Superhardness Testing

Evaluation of hardness of super- and ultrahard coatings presents challenges in nanomaterial characterization. The point is that currently artificial superhard nanocomposite coatings exhibit hardness levels that approach the hardness of diamond. It is known [763] that diamond tips (Vickers, Knoop, Berkovich) are used as indenters in hardness testers. In the case of superhard and ultrahard nanocomposites, the hardness of the material is evaluated by indenters with similar hardness [764, 765].

Currently, two methods have been put forward to solve this problem. The first one is to use in the capacity of nanoindenter a tip possessing hardness significantly higher than that of diamond [766]. The second one is to estimate hardness using methods based on other physical principles [767].

The correct use of microhardness measurements is currently of great concern in materials science for the evaluation of superhard coatings [580]. Finding trustworthy methods to determine the hardness of superhard/ultrahard coatings is a major challenge in the research and development of such coatings [324]. Here, "correctness" implies [580] that the value of microhardness should not depend on the load and not be affected by the substrate.

Hardness is defined as the ability of materials to resist plastic deformation and is measured as a result of plastic deformation [768]. The plastic deformation is created by the diamond indenter, which undergoes a force at any time. It is assumed that the diamond indenter is a perfectly rigid body, which has not undergone either plastic or elastic deformation. The diamond indenter satisfies the conditions for the hardness measurement of conventional hard materials that have a moderate hardness.

Usually, the bulk modulus appears in further evaluations of hardness. However, some researchers question the reliability of its usage. It is reckoned [769] that the shear modulus significantly better reflects hardness than the bulk modulus. Indeed, the equation for the calculation of the critical value of dislocation spacing in the pileup includes the shear modulus (not the bulk modulus) and hardness [341]. The relationship between the hardness (H) and the shear modulus (G) is expressed as follows [770]:

H = (Gb)/c where b is the numerical value of Burger's vector and c is a constant.

Both a microhardness tester with a diamond indenter of Knoop type [771] and a microhardness tester with a diamond indenter of Vickers type are used to measure plastic microhardness in coatings. A loading force of 50 mN, 100 mN, and 250 mN, which corresponds to a weight of 5 g, 10 g, and 25 g, respectively, is usually chosen to minimize errors due to the influence of a softer substrate than that of the coatings. Scanning electron microscopy (SEM) as well light microscopy (LM) is used to observe and to estimate small indentations at low measuring forces. SEM provides more reliable measurements of the indentation length than LM due to its better resolution over LM. The plastic micro-hardness of various coatings has been found to be reproducible to within 2 GPa [170].

Hardness is a function of many characteristics [772, 773]. Hardness depends on the test systems (i.e., Vickers, Knoop, etc.) [19], the test regimes (i.e., applied load, duration of the applied load, etc.) [19, 774], and the method of hardness evaluation [19].

As to the microhardness measurement of nanocomposite coatings, there are two issues of major concern. The coatings (see Tables 1 and 3) are, first, very thin and, second, very hard. Their thickness and hardness have a predominant influence on the final result.

The conventional Vickers microhardness tester is not applicable for the hardness estimation of thin coatings because the indenter penetration depth should be approximately 10% of the total coating thickness [775]. A composite hardness model uses an area law-of-mixtures approach, which [776, 777] is applied when the surface displacement is greater than the coating thickness.

Nanoindentation To overcome this challenge, nanoinden-tation hardness testing (NHT) for thin coatings (10 nm-10 ¡m) has been developed [778-782], for example, Triboscope Testing System (Hysitron Inc.) [783-785], Nanoindentor® (Oak Ridge National Laboratory) [786, 787], Nanoindentor (Nano Systems Inc.) [788], ND-100 [789], CSEM Nano Hardness Tester, and so on. Nanoin-dentation testing is widely used for hardness measurements [570, 788, 790-798]. Different types of nanoindentation equipment were tested and practically evaluated [799, 800]. Some strengths and weaknesses of the nanohardness measurements have been described elsewhere [789, 801, 802].

Computer-controlled nanoindenters record a load-penetration depth curve automatically in a continuous regime. The normal force (load) varies from 20 ¡N to 300 mN. A range of penetration from 10 nm to 200 ¡xm was considered in this case.

As reported [803], hardness keeps increasing with decreasing normal force. If hardness measured by nanoin-dentation is converted into micro-Vickers hardness, the value of the microhardness becomes significantly lower [775]. The nanoindentation requires a correction of Sned-don's solution for indentation [804].

The hardness is usually calculated as the maximum normal force divided by the area of the indentation after subtraction of the elastic deformation [789]. Both a scanning electron microscope [805] and an atomic force microscope [806-808] are used instead of an optical microscope, which is limited by a resolution of about 1 ¡m, to measure the imprint diagonal.

For correct microhardness measurement, first, the ratio (d/h) of the indenter penetration depth (d) to the total coating thickness (h) should be increased from 10% to 15%, and, second, a correct minimal load (Lmin) for a given microhardness should be chosen, that is, Lmin = 50 mN for about 70 GPa and Lmin = 100 mN for about 80 GPa [580].

The development of superhard and ultrahard coatings with hardness greater than 70 GPa requires novel methods for hardness evaluation [324]. There are plenty of factors, such as type of indenter [763], substrate effect [809-815], surface adsorption [816], and surface effects [817, 818], that influence microhardness. For example, compressive stress has been found to increase the hardness of the deposited coatings [577].

A new approach to hardness measurements of super-hard materials using a scanning force microscope with an ultrahard fullerite C60 tip was developed [766]. It has been demonstrated that diamond is plastically deformed under the harder C60 fullerite indenter at room temperature. The diamond hardness values were evaluated as 137 ± 6 GPa for (100) diamond face and 167 ± 6 GPa for (111) diamond face. Here, the C60 ultrahard fullerite tip can be considered as the perfectly rigid body, which is used for hardness testing. A subsequent ultrahard material, which will be harder than the C60 ultrahard fullerite, will be utilized for quantitative hardness measurement of the C60 fullerite.

Indirect Evaluation of Hardness Because there is currently no other suitable method for hardness testing, comparing the hardness tested by different methods, including indirect methods, can give relatively reliable values of hardness.

The evaluation of hardness from the absorption band tail is a nondestructive technique. The method has been based on the effect of mechanical stress on the optical absorption band tail [767]. The hardness (H) of coatings can be calculated from the following equation [819]:

H = 2.9[Y/(1 - y)](100.0/x)-n(Sa/a)l-n where Y is Young's modulus, y is the Poisson ratio, (Sa/a) is the strain, n is the strain-hardening coefficient, and x is the indentational strain.

The absorption coefficient (a) at any frequency (v) and the absorption coefficient (a0) at the band edge are used to plot the dependence of a/a0 on (Eg - hv) in order to obtain the strain (Sa/a) in the coating [820]. The stress (S) in the coating can be also calculated from the equation [819]:

This procedure has been used to evaluate the hardness and stress in nanocrystalline diamond coatings [46]. The evaluated hardness of these coatings with Young's modulus Y = 600 GPa and Poisson ratio v = 0.11 has been found to be in good agreement with the hardness estimated by conventional indentation techniques.

Alternatively, Young's modulus for ultrathin coatings can be experimentally measured using the laser-acoustic technique [821, 822]. The laser-acoustic method is a nondestructive method based on measuring the dispersion of surface acoustic waves. In particular, the laser-acoustic technique has been widely adopted in the evaluation of diamond and diamond-like carbon coatings [823-826] as well as multilay-ered coatings [827].

The brief overview of currently utilized techniques for nanostructure evaluation and for hardness determination has shown that there are distinguishing peculiarities in the application of the different methods in the evaluation of nanostructured coatings. Because of the low thickness and high hardness of nanocomposite coatings, the problem of hardness measurement still persists. The smart principle forming the basis of Mohs' scale, that is, every subsequent hard material surpasses all preceding ones, can be useful for a quantitative hardness evaluation of super- and ultrahard nanocomposite coatings.

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