Critical thickness for the

After the theory of Vrij (1966) surface waves play an important role. The critical thickness for the rupture of thin liquid films derived from the behaviour of surface waves is much smaller than the equilibrium thickness. Fig. 3.17. shows the thinning of a film due to surface waves generated by disturbances with squeesing modes. 

Thinning of free liquid films by surface waves the critical thickness for the film rupture is reached by this disturbance, - displacement of liquid elements, 2Rp - film diameter, h -equilibrium film thickness, according to Vrij (1966) and Fijnaut Joosten (1978)... 

The critical thickness for the rupture of such thin film was formulated by de Feijter (1988) using the Mandelstam s concept,... 

It was shown until now that the electronic stmcture which is manifested in the dlIdU spectra of clean Gd(OOOl) islands, i.e. the energetical position of the surface state and its intensity, does not dependent on the local coverage for loc > 4 ML. It is known, however, that the first monolayer of GdAV(llO) does not exhibit the surface state (cf. Fig. 3.8b). Consequently, the question arises What is the critical thickness for the surface state to appear in the tunneling spectra To unravel this... 

An understanding of strain effects in films is of critical importance for our subsequent discussion of superlattices in sect. 5. The topic of strain relief through interfacial accommodation began with Van der Merwe s treatment of critical thickness for the formation of interfacial dislocations (Van der Merwe 1950,1962) and has been the subject of reviews (Matthews 1979, Freund 1993). In the interest of brevity we present only a sketch of strain relief phenomena in what follows, and illustrate the substance of the discussion by relevant examples of magnetic behavior in thin rare-earth films. 

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