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RESEARCH

The Source Function . Several descriptors providing useful chemical insight may be extracted from the wave function. Among these, particularly interesting are those obtained also from experiment. In this line, we recently introduced the source function (SF) enabling one to retrieve the non l

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RESEARCH

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    1. RESEARCH

    2. The Source Function

    3. The Source Function

    4. The Source Function: Theory

    5. The Source Function

    6. The Source Function

    7. The Source Function

    8. Nano-engineering of novel thermoelectric materials

    9. Nano-engineering of novel thermoelectric materials

    10. Nano-engineering of novel thermoelectric materials

    11. NanoThermel

    12. NanoThermel

    13. NanoThermel

    14. Nano-engineering of novel thermoelectric materials

    15. The role of the theoretical modelling But let’s have a more precise insight on which is the role of theory within the project. Basically, from the band structure obtained from a first principles calculation, and using semi-classical Boltzman’s transport theory in its mono-electronic formulation, we may calculate –with some approximation - all quantities defining the electron transport properties of a well defined TM. In fact the Onsager coefficients Li which enter in the definition of sigma and the thermopower S depend on the band energies En and band velocities vn. F0 is the Fermi-Dirac distribution function and mu is the chemical potential, which depend on the T and may be both be evaluated from the knowledge of the band structure. If a constant relaxation time tau is assumed (independent on n and k), all quantities relevant to electronic transport may be evaluated. Within this assumption, S is made independent of the relaxation time and sigma depend linearly on the assumed costant relaxation time. The electronic contribution of the thermal conductivity can be expressed in term of sigma, in accord to the famous Wiedemann-Franz law. Evaluation of the lattice thermal conductivity on the other hand requires a full knowledge of vibrational eigenmodes and frequencies. This was at the moment beyond our computational capabilities. In practice upon substitution and/or doping we can model, predict and rationalize, for an assumed structural model and composition the changes in geometry (cell parameters and fractional coordinates), changes in the electronic structure (band gap, EDDs and their topologies, density of states, band sructure) and related changes in the transport properties outcomes. If a combination of different structures is present in the real material, the measured Seebeck coefficient will be the result of such a mixing. Theory can pick up which is the most beneficial structure and direct the synthesis efforts to increase the percentage of such a structure in the material. How dramatic may be the effect of dopant location on the electronic structure is shown by these DOSS plots for the parent skutterudite (top) , the skutterudite with a Te atom substituting for Sb in a 4 MR pnicogen ring (middle) , and a Te entering in a cubic void of the skutterudite (bottom). The parent is a semiconductor, with a sizeable band gap, the ring-substitued system is a n-doped skutterudite with enhanced electrical conductivity and only slightly worsened Seebeck coefficient, while the system with Te entering in the void behaves mostly as a a metal, with largely enhanced sigma, but with also highly decreased Sebbeck, thus yielding a much worse TM than the original skutterudite. More if needed For instance, a new TM material is synthesized by mixing reagents in given percentages. The material composition and structure may be characterized through diverse techniques (single crystal X-ray diffraction, powder diffraction, neutron diffraction) A thermoelectric evaluation of the TM may be performed. A theoretical modelling of such a material may produce several useful feedbacks: First among these, which is the influence on several parameters (cell geometry, thermochemical stability, electron density, electron transport properties, etc.) of the possible alternative structures that might be thought on the basis of the starting reagents. Second, modeling may help understanding the results of structural characterization, which not always are able to provide clear cut answers, especially so when small amounts of doping elements are present. Furthermore, while structural characterization by the techniques named above yields a space-time averaged information, theory may deconvolute such an information and provide a detailed understanding of the structural, electronic and thermoelectric properties of the different cells composing the structure Third, theory gives a careful description of the kind of chemical interactions existing between the dopant host/s and the framework material, thus suggesting whether alternative dopants and/or structures could be more suited in view of thermoelectric performances. Finally, modeling can predict the optimum doping level for a given, well characterized, reference material, within the frozen band approach. Alternatively, based on the insights sketched above, modeling may suggest new materials to be synthesized, alternative interpretation of structural characterization data, rationalization of hardly interpretable transport properties outcomes. For instance, the Seebeck coefficient values and trends are strongly dependent on where a dopant is actually sitting in the host structure. If a combination of different structures is present in the real material, the measured Seebeck coefficient will be the result of such a mixing. Theory can pick up which is the most beneficial structure and direct the synthesis efforts to increase the percentage of such a structure in the material. In other cases, if the measured transport properties are not in line with theoretical predictions, this might be an indication that the real status of the material is not what is being modeled, because, for instance, an oxidized layer has formed, prejudicing the material’s electrical conductivity. Or because some essential component has segregated from the material or because a new structural phase has been formed, after some specific treatment, like compaction, before measuring its thermoelectric properties. These are all cases where modeling may shed light on unexpected material’s behaviors and be the surge for a search of new approaches to material’s synthesis, if any are possible. But let’s have a more precise insight on which is the role of theory within the project. Basically, from the band structure obtained from a first principles calculation, and using semi-classical Boltzman’s transport theory in its mono-electronic formulation, we may calculate –with some approximation - all quantities defining the electron transport properties of a well defined TM. In fact the Onsager coefficients Li which enter in the definition of sigma and the thermopower S depend on the band energies En and band velocities vn. F0 is the Fermi-Dirac distribution function and mu is the chemical potential, which depend on the T and may be both be evaluated from the knowledge of the band structure. If a constant relaxation time tau is assumed (independent on n and k), all quantities relevant to electronic transport may be evaluated. Within this assumption, S is made independent of the relaxation time and sigma depend linearly on the assumed costant relaxation time. The electronic contribution of the thermal conductivity can be expressed in term of sigma, in accord to the famous Wiedemann-Franz law. Evaluation of the lattice thermal conductivity on the other hand requires a full knowledge of vibrational eigenmodes and frequencies. This was at the moment beyond our computational capabilities. In practice upon substitution and/or doping we can model, predict and rationalize, for an assumed structural model and composition the changes in geometry (cell parameters and fractional coordinates), changes in the electronic structure (band gap, EDDs and their topologies, density of states, band sructure) and related changes in the transport properties outcomes. If a combination of different structures is present in the real material, the measured Seebeck coefficient will be the result of such a mixing. Theory can pick up which is the most beneficial structure and direct the synthesis efforts to increase the percentage of such a structure in the material. How dramatic may be the effect of dopant location on the electronic structure is shown by these DOSS plots for the parent skutterudite (top) , the skutterudite with a Te atom substituting for Sb in a 4 MR pnicogen ring (middle) , and a Te entering in a cubic void of the skutterudite (bottom). The parent is a semiconductor, with a sizeable band gap, the ring-substitued system is a n-doped skutterudite with enhanced electrical conductivity and only slightly worsened Seebeck coefficient, while the system with Te entering in the void behaves mostly as a a metal, with largely enhanced sigma, but with also highly decreased Sebbeck, thus yielding a much worse TM than the original skutterudite. More if needed For instance, a new TM material is synthesized by mixing reagents in given percentages. The material composition and structure may be characterized through diverse techniques (single crystal X-ray diffraction, powder diffraction, neutron diffraction) A thermoelectric evaluation of the TM may be performed. A theoretical modelling of such a material may produce several useful feedbacks: First among these, which is the influence on several parameters (cell geometry, thermochemical stability, electron density, electron transport properties, etc.) of the possible alternative structures that might be thought on the basis of the starting reagents. Second, modeling may help understanding the results of structural characterization, which not always are able to provide clear cut answers, especially so when small amounts of doping elements are present. Furthermore, while structural characterization by the techniques named above yields a space-time averaged information, theory may deconvolute such an information and provide a detailed understanding of the structural, electronic and thermoelectric properties of the different cells composing the structure Third, theory gives a careful description of the kind of chemical interactions existing between the dopant host/s and the framework material, thus suggesting whether alternative dopants and/or structures could be more suited in view of thermoelectric performances. Finally, modeling can predict the optimum doping level for a given, well characterized, reference material, within the frozen band approach. Alternatively, based on the insights sketched above, modeling may suggest new materials to be synthesized, alternative interpretation of structural characterization data, rationalization of hardly interpretable transport properties outcomes. For instance, the Seebeck coefficient values and trends are strongly dependent on where a dopant is actually sitting in the host structure. If a combination of different structures is present in the real material, the measured Seebeck coefficient will be the result of such a mixing. Theory can pick up which is the most beneficial structure and direct the synthesis efforts to increase the percentage of such a structure in the material. In other cases, if the measured transport properties are not in line with theoretical predictions, this might be an indication that the real status of the material is not what is being modeled, because, for instance, an oxidized layer has formed, prejudicing the material’s electrical conductivity. Or because some essential component has segregated from the material or because a new structural phase has been formed, after some specific treatment, like compaction, before measuring its thermoelectric properties. These are all cases where modeling may shed light on unexpected material’s behaviors and be the surge for a search of new approaches to material’s synthesis, if any are possible.

    16. Comprehensive review on Chemical bonding in crystals: new directions http://www.zkristallogr.de C. Gatti, Zeitschrift für Kristallographie, 220, 399-457 (2005) special issue onComputational Crystallography, Artem Oganov Editor, ETH Zürich, CH

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