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H.p. Bonzel - One of the best experts on this subject based on the ideXlab platform.
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the three dimensional Equilibrium Crystal shape of pb recent results of theory and experiment
Applied Physics A, 2007Co-Authors: H.p. Bonzel, Matthias SchefflerAbstract:The three-dimensional Equilibrium Crystal shape (ECS) is constructed from a set of 35 orientation-dependent surface energies of fcc Pb which are calculated by density functional theory in the local-density approximation and distributed over the [110] and [001] zones of the stereographic triangle. Surface relaxation has a pronounced influence on the Equilibrium shape. The (111), (100), (110), (211), (221), (411), (665), (15,1,1), (410) and (320) facets are present after relaxation of all considered surfaces, while only the low-index facets (111), (100) and (110) exist for the unrelaxed ECS. The result for the relaxed Pb Crystal state is in support of the experimental ECS of Pb at 320–350 K. On the other hand, approximating the surface energies of vicinal surfaces by assuming a linear relationship between the Pb(111) first-principles surface energy and the number of broken bonds of surface atoms leads to a trivial ECS that shows only (111) and (100) facets, with a sixfold symmetric (111) facet instead of the correct threefold symmetry. It is concluded that the broken bond rule in this simple linear form is not a suitable approximation for obtaining the proper three-dimensional ECS and correct step formation energies.
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the stability of vicinal surfaces and the Equilibrium Crystal shape of pb by first principles theory
New Journal of Physics, 2006Co-Authors: H.p. Bonzel, Matthias SchefflerAbstract:The orientation-dependent surface energies of fcc Pb for more than 30 vicinal orientations, distributed over the (110) and (001) zones of the stereographic triangle, have been studied by density-functional theory. For bulk-truncated structures almost all vicinal surfaces are found to be unstable and would facet into (111) and (100) orientations. However, after surface relaxation, all vicinal surfaces are stable relative to faceting into (111) and (100) orientations. There are also regions of relaxed vicinal surfaces which will facet into nearby stable vicinal surfaces. Overall, surface relaxation significantly affects the Equilibrium Crystal shape (ECS) of Pb. In both the (110) and (001) Crystallographic zones the (110), (112), (221), and (023) facets are found on the ECS only after relaxation, in addition to (111) and (100). This result is in agreement with the experimental ECS of Pb at 353 K. Step formation energies for various vicinal orientations are estimated from facet diameters of the theoretical ECS and compared with experimental data.
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3d Equilibrium Crystal shapes of pb the significance of step resolved images
Progress in Surface Science, 2003Co-Authors: M. Nowicki, A. Emundts, H.p. BonzelAbstract:Abstract Scanning tunnelling microscopy has proven to be an extremely useful technique for imaging small Crystallites equilibrated at elevated temperature. As an example, we review recent work on three-dimensional Pb Crystallites of 1–2 μm diameter, supported on Ru(0 0 1). Large (1 1 1) facets and, depending on temperature, small (1 1 2) facets were observed in the top section of the Crystallites. The temperature dependent facet anisotropy was analyzed to yield the absolute step free energies of Pb(1 1 1) vicinal steps. The vicinal region close to the (1 1 1) facet was studied in detail to determine the shape exponent, the step–step interaction energy and the constant of the dipole interaction potential. Boundary conditions of the evaluated vicinal region have been specified for proving the universality of shapes, characterized by the exponent of 3/2, which is clear evidence for the 1/ x 2 step interaction potential. The role of the activation barrier for facet growth or shrinkage is discussed in the context of attaining 3D Equilibrium of Crystallites. A comparative study of Crystallites with defect-free and dislocated facets shows significant differences, providing direct evidence of the activation barrier. Reliable step–step interaction energies were obtained for dislocated Crystallites. Extrapolating the temperature dependent total step interaction energy to 0 K yields for the first time values of the structure dependent dipole–dipole step interaction energies of A- and B-steps.
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3D Equilibrium Crystal shapes in the new light of STM and AFM
Physics Reports, 2003Co-Authors: H.p. BonzelAbstract:Abstract A systematic study of 3D Equilibrium Crystal shapes (ECS) can yield important surface energetic quantities, such as step, kink, surface and step–step interaction free energies. Observations of the ECS, especially of flat facets and adjacent vicinal regions, will provide primarily relative step and surface free energies. An advanced goal is to determine absolute step free energies, kink formation and step interaction energies. Absolute values of these energies are important in governing Crystal growth morphologies, high temperature phase changes and kinetic processes associated with shape changes. Furthermore, absolute step and kink energies are the key to absolute surface free energies of well defined low-index orientations. We review new experiments where sections of the ECS are monitored as a function of temperature to extract characteristic morphological parameters, yielding absolute surface energetic quantities. Attention will be paid to the question of attaining true 3D Equilibrium of an ensemble of Crystallites. The special role of scanning tunneling and atomic force microscopies will be stressed. New ways of overcoming the problem of the activation barrier for facet growth (or shrinkage) through the study of dislocated Crystallites will be demonstrated. In the general context of 3D Crystallites, the study of 2D nano-Crystals, in the form of adatom or vacancy islands on extended flat surfaces, will be discussed. In particular, the connection between the temperature dependent shape of 2D islands and the absolute step and kink formation energies of the bounding steps, complementary to facet shape changes of 3D Crystallites, has emerged as an important topic of recent research. Finally, high temperature phase changes, such as surface roughening and surface melting, as they have been observed by scanning electron microscopy on 3D Crystallites, will be briefly reviewed.
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3D Equilibrium Crystal shapes in the new light of STM and AFM
Physics Reports, 2003Co-Authors: H.p. BonzelAbstract:A systematic study of 3D Equilibrium Crystal shapes (ECS) can yield important surface energetic quantities, such as step, kink, surface and step-step interaction free energies. Observations of the ECS, especially of flat facets and adjacent vicinal regions, will provide primarily relative step and surface free energies. An advanced goal is to determine absolute step free energies, kink formation and step interaction energies. Absolute values of these energies are important in governing Crystal growth morphologies, high temperature phase changes and kinetic processes associated with shape changes. Furthermore, absolute step and kink energies are the key to absolute surface free energies of well defined low-index orientations. We review new experiments where sections of the ECS are monitored as a function of temperature to extract characteristic morphological parameters, yielding absolute surface energetic quantities. Attention will be paid to the question of attaining true 3D Equilibrium of an ensemble of Crystallites. The special role of scanning tunneling and atomic force microscopies will be stressed. New ways of overcoming the problem of the activation barrier for facet growth (or shrinkage) through the study of dislocated Crystallites will be demonstrated. In the general context of 3D Crystallites, the study of 2D nano-Crystals, in the form of adatom or vacancy islands on extended flat surfaces, will be discussed. In particular, the connection between the temperature dependent shape of 2D islands and the absolute step and kink formation energies of the bounding steps, complementary to facet shape changes of 3D Crystallites, has emerged as an important topic of recent research. Finally, high temperature phase changes, such as surface roughening and surface melting, as they have been observed by scanning electron microscopy on 3D Crystallites, will be briefly reviewed. (C) 2003 Published by Elsevier B.V
Wolfgang Rheinheimer - One of the best experts on this subject based on the ideXlab platform.
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grain growth in nio mgo and its dependence on faceting and the Equilibrium Crystal shape
Scripta Materialia, 2020Co-Authors: Wolfgang Rheinheimer, David Lowing, John E BlendellAbstract:Abstract The impact of faceting on grain growth was approached by model experiments in NiO–MgO. Grain growth rates were found to be 10 times higher in NiO compared to MgO. As the self-diffusion acoefficients differ by a factor of 250, grain growth in NiO is unexpectedly slow compared to MgO. Recently, the movement of steps was identified as the atomic mechanism of grain boundary migration. According to the Equilibrium Crystal shape, grain boundaries in NiO are more faceted. The faceted grain boundaries of NiO have fewer steps at the grain boundaries resulting in a relatively lower mobility.
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Grain growth in Nio–MgO and its dependence on faceting and the Equilibrium Crystal shape
Scripta Materialia, 2020Co-Authors: Wolfgang Rheinheimer, David Lowing, John E BlendellAbstract:Abstract The impact of faceting on grain growth was approached by model experiments in NiO–MgO. Grain growth rates were found to be 10 times higher in NiO compared to MgO. As the self-diffusion acoefficients differ by a factor of 250, grain growth in NiO is unexpectedly slow compared to MgO. Recently, the movement of steps was identified as the atomic mechanism of grain boundary migration. According to the Equilibrium Crystal shape, grain boundaries in NiO are more faceted. The faceted grain boundaries of NiO have fewer steps at the grain boundaries resulting in a relatively lower mobility.
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Equilibrium and kinetic shapes of grains in polyCrystals
Acta Materialia, 2020Co-Authors: Wolfgang Rheinheimer, John E Blendell, Carol A HandwerkerAbstract:Abstract The Equilibrium Crystal shape is a convex shape bound by the lowest energy interfaces. In many polyCrystalline microstructures created by grain growth, the observed distribution of grain boundary planes appears to be dominated at low driving forces (after long grain growth times) by the planes present in the Equilibrium Crystal shape. However, at earlier stages of grain growth, it is expected that kinetic effects will play an important role in grain boundary motion and morphology. Analogous to the Equilibrium Crystal shape, the kinetic Crystal shape of seed Crystals growing from a liquid at higher supersaturations is bound by the slowest growing orientations. This study presents an equivalent construction for grain boundaries in polyCrystals and uses it to determine the kinetic Crystal shape for strontium titanate as a function of temperature. Relative grain boundary mobilities for strontium titanate for the low energy Crystallographic orientations from seeded polyCrystal experiments are used to calculate the kinetic Crystal shapes as a function of temperature and annealing atmosphere. The kinetic Crystal shapes are then compared to the morphologies and orientations of the interfaces of the growing seed Crystals, and to the Equilibrium Crystal shapes, as well. The conclusions are that (1) the kinetic Crystal shape is extremely anisotropic and displays significant transitions as a function of temperature that do not mirror changes in Equilibrium Crystal shape, (2) the kinetic shapes observed in the microstructures are dominated by the growing side of the interface (single Crystal) and not by the dissolving side (polyCrystalline matrix), and (3) faster growing orientations break up into macroscopic facets composed of slower growing orientations. The implications for grain growth underscore the applicability of Crystal growth models to grain growth in polyCrystals. In particular, in strontium titanate, the anisotropy of the grain boundary mobility as represented in the kinetic Crystal shape is expected to be reduced from five macroscopic parameters to two (interface normal) allowing for incorporation of growth rate anisotropy in simulations of microstructure evolution at the earliest stages of grain growth, i.e. at the highest driving forces.
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The Equilibrium Crystal shape of strontium titanate: Impact of donor doping
Scripta Materialia, 2017Co-Authors: Wolfgang Rheinheimer, Fabian J. Altermann, Michael J. HoffmannAbstract:Abstract The present study investigates the impact of point defect concentrations on the Equilibrium Crystal shape of strontium titanate. Therefore the shape of intergranular pores in coarse microstructures was observed. The point defect concentration was changed by donor-doping with Niobium (0.2 at.%–2.4 at.%). A decreasing surface energy anisotropy was found with increasing donor dopant concentration and with increasing temperature. These findings are correlated to the defect chemistry and grain growth behavior of strontium titanate.
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the Equilibrium Crystal shape of strontium titanate and its relationship to the grain boundary plane distribution
Acta Materialia, 2015Co-Authors: Wolfgang Rheinheimer, Gregory S Rohrer, John E Blendell, Michael Baurer, Harry Chien, Carol A Handwerker, Michael J. HoffmannAbstract:In this study, the Equilibrium Crystal shape (ECS) of a model system, strontium titanate, is compared with the grain boundary plane distribution (GBPD) as a function of temperature. Strontium titanate has a pronounced surface energy anisotropy and a grain growth anomaly, with the grain growth rate decreasing by orders of magnitude with increasing temperature. The ECS was determined from the shape of small intragranular pores and the GBPD was determined from orientation measurements on surfaces, with the relative areas of grain boundary planes in a polyCrystal correlated to the surface energy of both adjacent Crystal planes. The grain boundary energy has been previously proposed to be the sum of the surface energy of the adjacent grains less a binding energy that is assumed to be constant. While much experimental evidence exists for this assumption at a fixed temperature, the influence of temperature is not known. While the anisotropy of the ECS was found to decrease with temperature, the anisotropy of the GBPD increased with temperature. These findings indicate that changes in the binding energy with temperature must be considered, as the binding energy links the surface energy to the grain boundary energy. The results are discussed with respect to the grain growth anomaly of strontium titanate, in which the grain growth decreases with increasing temperature.
Michael J. Hoffmann - One of the best experts on this subject based on the ideXlab platform.
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The Equilibrium Crystal shape of strontium titanate: Impact of donor doping
Scripta Materialia, 2017Co-Authors: Wolfgang Rheinheimer, Fabian J. Altermann, Michael J. HoffmannAbstract:Abstract The present study investigates the impact of point defect concentrations on the Equilibrium Crystal shape of strontium titanate. Therefore the shape of intergranular pores in coarse microstructures was observed. The point defect concentration was changed by donor-doping with Niobium (0.2 at.%–2.4 at.%). A decreasing surface energy anisotropy was found with increasing donor dopant concentration and with increasing temperature. These findings are correlated to the defect chemistry and grain growth behavior of strontium titanate.
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the Equilibrium Crystal shape of strontium titanate and its relationship to the grain boundary plane distribution
Acta Materialia, 2015Co-Authors: Wolfgang Rheinheimer, Gregory S Rohrer, John E Blendell, Michael Baurer, Harry Chien, Carol A Handwerker, Michael J. HoffmannAbstract:In this study, the Equilibrium Crystal shape (ECS) of a model system, strontium titanate, is compared with the grain boundary plane distribution (GBPD) as a function of temperature. Strontium titanate has a pronounced surface energy anisotropy and a grain growth anomaly, with the grain growth rate decreasing by orders of magnitude with increasing temperature. The ECS was determined from the shape of small intragranular pores and the GBPD was determined from orientation measurements on surfaces, with the relative areas of grain boundary planes in a polyCrystal correlated to the surface energy of both adjacent Crystal planes. The grain boundary energy has been previously proposed to be the sum of the surface energy of the adjacent grains less a binding energy that is assumed to be constant. While much experimental evidence exists for this assumption at a fixed temperature, the influence of temperature is not known. While the anisotropy of the ECS was found to decrease with temperature, the anisotropy of the GBPD increased with temperature. These findings indicate that changes in the binding energy with temperature must be considered, as the binding energy links the surface energy to the grain boundary energy. The results are discussed with respect to the grain growth anomaly of strontium titanate, in which the grain growth decreases with increasing temperature.
Matthias Scheffler - One of the best experts on this subject based on the ideXlab platform.
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the three dimensional Equilibrium Crystal shape of pb recent results of theory and experiment
Applied Physics A, 2007Co-Authors: H.p. Bonzel, Matthias SchefflerAbstract:The three-dimensional Equilibrium Crystal shape (ECS) is constructed from a set of 35 orientation-dependent surface energies of fcc Pb which are calculated by density functional theory in the local-density approximation and distributed over the [110] and [001] zones of the stereographic triangle. Surface relaxation has a pronounced influence on the Equilibrium shape. The (111), (100), (110), (211), (221), (411), (665), (15,1,1), (410) and (320) facets are present after relaxation of all considered surfaces, while only the low-index facets (111), (100) and (110) exist for the unrelaxed ECS. The result for the relaxed Pb Crystal state is in support of the experimental ECS of Pb at 320–350 K. On the other hand, approximating the surface energies of vicinal surfaces by assuming a linear relationship between the Pb(111) first-principles surface energy and the number of broken bonds of surface atoms leads to a trivial ECS that shows only (111) and (100) facets, with a sixfold symmetric (111) facet instead of the correct threefold symmetry. It is concluded that the broken bond rule in this simple linear form is not a suitable approximation for obtaining the proper three-dimensional ECS and correct step formation energies.
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the stability of vicinal surfaces and the Equilibrium Crystal shape of pb by first principles theory
New Journal of Physics, 2006Co-Authors: H.p. Bonzel, Matthias SchefflerAbstract:The orientation-dependent surface energies of fcc Pb for more than 30 vicinal orientations, distributed over the (110) and (001) zones of the stereographic triangle, have been studied by density-functional theory. For bulk-truncated structures almost all vicinal surfaces are found to be unstable and would facet into (111) and (100) orientations. However, after surface relaxation, all vicinal surfaces are stable relative to faceting into (111) and (100) orientations. There are also regions of relaxed vicinal surfaces which will facet into nearby stable vicinal surfaces. Overall, surface relaxation significantly affects the Equilibrium Crystal shape (ECS) of Pb. In both the (110) and (001) Crystallographic zones the (110), (112), (221), and (023) facets are found on the ECS only after relaxation, in addition to (111) and (100). This result is in agreement with the experimental ECS of Pb at 353 K. Step formation energies for various vicinal orientations are estimated from facet diameters of the theoretical ECS and compared with experimental data.
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gaas Equilibrium Crystal shape from first principles
Physical Review B, 1996Co-Authors: Nikolaj Moll, Alexander Kley, Eckard Pehlke, Matthias SchefflerAbstract:Surface energies for different GaAs surface orientations have been calculated as a function of the chemical potential. We use an energy density formalism within the first-principles pseudopotential density-functional approach. The Equilibrium Crystal shape has been derived from the surface energies for the (110), (100), (111), and (1\ifmmode\bar\else\textasciimacron\fi{} 1\ifmmode\bar\else\textasciimacron\fi{} 1\ifmmode\bar\else\textasciimacron\fi{}) orientations. Under As-rich conditions all four considered surface orientations exist in thermodynamic Equilibrium, in agreement with experimental observations. Moreover, our calculations allow us to decide on previous contradictory theoretical values for the surface energies of the (111) and (1\ifmmode\bar\else\textasciimacron\fi{} 1\ifmmode\bar\else\textasciimacron\fi{} 1\ifmmode\bar\else\textasciimacron\fi{}) facets. \textcopyright{} 1996 The American Physical Society.
John E Blendell - One of the best experts on this subject based on the ideXlab platform.
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grain growth in nio mgo and its dependence on faceting and the Equilibrium Crystal shape
Scripta Materialia, 2020Co-Authors: Wolfgang Rheinheimer, David Lowing, John E BlendellAbstract:Abstract The impact of faceting on grain growth was approached by model experiments in NiO–MgO. Grain growth rates were found to be 10 times higher in NiO compared to MgO. As the self-diffusion acoefficients differ by a factor of 250, grain growth in NiO is unexpectedly slow compared to MgO. Recently, the movement of steps was identified as the atomic mechanism of grain boundary migration. According to the Equilibrium Crystal shape, grain boundaries in NiO are more faceted. The faceted grain boundaries of NiO have fewer steps at the grain boundaries resulting in a relatively lower mobility.
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Grain growth in Nio–MgO and its dependence on faceting and the Equilibrium Crystal shape
Scripta Materialia, 2020Co-Authors: Wolfgang Rheinheimer, David Lowing, John E BlendellAbstract:Abstract The impact of faceting on grain growth was approached by model experiments in NiO–MgO. Grain growth rates were found to be 10 times higher in NiO compared to MgO. As the self-diffusion acoefficients differ by a factor of 250, grain growth in NiO is unexpectedly slow compared to MgO. Recently, the movement of steps was identified as the atomic mechanism of grain boundary migration. According to the Equilibrium Crystal shape, grain boundaries in NiO are more faceted. The faceted grain boundaries of NiO have fewer steps at the grain boundaries resulting in a relatively lower mobility.
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Equilibrium and kinetic shapes of grains in polyCrystals
Acta Materialia, 2020Co-Authors: Wolfgang Rheinheimer, John E Blendell, Carol A HandwerkerAbstract:Abstract The Equilibrium Crystal shape is a convex shape bound by the lowest energy interfaces. In many polyCrystalline microstructures created by grain growth, the observed distribution of grain boundary planes appears to be dominated at low driving forces (after long grain growth times) by the planes present in the Equilibrium Crystal shape. However, at earlier stages of grain growth, it is expected that kinetic effects will play an important role in grain boundary motion and morphology. Analogous to the Equilibrium Crystal shape, the kinetic Crystal shape of seed Crystals growing from a liquid at higher supersaturations is bound by the slowest growing orientations. This study presents an equivalent construction for grain boundaries in polyCrystals and uses it to determine the kinetic Crystal shape for strontium titanate as a function of temperature. Relative grain boundary mobilities for strontium titanate for the low energy Crystallographic orientations from seeded polyCrystal experiments are used to calculate the kinetic Crystal shapes as a function of temperature and annealing atmosphere. The kinetic Crystal shapes are then compared to the morphologies and orientations of the interfaces of the growing seed Crystals, and to the Equilibrium Crystal shapes, as well. The conclusions are that (1) the kinetic Crystal shape is extremely anisotropic and displays significant transitions as a function of temperature that do not mirror changes in Equilibrium Crystal shape, (2) the kinetic shapes observed in the microstructures are dominated by the growing side of the interface (single Crystal) and not by the dissolving side (polyCrystalline matrix), and (3) faster growing orientations break up into macroscopic facets composed of slower growing orientations. The implications for grain growth underscore the applicability of Crystal growth models to grain growth in polyCrystals. In particular, in strontium titanate, the anisotropy of the grain boundary mobility as represented in the kinetic Crystal shape is expected to be reduced from five macroscopic parameters to two (interface normal) allowing for incorporation of growth rate anisotropy in simulations of microstructure evolution at the earliest stages of grain growth, i.e. at the highest driving forces.
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the Equilibrium Crystal shape of strontium titanate and its relationship to the grain boundary plane distribution
Acta Materialia, 2015Co-Authors: Wolfgang Rheinheimer, Gregory S Rohrer, John E Blendell, Michael Baurer, Harry Chien, Carol A Handwerker, Michael J. HoffmannAbstract:In this study, the Equilibrium Crystal shape (ECS) of a model system, strontium titanate, is compared with the grain boundary plane distribution (GBPD) as a function of temperature. Strontium titanate has a pronounced surface energy anisotropy and a grain growth anomaly, with the grain growth rate decreasing by orders of magnitude with increasing temperature. The ECS was determined from the shape of small intragranular pores and the GBPD was determined from orientation measurements on surfaces, with the relative areas of grain boundary planes in a polyCrystal correlated to the surface energy of both adjacent Crystal planes. The grain boundary energy has been previously proposed to be the sum of the surface energy of the adjacent grains less a binding energy that is assumed to be constant. While much experimental evidence exists for this assumption at a fixed temperature, the influence of temperature is not known. While the anisotropy of the ECS was found to decrease with temperature, the anisotropy of the GBPD increased with temperature. These findings indicate that changes in the binding energy with temperature must be considered, as the binding energy links the surface energy to the grain boundary energy. The results are discussed with respect to the grain growth anomaly of strontium titanate, in which the grain growth decreases with increasing temperature.
