Indentation Approach Research Articles

Effect of grain boundary on scratch behavior of polycrystalline copper

The anisotropy in the elastoplastic response of crystalline solids influences substantially their scratch resistance at the microscale. While grain boundaries typically act as obstacles to the motion of dislocations at the grain level, the scratch behavior in the vicinity of the grain boundary is influenced by other factors such as crystallographic orientation and pile-up topography. We performed a systematic set of nano-scratch simulations using the mechanism-based strain gradient crystal plasticity to study the evolution of scratch force and depth near grain boundaries. To validate our model, we conducted a nano-scratch test on a polycrystalline copper sample and compared the scratch depth profile for a specific grain boundary with the simulated result, where a good qualitative agreement was achieved. Our simulations showed that the scratch depth, force, and hardness vary between the corresponding values for the individual constitutive grains, and the variation decreases by reducing the grain size. Additionally, we analyzed the scratch response in terms of the pile-up topography and subsurface stresses and distinguished different regimes when the indenter approaches and scratches across the boundary. Our findings offer a new direction to optimize the scratch resistance of polycrystalline metals by tailoring the size and orientation of grains near the surface. Additionally, it introduces scratching as a robust material characterization method.

Analysis of failure characteristics and mechanical mechanisms of sandstone during spherical indenter intrusion based on acoustic emission experiment

This paper aims to investigate the effects of steel ball diameter on failure characteristics and mechanical mechanisms of sandstone during the spherical indenter intrusion process. By using equipment such as acoustic emission (AE), the process of spherical indenter intrusion into sandstone was monitored and recorded for analysis of the fracture characteristics, load-depth relationship, and specific energy of sandstone under spherical indenters with different diameters. The results showed that as the diameter of the spherical indenter increased, the peak load of the sandstone increased continuously, and the failure mode transitioned from “jump-type” to plastic, with the acoustic emission count exhibiting a staged variation characteristic. During this process, the accumulated acoustic emission count, intrusion coefficient, and specific energy of intrusion all exhibited a “parabolic” law of first decreasing and then increasing, all of which reached minimum values when the ratio of the diameter of indenter to sandstone was close to 1.0. This indicated that as the diameter of the indenter approaches that of the sandstone, the intrusion process becomes more facile and efficient. Finally, the study revealed the formation mechanism of dense core and crack inside the sandstone during intrusion, and discussed the law of the crushing rate in ball milling from the perspective of compression. The conclusions contribute to revealing the fragmentation mechanics of rocks in the ball milling process and aid in determining the ball loading parameters in the milling process based on rock properties, aiming to achieve energy-saving and cost reduction.

Machine learning based dual flat-spherical indentation approach for rough metallic surfaces

Instrumented indentation test (IIT) is regarded as one of the non-destructive test methods for mechanical characterization and safety assessment of engineering components. However, indentation test is very sensitive to surface topography i.e surface roughness, requiring specimens with ideally flat and smooth surface for producing reliable and reproducible test results. Recently, a dual flat-spherical indentation (DFSI) technique was proposed to extract material properties directly from rough metallic surface via indentation tests. Integration of DFSI technique with machine learning (ML) approach can facilitate reliable and fast characterization of rough metallic surfaces. Here, ML models including artificial neural network (ANN) and physics-informed artificial neural network (PI-ANN) are established, and then trained by using a database of indentation parameters generated via DFSI simulations. Spherical indentation techniques available in the literature are used to calculate the physics-informed loss in the PI-ANN model. The performances of trained ANN and PI-ANN models are compared, and an optimal ML model with hyperparameters is suggested based on validation study; PI-ANN model with sigmoid activation function shows a better performance than the ANN model and baseline model. The model performances are evaluated by performing DFSI experiments with SM45C and SS304. The applicability of ML based-DFSI method is demonstrated for extracting the mechanical properties from the rough surface of general metals.

Achieving Diamond-Like Wear in Ta-Rich Metallic Glasses.

Most metals and alloys suffer from high friction and wear due to their low hardness and lack of self-lubrication. Although plenty of strategies have been proposed, it is still a long-standing challenge to achieve diamond-like wear in metals. Metallic glasses (MGs) are supposed to possess low coefficient of friction (COF) because of their high hardness and fast surface mobility. However, their wear rate is larger than that of diamond-like materials. Here, this work reports the discovery of Ta-rich MGs that exhibit diamond-like wear. This work develops an indentation approach for high-throughput characterization of crack resistance. By employing deep indentation loading, this work is able to efficiently identify the alloys that exhibit better plasticity and crack resistance according to the differences of indent morphology. With high temperature stability, high hardness, improved plasticity, and crack resistance, the discovered Ta-based MGs exhibit diamond-like tribological properties, featured by COF as low as ≈0.05 for diamond ball test and ≈0.15 for steel ball test, and specific wear rate of only ≈10-7 mm3 N- 1 m-1 . The discovery approach and the discovered MGs exemplifie the promise to substantially reduce friction and wear of metals and may unleash the potential of MGs in tribological applications.

Cementing CO2 into C-S-H: A step toward concrete carbon neutrality.

Addressing the existing gap between currently available mitigation strategies for greenhouse gas emissions associated with ordinary Portland cement production and the 2050 carbon neutrality goal represents a significant challenge. In order to bridge this gap, one potential option is the direct gaseous sequestration and storage of anthropogenic CO2 in concrete through forced carbonate mineralization in both the cementing minerals and their aggregates. To better clarify the potential strategic benefits of these processes, here, we apply an integrated correlative time- and space-resolved Raman microscopy and indentation approach to investigate the underlying mechanisms and chemomechanics of cement carbonation over time scales ranging from the first few hours to several days using bicarbonate-substituted alite as a model system. In these reactions, the carbonation of transient disordered calcium hydroxide particles at the hydration site leads to the formation of a series of calcium carbonate polymorphs including disordered calcium carbonate, ikaite, vaterite, and calcite, which serve as nucleation sites for the formation of a calcium carbonate/calcium-silicate-hydrate (C-S-H) composite, and the subsequent acceleration of the curing process. The results from these studies reveal that in contrast to late-stage cement carbonation processes, these early stage (precure) out-of-equilibrium carbonation reactions do not compromise the material's structural integrity, while allowing significant quantities of CO2 (up to 15 w%) to be incorporated into the cementing matrix. The out-of-equilibrium carbonation of hydrating clinker thus provides an avenue for reducing the environmental footprint of cementitious materials via the uptake and long-term storage of anthropogenic CO2.

Comparison of Oliver-Pharr and Work of Indentation Approach to Determine the Mechanical Properties of Melt-Spun Al-12%Wt.Si-0.5%Sb Alloy

In this research, the hardness and reduced modulus of Al-%wt.12-%wt.0.5Sb melt-spun alloy were evaluated by using depth sensing indentation and atomic force microscopy techniques. We considered two approaches, Oliver-Pharr and Work of Indentation, to analyse the load-displacement curves. The ratio of final depth to maximum depth was found to be higher than the reported critical value of 0.70, which mean that pile-up was dominant in the melt-spun. A pile-up around the deformed surface was observed from atomic force microscope, which is consistent with the aferomentioned result. The hardness calculated by Oliver-Pharr method was higher than that calculated by Work of Indentation Approach. According to the results, Work of Indentation Approach was more reliable than the Oliver-Pharr approach because of reducing pile-up affect.

Modeling the indentation size effects of polymers, based on couple stress elasticity and shear transformation plasticity

This work attempts to construct models which can describe the size effects in modulus and hardness of polymers measured by indentation tests. Firstly, the origin of size effects in the procedure of nanoindentation is analyzed. The finding of the literature that the indentation size effects of polymers are of significant elastic nature is further discussed and confirmed. The elastic size effects are described by a model, through introducing a model of elastic unloading load with consideration of couple stress elasticity into the Oliver-Pharr indentation approach. The accordingly proposed modulus model and hardness model agree excellently with a large amount of experimental data obtained from literatures. The models show that the elastic size effects of polymers and their experimental observations are mainly determined by the molecular structures. The fitting results verify that the size effects in indentation hardness of polymers with complex molecular structures are significantly elastic. It is postulated that the plastic size effects in indentation hardness of polymers are only derived from their glassy components. A shear transformation plasticity formula of glassy polymers recently proposed by literature is slightly extended to characterize the size dependent deformations in indentation tests. A hardness model with consideration of size effects is accordingly obtained and agrees well with related experimental data.

A new spherical indentation approach to determine fracture toughness of high strength steels

Fracture toughness indicates the resistance to unstable crack growth that is very important in the assessment of structural integrity. As the Instrumented Indentation Test (IIT) technique is relatively simple to perform, it has been suggested as an alternative way to determine fracture toughness of engineering materials. This paper presents a new spherical IIT approach to predicting fracture toughness of engineering materials using the critical contact pressure. Firstly, according to Johnson’s maximum strain energy theory under indentation, the formula of critical contact pressure under IIT is derived by considering strain hardening and fundamental tensile properties. Secondly, by using an automatic iterative procedure of translating the input and output data between MATLAB and ANSYS, finite element analysis is carried out to build a dummy database of critical contact pressure versus strain hardening and tensile properties for a broad scale of engineering materials. Finally, for the sake of engineering applications, a general analytical formula is put forward according to the dummy database, by which the critical contact pressure and thus the critical indentation depth can be read directly. Fracture toughness of engineering materials is then determined using the concept of indentation energy to fracture at the critical indentation depth. Validation of predicted fracture toughness and tensile properties of four high strength steels is taken out using compact tension (CT) and standard tensile tests, respectively. Good agreements are found between the standard tests and IIT.

Adhesion Analysis considering van der Waals force

In the present paper, an adhesive contact analysis of a rigid sphere and a half-elastic region is conducted using DC-FFT method. In the analysis, the van der Waals force is taken into formulation of contact analysis. Values of surface energy used in the analysis are obtained through Tabor parameter. Dimensionless radii of spherical indenter are 5, 10 and 15. When the indenter approaches to the substrate, the substrate is firstly pulled up by tensile force, and adhesion occurs. The contact pressure is almost flat in the first adhesion area. When the indenter moves down, the compressive force occurs at the center of adhesion area. The tensile force exists around the edge of adhesion area. The gap between the indenter and the substrate at the edge of adhesion area varies with surface energy from ε0 to 1.2ε0.

Stress-Induced Transistor Degradation Studied by an Indentation Approach

The strain impact on integrated circuit performance is investigated by applying a novel indentation technique. The approach aims to investigate stress caused by CPI, particularly highly localized stress/strain with respect to the actual device geometry. Non-destructive elastic indentation is used to induce homogenous stress fields in the vicinity of the test structure by applying a contact with a spherical tip. Strain-sensitive ring oscillator structures manufactured in the 22 nm FDSOI CMOS technology node are designed to monitor the device and simultaneously the NMOS and PMOS strain behavior separately. Complementary FE-simulations provide a deeper insight into the obtained experimental results by transferring them from contact force into the stress/strain space and validating the indentation approach. Relevant layout and indentation dependent parameters are investigated and evaluated. The simulation of the strain-induced mobility shift and the comparison with the established correlation verifies the accuracy of the approach. The results provide an insight into package-related stress and resulting transistor degradation, aiming at establishing a versatile tool to estimate the effect of specific real-usage conditions.

The imperfection sensitivity of axially compressed steel conical shells – Lower bound curve

This paper presents the numerical results centered on the buckling behavior of axially compressed imperfect conical shells. It was assumed that the cone model was made from mild steel. The perfect cone will be subjected to multiple imperfection approaches such as (i) eigenmode imperfection, (ii) single and multiple load indentation approaches, (iii) crack imperfection, and (iv) uneven axial length imperfection to study the reduction of buckling strength of the structure. As predicted, imperfection severely affected the buckling strength of conical shells, and the decrease in buckling strength could be seen to be heavily reliant on the imperfection approach. It is apparent that for axially compressed cones with radius-to-thickness ratio, r1/t = 25, uneven axial length imperfection was seen to produce the lowest buckling load, followed by eigenmode imperfection, crack imperfection, and load indentation for imperfection amplitude 0 < A < 1.68. Increasing the imperfection amplitude, A, beyond this level, i.e., A ≥ 1.68, the highest reduction in buckling load was found to be eigenmode imperfection, followed by the uneven axial length, crack and load indentation. Furthermore, based on ECCS 2008 recommendation for imperfection tolerance, the lower bound curve, which can be used for design recommendation purposes, has been proposed for the worst imperfection approach case, i.e., uneven axial length and eigenmode imperfection for different conical shell geometry configurations. Finally, the proposed lower bound curve was compared with the plot of NASA SP-8019 recommended imperfection correlation factor for axially compressed cone. Results showed that the proposed lower bound curve for axially compressed conical shells with uneven axial length imperfection is notably higher than the NASA SP-8019 KDF by 7%, thus confirms the conservativeness of NASA SP-8019 KDF. However, axially compressed conical shells with eigenmode imperfection were seen to underestimate NASA's KDF by 55%, particularly for elastic buckling.

DEVELOPMENT OF AN APPROACH FOR ASSESSING THE HARDNESS OF COATINGS WITH DYNAMIC INDENTATION

The article discusses the features of the method for assessing the hardness of coating materials based on the dynamic indentation approach, the essence of which is the continuous registration of the process of contact interaction of the indenter with the material under study. According to the research results, a regression dependence was obtained in the form of a polynomial of the second degree, which makes it possible to assess the hardness of a galvanic nickel coating.

Measurement of fracture toughness of copper via constant-load microscratch with a spherical indenter

Fracture toughness can be measured by microscratch test from objective force and depth measurement, which is much convenient than indentation approach and conventional means, since initial notch or pre-crack is not required. Micro-scratch test was conducted on copper under a spherical probe of radius 105 μm and constant applied normal load with the aim of characterizing fracture toughness of copper by sliding technique with a sphere. Scratch variables such as normal load, lateral load, friction coefficient, and penetration depth were analyzed, and different methodologies for calculating fracture toughness were compared. Linear elastic fracture mechanics was found to be inapplicable to scratch of elastic-plastic material with sufficient plasticity under a spherical probe, while energetic size effect law can be successfully applied to characterize fracture toughness by microscratch test with a sphere abrading metallic material.

Indentation adhesion of hydrogels over a wide range of length and time scales

Hydrogels are both important engineering materials and living components. In both native and engineering settings, hydrogels often interface with other materials. Quantifying the adhesion properties and understanding the adhesion mechanisms of hydrogels are important. Among various measuring techniques, indentation is the most convenient method to be applied on hydrogels with the minimum requirement for sample preparation. It is also easy to be applied across a wide range of lengths scales. In this work, we use polystyrene spheres to probe polyacrylamide hydrogel surfaces. Using Atomic Force Microscope (AFM) and microindenter, we could carry out indentation measurements across a wide range of length scales with the contact radius ranging from 1.94 μm to 75.5 μm. As the indenter approaches and is pressed into the hydrogel, no long-range interaction is observed. The force–displacement curve during the loading period follows the Hertzian solution. The indenter is then held in a certain depth of indentation for a different amount of time and retracted from the surface until full separation. During the holding time, the hydrogel relaxes due to poroelasticity. Adhesion only plays a role during the retraction process. The pull-off force and energy of separation are observed increasing over contact time, and the time scale is independent of the poroelastic relaxation time scale of the hydrogel. The pull-off force and energy of separation are also found increasing with contact size and reaching plateaus at large contact sizes. This phenomenon cannot be modeled by the conventional adhesion theories, such as the JKR theory or the Maugis–Dugdale theory. In order to model adhesion hysteresis and the size-dependence and to extract intrinsic adhesion properties of the interfaces, we develop an analytical model. As the indenter is pulled up, a ring of cohesive zone is developed. As the indenter is pulled further, the cohesive zone size increases, but the apparent contact radius is kept constant until the energy release rate reaches the adhesion energy. Based on this picture, analytical solutions are developed, and the theoretical results fit well with experimental data. This systematic study provides more precise descriptions of the adhesive contact of hydrogels and provoke a deeper understanding of the adhesion mechanisms of hydrogels.

Disuse Impairs the Mechanical Competence of Bone by Regulating the Characterizations of Mineralized Collagen Fibrils in Cortical Bone

Bones are made of complex material comprising organic components and mineral hydroxyapatite, both of which formulate the unique hierarchical structure of bone and its mechanical properties. Bones are capable of optimizing their structure and mechanical properties according to the mechanical environment. Mineral loss is a well-known consequence of skeleton disuse. By contrast, the response of the non-mineral phase of bone, i.e., the collagen network, during disuse remain largely unknown. In this study, a tail-suspension mice model was used to induce bone loss. Atomic force microscopy-based imaging and indentation approaches were adopted to investigate the influence of disuse on the morphology and in situ mechanical behavior of the collagen fibrils, under both non-loaded and load-bearing conditions, in the cortical tibia of mice. The results indicate that disuse induced by hindlimb unloading did not alter the orientation and D-periodic spacing of the collagen fibril, but results in decreased collagen crosslinking which correlates with decreased elasticity and increased susceptibility to mechanical damage. More concretely, the collagen fibrils in the disused tibia were misaligned under mechanical loading. It therefore indicates that the disordered arrangement of the mineralized collagen fibrils is one of the characteristics of the weakened bone during elastic deformation. These findings reveals the unique adaptation regimes of the collagen fibrils in the cortical bone to disuse, as well as the deformation mechanisms of bone in the relevant pathological process at different scales.

Optimization on strength spot welding joint trough finite element modelling indentation approach

Failure behaviour of spot welding are important in order to design the weld strength on dissimilar spot welded joint as a significant step to reduce vehicle weight in the development of urban transportation systems. Environmental friendly. Including in this case to take positive measures to reduce CO2 emissions and reduce fuel consumption. The material failure behaviour, properties parameter of plastics materials and fracture of materials can be easily determined when the specimen material standards (i.e parent metal) but for the results of spot welding joint testing standards are not applicable to characterize the HAZ and spot welding nugget because it is constrained by a complex structure and a small sample size. One potential approach to be developed in the behaviour of material failure, parameter plastic properties of material is to combine the numerical-experimental method. Where ph-curve indentation experimental results combined with numerical approach through Finite Element (FE) modelling. Approach was established to be used for reverse (inverse) testing of the nature of constitutive material (i.e the yield stress (σy), the coefficient of strain hardening (n)) for nugget, HAZ and the parent material (base). In this approach the Load data of material deformation used as input data for finite element model (FE) which simulates the geometry and boundary conditions of the experiment. Finite element model (FE) Model-based approaches are developed, validated then used to predict the effect of nugget size and thickness of the sheet metal on the strength of the weld joint points with different materials (dissimilar material).

Corrections to the stiffness relationship in 3-sided and conical indentation problems

One key relationship in the depth-sensing indentation technique is the proportionality between the contact stiffness and the contact size, as can be proved from the Sneddon's solution of axisymmetric frictionless contact. However, Sneddon's solution is only accurate when the indenter approaches a half-space (e.g., for conical indenter, the half-apex angle approaches 90º) and the interface is frictionless. As Hay et al. (J. Mater. Res., 1999) pointed out, sharp indenters lead to a radial inward displacement on the sample surface, thus leading to extra indentation force needed to push the surface back to conform with the conical indenter. In this paper, we argue that the physical origin arises from the incorrect use of reference and deformed coordinates in the boundary conditions that define Sneddon's problem. This yields two correction factors for both load and depth solutions, which are needed for sharp pyramidal indenters and frictional contact. Approximate solutions are derived which compare favorably well with the finite element simulations. We also find that the stiffness correction factor of three-sided indenter is about 11∼15% times higher than that of conical indenter, and this multiplicative factor is only a weak function of the indenter angle but does not depend on the friction coefficient and Poisson's ratio.

Characterization of the Interfacial Toughness in a Novel “GaN-on-Diamond” Material for High-Power RF Devices

GaN thin film integrated to polycrystalline diamond substrates is a novel microwave transistor material with significantly improved heat dissipation capability. Due to the thermal and mechanical properties mismatch between GaN and diamond, a natural concern arises in terms of its interfacial stability as currently there is no established method to evaluate the interfacial toughness in GaN-on-diamond material. Using three generations of “GaN-on-Diamond” materials with varying process parameters, a comprehensive study has been carried out to identify the most appropriate fracture mechanics-based methods for reliable evaluation of the interfacial toughness in this novel material system. Several techniques were assessed, and the results are cross-compared; these include an ex situ nanoindentation induced buckling method and two-step indentation approach together with several analytical models. Additionally, a microcantilever bending method was adopted to measure an upper bound for the interfacial fracture toughness. For the three generations of materials, the interfacial toughness, GIc, was determined to be 0.7, 0.9, and 0.6 J·m–2, respectively. Postmortem analysis of the micro- and nanostructure of fractured interfaces indicated that the systems with better heat spreading capability displayed smoother fracture surfaces, i.e., were more brittle due to the lack of active toughening mechanisms. Potential modifications to the interface for improved mechanical stability were proposed based on the experimental results.

Depth sensing indentation of magnesium/boron nitride nanocomposites

Magnesium nanocomposites, considered as energy-saving lightweight materials of future, are a fairly new family of composite materials with enhanced specific strength and ductility compared to pure magnesium and/or magnesium alloys. In the present study, time-dependent plastic deformation of novel light-weight magnesium/boron nitride nanocomposites containing 0.5, 1.5 and 2.5 vol% of nano-boron nitride particulates is studied through a depth-sensing indentation approach against monolithic pure magnesium. The synthesis of magnesium–boron nitride nanocomposites was accomplished using powder metallurgy technique coupled with microwave sintering, followed by hot extrusion (end products are 8-mm diameter rods). The depth sensing indentation creep tests were conducted at room temperature (∼0.32Tm of magnesium) using an instrumented indentation platform via a self-similar pyramidal (Berkovich) indenter. To assess the influence of loading rate on the indentation-induced deformation behavior of the materials, a dual stage indentation creep including a constant loading rate followed by a constant load-holding scheme was used; indentation tests were performed on the specimens. The specimens were loaded at rates of 0.05, 0.5, 5, and 50 mN/s to a peak load of 50 mN then force was held constant for 400 s while load/displacement/time data were recorded continuously. The results of the depth sensing indentation tests were correlated and explained using the microstructural characteristics placing special emphasis on the volume fraction of reinforcement and the indentation loading rate. Finally, the controlling creep mechanisms of the magnesium–boron nitride nanocomposites and the base metal (pure magnesium) were discussed in the present paper. The results of this paper can be used as a baseline for high-temperature creep analysis of magnesium–boron nitride nanocomposites which is of engineering significance.

Influence of Tcnq Loading on the Mechanical Properties of Metal-Organic Framework Films

Bulk Metal-organic-framework (MOF) materials are designed scaffold-like compounds that consist of metal ions connected by organic ligands, forming highly ordered porous structures. Bulk MOFs yield typically powders with micron sized crystallites, which limit their applications. Many practical applications require instead suitably uniform MOF films. In recent years, efforts to grow highly oriented Surface Anchored Metal-Organic Framework (SURMOF) films of Cu3(BTC)2 (BTC: benzenetricarboxylic acid), known as HKUST-1 MOF, have been successful by utilizing a liquid phase epitaxy (LPE) spray method on surface functionalized gold coated silicon substrates. Originally MOFs were intended for gas storage due to high storage capacity inside the porous MOF bulk material. New potential device applications in thermoelectrics and microelectronics [1,2] were explored based on the premise that the electrical properties of the otherwise insulating MOF can be custom tailored by loading the porous MOF structure with metal clusters. For modulating the electrical conductivity of MOF films the most effective method is to infiltrate guest molecules inside the porous framework to transport ions, and hence to modulate the electrical properties of the host framework. Early work focused on the mechanical properties of pristine SURMOF films [3,4]. In this study, we have investigated the influence of loading pristine highly oriented MOF films with TCNQ on the mechanical properties by utilizing nanoindentation methods to measure the hardness and modulus of SURMOF films with and without TCNQ loading. Our findings reveal that undoped pristine SURMOF samples are relatively harder with an intrinsic hardness of ~ 1.6 GPa in the upper third of the MOF film. The hardness of the pristine SURMOF samples is steadily increasing as a function of the penetration depth. The hardness is approaching the substrate Si hardness as the indenter tip approaches the substrate. The measured modulus values of the pristine SURMOF samples are also steadily increasing as a function of the indentation depth. However, the TCNQ loaded SURMOF samples differ markedly and do not show a substrate effect. Interestingly the loaded SURMOF films are much softer and exhibit a constant hardness as a function of depth of ~ 0.5 GPa. As the indenter approaches the Si substrate there is no measurable change in the constant hardness and an absence of a substrate effect. The modulus values of TCNQ loaded SURMOF films is also significantly lower compared with the pristine sample and remains constant as a function of indenter penetration depth. Thus, loading the porous scaffolding of SURMOF films with TCNQ did not only alter the electrical conductivity but triggers marked changes in the mechanical properties, i.e., softening effect. This softening effect in TCNQ infiltrated MOF films can be accounted for by a widening of the lattice constant und the concomitant introduction of lattice defects that weaken the crystal and lead to a much lower hardness.