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Full-Text Articles in Physical Sciences and Mathematics

Material Formulation And Process Optimization Towards Fabricating Robust 3d Printed Structures, Austin Riggins Dec 2023

Material Formulation And Process Optimization Towards Fabricating Robust 3d Printed Structures, Austin Riggins

Doctoral Dissertations

This dissertation focuses on understanding and addressing the fundamental physicochemical phenomena that lead to weak interfaces and structural warpage in material extrusion 3D printing. Polymeric feedstocks used for this manufacturing technique were manipulated through the incorporation of additives that alter the dynamics of the matrix during and after printing. In Chapter II, adhesion between layers of structures printed from PEEK was strengthened through a combination of low-molecular weight additive incorporation and post-printing thermal annealing. Chapter III reports a method for decreasing the irreversible thermal strain of structures printed from poly(lactic acid) by introducing nanographene and photoinitiator additives into the feedstock …


Dinitrogen Functionalization Using A Molybdenum Atom: Bridging The Gap Between Small And Coordination Complexes Via Quantum Mechanical Methods, Maria Virginia White Aug 2023

Dinitrogen Functionalization Using A Molybdenum Atom: Bridging The Gap Between Small And Coordination Complexes Via Quantum Mechanical Methods, Maria Virginia White

Doctoral Dissertations

Chemistry devotes a significant amount of its research to understanding small molecule activation from an electronic structure perspective to help with the investigation of the reaction pathways of catalytically active substances that can promote biomimetic catalysis. A large portion of the energy used annually in our planet is used for the artificial nitrogen fixation (Haber-Bosch process), which renders dinitrogen activation a subject of study. Molybdenum, a fourth row transitional metal, has demonstrated its effectiveness as an essential component of the dinitrogen reduction catalytic process. To better understand the multiple dinitrogen molybdenum binding modes, the work described herein combines wave function …


Theoretical Studies Of Adsorption And Reactivity At The Gas-Solid Interface, Carson J. Mize Aug 2023

Theoretical Studies Of Adsorption And Reactivity At The Gas-Solid Interface, Carson J. Mize

Doctoral Dissertations

Catalytic transformations of small molecules is of great interest for both laboratory and industrial practices. Two specific transformations are ethylene to ethylene oxide and combinations of azides and alkenes into aziridine molecules. Ethylene oxide is an epoxide used as a feed-stock for many bulk reactions and commercial products such as antifreeze and various sterilization techniques, while molecules with the aziridine functional group are used for many ring opening and closing techniques as well as in pharmaceuticals and other drug treatments. For production of ethylene oxide, the combination of oxygen adsorbed onto a silver crystal is the known catalysts for thus …


Chirality, Symmetry-Breaking, And Chemical Substitution In Multiferroics, Kiman Park Aug 2023

Chirality, Symmetry-Breaking, And Chemical Substitution In Multiferroics, Kiman Park

Doctoral Dissertations

Multiferroic materials attract significant attention due to their potential utility in a broad range of device applications. The inclusion of heavy metal centers in these materials enhances their magnetoelectric properties, yielding fascinating physical phenomena such as the Dzyaloshinskii–Moriya interaction, nonreciprocal directional dichroism, enhancement of spin-phonon coupling, and spin-orbit-entangled ground states. This dissertation provides a comprehensive survey of magnetoelectric multiferroics containing heavy metal centers and explores spectroscopic techniques under extreme conditions. A microscopic examination of phase transitions, symmetry-breaking, and structure-property relationships enhances the fundamental understanding of coupling mechanisms.

In A2Mo3O8 (A = Fe, Zn, Ni, and Mn), we use optical spectroscopy …


Light Matter Interactions: A Study Of Soft Materials Using Linear And Nonlinear Spectroscopy, Muhammad Redwan Hassan Dec 2022

Light Matter Interactions: A Study Of Soft Materials Using Linear And Nonlinear Spectroscopy, Muhammad Redwan Hassan

Doctoral Dissertations

The adoption of complex fluids for various industrial applications is becoming normal. Complex fluids offer tunability, wide range solubility, and chemical and thermal stability which are the factors that conventional polar and non-polar solvents often lack. However, fundamental studies of these fluid systems are still lacking which is limiting the appropriate use of these complex fluids in many applications. The goal of this dissertation was to study and characterize complex fluids for application in electrolytes for redox flow batteries. Chapter 3 and chapter 4 feature the study of microemulsions and deep eutectic solvents (DES) by fluorescence techniques. Fluorescence studies of …


Driving Piezochromism And Metallicity In Van Der Waals Materials Under Compression, Nathan Harms Aug 2022

Driving Piezochromism And Metallicity In Van Der Waals Materials Under Compression, Nathan Harms

Doctoral Dissertations

Complex chalcogenides provide an important platform to explore the interplay between structure, charge, and spin across pressure-induced phase transitions. Where much of the previous research has been focused on tuning these materials towards the single-layer limit, we instead explore the modification of bond lengths and bond angles under compression. In the first project we revealed piezochromism in MnPS3. We combined high pressure optical spectroscopy and first-principles calculations to analyze the dramatic color change (green → yellow → red → black) that takes place as the charge gap shifts across the visible and into the near infrared region, moving …


The Exploration Of Small Molecules, Lanthanide Complexes, And Catalysis Using Electronic Structure Theory, Dynamics, And Machine Learning, Gavin Mccarver May 2022

The Exploration Of Small Molecules, Lanthanide Complexes, And Catalysis Using Electronic Structure Theory, Dynamics, And Machine Learning, Gavin Mccarver

Doctoral Dissertations

With the ever increasing availability of computational resources, more challenging chemical systems can be studied. Among these challenges are the rotational and vibrational spectra of diatomic molecules within spectroscopic accuracy, the environmental perturbations induced on a rotating water molecule, the prediction of free binding energies of lanthanide complexes using machine learning, and the study of catalytic mechanisms through a theoretical framework. High levels of electronic structure theory were combined with a rigorous treatment of either the anharmonic vibrational wave functions to study diatomic molecules or the rotational wave functions to study H2O-pH2 interactions. The former was initially …


Experimental Physical Chemistry Applications For Material Science: The Neutron Vibrational Spectrum Of Biaxially-Oriented Pet And Hkust-1 As A Qcm-Based Ethylene Sensor, Zachary D. Stroupe May 2022

Experimental Physical Chemistry Applications For Material Science: The Neutron Vibrational Spectrum Of Biaxially-Oriented Pet And Hkust-1 As A Qcm-Based Ethylene Sensor, Zachary D. Stroupe

Doctoral Dissertations

This work is divided into two comprehensive subjects exploiting fundamental properties of physical chemistry to understand applied materials. The two subjects will be: the inelastic neutron scattering of thin polyethylene terephthalate (PET) films and the design and development of a quartz crystal microbalance-based ethylene detector. For the work involving the thin films, the inelastic neutron scattering (INS) was accomplished using the high flux of the VISION vibrational spectrometer at the Spallation Neutron Source yielding the highest quality data currently available. The torsional vibrational modes of biaxially-oriented PET (bPET) will be reported with the help of DFT calculations to aid in …


Total Internal Reflection: Applications In Nonlinear Microscopy And Fluorescence Anisotropy, Brandon Colon Dec 2021

Total Internal Reflection: Applications In Nonlinear Microscopy And Fluorescence Anisotropy, Brandon Colon

Doctoral Dissertations

As technology advances to harness new energies and to create new cures, the sophistication of analysis grows not only in depth but in efficiency. Total internal reflection (TIR) has been coupled to microscopy leveraging its unique optical phenomenon on a breadth of topics. In this dissertation, the work presented will show how TIR was applied in two different instrumental analyses to evaluate two unique and complex systems. The first project features TIR paired with the transient absorption microscopy (TAM), a nonlinear optical technique, to gauge solvent mixing and diffusion in microreactors. Microreactors gained acclaim for their ability to produce high …


Using Applied Field, Pressure, And Light To Control Magnetic States Of Materials, Amanda J. Clune Aug 2021

Using Applied Field, Pressure, And Light To Control Magnetic States Of Materials, Amanda J. Clune

Doctoral Dissertations

Due to their low energy scales, flexible architectures, and unique exchange pathways, molecule-based multiferroics host a number of unique properties and phase transitions under external stimuli. In this dissertation, we reveal the magnetic- and pressure-driven transitions in [(CH3)2NH2]Mn(HCOO)3 and (NH4)2[FeCl5(H2O)], present a detailed investigation of these materials away from standard equilibrium phases, and develop rich two- and three-dimensional phase diagrams.

The first platform for exploring phase transitions is [(CH3)2NH2]Mn(HCOO)3. This type-I multiferroic contains Mn centers linked by …


Characterization Techniques And Cation Exchange Membrane For Non-Aqueous Redox Flow Battery, Kun Lou Aug 2021

Characterization Techniques And Cation Exchange Membrane For Non-Aqueous Redox Flow Battery, Kun Lou

Doctoral Dissertations

The motivation of this work comes from one of the major problems of emerging non-aqueous flow battery (NAFB) that a separator or membrane which facilitates conductivity and blocks redox species crossover does not exist. Although many aspects of principles can be mirrored from mature fuel cell and aqueous flow battery, it is found that some well-defined membrane properties in aqueous systems such as swelling, transport and interactions are different in non-aqueous solvents to some extent. However, the approach of this work does follow the way perfluorosulfonate ion exchange membrane (PFSA) facilitated development of fuel cell and aqueous flow battery in …


Development Of Density-Functional Tight-Binding Methods For Chemical Energy Science, Quan Vuong Aug 2021

Development Of Density-Functional Tight-Binding Methods For Chemical Energy Science, Quan Vuong

Doctoral Dissertations

Density-functional tight-binding (DFTB) method is an approximation to the popular first-principles density functional theory (DFT) method. Recently, DFTB has gained considerable visibility due to its inexpensive computational requirements that confer it the capability of sustaining long-timescale reactive molecular dynamics (MD) simulations while providing an explicit description of electronic structure at all time steps. This capability allows the description of bond formation and breaking processes, as well as charge polarization and charge transfer phenomena, with accuracy and transferability beyond comparable classical reactive force fields. It has thus been employed successfully in the simulation of many complex chemical processes. However, its applications …


Physical Adsorption Of Linear Hydrocarbon Quadrupoles On Graphite And Mgo (100): Effects Of The Compatibility Of Surface And Molecular Symmetries, Andrew J. Pedersen Aug 2021

Physical Adsorption Of Linear Hydrocarbon Quadrupoles On Graphite And Mgo (100): Effects Of The Compatibility Of Surface And Molecular Symmetries, Andrew J. Pedersen

Doctoral Dissertations

The process of physical adsorption finds a practical role in wide-ranging fields from catalysis, to lubrication, and even optoelectronics. Furthermore, it provides a mechanism to probe the fundamental understanding of intermolecular forces and how symmetries can play a role in the behavior of a system. Linear quadrupoles preferentially adopt square-T configurations when confined in two dimensions. This would lead the system to adopt a four-fold symmetry in the molecular lattice.

Two archetypal surfaces often studied in physisorption research are MgO (100), which has a four-fold symmetry of alternating charges, and the basal plane of graphite, which has a six-fold symmetry …


Small Molecule Activation By Transition Metal Complexes: Studies With Quantum Mechanical And Machine Learning Methodologies, Justin Kyle Kirkland May 2021

Small Molecule Activation By Transition Metal Complexes: Studies With Quantum Mechanical And Machine Learning Methodologies, Justin Kyle Kirkland

Doctoral Dissertations

One of the largest areas of study in the fields of chemistry and engineering is that of activation of small molecules such as nitrogen, oxygen and methane. Herein we study the activation of such molecules by transition metal compounds using quantum mechanical methods in order to understand the complex chemistry behind these processes. By understanding these processes, we can design and propose novel catalytic species, and through the use of data-driven machine learning methods, we are able to accelerate materials discovery.


Unifying Chemistry And Machine Learning For The Study Of Noncovalent Interactions, Jacob A. Townsend Dec 2020

Unifying Chemistry And Machine Learning For The Study Of Noncovalent Interactions, Jacob A. Townsend

Doctoral Dissertations

Gas separations are in great demand for carbon emission reduction, natural gas purification, oxygen isolation, and much more. Many of these separations rely on cost-prohibitive methods such as cryogenic distillation or strong-binding solvents. As a result, novel materials are being developed to subvert the energetic expense of gas separation processes. These studies focus on improving the performance of alternative materials, including (but not limited to) metal-organic frameworks, covalent organic frameworks, dense polymeric membranes, porous polymers, and ionic liquids.

In this work, the atomistic effects of functional units are explored for gas separations processes using electronic structure theory and machine learning. …


Providing Insight To Enable The Design Of Tailored, Nano-Structured Polymeric Surfaces And Interfaces, Onome J. Agori-Iwe Aug 2020

Providing Insight To Enable The Design Of Tailored, Nano-Structured Polymeric Surfaces And Interfaces, Onome J. Agori-Iwe

Doctoral Dissertations

Methods are presented for modifying polymeric material surfaces using: 1) selective surface segregation in binary branched/linear polymer blends, and 2) surface functionalization with polymer brushes. Using neutron reflectivity, elastic recoil detection, and other complementary techniques, the aim was to identify structure-property relationships and provide fundamental insight into the time evolution and formation of surfaces and interfaces in these materials.

In blends of poly(styrene) (PS) HyperMacs and DendriMacs in a linear deuterated PS (d-PS) matrix, smaller hyperbranched additives (<1E6 g/mol) move slower than their linear analogues. Larger (>1E6 g/mol) and less flexible hyperbranched additives with smaller fractal dimensions move faster than their linear analogues, suggesting that they are less …


Multiscale Modeling Approach To Understand Active Sites In Non-Conventional Catalyst Layers For Fuel Cell Applications, Diana Constanza Orozco Gallo Dec 2017

Multiscale Modeling Approach To Understand Active Sites In Non-Conventional Catalyst Layers For Fuel Cell Applications, Diana Constanza Orozco Gallo

Doctoral Dissertations

Fuel cells development required stable, active and more abundant catalytic materials. Oxygen reduction reaction (ORR) is the key process to enhance better activity and reduce the fabrication costs. Pt-based has proven to be the best catalyst for ORR and greater efforts has been made in terms of reducing the Pt content in the electrodes, reduce electrode thickness and enhance better catalytic activities. To overcome many of the challenges present, the catalyst layer studies are the great importance in the fuel cell community. Understanding catalyst layer with new catalytic materials, and configurations requires the development of methodological approach to relate structure, …


Analysis Of Primary Stripper Foils At The Spallation Neutron Source By An Electron Beam Foil Test Stand, Eric Paul Barrowclough Dec 2017

Analysis Of Primary Stripper Foils At The Spallation Neutron Source By An Electron Beam Foil Test Stand, Eric Paul Barrowclough

Doctoral Dissertations

Diamond films are used at the Spallation Neutron Source (SNS) as the primary charge exchange foils (i.e., stripper foils) of the accelerated 1 GeV (Gigaelectron volts) hydride ions. The most common type of film used is a nanocrystalline diamond film, typically 17 mm x 45 mm (millimeter) with an aerial density of 350 μg/cm2 (microgram per square centimeter). The diamond film is deposited on a corrugated silicon substrate using plasma-assisted chemical vapor deposition. After the growth of the diamond film, 30 mm of the silicon substrate is etched away, leaving a freestanding diamond foil with a silicon handle that …


Electronic And Magnetic Materials Under External Stimuli, Kenneth Robert O'Neal Aug 2017

Electronic And Magnetic Materials Under External Stimuli, Kenneth Robert O'Neal

Doctoral Dissertations

The interaction between spin, charge, and lattice degrees of freedom leads to exotic and useful properties in multifunctional materials. This delicate balance of energy scales allows external stimuli such as temperature, magnetic field, or pressure to drive to novel phases. As a local probe technique, spectroscopy can provide insight into the microscopic mechanism of the phase transitions. In this dissertation I present spectroscopic studies of functional materials under extreme conditions.

Nanomaterials have attracted attention because nanoscale confinement affects various material properties and often reduces energy scales or suppress phase transitions. Combining Raman and infrared spectroscopies reveals that the breakdown mechanism …


Understanding Three-Body Interactions In Hexagonal Close Packed Solid He-4, Ashleigh Locke Barnes May 2017

Understanding Three-Body Interactions In Hexagonal Close Packed Solid He-4, Ashleigh Locke Barnes

Doctoral Dissertations

The ground state properties of hexagonal close packed (hcp) solid 4He [He-4] are dominated by large atomic zero point motions which make the primary contribution to the solid’s low-temperature Debye-Waller (DW) factors. Preliminary investigations have also suggested that three-body interactions can play an important role in this system, particularly at higher densities. However, due to their computational cost, these interactions are not generally incorporated into theoretical models of solid 4He [He-4]. In order to accurately treat both zero point motion and three-body interactions, we have developed a perturbative treatment in which the three-body energy is added as a …


Investigating The Properties Of Superfluid He-4 Through Density Functional Calculations, Matthew Francis Dutra May 2017

Investigating The Properties Of Superfluid He-4 Through Density Functional Calculations, Matthew Francis Dutra

Doctoral Dissertations

We present a study of isotopically pure He-4 systems evaluated using helium density functional theory (He-DFT) with the intent of better understanding their ground state structural and energetic properties, particularly within the scope of singularly-doped helium droplets. We self-consistently solve for the density profiles and chemical potentials for a wide range of pure helium droplet sizes (up to 9500 atoms) via an imaginary time propagation method, and fit the resultant energetic data to a power law formula to be able to extrapolate values for even larger droplets. Subsequent calculations on singularly-doped droplets within the same size range yield accurate binding …


Interaction Between Charge-Transfer States Studied By Magnetic Field Effects, Mingxing Li Aug 2016

Interaction Between Charge-Transfer States Studied By Magnetic Field Effects, Mingxing Li

Doctoral Dissertations

Organic semiconducting materials, consisting mostly of carbon and hydrogen atoms, provide remarkable promise for electronic applications due to their easy processing, chemical tenability, low costs and environmental-friendly characteristics. For realizing electronic applications such as light emitting diodes and photovoltaic cells, charge-transfer states act as an important intermediate state for recombination and dissociation. Interestingly, magnetic field effects on semiconducting materials have been realized based on the suppression of spin mixing in the charge-transfer states. Although lots of studies have been carried out on investigating the properties of charge-transfer states, little has been done to consider the interaction between them. This thesis …


Mining Uranium From Seawater: A Coordination Chemistry Approach, Nada Mehio May 2016

Mining Uranium From Seawater: A Coordination Chemistry Approach, Nada Mehio

Doctoral Dissertations

Poly(acrylamidoxime) fibers are the current state-of-the-art adsorbent for mining uranium from seawater. However, the amidoxime group is not perfectly selective towards the uranyl cation, in particular, competition with transition metal cations remains a major challenge. In order for subsequent generations of chelating polymer adsorbents to be improved, the coordination chemistry of amidoxime-uranyl and -transition metal cation complexes needs to be better understood. While the coordination mode of amidoxime-uranyl complexes has been established in the literature, a number of amidoxime-transition metal cation complex binding motifs can be observed on the Cambridge Structrural Database. Likewise, the formation constants, or log K values, …


Thermodynamics Of Short Chain Perfluoroalkanes Adsorbed On The Surfaces Of The Graphite Basal Plane And Mgo (100), Nathaniel Keenan Bass May 2016

Thermodynamics Of Short Chain Perfluoroalkanes Adsorbed On The Surfaces Of The Graphite Basal Plane And Mgo (100), Nathaniel Keenan Bass

Doctoral Dissertations

Molecular adsorption of short-chain linear perfluoroalkanes was studied by volumetric isotherm and by molecular dynamics simulation. Isotherms of perfluoroethane, perfluoropropane, and perfluorobutane gas were measured on clean surfaces of the graphite basal plane nanometer-scale cubic magnesium oxide (100). Each system was measured over a range of temperatures, and thermodynamic determinations of the entropies, enthalpies, and heats of adsorption were determined as a result. Potential phase transitions between the surface structures were identified, and the constant-coverage heats of adsorption for each system were determined. Comparisons to molecular dynamics simulations provided guidance in the assignment of phase diagrams, giving insights to the …


Understanding The Influence Of Non-Covalent Interactions And Nanoparticle Geometries In Carbon Based Polymer Nanocomposites, Bradley Carroll Miller Dec 2015

Understanding The Influence Of Non-Covalent Interactions And Nanoparticle Geometries In Carbon Based Polymer Nanocomposites, Bradley Carroll Miller

Doctoral Dissertations

Low-loading polymer nanocomposites (PNC) are an area of great interest in polymer science. As nanoparticles (NP) are typically expensive in comparison to matrix materials; the low loading regime makes the most efficient use of materials, and represents the optimum for realizing cost effective, high-performance PNCs. However, formulating effective low-loading composites is not without challenges. In addition to the typical requirement of good dispersion for efficient translation of NP properties to the bulk, low-loading composites can sometimes exhibit anomalous (non-classical) dynamics, and unpredictable properties. It is within this context that this thesis aims to examine the effects of NP geometry and …


An Investigation Of Inorganic Compound Scattering., Karl Jay Bernstein May 2015

An Investigation Of Inorganic Compound Scattering., Karl Jay Bernstein

Doctoral Dissertations

Raman and its associated forms of spectroscopy are powerful tools that have been under-utilized. Presented within are three inorganic compounds studied with some form of Raman spectroscopy: normal Raman, hyper-Raman (HR), surface-enhanced Raman spectroscopy (SERS), surface-enhanced hyper-Raman spectroscopy (SEHRS), or resonance Raman spectroscopy (RR).

The first study involves the investigation of phosphine binding with silver metal. Phosphines find wide use in synthetic circles yet have had little study into their method of binding, unlike similar compounds comprised of sulfur. In order to understand the binding of phosphines, several tertiary phosphines, secondary phosphines and secondary phosphine oxides are examined with SERS. …


Development And Demonstration Of Critical Components Of Aluminum Based Energy Storage Devices Using The Chloroaluminate Ionic Liquids, Mengqi Zhang May 2015

Development And Demonstration Of Critical Components Of Aluminum Based Energy Storage Devices Using The Chloroaluminate Ionic Liquids, Mengqi Zhang

Doctoral Dissertations

This dissertation considers the development of porous carbon materials as the substrates for Al deposition/dissolution in an Al based ionic liquid flow battery (ILFB) and demonstration of an Al based hybrid supercapacitor. The Aluminum chloride/ 1-ethyl-3-methylimidazolium chloride chloroaluminate ionic liquid is utilized as the electrolyte for these Al based energy storage devices. The ILFB has less capital cost than the all-vanadium redox flow battery because of the inexpensive AlCl3. The feasibility to equip a tank of solid aluminum chloride in an ILFB system aiming to improve energy density is investigated. A critical range of temperature data (50-130 celsius …


Computational Electrodynamics And Second Hyper-Raman Scattering, Philip Dwaine Simmons Jr. May 2015

Computational Electrodynamics And Second Hyper-Raman Scattering, Philip Dwaine Simmons Jr.

Doctoral Dissertations

Surface-enhanced second hyper-Raman spectroscopy is a type of nonlinear light scattering in which three photons are simultaneously annihilated to produce one photon whose color is slightly shifted from its third harmonic. This process, while incredibly weak, can be magnified by many orders of magnitude with the aid of plasmonic substrates. In this dissertation, three different studies are presented probing both the nature of plasmonics and nonlinear Raman scattering. In the first, nanoparticle aggregates were dosed with two isotopologues of Rhodamine 6G to determine single-molecule activity. Plasmon maps of the aggregates were then generated from electron energy-loss spectroscopy (EELS) and 3D …


Computational Studies For Optimization And Design Of Extracting Agents For Separation Of Lanthanides And Actinides, Deborah Andrea Penchoff Dec 2014

Computational Studies For Optimization And Design Of Extracting Agents For Separation Of Lanthanides And Actinides, Deborah Andrea Penchoff

Doctoral Dissertations

Rare earths and actinides are of great interest given their varied applications in energy conversion and storage, such as in catalysis and batteries, and for advanced technological applications related to optical and magnetic properties (including electronics and automotive), amongst others. Many of the rare earth elements are considered endangered species due to their unique properties which have no clear alternatives that will maintain performance for important applications. The optimal approach is to find readily available alternatives for critical materials to ensure a certain standard of living and quality of life for future generations, but it is very likely that reusing …


Methods For Quantitative Local Structure Analysis Of Crystalline Materials Employing High Performance Computing, Tara Marie Michels-Clark May 2014

Methods For Quantitative Local Structure Analysis Of Crystalline Materials Employing High Performance Computing, Tara Marie Michels-Clark

Doctoral Dissertations

A fundamental computational methodology was investigated to extract quantitative local structure information from single crystal diffuse scattering data. The principles of a highly efficient, parallelizable local structure analysis using massively parallel computing resources at Oak Ridge National Laboratory (ORNL) are demonstrated on an organic hydrocarbon compound containing stacking faults, Tris(bicyclo[2.1.1]hexeno)benzene. A probabilistic model of the stacking variations with a five layer interaction depth was developed. The final model structure motif statistics are verified using the steady state distribution of Markov matrix representing the four to five layer transitions. The computations revealed that highly parallelizable “structure-clones” could replace less computationally efficient …