated mechanical impact [7]. Using this method, pure metallic coatings on dissimilar substrates can be obtained both from metal oxides and pure metallic powders, and alloy coatings of different compositions can be produced. The chemical process takes place in the solid state and is driven principally by the energy of mechanical impact, i.e. it does not require thermal treatment of the system. The mechanochemical deposition of pure chromium and titanium coatings on steel and aluminum substrates through the reduction of the relevant oxides was realized as a typical application [10]. It was revealed by multiple load indentation measurements that the coatings show a considerable increase of hardness compared to the bulk property of the same material, and also a moderate increase compared to the substrate. However, the deformation state (strains and stresses) and defect structure (dislocation density and arrangement) of such coatings have not been investigated in detail. Obviously, this information is necessary in order to understand the hardening mechanisms of the coatings by the proposed new technique of deposition. The objective of this article is to conduct X-ray diffraction analysis of deformation, subgrain structure and dislocation arrangement in Cu coatings deposited

on Al by mechanochemical technique as well as to discuss some fundamental aspects of the formation of coatings under mechanical impacts. The choice of Cu/ Al system is based on the good adhesion observed for this pair of materials, as well as on the technological prospects for Cu coatings deposited by the proposed technique. From the practical standpoint, in anticorrosion coatings like Ni/Cu/Al and Cr/Cu/Al the Cu transition sublayer serves for strong adhesion at the interfaces. In comparison to Al, the friction coefficient of Cu is lesser. Therefore, the other important example of applicability of the Cu/Al system is the possibility to decrease friction coefficient due to the Cu deposit. The authors expect that the method presented here may form the basis of an efficient technological coating process, holding good potential possibilities also for such applications as the functional coatings on pipes and aluminum sheets.

2. Experiment The deposition of the coatings was carried out in a vibration mill (LE-102/1, Kutec type: 2014, Budapest) at the vial amplitude of 2 mm and the frequency of vertical oscillations 25 Hz. The process of coating deposition was conducted at room temperature T0 ¼ 300 K. A specially designed ball mill vial was used with a volume of 0.3 l, which was filled to about 2/3 with steel balls of 8–15 mm in diameter. A schematic diagram of the coating chamber is shown in Fig. 1a. The substrate specimen was a rectangular sheet of aluminum alloy (UNS number A91100) with dimensions a 5 cm
10 cm deposition surface and a thickness of 3 mm. The precursor powder of the coating was copper powder (98.9% pure) with particle size from several micrometers up to 15 mm. The amount of powder used per unit area of the substrate surface was 0.02 g/cm2. The coating was formed by milling in air simultaneously treating the aluminum substrate and copper powder for 47.5 min. The mechanical milling is responsible for the in situ formation of highly active and cohesive metal powder and the eventual deposition of the coating. The X-ray diffraction pattern was recorded on a powder diffractometer DRON-3. The geometry of the diffraction scheme is presented in Fig. 2. For

V.S. Harutyunyan et al. / Applied Surface Science 222 (2004) 43–64

45

Fig. 1. (a) A schematic diagram of the coating apparatus: (1) coating chamber, (2) milling medium (steel balls), (3) metal powder, (4) cap, (5) substrate, (6) lever spring. (b) ‘‘ball–coating’’ individual collision. ANB, AMBCD, and ANBCD are cross-sections of impact area, volume V0, ðCu!AlÞ and volume Vim at xz plane, respectively. MA ¼ Rim , MN ¼ hmax , MK ¼ lz0 , and NK ¼ lz . MP ¼ tCu and PQ ¼ ld at t ¼ tdep . To gain a better understanding of the scheme, the length scale intentionally was not obeyed: in accordance with obtained estimates MA ¼ Rim @ MK ¼ lz0 (see Table 6).

monochromatization of the radiation the graphite monochromator was used. The X-ray diffraction spectrum was recorded in y–2y mode using Co Ka radiation (see Fig. 3). In order to investigate the possible inhomogeneity both of morphology and deformation state of the coating in the deposition plane the X-ray diffraction spectra were recorded in zx and zy scattering planes. (The orientation of axes of xyz rectangular coordinate system is presented in Fig. 2.) The detected diffraction peaks were identified as the (1 1 1), (2 0 0), (2 2 0), (3 1 1), and (2 2 2) reflections from both the Cu coating and the Al substrate. The contribution of Ka2 line was removed numerically [11]. Then the integral angular broadening of each Ka1 diffraction peak of the Cu coating

was reduced by the broadening due to instrumental aberrations. Further analysis of experimental results was carried out for Ka1 diffraction peaks of the Cu coating and the Al substrate which are approximately Gaussian in profile. The parameters characterizing the Co Ka1 reflections, diffraction peak angular position and integral width, are listed in Table 1. The X-ray diffraction spectrum was also recorded from Al substrate before the coating deposition in order to estimate the thickness of the coating from the changes in spectrum due to X-rays absorption. For independent measurement of the Cu coating thickness a cross-section image with magnification 450
from the Cu/Al system was recorded by optical microscope ‘‘Neophot-3’’ (Fig. 4).

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M

D Cu coating Transition layer (Al1-xCux alloy)

X-ray tube

b

(t )

Al substrate

z

x y Fig. 2. The applied X-ray diffraction scheme and the stresses in the Cu/Al system. M is the graphite monochromator, D the detector, xyz the coordinate system (the plane xy is parallel to the coating deposition plane), sb and s(t) are the compressive biaxial and tensile stresses acting on Cu coating and Al1xCux alloy (transition layer) at the deposition plane, respectively.

3. Analysis of experimental results 3.1. Determination of out-of-plane lattice parameter az and strain ez in Cu coating: estimation of the coating thickness The out-of-plane lattice parameter, az, of the Cu coating was determined using the standard extrapolating method [12]. Using the data of diffraction peaks’ angular positions (see Table 1, first row), on the basis

of above-mentioned extrapolating method the out-ofplane lattice parameter, az, and the corresponding strain component, ez ¼

az  a0 ; a0

(1)

were found and listed in Table 2. For unstrained lattice parameter of Cu, the value a0 ¼ 0:36150 nm was substituted in (1). The parameter az is determined with an accuracy 0.00002 nm. Thus, it is obtained

Fig. 3. The X-ray diffraction spectrum recorded in y–2y mode using Co Ka radiation.

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47

Table 1 Angular positions and integral widths of diffraction peaks in X-ray diffraction spectra recorded from Cu/Al system and Al substrate before coating deposition Peak parameters

Layer

Diffraction peak (hkl)

Angular position, 2y (8)

Cu coating Al1xCux transition layer Al substrate (before coating deposition)

Integral width, bhkl (8)

Cu coating

Fig. 4. Cross-sectional optical image with magnification 450
recorded from the Cu/Al system.

that deformation of coating in direction noramal to its surface is of tensile type. From the comparison of intensity maxima of Al diffraction peaks in spectra recorded from Al substrate (before the coating deposition) and Cu/Al system a value 11:70 1 mm was determined for the thickness of the Cu coating. This approach is based on traditional method taking into account the dependence of the attenuation of diffraction peak detected from substrate on the thickness of deposited film because

(1 1 1)

(2 0 0)

(2 2 0)

(3 1 1)

(2 2 2)

50.732 45.051 45.001

59.141 52.374 52.451

88.750 77.320 77.352

109.788 94.250 94.251

117.875 99.750 –

1.134

1.324

2.059

2.645

2.884

of X-ray absorption. The result of optical microscopy measurements (Fig. 4) of the Cu coating thickness is tCu ¼ tav Dtf ¼ 11:75 0:75 mm, where tav ¼ 11:75 mm is the average thickness of coating and Dtf ¼ 0:75 mm the amplitude of fluctuations of the coating thickness. As it follows from the presented data, the results obtained for the Cu coating thickness by two independent techniques are consistent. We did not observe any considerable difference between main characteristics (angular positions and broadenings of diffraction peaks) of spectra recorded in zx and zy scattering planes (Fig. 2). This shows that the Cu coating has homogeneous morphology and deformation state in the plane of deposition. 3.2. Determination of in-plane biaxial strain ei and biaxial stress sb of coating from its biaxial deformation It is assumed that the Cu coating in specimen is subjected to biaxial deformation in the plane of deposition (in xy plane; see Fig. 2). This assumption is justified, since every direction is equivalent in the

Table 2 Lattice parameters and strains in Cu/Al system and Al substrate before Cu deposition Layer

Out-of-plain lattice parameter, az (nm)

In-plane lattice parameter, ai (nm)

Out-of-plane biaxial strain, ez

In-plane biaxial strain, ei

Cu coating

0.36222

0.36088 0.36075 0.36082 0.40548 0.40511

2.0
103

1.7 2.1 1.9 1.3 4.2

Al1xCux transition layer Al substrate (before coating deposition)

0.36222 0.40548 0.40511

2.0
103 1.3
103 4.2
104








103 103 103 103 104

Model

Reuss Voigt Averaging over models Hydrostatic expansion Uniform hydrostatic expansion

Due to assumption on hydrostatic character of deformation, both for Al1xCux transition layer and Al substrate before Cu deposition, az ¼ ai and eh ez ¼ ei .

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plane of deposition. The relationships between the biaxial strain components and the biaxial stress of the coating are given as [13,14]. ei ¼

v1 ez ; 2v

sb ¼ Bei ¼

(2)

E ei ; 1v

(3)

where ai  a0 ; ei ¼ a0

(4)

ei and sb are the in-plain biaxial strain and stress, respectively, B ¼ E=ð1  vÞ is the biaxial modulus, E the Young modulus, v the Poisson ratio, ai the average in-plane lattice parameter, and the strain ez in (2) is given by (1). Using the value obtained for ez, the parameters ai, ei and sb are calculated from (1) to (4) and listed in Tables 2 and 4. Results derived by both the Reuss and Voigt models of deriving the elastic moduli v, E, and B and their average [15] are listed simultaneously (the values for elastic moduli are presented in Table 4). 3.3. Determination of coherent domain size LS, ðdÞ domain size dispersion LS and dispersion of ðdÞ out-of-plane strain ez If distributions of coherent domains in a polycrystalline material over sizes, L, and out-of-plane strain, e, can be approximated by a Gaussian, " # 1 ðL  LS Þ2 f ðLÞ ¼ pffiffiffiffiffiffi ðdÞ exp  and ðdÞ 2p LS 2ðLS Þ2 " # 1 ðe  ez Þ2 ; (5) f ðeÞ ¼ pffiffiffiffiffiffi ðdÞ exp  ðdÞ 2p ez 2ðez Þ2 then the following expression for the broadening of the diffraction peak is valid [16]: " #  2  2 ðdÞ 2 cos yhkl LS ðLS Þ 2 bhkl ¼ bhkl 1  2:5 bhkl ; ðdÞ l2 L2S þ ðLS Þ2 (6) where 2 b2hkl ¼ 8p tan2 yhkl ðeðdÞ z Þ þ

l2 ; L2S cos2 yhkl

(7)

bhkl is the integral width of the (hkl) diffraction peak due to the small sizes of the coherent domains and the ðdÞ dispersion of their out-of-plane strain, LS and LS are the average size and size dispersion of the coherent domains, respectively, ez and eðdÞ z are the out-of-plane strain and its dispersion, respectively, yhkl is the angular position of (hkl) diffraction peak, l the wavelength of the X-ray radiation. Eq. (7) connects the broadening of the diffraction peak bhkl with the average size of the coherent domains and the dispersion of strain [17], whereas expression (6) is a generalization of (7) that also takes into account the influence of the dispersion of the coherent domains size on peak broadening. Note ðdÞ that (6) reduces to (7) if LS ¼ 0. Supposing that in Cu coating the distributions of coherent domains in terms of strains and sizes are described by Gaussians, it is possible to determine the ðdÞ parameters LS, LS , and eðdÞ from the set of three z simultaneous equations obtained by writing up Eq. (6) for any three {(hkl)} reflections. The values for integral width bhkl of five diffraction peaks recorded from Cu coating are listed in Table 1. Using the data for peaks broadening bhkl from the Table 1, the abovementioned set of equations is solved by the program Mathematica-3 [11] for the groups of reflections {(1 1 1), (2 0 0), (2 2 0)}, {(1 1 1), (3 1 1), (2 2 2)}, {(1 1 1), (2 2 0), (3 1 1)}, {(2 0 0), (2 2 0), (3 1 1)}, and {(2 2 0), (3 1 1), (2 2 2)} and the following solutions are correspondingly determined for parameters ðdÞ eðdÞ z , LS (mm), and LS (mm): {0.0029, 0.008, 0.003}, {0.0052, 0.007, 0.002}, {0.0049, 0.007, 0.002}, {0.0050, 0.007, 0.002}, and {0.0057, 0.008, 0.002}. The result of averaging over these five solutions is presented in Table 3 (see first row). Thus, these averaged data obtained for parameters eðdÞ z , LS, and ðdÞ LS should be considered as ‘‘averaged information’’ over the crystallographic directions h1 1 1i, h1 0 0i, h1 1 0i, and h3 1 1i. For comparison, the parameters eðdÞ and LS were z determined also on the basis of Williamson–Hall plot [18]. This plot has been applied separately to two groups of reflections {(1 1 1), (2 0 0), (2 2 0), (3 1 1), (2 2 2)} and {(1 1 1), (2 2 2)}. The results are listed in Table 3 (see rows 2 and 3, respectively). The ðdÞ parameters eðdÞ z , LS, and LS are determined with an accuracy of 0.0005, 0.001 mm, and 0.001 mm, respectively. It is clear that the values for parameters eðdÞ z and LS obtained for the first group of diffraction

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49

Table 3 Parameters characterizing subgrains and dislocation arrangement and density at subgrain boundaries in Cu coating Method

This case Williamson–Hall plot

Averaging over crystallographic directions h1 1 1i, h1 1 0i, h1 1 1i, h1 1 0i, h1 1 1i

h1 0 0i, h3 1 1i h1 0 0i, h3 1 1i

Parameters characterizing coherent domains (subgrains) ðdÞ

eðdÞ z

LS (mm)

Ls

4.7
103

0.007

0.002

5.2
103

0.012

5.1
103

0.013

peaks is the result of averaging over the crystallographic directions h1 1 1i, h1 0 0i, h1 1 0i, and h3 1 1i, whereas the values determined for the second group should be referred to equivalent crystallographic directions h1 1 1i only. 3.4. Excess dislocation density rS, average spacing of excess dislocations hS and shear stress sS at subgrain boundaries: estimation of plastic shear strain eG of grains In f.c.c. metals, the {1 1 1} planes are slip planes for dislocations both of edge and screw type with Burgers vectors (a/2)h0 1 1i. The dislocation density in the Cu coating can be estimated from the dispersion of the out-of-plane strain, eðdÞ z , determined in the previous section. It is clear that in order to estimate the exact density of dislocations situated at the {1 1 1} atomic planes, it is necessary to use the value of strain dispersion evaluated from the group of reflections {(1 1 1), (2 2 2)} corresponding to one and the same crystallographic directions h1 1 1i (see Table 3, third row). As was shown in previous section, in average, for all crystallographic directions h1 1 1i, h1 0 0i, h1 1 0i, and h3 1 1i practically the same value, LS  0:01 mm, is determined for the average size of the coherent domains. Therefore, we believe that it is reasonable to suppose that the Cu coating is composed of grains divided into subgrains by subgrain boundaries (dislocation walls) with piled up dislocations (see Fig. 5a). Accordingly, we identify the subgrains with the coherent domains. Besides, it is also assumed that the excess dislocation density within the subgrains is negligibly small in comparison to the excess dislocation density at the subgrain boundaries. Assuming that half the dislocations are edges and

(mm)

Subgrains misorientation, aS (8)

Parameters characterizing dislocation arrangament l (mm)

hS (mm)

rS (cm2)

1.2

0.012

0.012

6.4
1011

screws, the strain dispersion, eðdÞ z , of {1 1 1} atomic plains and the excess dislocation density, rS, at the subgrain boundaries are connected by the relationship [19]  2 b ðdÞ 2 ðez Þ ¼ (8) r2 L2 pa ln½ð2r0 rS LS Þ1  2p2 S S where b ¼ 2:556 nm is the modulus of the Burgers vector, r0 (¼107 cm) the effective radius of the dislocation core, pa (¼0.6) the angular factor dependent on the spatial relations between dislocation and diffraction plane. The excess dislocation density is defined as rS ¼ jrþ  r j, where rþ and r are the densities of the positive and the negative dislocations, respec3 tively. Substituting the values eðdÞ and z ¼ 5
10 LS ¼ 0:013 mm determined in the previous section into Eq. (8) the value rS ¼ 6:4
1011 cm2 is obtained for excess of dislocation density. The average spacing hS of dislocations at the subgrain boundaries depends on the dislocation density as 1 hS ¼ : rS LS This relationship leads to estimate hS ¼ 0:012 mm, and hence, we arrive at the important result hS  LS , that is on average one dislocation is found per subgrain face. It also follows that for dislocations arranged at the {1 1 1} planes the out-of-plane spacing hS (in directions h1 1 1i) and the in-plane spacing l are equal in average (see Fig. 5a), and rS  1=L2S . At the {1 1 1} planes, the core of an edge dislocation cannot be parallel to the core of a screw dislocation. For certainty, in Fig. 5a, the excess edge and the screw dislocations with core orientations ½
2 1 1 and ½0
1 1 and Burgers vectors (a/2)½0 1
1 and (a/2)½0
1 1 are drawn, respectively. The determined results are listed in Table 3.

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[ 2 11] (111) plane(

be bs [0 1 1]

u Subgrains Adjacent grain

hG

LG

hS

l

LS

LS S

(a)

G

bF

2R

(b)

Frank dislocation loop

Shockley partial dislocations at {111} atomic plane

d

Fig. 5. (a) The proposed model for subgrains formation in Cu coating: LS and LG indicate the dimensions of subgrains (coherent domains) and grain, respectively, hS and hG are the dislocation spacings at the subgrain and grain boundaries, respectively, aS and aG are the misorientatin angles at the low angle tilt boundaries for subgrains and grains, respectively, bs and be are the Burgers vectors of screw and edge dislocations, respectively. (b) The arrangement of Frank and Shockley dislocations in the subgrain of coating. 2R and bF are the diameter and Burgers vector of Frank dislocation loop, d is the distance between pair of Shockley partial dislocations.

V.S. Harutyunyan et al. / Applied Surface Science 222 (2004) 43–64

Since the excess dislocations are of the same sign, the forces acting between them are repelling. This interaction at the dislocation slip planes {1 1 1} relates to the shear stress [15] sS ¼

Gb pffiffiffiffiffi rS ; 2pð1  vÞ

(9)

where G is the shear modulus. It was taken into account for the derivation of (9) that, in our case, the average distance between dislocations at the slip planes {1 1 1} is LS and rS  1=L2S . Analogous to the procedure to calculate the biaxial strain in Section 3.2, the shear stress was calculated from (9) both for the Reuss and Voigt models of averaging of elastic moduli v and G and then the average result was found (Table 4). For a proposed model of dislocation arrangement it is possible to estimate the upper limit of the plastic shear strain in grains of the coating. The formation of the coating driven by the mechanical point-impact by milling medium (steel balls), except for the development of normal strains, is accompanied by plastic deformation, i.e. by the appearance and slip of a large number of dislocations. A high level of dislocation density is supported by our estimate of rS ¼ 6:4
1011 cm2 for the excess dislocation density. Within proposed model it is assumed that the grains of the coating are split into subgrains, that form vertical columns separated by low angle tilt boundaries (see Fig. 5a). Within these columns the subgrains are separated by {1 1 1} dislocation slip planes. If we suppose that a grain is composed of more or less identical columns, and each column consists of n subgrains, then the plastic shear strain of the grain can be determined from the expression u ðn  1Þb eG ¼ ¼ ; LG nLS

(10)

51

where u ¼ ðn  1Þb is the total in-plane plastic shear displacement (parallel to coating surface) of the subgrains with respect to each other in one and the same direction (from left to the right in Fig. 5a), LG ¼ nLS is the height of the grains (also of the column). The expression u ¼ ðn  1Þb for displacement is written assuming, in accordance with the proposed model, that the plastic deformation of the grain was achieved by dislocation slip along n  1 slip planes within each column. Taking into account that before deposition the dimensions of even the smallest grains in the Cu powder (LG  1 mm) were much greater than the value determined for the size of the subgrains in the coating (LS  0:01 mm), the relation n @ 1 is fulfilled. Due to the last estimate, expression (10) reduces to eG 

b : LS

(11)

It follows from the procedure of the derivation that expression (11) defines the upper limit for the plastic shear strain of the grains. The major assumption leading to this limit is the assumption of uniform shear strain within a grain. However, the real situation can be more complicated (especially because of the possible existence of excess dislocation density within individual subgrains) and in order to estimate the average plastic strain within grains it is necessary to conduct additional investigations. The value of plastic shear strain evaluated from (11) is presented in Table 4. 3.5. Strain-hardening mechanism of constraint on dislocation motion A simple analysis shows that for the estimated average shear stress of sS ¼ 0:235 GPa at the {1 1 1} slip planes (see Table 4) and in-plane dimension of

Table 4 Biaxial and shear stresses and shear plastic strain in Cu coating Model

Young modulus, E (GPa)

Shear modulus, G (GPa)

Biaxial modulus, B (GPa)

Poisson ratio, v

Biaxial stress, sb (GPa)

Peierls stress, sP (GPa)

Shear stress, sS (GPa)

Shear plastic strain, eG

Reuss Voigt Averaged

110 145

40 55

174 214

0.37 0.32

0.30 0.44 0.37

0.9
103 1.5
103 1.2
103

0.21 0.26 0.235

2
102 2
102

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subgrains, l ¼ LS  0:01 mm (Table 3 and Fig. 5a) the formation of dislocation pile-up at a subgrain face situating at the {1 1 1} slip plane is not possible. For this analysis see the relevant expressions, for instance, in [15]. Therefore, the grain-size strengthening is not an effective mechanism in the present case, and strain-hardening is believed to be the main channel for constraint on the further motion of dislocations in the coating under investigation. Hence, the strength of coating can be evaluated from s ¼ sP þ sS ;

(12)

where   2G 2p að1 1 1Þ exp  sP ¼ ; 1v 1v b

(13)

sS is given by (9), sP is the Peierls stress [15] and a(1 1 1) the spacing between the {1 1 1} atomic planes. From the estimate for sP presented in Table 4, it follows that sP ! sS and s  sS . It is necessary to mention that expression (13) is only a first approximation of the Peierls stress, since it does not take into account the peculiarities of the local distortions of the crystal lattice [15]. However, most probably this account would not change the estimations sP ! sS and s  sS presented above. 3.6. Misorientations aS and aG between subgrains and grains As was mentioned in Section 3.4, in compliance with the proposed model (Fig 5a) for subgrain formation within a coating grain, it is assumed that the subgrains are separated by low angle tilt boundaries with piled up dislocations which form dislocation walls (formation of dislocation networks is not excluded either). Therefore, the tilt angle aS between adjacent subgrains can be estimated from the wellknown simple expression [15] aS 

b : hS

(14)

From (14) a value aS ¼ 1:2 is obtained for subgrain misorientation. Since a series of X-ray diffraction ‘‘polycrystalline’’ peaks were recorded from the Cu coating (Fig. 3), it is clear that the coating grains do not exhibit a strong texture and most probably are separated by high-angle

tilt boundaries (for these boundaries the tilt angle aG > aS ), where piled up dislocations are arranged with a spacing hG < hS (see Fig. 5a). However, within the present research the tilt angle of grains aG cannot be evaluated since the value hG is not known. 3.7. The possibility of partial dislocations within the coating subgrains In spite of our supposition (see Section 3.4) that half the dislocations are edges and screws in the coating, it is not excluded that the number of edge-type dislocations is larger than the number of screw dislocations. The dominant amount of edge dislocations might be due to more effective annihilation between screw dislocations with opposite signs under condition of a high stress. Therefore, it is interesting to compare the width of the splitting area (i.e. the extension of the stacking fault) between two Shockley partial dislocations with the average size of the subgrains, LS, in order to consider the possibility of splitting of perfect edge dislocation both inside a subgrain and at the subgrain boundary. For f.c.c. metals it is known that the perfect edge dislocation at the {1 1 1} slip planes can split into two Shockley partial dislocations in accordance to the dislocation reaction of the type: a a a ½0 1
1 ¼ ½
1 2
1 þ ½1 1
2; (15) 2 6 6 where a is the crystal lattice spacing, and the left and right sides of the equation represent the Burgers vectors of the perfect and partial dislocations. The distance between a pair of Shockley partial dislocations is given as [20]   Gb2 2  v 2v d¼ 1 cos 2j ; (16) 2v 8pg 1  v where g is the energy of the stacking fault between partial dislocations (we use a value g ¼ 70 erg/cm2 for Cu) and j is the angle between the full Burgers vector b and the strip of the stacking fault. For the dislocation reaction given by (15) j ¼ p=2. Using (16), the estimations of d obtained both for Reuss and Voigt models of averaging the elastic moduli v and G are listed in Table 5. In comparison to coherence length (i.e. the average size of the subgrains for our model), LS  0:01 mm, the estimated distance between the

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53

Table 5 Geometrical parameters of partial dislocations in coating Type of partial dislocation

Burgers vector

Shockley Frank

(a/6)h1 1 2i (a/3)h1 1 1i

Parameter of dislocation

Value/dispersion of parameter

Equilibrium distance for dislocations, d (mm) Diameter of disloca-tion loop, 2R (mm)

Shockley partial dislocations, d  0:006 mm, is less. However, the actual value of parameter d may differ from this calculated value, since expression (16) does not take into account the strong interaction of Shockley partial dislocations with the neighboring dislocations which is very probable in case of the high dislocation density rS ¼ 6:4
1011 cm2 determined for our case. Nevertheless, on the basis of our estimate d < LS we believe that the dislocation reaction (15) is possible under the conditions specified for the coating under investigation. A pair of Shockley partial dislocations is schematically drawn in Fig. 5b at the {1 1 1} atomic planes inside of subgrain. The other interesting question is the possibility of forming Frank dislocation loops with the Burgers vector (a/3)h1 1 1i in the coating. It is clear that due to high local temperature and stress gradients, the process of deposition by the proposed method is accompanied by the creation and partial annihilation of point defects, interstitials and vacancies. In turn, due to local temperature decrease and depending on character of the normal stress (compressive or tensile type) acting along the h1 1 1i crystallographic directions, the clusters of vacancies and interstitial atoms can be transformed at the {1 1 1} planes into the Frank dislocation loops. It seems that the most probable mechanism of forming a Frank dislocation loop is transformation of clusters of vacancies, since during the process of deposition the steel balls, impacting along the normal of the coating plane, ‘‘compress’’ the clusters of vacancies into dislocation loops with orientation parallel to the surface of deposition (the planes of loops are parallel to {1 1 1} atomic planes; see Fig. 5b). The linear dimensions of a Frank dislocation loop, corresponding to its stable state at the {1 1 1} plane, can be estimated from the following criterion [21]: ! rffiffiffi   2 2 1 Gb2 2R R2  ln g ; (17) 3 3 b0 4pð1  vÞ

Reuss model

Voigt model

0.0056 0.0008 < 2R < 0.018

0.0070 0.0008 < 2R < 0.026

where R is the radius of the dislocation loop, and the modulus of the Burgers vector b ¼ a. The estimates of the dispersion of the linear dimension of the dislocation loop, 2R, are obtained both for Reuss and Voigt models of averaging the elastic moduli v and G (see Table 5). If it is supposed that the dispersion of the loop diameter should be restricted by subgrain size, i.e. 2R < LS  0:01 mm, then the prediction 8
104 mm  2R  102 mm is obtained for limits of the diameter of dislocation loops which might originate in the coating under investigation. 3.8. Deformation states of Al substrate before Cu deposition and near Cu/Al interface in Cu/Al system Using the data on the angular positions of the diffraction peaks identified in recorded spectrum as Al diffraction peaks (Table 1, second row) and applying the same extrapolating method (applied for the coating in Section 3.1), one can obtain the out-of-plane average lattice parameter of Al substrate, az ¼ 0:40548 nm. For the relevant strain component the value ez ¼ 1:3
103 was calculated as the unstrained lattice parameter of Al is a0 ¼ 0:40494 nm [in our further consideration (see Section 4.3) these data of parameters az and ez are attributed to Al1xCux transition layer]. For comparative analysis, the lattice parameter of Al substrate was also determined from the X-ray spectrum recorded before Cu coating deposition (for relevant diffraction peak positions see the third row in Table 1). In this case for lattice parameter and strain the values az ¼ 0:40511 nm and ez ¼ 4:2
104 were determined, respectively. From the data presented above it follows that the lattice parameter in a top layer of substrate (this layer is below Cu/Al interface) has undergone a considerable change after coating deposition. The thickness of this layer, i.e. the effective penetration depth of X-rays into the substrate, can

54

V.S. Harutyunyan et al. / Applied Surface Science 222 (2004) 43–64

be estimated from absorption of X-rays in Cu coating and Al substrate. For the Cu coating thickness tCu  11:7 mm (see Section 3.1) and the normal linear absorption coefficient mCu ¼ 719 cm1 for Co Ka radiation [17], the absorption factor is found to be mCutCu ¼ 0:84. The estimated value of the factor mCutCu corresponds to intermediate level of absorption of X-rays in the coating and, hence, assumes further penetration of radiation into the substrate. Using the value mAl ¼ 204 cm1 [17] of the normal linear absorption coefficient in Al and taking into account absorption in the coating, it was estimated that the effective penetration depth of X-rays into the subðefÞ strate, tAl , is about 7 mm and, hence, is much less than the thickness of the substrate tAl ¼ 3 mm. Thus, the lattice parameter and the relevant strain found from positions of the Al diffraction peaks in the spectrum recorded from the Cu/Al system (see Fig. 3) should be attributed to thin interfacial layer of Al substrate of ðefÞ thickness tAl ¼ 7 1 mm. 4. Formation of Al1xCux alloy near Cu/Al interface 4.1. Local adiabatic temperature rise at Cu/Al system due to individual impact with the steel ball As was mentioned in Section 1, during deposition the mechanical impact conditions initiate and accelerate in coatings such physical processes as local melting (or at least local temperature increase) and solid phase diffusion. Mass diffusivity of a material is parameter substantially dependent on temperature. Therefore, in order to evaluate thermally activated diffusive run of Cu and Al atoms during their interdiffusion near Cu/Al interface it is necessary to estimate the level of impact temperature, Tim, and the effective time of diffusion, during which the temperature Tim is maintained at the given local region near Cu/Al interface. An individual impact of a rigid ball (impactor) with a target at loading s01 GPa, characteristic times of deformation (i.e. time of impact) tim 9103 s, and deformation rates e_ 0103 s1 excites in the target an intensive compression shock wave propagating with supersonic velocity in direction parallel to impact

velocity vim [22] (Fig. 1b, vim is parallel to z-axis). This wave disturbs corresponding thermal (temperature) wave propagating in the same direction. In a polycrystalline material, especially in a metallic media, both waves decay exponentially over depth. Therefore, a major part of mechanical energy of the compressive shock wave undergoes adiabatic transformation into the heat in the microscopic volume, Vim, localized in the vicinity of the impact area. In the schematic diagram presented in Fig. 1b, ANB and ANBCD are the cross-sections of the impact area and volume Vim at xz plane, respectively, and AMBCD is correspondingly the cross-section of the initial volume V0 transformed by impact into the volume Vim. Due to adiabatic heat release in the volume Vim, temperature here drastically increases up to temperature Tim, which is defined as impact temperature. In case of plastic deformation and temperature dehardening of the material at high Tim, it may be assumed that the in-plane linear sizes for both volumes V0 and Vim are the same and defined by the radius Rim of a circular impact area (in Fig. 1b Rim MA). It automatically means that, first, both volumes V0 and Vim are of near-cylindrical shape and, next, for x- and y-components of the impact ðimÞ ðimÞ strain it is fulfilled the condition ex ¼ ey ¼ 0. The in-depth size (along z-axis), lz0, of the volume V0 it is reasonable to introduce as distance which passes the shock initiated heat wave over impact time, tim: pffiffiffiffiffiffiffiffiffiffiffi lz0  kT tim ; (18) where kT is the thermal diffusivity of the material of target (in Fig. 1b, MK lz0 ). In other words, in (18) the parameter lz0 is defined as characteristic length of the impact temperature field Tim, which is attained and maintained in the local volume Vim of target over the impact time, tim. From Fig. 1b, the z-component of the impact deformation, eðimÞ may be introduced as z eðimÞ  z

lz  lz0 hmax ¼ ; lz0 lz0

(19)

where lz is the characteristic in-depth size of the volume Vim, hmax the maximal penetration depth of the ball into the target, and lz0 is given by (18) (in Fig. 1b NK lz and MN hmax ). Due to aboveintroduced assumption for the in-plane strain comðimÞ ðimÞ ponents, ex ¼ ey ¼ 0, the relative volumetric

V.S. Harutyunyan et al. / Applied Surface Science 222 (2004) 43–64

compression x Vim =V0 is connected with the impact strain z-component by the relationship x ¼ 1 þ eðimÞ : z

(20)

Thus, individual impact of a rigid ball with a target (in particular, with a flat target) at large loading and high deformation rate leads to local adiabatic transition (compression) of the target material from thermodynamic state (V0, T0) to state (Vim, Tim), where it is assumed that T0 is the initial temperature. Experimentally, it is established that there is a strong dependence Tim ¼ f ðxÞ of the impact temperature on parameter x. For many metals (in particular for Cu and Al) this dependence is well known [22]. Therefore, once the parameters tim and hmax are determined, the impact temperature, Tim, can be estimated from expressions (18) to (20) and dependence Tim ¼ f ðxÞ. In turn, it will enable to calculate the mass diffusivity at the temperature Tim and, hence, to estimate the thermally activated diffusive run of atoms (in our case, it is interdiffusion of Cu with Al) under conditions of mechanical impact. As a first approximation, in case of individual direct impact of a rigid (undeformable) ball with a deformable flat plate the parameters hmax and tim introduced above can be estimated from the following expressions [23]: hmax ¼ ZDb ; tim ¼ 1:47

hmax ; vim

(21) (22)

where    2=5 1 5p 2=5 1  v2 1  v2b 2=5 4=5 Z

þ rb vim ; 2 4 E Eb rb, vb, and Eb are the density, the Poisson ratio, and the Young’s modulus of material of the ball, respectively, Db is the ball diameter, v and E are the Poisson ratio and the Young’s modulus of the plate material, respectively, and vim is the initial velocity of impact (the velocity of ball with respect to plate). Eqs. (21) and (22) are derived on the assumption that the direction of vim is normal to the plate surface. In derivation of (22) it is assumed that over time tim the depth of ball penetration into the plate increases from zero to hmax. From expressions (21) and (22), it is clear that parameters hmax and tim can be estimated once the

55

velocity vim is known. In turn, the parameter vim could be introduced for our process of coating deposition in the following way. From the physical standpoint, it is obvious that the balls in coating chamber during coating growth are involved in process of constrained oscillations with the frequency of chamber oscillations (see Section 2 and Fig. 1a). Besides, it is reasonable to assume that z-component of the average velocity (with respect to Al substrate) of oscillating balls,
vz , is dependent mainly on the following three parameters: the average ball diameter, the frequency of oscillations of the chamber, and the ratio Vb =Vch , where Vb is the space in chamber filled by balls and Vch the volume of chamber. Next, for introduction of the parameter
vz in a relatively simple way the following assumptions can be made over the whole deposition process: (i) all balls execute preferably oscillating motion in vertical direction (along z-axis); (ii) in the vertical direction the collisions of balls with each other and the coating under deposition are either central or quasi-central impacts; mutual collisions of balls are elastic; (iii) in the average, each ball oscillates about individual oscillation center j localized in the region hDVj i ¼ Vch =Nb , where j ¼ 1; 2; . . . ; Nb and Nb is the total number of balls; it is assumed that positions of all oscillation centers do not change in time; (iv) oscillation centers of balls (Nb centers for Nb balls) are distributed uniformly (with threedimensional quasi-periodicity) over the volume of chamber; (v) the balls undergoing simultaneous (synchronous) collisions with the substrate execute with respect to substrate antiphase motion, i.e. at the beginning of the impact process the balls and the substrate move in opposite directions. The average velocity of oscillating balls, v
z , introduced above by its sense is identical with the velocity vim defined in (21) and (22). Therefore, taking into account that for our case the ratio Vb =Vch ¼ 2=3 (see Section 2), one is obtained for the impact velocity on the bases of above-presented assumptions (i)–(v): vim
vz ¼ vb þ vs ;

(23)

56

V.S. Harutyunyan et al. / Applied Surface Science 222 (2004) 43–64

where vb ¼ 4vch Ab ;

vS ¼ 4vch AS ;


b; Ab  ð16ÞD (24)

vb and vS are the average velocities of oscillation of the balls and the substrate in a laboratory coordinate system, respectively, vch is the frequency of the cham
b the average diameter of ber (substrate) oscillations, D balls, Ab and AS are the average amplitudes of oscillation of the balls and the substrate, respectively. It is important to note that due to assumption (v), in (23) both vb and vS are positive values. Steel is much stiffer than Cu and Al, therefore, we may assume that at ‘‘ball–substrate’’ collisions the balls do not undergo any considerable plastic deformation. Provided that hmax ! Db and Rim ! Db (for steel balls these conditions are realistic), one is obtained for the radius of individual impact area, Rim, from simple geometrical calculations Rim ¼ ðDb hmax Þ1=2 ;

(25)

where hmax is introduced in (19). The average rate of deformation over an individual impact process can be introduced as e_ ¼

eðimÞ z tim

:

Al the thermal diffusivity, kT, is the same within an accuracy of 5%, therefore, in application of Eq. (18) we may do not distinguish from each other materials of the coating and substrate. Substituting into the set of Eqs. (18)–(26), where necessary, the data vb ¼ 0:28, Eb ¼ 206 GPa, rb ¼ 7800 kg/m3, v ¼ 0:34, E ¼ 127:5 GPa, kT ¼ 1024 m2/s, vch ¼ 25 Hz, and AS ¼ 0:002 m, the parameters tim, lz0, Rim, eðimÞ , e_ z and x were determined for the three indicated values of the ball diameter. The calculated data are listed in the Table 6. From comparison of the coating measured (final) thickness, tCu  11:7 mm, with the estimated values of lz0 (see Table 6) and taking into account (18), the following important relationship is achieved for arbitrary fixed point M at the coating surface: ðMÞ

ðiÞ

ðCuÞ

lz0 lz0 ¼ lz0

ðAlÞ

þ lz0 ;

(27)

where ðCuÞ

lz0

ðAlÞ

lz0

  ti ðiÞ

tCu ¼ tCu ; tdep  qffiffiffiffiffiffiffiffiffiffiffi  ti ðiÞ ¼ kT tim  tCu ; tdep

i ¼ f1; 2; . . . ; Nim g;

(26)

As it follows from (18) to (26), all parameters hmax, tim, lz0, Rim, eðimÞ , e_ and x are dependent on the ball diameter z monotonically: hmax, Rim and tim are proportional to 1=2 Db, lz0 and eðimÞ are proportional to Db , e_ is proporz 1=2 tional to Db , and x is proportional to 1  const:
1=2 Db . In deposition of the Cu coating we have used the steel balls with diameters in the range 8  Db  15 mm (see Section 2), and it would be representative to compare the above-mentioned parameters calðminÞ culated for the minimal Db ¼ 8 mm, the maximal ðmaxÞ
b ¼ 11:5 mm Db ¼ 15 mm, and the average D values of the ball diameter. Fortunately, for Cu and

(28) ðMÞ lz0

is parameter lz0 attributed to fixed point M for i-th ðCuÞ ðAlÞ ‘‘ball–substrate’’ collision, lz0 and lz0 are the out-ofplane extensions of the impact temperature field Tim over the Cu coating and the Al substrate, respectively ðCuÞ ðAlÞ ðMÞ (in Fig. 1b lz0 MP, lz0 PK, and lz0 MK), ðiÞ tdep is the coating deposition time, tCu the instantaneous average thickness of the coating at the moment ti (0  ti  tdep ) when i-th ‘‘ball–coating’’ collision ðiÞ takes place in the vicinity of the point M, tim the impacttime(duration) ofi-th ‘‘ball–substrate’’ collision, and Nim the total number of the ‘‘ball–substrate’’ collisions in the vicinity of the point M over the time tdep.

Table 6 Parameters characterizing individual ‘‘ball–substrate’’ impact depending on ball diameter Db (mm)

tim (s)

lz0 (mm)

Rim (mm)

eðimÞ z

e_ (s21)

x

Tim (K)

D at Tim (m2/s)

8 11.5 15

1.9
105 2.7
105 3.5
105

43 52 59

199 286 373

0.11 0.14 0.16

6.2
103 5.2
103 4.5
103

0.89 0.86 0.84

660 900 960

5.2
1011 1.6
109 2.9
109

V.S. Harutyunyan et al. / Applied Surface Science 222 (2004) 43–64

Temperature, Tim ( K)

In (28) it is assumed that the ends of the time intervals ðiÞ tim and ti coincide. It is also assumed that for all these collisions the observation point M is situated at the impact area. From (27), (28), (21) and (22) it follows ðMÞ that eventually the parameter lz0 depends on the ball diameter only and varies discretely over the deposition process as a consequence of discrete variation of the parameter Db from collision to collision. Thus, supposing that for observation point M the successive collisions alternate for balls with different ðiÞ diameters, Db , in accidental manner, the process of the coating deposition over the whole deposition time, ðiÞ ðiÞ tdep, may be characterized by the set of data {Db , tim , ðiÞ ðiÞ ðiÞ ðimÞ ðiÞ lz0 , Rim , Vim , ez;i , e_ i , xi, Tim } for Nim collision events ðiÞ ðiÞ ðiÞ (i ¼ 1; 2; . . . ; Nim ), where Vim ¼ pðRim Þ2 lz0 . In comðiÞ pliance with (27), in this set of data the parameter lz0 defines the in-depth extension of the temperature field ðiÞ Tim for i-th ‘‘ball–substrate’’ collision event. The ðiÞ impact temperature, Tim , is introduced below. Both for Cu and Al the dependence Tim ¼ f ðxÞ is practically the same [22], and we may assume that for an individual collision the adiabatic temperature Tim is distributed homogeneously over the whole volume Vim. The relevant values of Tim presented in the Table 6 are taken from the reference [22]. We did not present here the dependence Tim ¼ f ðxÞ in analytical form since it is available in the cited work in tabulated form only. Using the relevant data from Table 6, the plot Tim versus Db for the values ðminÞ
ðmaxÞ Db , D of the ball diameter is presented b , and Db 1600 1400 1200 1000 800 600 400 200 0

Tm,Cu

0

2

4

in Fig. 6 along with the corresponding interpolating curve. As can be seen from the behavior of this interpolating curve, the impact temperature is about
b ¼ 11:5 mm melting point of Al, Tm;Al ¼ 933 K, at D and exceeds this value for collisions of balls with Db  12:5 mm. Thus, as it follows from the behavior of interpolating curve Tim (Db) presented in Fig. 6, any individual ‘‘ball–coating’’ collision in deposition process under consideration causes localized adiabatic temperature increment DTðDb Þ ¼ Tim ðDb Þ  T0 (in our case T0 ¼ 300 K, where T0 is the room temperature) substantially dependent on the ball diameter. The temperature increment, DT(Db), increases from 360 to 660 K when the ball diameter changes from 8 to 15 mm, respectively. 4.2. Temperature-activated diffusion of Cu atoms into Al substrate As it follows from estimates for parameters lz0 and Tim (see Table 6), even at ‘‘ball–coating’’ collisions for balls with minimal diameter the temperature field Tim considerably penetrates into the Al substrate. Therefore, it should be expected that due to a high level of the estimated in Section 4.1 temperature increment the process of coating deposition is accompanied at Cu/Al interface by intensive temperature activated interdiffusion of Cu atoms into the Al substrate and Al atoms into the Cu coating. For concentration diffusion (i.e. diffusion due to gradient of the impurity concentration) the diffusive run of impurity atoms is determined as l2d  DðTÞtd ;

Tm,Al

6

8

10 12 14 16 18 20

Steel ball diameter, Db ( mm ) Fig. 6. Plot of the impact temperature vs. ball diameter and the corresponding interpolating curve. In the plot, three solid dots ðminÞ
b ¼ 11:5 mm, and correspond to ball diameters Db ¼ 8 mm, D ðmaxÞ Db ¼ 15 mm. Horizontal lines indicate the melting points of Cu and Al.

57

(29)

where ld is the diffusive run of impurity atoms, D(T) the diffusivity at temperature T, and td the duration of the diffusion process. In (29) the parameter ld is substantially dependent on the temperature through the diffusivity. On the basis of expression (29), let us first estimate the diffusive run of Cu atoms into the Al substrate. In terms of diffusion process the diffusive run of Cu atoms into the Al substrate over the whole deposition ðiÞ ðiÞ process is characterized by the set of data {tim , Tim , ðiÞ Di ðTim Þ} for Nim ‘‘ball–coating’’ collision events (i ¼ 1; 2; . . . ; Nim ), where the diffusivity Di of Al for i-th collision (i.e. over the corresponding localized

58

V.S. Harutyunyan et al. / Applied Surface Science 222 (2004) 43–64 ðiÞ

volume Vim ) is also assumed to be dependent on the ðiÞ ðiÞ ðiÞ ball diameter, Db , through the dependence Tim ðDb Þ. For certainty, as in previous section, the set of data ðiÞ ðiÞ ðiÞ {tim , Tim , Di ðTim Þ} is attributed to fixed observation point M at the coating surface. In turn, for the fixed observation point we may define in the Al substrate the diffusive path PQ as follows (see Fig. 1b): PQ 

Nim \ ðiÞ Vim

and

ðCu!AlÞ

jPQj ld

;

i¼1 ðCu!AlÞ

where |PQ| is the length of the segment PQ, ld the diffusive run of Cu atoms into the Al substrate, Nim ðiÞ and Vim are parameters introduced in the previous section. Therefore, neglecting the diffusive run of atoms at room temperature, on the basis of expression (29) the temperature activated diffusive run of Cu atoms into the Al substrate may be determined to a first approximation as

i¼1

(30) where ðiÞ

ðiÞ

ðiÞ

Nim ¼ p Ndep ;

(31)

td is defined as duration of the diffusion process thermally activated due to i-th ‘‘ball–coating’’ collision, and the symbol h  i means the averaging over ðiÞ the Nim collision events. In (31) the parameter td is ðiÞ identified to impact time of the i-th collision, tim , since ðiÞ after each collision the localized temperature field Tim

(32)

where Ndep ¼ vch tdep ;

(33)

2

p¼

Nim X ðCu!AlÞ 2 ðiÞ ðiÞ ðiÞ ðiÞ ðld Þ  Di ðTim Þtim ¼ Nim hDi ðTim Þtim i;

tim td ;

in a metallic medium exponentially decays (relaxes) to room temperature over a characteristic time, trel, of order of 105 s [24]. Thus, in accordance with expression (30) the temperature activated diffusive run of Cu atoms into the Al substrate is achieved due to successive isothermal diffusion processes initiated by Nim ‘‘ball–coating’’ collision events. The diagram presented in Fig. 7 schematically shows variation of ðiÞ the temperature field Tim over the whole deposition time at the diffusive path PQ corresponding to a fixed observation point M at the coating surface (Fig. 1b). The average number of collisions Nim can be determined from the following relationships:

hpð2Rim Þ i ¼ 4pZ; hD2b i

(34)

Ndep is the number of ‘‘ball–coating’’ collision events per ball over the area hD2b i during deposition time tdep of the Cu coating, parameters vch , Rim and Z are introduced in (24), (25), and (21), respectively. In derivation of (34), we have used Eqs. (21) and (25). Parameter p given by (34) is the probability that a ‘‘ball–coating’’ collision from the set Ndep involves in its impact area the fixed observation point. Taking into account that for our process of coating deposition tdep  2850 s and vch ¼ 25 Hz and using from the previous section the relevant data for calculation of the parameter Z, the following results are obtained

Fig. 7. Schematic diagram of the impact temperature time-dependant oscillations in Cu/Al system over deposition process for a fixed observation point at coating surface. For i-th ‘‘ball–substrate’’ collision event the corresponding step-like profile of the temperature oscillation ðiÞ ðiÞ is characterized by the height Tim and the widthtim .

V.S. Harutyunyan et al. / Applied Surface Science 222 (2004) 43–64

59

from (32) to (34): Ndep ¼ 71250, p ¼ 7:76
103 , and Nim  553. From (32) and (34), we may estimate the average period, tper, between two ‘‘ball–coating’’ successive collisions over the set Nim: tdep 1 : (35) tper ¼ ¼ Nim vch p

Using (21) and (22), the function tim ðDb Þ in the integrand of (38) may be rewritten as

Substituting into (35) vch ¼ 25 Hz and p ¼ 7:76
103 , it is obtained that tper  5:2 s. Thus, for the diagram presented in Fig. 7 we have also estimated the next two important parameters, Nim and tper. From the obtained estimate tper  5:2 s an important relationship

and parameter vim is given by (23) and (24). For deposition process under consideration the coefficient given by (41) is calculated to be k1 ¼ 0:002318 s/m. In terms of diffusion process the covalent radii of the Cu and the Al atoms (rCu ¼ 0:135 nm, rAl ¼ 0:126 nm) are close to each other. Therefore, at a high level of the temperature field Tim (Fig. 6) we may in (37) replace the diffusivity of Cu atoms into the Al by the self-diffusion coefficient of Al, which is given as [25]:   9:7
1015 9:07Tm;Al DðDb Þ ¼ exp  ; (42) d T

ðiÞ

tper @ tim  trel  105 s;

(36) ðiÞ tim ),

is found (see Table 6 for parameter where trel is the characteristic time (discussed above) of the temperature decay to a room temperature. Due to condition (36), for the temperature time oscillations a step-like profile may be proposed (Fig. 7). From the diagram presented in Fig. 7 it follows that in the time scale, between the i-th and (i þ 1)-th ‘‘ball–coating’’ successive collisions, we may assume that at the observation diffusive path the room temperature is maintained over ðjþ1Þ the time interval tper  tim due to high rate of ðiÞ decay of the temperature field Tim . Relationship (36) supports expression (30), which assumes that effective (i.e. thermally activated) diffusive run of the Cu atoms intoPthe Al substrate takes place only over the time im ðiÞ  Ni¼1 tim . Due to a large value Nim  553 estimated above for collision events, in (30) the sum may be replaced by integration as follows: ðCu!AlÞ 2

ðld

ðiÞ

ðiÞ

Þ  Nim hDi ðTim Þtim i  Nim hDðDb Þtim ðDb Þi;

(37)

where hDðDb Þtim ðDb Þi ¼

Z

ðmaxÞ

Db

ðminÞ

f ðDb ÞDðDb Þtim ðDb Þ dDb ;

Db

(38) ðmaxÞ

f ðDb Þ ¼ ðDb

ðminÞ 1

 Db

Þ ;

tim ðDb Þ ¼ k1 Db ;

(40)

where k1 1:47Zv1 im

(41)

where T is the absolute temperature, Tm,Al the melting temperature of Al, and d the diffusive thickness of grain boundaries in Al expressed in units [m]. From broadening of Al diffraction peaks recorded in X-ray diffraction spectrum (Fig. 3) it was found that coherent domains of Al substrate is about 0.08 mm in size. Such small dimensions of domains in a polycrystalline material favour more effective diffusion process over the grain boundaries in comparison to volume diffusion. Therefore, we believe that in our estimates of the atomic diffusive run it is more realistic to apply the grain boundary diffusivity given by (42). Substituting into (42) parameters d ¼ 0:5 nm [25] and Tm;Al ¼ 933 K, the grain boundary diffusivity is calculated for the temperatures Tim ¼ 660, 900 and 960 K (i.e. for the ball diameters Db ¼ 8, 11.5 and 15 mm, respectively) indicated in Table 6. The results obtained for diffusivity are listed in Table 6. Further, from the data available in Table 6 for parameters Db and D, the following linear dependence is established applying interpolation procedure: DðDb Þ ¼ k2 Db þ b2 ;

(43) 7

(39)

f(Db) is the distribution function of balls over size, ðminÞ ðmaxÞ Db, in the range (Db ¼ 8 mm, Db ¼ 15 mm). In (39), the distribution f(Db) is defined as uniform in accordance with the experimental conditions.

where k2 ¼ 3:71
10 m/s and b2 ¼ 2:67
109 m2/s. Finally, substituting expressions (39), (40), and (43) into integrand in (38) and using the determined value of collision events Nim  553, after the integration one is estimated from (37) for the diffusive run of Cu

60

V.S. Harutyunyan et al. / Applied Surface Science 222 (2004) 43–64 ðCu!AlÞ

atoms into the Al substrate ld  5:1 mm. Assuming that in coating deposition process all points at the coating surface were, in average, at the same physical conditions, it should be expected formation of a Al1xCux transition layer with the homogeneous ðCu!AlÞ thickness of ld (x is the relative concentration of the Cu atoms). In order to estimate the diffusive run of Al atoms ðAl!CuÞ into the Cu coating, ld , it is necessary in (42) to replace the parameter Tm,Al by the melting temperature of Cu, Tm;Cu ¼ 1356 K. Then, from (37) to (42) we ðAl!CuÞ come in analogous way to the estimate ld  0:6 mm, which by an order of magnitude less than ðCu!AlÞ the diffusive run ld . 4.3. Al1xCux transition layer As is estimated in the Section 4.2, the diffusive run of Cu atoms into the Al substrate is about ðCu!AlÞ ld  5:1 mm. Due to a high level of the impact temperature and, hence, a huge increase of the equilibrium concentration of vacancies both in coating and Al substrate, the most probable mechanism for diffusion of the Cu atoms is the substitutional diffusion, i.e. diffusion over vacant positions of the Al atoms. For instance, the relevant estimates show that at temperatures T0 ¼ 300 K (room temperature) and hTim i  800 K the equilibrium relative concentration of vacancies in Al is about 1011 and 1:2
104 , respectively. Therefore, it is reasonable to assume that Al1xCux transition layer resulting from substitutional diffusion is a substitution alloy. On the other hand, in Section 3.8, it is justified that the out-of-plane strain ez ¼ 1:3
103 measured for Al substrate should be attributed to a thin near-interðefÞ facial layer of Al substrate of thickness tAl ¼ 7 1 mm. Comparing the results determined for ðCu!AlÞ ðefÞ parameters ld and tAl , as a first approximation, we may accept for the sample under consideration the following condition: ðCu!AlÞ

ld

ðefÞ

 tAl ;

ðCu!AlÞ

(44)

where ld is in fact the thickness of the transition layer Al1xCux. Hence, due to condition (44) the residual strain ez ¼ 1:3
103 measured for Al substrate may be considered as a value characterizing the deformation state of the Al matrix in transition layer

Al1xCux caused by incorporation effect of the Cu atoms. The positive sign of the measured strain ez and the condition rCu > rAl , which is fulfilled for covalent radii of the Cu and the Al atoms, count in favour of above presented assumption on transition layer Al1xCux to be a substitution alloy. Supposing that the measured strain, ez, is induced in Al matrix by substitutional Cu atoms, the compound parameter, x, of the Al1xCux transition layer can be determined from the Vegard’s law [26]: "  # 1 rCu 3 1 x; (45) eh ez ¼ 3 rAl where eh is the hydrostatic strain caused by substitutional point defects, and x the compound parameter indicating the relative concentration of the Cu atoms. Substituting the data ez ¼ 1:3
103 , rCu ¼ 0:135 nm, and rAl ¼ 0:126 nm into (45), one is obtained for compound parameter x  0:02.

5. Discussion As a most probable mechanism for the formation of Cu coating under mechanical impact, a ‘‘cold welding’’ mechanism is proposed. This mechanism implies process of deposition, which is accompanied by collisional heating and possible local melting in the absence of external heating. On the basis of approach developed in the Section 4.1 the estimates tim  105 s and e_  103 s1 are obtained for duration of the individual collision event and the deformation rate of the Cu/Al system, respectively (Table 6). On the basis of these estimates it was assumed that over each ‘‘ball–coating’’ collision event a major part of mechanical energy of the compressive shock wave undergoes adiabatic transformation into the heat within a microscopic volume Vim localized in the vicinity of the corresponding impact area. Due to this adiabatic heat release, the temperature over the volume Vim drastically increases up to a characteristic impact temperature, Tim, substantially dependent on the diameter of the ball under collision with the Cu coating (Fig. 6). From the one side, in accordance with (27) and (28), for all collisions the temperature field Tim penetrates both into Cu coating and Al substrate. From the other side, the plot in Fig. 6 shows that for

V.S. Harutyunyan et al. / Applied Surface Science 222 (2004) 43–64

collisions of balls with Db  12:5 mm the temperature Tim drops into the interval Tm;Al  Tim  960 K. Therefore, localized melting of the Al substrate in the vicinity of the Cu/Al interface is predicted for a considerable number of ‘‘ball–coating’’ collisions in the deposition process under consideration. In this prediction the key role belongs to expressions (19) and (18), which define the value of the plastic impact deformation, eðimÞ , and the in-depth extension of the z impact deformation filed in Cu/Al system, respectively. Taking into account, that parameters eðimÞ z and Tim are introduced for the same volume Vim, the deformation eðimÞ may be qualified as localized z thermoplastic deformation. In compliance with the diagram presented in Fig. 7, the process of coating deposition is accompanied by local heating/melting and quenching at very high rates, leading to the development of interfacial junctions which might be qualified as spot-welds forming the proposed transition layer of Cu/Al alloy. It should be expected that those ‘‘ball–coating’’ collisions, which lead to local melting of the Al substrate, most probably initiate effective adhesion of the Cu coating to the substrate. It may be assumed that during coating growth the quasi-periodical oscillations of the impact strains (stresses) and the impact temperature field (Fig. 7) activate both in Cu coating and Al near-interfacial layer the strain-hardening and dehardening processes with the same time-periodicity tper given by (35). It is known that for metals at high temperatures T00:5Tm (Tm is the melting temperature of a metal) the process of deformation is accompanied by strain dehardening through the two mechanisms: polygonization and recrystallization [27]. In compliance with the plot in Fig. 6, the above-mentioned condition, Tim 00:5Tm , is fulfilled in the case under consideration both for the Cu coating and the Al near-interfacial layer at all ‘‘ball–coating’’ collision events. Any mechanism of recrystallization cannot be discussed in the present research since the obtained experimental results do not allow judge whether in the Cu/Al system during formation of the coating any migration of high-angular grain boundaries takes place. However, in terms of the proposed model for dislocation configuration in the Cu coating (see Section 3.4; Fig. 5), the process of strain dehardening through the mechanism of polygonization seems realistic. Indeed, due to a high level of estimated impact temperature, Tim, it should be

61

expected that the dislocations, along with thermally activated slip in {1 1 1} atomic planes, are also involved in intensive process of climb leading to a strain relief (dehardening) in the Cu coating. The other important question is whether over an individual ‘‘ball–coating’’ collision event (i.e. impact time tim) the generation and annihilation of dislocations are in balance within the relevant impact volume, Vim. If such balance is achieved, then it should be expected that the dislocation density in the Cu coating, along with the coating hardness, remains practically constant over the whole deposition process. Otherwise, in compliance with expressions (9) and (12), we should expect that depending on behavior of dislocation density the coating hardness undergoes variation over deposition process and eventually depends on deposition time. As is considered in Sections 3.4 and 3.6, in the Cu coating the dislocation density controls also the average size of subgrains and their misorientation. Therefore, it may be predicted that if the dislocation density does not change over deposition time, then the morphology of coating in its arbitrary localized region undergoes periodical transformations (with the time-periodicity tper given by (35)) in such a way that between successive ‘‘ball–coating’’ collisions the coating recovers its morphology. In other words, equilibrium grain dimensions and misorientations are achieved immediately after each collision event, i.e. so-called repoligonization process takes place. Repoligonization process assumes periodical destruction and formation of subgrain boundaries in a material [28]. In opposite case, the time-dependent dislocation density should most probably lead to essential morphological changes in the Cu coating depending on deposition time. In our next work, we shall consider these questions on the basis of measurements for a series of Cu/Al coatings grown for different deposition times. Due to a high level of the impact temperature (Fig. 7) it may be predicted that temperature activated dislocation climb is a destructive channel for formation in the Cu coating of dislocation pile-ups against macroscopic defects such as grain and subgrain boundaries, precipitates, etc. Therefore, the strainhardening mechanism of constrain on dislocation motion proposed in Section 3.5 seems more realistic in comparison to grain-size strengthening. As is estimated in Section 4.3 for Al, if temperature changes from T0 ¼ 300 K to hTim i  800 K the

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relative vacancy concentration increases from 1011 to 1:2
104 , respectively. For the same temperatures, in Cu the vacancy concentration increases from 3:6
1021 to 9:7
108 , respectively. It should be noted that these estimates are performed for equilibrium vacancy concentrations. Apparently the estimated upper limits of vacancy concentration (1:2
104 and 9:7
108 for the Al and the Cu, respectively) exceed correspondingly the real concentrations in the Al near-interfacial layer and the Cu coating by the reason of adiabatic variation of the impact temperature. Nevertheless, it is reasonable to expect that repeated ball collisions over the deposition process gradually enhance the vacancy concentration in Cu/Al system up to considerable limits. Most probably that large thermoplastic impact deformation eðimÞ  0:1 estimated for Cu/Al system (Table 6) is z achieved in a certain degree due to generation of vacancies with a large concentration, which activate the diffusion mechanism of plastic deformation. Besides, in terms of discussion in Section 3.7, it should be expected that the large vacancy concentrations initiate vacancy clustering and formation of dislocation loops both in the Cu coating and Al substrate. On the basis of the model developed in Section 4, the interdiffusion process of the Cu and the Al atoms at Cu/Al interface is predicted for deposition process under investigation. It is assumed that two factors are mainly responsible for activation of the interdiffusion, the impact temperature and thermally activated high vacancy concentration in the vicinity of the Cu/Al interface. Therefore, as a consequence of this assumption, preference is given to substitutional mechanism of diffusion, i.e. diffusion over vacant atomic positions. Estimated in Section 4.2 diffusive run of Cu atoms into the Al substrate predicts formation of a Al1xCux transition layer of thickness ðCu!AlÞ ld  5:1 mm below Cu/Al interface. In its turn, it is expected that the opposite diffusive run of Al atoms into the Cu coating leads to appearance of a ðAl!CuÞ Cu1yAly layer of thickness ld  0:6 mm located over Cu/Al interface. Due to condition (44) the Al diffraction peaks recorded in X-ray spectrum (Fig. 3) are attributed to Al1xCux transition layer, and from their angular positions both residual strain and average compound parameter x ¼ 0:02 are found. In compliance with basic laws of diffusion process, most probably that in the sample under investigation the

compound parameter x decreases over depth. As it follows from analytic expressions presented in SecðCu!AlÞ , i.e. the tions 4.1 and 4.2, the diffusive run ld thickness of the Al1xCux transition layer, may be in a certain degree kept under control through the regulation of technological parameters vch , AS, and tdep and distribution function f(Db). From the one hand, due to lesser diffusivity (as it follows from (42)) and lesser equilibrium vacancy concentration (as it is estimated above) in the Cu, it should be expected that for compound parameter of the Cu1yAly layer the relationship y ! x is hold (x is the compound parameter of the transition layer Al1xCux). From the other hand, this layer was estimated to ðAl!CuÞ be much thinner than the Cu coating, ld (0.6 mm) ! tCu (11.7 mm). Therefore, contribution of the Cu1yAly layer into the diffraction peaks recorded from the Cu coating may be ignored, as was done by us in X-ray spectrum treatment. As it is concluded in Section 4.3, the Al1xCux transition layer is substitutional alloy with expanded crystal lattice (see expression (45) and Table 2). This fact is consistent with the negative in-plane biaxial strain determined for the Cu coating (see Section 3.2; Table 2). Indeed, because of mechanical interaction of the Cu coating with the Al1xCux underlying transition layer, it should be expected that at the coating deposition plane (in Fig. 2 it is xy plane) these layers are subjected to strains (stresses) of opposite signs. Due to compressive character of the in-pane strain of the Cu coating it may be predicted that at the deposition plane the coating is preserved from propagation of the macrocrack. We may not exclude that during process of deposition a certain amount of oxygen dissolves both in the Cu coating and Al1xCux transition layer. However, it is believed that their lattice parameters are mainly influenced by interdiffusion processes and mechanical stresses at the coating-substrtae interface, but not by oxygen incorporation. It is also not excluded that a dense network of misfit dislocations forms within the transition layer and penetrates as threading dislocations into the Cu coating [29]. The Cu coating of thickness 11.7 mm was deposited in 47.5 min. From these data, the deposition rate for growth technique under consideration is estimated to be about 4 nm s1. For instance, this deposition rate

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exceeds the rates of deposition by pulsed vacuum arc technique (0.3 nm s1 [30]) and radial beam assisted technique (2.5 nm s1 [31]).

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Acknowledgements The authors acknowledge Dr. E. Zargaryan and Dr. V. Mkrtchyan for assistance in measurements of X-ray diffraction spectra.

6. Conclusions 1. Under the chosen technological parameters, a coating of thickness 11.7 mm was deposited in 47.5 min. The deposition rate for this technique is about 4 nm s1. 2. On the basis of analysis of determined distributions of coherent domains (over the strains and sizes) and configuration of the excess dislocations at the {1 1 1} slip planes, a mechanism for subgrain formation in the Cu coating is proposed. It is established that the dimensions of subgrains are in the nanoscale range (10 nm). Within the proposed model, it is assumed that the grains of the coating are split into subgrains by low angle tilt boundaries and {1 1 1} dislocation slip planes. A large value close to 1012 cm2 is estimated for excess dislocation density at the subgrains boundaries. A high value of order of 0.1 GPa is determined both for the biaxial normal and the shear stress components in the coating. 3. The strain-hardening mechanism of constraint on dislocation motion is proposed to be a dominant channel for the strengthening of the coating. Due to compressive character of the in-pane strain of the Cu coating it may be predicted that at the deposition plane the coating is preserved from propagation of the macrocrack. 4. On the basis of the model developed for temperature activated interdiffusion process at the Cu/Al interface, formation of a Al1xCux transition layer of thickness 5.1 mm below the Cu coating is predicted. From Vegard’s law, it is concluded that this transition layer is substitutional alloy with compound parameter about x ¼ 0:02. 5. In order to establish in a reliable way how the strain-hardening and polygonization mechanisms in the coating eventually depend on the deposition time, it is necessary to conduct an additional investigation on the basis of measurements for a series of Cu/Al coatings grown for different deposition times.

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