Madelung energy | ScienceGate

Ewald's method is reconsidered to express the dependence of Madelung energy on the ionic charges explicitly, also taking into account the space-group symmetry of the structure. Upper bounds for the residues of the two partial series have been calculated by integral approximation; that relative to the direct-lattice series is shown to depend on the cube root of the unit-cell volume. The optimum value of the parameter A, which equalizes the rates of convergence of the two sums and minimizes the total number of terms, has been determined numerically for a given termination error and for a range of unit-cell dimensions. Theoretical results are tested by calculations on some specific crystal structures.

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Systematic Variation between the Madelung Energy and a Crystallographic Ratio in the Alkali Halides

physica status solidi (b) ◽

10.1002/1521-3951(199702)199:2<331::aid-pssb331>3.0.co;2-l ◽

1997 ◽

Vol 199 (2) ◽

pp. 331-334

Author(s):

A.K. Koh

Keyword(s):

Alkali Halides ◽

Systematic Variation ◽

Madelung Energy

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Tight-Binding Formalism for Ionic Fullerides and its Application to Alkali-C60 Polymers

MRS Proceedings ◽

10.1557/proc-491-395 ◽

1997 ◽

Vol 491 ◽

Author(s):

Susumu Saito ◽

Steven G. Louie ◽

Marvin L. Cohen

Keyword(s):

Density Wave ◽

Tight Binding ◽

Stable State ◽

Coulomb Repulsion ◽

Binding Model ◽

Wave State ◽

Madelung Energy ◽

The One ◽

Consistent Treatment ◽

Ionic Lattice

ABSTRACTWe present a tight-binding formalism which can properly treat various ionic füllendes. In the Hamiltonian we include the intrafullerene Coulomb repulsion energy and the Madelung energy of the ionic lattice, both of which depend on the possible charge disproportion between fullerenes. This Hamiltonian requires a self-consistent treatment, but it is applicable to much larger systems than first-principles methods. Using this formalism we have studied the electronic structure of the one-dimensional A1C60 polymer. The present generalization of the tight-binding model is found to be important for ionic füllendes and a moderate-amplitude charge-density-wave state is found to be a possible stable state.

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MADELUNG ENERGY AND STABILITY OF ORDERED LATTICE IN A(B′B″)O3

Modern Physics Letters B ◽

10.1142/s0217984991002161 ◽

1991 ◽

Vol 05 (27) ◽

pp. 1803-1807

Author(s):

QIANG WANG ◽

HAN RUSHAN ◽

Z.Z. GAN

Keyword(s):

Charge Distribution ◽

Structural Stability ◽

Ionic Crystal ◽

Ordered Structure ◽

Charge Distributions ◽

Madelung Energy ◽

Calculation Results ◽

The Difference ◽

Good Agreement

The Madelung energies of ionic crystal A(B′B″)O3 has been calculated for various B-site charge distributions, i.e., [Formula: see text], [Formula: see text] and [Formula: see text], and ordered superlattices, i.e., 1/2(111), 1/2(110) and 1/2(001). Calculation results show that the Madelung energy increases for a certain ordered structure as the difference in charge between B-site cations increases and demonstrate the experimental observations. Furthermore, the results point out that for a certain charge distribution the sequence of the structural stability is 1/2(001)<1/2(110)<1/2(111). This is in good agreement with experimental facts.

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Control of Valence States by a Codoping Method in P-Type GaN Materials

MRS Proceedings ◽

10.1557/proc-468-105 ◽

1997 ◽

Vol 468 ◽

Cited By ~ 2

Author(s):

T. Yamamoto ◽

H. Katayama-Yoshtoa

Keyword(s):

Control Method ◽

Electronic Band Structure ◽

Ionic Charge ◽

Electronic Band ◽

Valence States ◽

Madelung Energy ◽

Valence Control ◽

P Type ◽

Structure Calculations ◽

Codoping Method

ABSTRACTWe propose a new valence control method, the “codoping method (using both n- and p-type dopants at the same time)”, for the fabrication of low-resistivity p-type GaN crystals based on the ab-initio electronic band structure calculations. We have clarified that while doping of acceptor dopants, BeGa and MgGa, leads to destabilization of the ionic charge distributions in p-type GaN crystals, doping of Sica or ON give rise to p-type doped GaN with high doping levels due to a large decrease in the Madelung energy. The codoping of the n- and p-type dopants (the ratio of their concentrations is 1:2) leads to stabilization of the ionic charge distribution inp-type GaN crystals due to a decrease in the Madelung energy, to result in an increase in the net carrier densities.

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