The indentation load-displacement behavior of six materials tested with a Berkovich indenter has been carefully documented to establish an improved method for determining hardness and elastic modulus from indentation load-displacement data. The materials included fused silica, soda–lime glass, and single crystals of aluminum, tungsten, quartz, and sapphire. It is shown that the load–displacement curves during unloading in these materials are not linear, even in the initial stages, thereby suggesting that the flat punch approximation used so often in the analysis of unloading data is not entirely adequate. An analysis technique is presented that accounts for the curvature in the unloading data and provides a physically justifiable procedure for determining the depth which should be used in conjunction with the indenter shape function to establish the contact area at peak load. The hardnesses and elastic moduli of the six materials are computed using the analysis procedure and compared with values determined by independent means to assess the accuracy of the method. The results show that with good technique, moduli can be measured to within 5%.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/A53D45298E14F73B86495BBC056E16DC/S0884291400017039a.pdf/div-class-title-an-improved-technique-for-determining-hardness-and-elastic-modulus-using-load-and-displacement-sensing-indentation-experiments-div.pdf

An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments

The method we introduced in 1992 for measuring hardness and elastic modulus by instrumented indentation techniques has widely been adopted and used in the characterization of small-scale mechanical behavior. Since its original development, the method has undergone numerous refinements and changes brought about by improvements to testing equipment and techniques as well as from advances in our understanding of the mechanics of elastic–plastic contact. Here, we review our current understanding of the mechanics governing elastic–plastic indentation as they pertain to load and depth-sensing indentation testing of monolithic materials and provide an update of how we now implement the method to make the most accurate mechanical property measurements. The limitations of the method are also discussed.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0884291400085800

Measurement of hardness and elastic modulus by instrumented indentation: Advances in understanding and refinements to methodology

http://experimentationlab.berkeley.edu/sites/default/files/AFMImages/butt_AFM.pdf

Force measurements with the atomic force microscope: Technique, interpretation and applications

The mechanical properties of thin films on substrates are described and studied. It is shown that very large stresses may be present in the thin films that comprise integrated circuits and magnetic disks and that these stresses can cause deformation and fracture to occur. It is argued that the approaches that have proven useful in the study of bulk structural materials can be used to understand the mechanical behavior of thin film materials. Understanding the mechanical properties of thin films on substrates requires an understanding of the stresses in thin film structures as well as a knowledge of the mechanisms by which thin films deform. The fundamentals of these processes are reviewed. For a crystalline film on a nondeformable substrate, a key problem involves the movement of dislocations in the film. An analysis of this problem provides insight into both the formation of misfit dislocations in epitaxial thin films and the high strengths of thin metal films on substrates. It is demonstrated that the kinetics of dislocation motion at high temperatures are expecially important to the understanding of the formation of misfit dislocations in heteroepitaxial structures. The experimental study of mechanical properties of thin films requires the development and use of nontraditional mechanical testing techniques. Some of the techniques that have been developed recently are described. The measurement of substrate curvature by laser scanning is shown to be an effective way of measuring the biaxial stresses in thin films and studying the biaxial deformation properties at elevated temperatures. Submicron indentation testing techniques, which make use of the Nanoindenter, are also reviewed. The mechanical properties that can be studied using this instrument are described, including hardness, elastic modulus, and time-dependent deformation properties. Finally, a new testing technique involving the deflection of microbeam samples of thin film materials made by integrated circuit manufacturing methods is described. It is shown that both elastic and plastic properties of thin film materials can be measured using this technique.

Mechanical properties of thin films

The surface and materials science of tin oxide

The interaction between tip and flat surface in the STM and AFM is reviewed and a new, AC method to determine the absolute value of area of contact and interaction is presented. Evidence that the tip-surface interaction can be purely elastic down to the near single atom scale is obtained, and has been confirmed by TEM on Al2O3. Strengths close to that of an ideal lattice are observed. Applied to the Atomic Force Microscope this AC method will give operation at a controlled, drift free level of interaction. The effects of attractive (surface energy) forces in the STM geometry are discussed, and the equilibrium configurations and extent of inelastic processes for tip and flat are described. A new imaging mechanism in STM is proposed for the cases (e.g., graphite, point contact microscope) where significant tip-surface contact occurs.

https://iopscience.iop.org/article/10.1088/0031-8949/1987/T19A/010/pdf

Tip Surface Interactions in STM and AFM

An extensive study of indentation creep on the nanometre scale has been made on single-crystal indium, tungsten and gallium arsenide. We use the force modulation technique which gives a direct measure of contact stiffness and, being insensitive to thermal drift, allows the accurate observation of creep in small indents to be carried out over long time periods: We show that strain rate indices similar to those for macroscopic creep can be obtained for indium. Stress relaxation negative creep is also observed in a manner similar to macroscopic tests. Indentation of tungsten and gallium arsenide shows a distinct pop-in at a critical load, before which the deformation is essentially elastic and after which it is elastoplastic with significant dislocation multiplication. The creep behaviour is quite different before and after pop-in, clearly demonstrating the role of mobile dislocations in creep, even in nanometre-sized volumes of materials.

Nanoindentation creep of single-crystal tungsten and gallium arsenide

It is shown that at sufficiently small separations, ∼1–2 A, the tip and flat surfaces in the scanning tunneling microscope or atomic force microscope (AFM) will jump together, irrespective of apparatus construction. Both continuum and atomistic calculations are presented. We discuss the consequences of the resulting forbidden separations for the behavior of the vacuum barrier as it is quenched, and for the resolution of the AFM.

On the stability of a tip and flat at very small separations

A new, differential method for determining the stiffness of a sub-micron indentation contact area is presented. This allows measurement of elastic modulus as well as plastic hardness, continuously during a single indentation, and without the need for discrete unloading cycles. Some of the new experiments that become possible with this technique, especially at the nanometre scale, are described. We show quantitatively that electropolished tungsten reproducibly exhibits the ideal theoretical lattice strength at small indentation loads.

John B. Pethica

Papers

Tip Surface Interactions in STM and AFM

Nanoindentation creep of single-crystal tungsten and gallium arsenide

On the stability of a tip and flat at very small separations

Mechanical Properties of Nanometre Volumes of Material: use of the Elastic Response of Small Area Indentations

Adhesion and micromechanical properties of metal surfaces