Timothy C. Petersen

Hybrid approach for generating realistic amorphous carbon structure using metropolis and reverse Monte Carlo

An improved method for the modelling of carbon structures based on a hybrid reverse Monte Carlo (HRMC) method is presented. This algorithm incorporates an accurate environment dependent interaction potential (EDIP) in conjunction with the commonly used constraints derived from experimental data. In this work, we compare this new method with other modelling results for a small system of 2.9 g/cc amorphous carbon. We find that the new approach greatly improves the structural description, alleviating the common problem in standard reverse Monte Carlo method (RMC) of generating structures with a high proportion of unphysical small rings. The advantage of our method is that larger systems can now be modelled, allowing the incorporation of mesoscopic scale features.

Structural analysis of carbonaceous solids using an adapted reverse Monte Carlo algorithm

We present microstructural analysis of a disordered carbonaceous solid using simulations that employ a modified reverse Monte Carlo (RMC) algorithm. This algorithm incorporates an accurate environment dependent interaction potential (EDIP) in addition to commonly used constraints derived from experimental data, such as the sp2/sp3 bonding ratio. Our approach improves the microstructural description for carbon, alleviating the common problem in standard RMC of generating structures with large proportions of highly strained and physically unreasonable small rings. We also compare the electron diffraction data used in the modified RMC algorithm to our recent results from a neutron diffraction investigation of the carbonaceous material under consideration.

Atom probe trajectory mapping using experimental tip shape measurements.

Atom probe tomography is an accurate analytical and imaging technique which can reconstruct the complex structure and composition of a specimen in three dimensions. Despite providing locally high spatial resolution, atom probe tomography suffers from global distortions due to a complex projection function between the specimen and detector which is different for each experiment and can change during a single run. To aid characterization of this projection function, this work demonstrates a method for the reverse projection of ions from an arbitrary projection surface in 3D space back to an atom probe tomography specimen surface. Experimental data from transmission electron microscopy tilt tomography are combined with point cloud surface reconstruction algorithms and finite element modelling to generate a mapping back to the original tip surface in a physically and experimentally motivated manner. As a case study, aluminium tips are imaged using transmission electron microscopy before and after atom probe tomography, and the specimen profiles used as input in surface reconstruction methods. This reconstruction method is a general procedure that can be used to generate mappings between a selected surface and a known tip shape using numerical solutions to the electrostatic equation, with quantitative solutions to the projection problem readily achievable in tens of minutes on a contemporary workstation.

Influence of field evaporation on Radial Distribution Functions in Atom Probe Tomography

This paper examines the extraction of structural information in the form of Radial Distribution Functions (RDFs) using Atom Probe Tomography (APT) data. These functions are generated in a highly efficient manner, thus allowing for the analysis of large data sets typical of APT. Experimental RDF calculations were performed for crystalline aluminium and a Mg65Cu25Y10 bulk metallic glass. For the pure aluminium sample, significant pair distance information was extracted, the quality of which was found to vary throughout the data set. Through a novel analysis procedure, the measured total RDF was used to map the local pair distance quality about each reconstructed atom. Surprisingly, the RDF quality maps indicated improved pair distance quality around poles and zone lines. In the case of the metallic glass, however, significant pair correlations were not discernible within the data set, despite short-range ordering being observed using TEM diffraction. The lack of correlations is thought to be associated with a non-uniform ion desorption sequence, as observed in this study. This affects the uniform evaporation assumption that is implicit in current 3D APT reconstruction procedures.

Quantitative TEM-based phase retrieval of MgO nano-cubes using the transport of intensity equation.

Through focus series of images are collected from MgO nano-cube crystals in the transmission electron microscope (TEM). The experimental data is used to solve the transport of intensity equation (TIE) to retrieve phase maps, which portray the morphology of the cubes and are quantified by the mean inner potential V(0). Particular attention is given to the practical difficulties associated with TIE phase retrieval of non-conducting polyhedron particles.

The structure of disordered carbon solids studied using a hybrid reverse Monte Carlo algorithm

A hybrid reverse Monte Carlo (HRMC) algorithm, which incorporates both experimental and energy based constraints, is applied to investigate the microstructure of two disordered carbons of vastly different densities and bonding. We have developed a novel liquid quench procedure which in combination with the HRMC algorithm accurately describes the structure of these solids. Atomic networks generated by this approach are consistent with experimental and ab initio results and the method has been shown to overcome common difficulties associated with alternative approaches for modelling these complex systems. This procedure produces realistic large scale atomic structures which give a detailed picture of the structure of these solids.

Electron tomography using a geometric surface-tangent algorithm: Application to atom probe specimen morphology

To adapt electron tomography for the specific study of specimen morphology, a novel reconstruction algorithm is proposed which treats strong intensity gradients in images as arising from the projected edges of surfaces. Images portraying scattering interfaces arising from absorption, elastic, or Fresnel diffraction processes are used to identify edge maps that define the abscissa of projected surface tangents. Differential geometry is used to calculate the shape of these surfaces by considering smooth variations of measured tangent abscissa to infer local tangent intersections. The approach outlined here is not restricted to convex shapes and is designed for cases where morphology is more important than retrieval of the three-dimensional scattering density. The proposed algorithm is tested on simulated data, experimental benchmark specimens of MgO nanoparticles and is then applied to a nanosized atom probe tip, for which the approach here was specifically developed.

RDFTools: A software tool for quantifying short-range ordering in amorphous materials

A software package for computing radial distribution functions and other pair correlation functions from electron diffraction patterns of disordered solids is presented. The package, called RDFTools, is freely available via the internet and allows rapid in situ measurements of such quantities as interatomic nearest neighbor distances, average bond angles and coordination numbers. The software runs under DigitalMicrograph™ (Pleasanton, California, Gatan), a very widely used program in transmission electron microscopy. All implemented algorithms have been designed to compute diffraction integrals and data‐processing averages in a fast and efficient manner to enable quick processing of publication ready, quantitative pair distribution function information. In the development of RDFTools, significant attention was paid to provide a robust and intuitive user‐interface for deriving reliable semiquantitative information. For example, RDFTools enables accurate pair separation distances to be revealed upon immediate interrogation at the microscope; even for potentially thick specimens and/or regions of unknown elemental composition. Microsc. Res. Tech., 2011.

Macroscopic electrical field distribution and field-induced surface stresses of needle-shaped field emitters.

One major concern since the development of the field ion microscope is the mechanical strength of the specimens. The macroscopic shape of the imaging tip greatly influences field-induced stresses and there is merit in further study of this phenomenon from a classical perspective. Understanding the geometrical, as opposed to localized electronic, factors that affect the stress might improve the quality and success rate of atom probe experiments. This study uses macroscopic electrostatic principles and finite element modelling to investigate field-induced stresses in relation to the shape of the tip. Three two-dimensional idealized models are considered, namely hyperbolic, parabolic and sphere-on-orthogonal-cone; the shapes of which are compared to experimental tips prepared by electro-polishing. Three dimensional morphologies of both a nano-porous and single-crystal aluminium tip are measured using electron tomography to quantitatively test the assumption of cylindrical symmetry for electro-polished tips. The porous tip was prepared and studied to demonstrate a fragile specimen for which such finite element studies could determine potential mechanical failure, prior to any exhaustive atom probe investigation.

Short-range order in multicomponent materials.

The generalized multicomponent short-range order (GM-SRO) parameter has been adapted for the characterization of short-range order within the highly chemically and spatially resolved three-dimensional atomistic images provided by the microscopy technique of atom-probe tomography (APT). It is demonstrated that, despite the experimental limitations of APT, in many cases the GM-SRO results derived from APT data can provide a highly representative description of the atomic scale chemical arrangement in the original specimen. Further, based upon a target set of the GM-SRO parameters, measured from APT experiments, a Monte Carlo algorithm was utilized to simulate statistically equivalent atomistic systems which, unlike APT data, are complete and lattice based. The simulations replicate solute structures that are statistically consistent with other correlation measures such as solute cluster distributions, enable more quantitative characterization of nanostructural phenomena in the original specimen and, significantly, can be incorporated directly into other models and simulations.