Electron Tomography: A Three-Dimensional Analytic Tool for Hard and Soft Materials Research.

2.4. Differences Between Hard Materials and Soft/Biomaterials As mentioned previously, ET is used extensively in investigations of specimens for both physical and biological science. However, very few techniques are shared between these two fields. The physical constraints imposed by the constituent materials and the functional parameters that need to be measured both lead to very different types of solutions to investigate 3D structure. Early in the development of TEM, the biological community quickly realized that 2D projections of macromolecules were insufficient to understand their functionality, and then ET was initially developed to reconstruct biological macromolecules in 3D. Biological macromolecules generally consist of light atoms (H, C, N, O, etc.), and produce low contrast in TEM images, which can be difficult to detect above the background noise. Additionally, the structure of biological samples is sensitive to the electron beam, which mainly limits biological investigations. Electron–sample interactions lead to both elastic and inelastic scattering of the incident electrons, which either imparts momentum to atoms or deposits energy in the target material. Inelastic scattering produces free radicals with 5–100 eV energy that can damage biological samples by breaking covalent bonds and destroying their structure. Thus, biological samples can only sustain a limited dose, which results in even lower contrast images, and limits the 3D-reconstruction resolution of biological structures. Nonetheless, the low-resolution 3D structures of large macromolecules can still provide numerous insights into their function. Many techniques, as described in Section 4, have been developed to maximize resolution while keeping the biological structure intact. These techniques may also be applicable to research in physical sciences. Unlike biology, samples in physical science often contain crystalline materials, which produce diffraction contrast that cannot be used for ET reconstruction. Recently, STEM has provided high-contrast and high-resolution images with limited diffraction contrast, providing 3D ET reconstructions of nanoscale objects. Attaining high contrast and high resolution is possible in physical-science specimens due to the radiation hardness (strong bonding) of the materials involved. Radiation damage due to elastic scattering (knock-on effects) are more relevant to hard materials, compared to radiation damage from inelastic scattering events. Since permanent knock-on displacements occur above a certain threshold energy, radiation damage in hard materials can be limited by lowering the incident electron energy, and tends to be less of a concern compared to soft materials. Thinned TEM specimens of metals, such as Au and Ag, can be imaged at relatively high doses without significantly changing their internal bulk structure. Surfaces and defects exhibit much lower damage thresholds. [ 51 ] Carefully choosing the acceleration voltage and dose during imaging can produce much-improved results, as demonstrated recently by images of Si with much-reduced beam damage. [ 52 ] The separate development of ET in both physical and biological fields has led to very different techniques, which are shown in the following sections. New classes of hybrid materials are being developed, which incorporate both hard and soft materials, such as metal–organic frameworks (MOFs) [ 53 ] and polymer/metal interfaces in solid-state battery electrodes. [ 54 ] Current 2D and 3D analysis techniques are incapable of simultaneously imaging both hard and soft materials, especially at interfaces. There exists the opportunity to incorporate ET techniques from both biological and physical sciences to provide a robust analytical tool for a wide range of hybrid matter systems.

3.4.2.

Methods for Non-linear Projections

The two traditional reconstruction algorithms (WBP and SIRT) assume a linear relationship between the projected density and the image intensity. This is a good approximation in most cases for HAADF-STEM images, but non-linear and non-monotonic deviations are known to exist. [ 62 ] Furthermore, traditional reconstruction algorithms do not account for the noise characteristics of HAADF-STEM. Methods that compensate for non-linear scattering, originally developed for medical CAT, can incorporate the known physics of particle scattering into the reconstruction algorithm. [ 98 , 99 ] Utilizing the physics of the imaging process during reconstruction can include factors such as exponential signal attenuation inside thick specimens (known as Beer’s law) and nonlinear diffraction contrast. [ 100 ] Intensities in HAADF-STEM images are dominated by incoherently scattered electrons, but the low flux of highly scattered electrons requires a large electron dose to achieve a good SNR. Improved dose efficiency can be achieved at the cost of a less-linear signal by using electrons scattered at lower angles (including Bragg scattering). A model-based iterative reconstruction (MBIR) technique (not to be confused with the density model used to align projection images in biology) can account for noise and non-linear intensities during a reconstruction based on the scattering processes involved in image formation. [ 101 ] This approach has also been utilized to produce reliable reconstructions from highly non-linear imaging methods such as bright-field (BF) STEM. [ 102 ] MBIR can also be used to produce quantitative reconstructions where the voxel intensity provides a real measure of the local material property, such as a scattering cross-section, rather than relative density. MBIR has been shown to reduce artifacts and improve contrast, even with fewer projections, using rational physical constraints imposed on the system to eliminate unphysical results. [ 103 ]

3.6. Beyond Density: Measurement of Intrinsic Material Properties in 3D The main focus of ET until recently was to determine the 3D density distribution of an object, but TEM is a very versatile tool capable of measuring more than just the projected density of materials. Recent advances in hardware and software provide electron microscopists with vastly more-stable and powerful microscopes enabling STEM and TEM to achieve new milestones in analytical capabilities, such as quantitative sensitivity to spectroscopic, [ 58 , 116 ] magnetic, [ 117 ] and electronic [ 118 ] properties of materials, even with atomic resolution. Some of these advanced TEM experiments satisfy the projection requirement for tomography, opening up the possibility of directly measuring functional properties in 3D at the nanoscale. 3.6.1.

Spectroscopic Tomography

HAADF-STEM is useful to distinguish between materials with large differences in atomic number (Au and C), and has been used to determine distributions of metals in core/shell structures at high resolution. [ 119 ] Small differences are much more difficult to detect (Co and Ni). Initial experiments that retrieved more than a single density measurement per voxel involved spectroscopic methods such as EELS [ 120 ] and X-ray energy-dispersive spectroscopy (X-EDS) [ 121 ] in TEM or STEM mode. Both spectroscopic methods are very powerful for measuring elemental distributions at the nanometer scale, producing signals that conform to projection theorems. [ 122 , 123 ] These methods are very dose intensive because the scattering cross-sections for inelastic (energy loss) events are extremely low, leading to long acquisition times. Until recently, even 2D mapping of structures in a single projection had proved difficult due to limited stability and beam current over hour(s) long acquisitions. Advances in detectors, electron-source brightness, and collection optics have all provided sufficient beam current and collection efficiency to reduce acquisition times of 2D maps from hours to minutes. EELS and X-EDS are therefore used to unambiguously distinguish elements in 2D, even within mixtures of materials, and 3D measurements have become more practical. [ 124 ] For example, EELS measurements of the 3D distribution of surface plasmon modes of cubic metal nanoparticles, which could not be determined without spectroscopic imaging, were recently reported. [ 107 ] Although neither of these spectroscopic techniques applies a low dose on the specimen during imaging, the resulting noisy tilt series could benefit from techniques developed in biological sciences for low-SNR reconstruction to improve elemental mapping in 3D at the nanoscale. The quality of a spectroscopic signal from nanostructures also greatly depends on the thickness of the specimen, and spectroscopic tomography was partially made possible by the preparation of the needle-like samples discussed in Section 3.5. [ 109 ] For EELS, specimens much thicker than the incident electron mean-free path produces multiple scattering, which increases the signal background. [ 120 ] For X-EDS, the spectrum intensities depend on the path of the incident electron and the path of the generated X-rays, and thickness corrections must be applied even for relatively thin samples to achieve quantitative results. [ 116 , 125 ] For tomography, these corrections may need to be applied for each separate tilt angle. Reconstruction of 200 nm LiNiMnO 2 nanoparticles showed the segregation of one species (Ni in this case) to the surface of the particle even for low-contrast materials that would not be visible in a typical HAADF-STEM 3D reconstruction. [ 126 ] Although powerful enough to unambiguously differentiate elemental species in 3D, spectroscopic tomography only produces the morphology of the object of interest. Other TEM imaging projection methods have been used to investigate materials properties, such as magnetic fields at the nanometer scale in 3D. 3.6.2. Measuring Magnetic Fields The magnetic properties of materials are important aspects of device functionality in advanced technologies such as magnetic hard drives. Continued improvement of such devices requires quantitative measurements of magnetic fields within and around nanoscale features, which are independent of density. For example, the size of magnetic domains that define storage bits on magnetic hard drives is limited due to magnetic interactions at the nanoscale. [ 127 ] Unfortunately, the objective lens in STEM and TEM produces a strong magnetic field of ca. 2 T perpendicular to the sample surface, which magnetizes almost all material perpendicular to the sample. Removing this strong magnetic field provides a field-free imaging condition, generally referred to as Lorentz TEM, sensitive to the intrinsic in-plane magnetization of the material, although the resolution is degraded to >1 nm. [ 128 ] Nanoscale resolution is sufficient to analyze many magnetic structures, but generating images with contrast that can be related to measurable magnetic properties is difficult. We discuss two quantitative techniques used in Lorentz microscopy that determine the relative phase shifts of the incident electron beam, which can be related to the object’s intrinsic magnetic field. Fresnel image contrast measures effects of phase shifts in TEM image intensities, and off-axis holography accurately measures the electron phase shifts of the complex electron wave. Fresnel Imaging Contrast The most-common technique in Lorentz microscopy to produce magnetic contrast, called Fresnel imaging, is achieved by simply defocusing the imaging lens in field-free conditions to enhance coherent interference. [ 129 ] Adjacent magnetic grains in a thin film are separated by a boundary called a magnetic domain wall where the in-plane magnetic field changes direction. The path of an electron traveling perpendicular to the sample surface is deflected according to the strength of the in-plane field. At a magnetic domain wall, grains with opposing magnetic fields will produce bright or dark lines according to their direction and the lens defocus. The diagram in Figure 9 shows how deflected electrons overlap in a defocused image to produce bright or dark lines according to the magnetic orientation of neighboring grains. This technique highlights the grain boundaries in a 2D projection of a thin film. For quantitative measurements, a digital phase-retrieval algorithm, such as the transport of intensity equation, is necessary to measure the projected phase change of the electrons from a series of defocused images ( Figure 9a–d ). [ 130 ] The in-plane magnetic induction is then calculated from the relative phase changes at each position. The image of the magnetic field provides a measure of the projected in-plane component of a 3D magnetic vector, [ 131 ] and a double-tilt ET experiment [ 50 ] is required to determine the full 3D magnetic vector field. [ 132 ] In practice, the object is removed from the microscope and rotated 90° in the holder after the acquisition of each tilt series. [ 132 ] Further developments in equipment, image acquisition techniques, and post-processing algorithms are needed to fully realize the potential of 3D Fresnel imaging in Lorentz microscopy to study nanoscale magnetic devices. Off-Axis Electron Holography Off-axis electron holography is a powerful technique that uses interference to measure both the amplitude and phase of the electron wave after it passes through the sample. [ 133 ] This is unlike typical TEM, because an imaging detector measures the intensity (or magnitude squared) of the complex electron wave. [ 134 ] The technique utilizes a post-specimen electrostatic biprism to interfere with one portion of the electron beam that passes through vacuum and a separate portion that passes through the sample. A fringe pattern is created on the imaging detector, and digital processing of the fringe pattern is used to determine the complex values of the electron wave. For most materials, the phase is directly related to the projected mean inner potential (MIP) and magnetic field of the underlying structure. The technique can quantitatively measure electrostatic and magnetic properties of materials with sub-nanometer resolution, such as the potential of pn-junctions, dopant profiles, and the magnetization distribution in and around objects. [ 135 ] Projection measurements from off-axis holography conform to the projection theorem of ET, providing the ability to quantitatively measure 3D electrostatic potentials of core–shell nanowires and semiconductor devices. [ 136 , 137 ] When used in a field-free Lorentz TEM, magnetic fields are particularly interesting to study in 3D by electron holography, because even field lines in vacuum around the sample can even be measured. [ 138 ] However, just as with Fresnel imaging, determination of the magnitude and direction of the 3D vector field requires acquisition of two tilt series with a 90° rotation between them. [ 139 ] Outlook The applications of 3D magnetic Lorentz tomography and off-axis electron holography are currently limited due to the specialized equipment required to accomplish the experiments. For both techniques, Lorentz TEM has relatively low resolution compared with normal TEM, although recent developments in aberration correction will provide higher-resolution, field-free imaging in the near future. [ 140 ] Off-axis electron holography requires a highly coherent source (such as an FEG), a biprism, and a special electron optical setup. [ 141 ] Other important limitations to consider are the field-of-view and hologram fringe contrast (peak to valley measurements), which have direct effects on the achievable lateral resolution and phase resolution in the reconstructed exit wave. [ 142 ]

4. Advances in ET for Soft-Materials and Biomaterials Research 4.1. Background ET has contributed effectively to the study of a wide variety of biological molecules, from a single macromolecule to a whole cell. Examples include the nuclear pore, [ 143 ] viruses, [ 144 ] micro-tubules, [ 145 ] bacterial ultrastructure, [ 146 ] molecular motors, [ 147 ] and cell sections. [ 148 ] More recently, the technique enabled the study of conformational dynamics based on the structure of a single protein. [ 37 , 38 ] Tilt series ET has several advantages over X-ray crystal diffraction and single-particle reconstruction. X-ray crystallography captures diffraction patterns from crystallized molecules and then solves for the real-space density. Single-particle reconstruction uses tens of thousands of images of immobilized particles in random orientations. Those 2D images are organized into different classes based on particle 3D orientations before being averaged into a 3D reconstruction. In ET, 3D reconstruction from a single object can avoid possible artifacts introduced through averaging a large number of images of flexible proteins in different conformations. Structurally flexible proteins show significant variability in solution, making them difficult to classify accurately prior to identifying their orientations. [ 149 – 151 ] Moreover, aligning ET images is, in principle, simple compared to aligning images in single-particle reconstructions, which requires a reference model. In addition, ET enables 3D structural determinations of a wide variety of macromolecules and macromolecular processes, such as large complexes [ 39 ] and aggregates. However, the resolution achieved directly from ET (without averaging) is rarely beyond ca. 2 nm. Many factors need to be considered before 3D reconstruction in soft materials or biomaterials. In terms of the sample environment, the sample itself tends to lower the quality of the recorded images due to the solvent background, stain effects, temperature-related drift, sample surface charging, and beam-induced motion. [ 152 , 153 ] In terms of TEM operation, limitations are related to the use of a high-defocus (trading low-resolution details for high-resolution), [ 154 , 155 ] detector shot noise, and detector quantum efficiency. [ 156 , 157 ] In terms of the instrument, the quality of the recorded images is affected by instabilities in the TEM source and lenses (beam coherence), [ 158 ] lens astigmatism, [ 159 ] spherical aberrations, [ 12 ] energy filter distortion, [ 160 ] and mechanical tilting. Ideally, all of the above parameters should to be adjusted, optimized, corrected, and compensated before or during ET data acquisition and 3D reconstruction. 4.2. Strategies in ET The following section provides a brief account of selected aspects of sample preparation, data acquisition, tilt-series alignment, and 3D-reconstruction techniques. 4.2.1.

Sample Preparation

Biological samples have generally poor contrast to their image background, typically amorphous carbon, and can be easily damaged by the electron beam during imaging. As a result, numerous methods have been developed to both enhance sample contrast, and improve sample integrity under illumination. For the purpose of the following discussion, we broadly categorize these methods into three groups based on the main strategy used in the sample preparation: staining-based methods, cryogenic methods (cryofixation) and combinations of both staining and cryofixation. The method of choice usually depends on the targeted resolution, the purpose of the study, and the nature of the sample, which can vary from individual molecules to whole cells or tissues.

Staining-Based Sample Preparation

Staining-based sample preparation, used to improve image contrast, includes negative staining [ 161 ] and positive staining. [ 162 ] Negative staining is the most-popular technique, in which the sample is surrounded with a layer of charged heavy-metal salts. The stain appears as dark regions on the edges of molecules in images, thus highlighting their shape in a “negative” contrast image. [ 163 ] When the stain is sufficiently thin, only barely covering the sample surface, a “positive” contrast image is generated, termed positive staining. The high image contrast, in both cases, is due to the fact that the heavy-metal ions scatter more electrons compared with the lighter atoms in the sample. [ 164 – 166 ] The heavy-metal coating on the sample permits a high dose with high contrast for easier determination of particle orientation in 3D reconstructions. [ 167 ] Negative-staining reagents include phosphotungstic acid salts, ammonium molybdate, uranyl acetate, uranyl formate, and methylamine vanadate. Phosphotungstic acid is particularly widely used in standard protocols due to its near physiological pH. [ 168 ] In general, preparation of stained samples is simple and efficient compared to cryo-electron-microscopy (cryo-EM). It therefore permits the screening of a large number of samples and conditions. Although TEM studies that utilized negative staining were able to observe macromolecules, the fine details of those molecules remained unresolved. [ 34 ] It was generally believed that a detailed particle structure was preserved and stabilized with negative staining. [ 169 ] Other studies showed that the stain could introduce distortions to some molecules, such as general aggregation, molecular dissociation, and flattening. [ 167 , 170 , 171 ] For example, a common artifact due to negative staining of lipid-related proteins is that particles stacked and packed together into a structure called a rouleaux. [ 163 , 172 – 176 ] Recently, an optimized negative-staining (OpNS) method [ 177 – 179 ] was proposed via a refined conventional protocol ( Figure 10 ). [ 180 ] The OpNS protocol has been validated by proteins with a known structure, [ 179 ] including cholesterol ester transfer protein (CETP), [ 162 ] GroEL, and proteasome ( Figure 11 ), [ 181 ] and applied to examine the structures of lipoproteins [ 177 , 178 ] and flexible antibodies. [ 37 ] Cryo-EM The main advantage of cryo-EM is that the samples can be examined in their hydrated native state. [ 23 , 182 – 184 ] Samples embedded in a physiological buffer or even inside cells could avoid potential artifacts induced by dehydration, chemical fixation, or staining. [ 185 ] Unlike for hard materials, images from soft materials and biomaterials exhibit low contrast, which arises from differences between the scattering densities of the biomolecules and the solvent. Small proteins are difficult to be visualized or identified, although the image contrast of the overall shape of biomolecules can be enhanced by defocusing. [ 186 , 187 ] Cryofixation of hydrated samples is currently the most-common ET method to examine micrometer- to nanometer-scale objects, including 2D molecular crystals and helical structures. Samples are fixed by rapid freezing with liquid ethane using a plunger and then transferred to liquid nitrogen (or liquid helium) for storage. TEM imaging is accomplished while the sample is maintained at liquid-nitrogen temperature in a cryo-holder ( Figure 12 ). [ 185 , 188 – 191 ] Cryo-EM of vitrified sections (called CEMOVIS) is a method to prepare thicker samples using a high-pressure freezing machine. The machine, operating under more than 10 3 bar pressure, enables rapid cooling of thick samples before the formation of ice crystals. [ 194 ] The vitrified sample is then sectioned by a cryo-microtome to obtain a thin layer of sample, such as a thickness of ca. 50 nm. The technique has been applied to several studies, including ET of cells. [ 195 , 196 ] The limitation of this method includes potential artifacts at the cutting surface, such as compressions or crevasses, which can be several nanometers deep. [ 197 ] Cryo-Negative and Cryo-Positive Staining In cryo-EM, small proteins (