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Branton Campbell in the lab

Branton J. Campbell

Professor

Department of Physics & Astronomy

Brigham Young University

Provo, UT 84602, USA

Tel: 801-422-5758, Fax: 801-422-0553

Email: branton_campbell[at]byu.edu

//physics.byu.edu/faculty/campbell/

Research Interests

I apply state-of-the-art x-ray and neutron scattering techniques to study local and long-range structures in a variety of complex solids, including fast-ion conductors, ferroelectric relaxors, high-temperature superconductors, and colossal magnetoresistive manganites, where nanoscale structural features influence macroscopic physical properties. This includes the development of symmetry-mode analysis as a tool for the determination, refinement and interpretation of distorted structures involving lattice strains, atomic displacements, magnetic moments and occupational orderings at both commensurate and incommensurate wavevectors.

Modulated Crystal Structures

Wave-like modulations with non-lattice periodicities accompany a variety of important physical phenomena (e.g. magnetism and superconductivity) and dramatically complicate any quantitative crystal-structure analysis. An exhaustive group-theoretical enumeration of the order parameters that can arise from 1D incommensurate modulations now make it much easier to characterize crystals that behave this way. Figure: Short-range modulation in La1.8Sr2.2Mn2O7.

The superstructure determination of displacive distortions via symmetry-mode analysis

Sean Kerman, Branton J. Campbell, Kiran K. Satyavarapu, and Harold T. Stokes (et al.)

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. Because most symmetry modes tend to be inactive, and only a relatively small number of mode amplitudes are dominant in producing the observed distortion, symmetry-mode analysis can greatly simplify the determination of a displacively distorted structure from powder diffraction data. This is an important capability when peak splittings are small, superlattice intensities are weak or systematic absences fail to distinguish between candidate symmetries. Here, the symmetry-mode basis is treated as a binary (on/off) parameter set that spans the space of all possible P1 symmetry distortions within the experimentally determined supercell. Using the average Rwp over repeated local minimizations from random starting points as a cost function for a given mode set, global search strategies are employed to identify the active modes of the distortion. This procedure automatically yields the amplitudes of the active modes and the associated atomic coordinates. The active modes are then used to detect the space-group symmetry of the distorted phase (i.e. the type and location of each of the parent symmetry elements that remain within the distorted supercell). Once a handful of active modes are identified, traditional refinement methods readily yield their amplitudes and the resulting atomic coordinates. A final symmetry-mode refinement is then performed in the correct space-group symmetry to improve the sensitivity to any secondary modes present.

Generation of (3+d)-dimensional superspace groups for describing the symmetry of modulated crystalline structures

Harold T. Stokes and Branton J. Campbell (et al.)

A complete table of (3 + 1)D, (3 + 2)D and (3 + 3)D superspace groups (SSGs) has been enumerated that corrects omissions and duplicate entries in previous tables of superspace groups and Bravais classes. The theoretical methods employed are not new, though the implementation is both novel and robust. The paper also describes conventions for assigning a unique one-line symbol for each group in the table. Finally, a new online data repository is introduced that delivers more complete information about each SSG than has been presented previously.

Quantitative Local Atomic Displacements from Huang Scattering Normalized by Thermal Diffuse Scattering

Branton J. Campbell

The three-dimensional (3-D) pattern of atomic displacements at the core of a small defect or defect cluster embedded in a bulk crystal is possible to measure in principle, but difficult to obtain in practice, especially if quantitative displacements are desired. Here, it is demonstrated that a least-squares fit to the single-crystal X-ray Huang-scattering distribution surrounding an intense Bragg peak is a practical means of obtaining quantitative displacements when thermal diffuse scattering is used as an internal intensity standard. After fitting a model based on local Kanzaki forces embedded within an elastic continuum, the use of finite-defect and point-defect methods of computing and interpreting the pattern of local displacements are compared and contrasted. To make the analysis general with regard to both crystal symmetry and defect symmetry, numerical Fourier transforms are employed rather than pursuing analytical expressions for the displacements.

Direct Access to the Order Parameter: Parameterized Symmetry Modes and Rigid Body Movements as a Function of Temperature

Branton J. Campbell (et al.)

The first order phase transition of CsFeO2 was investigated using synchrotron powder diffraction data as a function of temperature. Two alternative approaches were used to describe the deviation of the framework crystal structure relative to the high-symmetry parent structure: symmetry (a.k.a. distortion) modes and polyhedral-tilt parameters. In both cases, the relevant parameters were refined as a function of temperature using the method of parametric Rietveld refinement. We demonstrate a semi-automated and generally applicable method for the determination of spontaneous lattice strain variations, order parameters and power-law exponents as derived from Landau theory.

Gd₅Si_4-xBi_x Structures: Novel Slab Sequences Achieved by Turning off the Directionality of Nearest-Slab Interactions

Branton J. Campbell (et al.)

Substitution of Bi for Si leads to the complete cleavage of the interslab dimers T-T in the Gd5Si4-xBix system with x = 1.58 - 2.42 (T is a mixture of Si and Bi). Equivalence of the interslab T ... T contacts, achieved through combination of the electronic and geometrical parameters, removes directionality of nearest-slab interactions and allows for a novel slab stacking. Two new slab sequences, ABCDABCD (x = 2.07, I4(1)/acd space group) and ABADABAD (x = 2.42, P4(2)bc), have been discovered in Gd5Si4-xBix in addition to the known one, ABAB, that is dominant among the RE5X4 phases (RE is a rare-earth element, X is a p-element). The slab stacking for x = 2.07 and x = 2.42 is dictated by the second-nearest slab interactions which promote an origin shift either for the entire slab sequence as in ABCDABCD or for every other second-nearest slab pair as in ABADABAD. The loss of the directionality of the nearest-slab bonding allows for extensive stacking faults and leads to diffuse scattering.