By fitting to a database of ab-initio forces and energies, we can extract pair potentials for all... more By fitting to a database of ab-initio forces and energies, we can extract pair potentials for alloys, with a simple six-parameter analytic form including Friedel oscillations, which give a remarkably faithful account of many complex intermetallic compounds. As examples we show results for (crystal or quasicrystal) structure prediction and phonon spectrum for three systems: Fe--B, Al--Mg--Zn, and Al--Cu--Fe.
We employ first principles total energy and phonon calculations to address the structure and stab... more We employ first principles total energy and phonon calculations to address the structure and stability of Al_2Fe. This structure, which is reported as stable in the assessed Al-Fe phase diagram, is distinguished by an unusually low triclinic symmetry. The initial crystallographic structure determination additionally featured an unusual hole large enough to accommodate an additional atom. Our calculations indicate the hole must be filled, but predict the triclinic structure is unstable relative to a simpler structure based on the prototype MoSi_2. This MoSi_2 structure is interesting because it is predicted to be nonmagnetic, electrically insulating and high density, while the triclinic structure is magnetic, metallic and low density. We reconcile this seeming contradiction by demonstrating a high vibrational entropy that explains why the triclinic structure is stable at high temperatures. Finally, we note that Al_5Fe_2 poses a similar problem of unexplained stability.
Quasicrystals are metal alloys whose noncrystallographic symmetry and lack of structural periodic... more Quasicrystals are metal alloys whose noncrystallographic symmetry and lack of structural periodicity challenge methods of experimental structure determination. Here we employ quantum-based total-energy calculations to predict the structure of a decagonal quasicrystal from first principles considerations. We employ Monte Carlo simulations, taking as input the knowledge that a decagonal phase occurs in Al-Ni-Co near a given composition, and using a few features of the experimental Patterson function. The resulting structure obeys a nearly deterministic decoration of tiles on a hierarchy of length scales related by powers of τ, the golden mean. 1 Al-Ni-Co forms thermodynamically stable and highly perfect decagonal quasicrystalline samples over a range of compositions [1]. Of special interest is the composition Al0.70Ni0.21Co0.09 for which the structure is periodic along the z axis with a period of c = 4.08 ˚A, and quasiperiodic perpendicular to this axis with a characteristic length (t...
We incorporate realistic pair potential energies directly into a non-linear least-square fit of d... more We incorporate realistic pair potential energies directly into a non-linear least-square fit of diffraction data to quantitatively compare structure models with experiment for the Ni-rich d(AlNiCo) quasicrystal. The initial structure models are derived from a few a priori assumptions (gross features of the Patterson function) and the pair potentials. In place of the common hyperspace approach to the structure refinement of quasicrystals, we use a real-space tile decoration scheme, which does not rely on strict quasiperiodicity, and makes it easy to enforce sensible local arrangements of the atoms. Inclusion of the energies provides information complementary to the diffraction data and protects the fit procedure from converging on spurious solutions. The method pinpoints sites which are likely to break the symmetry of their local environment.
We investigate the high temperature decagonal quasicrystalline phase of Al72Ni20Co8 using a quasi... more We investigate the high temperature decagonal quasicrystalline phase of Al72Ni20Co8 using a quasilattice gas Monte-Carlo simulation. To avoid biasing towards a specific model we use an over-dense site list with a large fraction of free sites, permitting the simulation to explore an extended region of perpendicular space. Representing the atomic surface occupancy in a basis of harmonic functions directly reveals the 5-fold symmetric component of our data. Occupancy is examined in physical and perpendicular space.
Abstract. How, in principle, could one solve the atomic structure of a quasicrystal, modeled as a... more Abstract. How, in principle, could one solve the atomic structure of a quasicrystal, modeled as a random tiling decorated by atoms, and what techniques are available to do it? One path is to solve the phase problem first, obtaining the density in a higher dimensional space which yields the averaged scattering density in 3-dimensional space by the usual construction of an incommensurate cut. A novel direct method for this is summarized and applied to an i(AlPdMn) data set. This averaged density falls short of a true structure determination (which would reveal the typical unaveraged atomic patterns.) We discuss the problematic validity of inferring an ideal structure by simply factoring out a “perpspace” Debye-Waller factor, and we test this using simulations of rhombohedral tilings. A second, “unified ” path is to relate the measured and modeled intensities directly, by adjusting parameters in a simulation to optimize the fit. This approach is well suited for unifying structural info...
We identify several new quasicrystal approximants in alloy systems in which quasicrystals have no... more We identify several new quasicrystal approximants in alloy systems in which quasicrystals have not been previously reported. Some occur in alloys with large size contrast between the constituent elements, either containing small Boron atoms, or large Ca/Eu atoms, leading to quasicrystal structures quite different from currently known systems where the size contrast is smaller. Another group of the approximants are layered Frank–Kasper structures, demonstrating competition between decagonal and dodecagonal ordering within this family of structures.
The phase diagram of the Al-Co binary alloy system is intensively studied because of its importan... more The phase diagram of the Al-Co binary alloy system is intensively studied because of its importance for understanding decagonal quasicrystals, but remains imprecisely known due to the occurence of many competing complex structures with composition close to Al13Co4. We apply first-principles total energy calculations to compare the cohesive energies of known and hypothetical structures. Our results confirm the experimentally established phase diagram in every detail except near Al13Co4, where the reported phases (Pearson symbols mC102 and oP102, both well known decagonal quasicrystal approximants) turn out to be unstable at low temperatures. They may be stabilized at high temperatures by the entropy of Aluminum vacancy hopping and low frequency vibrational modes. A subset of Al atoms displays nearly liquid diffusive motion.
We use ab-initio total energy calculations to refine chemical ordering of the W-AlCoNi approximan... more We use ab-initio total energy calculations to refine chemical ordering of the W-AlCoNi approximant structure, and calculate its stability relative to other ternary and binary competing compounds. This approximant structure has 8 Å stacking periodicity along its pseudo-5-fold axis and can be interpreted as stacking of two identical adjacent 4 Å slabs with stacking vector inclined relative to the pseudo-5-fold axis. We generalize this stacking motif to model the 8 Å quasicrystal. Starting with 4 Å slabs forming a “binary” (3-level) decagonal tiling, we introduce tile flips between adjacent slabs analogous to the “octagon” tile-reshuffling update move for binary Penrose tiling. These tile flips lower the total energy, implying 8 Å superorder for the quasicrystal at low temperatures, consistent with experiment
We investigate the atomic surface structure of the high temperature decagonal quasicrystalline ph... more We investigate the atomic surface structure of the high temperature decagonal quasicrystalline phase of Al72Ni20Co8 using a lattice gas Monte-Carlo simulation. To avoid biasing towards a specific model we use an over-dense site list with a large fraction of free sites, permitting the simulation to explore an extended region of perpendicular space. Representing the atomic surface occupancy in a basis of harmonic functions aids our analysis by directly revealing the 5-fold symmetric component of our data. Patterns of occupancy are examined in both physical (“parallel”) and perpendicular space, and compared with experiment in both cases. Additionally we compute the Patterson function representing correlations among atomic positions. Our results yield atomic surface structure with smooth variation of occupation and chemistry. Short distances in this model are avoided through correlations among partially occupied sites. The model naturally incorporates both an idealized average structure...
We investigate the high temperature decagonal quasicrystalline phase of Al72Ni20Co8 using a quasi... more We investigate the high temperature decagonal quasicrystalline phase of Al72Ni20Co8 using a quasilattice gas Monte-Carlo simulation. To avoid biasing towards a specific model we use an over-dense site list with a large fraction of free sites, permitting the simulation to explore an extended region of perpendicular space. Representing the atomic surface occupancy in a basis of harmonic functions directly reveals the 5-fold symmetric component of our data. Occupancy is examined in physical and perpendicular space.
By fitting to a database of ab-initio forces and energies, we can extract pair potentials for all... more By fitting to a database of ab-initio forces and energies, we can extract pair potentials for alloys, with a simple six-parameter analytic form including Friedel oscillations, which give a remarkably faithful account of many complex intermetallic compounds. As examples we show results for (crystal or quasicrystal) structure prediction and phonon spectrum for three systems: Fe--B, Al--Mg--Zn, and Al--Cu--Fe.
We employ first principles total energy and phonon calculations to address the structure and stab... more We employ first principles total energy and phonon calculations to address the structure and stability of Al_2Fe. This structure, which is reported as stable in the assessed Al-Fe phase diagram, is distinguished by an unusually low triclinic symmetry. The initial crystallographic structure determination additionally featured an unusual hole large enough to accommodate an additional atom. Our calculations indicate the hole must be filled, but predict the triclinic structure is unstable relative to a simpler structure based on the prototype MoSi_2. This MoSi_2 structure is interesting because it is predicted to be nonmagnetic, electrically insulating and high density, while the triclinic structure is magnetic, metallic and low density. We reconcile this seeming contradiction by demonstrating a high vibrational entropy that explains why the triclinic structure is stable at high temperatures. Finally, we note that Al_5Fe_2 poses a similar problem of unexplained stability.
Quasicrystals are metal alloys whose noncrystallographic symmetry and lack of structural periodic... more Quasicrystals are metal alloys whose noncrystallographic symmetry and lack of structural periodicity challenge methods of experimental structure determination. Here we employ quantum-based total-energy calculations to predict the structure of a decagonal quasicrystal from first principles considerations. We employ Monte Carlo simulations, taking as input the knowledge that a decagonal phase occurs in Al-Ni-Co near a given composition, and using a few features of the experimental Patterson function. The resulting structure obeys a nearly deterministic decoration of tiles on a hierarchy of length scales related by powers of τ, the golden mean. 1 Al-Ni-Co forms thermodynamically stable and highly perfect decagonal quasicrystalline samples over a range of compositions [1]. Of special interest is the composition Al0.70Ni0.21Co0.09 for which the structure is periodic along the z axis with a period of c = 4.08 ˚A, and quasiperiodic perpendicular to this axis with a characteristic length (t...
We incorporate realistic pair potential energies directly into a non-linear least-square fit of d... more We incorporate realistic pair potential energies directly into a non-linear least-square fit of diffraction data to quantitatively compare structure models with experiment for the Ni-rich d(AlNiCo) quasicrystal. The initial structure models are derived from a few a priori assumptions (gross features of the Patterson function) and the pair potentials. In place of the common hyperspace approach to the structure refinement of quasicrystals, we use a real-space tile decoration scheme, which does not rely on strict quasiperiodicity, and makes it easy to enforce sensible local arrangements of the atoms. Inclusion of the energies provides information complementary to the diffraction data and protects the fit procedure from converging on spurious solutions. The method pinpoints sites which are likely to break the symmetry of their local environment.
We investigate the high temperature decagonal quasicrystalline phase of Al72Ni20Co8 using a quasi... more We investigate the high temperature decagonal quasicrystalline phase of Al72Ni20Co8 using a quasilattice gas Monte-Carlo simulation. To avoid biasing towards a specific model we use an over-dense site list with a large fraction of free sites, permitting the simulation to explore an extended region of perpendicular space. Representing the atomic surface occupancy in a basis of harmonic functions directly reveals the 5-fold symmetric component of our data. Occupancy is examined in physical and perpendicular space.
Abstract. How, in principle, could one solve the atomic structure of a quasicrystal, modeled as a... more Abstract. How, in principle, could one solve the atomic structure of a quasicrystal, modeled as a random tiling decorated by atoms, and what techniques are available to do it? One path is to solve the phase problem first, obtaining the density in a higher dimensional space which yields the averaged scattering density in 3-dimensional space by the usual construction of an incommensurate cut. A novel direct method for this is summarized and applied to an i(AlPdMn) data set. This averaged density falls short of a true structure determination (which would reveal the typical unaveraged atomic patterns.) We discuss the problematic validity of inferring an ideal structure by simply factoring out a “perpspace” Debye-Waller factor, and we test this using simulations of rhombohedral tilings. A second, “unified ” path is to relate the measured and modeled intensities directly, by adjusting parameters in a simulation to optimize the fit. This approach is well suited for unifying structural info...
We identify several new quasicrystal approximants in alloy systems in which quasicrystals have no... more We identify several new quasicrystal approximants in alloy systems in which quasicrystals have not been previously reported. Some occur in alloys with large size contrast between the constituent elements, either containing small Boron atoms, or large Ca/Eu atoms, leading to quasicrystal structures quite different from currently known systems where the size contrast is smaller. Another group of the approximants are layered Frank–Kasper structures, demonstrating competition between decagonal and dodecagonal ordering within this family of structures.
The phase diagram of the Al-Co binary alloy system is intensively studied because of its importan... more The phase diagram of the Al-Co binary alloy system is intensively studied because of its importance for understanding decagonal quasicrystals, but remains imprecisely known due to the occurence of many competing complex structures with composition close to Al13Co4. We apply first-principles total energy calculations to compare the cohesive energies of known and hypothetical structures. Our results confirm the experimentally established phase diagram in every detail except near Al13Co4, where the reported phases (Pearson symbols mC102 and oP102, both well known decagonal quasicrystal approximants) turn out to be unstable at low temperatures. They may be stabilized at high temperatures by the entropy of Aluminum vacancy hopping and low frequency vibrational modes. A subset of Al atoms displays nearly liquid diffusive motion.
We use ab-initio total energy calculations to refine chemical ordering of the W-AlCoNi approximan... more We use ab-initio total energy calculations to refine chemical ordering of the W-AlCoNi approximant structure, and calculate its stability relative to other ternary and binary competing compounds. This approximant structure has 8 Å stacking periodicity along its pseudo-5-fold axis and can be interpreted as stacking of two identical adjacent 4 Å slabs with stacking vector inclined relative to the pseudo-5-fold axis. We generalize this stacking motif to model the 8 Å quasicrystal. Starting with 4 Å slabs forming a “binary” (3-level) decagonal tiling, we introduce tile flips between adjacent slabs analogous to the “octagon” tile-reshuffling update move for binary Penrose tiling. These tile flips lower the total energy, implying 8 Å superorder for the quasicrystal at low temperatures, consistent with experiment
We investigate the atomic surface structure of the high temperature decagonal quasicrystalline ph... more We investigate the atomic surface structure of the high temperature decagonal quasicrystalline phase of Al72Ni20Co8 using a lattice gas Monte-Carlo simulation. To avoid biasing towards a specific model we use an over-dense site list with a large fraction of free sites, permitting the simulation to explore an extended region of perpendicular space. Representing the atomic surface occupancy in a basis of harmonic functions aids our analysis by directly revealing the 5-fold symmetric component of our data. Patterns of occupancy are examined in both physical (“parallel”) and perpendicular space, and compared with experiment in both cases. Additionally we compute the Patterson function representing correlations among atomic positions. Our results yield atomic surface structure with smooth variation of occupation and chemistry. Short distances in this model are avoided through correlations among partially occupied sites. The model naturally incorporates both an idealized average structure...
We investigate the high temperature decagonal quasicrystalline phase of Al72Ni20Co8 using a quasi... more We investigate the high temperature decagonal quasicrystalline phase of Al72Ni20Co8 using a quasilattice gas Monte-Carlo simulation. To avoid biasing towards a specific model we use an over-dense site list with a large fraction of free sites, permitting the simulation to explore an extended region of perpendicular space. Representing the atomic surface occupancy in a basis of harmonic functions directly reveals the 5-fold symmetric component of our data. Occupancy is examined in physical and perpendicular space.
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Papers by M. Mihalkovič