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The study presents a multi-scale microstructural characterization of three-dimensional (3-D) micro-textured surface of titanium nitride (TiN) thin films prepared by reactive DC magnetron sputtering in correlation with substrate temperature variation. Topographical characterization of the surfaces, obtained by atomic force microscopy (AFM) analysis, was realized by an innovative multifractal method which may be applied for AFM data. The surface micromorphology demonstrates that the multifractal geometry of TiN thin films can be characterized at nanometer scale by the generalized dimensions D q and the singularity spectrum f(α). Furthermore, to improve the 3-D surface characterization according with ISO 25178-2:2012, the most relevant 3-D surface roughness parameters were calculated. To quantify the 3-D nanostructure surface of TiN thin films a multifractal approach was developed and validated, which can be used for the characterization of topographical changes due to the substrate temperature variation.

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This study presents a multifractal approach to characterize the structural complexity of 3D surface roughness of electrodeposited Ni-P (10.65 at% P) coatings thermally treated at three temperatures (400 • C, 500 • C and 600 • C), obtained with atomic force microscopy (AFM) analysis. 3D surface roughness was studied in air (ex-situ), on square areas of 2.5 μm x 2.5 μm. The singularity spectrum f(α) provided quantitative values data to characterize the local scale properties of Ni-P coatings surface geometry at nanometer scale. The results showed that the Ni-P coatings (10.6 at% P) that were thermally treated at 500 • C possessed the best surface finish. Multifractal analysis provides different yet complementary information to that offered by traditional surface statistical parameters.Due to their unique physical characteristics such as hardness, wear and corrosion resistance, as well as a low friction coefficient, Ni-P alloys are among the common engineering materials used in a wide range of industries, including aerospace, automotive and electronic. [1][2][3][4] For these reasons, research on deposition mechanism and characterization of Ni-P coating has increased considerably over the last few decades.In this regard, Malfatti et al. 5 found a progressive transition of the Ni-P coatings from crystalline to amorphous structure as a function of the phosphorous content, resulting in amorphous structure when the phosphorous content is above 15 at%.The amorphous Ni-P alloys can be crystallized to Ni 3 P and facecentered cubic (fcc) nickel crystals at temperatures above 350 • C. 6 Likewise, by determination of appropriate heat-treatment, 7-10 the physical characteristics of the Ni-P coatings such as wear resistance can generally be improved. This phenomenon can be attributed to precipitation of fine Ni crystallites and hard intermetallic Ni 3 P particles during the crystallization of the amorphous phase. 11 It has been reported that nanocrystalline Ni-P coatings with a P content of only 2-8% exhibit a significantly higher wear resistance than those with a higher P content. 9 The phosphorus content is directly related to the passivation film formation 1,12-14 and as a consequence to the protection capacity of the Ni-P coatings. Moreover, after a heat-treatment of the Ni-P electroless coatings at 400 • C, Wang et al 15 achieved an improvement of the corrosion resistance over two orders of magnitude better than hard Cr deposits in several media.Recently Nava et al., 16 reported the effect of heat-treatment evaluated at various temperatures in the range 200 to 600 • C on some physical properties of a Ni-P alloy (10.6 at% P) formed by electrochemical means. Ni-P coatings treated at 500 • C exhibited the best physical properties such as high hardness value (990 Hv). In the same study it was shown that at this temperature treatment the obtained alloy is originally amorphous and then transformed into a mixture of amorphous and crystalline phases.In order to quantitatively describe the changes in the surface structure of the Ni-...