1998 MRS Spring Meeting & Exhibit

Chairs 

Nancy Burnham
Dept de Physique-IGA
Ecole Polytechnique Federale
Lausanne, CH-1015 SWITZERLAND
41-21-6934320

William Gerberich 
Dept of Chem Engr & Matls Sci 
Univ of Minnesota 
151 Amundson Hall 
Minneapolis, MN 55455 
612-625-8548

Neville Moody
Sandia National Laboratories
MS 9403
Livermore, CA 94551-0969
510-294-2622

* Invited paper

TUTORIAL 

STT: ³MEASURING MECHANCIAL PROPERTIES IN THE NANOMETER REGIME² 
Sunday, April 12, 1:00 - 5:00 p.m. 
Pacific J 

of the mechanical properties of very small volumes has become increasingly important as it has come to be recognized that materials in small dimensions may have mechanical properties that are significantly different from those of the same materials in bulk. In the field of tribology, concerns about effects of the mechanical behavior of layers having thicknesses between 1 and 100 nanomenter on wear behavior have led to the development and application of contact measurements using nanoindentation and scanning force microscopy methods. In order to access the nanometer regime, attempts have been made to combine these methods utilizing the quantitative data analysis models of nanoindentation as well as the high resolution of scanning probes. To date, these methods have remained controversial. In this Tutorial, an overview of mechanical property measurements using both nanoindentation and scanning force microcopy methods will be presented. Current trends in experimentation and data analysis models will be reviewed, and similarities and differences between the two approaches will be discussed and clarified. Emphasis will be placed on recent developments in the study of tribological phenomena. Attendees of Symposium T will find in this tutorial suitable background material for active participation in, and understanding of, the symposium. 

Instructors: 
Shefford P. Baker, Cornell University 
Nancy Burnham, Ecole Polytechnique Federale de Lausanne 

SESSION T1: THEORY AND TECHNIQUES 
Chairs: Shefford P. Baker and William W. Gerberich 
Monday Morning, April 13, 1998 
Salon 3/4

8:30 AM *T1.1 
DETERMINATION OF MECHANICAL PROPERTIES OF BULK AND THIN FILM MATERIALS BY NANOINDENTATION: CONTACT AREA PROBLEMS AND SUBSTRATE STIFFNESS EFFECTS. W.D. Nix, R. Saha, E.T. Lilleodden, K.W. McElhaney, J.J. Vlassak, Department of Materials Science and Engineering; and H. Gao, Division of Mechanics and Computation, Mechanical Engineering Department, Stanford University, Stanford, CA . 

Pile-up and sink-in effects associated with nanoindentation must be taken into account to obtain accurate measures of the indentation modulus and hardness of materials. These effects lead to contact areas that are either greater than or less than the cross-sectional area of the indenter at a given depth. To account for these effects, a method of indenter tip shape calibration has been developed, based on measurements of both the contact compliance and the actual contact areas of large indentations. Application of this calibration technique to strain-hardened (pile-up) and annealed (sink-in) Cu leads to a unique tip shape calibration for the diamond indenter itself, as well as to a material parameter which characterizes the extent of pile-up or sink-in. Using this approach, it is possible to make accurate absolute measurements of hardness and indentation modulus of Cu by nanoindentation. 
After accounting for the effects of pile-up and sink-in, we find large indentation size effects for Cu, which can be accurately modeled using the concept of geometrically necessary dislocations. The model leads to a characteristic form for the depth dependence of the hardness, wherein the square of the hardness varies inversely with the depth of indentation. This result is shown to have important implications for the theory of strain gradient plasticity and leads to a material length scale for characterizing effects of strain gradients on the flow stress of metals. 
The material parameter for characterizing the extent of pile-up and sink-in may not be accurate for very small indentations where the indenter shape is not self similar. In such cases, direct AFM imaging of the contact areas may be required. Recent experiments with the Hysitron to compare imaged contact areas with those deduced from contact compliance are described. We also report on preliminary efforts to account for substrate stiffness effects in determining the indentation modulus of thin films by nanoindentation, using Al on alumina as the test system. 

9:00 AM T1.2 
CHARACTERIZATION OF POINTED AND SPHERICAL INDENTER TIPS. Trevor Bell, John Field, Frank Lesha and Michael Swain, CSIRO Telecommunications and Industrial Physics, Lindfield NSW, AUSTRALIA. 

It has so far proved impossible to manufacture a perfect pointed or spherical diamond indenter tip. Pointed triangular tipped indenters invariably have a rounded tip with a radius somewhere between 50 and 500nm which may change during the course of the life of the indenter. Spherical tipped diamond indenter are generally influenced by the crystallographic anisotropy of this material and the ability to mechanically polish a specific radius on a conical indenter stem. This study will describe approaches to quantify the tip shape of three triangular pyramid indenters with apical angles of 35.3 (corner cube), 45 and 65.3 (Berkovich) and small spherical indenter tips from nominally 1 to 20 microns. The pointed indenters were evaluated using the approach suggested by Oliver and Pharr and AFM images of the residual impressions in steel and silica. The spherical tips were evaluated with a modification of the simple Hertzian contact mechanics analysis and with direct AFM images of the indenter tips. Observations of the contact pressure and elastic modulus versus depth of penetration for all indenters on steel and silica are compared. 

9:15 AM T1.3 
EVOLUTION OF CONTACT AREA AND PILE-UP DURING THE NANOINDENTATION OF SOFT COATINGS ON HARD SUBSTRATES. Nick Randall and Claudine Julis-Schmutz, CSEM Instruments, Neuchatel, SWITZERLAND. 

The mechanical properties of thin films can be measured by a variety of different techniques, with nanoindentation being one of the most recent developments in this growing field. By using a depth-sensing indentation method it is possible to obtain quantitative values for the hardness and modulus, and thus gain better insight into the response of a material to controlled deformation at such small scales. However, previous work [1] has shown that the effects of pile-up, particularly in soft films deposited on hard substrates, can produce significant overestimation of the hardness and modulus due to an underestimation of the true contact area by common nanoindentation analysis procedures. By measuring the topography of the residual indent using Scanning Force Microscopy (SFM) and combining this infomation with the indentation data, it is possible to gain a fuller understanding of the indentation method and its effects on the material being tested. In addition, the true contact area can be directly measured from the SFM images and subsequently used to calculate the hardness of the material more accuratly. Experimental results are presented for a selection of soft films on hard substrates where SFM analysis of indentations at varying depths gives significant additional information concerning the true response of the system to instrumented indentation at a nanometric scale. Pile-up effects can be precisely monitored as a function of depth and correlated to hardness variations encountered across the coating/substrate interface. 

9:30 AM T1.4 
THE IMPORTANCE OF CONTACT RADIUS FOR SUBSTRATE-INDEPENDENT MEASUREMENTS ON THIN FILMS. M.E. O'Hern, J.L. Hay, W.C. Oliver; Nano Instruments, Inc., Oak Ridge, TN. 

In indentation literature, there is ample support for the proposition that the extents of the elastic and plastic fields scale with the contact radius. As an example, for two bodies in Hertzian contact, lines of constant shear stress scale with the contact radius. This idea has significant consequences with respect to measuring substrate-independent properties of thin films. If it is the contact radius that determines the extent of the elastic and plastic fields, then the general rule (that the contact depth should be less than 10% of the total depth) is only appropriate for one indenter geometry. In this work, we use several different indenter geometries to measure the hardness for a thin film. For all geometries, both the contact depth and contact radius are determined for the point at which the substrate first starts to influence the measurements. 

9:45 AM T1.5 
PILE-UP BEHAVIOR OF SPHERICAL INDENTATIONS IN ENGINEERING MATERIALS. Bostjan Taljat, Thomas Zacharia, Oak Ridge National Laboratory, Matals and Ceramics Division, Oak Ridge, TN; George M. Pharr, Department of Materials Science, Rice University, Houston, TX. 

The spherical indentation process has been modeled by the finite element method to study the pile-up behavior of elastic-plastic materials with different degrees of stain hardersng. A wide range of materials was examined characterized by different elastic Moduli, yield stresses, and strain hardening exponents. The geometry of the contact impressions was examined in both the loaded and unloaded conditions. Results show that pile-up behavior in elastic-plastic materials can not be related solely to the strain hardening exponent, as has often been done in the past. Relating the pile-up behavior strictly to the strain hardening exponent may lead to significant errors in the calculated contact area for materials with modulus to yield stress ratios lower than about 500. The study also reveals that contact friction affects the pile-up height by as much as 50 of material properties and stage of development of the contact impression on the pile-up behavior is described. 

10:30 AM *T1.6 
THE DYNAMICS OF FREQUENCY SPECIFIC DEPTH-SENSING INDENTATION TESTING. W.C. Oliver, B.N. Lucas, J.E. Swindeman, Nano Instruments, Inc., Oak Ridge, TN. 

Depth-sensing indentation involves applying a specific force-time history on a rigid indenter with the displacement of the indenter into the surface of a material being monitored continuously. Frequency specific depth-sensing indentation testing involves adding a small harmonic force on the indenter and measuring the harmonic response of the indenter at the excitation frequency. While often taken for granted, understanding the dynamics behind these frequency specific measurements is of vital importance in the determination of quantitative mechanical properties. This talk will focus on the dynamics of a variety of depth-sensing indentation systems and how these dynamics effect such parameters as detecting the point of surface contact, environmental sensitivity, dynamic frequency range, and the range contact stiffnesses and moduli that can be accurately measured. 

11:00 AM T1.7 
CRITICAL EVALUATION OF THE APPLICATION OF HERTZ AND SNEDDON CONTINUUM ELASTIC CONTACT THEORIES TO NANOSCALE INDENTATION. O.L. Warren, J.F. Graham, P.R. Norton, University of Western Ontario, Dept of Chemistry and Interface Science Western, London, Ontario, CANADA. 

The subtle relationships between Hertz and Sneddon continuum elastic contact theories have not been fully appreciated in the literature, leading to the publication of at least one additional but erroneous theory. Sneddon theory, when applied to indentation with a paraboloid of revolution, corresponds to Hertz theory evaluated in the limit of a rigid indenter pressed into a flat surface. This relationship illustrates that Hertz theory is in the strictest sense a description for parabolic (not spherical) indenters. Nevertheless Hertz theory is applicable to spherical indenters as long as the contact radius remains much smaller than the indenter radius, by virtue of the geometric similarity between a sphere and the apex of a paraboloid of revolution. In fact it can be shown that Sneddon theory, when applied to shallow indentations with a spherical indenter, converges to Hertz theory evaluated under the same rigid indenter-flat sample constraints, even though the equations of Sneddon's spherical theory do not closely resemble those of Hertz. In this study we have applied these contact theories to nanoscale indentation measurements made on a number of engineering materials with the interfacial force microscope (IFM). The IFM is unique in its ability to prevent the force transducer from deflecting while obtaining quantitative force-displacement curves. Our analysis of the nanoindentation data focusses on the role of the indenter radius in extending the initial elastic portion of the loading curve, thereby testing the valid range of small-strain elastic contact theories, and also on the inadequacy of the continuum aspect of these theories in describing the nanomechanical response of highly anisotropic materials. 

11:15 AM T1.8 
FINITE-ELEMENT MODELING OF NANOINDENTATION FOR EVALUATING MECHANICAL PROPERTIES OF THIN LAYERS. J.A. Knapp, D.M. Follstaedt and T.A. Friedmann, Sandia National Laboratories, Albuquerque, NM. 

Depth-sensing indentation is widely used to measure the mechanical properties of thin films and surface treatments, but for very thin layers or depth-dependent treatments such as ion implantation, it is difficult using analytical methods to separate the properties of the layer from those of the underlying substrate. An accurate determination of layer properties can then only be obtained using detailed finite-element modeling of the problem. In order to routinely apply such modeling to indentations of our thin-film materials, we have developed utilities and procedures for setting up and analyzing results from a series of finite-element simulations. The simulations are performed using ABAQUS, a commercial finite-element code. The method accurately deduces the yield stress, Young's modulus, and hardness from indentations as deep as 50% of the layer thickness. Deformation of the indenter tip, friction between tip and surface, and pre-existing stress in the layers are all modeled. The yield stress and Young's modulus specific to the layer material are extracted from the fit of simulation to experiment, and the intrinsic hardness of the material is then deduced by an additional simulation using its yield stress and Young's modulus for a hypothetical bulk ''sample''. We have recently found that for extremely hard materials such as deposited ''diamond-like'' carbon layers, the modeling is required even for layers as thick as a micron. For such very hard materials (up to 88 GPa) the influence of the substrate on the apparent elasticity is much more pronounced, and deformation of the diamond indenter tip also becomes significant, which in turn reduces the accuracy of the approximations inherent in an analytical approach. We will demonstrate how the finite-element modeling can be used to give accurate results even for this difficult case.

11:30 AM T1.9 
AN EXPERIMENTAL ASSESSMENT OF INDENTER ANGLE AND POISSON RATIO EFFECTS ON PROPERTY MEASUREMENTS BY NANOINDENTATION. Jack C. Hay, Oak Ridge National Laboratory, Oak Ridge, TN; G.M. Pharr, Rice University, Dept. of Materials Science, Houston, TX. 

Experimental studies have been conducted to explore the hypothesis that the Sneddon solution for indentation by a rigid cone underestimates contact areas and loads in a manner which depends on the Poisson ratio of the indented material and the cone angle. An approximate analytical solution, based largely on Sneddon's solution, has been developed which accounts for these effects. The approximate solution indicates that one can expect deviations from the Sneddon solution of up to 9% and 27% in the contact radius for conical indenters with half-included angles of 70.32ƒ and 42.28ƒ (equivalent cone angles for the Berkovich and cube-corner indenters). The objectives for the experimental studies were twofold. First, the modified solution was used to calibrate a cube-corner diamond tip, a task previously unsuccessful by analysis with the standard Sneddon solution. Second, in the present methods of determining the Young's modulus by nanoindentation one must either know or assume the Poisson ratio for the indented material. The modified solution allows one to uniquely determine the Poisson ratio in addition to the Young's modulus by performing indentation experiments with two different indenter angles. 

11:45 AM T1.10 
3D QUASICONTINUUM SIMULATION OF NANOINDENTATION. David Rodney and Rob Phillips, Brown University, Division of Engineering, Providence, RI. 

Nanoindentation produces intense stresses beneath the tip of the indenter, and elastic stresses on a much larger length scale. Mixed atomistic/continuum techniques, such as the quasicontinuum method used here, are viable tools to study the initial stages of indentation tests. The present work aims to investigate, on the basis of fully three-dimensional calculations, the mechanisms whereby dislocations are nucleated and their subsequent interactions. Information that emerges from such calculations, such as the yield stress or dislocation geometries, can be used in continuum-based computations to simulate the later stages of indentation. The effect of the indenter geometry, the film crystallography or the presence of free surfaces are also examined. The structures obtained are compared to experimental observations.

SESSION T2: DEFORMATION 
Chairs: Neville R. Moody and John B. Pethica 
Monday Afternoon, April 13, 1998 
Salon 3/4

1:30 PM *T2.1 
INDENTATION OF METALS: ATOMISTIC CALCULATIONS OF PLASTICITY. J.C. Hamilton and C.L. Kelchner, Sandia National Laboratories, Livermore, CA. 

With the advent of powerful parallel processing computers, it is possible to calculate the position of every atom in a slab during indentation. We present the results of such calculations for indentation of passivated gold single crystals by an 80radius indenter, using a slab with 500,000 gold atoms modeled by EAM potentials. These calculations bridge the gap between the understanding derived from a classical elasticity solution and the complex force vs. displacement measurements characteristic of plastic deformation during indentation. Two key developments were essential to this work. First, a simple spherically symmetric repulsive potential was used to represent the indenter in contact with a passivated surface. Thus the indenter is a hard sphere as in a Hertzian model and is not treated at an atomic level. Second, a centrosymmetry parameter was used to image stacking faults and dislocations in the plastically deformed lattice. We will discuss issues such as the effect of anisotropy on the effective indentation modulus, the orientation of dislocation networks as a function of crystal orientation, and the process of nucleation of dislocations. 

2:00 PM T2.2 
3D MODELING OF NANOINDENTATION TESTING : SIMULATION. Marc C. Fivel¹, Christian Robertson², Marc Verdier³, ¹GPM2 / ENSPG, St Martin d'Heres, FRANCE, ²SRMP, Saclay, FRANCE, ³LTPCM^* / ENSEEG, St Martin d'Heres, FRANCE, ^*Present location : Los Alamos Nat. Lab, NM. 

A 3D simulation of the collective dynamic behavior of dislocations at a mesoscopic scale has been developed in the last few years [1-3]. It appears to be a powerful numerical tool that helps to understand the formation of microstructures in the case of the deformation of a bulk crystal. The nanoindentation test can also be simulated by such a code but it is necessary to take into account the boundary conditions applied on the finite volume containing the dislocations. Such a procedure has recently been developed using the superimposition principle [4-5]. The stress field felt by each segment of dislocation is then the summation of the two elastic stress fields coming from : i- the dislocations as if they were in an infinite medium, ii- the boundary conditions which include the image forces. The simulation of the nanoindentation test requires to define a set of rules modeling the nucleation of dislocation loops under the indenter. Two rules are ntroduced in the code, the first defines the shape and the location of the nucleated dislocations and the second one defines the loading at which dislocations are nucleated. Each of these rules is based on experimental observations (Part 1). Results of the simulation of the nanoindentation of a copper single crystal at a depth of fifty nanometers is shown for two different orientations of the indentation axis : [001] and [110]. The obtained microstructure as well as the indent induced plastic zone are compared to the experimental observations and a local criterion for the nucleation is also proposed. 

2:15 PM T2.3 
NANOINDENTATION STUDY OF VERY LOW STRESS PLASTICITY. Jacques Woirgard, Christophe Tromas, Valerie Audurier, Jean-Christophe Girard, University of Poitiers, Laboratoire de Metallurgie Physique, Poitiers, FRANCE. 

Yield points have been observed at very low loads, during nanoindentation tests, in ceramic materials and metals. These micro yieldings corresponds to an abrupt increases in the displacement during load controlled experiments, and fast drops of the applied force during, penetration controlled experiments. They have been mostly observed during loading but also, in a few cases, at the beginning of unloading. Hardness values close to the theoretical strength of the material are sometimes measured, indicating that the process initiates in defect free volumes. For cleaved or very well polished surfaces reproducible effects are observed. The influence of the impact velocity or the loading rate have also been studied. On freshly cleaved (001) MgO surfaces, the fine topography of the indented surfaces have been detailed by Atomic Force Microscopy, allowing to analyse the very early stage of indentation in two sequential steps : a sudden punching mechanism at the yield point, followed by the developpement of rosette arms of defined crystallographic orientations. Finally a preliminary dislocation model is proposed. 

2:30 PM T2.4 
FIB/TEM OBSERVATION OF DEFECT STRUCTURE UNDERNEATH AN INDENTATION. H. Saka, S. Abe, Suprijadi, T. Matsunaga, Nagoya Univ., Dept of Quantum Engineering, Nagoya, JAPAN. 

A new technique which combines focused ion beam(FIB) milling and transmission electon microscopy (TEM) was developed in oder to observe defect structure of the wide area underneath an indent. Si,MgO, alumina and SrTiO₃ were examined. When MgO and SrTiO₃ were indented at room temperature, many dislocations were activated and glided out of the regionjust beneath the indentations. In alumina deformation twins was formed. On the other hand, in Si dislocations were restricted to the area just beneath the indents. When an indented Si was heated in the bulk state, dislocations were nucleated at the crack surfaces in the wake of a crack tip. When heated In- situinside a HVEM dislocations were emitted at or near a crack tip. Emission of dislocations will be shown by a video movie. Effect of the size of the indentation on the defect structure was also studied. 

2:45 PM T2.5 
PLASTIC BEHAVIOUR OF CU-NI MULTILAYERS DEPOSITED ON CU SINGLE CRYSTALS. Marc Verdier, Los Alamos National Lab., CMS, Los Alamos, NM; Marek Niewczas, David Embury, McMaster University, Department of Materials Science and Engineering, Hamilton, CANADA; Michael Nastasi, Los Alamos National Lab., MST, Los Alamos, NM. 

In order to study the plasticity in Cu-Ni multilayers deposited on single crystals of Cu, we have investigated the mechanical properties of the multilayers both by nanoindentation measurements, and by the transmission of well characterized dislocations from the underlying substrate by tensile deformation of Cu single crystals. Various multilayers were deposited by physical vapor deposition on Cu single crystal with layer thicknesses varying between 1000 and 20 Angstroms. The Cu single crystal used as substrates have a long axis parallel to <541>direction and the multilayers were deposited on faces parallel to 123 planes. This geometry allows the activation of only one dislocation system during tensile tests at liquid nitrogen temperature. Moreover, the (123) face is a plane parallel to the emergent edge dislocations, thus with this experimental procedure, we can control the emission of dislocations through the multilayer and study the influence of the layer thickness. This communication reports the results from the nanoindentation measurements, as well as the observations of slip on the surface. We observed through the injection of dislocations by nanoindentation that the multilayers hardens with refinement of the layer structure. After tensile testing of the substrate, the slip patterns at the surface of the multilayer evolves with layer thicknesses from slip lines to fracture lines, still oriented along the substrate slip lines. Experimental observations are discussed in terms of the influence of the layer thickness on the plastic deformation of the Cu-Ni multilayers. 

3:30 PM *T2.6 
NANOINDENTATION EXPERIMENTS ON COATED SYSTEMS - APPROACHES USING CONTINUOUS STIFFNESS TECHNIQUES. Trevor Page, Materials Division, University of Newcastle, Newcastle upon Tyne, UNITED KINGDOM; George Pharr & Jack Hay, Metals & Ceramics Division, Oak Ridge National Laboratory, Oak Ridge, TN; Warren Oliver Barry Lucas and Eric Herbert, Nano Instruments, Inc., Oak Ridge, TN; and Laura Riester, HTML, Oak Ridge National Laboratory, Oak Ridge, TN. 

We are exploring the use of continuous stiffness (superposed AC) techniques for studying the mechanical properties of coated systems using nanoindentation. A long-term objective is to critically assess the differing information available from simple load-displacement (P-) curves, P- analyses and load versus (contact stiffiness(S))2 data. A preliminary, but maior question, has been to examine whether superposition of the small AC signal used to measure contact stiffness has any marked effect on the sample response when compared to similar data obtained with basic load-displacement tests. We have employed a range of carefully-calibrated Nanolndenter II and NanoIndenter XP instruments for data acquisition, together with transmission electron microscopy (TEM) and high resolution scanning electron microscopy (HRSEM) to characterise the resultant deformation structures. Apart from some sneak statistical vanation in the loads at which initial cracks are generated in some hard-coated systems, TEM and HRSEM studies have shown no detectable difference between indentation sites in samples indented with and without the superimposed AC signal (typically a 1nm oscillating displacement imposed at 45Hz). Further, plots of P- and P, are indistinguishable. We have also been able to construct plots of elastic modulus, E, and system hardness, H, as a functional indenter displacement for a number of coated systems and explore the parameters of P/ and P/S².