Walter Arnold

Local elastic properties of a metallic glass

The nature of non-crystalline materials causes the local potential energy of a cluster of atoms or molecules to vary significantly in space. Different configurations of an ensemble of atoms in a metallic glass lead therefore to a distribution of elastic constants which also changes in space. This is totally different to their crystalline counterparts, where a long-range order exists in space and therefore a much more unified elastic modulus is expected. Using atomic force acoustic microscopy, we present data which show that the local so-called indentation modulus M indeed exhibits a wide distribution on a scale below 10 nm in amorphous PdCuSi, with ΔM/M≈30%. About 10(4) atoms are probed in an individual measurement. Crystallized PdCuSi shows a variation that is 10-30 times smaller and which is determined by the resolution of the microscope and by the polycrystalline structure of the material.

High-frequency response of atomic-force microscope cantilevers

Recent advances in atomic-force microscopy have moved beyond the original quasistatic implementation into a fully dynamic regime in which the atomic-force microscope cantilever is in contact with an insonified sample. The resulting dynamical system is complex and highly nonlinear. Simplification of this problem is often realized by modeling the cantilever as a one degree of freedom system. This type of first-mode approximation (FMA), or point-mass model, has been successful in advancing material property measurement techniques. The limits and validity of such an approximation have not, however, been fully addressed. In this article, the complete flexural beam equation is examined and compared directly with the FMA using both linear and nonlinear examples. These comparisons are made using analytical and finite difference numerical techniques. The two systems are shown to have differences in drive-point impedance and are influenced differently by the interaction damping. It is shown that the higher modes must be included for excitations above the first resonance if both the low and high frequency dynamics are to be modeled accurately.

The landing(s) of Philae and inferences about comet surface mechanical properties

The Philae lander, part of the Rosetta mission to investigate comet 67P/Churyumov-Gerasimenko, was delivered to the cometary surface in November 2014. Here we report the precise circumstances of the multiple landings of Philae, including the bouncing trajectory and rebound parameters, based on engineering data in conjunction with operational instrument data. These data also provide information on the mechanical properties (strength and layering) of the comet surface. The first touchdown site, Agilkia, appears to have a granular soft surface (with a compressive strength of 1 kilopascal) at least ~20 cm thick, possibly on top of a more rigid layer. The final landing site, Abydos, has a hard surface.

A single shear band in a metallic glass: Local core and wide soft zone

Two dimensional mapping of structural properties near a single shear band in a Zr-based bulk metallic glass reveals the presence of hardness and modulus reductions at a micrometer length scale. The isolated shear band had carried all the macroscopic plastic strain and the material near the shear-band exhibits structural variations both along and normal to the shear plane. Analyzing the nanoindentation data indicates that long range internal stresses are the primary cause of the spatially varying structure. The results demonstrate that a nano-scale defect in a metallic glass may have a micrometer range signature.

Quantitative Evaluation of Elastic Properties of Nano-Crystalline Nickel Using Atomic Force Acoustic Microscopy

Atomic force acoustic microscopy (AFAM) is a near-field technique, where the vibration behavior of a micro-fabricated elastic cantilever beam in contact with a sample surface is sensitive to its local elastic properties. The resolution of this technique is given by the contact radius ac of the atomic force microscope sensor-tip on the sample surface. Taking into account only the Hertzian forces, ac depends on the static load applied by the cantilever, on the elastic constants of the tip and the sample and on the geometry of the contacting bodies. The shape of the sensor tip used in atomic force acoustic microscopy is between a sphere and a flat punch. Hence ac extends from just below 10nm to a few tens of nanometers. In this review, we give an overview of the AFAM technique, present data on the indentation moduli of nanocrystalline nickel, and discuss some of the error sources in quantitative AFAM. The AFAM indentation moduli measured are comparable to the values obtained by nanoindentation and lower than the indentation moduli calculated from ultrasonic velocity measurements. There seems to be a decrease of the indentation modulus with decreasing grain size for grain sizes below 30nm. The data are discussed taking into account X-ray diffraction and electron back-scattering data revealing some texture and macro-strain due to internal stresses in the samples investigated.

Imaging using lateral bending modes of atomic force microscope cantilevers

Using scanning probe techniques, surface properties such as shear stiffness and friction can be measured with a resolution in the nanometer range. The torsional deflection or buckling of atomic force microscope cantilevers has previously been used in order to measure the lateral forces acting on the tip. This letter shows that the flexural vibration modes of cantilevers oscillating in their width direction parallel to the sample surface can also be used for imaging. These lateral cantilever modes exhibit vertical deflection amplitudes if the cantilever is asymmetric in thickness direction, e.g., by a trapezoidal cross section.

Dynamical and quasistatic structural relaxation paths in Pd40Ni40P20 glass

By sequential heat treatment of a Pd_(40)Ni_(40)P_(20) metallic glass at temperatures and durations for which α-relaxation is not possible, dynamic, and quasistatic relaxation paths below the glass transition are identified via ex situ ultrasonic measurements following each heat treatment. The dynamic relaxation paths are associated with hopping between nonequilibrium potential energy states of the glass, while the quasistatic relaxation path is associated with reversible β-relaxation events toward quasiequilibrium states. These quasiequilibrium states are identified with secondary potential energy minima that exist within the inherent energy minimum of the glass, thereby supporting the concept of the sub-basin/metabasin organization of the potential-energy landscape.

Imaging of subsurface structures using atomic force acoustic microscopy at GHz frequencies

We describe a technique to image subsurface structures using atomic force acoustic microscopy operated at 1 GHz. The devices to be imaged are insonified with 1 GHz ultrasonic waves which are amplitude-modulated at a fraction or multiple frequency of cantilever contact resonance. The transmitted signals are demodulated by the nonlinear tip–surface interaction, enabling one to image defects in the device based on their ultrasonic scattering power which is determined by the ultrasonic frequency, the acoustic mismatch between the elastic properties of the host material and the defects, by their geometry, and by diffraction effects.

Reconstruction of the defect shape from lock-in thermography phase images

We present a method for reconstructing the shape of buried planar defects supposed to be infinitely thick from optical lock-in thermography phase images. Several image processing algorithms are combined, to extract quantitative defect information from a series of phase images (phasegram) in a semi-automatic way. It is shown, that the depth and the shape of a planar defect can be retrieved.

Mapping of elasticity and damping in an α + β titanium alloy through atomic force acoustic microscopy

Summary The distribution of elastic stiffness and damping of individual phases in an α + β titanium alloy (Ti-6Al-4V) measured by using atomic force acoustic microscopy (AFAM) is reported in the present study. The real and imaginary parts of the contact stiffness k * are obtained from the contact-resonance spectra and by using these two quantities, the maps of local elastic stiffness and the damping factor are derived. The evaluation of the data is based on the mass distribution of the cantilever with damped flexural modes. The cantilever dynamics model considering damping, which was proposed recently, has been used for mapping of indentation modulus and damping of different phases in a metallic structural material. The study indicated that in a Ti-6Al-4V alloy the metastable β phase has the minimum modulus and the maximum damping followed by α′- and α-phases. Volume fractions of the individual phases were determined by using a commercial material property evaluation software and were validated by using X-ray diffraction (XRD) and electron back-scatter diffraction (EBSD) studies on one of the heat-treated samples. The volume fractions of the phases and the modulus measured through AFAM are used to derive average modulus of the bulk sample which is correlated with the bulk elastic properties obtained by ultrasonic velocity measurements. The average modulus of the specimens estimated by AFAM technique is found to be within 5% of that obtained by ultrasonic velocity measurements. The effect of heat treatments on the ultrasonic attenuation in the bulk sample could also be understood based on the damping measurements on individual phases using AFAM.