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Study of TiN and Ti/TiN coatings produced by pulsed-arc discharge Alfonso Devia Cubillos, Elisabeth Restrepo Parra * , Belarmino Segura Giraldo, Yulieth Cristina Arango, Diego Fernando Arias Mateus Laboratorio de Fı ´sica del Plasma, Universidad Nacional de Colombia, Manizales Branch, Cra. 27 No. 64-60, Manizales, Colombia Received 10 July 2003; accepted in revised form 14 July 2004 Available online 11 September 2004 Abstract TiN coatings on steel substrates and silicon (100), and Ti/TiN bilayers on silicon (100) are produced using vacuum arc processes by means of plasma-assisted techniques. These films are prepared by using a Ti and nitrogen gas target at 1.7 mbar for TiN films and argon at 1.3 mbar for Ti coatings. The system is composed of a vacuum chamber with two opposite electrodes upon which there is a 300-V discharge. The films obtained are characterized in composition by means of X-ray diffraction (XRD) techniques, observing a preferential orientation for TiN on a (200) plane. Moreover, the crystallite size and the lattice microstrain were calculated, showing random behaviors when the number of pulsed discharges is increased, due to the continuous processes of relaxation and formation of dislocations into the film. A morphological analysis was done using atomic force microscopy (AFM) techniques, observing an increase of roughness and grain size as a function of the number of pulsed discharges. Furthermore, approximate thicknesses of the films were calculated, obtaining values in the order of nanometers. D 2004 Elsevier B.V. All rights reserved. Keywords: Pulsed arcs; Coatings; Titanium; Diffraction analysis; Morphology 1. Introduction Ti and TiN films have been employed for several technological applications in integrated circuits such as: diffusion barrier, glue layer at the contact/via level and anti- reflection coating layer in the interconnection stack [1,2]. Owing to their mechanical properties, titanium nitride films are widely utilized in many industrial areas where high- abrasion resistance, low-friction coefficient, high-temper- ature stability and high hardness are required [3]. Arc discharge is one of the main techniques used to deposit thin films of different materials, since it generates a much higher degree of ionization than other processes and provides better film adhesion and higher densities. The major obstacle for its broad application is the presence of micro- and nano- particles (bdropletsQ or bmacroparticlesQ) in the plasma, emphasizing on their massive nature as compared to ions and electrons. In order to solve this problem, many different kinds of filters have served to eliminate the presence of the macroparticles on the substrate [4]. The utilization of these filters have allowed the use of arc deposition techniques in coatings production for optics and electronics [5,6]. For tribological applications, macroparticles are not a really important problem, while their size is not too great. An increase on coating properties results in requirements and trends to develop new systems and promising production methods, like multilayer coatings and gradient coatings. Moreover, the mechanical performance of the coatings is strongly influenced by the substrate on which these are deposited [7]. Most studies concerning microstructural evolution during plasma vapor deposition (PVD) growth focus on films deposited onto very flat surfaces, such as polished-Si substrates. However, in most applications (i.e., tribological films, anticorrosion films, thermal barriers, multilayer thin films and semiconductor devices), films are grown onto non-ideal, rough surfaces [8]. The role of this work is to study the influence of roughness on microstructural and morphological evolution during the deposition. 0257-8972/$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.surfcoat.2004.07.082 * Corresponding author. Tel./fax: +57 6 8745410. E-mail addresses: [email protected], [email protected] (E.R. Parra). Surface & Coatings Technology 190 (2005) 83– 89 www.elsevier.com/locate/surfcoat
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Study of TiN and Ti/TiN coatings produced by pulsed-arc discharge

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Page 1: Study of TiN and Ti/TiN coatings produced by pulsed-arc discharge

www.elsevier.com/locate/surfcoat

Surface & Coatings Techno

Study of TiN and Ti/TiN coatings produced by pulsed-arc discharge

Alfonso Devia Cubillos, Elisabeth Restrepo Parra*, Belarmino Segura Giraldo,

Yulieth Cristina Arango, Diego Fernando Arias Mateus

Laboratorio de Fı́sica del Plasma, Universidad Nacional de Colombia, Manizales Branch, Cra. 27 No. 64-60, Manizales, Colombia

Received 10 July 2003; accepted in revised form 14 July 2004

Available online 11 September 2004

Abstract

TiN coatings on steel substrates and silicon (100), and Ti/TiN bilayers on silicon (100) are produced using vacuum arc processes by means

of plasma-assisted techniques. These films are prepared by using a Ti and nitrogen gas target at 1.7 mbar for TiN films and argon at 1.3 mbar

for Ti coatings. The system is composed of a vacuum chamber with two opposite electrodes upon which there is a 300-V discharge. The films

obtained are characterized in composition by means of X-ray diffraction (XRD) techniques, observing a preferential orientation for TiN on a

(200) plane. Moreover, the crystallite size and the lattice microstrain were calculated, showing random behaviors when the number of pulsed

discharges is increased, due to the continuous processes of relaxation and formation of dislocations into the film. A morphological analysis

was done using atomic force microscopy (AFM) techniques, observing an increase of roughness and grain size as a function of the number of

pulsed discharges. Furthermore, approximate thicknesses of the films were calculated, obtaining values in the order of nanometers.

D 2004 Elsevier B.V. All rights reserved.

Keywords: Pulsed arcs; Coatings; Titanium; Diffraction analysis; Morphology

1. Introduction

Ti and TiN films have been employed for several

technological applications in integrated circuits such as:

diffusion barrier, glue layer at the contact/via level and anti-

reflection coating layer in the interconnection stack [1,2].

Owing to their mechanical properties, titanium nitride films

are widely utilized in many industrial areas where high-

abrasion resistance, low-friction coefficient, high-temper-

ature stability and high hardness are required [3]. Arc

discharge is one of the main techniques used to deposit thin

films of different materials, since it generates a much higher

degree of ionization than other processes and provides better

film adhesion and higher densities. The major obstacle for

its broad application is the presence of micro- and nano-

particles (bdropletsQ or bmacroparticlesQ) in the plasma,

emphasizing on their massive nature as compared to ions

0257-8972/$ - see front matter D 2004 Elsevier B.V. All rights reserved.

doi:10.1016/j.surfcoat.2004.07.082

* Corresponding author. Tel./fax: +57 6 8745410.

E-mail addresses: [email protected],

[email protected] (E.R. Parra).

and electrons. In order to solve this problem, many different

kinds of filters have served to eliminate the presence of the

macroparticles on the substrate [4]. The utilization of these

filters have allowed the use of arc deposition techniques in

coatings production for optics and electronics [5,6]. For

tribological applications, macroparticles are not a really

important problem, while their size is not too great. An

increase on coating properties results in requirements and

trends to develop new systems and promising production

methods, like multilayer coatings and gradient coatings.

Moreover, the mechanical performance of the coatings is

strongly influenced by the substrate on which these are

deposited [7]. Most studies concerning microstructural

evolution during plasma vapor deposition (PVD) growth

focus on films deposited onto very flat surfaces, such as

polished-Si substrates. However, in most applications (i.e.,

tribological films, anticorrosion films, thermal barriers,

multilayer thin films and semiconductor devices), films

are grown onto non-ideal, rough surfaces [8]. The role of

this work is to study the influence of roughness on

microstructural and morphological evolution during the

deposition.

logy 190 (2005) 83–89

Page 2: Study of TiN and Ti/TiN coatings produced by pulsed-arc discharge

A.D. Cubillos et al. / Surface & Coatings Technology 190 (2005) 83–8984

In this paper, Ti/TiN multilayer films were deposited

onto oriented Si(100) and onto stainless steel, in order to

study the influence of the substrate and the growth of

interlayer in the coating’s morphology. Multilayer coatings

can solve various requirements at the substrate/coating

interface, as well as the upper functional part of the coating.

Energy evolved during the coating growth can dissipate and

prevent breakage of the coating during mechanical loading

[9]. A mechanism to compare properties between TiN and

Ti/TiN, as a function of the number of pulsed discharges

(each one produces material deposition during 30 ms,

approximately), was discussed based on X-ray diffraction

(XRD) and atomic force microscopy (AFM). The preferred

orientation of films grown via physical vapor deposition is

decided by conditions resulting in lowest energy in a

competition among the surface strain energies. Therefore, a

film should exhibit preferred orientation of lowest strain

energy after deposition of a few laminae, but that of lowest

surface energy after deposition of many laminae. Morphol-

ogy differences of different coatings can be studied by

AFM. Roughness is an important parameter that allows

explaining the behavior of the substrate/coating interface

[10].

Fig. 1. Experimental setup.

2. Experimental setup

The plasma-assisted physical vapor deposition equip-

ment used to produce the coatings is composed of a vacuum

system that works at pressures between 10�5 and 102 mbar

and an electric circuit that allows for the generation of a

pulsed-arc discharge with currents between 100 and 170 A,

in about 30 ms. Within the reaction chamber, there is an

arrangement of electrodes formed by an anode, where the Si

substrate is placed, and a cathode with the Ti target. When

TiN films are to be produced, the chamber is filled with

nitrogen at a pressure of 1.7 mbar. The electrical system,

composed of an RLC circuit (R=0.54 V, L=2.3 mH, C=54

mF), produces a critically damped discharge between the

electrodes; the discharge is obtained when the capacitor

bank is charged at 300 V, generating a burning voltage, used

to refer to the potential difference between anode and

cathode of 22 V, similar to that reported in the literature

[11]. TiN films were produced on silicon and stainless steel

substrates with and without Ti interlayers with a number of

discharges between 1 and 5. The Ti interlayer was obtained

by filling the reaction chamber with argon. For this

interlayer, work conditions were 1.2 mbar and the capacitor

bank is charged to 300 V; an illustration of the experimental

setup is presented in Fig. 1 [12].

To characterize the coatings, a Scanning Probe Micro-

scopy Autoprobe CP Park in Contact AFM mode was used.

With this equipment, roughness, grain size and thickness

were obtained. The current phases, lattice parameter,

crystallite size, along with microstress and crystallographic

texture, were determined by XRD with parallel beams. For

morphological measurements, the values presented in this

work are the result of an average taken from five samples.

3. Results and discussion

3.1. Morphologic study

The morphology of the coatings is basically controlled

by the process characteristics, substrate roughness and

temperature [13]. Fig. 2 shows AFM images of TiN coatings

without Ti interlayers and with Ti onto silicon and stainless

steel substrates produced with five pulsed discharges. The

Rrms factor roughness of these substrates is 1.28 and 110 2,respectively. This factor maintains the same order of

magnitude after the coating is deposited; furthermore, it

increases when the number of pulsed discharges increases,

as observed in Fig. 3. It is known that coatings obtained via

vacuum-arc processes generally have high roughness caused

by the micro- and nanodroplets produced, due to high-

current densities present in the target (spots) [14]. These

microparticles are adhered to the substrate, increasing

roughness. If more pulsed discharges are produced, more

microparticles are generated. In many cases, roughness

improves adherence and sometimes it is intentionally

produced, although if exaggeratedly increased, porous

coatings can be obtained [15].

Fig. 2(c) shows an AFM image for a TiN coating with Ti

interlayers on Si substrate. Moreover, the roughness and its

growth rate for the Ti/TiN coatings are higher than for the

film without interlayer, as shown in Fig. 3. It was previously

explained that sometimes roughness improves adherence;

nevertheless, in this work we did not determine this

characteristic. It can be observed that one of the reasons

the interlayer is placed between the substrate and the film

could be to increase roughness and, possibly, adherence.

Coating thickness was measured by the AFM technique.

Fig. 4 shows AFM images revealing a step that allows for

determining the thickness of coatings produced with 5

pulsed discharges. Table 1 shows the values of the thickness

Page 3: Study of TiN and Ti/TiN coatings produced by pulsed-arc discharge

Fig. 3. Graphic of roughness as a function of number of pulsed discharges.

Fig. 2. AFM images for five pulsed discharges (a) TiN on stainless steel, (b)

TiN on silicon (100) and (c) Ti/TiN on silicon (100).

A.D. Cubillos et al. / Surface & Coatings Technology 190 (2005) 83–89 85

for different coatings. Coating thickness on stainless steel

substrate (316 nm) is higher than the coating on the silicon

substrate (113 nm). This could be attributed to the difference

in resistivity between both materials. For the plasma-

assisted processes by arc discharge, most of the field energy

is used to accelerate the ions from the plasma boundary to

the cathode and, hence, to bombard the cathode. But part of

this energy is returned to the plasma; another part is used in

collisions and the remaining energy is lost as heat in the

electrodes. The electrodes may be good electrical conduc-

tors to allow for the flow of current. Knowing that steel has

lower resistivity than silicon (qst=10�8 V m and qsi=640 V

m), it is possible that in the steel substrate current transport

could be easier than in the Si substrate. Evidently, thickness

does not increase linearly as a function of the number of

pulsed discharges. One would expect that the thickness of

Ti/TiN coatings was due to the addition of the Ti and TiN

thickness, but the values in the table show such to be untrue.

This could be explained considering that it is different to

produce a coating onto a substrate with and without

interlayers. The interdiffusion of the coating material on

the substrate could be different.

Grain size was studied for the different cases. Fig. 5

illustrates grain size as a function of the number of

discharges. Such increases when more material is deposited,

as explained by current literature [16], in that, during film

growth, it starts forming very small grain structures

determining the nucleus, because at the borders they are

not in movement. When the layer is continuous, surface

diffusion enables the migration of adatoms between

neighboring grains. Also, the crystals with smaller energy

incorporate more material and grow above the neighboring,

higher-energy crystals. This competitive growth caused

grain size to increase in a bVQ shape, being longer when

thickness increases. All of this results on a dense lattice of

crystals in columnar form, according to the qualitative

model of Movchan and Demchishin modified by Thornton

[13,17], which defines the microstructure for the layers

obtained using evaporation techniques with different values

of T/Tf (relation between substrate temperature and melting

temperature of the material). In this case, the coatings are

produced in the T zone (0.1bT/Tfb0.3), since the substrate

temperature is 200 8C and the melting temperature of

titanium is 1660 8C. Although this model is applied

specifically to sputtering techniques [13], we found a strong

Page 4: Study of TiN and Ti/TiN coatings produced by pulsed-arc discharge

Table 1

Thickness of the coatings for five pulsed discharges

Material Thickness (Am)

TiN onto stainless steel substrate 316

Ti/TiN onto silicon substrate 164

TiN onto silicon substrate 113

Ti onto silicon substrate 81

Fig. 5. Grain size as a function of number of pulsed discharges.

Fig. 4. AFM images used to measure the thickness for five pulsed

discharges.

A.D. Cubillos et al. / Surface & Coatings Technology 190 (2005) 83–8986

similarity with our results, observing grain size variations

when more material was deposited. However, it is necessary

to take into account that most of the literature studies the

growth of the films and the condensation process when the

substrate is biased or heating [18,19], different to the case

presented here, where the heating of the substrate is

produced directly by the arc.

3.2. XRD analysis

Fig. 6 shows X-ray diffraction graphics of TiN onto

stainless steel along with TiN and Ti/TiN onto silicon

substrates, varying the number of pulsed discharges. It is

notable that the intensities of the lines increase as a function

of this parameter. The diffraction line with the highest

intensity is the one produced by the (200) plane.

The preferred orientation describing the crystalline

structure of a thin film can be calculated by using the

crystallographic texture coefficient, (Tc(hkl)) [20].

Tc 200ð Þ ¼ I 200ð ÞI 200ð Þ þ I 111ð Þ ð1Þ

The values for Tc are higher for the (200) plane. In Table

2, the variation of this coefficient as a function of the

number of pulsed discharges is observed. The value for one

pulse discharge is lower than the others. This is because

there is little amount of material deposited with only one

pulse discharge. Moreover, it is possible to see an increase

of Tc for TiN onto Si substrate, different for TiN onto

stainless steel substrate. In recent studies, the origin of the

crystallographic structure was explained by the lowest

energy in a competition between surface and strain energies

(thermodynamic contributions) [21,22]. It was demonstrated

that for TiN the lowest surface energy occurs for (200)

planes [23].

The lattice parameter as a function of the number of pulse

discharges was studied. Fig. 7 shows these values for the

different cases. The horizontal line indicates the lattice

parameter for the strain-free material. For TiN coatings on

stainless steel, the lattice parameter changes strongly, going

Page 5: Study of TiN and Ti/TiN coatings produced by pulsed-arc discharge

Table 2

Crystallographic texture coefficient (Tc(hkl)) and FWHM values of

diffraction lines

Number of pulsed

discharges

TiN silicon TiN

stainless steel

Ti/TiN

silicon

1 0.71 0.68 0.70

2 0.62 0.80 0.66

3 0.65 0.82 0.70

4 0.65 0.85 0.71

5 0.64 0.84 0.70

Fig. 6. XRD as a function of number of pulsed discharges (a) TiN on

stainless steel, (b) TiN on silicon (100) and (c) Ti/TiN on silicon (100).

A.D. Cubillos et al. / Surface & Coatings Technology 190 (2005) 83–89 87

from very low (compressive stress) to very high (tensile

stress). For TiN coatings on silicon, the lattice parameter

remains lower than the stress-free material. And, finally, for

Ti/TiN coatings on silicon, the values vary around the stress-

free material but more slight in the first case. Since the

number of pulse discharges is related to the thickness of the

film, one can obtain the appropriate quantity of deposited

material that allows for a coating with less strain. The

changes between compressive and tensile strains in a film

are because the lattice is relaxed by forming dislocations

[24]. A Ti interlayer can couple the lattice parameters of the

substrate and the coating. It acts as an elastic and resistant

interlayer reducing the sharp stress and making fault

propagation difficult.

Diffraction peaks are the sum of interference functions

produced by each crystallite. The broadening of the

interference function depends upon the size of the

crystallite. A crystallite is the smallest diffracting domain

in a material. Crystallite size, sometimes called grain size,

is not to be confused with particle size. A particle or grain

may be comprised of many crystallites, depending upon

the crystal perfection (e.g., grain boundaries, stacking

faults, etc.) [25].

In materials with plastic deformation, the increase of the

dislocation densities produces two effects: diminishing of

crystallite size and variations of the inter-planar distance

between crystallites (microstrain of the lattice). Both the

Fig. 7. Parameter lattice as a function of number of pulsed discharges.

Page 6: Study of TiN and Ti/TiN coatings produced by pulsed-arc discharge

Table 3

Values of crystallite size and microstrain of the lattice

Number of

pulsed discharges

TiN silicon TiN stainless steel Ti/TiN silicon

D (nm) e D (nm) e D (nm) e

1 – – 12.5 0.00051 – –

2 13.78 0.00372 12.6 0.00372 – –

3 11.21 0.00438 13.2 0.00455 14.06 0.00644

4 17.59 0.00571 11.4 0.00291 12.31 0.00599

5 17.21 0.00526 11.6 0.00315 11.38 0.00237

A.D. Cubillos et al. / Surface & Coatings Technology 190 (2005) 83–8988

crystallite size and the lattice microstrain produce a broad-

ening of the diffraction peaks, related to the diffraction angle

h. Crystallite size is a function of 1/cosh, while the lattice

microstrain depends on tanh. Finally, the equipment also

contributes to this broadening. The equation to describe all

the causes is [26]:

b2 ¼ 0:9kDcosh

�2

þ 4etanhð Þ2 þ b20

ð2Þ

where b0 is the instrumental broadening, which is 0.035148,e is the lattice microstrain and D is the crystallite size.

Using Eq. (2) and the values of FWHM (Table 3), it was

possible to obtain, through statistical methods, the crystal-

lite size (D) and the microstrain averages (e) as functions ofthe number of pulsed discharges. Table 3 illustrates these

values.

The behavior of the coatings produced on each substrate

is very different. According to results annotated in Table 3,

variations of the crystallite size and lattice microstrain

can be caused by changes in the density of dislocations that

can be formed by plastic deformations, incorrect atomic

coupling or condensation of vacancies [25]. Further, there

is an interlayer between the material deposited for each

pulsed discharge, avoiding a normal perfect continuity to

the surface in the film and eliminating ways for fissures to

propagate.

4. Conclusions

In summary, the characteristics of TiN coatings grown on

two different substrates (stainless steel and silicon) and Ti/

TiN coatings on Si substrates were studied. Coating rough-

ness depends on the substrate and increases with the number

of pulsed discharges, as well as the grain size, caused by

columnar growth in bVQ form.

Film thickness increases faster for the stainless steel

substrates, because this material has less resistivity; thereby,

favoring conduction between electrodes.

XRD analysis reveals a preferential orientation for the

TiN in (200) plane. Moreover, the microstrain and the

crystallite size have a random behavior, due to the

continuous relaxation of the lattice and the production of

dislocation when the material is being deposited.

Acknowledgments

This research endeavor was carried out with the

financial support granted by the Instituto Colombiano

para el Desarrollo de la Ciencia y la Tecnologı́a—the

Colombian Institute for the Development of Science and

Technology—(COLCIENCIAS), the financial support

from El Banco Interamericano para el Desarrollo—the

Interamerican Bank for Development—(BID) through

the RC1952002 Project, and the financial support from

the Universidad Nacional de Colombia, Manizales

branch.

References

[1] B.K. Tay, X. Shi, H.S. Yang, H.S. Tan, D. Chua, S.Y. Teo, Surf. Coat.

Technol. 111 (1999) 223.

[2] M.F. Tabet, U. Kelkar, W.A. McGahan, J. Vac. Sci. Technol., A, Vac.

Surf. Films 18 (4) (2000) 1704.

[3] M.H. Staia, E.S. Puchi, D.B. Lewis, J. Cawley, D. Morel, Surf. Coat.

Technol. 86–87 (1996) 432.

[4] A. Anders, Surf. Coat. Technol. 120–121 (1999) 319.

[5] O.R. Monteiro, J. Vac. Sci. Technol., B 17 (3) (1999) 1094.

[6] N. Vershinin, B. Straumal, W. Gust, J. Vac. Sci. Technol., A, Vac.

Surf. Films 14 (6) (1996) 3252.

[7] S.V. Hainsworth, W.C. Soh, Surf. Coat. Technol. 163–164 (2003) 515.

[8] J.F. Whitacre, Z.U. Rek, J.C. Bilello, S.M. Yalisove, J. Appl. Phys. 84

(3) (1998) 1346.

[9] T. Mori, S. Fukuda, Y. Takemura, Surf. Coat. Technol. 140 (2001)

122.

[10] T.S. Li, H. Li, F. Pan, Surf. Coat. Technol. 137 (2001) 225.

[11] A. Anders, B. Yotsombat, R. Binder, J. Vac. Sci. Technol., A, Vac.

Surf. Films 89 (12) (2001) 7764.

[12] E. Restrepo, A. Devia, J. Vac. Sci. Technol., A, Vac. Surf. Films 22 (2)

(2004) 377.

[13] D.M. Mattox, Adhesion and surface preparation, in: R.F. Bunshah

(Ed.), Deposition Technologies for Films and Coatings, Noyes, Park

Ridge, NJ, 1982, pp. 710.

[14] I.I. Beilis, IEEE Trans. Plasma Sci. 29 (5) (2001) 657.

[15] M. Oring, The Material Science of Thin Films, Academic Press,

London, 1992, p. 442.

[16] P.J. Martin, Coating from vacuum arc, in: R.L. Boxman, P.J. Martin,

D.M. Sanders (Eds.), Handbook of Vacuum Arc Science and

Technology, Noyes, Park Ridge, NJ, 1995, pp. 367.

[17] J.A. Thornton, J. Vac. Sci. Technol. 11 (1974) 666.

[18] J.C. Collogon, J. Vac. Sci. Technol., A, Vac. Surf. Films 13 (3) (1995)

1649.

[19] H. Ljungcrantz, L. Hultman, J.-E. Sundgren, L. Karlsson, J. Appl.

Phys. 78 (2) (1995) 832.

[20] D.E. Wolfe, J. Singh, K. Narasimhan, Surf. Coat. Technol. 160 (2002)

206.

Page 7: Study of TiN and Ti/TiN coatings produced by pulsed-arc discharge

A.D. Cubillos et al. / Surface & Coatings Technology 190 (2005) 83–89 89

[21] L. Hultman, J.E. Sundgren, J.E. Greene, D.B. Bergstrom, I. Petrov,

J. Appl. Phys. 78 (9) (1995) 5395.

[22] C.H. Ma, J.H. Huang, H. Chen, Surf. Coat. Technol. 133–134 (2000)

289.

[23] J. Pelleg, L.Z. Zevin, S. Lungo, N. Croitoru, Thin Solid Films 197

(1991) 117.

[24] Y. Setsuhara, M. Kumagai, M. Suzuki, T. Suzuki, S. Miyake, Surf.

Coat. Technol. 116–119 (1999) 100.

[25] C.O. Paiva–Santos, H. Gouveia, W.C. Las, J.A. Varela, Mat. Struct. 6

(2) (1999) 111.

[26] A.L. Ortiz, L. Shaw, Acta Mater. 52 (2004) 2185.