Abstract The existence of relationships between structure and properties provides one avenue perm... more Abstract The existence of relationships between structure and properties provides one avenue permitting the design of materials with chosen properties. Unfortunately, rules relating the properties of intermetallic alloys to their crystal structure have not been forthcoming. We believe that this is because the structure of intermetallic alloys is interpreted too narrowly. By extending the definition of structure to include elements of the electronic charge distribution we show, through examples, that there may in fact be relationships between intrinsic mechanical properties and this extended structure. A description of this extended structure requires only a knowledge of the critical points of the total charge density. This knowledge can be obtained through any method of electronic structure or, in principle, through experimental techniques.
The advent of new materials processing and fabrication techniques has made it possible to control... more The advent of new materials processing and fabrication techniques has made it possible to control atomic-scale structure to an extent only dreamed of as recently as 20 years ago. This improved structure control takes us one step closer to synthesizing materials with a combination of properties tailored to the intended application. It is this ability to control structure that will accelerate the pace of technological advancement which is limited by the rate of materials development.Mechanical performance of materials restricts their use, even for nonstructural applications. Magnetic composites used in recording heads are an example. The mechanical and tribological properties of these materials are a major consideration when designing reliable components.Another example is electronic materials, where the strength of the interface between the polymer packaging and the semiconductor controls the lifetime of the semiconductor device. The semiconductor device undergoes thermal cycling as ...
One of the ultimate objectives for the electronic structure theory of solids is the first-princip... more One of the ultimate objectives for the electronic structure theory of solids is the first-principles design of materials. Major steps in this direction have already been taken in the form of parameter-free calculations, which are capable of yielding accurate descriptions of a number of structural, electronic, and magnetic properties of metals, semiconductors and even disordered alloys. Furthermore, extensions of these approaches to point defects (substitutional impurities, interstitials, and vacancies) and to interfaces and clean and covered surfaces are showing great promise. However, only recently has there been an attempt to correlate the results of electronic structure calculations with mechanical properties, and only in the past few years have the specific features of electronic structure that could give rise, for example, to brittle versus ductile behavior,1-5 been addressed. Indeed, despite the complex and manifold origins of mechanical behavior and the relatively poor characterization of the pertinent structures at the atomic level, general trends in certain mechanical properties may be correlated with specific features of electronic structure. An interesting illustration is the control of mechanical properties of semiconductors by electrically-active impurities.6 At relatively low temperatures (≲500°C) the dopants have been shown to affect yield stress and hardness through their influence on dislocation velocities,6-7 the effect being a particularly strong function of dopant concentration in Si and Ge.*
Stacking faults in close-packed metals are known to play a crucial role in determining mechanical... more Stacking faults in close-packed metals are known to play a crucial role in determining mechanical behaviour. Extending recent layer Korringa-Kohn-Rostoker calculations on twin faults in a variety of FCC crystals, we study in detail the aluminium defect and develop an atomistic understanding of the modifying behaviour of small concentrations of impurity atoms.
Bulk metallic glasses (BMGs) are characterized by a number of remarkable physical and mechanical ... more Bulk metallic glasses (BMGs) are characterized by a number of remarkable physical and mechanical properties. Unfortunately, these same materials are often intrinsically brittle, which limits their utility. Consequently, considerable effort has been expended searching for correlations between the phenomenologically complex mechanical properties of metallic glasses and more basic properties, such correlations might provide insight into the structure and bonding controlling the deformation properties of BMGs. While conducting such a search, we uncovered a weak correlation between a BMG's work function and its susceptibility to brittle behavior. We argue that the basis for this correlation is a consequence of a component of the work function - the surface dipole - and a fundamental bond property related to the shape of the charge density at a bond critical point. Together these observations suggest that simple first principle calculations might be useful in the search for tougher BMGs.
There is a significant challenge in designing new materials for targeted properties based on thei... more There is a significant challenge in designing new materials for targeted properties based on their electronic structure. While in principle this goal can be met using knowledge of the electron charge density, the relationships between the density and properties are largely unknown. To help overcome this problem we develop a quantitative structure-property relationship (QSPR) between the charge density and the elastic constants for B2 intermetallics. Using a combination of informatics techniques for screening all the potentially relevant charge density descriptors, we find that C 11 and C 44 are determined solely from the magnitude of the charge density at its critical points, while C 12 is determined by the shape of the charge density at its critical points. From this reduced charge density selection space, we develop models for predicting the elastic constants of an expanded number of intermetallic systems, which we then use to predict the mechanical stability of new systems. Having reduced the descriptors necessary for modeling elastic constants, statistical learning approaches may then be used to predict the reduced knowledge-based required as a function of the constituent characteristics.
We briefly review the method by which the electron charge density of atomic systems is decomposed... more We briefly review the method by which the electron charge density of atomic systems is decomposed into unique volumes called bond bundles, which are characterized by well-defined and additive properties. We then show that boundaries of bond bundles topologically constrain their chemical reactivity. To illustrate this fact, we model the response of the bond bundles of ethane and ethene to electrophilic attack and from the results of these models posit that functional group properties can be inferred from the shapes of their bond bundles. By relating functionality to bond bundle shape, it is possible to see subtle changes in chemical reactivity that are otherwise difficult to explain, as is illustrated by comparing bond bundles through a series of impact sensitive polynitroaromatic molecules.
Colloidal iron pyrite nanocrystals (or FeS 2 NC inks) are desirable as active materials in lithiu... more Colloidal iron pyrite nanocrystals (or FeS 2 NC inks) are desirable as active materials in lithium ion batteries and photovoltaics, and are particularly suitable for large-scale, roll-to-roll deposition or ink-jet printing. However, to date, FeS 2 NC inks have only been synthesized using the hot-injection technique, which requires air-free conditions and may not be desirable at an industrial scale. Here, we report the synthesis of monodisperse, colloidal, spherical, and phase-pure FeS 2 NCs of 5.5 ± 0.3 nm in diameter via a scalable solvothermal method using iron diethyldithiocarbamate as the precursor, combined with a post digestive ripening process. The phase purity and crystallinity are determined using X-ray diffraction, transmission electron microscopy, far-infrared spectroscopy, and Raman spectroscopy techniques. Through this study, a hypothesis has been verified that solvothermal syntheses can also produce FeS 2 NC inks by incorporating three experimental conditions: high solubility of the precursor, efficient mass transport, and sufficient stabilizing ligands. The addition of ligands and stirring decrease the NC size and led to a narrow size distribution. Moreover, using density functional theory calculations, we have identified an acid-mediated decomposition of the precursor as the initial and critical step in the synthesis of FeS 2 from iron diethyldithiocarbamate.
ABSTRACT The chemical bond, as a link between atoms, is an intrinsic property of the charge densi... more ABSTRACT The chemical bond, as a link between atoms, is an intrinsic property of the charge density. However, bond energy, which is commonly seen as the energy difference between a molecular state and an arbitrary dissociated state, depends extrinsically on the charge density. This view of a bond as a natural link possessing properties that are externally determined is at best clumsy, and often leads to contradictory interpretations as to the origins of the structure and properties of molecules and solids. Ideally, one would like to uncover an intrinsic property of the chemical bond that gives similar information content as that provided by bond energy. To this end, we report on our ongoing work exploring the intrinsic geometry imposed on the charge density by mapping it onto the smallest volumes bounded by zero flux surfaces in the gradient of the charge density. These natural volume elements of the Quantum Theory of Atoms in Molecules have well defined properties, and hence, this mapping produces a set of property distributions with a quantifiable geometric structure that varies from molecule to molecule. Here, we examine the intrinsic geometry of the kinetic energy distribution for a series of homonuclear dimers and compare the geometric properties of these distributions with the bond energies of the same dimers.
Modem chemistry frequently describes the structure and reaction dynamics of molecules in terms of... more Modem chemistry frequently describes the structure and reaction dynamics of molecules in terms of the general principle of "competition for bonds"; consequently, bonding forms the basis of the language of chemistry. The actual models used to represent these bonds are frequently system specific. Organic reactions are described in terms of bonds based on pairs of atomic valence electrons. Reactions of inorganic coordination complexes are described in terms of bonds based on a molecular orbital representation. In analogy to those chemistries, a representation for a bond and bond strength, suitable for describing the cohesive and adhesive properties of all classes of materials, is introduced. This representation proves to yield an explanation for the observed cohesive properties of a specific class of materials (cleavage in bcc metals), and it also provides a framework for exploring and analyzing the 10 10 12 4.
Abstract The self-consistent-field Xα scattered-wave technique is used to analyze the electronic ... more Abstract The self-consistent-field Xα scattered-wave technique is used to analyze the electronic structure of strained SiSi bonds in amorphous silicon alloys. A Si 2 (sat) 6 cluster, which has been shown to be an effective model for the SiSi bond, was used to analyze a local region of moderate strain resulting in a bond length of 2.5 A. The strain was relieved by allowing relaxation from this nearly tetrahedral configuration (T 4 ′) to a trigonal configuration (T 3 ) at one end of the cluster. Transition-state calculations show that the separation in energy. ΔE, between the highesto occupied and lowest unoccupied molecular orbitals is a maximum at the 2.5A SiSi distance; as this distance is increased, ΔE decreases to zero near 3.0A and charge leaves the relaxed Si aton, producing a T + 3 defect. These results lead us to suggest a new model for the Staebler-Wronski effect.
Abstract The self-consistent-field X-alpha scattered-wave technique has been used to investigate ... more Abstract The self-consistent-field X-alpha scattered-wave technique has been used to investigate the electronic structure of aromatic silicon-based clusters which can be expected to form some of the defect centers in hydrogenated amorphous silicon (a-Si:H) thin films. These clusters, which are planar rings containing 4n+2 π-electrons, exhibit resonance stabilization and give rise to the silicon analogue of aromatic hydrocarbons. We have studied Si 6 (sat) 6 and Si 4 O(sat) 4 clusters in comparison to benzene (C 6 H 6 ). The silicon-based clusters are less stable than benzene due to larger interatomic separations as well as shielding effects of the Si 3s electrons. However, our results show that Si 4 O(sat) 4 is more stable than Si 6 (sat) 6 . The introduction of oxygen into such resonant rings adds stability by increasing the strength of π-bonding throughout the ring. As a result, we show how the presence of such structures in a-Si:H can account for the photostructural effects observed in thin films of these materials.
Abstract The self-consistent-field X-alpha scattered-wave technique has been used to investigate ... more Abstract The self-consistent-field X-alpha scattered-wave technique has been used to investigate the electronic structure of aromatic silicon-based clusters which are expected to form defect centers in hydrogenated amorphous silicon (a-Si:H) thin films. These clusters, which are planar rings containing 4n+2 π-electrons, represent the analogue of aromatic hydrocarbons. We have studied Si 6 (sat) 6 and Si 4 O(sat) 4 clusters in comparison to benzene. While both Si-based clusters are less stable than benzene, our results show that Si 4 O(sat) 4 is more stable than Si 6 (sat) 6 . The introduction of oxygen into such resonant rings adds stability by increasing the strength of π-bonding throughout the ring. We show how the presence of such structures in a-Si:H can account for the Staebler-Wronski effect observed in thin films of these materials.
The search for principles governing the relationships between electronic structure and properties... more The search for principles governing the relationships between electronic structure and properties has been underway for more than three quarters of a century and has yet to produce results useful in the design of metallic materials. If the power of informatics is not to meet the same fate, a new way to describe electronic structure must be found. The authors
Skip to Main Content. There will be a release of Wiley Online Library scheduled for Saturday 27th... more Skip to Main Content. There will be a release of Wiley Online Library scheduled for Saturday 27th November 2010. Access to the website will be disrupted as follows: New York 0630 EDT to 0830 EDT; London 1130 GMT to 1330 GMT; Singapore 1730 SGT to 1930 SGT. ...
Shortly before his death, Richard Bader commented in this Journal on the dichotomy that exists wi... more Shortly before his death, Richard Bader commented in this Journal on the dichotomy that exists within chemistry and between chemists. We believe that the dichotomy results from different goals and objectives inherent in the chemical disciplines. At one extreme are designers who synthesize new molecules with interesting properties. For these chemists, the rationale underpinning molecular synthesis is far less important than the end product-the molecules themselves. At the other extreme are the chemists who seek a fundamental understanding of molecular properties. We suggest that the Quantum Theory of Atoms in Molecules, by virtue of the rich hierarchical structure inherent in the theory, offers a bridge through which to unite these two groups. However, if there is to be reconciliation, it falls to the theorists to develop ''quantum mechanically'' correct tools and concepts useful to the synthetic and applied chemist.
Abstract The existence of relationships between structure and properties provides one avenue perm... more Abstract The existence of relationships between structure and properties provides one avenue permitting the design of materials with chosen properties. Unfortunately, rules relating the properties of intermetallic alloys to their crystal structure have not been forthcoming. We believe that this is because the structure of intermetallic alloys is interpreted too narrowly. By extending the definition of structure to include elements of the electronic charge distribution we show, through examples, that there may in fact be relationships between intrinsic mechanical properties and this extended structure. A description of this extended structure requires only a knowledge of the critical points of the total charge density. This knowledge can be obtained through any method of electronic structure or, in principle, through experimental techniques.
The advent of new materials processing and fabrication techniques has made it possible to control... more The advent of new materials processing and fabrication techniques has made it possible to control atomic-scale structure to an extent only dreamed of as recently as 20 years ago. This improved structure control takes us one step closer to synthesizing materials with a combination of properties tailored to the intended application. It is this ability to control structure that will accelerate the pace of technological advancement which is limited by the rate of materials development.Mechanical performance of materials restricts their use, even for nonstructural applications. Magnetic composites used in recording heads are an example. The mechanical and tribological properties of these materials are a major consideration when designing reliable components.Another example is electronic materials, where the strength of the interface between the polymer packaging and the semiconductor controls the lifetime of the semiconductor device. The semiconductor device undergoes thermal cycling as ...
One of the ultimate objectives for the electronic structure theory of solids is the first-princip... more One of the ultimate objectives for the electronic structure theory of solids is the first-principles design of materials. Major steps in this direction have already been taken in the form of parameter-free calculations, which are capable of yielding accurate descriptions of a number of structural, electronic, and magnetic properties of metals, semiconductors and even disordered alloys. Furthermore, extensions of these approaches to point defects (substitutional impurities, interstitials, and vacancies) and to interfaces and clean and covered surfaces are showing great promise. However, only recently has there been an attempt to correlate the results of electronic structure calculations with mechanical properties, and only in the past few years have the specific features of electronic structure that could give rise, for example, to brittle versus ductile behavior,1-5 been addressed. Indeed, despite the complex and manifold origins of mechanical behavior and the relatively poor characterization of the pertinent structures at the atomic level, general trends in certain mechanical properties may be correlated with specific features of electronic structure. An interesting illustration is the control of mechanical properties of semiconductors by electrically-active impurities.6 At relatively low temperatures (≲500°C) the dopants have been shown to affect yield stress and hardness through their influence on dislocation velocities,6-7 the effect being a particularly strong function of dopant concentration in Si and Ge.*
Stacking faults in close-packed metals are known to play a crucial role in determining mechanical... more Stacking faults in close-packed metals are known to play a crucial role in determining mechanical behaviour. Extending recent layer Korringa-Kohn-Rostoker calculations on twin faults in a variety of FCC crystals, we study in detail the aluminium defect and develop an atomistic understanding of the modifying behaviour of small concentrations of impurity atoms.
Bulk metallic glasses (BMGs) are characterized by a number of remarkable physical and mechanical ... more Bulk metallic glasses (BMGs) are characterized by a number of remarkable physical and mechanical properties. Unfortunately, these same materials are often intrinsically brittle, which limits their utility. Consequently, considerable effort has been expended searching for correlations between the phenomenologically complex mechanical properties of metallic glasses and more basic properties, such correlations might provide insight into the structure and bonding controlling the deformation properties of BMGs. While conducting such a search, we uncovered a weak correlation between a BMG's work function and its susceptibility to brittle behavior. We argue that the basis for this correlation is a consequence of a component of the work function - the surface dipole - and a fundamental bond property related to the shape of the charge density at a bond critical point. Together these observations suggest that simple first principle calculations might be useful in the search for tougher BMGs.
There is a significant challenge in designing new materials for targeted properties based on thei... more There is a significant challenge in designing new materials for targeted properties based on their electronic structure. While in principle this goal can be met using knowledge of the electron charge density, the relationships between the density and properties are largely unknown. To help overcome this problem we develop a quantitative structure-property relationship (QSPR) between the charge density and the elastic constants for B2 intermetallics. Using a combination of informatics techniques for screening all the potentially relevant charge density descriptors, we find that C 11 and C 44 are determined solely from the magnitude of the charge density at its critical points, while C 12 is determined by the shape of the charge density at its critical points. From this reduced charge density selection space, we develop models for predicting the elastic constants of an expanded number of intermetallic systems, which we then use to predict the mechanical stability of new systems. Having reduced the descriptors necessary for modeling elastic constants, statistical learning approaches may then be used to predict the reduced knowledge-based required as a function of the constituent characteristics.
We briefly review the method by which the electron charge density of atomic systems is decomposed... more We briefly review the method by which the electron charge density of atomic systems is decomposed into unique volumes called bond bundles, which are characterized by well-defined and additive properties. We then show that boundaries of bond bundles topologically constrain their chemical reactivity. To illustrate this fact, we model the response of the bond bundles of ethane and ethene to electrophilic attack and from the results of these models posit that functional group properties can be inferred from the shapes of their bond bundles. By relating functionality to bond bundle shape, it is possible to see subtle changes in chemical reactivity that are otherwise difficult to explain, as is illustrated by comparing bond bundles through a series of impact sensitive polynitroaromatic molecules.
Colloidal iron pyrite nanocrystals (or FeS 2 NC inks) are desirable as active materials in lithiu... more Colloidal iron pyrite nanocrystals (or FeS 2 NC inks) are desirable as active materials in lithium ion batteries and photovoltaics, and are particularly suitable for large-scale, roll-to-roll deposition or ink-jet printing. However, to date, FeS 2 NC inks have only been synthesized using the hot-injection technique, which requires air-free conditions and may not be desirable at an industrial scale. Here, we report the synthesis of monodisperse, colloidal, spherical, and phase-pure FeS 2 NCs of 5.5 ± 0.3 nm in diameter via a scalable solvothermal method using iron diethyldithiocarbamate as the precursor, combined with a post digestive ripening process. The phase purity and crystallinity are determined using X-ray diffraction, transmission electron microscopy, far-infrared spectroscopy, and Raman spectroscopy techniques. Through this study, a hypothesis has been verified that solvothermal syntheses can also produce FeS 2 NC inks by incorporating three experimental conditions: high solubility of the precursor, efficient mass transport, and sufficient stabilizing ligands. The addition of ligands and stirring decrease the NC size and led to a narrow size distribution. Moreover, using density functional theory calculations, we have identified an acid-mediated decomposition of the precursor as the initial and critical step in the synthesis of FeS 2 from iron diethyldithiocarbamate.
ABSTRACT The chemical bond, as a link between atoms, is an intrinsic property of the charge densi... more ABSTRACT The chemical bond, as a link between atoms, is an intrinsic property of the charge density. However, bond energy, which is commonly seen as the energy difference between a molecular state and an arbitrary dissociated state, depends extrinsically on the charge density. This view of a bond as a natural link possessing properties that are externally determined is at best clumsy, and often leads to contradictory interpretations as to the origins of the structure and properties of molecules and solids. Ideally, one would like to uncover an intrinsic property of the chemical bond that gives similar information content as that provided by bond energy. To this end, we report on our ongoing work exploring the intrinsic geometry imposed on the charge density by mapping it onto the smallest volumes bounded by zero flux surfaces in the gradient of the charge density. These natural volume elements of the Quantum Theory of Atoms in Molecules have well defined properties, and hence, this mapping produces a set of property distributions with a quantifiable geometric structure that varies from molecule to molecule. Here, we examine the intrinsic geometry of the kinetic energy distribution for a series of homonuclear dimers and compare the geometric properties of these distributions with the bond energies of the same dimers.
Modem chemistry frequently describes the structure and reaction dynamics of molecules in terms of... more Modem chemistry frequently describes the structure and reaction dynamics of molecules in terms of the general principle of "competition for bonds"; consequently, bonding forms the basis of the language of chemistry. The actual models used to represent these bonds are frequently system specific. Organic reactions are described in terms of bonds based on pairs of atomic valence electrons. Reactions of inorganic coordination complexes are described in terms of bonds based on a molecular orbital representation. In analogy to those chemistries, a representation for a bond and bond strength, suitable for describing the cohesive and adhesive properties of all classes of materials, is introduced. This representation proves to yield an explanation for the observed cohesive properties of a specific class of materials (cleavage in bcc metals), and it also provides a framework for exploring and analyzing the 10 10 12 4.
Abstract The self-consistent-field Xα scattered-wave technique is used to analyze the electronic ... more Abstract The self-consistent-field Xα scattered-wave technique is used to analyze the electronic structure of strained SiSi bonds in amorphous silicon alloys. A Si 2 (sat) 6 cluster, which has been shown to be an effective model for the SiSi bond, was used to analyze a local region of moderate strain resulting in a bond length of 2.5 A. The strain was relieved by allowing relaxation from this nearly tetrahedral configuration (T 4 ′) to a trigonal configuration (T 3 ) at one end of the cluster. Transition-state calculations show that the separation in energy. ΔE, between the highesto occupied and lowest unoccupied molecular orbitals is a maximum at the 2.5A SiSi distance; as this distance is increased, ΔE decreases to zero near 3.0A and charge leaves the relaxed Si aton, producing a T + 3 defect. These results lead us to suggest a new model for the Staebler-Wronski effect.
Abstract The self-consistent-field X-alpha scattered-wave technique has been used to investigate ... more Abstract The self-consistent-field X-alpha scattered-wave technique has been used to investigate the electronic structure of aromatic silicon-based clusters which can be expected to form some of the defect centers in hydrogenated amorphous silicon (a-Si:H) thin films. These clusters, which are planar rings containing 4n+2 π-electrons, exhibit resonance stabilization and give rise to the silicon analogue of aromatic hydrocarbons. We have studied Si 6 (sat) 6 and Si 4 O(sat) 4 clusters in comparison to benzene (C 6 H 6 ). The silicon-based clusters are less stable than benzene due to larger interatomic separations as well as shielding effects of the Si 3s electrons. However, our results show that Si 4 O(sat) 4 is more stable than Si 6 (sat) 6 . The introduction of oxygen into such resonant rings adds stability by increasing the strength of π-bonding throughout the ring. As a result, we show how the presence of such structures in a-Si:H can account for the photostructural effects observed in thin films of these materials.
Abstract The self-consistent-field X-alpha scattered-wave technique has been used to investigate ... more Abstract The self-consistent-field X-alpha scattered-wave technique has been used to investigate the electronic structure of aromatic silicon-based clusters which are expected to form defect centers in hydrogenated amorphous silicon (a-Si:H) thin films. These clusters, which are planar rings containing 4n+2 π-electrons, represent the analogue of aromatic hydrocarbons. We have studied Si 6 (sat) 6 and Si 4 O(sat) 4 clusters in comparison to benzene. While both Si-based clusters are less stable than benzene, our results show that Si 4 O(sat) 4 is more stable than Si 6 (sat) 6 . The introduction of oxygen into such resonant rings adds stability by increasing the strength of π-bonding throughout the ring. We show how the presence of such structures in a-Si:H can account for the Staebler-Wronski effect observed in thin films of these materials.
The search for principles governing the relationships between electronic structure and properties... more The search for principles governing the relationships between electronic structure and properties has been underway for more than three quarters of a century and has yet to produce results useful in the design of metallic materials. If the power of informatics is not to meet the same fate, a new way to describe electronic structure must be found. The authors
Skip to Main Content. There will be a release of Wiley Online Library scheduled for Saturday 27th... more Skip to Main Content. There will be a release of Wiley Online Library scheduled for Saturday 27th November 2010. Access to the website will be disrupted as follows: New York 0630 EDT to 0830 EDT; London 1130 GMT to 1330 GMT; Singapore 1730 SGT to 1930 SGT. ...
Shortly before his death, Richard Bader commented in this Journal on the dichotomy that exists wi... more Shortly before his death, Richard Bader commented in this Journal on the dichotomy that exists within chemistry and between chemists. We believe that the dichotomy results from different goals and objectives inherent in the chemical disciplines. At one extreme are designers who synthesize new molecules with interesting properties. For these chemists, the rationale underpinning molecular synthesis is far less important than the end product-the molecules themselves. At the other extreme are the chemists who seek a fundamental understanding of molecular properties. We suggest that the Quantum Theory of Atoms in Molecules, by virtue of the rich hierarchical structure inherent in the theory, offers a bridge through which to unite these two groups. However, if there is to be reconciliation, it falls to the theorists to develop ''quantum mechanically'' correct tools and concepts useful to the synthetic and applied chemist.
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Papers by mark eberhart