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Acronyme/acronym : MecaNIX Mechanics of Nanostructures probed In-situ by X-rays: In situ evaluation of strain and defects (Coherent X-ray diffraction) in nanostructures during mechanical loading (AFM) Cadre/Frame : ANR Programme BLANC Edition 2011 Coordination : Im2np, Olivier Thomas
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Abstract : This project is aimed at a deeper understanding of the mechanical properties of single nanostructures and the influence of size effects on the material properties. The elastic as well as the plastic behaviour will be studied in situ combining contact atomic force microscopy and coherent X-ray diffraction with highly focused synchrotron beams. Both semiconductor (GaAs, GaN) and metallic nanostructures, of various geometries (wires, islands) will be studied. Mechanical tests on nanostructures, e.g. bending tests on the wires, are performed employing contact atomic force microscopy and the mechanical properties are determined from the force vs. deflection curves. The in situ combination with coherent X-ray diffraction, which is basically a non-invasive technique, allows recording complete strain maps in the nanostructures under external load. The sharpness and inner structure of the diffraction peaks, also measured by Laue methods, contain information about the elastic stress as well as imperfections of the crystalline lattice such as dislocations, stacking faults, etc.
The partners in this project (IM2NP, SIMaP, INAC, ESRF-ID01, LPS and MPI Stuttgart) are well recognised experts in the field of the growth of nanostructures, coherent x-ray diffraction, nano-mechanics and simulation.
Beyond its interest for basic sciences this project should bring invaluable informations on the mechanical behaviour of materials at the nano-scale. Such informations are critical for reliability and design of micro- and nano-systems.
Nanoscience is mostly aimed at evaluating, understanding and tailoring physical and chemical properties as a function of size, down to the nanometre scale. The influence of size on mechanical properties is on one hand an old problem (e.g. it has been known for 50 years that grain size influences yield stress, as rationalized by Hall & Petch law) but on the other hand the knowledge and understanding of mechanical properties (elastic and plastic) down to the nanoscale is a very vivid research area. In
This project brings together 5 French partners: IM2NP in Marseille, SIMaP in
The evaluation of mechanical properties in small dimensions or the influence of nanostructuring on mechanical properties remain very fundamental and active research topics [Suresh2008, Lu2009]. It is now well established that mechanical properties of small objects differ fundamentally from their bulk counterpart and more specifically that “smaller is stronger” i.e. nanomaterials exhibit higher yield strengths. Many unsolved questions arise, however, concerning the strength of small (below 1000 – 100 nm) objects: “How do dislocations nucleate and annihilate ? What is the role of diffusion in stress relaxation ? …” Considering size effects on elastic properties one may expect that it should occur at much smaller scales [Müller2000, Wu2005]: typically a few nm but conflicting results still question this expectation. At these latter dimensions surface stress and surface strain influence directly lattice spacing in nanocrystals [Huang2008]. The understanding of mechanical properties in small dimensions is thus an issue of general scientific knowledge. It is also important to underline that this is also extremely critical for the reliability of micro-components such as microelectronic devices or MEMS (Micro ElectroMechanical Systems).
Studying mechanical properties in small dimensions was first pioneered by W. Nix and his co-workers in Stanford [Doerner1988] where mechanical properties of thin films have been evaluated as a function of film thickness and microstructure. Many groups in the world have pursued similar goals spurred both by a fundamental interest in mechanical properties of thin layers but also because of a strong need to master thermomechanical reliability of electronic devices. We shall not try being exhaustive here but one should at least quote the groups of E. Arzt in
More recently an important research activity aimed at testing the mechanical properties of nanostructures (islands, nanowires, etc) has developed. With the advent of Focused Ion Beams (FIB) it has been possible to fabricate sub-micron pillars out of bulk materials [Uchic2004, Uchic2005]. Such objects have been tested under compression [Uchic2004, Uchic2005] and have shown most of the time size effects. More recently tensile tests have also been achieved [Kiener2008]. Since FIB-machining creates defects and may amorphize the surface it has been argued that the mechanical properties of such pillars are FIB-related [Maass2006]. Mechanical testing of pillars prepared by other techniques such as direct deposition into pores [Jennings2010] or wet etching [Bei2007a, Bei2007b] seem to indicate that similar size effects may be observed even in the absence of any FIB-machining. The majority of studies reported in the literature are performed on simple FCC metals (Cu, Ni, Au, Al). More recently BCC metals have been studied [Bei2007a] and also semi-conductors such as GaAs [Michler2007], Si [Ostlund2009]. Because of deep Peierls valleys semi-conductors are brittle at room temperature. Surprisingly this is not true anymore in small dimensions: small diameter semiconductor pillars exhibit ductile behaviour [Michler2007].
Nanowires grown by VLS (Vapor-Liquid-Solid) or similar techniques have attracted considerable attention. The increasing ability to control the growth of sophisticated structures (core-shells, axial heterostructures) is very promising for future nano-devices. The mechanical properties of these nano-objects are being investigated by various ways. Tensile testing of Cu nanowires has been reported by Richter et al. [Richter2009]. Suspended nanowires have been bent with an AFM tip [Cuenot2004, Wu2005, Wen2008]. MEMS structures may also be used to perform tension tests [Agrawal2008]. These difficult experiments produce sometimes conflicting results and it is still difficult to decide whether this comes from the material under test or the test itself. Figure 1 (from [Legros2010]) shows a compilation of results where the flow stress is plotted as a function of sample’s dimension in a log-log plot. In this plot the early results from Brenner [Brenner1956] are also reported. The general trend is clear: smaller is stronger. On the other hand defect-free wires can be stressed until the theoretical shear strength, which does not depend on the size. A single parameter like the flow stress does not, however, capture the full mechanical behaviour of these objects: when the size decreases the number of defects (dislocations, twins, etc) is reduced and a stochastic behaviour is observed where sudden bursts occur in the stress-strain plot. Such behaviours call for in situ observation of defects and strain field during straining. When it comes to elastic properties there is still a lot of confusion in the literature [Park2009, Cuenot2004, Wu2005, Wen2008, Agrawal2008, He2008]: size effects are evidenced by some groups at diameters as large as 100 nm [Agarwal2008, He2008], whereas others do not detect any influence of size on the elastic modulus down to 50 nm [Wu2005, Wen2008].
As mentioned above in situ observation of nano-objects during mechanical testing brings a lot of valuable information on the defects involved in the deformation process as well as on the local strains. Scanning Electron Microscopy coupled with tensile or compressive testing [Kiener2008, Kiener2009, Uchic2005, Michler2007] allows one to look at the change in sample shape as well as visualize the appearance of slip traces at the sample surface. In situ Transmission Electron Microscopy is more challenging but has the distinct advantage of visualizing individual dislocations movement [Dehm2000, Oh2007, Legros2008, Minor2002].
Figure 1 – A short compilation of normalize strength vs size in simple FCC metals, from [Legros2010]
Microbeam Laue diffraction performed during compression or tension of micropillars [Maass2007, Maass2008, Kirchlechner2010, Barabash2003] has the great advantage of being non-destructive. The streaking of Laue spots [Ice2006] contains information on the activated slip systems and the density of dislocations whereas the position of Laue spots yields the deviatoric strain tensor. All these informations are obtained with a spatial resolution of the order of the beam size i. e.
Coherent x-ray scattering is a fairly recent synchrotron technique consisting of using a near-fully coherent x-ray beam to perform various types of scattering experiments, including diffraction. Usual x-ray beams blur out most interference processes by averaging the scattered pattern over several “volumes of coherence”, so that one measures only the average properties of the scatterers (i.e. mean lattice parameters and correlation lengths in the case of diffraction by crystalline samples). Conversely, using a coherent x-ray beam enables the measurement of a contrasted “speckle pattern”, a figure of interference directly related with the local order AND disorder of the scatterers. For instance, it has been shown that a single dislocation in a crystal has a clear signature on Bragg peaks measured with a coherent x-ray beam. Such techniques were first developed by Sutton et al [Sutton1991] on a bending-magnet beamline, by slitting down drastically the x-ray beam to obtain a coherent beam, but nowadays the technique is commonly used on undulator beamlines, which naturally provide x-ray beam of much higher brilliance. The technique is promised a “bright” future with the development of so-called 4th generation sources, such as Free-Electron Lasers, which by nature deliver fully coherent x-ray beams, orders of magnitude more intense than synchrotron facility x-ray beams, and with temporal structure allowing the study of dynamics with a time-scale down to a few tens of femtoseconds.
There are two main applications of coherent x-ray scattering, both of them applying to the case of diffraction. The first one is to observe the speckle pattern in reciprocal space and study its fluctuations. Since there is generally a one to one correspondence between the scatterer configuration and the speckle pattern, this allows studying the dynamics of the sample as a function of time, temperature, pressure/stress, electric/magnetic field, etc...[Livet2007]. The second application is to “invert” the speckle pattern (by holographic or numerical techniques) to retrieve an image of the sample in real space. In the case of crystals of micrometre size or less, I.K. Robinson and his group [Pfeifer2006, Robinson2009, Robinson2001, Newton2010] have shown that it was possible to obtain a 3D image of the crystal, its electronic density, and its crystalline elastic strain field with a resolution of a few nanometres, from the coherent X-ray diffraction pattern measured at one or several Bragg peaks (at least 3 for the full strain field). By measuring a Bragg reflection of a small crystal in 3D, one can reconstruct an image of its shape and density [Williams2003] with a resolution down to 5 nm [Schroer2008]. A Bragg reflection is conveniently recorded in 3D by measuring a series of 2D patterns (on an area detector) along a rocking curve. The Coherent X-ray Diffraction (CXD) pattern of a Bragg reflection is not always centro-symmetrical, and this is a signature of the crystal strain field. In fact, one can develop the expression of the scattered intensity I(q)=|F(q)|² in the vicinity of a Bragg reflection Q and show that the scattering function can be considered as a complex electron density with its imaginary part related to the atomic displacement field u(r) in the crystal [Takagi1969]:
with
In this development, the measured intensity appears as the squared modulus of the Fourier transform of the complex electronic density ρ'(r), or in other words that the complex electronic density ρ'(r) can be seen as the scattering function. Using this approach, one can use inversion algorithms and retrieve the atomic displacement field projected onto the Bragg vector Q [Pfeifer2006], and with at least 3 well chosen Bragg peaks one can retrieve the 3D atomic displacement field [Newton2010]. While this works well for weakly strained crystals, the case of highly strained crystals is more complicated and the development of phase retrieval algorithms is still an area of intense research [Minkevich2007, Minkevich2008]. An alternative approach is to use simulations with the Finite-Elements Method (FEM) to estimate the strain field, calculate the corresponding diffraction pattern and compare it to the measurements [Proudhon2010, Diaz2010, Gailhanou2007]. Another experimental approach is the holographic method, using a reference crystal to encode the phase of the crystal of interest [Chamard2010], but the resolution is then limited by the size of the reference crystal. In any case, we see that CXD is a unique non-destructive probe of the atomic displacement fields in crystalline materials: It is non-destructive and can yield a strain map with a resolution of 5 to 8 nm. Moreover it has been shown to have a very high sensitivity to defects such as dislocations [Robinson2005, Jacques2009, Jacques2010, LeBolloch2005], which opens the way to the study of the first stages of plasticity.
In situ coherent X-ray diffraction during thermomechanical straining has been performed recently on a single 400 nm Au grain up to
Figure 2 – Cu 002 Coherent diffraction pattern from a Cu island grown on Ta [Exp2010] before (right) and after (left) compression with the AFM tip.
Im2np UMR CNRS 6242 • Faculté des Sciences • Avenue Escadrille Normandie Niemen • Case 142 • F 13397 Marseille Cedex 20 • France
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Partner 2
SIMAP
(Science et Ingénierie des Matériaux et Procédés, UMR 5266, CNRS – Grenoble-INP – Université Joseph Fourier)
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simap.grenoble-inp.fr |
Partner 3
INAC Institut des Nanosciences et Cryogénie, CEA2 Grenoble,
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inac.cea.fr/ |
Partner 4
ESRF ID01: The European Synchrotron Radiation Facility (ESRF) in
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Partner 5
LPS Laboratoire de Physique des Solides, Université Paris-sud, Bât 510, UMR8502, 91405 Orsay, France
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Partner 6
MPI Max Planck Institute for Metals Research, Heisenbergstrasse 3, D-70569 Stuttgart, Germany
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This project aims at in situ studies of the mechanical behaviour of low-dimensional materials, in particular, of nanowires (or pillars to limit their length). To perform in situ nanoscale mechanical experiments, an instrument needs to have two basic functions: (i) to visualize a nanostructure and (ii) to deform the nanostructure in situ. In recent years, various in situ instruments were developed and in situ mechanical tests were conducted. Tensile test apparatuses have been implemented in scanning electron microscopes (SEM) and in situ studies on micropillars and metal nanowires were performed by Kiener et al. [Kiener2008], Kirchlechner et al. [Kirchlechner2010], and G. Richter et al. [Richter2009], respectively. Moreover, in situ indentation devices have been implemented in transmission electron microscopes (TEM). Furthermore, several different instruments exist for in situ mechanical tests in combination with microfocused white beam X-ray diffraction at third generation synchrotrons such as SOLEIL, ESRF, and SLS. These tools allow for tensile tests on thin films [Girault2008] as well as for bending experiments and for compression studies on micropillars [Maass2007].
In this work, an in situ atomic force microscope (AFM) will be combined with X-ray diffraction using highly focused coherent X-ray beams. Such an instrument has been developed at the ID01 beamline at ESRF and this tool has been applied for in situ compression tests on nanoislands [Scheler2009, Rodrigues2009]. On the one hand, the AFM allows for probing the mechanical properties of nanostructure due to both nanoscale force and displacement sensing capabilities. The AFM contact force mode will be used to bend 1D nanostructures such as nanotubes and nanowires of various materials in either three-point bending or cantilever configurations. The corresponding AFM-tip force-deflection curves contain information about the deformation behaviour of the nanostructures from which the mechanical properties such as Young modulus and yield strength are derived. Moreover, with its imaging capabilities micrographs with high spatial resolution are acquired before and after the mechanical test. On the other hand, X-ray diffraction is a non-invasive technique in contrast to TEM where electron-transparent samples have to be prepared e.g. by microtomy or by FIB milling. It allows the determination of the complete strain tensor in a material with high precision as well as the detection of defects – grain boundaries, stacking faults, dislocations – by analysing the position and the shape of symmetric and asymmetric Bragg reflections. Additionally, Coherent X-ray Diffraction (CXD) imaging is a rapidly advancing form of microscopy: diffraction patterns, measured using the latest third-generation synchrotron radiation sources, can be inverted to obtain full three-dimensional images of the interior density within nanocrystals [Diaz2009, Schroer2008, Favre-Nicolin2009, Chamard2010, Robinson2009].
Description du programme de travail / Description of the program :
As it has been described in the previous section this ambitious project aims at investigating the mechanical properties of nano-objects via the combination of mechanical loading with an AFM tip and coherent X-ray diffraction. As we show in the next sections the partners in this project (IM2NP, SIMaP, INAC, ESRF-ID01, LPS and MPI Stuttgart) have the expertise in mechanics, coherent x-ray diffraction, growth of nanostructures and simulation to tackle such an important challenge. Moreover preliminary experiments have been performed, which show that this goal can be attained. Another important goal of this project is the design and building of a new XRD-compatible AFM stage that will profit from the previous experience of ID01-ESRF. It will be made available to the community and should be compatible with various synchrotron beamlines. Some tests will be planned during this project with the French CRG BM32 beamline equipped with a white beam microfocussing Laue setup. We have chosen a time scale of 4 years in order to ensure that sufficient time is given for hiring of PhD students and to be consistent with the international competition for synchrotron beamtime allocation. The scientific program is organized in 5 tasks:
Task 1: Coordination – Responsible O. Thomas, IM2NP
Task 2: Growth of Nanostructures – Responsible J. Eymery, INAC
Task3: AFM design and building – Responsible T. Cornelius, ID01 ESRF
Task4: Coherent diffraction – Responsible G. Beutier, SIMaP
Task5 : Modelling at different scales – Responsible G. Parry, SIMaP
This organization is rather straightforward. Since our aim is to push forward concepts and experiments that we are already developing, the basic tools are available and can be applied from the very first day of the project. As usual in such projects a key factor will be the exchange of information between the partners on a regular basis.
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