Abstract

Normal subgroups can be thought of as the primary building blocks for decomposing mathematicalgroups into quotient groups. The properties of the resulting quotient groups are oftenused to determine properties of the group itself. This thesis considers normal subgroups of threedimensionalcrystallographic space groups that are themselves three-dimensional crystallographicspace groups; for convenience, we refer to such a subgroup as a csg-normal subgroup. We identifypractical restrictions on csg-normal subgroups that facilitate their tabulation. First, the point groupof an csg-normal subgroup must be a normal subgroup of the crystallographic point group of thespace group, which we refer to for convenience as a cpg-normal subgroup. For each of the cpgnormalsubgroups, which are all well known, we identify the abstract quotient group. Secondly,we identify necessary conditions on the sublattice basis of any csg-normal subgroup, and tabulatethe “normally supportive“ sublattices that meet these conditions, where some tables are symbolicforms that represent infinite families of sublattices. For a given space group, every csg-normalsubgroup must be an extension of such a normally supportive sublattice, though some normallysupportive sublattices may not actually support such extensions.

Christopher Yost (Senior Thesis, June 2018,
Advisor: Branton Campbell
)

Abstract

Crystalline solids consisting of three-dimensional networks of interconnected polyhedra or other rigid polyatomic units are ubiquitous amongst functional materials. In many cases, application-critical properties are sensitive to the rotations of individual rigid units. But the shared atoms that connect the rigid units together impose severe constraints on any rotational degrees of freedom, which must then be cooperative throughout the entire network. A purely algebraic approach to the identification of such cooperative rotational rigid-unit modes (RUMs) has been developed, wherein the constraints of interconnectedness are linearized in the limit of small rotation angles to form a homogeneous linear system of equations. This approach has been integrated into a software package named ISOTILT wherein a user can determine the allowed RUMs of a given network. We’ll explain details of software as well as underlying algorithms used to generate and solve the system of equations.

Eric Gibbs (Senior Thesis, August 2013,
Advisor: Branton Campbell
)

Abstract

Symmetry-mode analysis (SMA) has proven to be an effective tool in solving a nuclear crystal structure from powder diffraction data. The principles of SMA have also been applied to magnetic structures though previous work has been limited to the set of modes associated with a single k vector. Here we demonstrate the capabilities of fully-general SMA by solving both the nuclear and magnetic structures of La_0.5Ca_0.5MnO_3 from data collected at the POWGEN beam line at the Spallation Neutron Source at Oak Ridge Tennessee. The low-temperature antiferromagnetic structure of La_0.5Ca_0.5MnO_3 (LCMO) combines many k vectors and possesses a monoclinic 2√2×2√2×2 supercell relative to the cubic-perovskite parent. Starting with a P21/m-symmetry model for the nuclear structure, based on previous work, symmetry-mode inclusion/exclusion cycles added considerable detail to the final result. A list of candidate active magnetic modes were initially determined in P1 symmetry, which indicated magnetic space-group Pa21/m (also consistent with previous work), where 9 magnetic degrees of freedom are present. Constrained by this symmetry, subsequent simulated-annealing runs yielded several distinct structures with comparable fits resulting due to the pseudo-orthorhombic metric of LCMO. Physical considerations then guide our choice of the final structure.

Lauren Richey (Senior Thesis, June 2013,
Advisor: Branton Campbell
)

Abstract

Kay Erb (Senior Thesis, July 2012,
Advisor: Branton Campbell
)

Abstract

We analyze Pt3Cu to determine its crystal structure using three methods: x-ray diffraction by reflection from a poly-crystalline surface, x-ray diffraction by transmission through a powdered sample, and x-ray diffraction by transmission through a poly-crystalline foil. We designed and built a double angle sample spinner. This device allows the sample to spin through a wide range of orientations while exposed to x-rays so that an average of crystal orientations is observed. Using this device we obtained powder diffraction data which is suitable for quantitative analysis. We then compare our results to theoretical predictions of the structure, and find that the structure is an L13-like structure which has been predicted but not yet observed in nature.

Benjamin Frandsen (Honors Thesis, August 2011,
Advisor: Branton Campbell
)

Abstract

The remarkable piezoelectric and dielectric properties of relaxor ferroelectric material lead-zinc-niobate lead-titanate (PZN-PT), with chemical formula Pb(Zn1/3Nb2/3)O3 –PbTiO3, have attracted much attention within the last decade due to their potential for technological application. X-ray diffuse scattering measurements of single-crystal samples of PZN-PT with and without an applied electric field have been shown to be an effective means of investigating the origin of the material’s unique behavior. Although a variety of qualitative models have been proposed to explain the striking three-dimensional diffuse-scattering patterns and the changes observed in the presence of an external electric field, a quantitative and physically meaningful model has remained elusive. Using data collected from two synchrotron scattering experiments with single-crystal samples of PZN-PT, three-dimensional reconstructions of the diffuse-scattering distributions in reciprocal space have been created to allow quantitative evaluation of different models. We introduce a novel model based on the phenomena of thermal diffuse scattering and Huang defect scattering that correctly reproduces the observed diffuse scattering pattern in PZN-PT with no applied electric field. The implications of this model, which differs significantly from phenomenological models currently in the literature, are discussed. It is found that our model must be altered slightly in a subtle yet surprising way to accurately reproduce the changes observed when an electric field is applied. The physical meaning of this unexpected modification to our model is explored.

Abstract

For any crystal structure that can be viewed as a low-symmetry distortion of some higher-symmetry parent structure, one can represent the details of the distorted structure in terms of symmetry-adapted distortion modes of the parent structure rather than the traditional list of atomic xyz coordinates. Symmetry-mode analysis (SMA) often simplifies the refinement of a distorted structure because most symmetry modes tend to be inactive, while a relatively small number of mode amplitudes are dominant in producing the observed distortion. Here, we demonstrate that a symmetry-mode refinement against powder-diffraction data, when combined with a global-search algorithm, enables one to directly detect the space-group symmetry of the distorted phase, which includes both the space-group type and the locations of its symmetry elements relative to the parent lattice. This is an important capability when peak splittings are small, superlattice intensities are weak, or systematic absences fail to distinguish between candidate symmetries. Because the symmetry-detection process automatically reveals which of the modes belonging to the detected symmetry are active, the subsequent determination of the superstructure (i.e. the phasing of the superlattice peaks) is greatly simplified

Nichole Maughan (Senior Thesis, August 2011,
Advisor: Branton Campbell
)

Abstract

Zeolite analogs have structures that are topologically analogous to zeolite alumino-silicates but have different compositions in which some or all of the T-sites are replaced with other types of atoms, such as aluminum and phosphorus. Several zeolite analogs exhibit strong diffuse scattering patterns in addition to the expected Bragg scattering. Defects break the translational symmetry of a crystal, and thereby transfer scattered intensity out of the compact Bragg reflections and into a continuous but structured diffuse background, which appears as fuzzy streaks in CCD X-ray scattering images. Aluminophosphate-5, or AlPO-5, is a zeolite analog that is prone to topological defects as suggested by the single-crystal X-ray diffraction data. We are generating a number of candidate defect models, some involving statistical analysis, and calculating their corresponding diffuse scattering patterns in order to compare them against the experimental data of AlPO-5, a zeolite anaolog. Ultimately, we aim to find an atomistic-defect model that accurately explains the data.

Jared Dickson (Capstone, April 2008,
Advisor: Branton Campbell
)

Abstract

Open-framework compounds play a critical role in modern technology. Defects in these structures can change the properties of these compounds. Research was done to enable the detection of frame-work defect structures in zeolite mordenite using laboratory powder patterns. Both columnar and planar defects were examined. The DISCUS software package (Th. Proffen and R.B. Neder, J. Appl. Cryst. 32, 838, 1999) and Mathematica were used to generate large scale defect models and their resulting powder patterns. We attempted to quantify the relationship between defect concentration and 00L peak width and intensities.

Abstract

Due to a variety of potential scientific and industrial applications, a new phase of titanium dioxide (TiO2) would be very exciting. I have investigated a powder sample, which based on preliminary chemical and structural analyses, appeared to be such a new phase. Through subsequent high-resolution x-ray powder diffraction, energy dispersive x-ray spectroscopy, and electron diffraction measurements, the sample has been identified as a dual-phase mixture of catalogued Na2Ti3O7 and Na2Ti6O13.

Brett Guisti (Senior Thesis, April 2005,
Advisor: Branton Campbell
)

Abstract

n/a

Abstract

Large amounts of money are being applied to the construction of the next generation of spallation sources for neutron scattering. Neutron powder diffraction instruments will be an important element of these facilities and the incorporation of detectors into these instruments with a high neutron capture efficiency is desirable. A new detector design named the Flexible Embedded Fiber Detector (FEFD) has been developed and tested for this thesis. This detector is based on wavelength shifting fibers embedded in a zinc-sulfide lithium-fluoride based scintillator. The virtue of this design is that the detecting surface can be curved around the Debye-Scherrer rings. This virtue is lacking in other detector designs, making them more complex and poorer in performance than our FEFD detectors. Monte Carlo calculations were performed to determine the neutron capture efficiencies of our FEFD detectors, which proved to be much higher than those of the proposed powder diffractometer design for the Spallation Neutron Source and about equal with the efficiency for the ISIS powder diffractometer design. Four FEFD detector prototypes were then fabricated and tested at the Intense Pulsed Neutron Source at Argonne National Laboratory. We find that our measured and calculated relative efficiencies are in good agreement.

Bradley Underwood (Senior Thesis, April 2005,
Advisor: Branton Campbell
)

Abstract

n/a

Thomas McKnight (Senior Thesis, August 2001,
Advisor: Branton Campbell, Bart Czirr
)

Abstract