adapted from Garcia Ferré et al. 2013). Stiffness parameters for an alumina coating, obtained by the combination of ellipsometry, BS and indentation (see Fig. 2).
New techniques are continuously being developed to produce films and thin films, which have a variety of properties and are exploited by an ever increasing number of technologies. The properties of films typically depend on the preparation process, and can be significantly different from those of the material in bulk form, due to the different micro- and nano- structures obtained by the various production processes. Although new techniques are also introduced to measure the film properties, the characterization of thin layers remains an open issue. A precise knowledge of the mechanical properties is crucial in several cases. Namely, whenever the films have structural functions, as it happens in several micro electro-mechanical systems (MEMS), and when the operation of a device is based on acoustic waves, as it happens in various types of micro-devices, for either sensing or signal processing purposes. But since the mechanical properties depend on the microstructural properties, they are also of more general interest, because they can be a good indicator also for properties which are not strictly mechanical, but for instance depend on the degree of compactness of the film.
A full mechanical characterization includes the determination of both the elastic properties, which characterize the reversible deformations, and the properties which characterize the irreversible behaviour. In most cases the elastic behaviour can be completely characterized by the elastic moduli, or equivalently by the components of the elastic tensor. It is well known that also in the simplest case, the homogeneous isotropic continuum, the elastic stiffness cannot be characterized by a single parameter, but needs two independent parameters. These can be taken as, for instance, the bulk modulus
A wide variety of methods has been developed to perform the mechanical characterization of bulk specimens. Among them, a specific class exploits vibrations of acoustic nature as a probe of the material behaviour. These methods are non destructive, and involve only elastic strains; therefore, they are intrinsically unable to give indications about any inelastic behaviour. On the other hand, due to the complete absence of inelastic strains, the relationship between the raw measurement results and the stiffness parameters can be more straightforward, and less subjected to uncertainties or to spurious effects, possibly allowing better accuracies.
The mechanical characterization of supported films typically requires specific methods. The most widespread technique is indentation, for which a specific standard exists: instrumented indentation, ISO 14577. Indentation induces both elastic and inelastic strains, and supplies significant information about irreversible deformation, namely the hardness value, but the extraction of the information concerning the elastic behaviour is non trivial. The most frequently adopted analysis technique (Oliver & Pharr, 1992; Bhushan & Li, 2003) gives access, once the compliance of the indenter is taken into account, to a single parameter, usually referred to as “indentation modulus”. If a reasonable assumption about the value of Poisson’s ratio is available, a value of Young modulus can be derived, which obviously depends on the reliability of the adopted assumption. In the case of films, since the nano- and micro-structure can be different from that of bulk samples, a well grounded assumption about the value of Poisson’s ratio might be not available. It is also well known that, when supported films are measured, care must be exercised to avoid the influence of the substrate properties.
Methods which exploit vibrations of acoustic character have been developed also for supported films. Acoustic properties depend on stiffness and inertia; therefore, as it happens for bulky samples, acoustic methods require a value of mass density, independently measured. However in acoustic methods the intrinsic absence of inelastic strains makes the derivation of the stiffness parameters less subjected to spurious effects, and less dependent on specific modelling assumptions.
Among the techniques based on acoustic excitations, the so called laser ultrasonics techniques rely on impulsive, therefore broadband, excitation, requiring an analysis of the response in the frequency domain. Excitation is performed by a laser pulse, and the response is measured by piezoelectric or optical means. Quantitative acoustic microscopy relies instead on monochromatic excitation by a piezoelectric transducer, which typically is also exploited as sensor. In the detection of vibrational excitations, substantial advantages are offered by light, a contact-less and inertia-less probe; such advantages are particularly relevant in the measurement of films and small structures. They are exploited by Brillouin spectroscopy, which relies on Brillouin scattering: the inelastic scattering of light by acoustic excitations. Brillouin spectrometry, like Raman spectrometry, is not performed by specifically exciting vibrations, but relies on thermal excitation (anti-Stokes events) and on the excitation produced by the scattering process itself (Stokes events). In both cases excitation has a small amplitude, but it has the broadest band, allowing access to the GHz and multi GHz band, accessible by piezo-electric transducers only with specific transducer structures.
For all these methods, the outcome is the measurement of the propagation velocity of one or more acoustic modes. If sufficient information is gathered, because several acoustic modes are detected and/or their velocities are measured for a sufficiently wide interval of frequencies, a full elastic characterization can be achieved by purely vibrational means, if an independent value of the mass density is available (Comins et al., 2000; Zhang et al., 2001; Djemia et al., 2004; Beghi et al., 2011).
However, a complete elastic characterization by only acoustic means is not always achievable, as it happens when only one acoustic mode is measurable. The results of acoustic methods and of indentation can therefore be combined, with the purpose to obtain a complete elastic characterization, not achievable by each of the techniques alone. This can be particularly useful in the case of new materials or of films of unconventional structures, for which a reliable assumption about the value of Poisson’s ratio, needed by indentation, is not available. And even when a full elastic characterization by acoustic techniques is achievable, the combination with indentation offers a useful cross-check among techniques based on completely different principles and also supplies the hardness value, intrinsically out of reach of the acoustic techniques.
This chapter is devoted to this combination of indentation with acoustic techniques, namely quantitative acoustic microscopy (Bamber et al., 2001; Goodman & Derby, 2011) and Brillouin spectroscopy (Garcia Ferré et al, 2013).
2. Acoustic modes in elastic solids
Some basic elements of the acoustics of homogeneous and of layered solids are briefly recalled here for sake of completeness. For an elastic continuum undergoing deformation the mechanical state can be represented by the displacement vector field, where is the position vector and
In the simplest case, the isotropic continuum, which we will mainly consider, the matrix of the elastic constants is fully determined by only two independent quantities; the only non null matrix elements are C
In an isotropic continuum the phase velocities do not depend on the direction of
In non isotropic continua more than two independent quantities are needed to determine the matrix of the elastic constants, and the phase velocities, beside depending on the direction of
In a homogeneous semi-infinite solid the free surface breaks the translational symmetry in the direction perpendicular to the surface, causing new phenomena: the reflection of bulk waves, and the existence of surface acoustic waves (SAWs). Namely, at a stress free surface, Eqs. (1) admit, for an isotropic continuum, a further solution: the Rayleigh wave, the paradigm of SAW. Such waves have peculiar characters (Farnell & Adler, 1972): a displacement field confined in the neighborhood of the surface, with the amplitude which declines with depth, a wavevector parallel to the surface, and a velocity lower than that of any bulk wave, such that the surface wave cannot couple to bulk waves, and does not lose its energy irradiating it towards the bulk. Pseudo-surface acoustic waves can also exist, which violate this last condition. The velocity of the Rayleigh wave cannot be given in closed form; a good approximation is (Farnell & Adler, 1972)
The continuum model of a homogeneous solid does not contain any intrinsic length scale. Accordingly, all the solutions for this model are non dispersive, meaning that the velocities (Eqs. (7) and (8)) are independent from wavelength (or frequency).
More complex modes occur in non homogeneous media. Layered media, like a supported film, are a particularly relevant case, in which new types of acoustic modes can occur (Farnell & Adler, 1972); namely, modes confined around an interface (Stoneley waves) and modes which are essentially guided by one layer (Sezawa waves). All these modes have a wavevector parallel to the surface. In this case the medium does have an intrinsic length scale, given by the layer thicknesses, and the modes become dispersive: their velocities depend on wavelength, or, more precisely, on the wavelength to thickness ratio(s). When the wavelength is comparable to the layer thicknesses, the displacement fields of the acoustic modes extend over several layers: the modes are modes of the whole structure. Their velocities therefore depend on the properties of at least two adjacent layers, and can be computed only numerically, as non trivial functions of the properties of the substrate and the layer(s), and of the wavelength to thickness ratio. The dispersion relations orcan thus be obtained.
In particular, in the design and analysis of measurement methods for a supported film, two basic cases can be distinguished: ‘high’ and ‘low’ thicknesses. Thickness is ‘high’ or low’ in comparison with the acoustic wavelength involved in the measurement; therefore a same thickness can be ‘low’ in an experiment which exploits relatively low frequencies, and ‘high’ in an experiment performed at higher frequencies, i.e. smaller wavelengths.
The thickness is ‘high’ when it is significantly larger than the involved acoustic wavelength. In this case the film behaves acoustically as a semi-infinite medium: it supports acoustic waves of bulk type, both longitudinal and transverse, as if it was infinite, and, at the free surface, supports the Rayleigh surface wave, as if it was semi-infinite. In this case all these acoustic modes are non dispersive, their properties depend on the material properties of the film alone, and in the analysis of experimental results the thickness value is irrelevant. It turns out, experimentally, that this regime is achieved for thicknesses of the order of a few wavelengths, without requiring thicknesses which exceed the wavelengths by orders of magnitude.
Thicknesses are ‘low’ when they are comparable to or smaller than the acoustic wavelength. The bulk waves cannot be fully developed in the film, the Rayleigh wave becomes a so called ‘modified Rayleigh wave’, whose displacement field penetrates in the substrate, and Sezawa waves can be supported, whose displacement fields also penetrate in the substrate. Therefore the properties of all these acoustic modes depend on the material properties of the film, but also on the film thickness, whose value becomes a crucial parameter, and on the properties of the substrate. In particular, the velocities of both the modified Rayleigh wave and the Sezawa waves depend on the wavelength to thickness ratio: these modes are dispersive. This must be taken into account in the analysis of experimental results.
A gradual transition from the ‘low’ to ‘high’ thickness behaviour occurs at intermediate values. For instance, when the film thickness is very small the Rayleigh wave has a displacement field which mainly extends in the substrate, and a velocity which approaches the Rayleigh wave velocity of the substrate. For increasing thickness the fraction of the acoustic energy which is in the substrate decreases, and the velocity gradually approaches the Rayleigh wave velocity of the film material; the latter is reached when the displacement field amplitude becomes negligible before reaching the substrate.
3. Measurement techniques
Some observations are recalled here concerning two methods to measure the acoustic velocities, namely quantitative acoustic microscopy (AM) and Brillouin spectroscopy (BS), and micro-indentation. It should be recalled that, unlike polymers which exhibit a frequency dependent mechanical response, the viscous effects in ceramic-like materials and in metals is generally negligible, such that the high and low frequency properties are essentially indistinguishable. It can also be remembered that the acoustic methods measure the adiabatic stiffness, which does not coincide with the isothermal one, measured in monotonic tests (if strain rate is not too high); however, in elastic solids the difference between adiabatic and isothermal moduli seldom exceeds the measurement uncertainties (Every, 2001). It is also worth remembering that in most metals and ceramics the acoustic velocities are of the order of a few km/s = μm×GHz.
3.1. Acoustic microscopy
Acoustic microscopy (Zinin, 2001; Zinin et al., 2012) is one of the techniques which adopt harmonic excitation. It exploits a piezoelectric actuator coupled to sapphire acoustic lens, which operates also as a transducer, in a pulse-echo operation mode. The acoustic lens is mechanically coupled to the sample by a liquid drop, often distilled water. Acoustic microscopy can be operated with imaging purposes; in the quantitative acoustic microscopy version (Zinin, 2001) it allows to measure the acoustic properties of the sample.
Experiments are performed by first adjusting the lens to sample distance
When the Rayleigh wave has the dominant role, the measurement of the period
where is the acoustic velocity in the fluid and
3.2. Brillouin spectroscopy
Brillouin scattering is the inelastic scattering of light by vibrational excitations of acoustic nature, or by long wavelength acoustic phonons; the scattering mechanisms are discussed elsewhere. In BS measurements a focused laser beam, of angular frequency Ω
BS thus measures the velocities of bulk and surface acoustic waves in a fully optical, and therefore contact-less, way. Obviously, bulk waves are detectable only in sufficiently transparent media. The probed acoustic wavelengths and are determined by the optical wavelength and the scattering geometry: with visible light they are typically sub-micrometric, resulting in acoustic frequencies in the GHz to tens of GHz range. Wavelengths in this range are three orders of magnitude larger than interatomic distances, making the continuum description (Eq. (1)) fully appropriate.
Although BS can be performed in various geometries (Grimsditch, 2001; Beghi et al., 2011; 2012), the most frequent one is backscattering (), which maximizes. This geometry selects, for scattering by bulk waves in isotropic media, the specific probed wavevector, where
During nano-indentation tests, an indenter is pressed onto the surface of the material that has to be characterized. The tip of the indenter, that can have different shapes, is made of a hard material, usually diamond. During the test, the load
The key parameter when analyzing indentation is the reduced modulus
From the theory of contact mechanics between an isotropic elastic half space and an elastic sphere (Hertz, 1881), the relationship between the contact force
where and are the Young modulus and the Poisson’s ratio of the indenter. In case of diamond, it is and.
The above solution, holding for a spherical indenter, has been extended to conical indenters by Sneddon (Sneddon, 1965). By using simple geometrical arguments on the geometry of the tip, he obtained the following force-displacement relationship:
in which is the opening half angle of the conical tip and
A simple relationship between the elastic parameter
Oliver and Pharr (Oliver and Pharr 1992) introduced a generalized method to determine the reduced modulus
in wich an adjusting empirical parameter
The contact area
The Oliver and Pharr method provides a simple relationship for the experimental determination of the contact depth
which is used to calculate the contact area and the reduced modulus
The ability of the nanoindentation technique to probe small amount of material by shallow penetration depths enables one to probe the mechanical properties of thin coatings without removing the film from the substrate.
The main difficulty in nanoindentation of thin films is to ensure that the properties of the substrate are not affecting the characterization of the coatings. To achieve this aim, a simple rule to restrict the maximum penetration depth to no more than 1/10 of the coating thickness is usually applied.
However, for measurement of the elastic properties, the influence of the substrate compliance is unavoidable. Despite this intrinsic difficulties, methods to determine film thickness out of nanoindentation on film/substrate systems are available. As an example, Doener and Nix (Doener and Nix 1986) determined a relationship between an effective reduced modulus (which is strictly related to
in which the subscripts
For deep indentations, i.e. for small
4. Data analysis
Data analysis is first discussed for the case of an isotropic semi-infinite medium. This analysis applies to the ‘high thickness’ films as well, either supported or free standing; with AM this regime can be achieved only by thicknesses of many micrometres, while with BS it is already achieved by thicknesses of a couple of micrometres.
The assumption of a semi-infinite medium, or of a film of ‘high thickness’, implies that the velocities of all the acoustic modes do not depend on the wavevector (Farnell & Adler, 1972). The crude outcome of measurements is a set of
The assumption of an isotropic medium implies that the stiffness is fully identified by two independent parameters: therefore it is intrinsically a two-dimensional quantity, which can be represented by a point in a two dimensional ‘stiffness space’. The ‘stiffness space’, in turn, can be represented by the (
4.1. Graphical method
The condition identifies a line in the ‘stiffness space’, and the condition identifies a confidence band, or a ‘stripe’. The same happens for, and, when available. A first analysis procedure is graphical, and basically consists of drawing the available curves, or bands, in the stiffness space. If two of them are available, typically and from AM (Bamber et al., 2001; Goodman & Derby, 2011), their intersection fully identifies the stiffness, and allows a semi-quantitative estimate of its uncertainty. If three or more lines are available, as it can happen with BS from sufficiently transparent samples (Beghi et al., 2011; Garcia Ferré et al, 2013), all their intersections typically do not coincide exactly, but the amplitude of the region which contains them allows a qualitative estimation of the consistency of the different measurement techniques. In particular, a confidence band which lies beside the intersection of the others is a hint to a possible systematic error in one of the measurement techniques.
Validations of the data analysis procedure have been performed exploiting fused silica samples supplied for calibration of the indentation equipment (Bamber et al., 2001; Garcia Ferré et al, 2013). In the derivation of stiffness values from the measured acoustic velocity the widely accepted value of 2200 kg/m3 was adopted for the mass density of fused silica. Fig. 1 shows a recent result obtained by BS, which allows to measure also the doublets due
to bulk waves (Garcia Ferré et al, 2013), In the derivation of the corresponding velocity the value of the refractive index
4.2. Least squares estimation method
A more detailed statistical analysis can be performed by a least squares minimization procedure. Following standard non linear estimation theory (Seber & Wild, 2003), a least square estimator
the weights being determined by the uncertainties. Obviously, the sum over the values is present only if the measurement of the bulk longitudinal wave is available. If the bulk transversal wave is also measurable, a further summation over the values is also present in Eq. (18). The minimum of identifies the most probable value of the couple, and the isolevel curves of the normalized estimator
identify the confidence region at any predetermined confidence level (Lefeuvre et al., 1999; Beghi et al., 2001, 2011, 2013). The value of
The estimation of stiffness is performed computing the normalized estimator
The robustness of this outcome was exploited to define the following procedure to pick the final results of the evaluation: for each parameter, the minimum and the maximum of the values falling within the confidence region are taken. Their average value is taken as the estimate of the parameter, and the semi-amplitude of the interval is taken as the estimate of its uncertainty. Graphically, this means taking, instead of the point at which the estimator is at its minimum and of the precise shape of the confidence region, the rectangle, with sides parallel to the axes, circumscribed to the confidence region, and its centre (see Fig. 2a). This gives a simple and clearly defined algorithm to identify the measured value and its uncertainty, for each of the parameters, namely for
The two-dimensional nature of stiffness must however be taken into account when seeking the values of the other parameters (such as
The most rigorous way to estimate the values and the uncertainties of all the parameters would require, as mentioned above, the estimation of the whole covariance matrix. A simpler procedure, which however fully takes into account the two-dimensional nature of stiffness, replicates the ‘circumscribed rectangle’ algorithm indicated above. Considering for instance
4.3. Anisotropic and non homogeneous cases
Until now, the data analysis procedure was discussed under the assumptions of isotropic and homogeneous medium, remembering that ‘homogeneous’ also includes layers in the ‘high thickness’ regime, in which the presence and the properties of the substrate are essentially irrelevant. The extension of the procedure beyond these assumptions is briefly indicated here.
In the case of an anisotropic, but still homogeneous, medium, the number of independent parameters needed to fully identify the tensor of the elastic constants is larger than two, meaning that stiffness is not a two-dimensional quantity, but a multi-dimensional one. Considering here for example the cubic symmetry, the independent parameters are three, which can be taken as C
From the acoustic point of view, in a homogeneous anisotropic medium the acoustic waves can be not exactly longitudinal and transverse, and, more importantly, their velocity depends on the direction of the wavevector
It is thus evident that the anisotropic case requires a data analysis which is substantially more complex, and, perhaps even more importantly, it requires measurements performed on surfaces of various orientations. This typically requires crystals with different cuts, which, in the case of films, might be not achievable. In the case of supported films, and remembering that we are now dealing with the ‘high thickness’ regime, it seems that the only type of anisotropy which can be characterized in detail is the transverse isotropy, meaning a film which is isotropic in its plane and has different properties in the perpendicular direction.
Remaining instead in the isotropic case, but relaxing the assumption of homogeneous medium, a couple of cases seem to be tractable in some detail. The first one is that of a homogeneous substrate with a homogeneous supported film in the ‘low thickness’ regime, in which the substrate becomes relevant. In this case ‘non homogeneous’ means a sharp discontinuity between two homogeneous media. The second case is that of a mild gradient of properties, distributed over a superficial layer.
In a homogeneous supported film, beside the Rayleigh wave of velocity, other surface waves can exist (Sezawa waves). For all of them, for given substrate properties and film thickness
From the indentation point of view, the critical point for a supported film in the ‘low thickness’ regime is the avoidance of the influence of the substrate. With BS the ‘low thickness’ regime occurs at thicknesses of the order of one micrometre or less, for which the avoidance of substrate influences is a crucial point, but it can be dealt with using sharp tips with accurate diamond area function calibrations (Barone et al. 2010) and shallow penetration depths. With AM, as discussed above, the ‘low thickness’ regime can occur at thicknesses of several micrometres, for which indentation can be easily performed avoiding the substrate influences. Therefore, for films of this thickness, the characterization by AM can be substantially improved by the combination with indentation.
The second case, that of a mild gradient of properties distributed over a finite depth, can be treated in an approximate way considering the average properties over the explored depth. In this case it is crucial that the indentation depth be comparable to the exploited acoustic wavelength(s) (Goodman & Derby, 2011). Although the two techniques do not average in the same way the properties at different depths, the above condition ensures that averaging is performed over the same depth interval. This procedure approximates the actual superficial gradient by a homogeneous equivalent film of average properties, over a perfectly homogeneous substrate of slightly different properties.
5. Experimental results
The combination of AM and indentation, after successful validation by a fused silica sample, was exploited to characterize TiN/NbN multilayers deposited by closed field magnetron sputtering (Bamber et al., 2001), assuming for the mass density of the multilayer the same value of TiN, 5210 kg/m3. Since the thicknesses of the single layers are much smaller than the acoustic wavelengths at which they are probed, the whole multilayer coating acoustically behaves as an equivalent homogeneous medium. In this case, the same authors state that the results were not conclusive, and they present a detailed analysis, focusing on the interpretation of the indentation results: they show that a main source of uncertainty lies in the analysis of indentation results from a multilayer.
Other two possible sources of uncertainty can be considered. Firstly, since the thickness of the whole multilayer is smaller than the acoustic wavelength, the layer is not in the ‘high thickness regime’, meaning that also for the acoustic behaviour the influence of the substrate is not negligible, and that the speed of the Rayleigh wave depends on frequency. The authors mention that by performing AM measurements at various frequencies the dispersion relation can be measured, but they do not give details on how they exploited this possibility. Secondly, by its same geometry a multilayer is not isotropic. It has in-plane isotropy, but different properties in the normal direction. This type of anisotropy corresponds to hexagonal symmetry (transverse isotropy), which requires five independent parameters to fully specify the elastic tensor. An isotropic model is the best approximation currently available with the experimental information, but it obviously introduces approximations.
A similar investigation (Goodman & Derby, 2011) was aimed at comparing the properties of the air side and the tin side of float glass, which is produced by floating molten glass on molten tin. The mass density values were taken from previous studies on the properties of soda-lime glass, and on the influence of the tin content. In this case, despite the need of considering a possible gradient of properties in the superficial layer, due to the occurrence of microdefects and to diffusion of tin, higher precision results were obtained, allowing to detect a measurable difference between the two sides. Due to the possible gradient of properties close to the surface, it was ensured that the depths probed by indentation and by AM be strictly comparable.
In a recent investigation (Garcia Ferré et al, 2013), the combination of indentation and BS was exploited to achieve a complete mechanical characterization of Al2O3 coatings deposited by pulsed laser deposition (PLD). Coatings were deposited on silicon wafer and on stainless steel substrates, ablating a 99.99% pure polycrystalline alumina target, and obtaining ultra-smooth samples (RMS <0,1 nm). SEM observations show a uniform, compact and fully dense microstructure; Raman spectroscopy and X-ray diffraction supply evidence of the amorphous structure of the coatings. Due to the absence of a crystalline structure and of a structure at mesoscopic level, like e.g. a columnar structure, the coating properties are assumed to be isotropic. The thickness of the measured coatings were between 4 and 8 μm. This means that by BS the layer is acoustically in the ‘high thickness’ regime, and that indentation can be performed with penetration depths, ranging from 300 to 500 nm, below one tenth of the layer thickness, thus avoiding the effect of the substrate.
Nanoindentation measurements were carried out by a nanoindenter (Micro-Materials, Ltd., Wrexham, UK) equipped with a diamond Berkovich tip. The reduced Young’s modulus and hardness were assessed from the indentation curves following the Oliver and Pharr approach discussed above. BS measurements were performed in the backscattering geometry, with incidence angles from 30° to 70°, using an Ar+ laser at the wavelength of 514,5 nm, and analyzing the scattered light by a tandem multipass Fabry-Perot interferometer of the Sandercock type.
Since the coatings are transparent, BS can measure bulk acoustic modes, but only the longitudinal one could be reliably measured. In the analysis of the corresponding data the value of the refractive index is needed: ellipsometric measurements supplied
This combination of ellipsometry, BS and nanoindentation was called ‘EBN procedure’ (Garcia Ferré et al., 2013). Its validation was achieved by a bulk silica sample supplied by the producer of the indenter for calibration purposes, of nominal properties
For the silica sample the results from BS and from indentation are shown in Fig.1: the confidence bands resulting from the various measurements all intersect in a small region, showing a high degree of consistency among measurement techniques of completely different nature.
For the alumina coatings indentation measurements gave for the reduced modulus
The results of Table 1 show that the stiffness of these PLD deposited alumina coating is significantly different from that of most ceramic coatings: namely, Young modulus is lower and Poisson’s ratio is higher, resulting in a stiffness which is close to that of steel. This finding could be rationalized in the light of TEM analysis, which shows that the coatings consist of a homogeneous dispersion of ultra-fine (2-5 nm) Al2O3 nanoparticles in an amorphous alumina matrix (Garcia Ferré et al., 2013). This metal-like stiffness is interesting, because at the substrate/coating interface a stress concentration occurs, due to the discontinuity of mechanical properties. The stress concentration can promote delamination, therefore a smaller stiffness discontinuity, reducing the stress concentration, can favour the durability of adhesion.
|195.3 ± 7.6|
|0.294 ± 0.020|
|75.5 ± 3.8|
|159.2 ± 11.8|
|C11 (GPa)||259.8 ± 9.7|
Nanoindentation is among the most widespread techniques to perform the mechanical characterization of materials. It is applicable to bulk materials, and it is the standard characterization route for supported films whose thickness is not too low. Beside the value of hardness, instrumented indentation can supply a measurement of stiffness, by the careful analysis of a deformation process which involves both elastic and inelastic strains. However, stiffness is a two-dimensional quantity for isotropic materials, and has a higher number of dimensions in the anisotropic cases. Indentation supplies a one-dimensional estimate, and can achieve a full estimate only by some kind of assumption, typically about the value of Poisson’s ratio. The techniques which exploit propagating acoustic waves involve exclusively elastic strains: they therefore offer the most direct access to the elastic properties, and potentially their most accurate measurements. However, if only one acoustic mode can be detected, as it typically happens with AM and with BS of metallic samples, also acoustic techniques only supply a one-dimensional estimate. The combination of indentation and an acoustic method then allows to obtain the full two-dimensional measurement of stiffness, avoiding any assumption. With sufficiently transparent samples BS can detect further acoustic modes, supplying additional information and allowing to reduce the uncertainties. The consistency of results obtained by the two completely different methods could be checked by reference samples. The combined procedure, which is able to achieve the complete elastic characterization without needing assumptions, is particularly useful in the case of materials with novel properties, either for the novelty of the material or for the novelty of the production process. In these cases any assumption is not sufficiently grounded, and might lead to misleading results; the combined procedure then achieves a characterization of stiffness whose accuracy and reliability would not be reachable by each of the techniques alone. Furthermore, the presence of indentation simultaneously provides the measurement of hardness, intrinsically out of the reach of acoustic methods.
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