nature INSIGHT I REVIEW ARTICLES materials PUBLISHED ONLINE:24 MARCH 2009 DOI:10.1038/NMAT2400 Coherent X-ray diffraction imaging of strain at the nanoscale lan Robinson1*and Ross Harder2 The understanding and management of strain is of fundamental importance in the design and implementation of materials. The strain properties of nanocrystalline materials are different from those of the bulk because of the strong influence of their surfaces and interfaces,which can be used to augment their function and introduce desirable characteristics.Here we explain how new X-ray diffraction techniques,which take advantage of the latest synchrotron radiation sources,can be used to obtain quantitative three-dimensional images of strain.These methods will lead,in the near future,to new knowledge of how nanomaterials behave within active devices and on unprecedented timescales. -ray diffraction methods lie at the foundation of materials cause characteristic patterns of strain,often with associated domain science.Determination of the crystal structures of natural formation on the nanoscale.Classical defect structures,such as free minerals and,later,of crystals grown in the laboratory led dislocations,dislocation loops and stacking-fault tetrahedra all have to our considerable understanding of chemical bonding and cohe- characteristic strain fields that can be used to identify the defect sion that is the basis of the solid-state sciences'.Nanoscale materials modes present,given sufficient resolution.Whereas pure elasticity are emerging that have promising new properties,many of which effects are expected to behave according to classical theory down are associated with previously unknown structures,quantifable to a very small size scale,this is not the case for plasticity.Yield as strains that can be detected by X-ray methods.Here we review stresses are found to increase substantially in crystal grains smaller some of the advances in X-ray diffraction methods and their aug- than a micrometre and continue to deviate on the nanoscale,fol- mentation with the use of the laser-like beams available at the latest lowing a'smaller is stronger'trends.The complete understanding sources of synchrotron radiation,which are now providing spatially of such trends demands suitable methods of strain imaging on resolved structures of nanoscale objects.We will specifically explain the nanoscale. the isostrain method,high-resolution methods and coherent X-ray Looking to the future,imaging of strain dynamicss associated diffraction methods. with transients on the femtosecond timescale will become possible Nanomaterials are defined as those with crystal grain sizes in once the planned hard-X-ray free-electron lasers start operating the range of 100 nm or less.Such materials can possess properties The experimental methods under development today,as described remarkably different from their bulk counterparts,most obviously in this article,will become the methods of choice for producing detected as reduced melting points2,enhanced reactivities'or sig- single snapshots of excited matter at the future facilities?.A shock nificantly modified electronic band structures'.Numerous applica- wave would completely traverse a 100-nm crystal in 100 ps,allow- tions of these new properties are being developed in the new field ing plenty of opportunity to reveal its evolution at the expected of nanotechnology.The simplest explanation of why the properties time resolution of 100 fs.Crystallographic 'difference map'meth- of nanocrystals differ from the bulk is that a considerable fraction ods applied to fully phased starting structures will be very effective of the volume of nanocrystals lies close to external surfaces and for examining localized changes in single-shot applications that can interfaces.The different chemical and physical properties of those destroy the sample. surfaces therefore dominate the bulk behaviour. X-ray diffraction methods are by no means the only method of Strain is the physical concept used to describe the structural measuring strain distributions on the nanoscale.Transmission elec- deviation of the crystal from the ideal bulk state.It is defined as the tron microscopy (TEM)and related off-axis electron holography spatial derivative of the displacement of the material from an ideal methodss can achieve higher resolution than current X-ray meth- lattice,and hence has a tensorial nature.It is connected through ods and may also be quantitative.Transmission electron microscopy elasticity theory with stress,which is generally thought to be the methods are reviewed in a companion article.Both methods meas- origin of strain and can arise from chemical,electrical,magnetic, ure strain as a phase,but one slight distinction is that X-ray diffrac- mechanical and other forces associated with the local environment tion measures the three-dimensional(3D)distribution of a particular of the crystal.Because of the enhanced role of their surfaces,strain component of the strain field whereas electron holography measures in nanomaterials is expected to be significantly enhanced relative the vector strain field in a particular projection.Conventional and to bulk materials,thus opening significant opportunities for nano- aberration-corrected TEM can also map strain at high resolution technology.In this review,we illustrate how strain in nanomateri- by direct imaging.Furthermore,TEM can be used to map both the als can be measured using X-ray diffraction. strain and its relationship to the surrounding device structure that A strong reason for developing the capability to image strain in contains it' nanocrystals in the context of materials science is that the strain can Scanning probe X-ray methods are also not reviewed here. be altered substantially by processing of the material,either as part Spectroscopic methods,reviewed in a related article in this Insight"4, of its designed function or to test fundamental materials science are not directly sensitive to strain.Newly implemented ptycho- principles.Shock waves,ion irradiation tracks,chemical modifica- graphic methods's could be made sensitive to strain,which would tion or external fields applied to a crystalline grain are all expected to appear as a complex density (see below),by introducing Bragg London Centre for Nanotechnology,University College,17-19 Gordon Street,London WC1H OAH,UK and Diamond Light Source,Harwell Campus,Didcot Oxfordshire OX11 ODE,UK.2Advanced Photon Source,Argonne,Illinois 60439,USA."e-mail:i.robinson@ucl.ac.uk NATURE MATERIALS VOL 8|APRIL 2009 www.nature.com/naturematerials 291 2009 Macmillan Publishers Limited.All rights reservednature materials | VOL 8 | APRIL 2009 | www.nature.com/naturematerials 291 insight | review articles Published online: 24 march 2009 | doi: 10.1038/nmat2400 X-ray diffraction methods lie at the foundation of materials science. Determination of the crystal structures of natural minerals and, later, of crystals grown in the laboratory led to our considerable understanding of chemical bonding and cohe￾sion that is the basis of the solid-state sciences1 . Nanoscale materials are emerging that have promising new properties, many of which are associated with previously unknown structures, quantifiable as strains that can be detected by X-ray methods. Here we review some of the advances in X-ray diffraction methods and their aug￾mentation with the use of the laser-like beams available at the latest sources of synchrotron radiation, which are now providing spatially resolved structures of nanoscale objects. We will specifically explain the isostrain method, high-resolution methods and coherent X-ray diffraction methods. Nanomaterials are defined as those with crystal grain sizes in the range of 100 nm or less. Such materials can possess properties remarkably different from their bulk counterparts, most obviously detected as reduced melting points2 , enhanced reactivities3 or sig￾nificantly modified electronic band structures4 . Numerous applica￾tions of these new properties are being developed in the new field of nanotechnology. The simplest explanation of why the properties of nanocrystals differ from the bulk is that a considerable fraction of the volume of nanocrystals lies close to external surfaces and interfaces. The different chemical and physical properties of those surfaces therefore dominate the bulk behaviour. Strain is the physical concept used to describe the structural deviation of the crystal from the ideal bulk state. It is defined as the spatial derivative of the displacement of the material from an ideal lattice, and hence has a tensorial nature. It is connected through elasticity theory with stress, which is generally thought to be the origin of strain and can arise from chemical, electrical, magnetic, mechanical and other forces associated with the local environment of the crystal. Because of the enhanced role of their surfaces, strain in nanomaterials is expected to be significantly enhanced relative to bulk materials, thus opening significant opportunities for nano￾technology. In this review, we illustrate how strain in nanomateri￾als can be measured using X-ray diffraction. A strong reason for developing the capability to image strain in nanocrystals in the context of materials science is that the strain can be altered substantially by processing of the material, either as part of its designed function or to test fundamental materials science principles. Shock waves, ion irradiation tracks, chemical modifica￾tion or external fields applied to a crystalline grain are all expected to coherent X-ray diffraction imaging of strain at the nanoscale ian robinson1 * and ross harder2 The understanding and management of strain is of fundamental importance in the design and implementation of materials. The strain properties of nanocrystalline materials are different from those of the bulk because of the strong influence of their surfaces and interfaces, which can be used to augment their function and introduce desirable characteristics. Here we explain how new X-ray diffraction techniques, which take advantage of the latest synchrotron radiation sources, can be used to obtain quantitative three-dimensional images of strain. These methods will lead, in the near future, to new knowledge of how nanomaterials behave within active devices and on unprecedented timescales. cause characteristic patterns of strain, often with associated domain formation on the nanoscale. Classical defect structures, such as free dislocations, dislocation loops and stacking-fault tetrahedra all have characteristic strain fields that can be used to identify the defect modes present, given sufficient resolution. Whereas pure elasticity effects are expected to behave according to classical theory down to a very small size scale, this is not the case for plasticity. Yield stresses are found to increase substantially in crystal grains smaller than a micrometre and continue to deviate on the nanoscale, fol￾lowing a ‘smaller is stronger’ trend5 . The complete understanding of such trends demands suitable methods of strain imaging on the nanoscale. Looking to the future, imaging of strain dynamics6 associated with transients on the femtosecond timescale will become possible once the planned hard-X-ray free-electron lasers start operating. The experimental methods under development today, as described in this article, will become the methods of choice for producing single snapshots of excited matter at the future facilities7 . A shock wave would completely traverse a 100-nm crystal in 100 ps, allow￾ing plenty of opportunity to reveal its evolution at the expected time resolution of 100 fs. Crystallographic ‘difference map’ meth￾ods applied to fully phased starting structures will be very effective for examining localized changes in single-shot applications that can destroy the sample. X-ray diffraction methods are by no means the only method of measuring strain distributions on the nanoscale. Transmission elec￾tron microscopy (TEM) and related off-axis electron holography methods8 can achieve higher resolution than current X-ray meth￾ods and may also be quantitative. Transmission electron microscopy methods are reviewed in a companion article9 . Both methods meas￾ure strain as a phase, but one slight distinction is that X-ray diffrac￾tion measures the three-dimensional (3D) distribution of a particular component of the strain field whereas electron holography measures the vector strain field in a particular projection. Conventional10 and aberration-corrected11,12 TEM can also map strain at high resolution by direct imaging. Furthermore, TEM can be used to map both the strain and its relationship to the surrounding device structure that contains it13. Scanning probe X-ray methods are also not reviewed here. Spectroscopic methods, reviewed in a related article in this Insight14, are not directly sensitive to strain. Newly implemented ptycho￾graphic methods15,16 could be made sensitive to strain, which would appear as a complex density (see below), by introducing Bragg 1 London Centre for Nanotechnology, University College, 17–19 Gordon Street, London WC1H 0AH, UK and Diamond Light Source, Harwell Campus, Didcot, Oxfordshire OX11 0DE, UK. 2 Advanced Photon Source, Argonne, Illinois 60439, USA.*e-mail: i.robinson@ucl.ac.uk nmat_2400_APR09.indd 291 13/3/09 12:04:27 © 2009 Macmillan Publishers Limited. All rights reserved