Quantitative Electron Diffraction Research Articles

Nanoscale Disorder inCaCu3Ti4O12: A New Route to the Enhanced Dielectric Response

Significant nanoscale disorder of Cu and Ca atomic substitution is observed in ${\mathrm{CaCu}}_{3}{\mathrm{Ti}}_{4}{\mathrm{O}}_{12}$, based on our integrated study using quantitative electron diffraction and extended x-ray absorption fine structure. Unambiguous identification of this previously omitted disorder is made possible by the unique sensitivity of these probes to valence-electron distribution and short-range order. Furthermore, first-principles-based theoretical analysis indicates that the Ca-site Cu atoms possess partially filled degenerate ${e}_{g}$ states, suggesting significant boost of dielectric response from additional low-energy electronic contributions. Our study points to a new route of enhancing dielectric response in transitional metal oxides by exploiting the strong electronic correlation beyond classical static pictures.

Unit cell refinement of nano-sized Ni4Ti3precipitates by quantitative electron diffraction

One of the major benefits of gathering diffraction data by using the electron beam in a TEM is that the probe diameter can be very small, down to a few nm if needed, and the beam might be positioned accurately in the area of interest. Furthermore by a using CCD camera or imaging plates the reflection intensities can be measured in an accurate way, needed for quantitative analyses. This asset is of great benefit when refinement needs to be done of nano-sized particles or areas for which traditional neutron or X-ray crystallography might not be of usage. An example of this are the Ni4Ti3 precipitates occurring in NiTi shape memory alloys; they only exist as a solid solution in the NiTi matrix and have sizes of a few nm up to a few microns. Moreover, these precipitates are a superstructure of the B2 NiTi matrix and the unit cell is rhombohedral having space-group R-3 resulting in 8 orientation variants. Up to now the atomic coordinates were only roughly estimated by Tadaki et al. [1] based on traditional electron diffraction techniques. In this work quantitative electron diffraction is used to refine the atomic coordinates of the Ni4Ti3 unit cell. Since the diffraction data obtained in this way is dynamical in nature (multiple scattering) this needs to be incorporated in the refinement procedure and in order to do so the MSLS (Multi Slice Least Squares) method, developed by J. Jansen [2], was used. Similar to what is used in other refinement methods, the R-factor is defined as a goodness of fit indicator and isminimized by the procedure. The diffraction data was obtained with a CM30 microscope with an accelerating voltage of 300kV and recordings made on a 1K CCD camera. Two zone orientations in reference to the rhombic unit cell were used, namely the and . For each zone several patterns were taken from areas with different thicknesses resulting in a final set of 651 reflections used in the refinement procedure.A good starting structure was needed, in order not to refine to a local minimum of R resulting in a wrong structure; for this reason a density functional calculation was used starting from the atom positions of the known structure. This structure was then further refined by the MSLS method and resulted in a final one with R-factor 8.2% which is an improvement compared to the R-factor of 12.5% obtained for the original structure. During refinement the rhombohedral unit cell was maintained, as well as the R-3 space-group symmetry and composition. An evaluation of the newly refined coordinates points out that the shrinking of the unit cell compared to the matrix is explained in a better way and that a DFT calculation of the structures total energy shows a decrease of 0.063eV/atom compared to the original one.

Quantitative determination of the crystal structure of Ni 4Ti 3 precipitates

The structure of Ni 4Ti 3, which occurs as a precipitate in Ni-rich NiTi, has already been determined of having the R-3 space group. This was done using basic electron diffraction by Tadaki et al. also providing an approximation of the atomic coordinates. In the present work a least squares refinement method based on quantitative electron diffraction is used to optimise the structure of the Ni 4Ti 3 unit cell. This method, in combination with Density Functional Theory (DFT) calculations, results in a structure for which the composition and R-3 space group of the Tadaki model is maintained but the atom positions are clearly shuffled. The R-factor (similar to the one used in X-ray diffraction refinement) drops from 12.5% for the original Tadaki structure to 8.2% for the newly refined one, and moreover the change of atomic coordinates explains in a better manner the shrinking of the Ni 4Ti 3 unit cell in reference to the NiTi matrix.

Nanostructure of atmospheric soot particles

We studied the structure of atmospheric soot using electron-diffraction-based pair distribution function (PDF) analysis, and compared it with other carbon structures. Two reference materials were used: hydrogen-free amorphous carbon and a kerogen sample with a H/C ratio of 0.61. First-neighbour atomic distances in atmospheric soot are as small as 0.134 nm, much shorter than in graphite (0.142 nm) or in amorphous carbon (0.141–143 nm), but larger than the typical value (0.131–0.132 nm) for kerogen. These results suggest that a high molar ratio of hydrogen is present in soot in small-sized aromatic clusters. Such aromatic components can strongly influence the optical properties of soot particles. We found that the quantitative electron diffraction method is an independent and efficient alternative to the commonly used spectroscopic methods for the analysis of the atomic structure of individual soot particles.

Nanoscale stress analysis of strained-Si metal-oxide-semiconductor field-effect transistors by quantitative electron diffraction contrast imaging

A technique that uses quantitative electron diffraction contrast imaging (EDCI) to measure stress with a spatial resolution on the order of 10nm and sensitivity on the order of tens of MPa is applied to strained-Si metal-oxide-semiconductor field-effect transistors. This is accomplished by utilizing transmission electron microscopy and focused ion beam micromachining in conjunction with finite element modeling and electron diffraction contrast simulations. Our techniques enable quantitative interpretation of EDCI intensity, as a function of the magnitude of the local stress field. Analysis shows that the stress distribution in the strained-Si channel is very sensitive to the stress state of the surrounding materials, especially TiSi2, which can modify the stress distribution in the channel by well over 100MPa.

Refinement of the crystal structural parameters of La2/3Ca1/3MnO3using quantitative convergent-beam electron diffraction

Crystal structural parameters (seven positional parameters and four isotropic Debye-Waller factors) of La(2/3)Ca(1/3)MnO(3) have been refined using the quantitative convergent-beam electron diffraction (QCBED) method. Using intensity information of many higher-order Laue-zone reflections simultaneously is essential to refine structural parameters accurately. The effective global optimization algorithm was used to avoid the problems of input values and local minima. The fittings of the differential coefficients of one-dimensional experimental intensities and theoretical ones calculated by the dynamical diffraction theory were carried out with the normalized Euclidean distance criterion. Thus, all of these improve the accuracy and reliability of the analysis. The calculated results with the refined parameters agree with the experiments. The refined parameters also agree with the Rietveld refinement results of neutron diffraction.

Quantitative Electron Diffraction Data of Amorphous Materials

A method has been developed to obtain quantitative electron diffraction data up to a value of Q = 20 Å−1 of the modulus of the scattering vector. The experiments were performed on a commercially available transmission electron microscope equipped with a so-called omega energy filter. An analytical multiple scattering correction was applied. The electron diffraction results obtained with amorphous germanium were compared with X-ray and neutron diffraction data and showed good agreement. For an amorphous Ni63Nb37 sample it was shown that it is possible to estimate the multiple scattering intensity without exact knowledge of the sample thickness. This technique was applied to derive the structure factor for electron diffraction of two precursor-derived amorphous Si-C-N ceramics (a-Si24C43N33 and a-Si40C24N36). The results are consistent with corresponding X-ray diffraction data and with an existing structural model for such ceramics.

A study of charge density in copper

Quantitative convergent-beam electron diffraction (QCBED) experiments allow absolute scale measurements of low-order structure factors with very high accuracy. In this paper, eight low-order structure factors for copper measured by QCBED have been combined with the higher-order gamma-ray structure factors in order to obtain a larger highly accurate experimental data set. The gamma-ray values were relativistically corrected and rescaled. The new data set was then used for studying the charge distribution in copper. Charge deformation maps have been produced and both a maximum-entropy and a multipole analysis have been applied to the data. The result is compared to density functional theory calculations. An almost spherical charge depletion is found around the atomic sites showing typical metal bonding in copper.

Quantitative electron diffraction in studies of electron distribution in crystals

Quantitative electron diffraction in studies of electron distribution in crystals

Extinction-free electron diffraction refinement of bonding in SrTiO3.

Accurate low-order Fourier coefficients of the crystal potential of SrTiO(3) are measured by quantitative convergent-beam electron diffraction. The accuracy in the corresponding derived X-ray structure factors is about 0.1% for the strong low-order reflections (sin theta/lambda < 0.3 A(-1)). This accuracy is better than for conventional X-ray diffraction and equivalent to the accuracy of the X-ray Pendellosung method. Combination of these structure factors with high-order X-ray diffraction measurements allows accurate bonding information to be obtained from a multipole model fitted to the experimental data. It is shown that Ti-O has a covalent component and that the Sr-O bond is mainly ionic. The role of Ti 3d electrons in Ti-O bonding is also discussed.

Quantitative electron diffraction structure analysis

Quantitative electron diffraction structure analysis

Quantitative electron diffraction structure analysis

Quantitative electron diffraction structure analysis

Electron density and implication for bonding in Cu

We report highly accurate measurements for the low-order Fourier components of the crystal potential in copper. These were obtained by transmission electron diffraction using a small probe and multiple scattering analysis. They were used to refine the $\text{Cu}\phantom{\rule{0.3em}{0ex}}3d$ radial wave function. An accurate charge-deformation map and a $3d$ orbital radial wave function were obtained by using a multipole refinement of the structure factors obtained from combined quantitative electron diffraction and $\ensuremath{\gamma}$-ray diffraction measurements. The results show a large change in the $3d$ orbital radial function from $d$-band formation and $d\ensuremath{-}s$ band crossing ($d\ensuremath{-}s$ hybridization). Band theory calculations are in excellent agreement with the measurements and show that the charge deformation in Ag is very similar to that in Cu. Our findings are in general agreement with the monovalent description of these metals.

The precession technique in electron diffraction and its application to structure determination of nano-size precipitates in alloys.

Crystal structure of nano-scale precipitates in age-hardening aluminum alloys is a challenge to crystallography. The utility of selected area electron diffraction intensities from embedded precipitates is limited by double scattering via matrix reflections. This effect can be signally reduced by the precession technique, which we have used to collect extensive intensity data from the semicoherent, metastable eta-precipitate in the Al-Zn-Mg alloy system. A structure model in the space group P-62c is proposed from high-resolution microscopy and electron diffraction intensities. The advantages of using the precession technique for quantitative electron diffraction is discussed.

Interfacial activity and leaching patterns of Leptospirillum ferrooxidans on pyrite

The leaching ability of Leptospirillum ferrooxidans goes beyond the mere oxidation of Fe 2+ to Fe 3+. Addition of these bacteria to pyrite triggers interfacial phenomena that lead to bacterial attachment and local forms of corrosion (surface pitting). As the leaching process proceeds, bacterial cells undergo changes, characterized by the release of extracellular polymeric substances (EPS) and the uptake and storage of electro-dense nanoparticles. The latter are embedded in an exopolymeric capsule, which coats the bacterial surface leading to distinctive biomineralized assemblages. High-resolution scanning electron microscopy (SEM) and transmission electron microscopy (TEM) analyses, quantitative energy-dispersive X-ray measurements and electron diffraction established that the embedded electron-dense nanoparticles comprise pyrite with a well-defined stoichiometry. Addition of Fe 3+ alone did not induce any form of local corrosion on pyrite, which indicates that the reactions taking place between the attached bacteria and the underlying pyrite surface are responsible for the leaching patterns observed in this study. The observed corrosion process resembles that of ‘electrochemical machining’, because it uses a corrosion promoter, namely the locally concentrated Fe 3+ in the biofilm environment, formed by the attached cells.

A unique determination of boundary condition in quantitative electron diffraction: Application to accurate measurements of mean inner potentials

We combine off-axis electron holography and electron shadow imaging to accurately determine the specimen thickness and the incident electron beam direction over the illuminated area of a crystal. We, furthermore, quantify the variations in diffraction intensity with position over the same area. This unique solution to the experimental boundary condition problem enables us to make precise measurements of mean inner electrostatic potentials and structure factors that are sensitive to the bonding characteristics of materials. In this paper, we present the results of mean-inner potential determination from silicon and the newly discovered magnesiumdiboride superconductor.

A Combination Method of Charge Density Measurement in Hard Materials Using Accurate, Quantitative Electron and X-ray Diffraction: The α-Al2O3 Case

Current X-ray diffraction techniques intended for "ideally imperfect" specimens provide structure factors only on a relative scale and ever-present multiple scattering in strong low-angle Bragg reflections is difficult to correct. Multiple scattering is implicit in the quantitative convergent beam electron diffraction (QCBED) method, which provides absolutely scaled structure factors. Conventional single crystal X-ray diffraction has proved adequate in softer materials where crystal perfection is limited. In hard materials, the highly perfect nature of the crystals is often a difficulty, due to the inadequacy of the conventional corrections for multiple scattering (extinction corrections). The present study on alpha-Al2O3 exploits the complementarity of synchrotron X-ray measurements for weak and medium intensities and QCBED measurement of the strong low-angle reflections. Two-dimensional near zone axis QCBED data from different crystals at various accelerating voltages, thicknesses, and orientations have been matched using Bloch-wave and multislice methods. The reproducibility of QCBED data is better than 0.5%. The low-angle strong QCBED structure factors were combined with middle and high-angle extinction-free data from synchrotron X-ray diffraction measurements. Static deformation charge density maps for alpha-Al2O3 have been calculated from a multipole expansion model refined using the combined QCBED and X-ray data.

Structural study of new hydrocarbon nano-crystals by energy-filtered electron diffraction

A new brittle hydrocarbon has been successfully synthesized in polycrystalline form, and its crystal structure solved by quantitative electron diffraction. By 3D tilting of the nano-crystals, the lattice type and unit cell parameters were determined. (Triclinic, a=6.03 Å, b=6.23 Å, c=13.86 Å, α=87.26°, β=106.69°, and γ=119.01°.) Spot diffraction patterns were obtained at −165°C using the Koehler selected-area mode on a LEO 912 TEM fitted with an omega in-column elastic energy filter. The direct methods algorithm was then applied to merged intensities and a trial structure obtained assuming single scattering. This was further refined to obtain good agreement with a small residual of about 10% using multiple scattering calculations. A diagram of the proposed structure is given.

Structure and bonding in alpha-copper phthalocyanine by electron diffraction.

Energy-filtered quantitative electron diffraction at liquid nitrogen temperature has been used to examine the atomic structure and bonding of metastable alpha-Cu phthalocyanine crystals. Three theoretical methods (kinematic, kinematic with excitation errors and Bloch wave) were employed for the intensity calculations. The Bloch-wave method was found to account for dynamical effects by greatly reducing the residual factor between experimental and simulated results. A new method for calculating electron scattering factors for partially charged ions is proposed and the sensitivity of electron diffraction to charge transfer is discussed. The atomic charge states were analyzed for alpha-Cu phthalocyanine using a charge cloud model in which the Gaussian bond charge is positioned along the bonds. Spot patterns were collected in the Kohler mode at two beam energies to reduce error. Using the best-fitting model, a deformation charge-density map is produced and compared to the neutral-atom model. From this, the main features of atomic charge transfer in the alpha-Cu phthalocyanine structure can be seen in the (010) plane.

Combined HREM and Quantitative Electron Diffraction Characterization of Individual Pd2Si Nanostructures on Si(111) Surfaces

Combined HREM and Quantitative Electron Diffraction Characterization of Individual Pd2Si Nanostructures on Si(111) Surfaces