lattice parameters of both phases decreased and subgrain sizes increased slightly. Numeric data are presented in Table 3. Grain sizes Ø are of the same order as layer thicknesses. Also, Ø is decreasing when layers get thinner. This will be of importance for layer hardness.

Helming [18] has determined the texture of both single layers and a MuL utilizing an area detector [19]. The texture of single VC was found the most pronounced (half width < 10˚). (110) planes of VC were almost parallel to the substrate normal. While (110) planes of single TiC deviated most, the MuL system seemed to be an average of both single layers. Note that the slip system of TiC at room temperature is {110} <1 - 10> changing at elevated temperatures to {111} <1 - 10>. Normal stress applied at room temperature upon the MuL would thus give rise to vanishing shear stress along the slip planes thus increasing the resistance against deformation.

For an assessment of structure gradients inside MuLs, measurements of short range order were performed employing fluorescence EXAFS experiments (Figure 4). They were carried out at the beam line E4 at HASYLAB using a Si 111 double crystal monochromator, a nitrogen filled ionization chamber and an energy dispersive Ge detector (step width 0.5 eV around the edges, sampling time 2 - 9 s) [20]. Fourier transform of the EXAFS function yielded a measure of the radial distribution of atoms near the fluorescent species. Figure 5 shows an example. Fitting a model function to experimental data yielded interatomic distances and coordination numbers. A special feature of the present experimental set-up was a specimen

holder, enabling the orientation of the linearly polarized synchrotron radiation to be varied. So, the short-range order parallel to the multilayer (“in-plane”) and perpendicular to it (“off-plane”) could be distinguished. Figure 6" target="_self"> Figure 6 indicates the geometry of the experiment schematically. Arrows are parallel to the polarization vector of the synchrotron radiation. If the specimen is “off-plane” oriented, the neighborhood of the fluorescent metal atoms is probed mainly perpendicular to the layer, in the “inplane” case mainly parallel to it. Experimental data of orientation dependent nearest-neighbor distances of each multilayer sample were taken to identify a cubic lattice parameter parallel and perpendicular to the layer.

Results in Figure 7 show that lattice parameters of NaCl-type compounds TiC (bulk 4.328 Å) and VC (bulk 4.165 Å) approached one another for in-plane and out-ofplane values separately, when the double layer period λ was decreasing. This gives rise to tensile stress in VC and to compressive stress in TiC along the interface. There is no cubic symmetry whatever λ may be prior to annealing. The effect of annealing at 500˚C is demonstrated for very small and very large MuL thicknesses: in the former case, in-plane distances of both VC and TiC cells were increasing compared to the pre-annealing value, at the same time approaching each other. Correspondingly, out-of-plane spacings were decreasing. For large double layer periods in-plane and out-of-plane distances of VC become equal after annealing, i.e., the influence of epitaxial strain is negligible. TiC could not be determined. Decreasing the double layer thickness λ of the NaCl-type compounds TiC and VC, lattice parameters of TiC (bulk 4.328 Å) and VC (4.17 Å) monolayers approach one another giving rise to tensile or compressive stress. For λ ~ 4 nm in-plane lattice parameters of TiC and VC become equal presumably due to strong epitaxial interaction. Single layers on sapphire > 20 nm

thick retain their tetrahedral cell. Cubic lattice parameters of powdered targets derived from powder diffraction are indicated for comparison. Investigating these identical specimens with the aid of transmission EXAFS at HASYLAB and analyzing them afterwards with codes FEFF6.01 und FEFFIT, yielded values smaller than obtained from powder diffraction. Therefrom a correction factor has been derived to adjust all EXAFS lattice parameters in Figure 7. This way the lattice parameter of solid solution TiVC₂ appeared close to the out-of-plane figure of thin multilayers.

Provided that no intermixing of layers took place, strain can be used to estimate internal stress in the layer system. Assuming Young’s modulus for TiC or VC to be E » 300 GPa, the internal stress σ = Eε = EΔa/a is of the order of σ » ±3 GPa for Δa/a » 0.01.

2.3. Mechanical Characterization with the Aid of Nanoindentation

Nanoindentation (cf., e.g., [21]) was carried out under ambient conditions using a commercial nanoindenter (Hysitron Tribo Scope), which was attached to a scanning probe microscope (Nano Scope III Multimode). For experimental details we refer to [22]. Applying the procedure of [23], hardness H and the (reduced) Young’s modulus E_r were evaluated. The Meyer hardness [24] H used here is defined as H = F(h_c)/A(h_c), where F is the applied force and A(h_c) is the area of the indent projected onto the surface. h_c is the true contact depth taking into account only that part of the penetration depth which is defined by an indenter-specimen contact.

Examples of load-penetration curves are displayed in Figure 8 for bulk trigonal sapphire prior to coating with TiC/VC multilayers. The first part of the hysteresis F(h) in Figure 8 can be fitted quite nicely on the basis of elastic deformation (Elastica [25]), where F ~ h^1.53 holds, up to a critical force (or stress). Then plastic deformation starts (“pop-in”), whereby the nature of this process remains to be identified. Coating sapphire and silicon with TiC/VC MuLs changes the resistance against indentation. For a total layer thickness of about 200 nm the effect of MuLs is illustrated quantitatively in Figure 9. Note that the maximum penetration depth is smaller than the total layer thickness. Nevertheless, the substrate will be involved in the irreversible strain. The large pop-in of Figure 8 did not show-up again. Instead, smaller discontinuities occurred.

Hardness H of the MuL/substrate system obviously depends on the indentation depth h. We will come back to that and the way to attribute values of H in Figure 14

below.

Hardness H and reduced Young’s modulus E_r have been evaluated from F(h) curves and plotted in Figures 10 and 11. Obviously, MuLs are enhancing H of Si as well as of sapphire at the penetration depths investigated (Figure 10). The H values of the MuLs achieved exceed those of bulk carbides and bulk substrates. If the depth of the indent approaches the total MuL thickness, the hardness gain due to the coating is diminished. Young’s modulus (see Figure 11) is practically unchanged by 200 nm coatings.

There is a small maximum of hardness as a function of layer period for samples with sapphire substrate (Figure 12). Data depend on the state of annealing. They prove hardest for a superlattice parameter λ » 10 nm. On this scale, MuLs of TiC/VC show a superlattice hardening effect.

2.4. Microstructure

For transmission electron microscopy (TEM) and High Resolution TEM (HRTEM) using a Philips microscope

CM30FEG, thin foils were prepared of as-received samples with orientations parallel and perpendicular to the surface of the MuL/substrate. Standard preparation techniques involving mechanical grinding, mechanical dimpling and ion milling to perforation have been applied.

Figure 13 shows that nanograins have formed inside MuLs@sapphire. Secondly, columns of grains perpendicular to the layer plane have grown penetrating the layer interfaces. Subgrain and phase boundaries experienced sharpening during annealing. Mechanical properties measured with the aid of nanoindentation were E_r = 313 GPa and 306 GPa as well as H = 37.2 GPa and 37.6 GPa prior to and after annealing.

3. Discussion

Two phenomena of the present results shall be recalled:

1) The general enhancement of hardness of substrates Si and Al₂O₃ due to coating with TiC/VC MuLs and 2) the enhancement of TiC/VC MuL hardness compared to TiC and VC bulk hardness. Since bulk H values of the carbides exceed those of substrates, the result 1) seems trivial. Looking more closely, the question arises what the load carrying capacity of a certain layer and the influence of the substrate deformation is like.

In Figure 14, taking advantage of the model of Korsunsky et al. [26], hardness values of substrate, H_s, and of the MuL, H_MuL, were separated.

Authors decompose the total energy expenditure into the plastic work of deformation in the substrate and the deformation and fracture energy in the coating. The composite hardness, H_c, may be written H_c = H_s + (H_MuL – H_s)/(1 + ß²[t/α]), where ß ≡ h/t denotes the indentation depth h normalized with respect to the MuL thickness t. α is a characteristic length of the order of t and hence t/α » const. This formulae takes the asymptotic behavior for ß ® ∞ (H_c = H_s + (α [H_f – H_s])/ß²t) and for ß ® 0 (H_c = H_MuL) into account and hence covers the entire range of penetration depths. Numerical values of TiC/VC@Si are H_s = 13 GPa and H_MuL = 32.9 GPa. H_s is in good agreement with the data of uncoated Si and H_MuL is a plausible average of TiC and VC. Doing the same analysis with TiC/VC@ Al₂O₃ yielded H_s = 30 GPa and H_MuL = 41.5 GPa.

The difference between H_MuL = 32.9 GPa and H_MuL = 41.5 GPa for the same MuL system on distinct substrates may be due to differences in microstructure or in interface structure or to both.

Turning now to the strengthening effect 2), we refer to Table 3 and Figure 13. Obviously, there is a structure beyond layering. Various nanoscaled mechanisms have been put forward to explain layer thickness dependent hardness. Misra et al. [7] proposed dislocation pile-ups (i.e. Hall-Petch behavior [27,28]) yielding the stress σ (λ) as σ ~ λ^–0.5 for layer periods λ > 10 nm, bowing out of single dislocations inside a layer σ ~ (1/λ) lnλ for λ » 10 nm and interface crossing σ ~ λⁿ for λ ≤ 1 nm. Plotting the present experimental H values for λ >10 nm is in support of a Hall-Petch mechanism (Figure 15). For λ < 10 nm H is almost constant. So, the behavior of the present thick MuLs is Hall-Petchlike. The slope dH/dλ of the H(λ^–1/2) curve in Figure 15 amounts to 0.22 MN/m^3/2. This is within the range of experimental findings for various metals (0.07 ∙∙∙ 1.7 MN/m^3/2) given by Courtney [29]. However, a direct interpretation of MuL boundaries as rate-controlling dislocation obstacles seems less comprehensible when looking at Figure 13. Therefore, we adopt the view of Li [30] to avoid the pile-up model, i.e., we consider rather the empirical relationship λ ~ 1/ρ between obstacle spacing or grain size λ and dislocation density ρ. Then the increase of H (for λ > 10 nm) appears

as consequence of an increase of average dislocation density according to H ~ ρ^1/2. For MuLs with λ ® 0, H is approaching a level corresponding to the response of a solid solution of TiC and VC.

In Figure 16 ending inserted half-planes of edge dislocations may be recognized directly. Note that distances between dislocation cores may be as small as of the order of nanometer.

While TiC/VC MuLs enhance the hardness of Si and sapphire (Figure 8), the relative load support of the MuL system, however, is distinct for “soft” and “hard” substrates. Figure 17 demonstrates the relative benefice derived from F(h) curves like those of Figure 8, the effect being larger for soft substrates. Furthermore, covering with MuLs is beneficial for low loads. For example resistance against scratching could be improved that way.

Recently, Kizler and Schmauder [31] have performed atomistic simulations of the penetration process connected with nanohardness tests of TiC/NbC MuLs on a rigid substrate employing a rigid indenter. A volume of 82.6 × 4.3 × 27.5 nm³ corresponding to ~720,000 atoms had been treated. Despite a number of simplifications,

the following results seem of relevance to the present material. At the beginning of the indentation process, amorphization took place very close to the indenter/layer interface. This is, however, hard to detect experimentally. Comparison of Ti-Ti and Ti-C pair correlation functions under stress and after stress relief indicated some persistence of disorder after deformation. Peak values of those functions behave like interatomic distances prior to and after annealing (cf. Figure 7).

Glide bands and dislocations showed up as expected from slip in real TiC single crystals [32], obeying the constraint of preserving stoichiometry. Note that the single layer thickness dealt with was 4 nm [31], i.e., λ = 8 nm is a little below the period, where Hall-Petch applies according to the present results. Authors presume that, in addition to dislocation movement, some other not specified mechanisms should be active. A grain-like substructure of MuLs weakens the system compared to a defectfree single crystal. This might explain why hardness increased after annealing. On the other hand, looking at Figure 13, smaller subgrains may give rise to higher dislocation density in the λ > 10 nm region and hence to higher H values. Columnar walls in the layer structure, as to be seen in Figure 13, act as obstacles to plastic deformation.

4. Conclusion

By coating silicon and sapphire single crystals with TiC/ VC MuLs, nanohardness was found enhanced for indentation depths up to the total layer thickness, whereas Young’s modulus as derived from force-penetration curves remained almost constant. The contact pressure to start plastic deformation was increased by covering the substrate. A weak superlattice hardening effect of the MuLs has been observed for sapphire. The MuL period of maximum hardness amounted to about 10 nm or less. Hardness enhancement for periods above this value could be attributed to a Hall-Petch behavior, at least for annealed MuLs on sapphire. Reduction of hardness for small MuL periods goes along with the loss of interphase boundaries. The microstructure of MuLs is characterized by a layer substructure consisting of crystalline and some amorphous parts. Interatomic distances in TiC and VC layers approach each other for small MuL periods like in solid solutions. Taking recent computer simulations of a similar system and present TEM images together, our view is supported that dislocations play a distinct role in this material.

5. Acknowledgements

The authors would like to thank the German Research Foundation (DFG) for financial support. A.B. gratefully acknowledges the hospitality of the Fraunhofer-Institutfür Werkstoff und Strahltechnik IWS Dresden and the competent support to prepare the samples. He also enjoyed assistance of the staff of HASYLAB, when doing EXAFS studies. We are also thankful to Dr. B. Wolf for various help with the nanoindentation technique, to Dr. A. Levin for his support of reflectometry studies, to Dr. K. Helming for texture analysis. Ms. Heide Müller is thanked for her skillful preparation of HRTEM samples. The stimulating collaboration with Prof. S. Schmauder and Dr. P. Kizler is also thankfully mentioned.

REFERENCES

NOTES

^*Corresponding author.