The origins of chemomechanical effects in the low-load indentation hardness and tribology of ceramic materials

Abstract

We have used high-resolution techniques (nanoindentation, atomic force microscopy) to further isolate and identify environmental effects previously reported as possibly affecting both the microindentation response of a range of ceramic materials and their tribological behaviour. In order to make meaningful comparisons, these new experiments have been conducted alongside conventional Knoop and Vickers microhardness experiments conducted under identical conditions on the same samples. A range of polycrystalline, single crystal and amorphous ceramic materials have been studied including some only available as coatings. Our results show that thin adsorbate-modified layers (of dimensions ~1 nm) are almost invariably present on all the materials studied but their presence is not directly identifiable even by nanoindentation in most cases even if it does affect friction response. However, in crystalline materials, [$\left( {10\bar{1}2} \right)$ sapphire and ZnO], we have been able to distinguish a further softening effect seen as a thicker layer (tens of nm) and believed associated with an adsorption-induced near-surface band-structure change affecting the motion of charged dislocations. This produces a measurable softening that is clearly evident in nanoindentation tests but less clear in microindentation tests. Finally, we present conclusions on the suitability of indentation testing for studying these phenomena, together with the implications of chemomechanical effects for influencing tribological performance and, thus, materials selection.

Appendix: soft surface layer modelling: volume law-of-mixtures with no constraints

Introduction

Following the work of Buckle [48] a number of simple models for the hardness of a coating on a substrate have been developed based on different law-of-mixtures models [54–57]. The most successful of these models are based on the volume law-of-mixtures where the extent of plastic deformation in the coating and substrate is determined by the proportions of the (assumed) hemispherical deforming volume below the indenter lying partly in the coating and partly in the substrate. In the simplest model the difference in properties between the coating and substrate are assumed not to significantly change the radius and shape of the deforming volume and simple geometry can be used to predict the hardness behaviour of the coating substrate composite [58]. This is the case when considering very thin soft layers on a harder substrate where the deforming volume in the substrate is significant and controls the plastic deformation in the thin surface layer.

Modelling of a thin soft layer on a harder substrate

Consider a hemispherical plastic zone, beneath the indenter, of radius, R _p. The deforming volumes in the coating and substrate, V _c and V _s, are given by the volumes of slices through a hemisphere as shown in Fig. 11. Here, t is the coating thickness and H _c and H _s are the hardness of the coating and substrate respectively. The radius of the plastic zone is calculated from the maximum displacement, δ _max, via [59]:

$$ R_{\text{p}} = \left( {4.5451 - 12.07H/E} \right)\delta_{\hbox{max} } $$

(A1)

Fig. 11

Deforming volumes and material properties for a single layer volume law-of-mixtures model

Since the soft surface layer is very thin and behaviour is controlled by the underlying hard material we use H and E for the bulk, unsoftened material to determine the plastic zone radius. The plastic contact depth, δ _c (which is used to calculate hardness), is found to be a constant fraction of the maximum indenter displacement which include elastic and plastic contributions [36] and can be found from fits to experimental data.

For the situation in Fig. 11 expressions for the deforming volumes can then be easily determined from the appropriate volume integrals.

$$ V_{\text{c}} = \pi R^{2} t - \frac{{\pi t^{3} }}{3} $$

(A2)

$$ V_{\text{s}} = \frac{2}{3}\pi R^{3} - \pi R^{2} t + \frac{{\pi t^{3} }}{3} $$

(A3)

The total deforming volume, V _t = V _c + V _s and thus for a hemispherical deforming volume

$$ V_{\text{t}} = \frac{2}{3}\pi R^{3} $$

(A4)

Then the effective hardness of the coating/substrate composite, H _eff, is given by

$$ H_{\text{eff}} = \frac{{H_{\text{c}} V_{\text{c}} + H_{\text{s}} V_{\text{s}} }}{{V_{\text{t}} }} $$

(A5)

This may be extended to a double layer model where V _i , H _i and t _i are the deforming volume, hardness and thickness of a layer intermediate between the coating and substrate.

$$ V_{\text{c}} = \pi R^{2} t_{\text{c}} - \frac{{\pi t_{\text{c}}^{3} }}{3} $$

(A6)

$$ V_{i} = \pi R^{2} t_{i} - \frac{{\pi \left( {t_{\text{c}} + t_{i} } \right)^{3} }}{3} - \frac{{\pi t_{i}^{3} }}{3} $$

(A7)

$$ V_{\text{s}} = \frac{2}{3}\pi R^{3} - \pi R^{2} (t_{\text{c}} + t_{i} ) + \frac{{\pi (t_{\text{c}} + t_{i} )^{3} }}{3} $$

(A8)

Thus

$$ H_{\text{eff}} = \frac{{H_{\text{c}} V_{\text{c}} + H_{i} V_{i} + H_{\text{s}} V_{\text{s}} }}{{V_{\text{t}} }} $$

(A9)

Application of the models

Most materials show a very thin adsorbate modified layer (AML) which is usually only a few nanometres thick. An example of this is the very thin water-affected layer on fused silica seen in AFM scans of the fused silica nanoindentation standard in Fig. 12. The origins of this layer are materials-sensitive and depend on adsorbed species on the surface, surface roughness and reconstructions, surface porosity and composition changes due to, for instance leaching or segregation. In the case of fused silica, the thin layer is around 2 nm thick and can be scraped off by progressively increasing the force on the AFM cantilever during scanning. However, there is no apparent soft surface layer in the load displacement curves in fused silica. For the purpose of modelling it is assumed that the hardness of this layer is very low (H _c = 0.5 GPa) and the hardness of the fused silica bulk is 10 GPa. From experimental data for fused silica, δ _max = 1.3745δ _c.

Fig. 12

Contact mode AFM scan of the region around a spherical indentation in fused silica. A soft surface layer has been occasionally scratched off the surface of the substrate material during imaging. The intermittent nature of the layer removal probably arises from local differences in adhesion etc. Despite this observation, no soft layer was detected by low-load indentation

A single soft surface layer 2 nm thick with hardness 0.5 GPa on fused silica with hardness 10 GPa is modelled in Fig. 14 using Eq. (A5). The grey box marks the region where experimental data is usually observable including experimental errors based on a 10 GPa hardness and 5 % scatter in measurements. The vertical line marks the experimental boundary between elastic (LHS) and elastic–plastic (RHS) indentations—the precise position of the line is dependent of the tip end radius but, in Fig. 13, a typical value for the minimum contact depth observed in elastic–plastic indentations in fused silica with a new Berkovich tip is used. Only valid experimental data is expected to the right of this line i.e. at higher contact depths.

Fig. 13

Predicted variation of hardness with contact depth for fused silica with a 2 nm soft surface layer (H _c = 0.5 GPa, H _s = 10 GPa). The grey box marks the typical scatter in experimental data based on a 10 GPa hardness with 5 % variation. Only valid hardness measurements from plastic deforming indentations are observed to the right of the vertical line so the soft surface layer cannot be seen in the experimental data

Elastic indentations are observed in low-load tests and the smallest measurable contact depth for an elastic–plastic indentation for fused silica is around 5 nm. Thus the modelled data to the left of the vertical line should be ignored as not measureable. To the right of the line the modelled data falls in the experimental scatter band for unsoftened material so no soft surface layer is likely to be observed.

In the same way, it is expected that the majority of adsorbate modified layers (AML) are likely to be invisible in the nanoindentation hardness data, even though they may have a significant effect on the tribological (friction) behaviour of the material.

There are cases where more significant surface softening is observed on a glassy material—for instance on float glass that has been dish-washed with deionised water (as part of the manufacturing process) for cleaning prior to coating deposition. This is shown in Fig. 14, but the softening effect is usually small and only statistically significant when the contact depth is less than 20 nm which is consistent with the results of modelling the effect of a slightly thicker (~5 nm) soft layer on a silica substrate. In this case there has been some leaching of the alkali modifier from the glass surface and reduction in surface density. Again, this would be statistically undetectable in indentation experiments.

Fig. 14

Effect of dishwashing on the surface hardness of soda-lime glass

For sapphire there is an approximately 5 nm thick soft surface layer visible in the early part of the nanoindentation load–displacement curve. This cannot easily be explained by the adsorbate modified layer and it is suggested that a second mechanism is operating and this is evidence of a band-modified layer (BML) affecting dislocation mobility and hardness. This hypothesis can be tested by modelling two cases. In the single layer model (Eq. A5) a 1 nm layer with 2 GPa hardness is present on a bulk material with 25 GPa hardness and 350 GPa modulus. For the double layer model (Eq. A9) we insert a 5 nm layer of 20 GPa hardness between these. For sapphire, δ _max = 1.242δ _c from experimental data. These models are compared in Fig. 15. Again the grey region marks the scatter in experimental data from an unsoftened substrate and the vertical line marks the boundary between elastic indentation (where hardness is not defined) and elastic–plastic indentation where valid hardness measurements are obtained.

Fig. 15

Variation of hardness with contact depth for sapphire with different soft surface layers

In the single layer model the soft surface layer effect only persists to less than 15 nm contact depth and would be only just measurable. The softening effect persists to 30 nm contact depth exactly as observed in the hardness data in the double layer model. The effect of these layers should therefore be observable in the nanoindentation data as we have found.

The model could be updated to investigate the effect of a soft surface layer on the early stages of the load displacement curve to determine if this would be visible in experimental data. This is a topic for future work.