Quantitative Convergent Beam Electron Diffraction Research Articles

An Anomalous Electron Configuration Among 3d Transition Metal Atoms.

Physical properties of materials are mainly determined by valence electron configurations, where different valence shells would induce divergent phenomena. In compounds containing Sc2+ , 3d electron occupancy is expected, the same as other transition metal atoms like Ti3+ . But this situation still awaits experimental verification in inorganic materials. Here, we selected ScS to measure the valence electron density and orbital population of Sc2+ through delicate quantitative convergent-beam electron diffraction. With the absence of 3d orbital features around Sc-atom sites and the nearly bare population of t2g orbital, the unintuitive occupation of 4s orbital in Sc2+ is concluded. It should be the first time to report such a special electron configuration in a transition metal compound, in which 4s rather than 3d orbital is preferred. Our findings reveal the distinct behavior of Sc and probable ways to modulate material properties by controlling electron orbitals.

Real-space measurement of orbital electron populations for Li1-xCoO2

The operation of lithium-ion batteries involves electron removal from and filling into the redox orbitals of cathode materials, experimentally probing the orbital electron population thus is highly desirable to resolve the redox processes and charge compensation mechanism. Here, we combine quantitative convergent-beam electron diffraction with high-energy synchrotron powder X-ray diffraction to quantify the orbital populations of Co and O in the archetypal cathode material LiCoO2. The results indicate that removing Li ions from LiCoO2 decreases Co t2g orbital population, and the intensified covalency of Co–O bond upon delithiation enables charge transfer from O 2p orbital to Co eg orbital, leading to increased Co eg orbital population and oxygen oxidation. Theoretical calculations verify these experimental findings, which not only provide an intuitive picture of the redox reaction process in real space, but also offer a guidance for designing high-capacity electrodes by mediating the covalency of the TM–O interactions.

Detecting minute amounts of nitrogen in GaNAs thin films using STEM and CBED

Nitrogen (N) is a common element added to GaAs for band gap engineering and strain compensation. However, detection of small amounts of N is difficult for electron microscopy as well as for other chemical analysis techniques. In this work, N in GaAs is examined by using different transmission electron microscopy (TEM) techniques. While both dark-field TEM imaging using the composition sensitive (002) reflections and selected area diffraction reveal a significant difference between the doped thin-film and the GaAs substrate, spectroscopy techniques such as electron energy loss and energy dispersive X-ray spectroscopy are not able to detect N. To quantify the N content, quantitative convergent beam electron diffraction (QCBED) is used, which gives a direct evidence of N substitution and As vacancies. The measurements are enabled by the electron energy-filtered scanning CBED technique. These results demonstrate a sensitive method for composition analysis based on quantitative electron diffraction.

Measuring Density Functional Parameters from Electron Diffraction Patterns.

We integrate density functional theory (DFT) into quantitative convergent-beam electron diffraction (QCBED) to create a synergy between experiment and theory called QCBED-DFT. This synergy resides entirely in the electron density which, in real materials, gives rise to the experimental CBED patterns used by QCBED-DFT to refine DFT model parameters. We use it to measure the Hubbard energy U for two strongly correlated electron systems, NiO and CeB_{6} (U=7.4±0.6  eV for d orbitals in NiO and U=3.0±0.6  eV for f orbitals in CeB_{6}), and the boron position parameter x for CeB_{6} (x=0.1992±0.0003). In verifying our measurements, we demonstrate an accuracy test for any modeled electron density.

Mapping valence electron distributions with multipole density formalism using 4D-STEM

Recent advancement in aberration correction and detector technology opened a door to various applications using 4D-STEM, which yields a diffraction pattern for each scanning position within a crystal unit-cell in scanning transmission electron microscopy (STEM) and generates incredible amounts of data in momentum space. Currently 4D-STEM analysis relies on the center-of-mass of the diffraction patterns in electric field and charge density mapping. It only derives the total projected charge density and is limited to phase objects, e.g. extremely thin samples. Here, we propose a new analytical method to accurately map aspherical valence electron distributions with atom-centered multipolar functions formalism using the whole 4D-STEM dataset. We demonstrate that, with the full dynamical calculations for various sample thicknesses, the method is sensitive not only to the miniscule charge transfer, but also to the atomic site symmetry and aspherical electron orbitals. The process of the refinement is much more robust and reliable than quantitative convergent beam electron diffraction.

Identification of the impurity phase in high-purity CeB6 by convergent-beam electron diffraction.

The rare earth hexaborides are known for their tendency towards very high crystal perfection. They can be grown into large single crystals of very high purity by inert gas arc floating zone refinement. The authors have found that single-crystal cerium hexaboride grown in this manner contains a significant number of inclusions of an impurity phase that interrupts the otherwise single crystallinity of this prominent cathode material. An iterative approach is used to unequivocally determine the space group and the lattice parameters of the impurity phase based on geometries of convergent-beam electron diffraction (CBED) patterns and the symmetry elements that they possess in their intensity distributions. It is found that the impurity phase has a tetragonal unit cell with space group P4/mbm and lattice parameters a = b = 7.23±0.03 and c = 4.09±0.02 Å. These agree very well with those of a known material, CeB4. Confirmation that this is indeed the identity of the impurity phase is provided by quantitative CBED (QCBED) where the very close match between experimental and calculated CBED patterns has confirmed the atomic structure. Further confirmation is provided by a density functional theory calculation and also by high-angle annular dark-field scanning transmission electron microscopy.

Quantitative convergent-beam electron diffraction and quantum crystallography—the metallic bond in aluminium

The technique of quantitative convergent-beam electron diffraction (QCBED) is reviewed as a method for making very accurate and precise measurements of low-order bonding-sensitive structure factors. As such, it is a technique with the potential to make significant contributions to the field of quantum crystallography. To demonstrate this, the application of QCBED in determining the nature of the metallic bond in aluminium is examined in detail. The importance of precision in structure factor measurement when it comes to determining bonding electron distributions, especially in metals, becomes obvious from this examination. Uncertainties as low as ±0.1% are routinely attainable by QCBED and are shown to be important in reliably locating bonding charge. In the case of aluminium, a nearly free electron gas metal where the bonding electron distribution is subtler than in most other materials, the bonds are entirely tetrahedrally centred. This is a conclusion that could not have been reached experimentally without the levels of precision offered by QCBED.

How do specimen preparation and crystal perfection affect structure factor measurements by quantitative convergent-beam electron diffraction?

The effectiveness of tripod polishing and crushing as methods of mechanically preparing transmission electron microscopy specimens of hard brittle inorganic crystalline materials is investigatedviathe example of cerium hexaboride (CeB6). It is shown that tripod polishing produces very large electron-transparent regions of very high crystal perfection compared to the more rapid technique of crushing, which produces crystallites with a high density of imperfections and significant mosaicity in the case studied here where the main crystallite facets are not along the natural {001} cleavage planes of CeB6. The role of specimen quality in limiting the accuracy of structure factor measurements by quantitative convergent-beam electron diffraction (QCBED) is investigated. It is found that the bonding component of structure factors refined from CBED patterns obtained from crushed and tripod-polished specimens varies very significantly. It is shown that tripod-polished specimens yield CBED patterns of much greater integrity than crushed specimens and that the mismatch error that remains in QCBED pattern matching of data from tripod-polished specimens is essentially nonsystematic in nature. This stands in contrast to QCBED using crushed specimens and lends much greater confidence to the accuracy and precision of bonding measurements by QCBED from tripod-polished specimens.

Exploring the Possibility of Deformation Twinning in Pure Aluminum

Can aluminum generate deformation twins? Contradictories exist among the experimental results, theoretical predictions, and molecular dynamics simulations. Our first-principles calculations based on the full-potential linearly augmented plane wave method show that the bonding electron density of aluminum gathers at the tetrahedral interstices, and this specific electronic structure is in agreement with the experimental data from quantitative convergent-beam electron diffraction. In terms of this characteristic, the matching between the cohesive energy of local deformation twins with different thickness and global matrix can shed light on deformation twins in aluminum. This study may give a lane to insight into deformation twins in different metals.

Strong Coupling of the Iron-Quadrupole and Anion-Dipole Polarizations inBa(Fe1−xCox)2As2

We use a quantitative convergent beam electron diffraction based method to image the valence electron density distribution in Ba(Fe1-xCox)2As2. We show a remarkable increase in both the charge quadrupole of the Fe cations and the charge dipole of the arsenic anions upon Co doping from x=0 (Tc=0  K) to x=0.1 (Tc=22.5  K). Our data suggest that an unexpected electronic correlation effect, namely strong coupling of Fe orbital fluctuation and anion electronic polarization, is present in iron-based superconductors.

Determination of fluctuations in local symmetry and measurement by convergent beam electron diffraction: applications to a relaxor-based ferroelectric crystal after thermal annealing

Single crystals of Pb(Mg1/3Nb2/3)O3–31%PbTiO3(PMN–31%PT) are known for their complex domain structures at the nanometre scale. While their average symmetry has been studied by X-ray, neutron and electron diffraction methods, there is little knowledge about variations in symmetry at the local scale. Here, direct evidence is provided for the volume dependence and spatial dependence of symmetry fluctuations by using quantitative convergent beam electron diffraction and energy dispersive X-ray spectroscopy. Fluctuations in symmetry were determined by using different electron beam probe sizes ranging from ∼2 to 25 nm from a crystal ∼62 nm thick. The symmetry of PMN–31%PT was found to increase linearly as the average volume increased, and the local symmetry fluctuated from one location to another at the nanoscale. Energy dispersive X-ray spectroscopy indicates that chemical fluctuations are significant when the probe size decreases to ∼2 nm. The symmetry fluctuation is attributed to locally varying composition-dependent ionic displacements and spontaneous polarization.

Validation of density functionals for transition metals and intermetallics using data from quantitative electron diffraction

Accurate low-order structure factors (Fg) measured by quantitative convergent beam electron diffraction (QCBED) were used for validation of different density functional theory (DFT) approximations. Twenty-three low-order Fg were measured for the transition metals Cr, Fe, Co, Ni, and Cu, and the transition metal based intermetallic phases γ-TiAl, β-NiAl, and γ1-FePd using a multi-beam off-zone axis QCBED method and then compared with Fg calculated by ab initio DFT using the local density approximation (LDA) and LDA + U, and different generalized gradient approximations (GGA) functionals. Different functionals perform very differently for different materials and crystal structures regarding prediction of low-order Fg. All the GGA functionals tested in the paper except for EV93 achieve good overall agreement with the experimentally determined low-order Fg for BCC Cr and Fe, while EV93 performs the best for FCC Ni and Cu. The LDA and GGA functional fail to predict accurately the low-order Fg for β-NiAl and γ1-FePd. The LDA + U approach, through tuning of U, can achieve excellent matches with the experimentally measured Fg for all the metallic systems investigated in this paper. The use of experimentally accessible low order Fg as an additional set of metrics in approaches of validation of DFT calculations is discussed and has potential to assist in and to stimulate development of improved functionals.

Comparison of convergent beam electron diffraction methods for simultaneous structure and Debye Waller factor determination

The measurement of accurate and precise structure factors and Debye Waller (DW) factors by quantitative convergent beam electron diffraction (QCBED) permits experimental determination of the electron density distribution and probing of interatomic bonding in crystals. The three QCBED methods used successfully for high precision measurements of low order structure factors to date, namely the zone axis pattern (ZAP) method, the excited row ER method and the multi-beam off-zone axis (MBOZA) technique, differ from each other regarding the crystal orientation relative to the incident electron beam. Consequently, the details of their respective dispersion surface representations differ regarding the number, relative amplitudes and phases of excited Bloch wave branches. Under the same experimental setup conditions, the factors most important to the degree of accuracy and precision achievable in electron density determination for crystals with QCBED methods ultimately depend on the sensitivity of the excited Bloch wave branches and the resultant contrast in the respective CBED patterns to changes in both structure and DW factors. In general, a QCBED pattern will be more sensitive to changes in both structure and DW factor, if it contains more and stronger excited Bloch wave branches, as dynamic interactions of the Bloch waves increase the sensitivity of the pattern. In this work we analyzed Bloch wave excitation and dispersion surfaces for the three most popular QCBED methods. The analysis indicates, that the QCBED patterns obtained using the MBOZA orientation generally contain more and stronger excited Bloch wave branches. Hence, MBOZA diffraction patterns are more sensitive than the ZAP and the ER patterns to changes in both DW and structure factors and therefore allow in differences to the other two methods simultaneous refinements effectively and robustly.

High precision electronic charge density determination for L10-ordered γ-TiAl by quantitative convergent beam electron diffraction

Low order structure and Debye–Waller (DW) factors for tetragonal L10-ordered γ-TiAl were measured simultaneously using quantitative convergent beam electron diffraction. The high precision and accuracy (largest error <0.5%) measurements allowed the construction of charge density difference maps from full sets of structure and DW factors, suitable for validation of first principles density functional theory (DFT) calculation results. Comparison of the experimentally determined charge density distribution with theoretical DFT predictions shows excellent qualitative agreement in this study. The three-dimensional charge density representations indicate a large electron charge localisation centred about the tetrahedral site at ¼, ¼, ¼, which is coordinated by two Ti atoms at 0, 0, 0 and ½, ½, 0 and two Al atoms at ½, 0, ½ and 0, ½, ½, respectively. Compared to experimental data, the DFT calculations based on full-potential linearised augmented plane wave (LAPW) method (implemented in WIEN2K) were found to quantitatively overestimate charge density between Ti–Ti second nearest neighbour atoms. Moreover, the results from the DFT method based on the projector-augmented wave (PAW) method and a plane wave basis set (implemented in VASP) were found to differ appreciably from both the experimental and LAPW-DFT results, implying that the PAW approach may not accurately describe the bonding in the intermetallic systems with 3 d electrons, such as γ-TiAl.

In situ quantification of noise as a function of signal in digital images

An efficient and accurate algorithm for determining the magnitude of noise as a function of signal in an arbitrary digital image is presented and demonstrated. The algorithm is robust and largely independent of the form of the image, returning the noise function with subcount error across the full dynamic range of a synthetic test image where noise of a known form has been added. The noise performance of a CCD under different image recording and processing conditions is examined using the algorithm. The effect of different noise functions on pattern-matching measurements of electronic structure by quantitative convergent beam electron diffraction is investigated.

Real space charge density mapping by quantitative convergent beam electron diffraction (QCBED)

Real space charge density mapping by quantitative convergent beam electron diffraction (QCBED)

Determination of Debye–Waller factor and structure factors for Si by quantitative convergent-beam electron diffraction using off-axis multi-beam orientations

Debye-Waller (DW) factors and structure factors have been measured for Si using convergent-beam electron diffraction (CBED) experiments with a transmission electron microscope equipped with a field-emission gun and a post-column energy-filtering device. Si has been used here to evaluate the accuracy of multi-beam near-zone-axis orientations for the simultaneous refinement of DW factors and multiple structure factors. Strong dynamic interactions among different beams are obtained by tilting the crystal to specific four- or six-beam orientations near major zone axes, which provide sufficient sensitivity to determine accurate DW factors and structure factors. The DW factors of Si were measured using four-beam conditions near the [001] zone axis for temperatures ranging from 96 to 300 K. A comparison of the multi-beam near-zone-axis orientations with other CBED methods for DW and structure factor F(g) refinement is presented.

Differential convergent beam electron diffraction: Experiment and theory

The derivative of intensity with respect to scattering angle in an electron diffraction pattern is shown to be almost completely independent of whether the pattern has been energy filtered or not. This is attributed to the diffuse nature of inelastic scattering. A simple approach to quantitative convergent beam electron diffraction (QCBED), developed on this basis and tested on a corresponding pair of energy-filtered and unfiltered diffraction patterns from $\ensuremath{\alpha}{\text{-Al}}_{2}{\text{O}}_{3}$, produces a fit between experimental and theoretical differential CBED patterns that is well within experimental uncertainty. Structure factors measured from the unfiltered data are indistinguishable from those from the filtered data. Furthermore, those measurements made by angular-difference QCBED appear to be less influenced by parameter correlation and the inelastic components of CBED patterns than those made by conventional QCBED. The outcome is a new avenue for accurate charge density studies that does not depend on energy-filtering optics or acquisition of multiple patterns requiring translation of the specimen.

Differential quantitative analysis of background structure in energy-filtered convergent-beam electron diffraction patterns

Measurements of electronic structure in solids by quantitative convergent-beam electron diffraction (QCBED) will not reach their ultimate accuracy or precision until the contribution of the background to the reflections in energy-filtered CBED patterns is fully accounted for. Apart from the well known diffuse background that arises from thermal diffuse scattering of electrons, there is a component that has a much higher angular frequency. The present work reports experimental evidence that this component mimics the angular distribution of the elastically scattered electrons within each reflection. A differential approach to QCBED is suggested as a means of quantitatively accounting for the background in energy-filtered CBED data.

Local trimer orbital ordering in LiNiO 2 studied by quantitative convergent beam electron diffraction technique

A local trimer orbital ordering model of LiNiO 2 was studied by means of theoretical calculation and experimental measurement of electron structure factors. Based on the trimer model, the electron structure factors were calculated by using the scattering factor of non-spherical Ni 3+ ion. From these results, it is found that the effect of local orbital ordering on the electron structure factors of several subtle reflections, such as (202) and (107), is very large. The electron structure factors of these subtle reflections were measured by quantitative convergent beam electron diffraction method. The experimentally measured electron structure factor values of these reflections indicate that the trimer orbital ordering model is more close to the true structure of LiNiO 2.