The following documentation is an evaluation of the two-dimensional Madelung constant for the NaCl structure. The infinite series for the structure is formulted asThe first term in the formula converges to 41n2. The s...The following documentation is an evaluation of the two-dimensional Madelung constant for the NaCl structure. The infinite series for the structure is formulted asThe first term in the formula converges to 41n2. The series after K =2 in the second term is put together with the third term and a constant- 4/ 2 is left. The combination of the third term and the series after K=2 in the second term is assumed to be 8 Sn. The converging series Sn can be solved on a computer. The seven significant figures of the two-dimensional Madelung constant for the NaCl structure is then determined as 1. 615558.展开更多
Surface cell Madelung constant is firstly defined for calculating the surface free energy of nanosized crystal grains, which explains the physical performance of small crystals and may be greatly beneficial to the ana...Surface cell Madelung constant is firstly defined for calculating the surface free energy of nanosized crystal grains, which explains the physical performance of small crystals and may be greatly beneficial to the analysis of surface states and the study of the dynamics of crystal nucleation and growth. A new approximative expression of the surface energy and relevant thermodynamic data are used in this calculation. New formula and computing method for calculating the Madelung constant α of any complex crystals are proposed, and the surface free energies and surface electrostatic energies of nanosized crystal grains and the Madelung constant of some complex crystals are theoretically calculated in this paper. The surface free energy of nanosized-crystal-grain TiO2 and the surface electrostatic energy（absolute value） of nanosized-crystal-grain α-Al2O3 are found to be the biggest among all the crystal grains including those of other species.展开更多
Surface cell Madelung constant is firstly defined in calculating surface free energy of nanosized crystal grains, which explains the physical performance of small crystals and may be great benefit to make surface anal...Surface cell Madelung constant is firstly defined in calculating surface free energy of nanosized crystal grains, which explains the physical performance of small crystals and may be great benefit to make surface analysis and study dynamics of crystal nucleus growth. A new approximative expression of surface energy and relevant thermodynamic data was used in this calculation. A new formula and computing method for calculating the Madelung constant a of any complex crystals is proposed, and surface free energies and surface electrostatic energies of nanosized crystal grains as well as Madelung constant of some complex crystals are theoretically calculated in this paper. The surface free energy of nanosized crystal grain TiO2 and surface electrostatic energy（absolute value） of nanosized crystal grain α-A12O3 are found to be the biggest among other crystal grains.展开更多
In fairly good agreement with the consensus range of dark energy to matter this ratio of the critical density is suggested to be connected with the golden mean φ=0.6180339887, yielding for dark energy to matte...In fairly good agreement with the consensus range of dark energy to matter this ratio of the critical density is suggested to be connected with the golden mean φ=0.6180339887, yielding for dark energy to matter mass fractions .?Assuming the baryonic matter to be only 4.432%, the ratio of matter to baryonic matter would be , and further the ratio of dark matter to baryonic one . If one subtracts from the dark matter a contribution of antimatter with the same mass of baryonic matter, according to the antigravity theories of Villata respectively Hajdukovic, the remaining mass ratio would yield . Replacing the “Madelung” constant α of Villata’s “lattice universe” by φ, one reaches again 1 + φas the ratio of the repulsive mass contribution to the attractive one. Assuming instead of a 3D lattice a flat 2D one of rocksalt type, the numerical similarity between the Madelung constant and φ−1 could not be just coincidence. The proposed scaling of the cosmological mass fractions with the square of the most irrational universal number φmay indicate that the chaotic cosmological processes have reached a quite stable equilibrium. This may be confirmed by another, but similar representation of the mass constituents by the Archimedes’ constant π, giving for respectively for the dark components . However, the intimate connection of φ with its reciprocal may ignite the discussion whether our universe is intertwined with another universe or even part of a multiverse with the dark constituents contributed from there.展开更多
文摘The following documentation is an evaluation of the two-dimensional Madelung constant for the NaCl structure. The infinite series for the structure is formulted asThe first term in the formula converges to 41n2. The series after K =2 in the second term is put together with the third term and a constant- 4/ 2 is left. The combination of the third term and the series after K=2 in the second term is assumed to be 8 Sn. The converging series Sn can be solved on a computer. The seven significant figures of the two-dimensional Madelung constant for the NaCl structure is then determined as 1. 615558.
文摘Surface cell Madelung constant is firstly defined for calculating the surface free energy of nanosized crystal grains, which explains the physical performance of small crystals and may be greatly beneficial to the analysis of surface states and the study of the dynamics of crystal nucleation and growth. A new approximative expression of the surface energy and relevant thermodynamic data are used in this calculation. New formula and computing method for calculating the Madelung constant α of any complex crystals are proposed, and the surface free energies and surface electrostatic energies of nanosized crystal grains and the Madelung constant of some complex crystals are theoretically calculated in this paper. The surface free energy of nanosized-crystal-grain TiO2 and the surface electrostatic energy（absolute value） of nanosized-crystal-grain α-Al2O3 are found to be the biggest among all the crystal grains including those of other species.
文摘Surface cell Madelung constant is firstly defined in calculating surface free energy of nanosized crystal grains, which explains the physical performance of small crystals and may be great benefit to make surface analysis and study dynamics of crystal nucleus growth. A new approximative expression of surface energy and relevant thermodynamic data was used in this calculation. A new formula and computing method for calculating the Madelung constant a of any complex crystals is proposed, and surface free energies and surface electrostatic energies of nanosized crystal grains as well as Madelung constant of some complex crystals are theoretically calculated in this paper. The surface free energy of nanosized crystal grain TiO2 and surface electrostatic energy（absolute value） of nanosized crystal grain α-A12O3 are found to be the biggest among other crystal grains.
文摘In fairly good agreement with the consensus range of dark energy to matter this ratio of the critical density is suggested to be connected with the golden mean φ=0.6180339887, yielding for dark energy to matter mass fractions .?Assuming the baryonic matter to be only 4.432%, the ratio of matter to baryonic matter would be , and further the ratio of dark matter to baryonic one . If one subtracts from the dark matter a contribution of antimatter with the same mass of baryonic matter, according to the antigravity theories of Villata respectively Hajdukovic, the remaining mass ratio would yield . Replacing the “Madelung” constant α of Villata’s “lattice universe” by φ, one reaches again 1 + φas the ratio of the repulsive mass contribution to the attractive one. Assuming instead of a 3D lattice a flat 2D one of rocksalt type, the numerical similarity between the Madelung constant and φ−1 could not be just coincidence. The proposed scaling of the cosmological mass fractions with the square of the most irrational universal number φmay indicate that the chaotic cosmological processes have reached a quite stable equilibrium. This may be confirmed by another, but similar representation of the mass constituents by the Archimedes’ constant π, giving for respectively for the dark components . However, the intimate connection of φ with its reciprocal may ignite the discussion whether our universe is intertwined with another universe or even part of a multiverse with the dark constituents contributed from there.
