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# A new model for the composite hardness of thin films

 type de publication communication internationale avec actes publiés date de publication 2002 auteur(s) Lesage Jacky; Pertuz Alberto; Chicot Didier conférence Simposio Materia 2002 dates de 12-11-2002 à 15-11-2002 lieu Santiago (Chili) nom des actes Proceeding of the CONAMET/SAM pages 973 – 978 résumé Measuring hardness of thin films, namely films of less than 10 µm thick, using standard microhardness testers is a very complicated task for several reasons. Among them, the most important one is due to the range of indentation loads that are available with these testers. These loads are too high, in effect, to allow the determination of the hardness without involving a contribution of the substrate. In order to determine the hardness of the film it is necessary to separate the two contributions by means of a mathematical model. For that purpose, it is possible to use either one or the other models available in literature. Their application, though, requires the introduction of coefficients and data which have to be deduced from other experiments or from literature. The objective of the present work is to propose a new model, likely to avoid the knowledge of other data than that obtained easily from standard experimentation. As a general rule, all the models found in literature are based on a linear additive law expressing the measured apparent hardness (composite hardness) in function of the film and substrate hardness. From the observation that any model for the composite hardness should allow the transition between a substrate hardness tendency and a film hardness tendency when applying decreasing loads, we propose to combine two types of additive laws, series and parallel, associated respectively to each of these behaviors. The ratio (t/d)n of the thickness t of the film to the diagonal d of the indent at a power n, was found to be a pertinent parameter to express the variation of the composite hardness with the indentation load. A method was proposed to determine the value of n, and finally, the procedure was applied to determine the hardness of various films Ti, TiN, TiNx, TiC, TiCN, Cr and DLC. mots clés thin film, hardness, model
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