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At least 109 records · Page 6

Multi-Scale Modeling of Cross-Linked Nanotube Materials

The effect of cross-linking single-walled carbon nanotubes on the Young's modulus of a nanotube-reinforced composite is modeled with a multi-scale method. The Young's modulus is predicted as a function of nanotube volume fraction and cross-link density. In this method, the constitutive properties of molecular representative volume elements are determined using molecular dynamics simulation and equivalent-continuum modeling. The Young's modulus is subsequently calculated for cross-linked nanotubes in a matrix which consists of the unreacted cross-linking agent. Two different cross-linking agents are used in this study, one that is short and rigid (Molecule A), and one that is long and flexible (Molecule B). Direct comparisons between the predicted elastic constants are made for the models in which the nanotubes are either covalently bonded or not chemically bonded to the cross-linking agent. At a nanotube volume fraction of 10%, the Young's modulus of Material A is not affected by nanotube crosslinking, while the Young's modulus of Material B is reduced by 64% when the nanotubes are cross-linked relative to the non-cross-linked material with the same matrix.

Frankland, S. J. V.↗

Surface Functionalization of Black Phosphorus with Nitrenes: Identification of P=N Bonds Using Isotopic Labeling

Abstract: Surface functionalization of two-dimensional crystals is a key path to tuning their intrinsic physical and chemical properties. However, synthetic protocols and experimental strategies to directly probe chemical bonding in modified surfaces are scarce. Introduced here is a mild, surface-specific protocol for the surface functionalization of few-layer black phosphorus nanosheets using a family of photolytically generated nitrenes (RN) from the corresponding azides. By embedding spectroscopic tags in the organic backbone, a multitude of characterization techniques are employed to investigate in detail the chemical structure of the modified nanosheets, including vibrational (infrared, Raman), Xray (emission, photoelectron), CPMAS NMR, and UV-vis spectroscopy. To directly probe the functional groups introduced on the surface, R fragments were selected such that in conjunction with vibrational spectroscopy, 15N-labeling experiments, and DFT methods, diagnostic P=N vibrational modes indicative of iminophosphorane units on the nanosheet surface could be conclusively identified.

Walz, Kendall↗

Final Technical Report on Investigation of Short-range Ordering in Transition Metal Compounds by Diffuse Scattering

Future energy needs and sustainability require new materials with novel properties for such applications as energy production, storage and transport and microelectronics. Quantum materials with several competing interactions at the electronic level offer tremendous opportunity to discover, design and tune properties for such applications. Although it has been recognized that small deviations in atomic positions, driven by the competing electronic interactions, in crystalline materials can have significant impact on properties, it remains a challenge to accurately characterize such deviations (short-range order) due to the lack of advanced instruments and analysis tools to characterize them. This project used the powerful neutron and x-ray scattering instruments recently developed at the DOE user facilities to address this challenge. New methods and efficient analysis tools were employed to uncover the hidden ordering that is behind the unique properties of transition metal compounds. One example of hidden order revealed by this project comes from vanadium (IV) oxide (VO 2 ) and related compounds. The project found that the chemical bonds in VO 2 compete against each other, unlike most crystalline compounds where the chemical bonds cooperate to yield the ordered structure. This helps explain why different measurements yielded different, competing pictures about the nature of VO 2 , which has led to disagreement about where its physical properties come from. Another example from this project of hidden ordering comes from a class of compounds known as condensed Chevrel phases, which are superconducting compounds that are generally believed to be non-magnetic. The neutron scattering methods used in this project revealed evidence of magnetism, which usually does not coexist with superconductivity. In this case, magnetism is believed to be one part of a special type of electronic behavior that can occur in compounds that have one-dimensional bonding character.

36 MATERIALS SCIENCE↗

The Curious Case of Pu + : Insight on 5f Orbital Activity from Inductively Coupled Plasma Tandem Mass Spectrometry (ICP-MS/MS) Reactions

A comprehensive understanding of when and how 5f orbitals participate in complex chemical bonding is important for a variety of applications. The actinides are unique in that they possess 5f orbitals and can access high oxidation states, which make them attractive for use in catalysis. Fundamental studies of actinide–ligand interactions offer a mechanism to examine the activation of the 5f orbitals so that the selectivity of 5f orbitals can be assessed. A previous study examined the reaction of Pu + + CO 2 and determined that the reaction efficiency is restricted by a barrier, namely, promotion from the Pu + ground-state configuration, 5f 6 7s, to a reactive-state configuration, 5f 5 6d 2 . Here, the present study illustrates the benefit of activation of Pu’s 5f orbitals when studying the reaction of Pu + + NO. In this reaction, PuO + forms in an exothermic, barrierless process. The 5f orbitals can and do participate in forming a linear intermediate, [N-Pu-O] + , and this drives the exothermic reaction. Understanding the conditions under which 5f orbitals are active in chemical bonding is the key to exploiting the actinides’ selective catalytic capabilities.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Chemo–mechanical properties of carbon fiber reinforced geopolymer interphase

Geopolymers, as a potentially environmentally friendly alternative to Portland cement, are increasingly attracting attention in the construction industry. Various methods have been applied for customizing the properties of geopolymers and improving their commercial viability. One of the promising methods for refining the properties of geopolymers such as their toughness is the use of short fibers. The effectiveness of a high-strength short fiber in the geopolymer matrix is largely dependent on the interfacial bonding between the fiber and its surrounding matrix. While the importance of this interfacial chemistry is highlighted in the literature, the characteristics of this bonding structure have not been fully understood. In this paper, we aim to investigate the bonding mechanism between the carbon fiber and metakaolin-based geopolymer matrix. For the first time, the existence and nature of the chemical bonding at the interfacial region (interphase) between carbon fiber and geopolymer matrix has been revealed. X-ray pair distribution function computed tomography (PDF-CT), field emission-scanning electron microscopy imaging, and nanoindentation techniques are employed to discern the chemo-mechanical properties of the interphase. PDF-CT results show the emergence of a new atom-atom correlation at the interfacial region (around 1.82 angstrom). This correlation is a characteristic of interfacial bonding between the fiber and its surrounding matrix, where the existence of chemical linkages (potentially Al-V-O-C) between fibers and the matrix contributes to the adhesion between the two constituents making up the composite. Due to such chemical bonding, the nanomechanical properties of the interfacial region fall between that of the carbon fiber and geopolymer. The combination of advanced techniques is proved useful for enhancing our understanding of the interfacial chemistry between fibers and the binding matrix. This level of knowledge facilitates the engineering of composite systems through the manipulation of their nanostructure.

36 MATERIALS SCIENCE↗

Chemical and bonding analysis of liquids using liquid cell electron microscopy

Liquid cell transmission electron microscopy (TEM) has become an essential tool for studying the structure and properties of both hard and soft condensed-matter samples, as well as liquids themselves. Liquid cell sample holders, often consisting of two thin window layers separating the liquid sample from the high vacuum of the microscope column, have been designed to control in situ conditions, including temperature, voltage/current, or flow through the window region. While high-resolution and time-resolved TEM imaging probes the structure, shape, and dynamics of liquid cell samples, information about the chemical composition and spatially resolved bonding is often difficult to obtain due to the liquid thickness, the window layers, the holder configuration, or beam-induced radiolysis. Here, we review different approaches to quantitative liquid cell electron microscopy, including recent developments to perform energy-dispersive x-ray and electron energy-loss spectroscopy experiments on samples in a liquid environment or the liquid itself. We also cover graphene liquid cells and other ultrathin window layer holders.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Pressure modulated charge transfer and phonon interactions drive phase transitions in uranium–aluminum laves phases

Lanthanide AB 2 intermetallic compounds known as Laves phases have itinerant 3d and localized 4f electrons, which lead to interesting physical properties such as magnetic anisotropy and high Curie temperatures. Actinide Laves phases can display physical properties that are similarly intriguing. However, at reduced A–A spacing the C14 and C15 polytypes may exhibit larger wavefunction overlap for their 5f electron states and distinct characteristics for phases with more delocalized chemical bonding. The C36 polytype, on the other hand, is extraordinarily rare (<5% of known Laves phases). UAl 2 is the only known actinide Laves phase to show a pressure-controllable C15 → C36 transition. Here, we apply first principles calculations to determine the origin of the C15 → C36 phase transition and reveal the differences between the corresponding properties of each phase. Pressure increases lead to bond compression–induced electron transfer from Al to U, which drives dynamic instability in the C15 phonon modes because of the uniform U–U bonding environment. Further, the opposite phenomena is observed in C36: varied U–U bonding environments are vibronically more stable after charge transfer. We find that the interplay between charge transfer, chemical bonding, and phononic stability are central to predicting phase transitions and corresponding changes in physical properties for both C15 and C36 UAl 2 .

36 MATERIALS SCIENCE↗

Chemical order-disorder nanodomains in Fe 3 Pt bulk alloy

Chemical ordering is a common phenomenon and highly correlated with the properties of solid materials. By means of the redistribution of atoms and chemical bonds, it invokes an effective lattice adjustment and tailors corresponding physical properties. To date, however, directly probing the 3D interfacial interactions of chemical ordering remains a big challenge. In this work, we deciphered the interlaced distribution of nanosized domains with chemical order/disorder in Fe 3 Pt bulk alloy. HAADF-STEM images evidence the existence of such nanodomains. The reverse Monte Carlo method with the X-ray pair distribution function data reveal the 3D distribution of local structures and the tensile effect in the disordered domains at the single-atomic level. The chemical bonding around the domain boundary changes the bonding feature in the disordered side and reduces the local magnetic moment of Fe atoms. This results in a suppressed negative thermal expansion and extended temperature range in Fe 3 Pt bulk alloy with nanodomains. Our study demonstrates a local revelation for the chemical order/disorder nanodomains in bulk alloy. The understanding gained from atomic short-range interactions within the domain boundaries provides useful insights with regard to designing new functional compounds.

36 MATERIALS SCIENCE↗

Direct observation of elemental fluctuation and oxygen octahedral distortion-dependent charge distribution in high entropy oxides

The enhanced compositional flexibility to incorporate multiple-principal cations in high entropy oxides (HEOs) offers the opportunity to expand boundaries for accessible compositions and unconventional properties in oxides. Attractive functionalities have been reported in some bulk HEOs, which are attributed to the long-range compositional homogeneity, lattice distortion, and local chemical bonding characteristics in materials. However, the intricate details of local composition fluctuation, metal-oxygen bond distortion and covalency are difficult to visualize experimentally, especially on the atomic scale. Here, we study the atomic structure-chemical bonding-property correlations in a series of perovskite-HEOs utilizing the recently developed four-dimensional scanning transmission electron microscopy techniques which enables to determine the structure, chemical bonding, electric field, and charge density on the atomic scale. The existence of compositional fluctuations along with significant composition-dependent distortion of metal-oxygen bonds is observed. Consequently, distinct variations of metal-oxygen bonding covalency are shown by the real-space charge-density distribution maps with sub-ångström resolution. The observed atomic features not only provide a realistic picture of the local physico-chemistry of chemically complex HEOs but can also be directly correlated to their distinctive magneto-electronic properties.

36 MATERIALS SCIENCE↗

When Is a Bond Broken? The Polarizability Perspective.

Abstract The question of when a chemical bond can be said to be broken is of fundamental chemical interest but has not been widely studied. Herein we propose that the maxima of static polarizability along bond dissociation coordinates naturally define cutoff points for bond rupture, as they represent the onset of localization of shared electron density into constituent fragments. Examples of computed polarizability maxima over the course of bond cleavage in main‐group and transition metal compounds are provided, across covalent, dative and charge‐shift bonds. The behavior along reaction paths is also considered. Overall, the static polarizability is found to be a sensitive reporter of electronic structure reorganization associated with bond stretching, and thus can serve as a metric for describing bond cleavage (or diagnose the absence of a chemical bond).

Hait, Diptarka↗

When Is a Bond Broken? The Polarizability Perspective.

Abstract The question of when a chemical bond can be said to be broken is of fundamental chemical interest but has not been widely studied. Herein we propose that the maxima of static polarizability along bond dissociation coordinates naturally define cutoff points for bond rupture, as they represent the onset of localization of shared electron density into constituent fragments. Examples of computed polarizability maxima over the course of bond cleavage in main‐group and transition metal compounds are provided, across covalent, dative and charge‐shift bonds. The behavior along reaction paths is also considered. Overall, the static polarizability is found to be a sensitive reporter of electronic structure reorganization associated with bond stretching, and thus can serve as a metric for describing bond cleavage (or diagnose the absence of a chemical bond).

Hait, Diptarka↗

Nucleation, Growth, Annealing, and Coagulation of Refractory Oxides and Metals: Recent Experimental Progress and Applications to Astrophysical Systems

Starting with cooling, refractory vapors diluted in significant quantities of H and He there are four processes that most natural systems will undergo: nucleation, growth, annealing, and coagulation. Nucleation is the processes by which the first stable refractory nuclei form in the vapor. These are the seeds onto which the remaining vapors will condense during the growth stage. Solids of any composition will try to arrange themselves into the least energetic configuration, provided that there is sufficient energy available to support such processes as diffusion and the breaking of chemical bonds. There is a significant activation energy associated with the annealing process in refractory solids due to the relatively high energy of the chemical bonds in solids. The grains formed in most cosmochemical systems are extremely small and often tightly coupled to the gas. Because of their small physical cross sections coagulation may be a very slow process unless there is another driving force involved in addition to normal Brownian motion. In what follows we will briefly cover each of these four stages for refractory oxide and metal grains, although in inverse order.

Nuth, J. A.↗

Strong Structural and Electronic Coupling in Metavalent PbS Moiré Superlattices

Moiré superlattices are twisted bilayer materials in which the tunable interlayer quantum confinement offers access to new physics and novel device functionalities. Previously, moiré superlattices were built exclusively using materials with weak van der Waals interactions, and synthesizing moiré superlattices with strong interlayer chemical bonding was considered to be impractical. Here, in this study, using lead sulfide (PbS) as an example, we report a strategy for synthesizing moiré superlattices coupled by strong chemical bonding. We use water-soluble ligands as a removable template to obtain free-standing ultrathin PbS nanosheets and assemble them into direct-contact bilayers with various twist angles. Atomic-resolution imaging shows the moiré periodic structural reconstruction at the superlattice interface due to the strong metavalent coupling. Electron energy loss spectroscopy and theoretical calculations collectively reveal the twist-angle-dependent electronic structure, especially the emergent separation of flat bands at small twist angles. The localized states of flat bands are similar to well-arranged quantum dots, promising an application in devices. This study opens a new door to the exploration of deep energy modulations within moiré superlattices alternative to van der Waals twistronics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

The Uranium-Containing and Thorium-Containing Anions Studied by Photoelectron Spectroscopy

An in-depth knowledge of actinide chemistry is fundamental to many aspects of nuclear science and technology, including the synthesis and processing of materials and the remediation of waste disposal sites. Among the actinides, the chemical bonding behaviors of actinium and thorium resemble those of the transition metals; the 5f-electrons of protactinium, uranium, neptunium, and plutonium often play important roles in their bonding; and among the still heavier elements, their bonding tends to mimic the lanthanide elements in terms of electron shielding and their f-electron contributions. Bonding that involves 5f-electrons, however, is especially important, in part because of the significance of uranium and plutonium, but also because these elements are among the few where f-electron participation in bonding is relatively common. This work focused on studying uranium-containing and thorium-containing anions in the gas phase using negative ion photoelectron spectroscopy. Since this technique directly probed valence electrons, it was uniquely positioned to address open questions regarding molecular bonding and electron configurations. A particularly important issue concerned how bonding in actinide-containing molecules was affected by modifications to their actinide atoms’ environment, i.e., due to their interaction with ligands. A closely related question was how actinide atoms’ suborbitals were qualitatively reordered and their energies quantitatively shifted as a result of their ligated environments. These were especially relevant issues in regard to uranium due to it having multiple possible oxidation states (OS) and the potential for 5f electron participation in bonding. The effects of ligands on oxidation states and 5f-orbital energies in uranium bonding was expected to be pronounced. Both ligands and excess electrons were seen as probes of actinide atoms within actinide-containing molecules. Our strategy for advancing knowledge of chemical bonding in the actinide-containing species utilized the synergy between experiments and theory, where in some cases experimental results validated theory and where in others computational results assisted in interpreting experiments. Calculations on actinide systems are terrifically challenging due to large spin-orbit interactions, relativistic effects, and just the sheer number of electrons involved. Even in the simplest species, e.g., U and U2, the most sophisticated, modern calculations carried out by the most experienced theorists often only approximate experimentally-measured values, such as electron affinities. For theory to provide confident predictions that can be used to solve real problems it needed an iterative and ultimately corrective mechanism by which its methods can develop further. Experiments can be used to identify when theory has failed; whereupon the subsequent process of using the experiment-theory interplay can be used to find the cause of the failure. Upon fixing it in one case, different test species can be proposed and studied by the experiment-theory combination to determine whether the problem has been corrected. Thus, experiments not only measure the values of molecular properties, they also provide navigational 3 beacons that keep computations off the reefs in an otherwise dark sea with few reference points. Experimental measurements in the actinide field are not only important, they are in actuality essential to computational progress. While it was not always possible to compare the theoreticallydetermined quantity of interest directly with the same experimentally-measured observable, it was usually possible to compare consequential properties that are both calculable and measurable. In the work completed here electron affinities and electronic state spacings were often sensitive consequential parameters. Reasonable agreement between measured and computational values signaled that a calculation that was very likely to be on-track. We had established collaborative relationships with five computational groups, all of which have expertise in computational actinide chemistry. Their PI’s are L. Cheng, D. Dixon, L. Gagliardi, K. Peterson, and B. Vlaisavljevich. Our close interaction with our theory partners led to us suggesting systems to them and them to us. This reciprocal interaction between our experimental and their computational results was among the most important strengths of this work and was a thread woven throughout. Even though anion photoelectron spectroscopic studies are conducted on anions, much of the information that they provide, pertains to the electronic structure of the neutral counterparts of those anions; among these are electron affinities and electronically excited state spacings. Our experimental tools included several specialized ion sources for forming the anionic species of interest, a mass spectrometer for identifying and mass-selecting them, and an anion photoelectron spectrometer for determining their electron affinities (EA) and characterizing the electronic states of the selected anions’ neutral counterparts. Anion photoelectron spectroscopy is conducted by crossing a mass-selected beam of anions with a fixed-frequency laser beam and energy-analyzing the resultant photodetached electrons. The photodetachment process is governed by the energyconserving relationship: hν = EBE + EKE, where hν is the photon’s energy, EBE is the electron binding (photodetachment transition) energy, and EKE is the electron’s kinetic energy. In our apparatus mass-selection is accomplished via time-of-flight mass spectrometry (TOF-MS), electron energy analysis is achieved with either a magnetic bottle or by velocity mapped imaging. Photodetachment of electrons from anions is implemented via either Nd:YAG or excimer lasers. The photodetachment transition energy, i.e., the EBE, between the ground vibrational and electronic state of an anion and the ground vibrational and electronic state of that anion’s neutral counterpart is the adiabatic electron affinity (EA) of that neutral molecule. Likewise, photodetachment transitions between the ground vibrational and electronic state of an anion and the various electronically-excited states of that anion’s corresponding neutral map the electronic spectrum of that neutral species, i.e., the spectral spacings in the photoelectron spectrum are a mirror image of the neutral’s electronic spectrum. It was, of course, crucial to be able to form the anionic species of interest. There, we had a particularly broad field of anion sources from which to choose. These included several variants of pulsed laser vaporization (LV), laser photoemission, infrared desorption plus photoemission, pulsed arc discharge (PACIS), electrospray ionization (ESI), and Rydberg electron transfer (RET). Each of these anion sources were readily combined with, i.e., connected to, the anion photoelectron spectroscopic portion of our apparatus as described above. Among the sources that utilize lasers, visible light for LV sources as well as IR for desorption sources are provided by Nd:YAG lasers. Ultraviolet photons are provided by both Nd:YAG and excimer lasers, whereas the excitation wavelengths for RET experiments come from two Nd:YAG-pumped dye lasers.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Hydrogen-Bond-Driven Chemical Separations: Elucidating the Interfacial Steps of Self-Assembly in Solvent Extraction

Chemical separations, particularly liquid extractions, are pervasive in academic and industrial laboratories, yet a mechanistic understanding of the events governing their function are obscured by interfacial phenomena that are notoriously difficult to measure. In this work, we investigate the fundamental steps of ligand self-assembly as driven by changes in the interfacial H-bonding network using vibrational sum frequency generation. Our results show how the bulk pH modulates the interfacial structure of extractants at the buried oil/aqueous interface via the formation of unique H-bonding networks that order and bridge ligands to produce self-assembled aggregates. These extended H-bonded structures are key to the subsequent extraction of Co2+ from the aqueous phase in promoting micelle formation and subsequent ejection of the said micelle into the oil phase. The combination of static and time-resolved measurements reveals the events underlying complexities of liquid extractions at high [Co2+]:[ligand] ratios by showing an evolution of interfacially assembled structures that are readily tuned on a chemical basis by altering the compositions of the aqueous phase. The results of this work point to new principles to design-applied separations through the manipulation of surface charge, electrostatic screening, and the associated H-bonding networks that arise at the interface to facilitate organization and subsequent extraction.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Early stages in the evolution of the atmosphere and climate on the Earth-group planets

The early evolution of the atmospheres and climate of the Earth, Mars and Venus is discussed, based on a concept of common initial conditions and main processes (besides known differences in chemical composition and outgassing rate). It is concluded that: (1) liquid water appeared on the surface of the earth in the first few hundred million years; the average surface temperature was near the melting point for about the first two eons; CO2 was the main component of the atmosphere in the first 100-500 million years; (2) much more temperate outgassing and low solar heating led to the much later appearance of liquid water on the Martian surface, only one to two billion years ago; the Martian era of rivers, relatively dense atmosphere and warm climate ended as a result of irreversible chemical bonding of CO2 by Urey equilibrium processes; (3) a great lack of water in the primordial material of Venus is proposed; liquid water never was present on the surface of the planet, and there was practically no chemical bonding of CO2; the surface temperature was over 600 K four billion years ago.

Moroz, V. I.↗

The effect of Tricresyl-Phosphate (TCP) as an additive on wear of Iron (Fe)

The effect of tricresyl phosphate (TCP) as an antiwear additive in lubricant trimethyol propane triheptanoate (TMPTH) was investigated. The objective was to examine step loading wear by use of surface analysis, wetting, and chemical bonding changes in the lubricant. The investigation consisted of steploading wear studies by a pin or disk tribometer, the effects on wear related to wetting by contact angle and surface tension measurements of various liquid systems, the chemical bonding changes between lubricant and TCP chromatographic analysis, and by determining the reaction between the TCP and metal surfaces through wear scar analysis by Auger emission spectroscopy (AES). The steploading curve for the base fluid alone shows rapid increase of wear rate with load. The steploading curve for the base fluid in presence of 4.25 percent by volume TCP under dry air purge has shown a great reduction of wear rate with all loads studied. It has also been found that the addition of 4.25 percent by volume TCP plus 0.33 percent by volume water to the base lubricant under N2 purge also greatly reduces the wear rate with all loads studied. AES surface analysis reveals a phosphate type wear resistant film, which greatly increases load-bearing capacity, formed on the iron disk. Preliminary chromatographic studies suggest that this film forms either because of ester oxidation or TCP degradation. Wetting studies show direct correlation between the spreading coefficient and the wear rate.

Ghose, Hiren M.↗

Mechanical Properties of Nanostructured Materials Determined Through Molecular Modeling Techniques

The potential for gains in material properties over conventional materials has motivated an effort to develop novel nanostructured materials for aerospace applications. These novel materials typically consist of a polymer matrix reinforced with particles on the nanometer length scale. In this study, molecular modeling is used to construct fully atomistic models of a carbon nanotube embedded in an epoxy polymer matrix. Functionalization of the nanotube which consists of the introduction of direct chemical bonding between the polymer matrix and the nanotube, hence providing a load transfer mechanism, is systematically varied. The relative effectiveness of functionalization in a nanostructured material may depend on a variety of factors related to the details of the chemical bonding and the polymer structure at the nanotube-polymer interface. The objective of this modeling is to determine what influence the details of functionalization of the carbon nanotube with the polymer matrix has on the resulting mechanical properties. By considering a range of degree of functionalization, the structure-property relationships of these materials is examined and mechanical properties of these models are calculated using standard techniques.

Clancy, Thomas C.↗