The Madelung Function of Elpasolites

Marx, V.; Hundhammer, B.

doi:10.1515/znb-2000-1007

Cited by 3 publications

(6 citation statements)

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“…In order to illustrate this, we consider the case of K 2 NaScF 6 , an example of the ternary mineral type elpasolite. 15, 16 Marx has determined the enthalpy of formation from a Born−Haber−Fajans thermochemical cycle, 15 using the enthalpic properties of the individual ions, as −3397.6 kJ mol −1 , and has calculated a corresponding lattice energy of 8162.2 kJ mol −1 , using a Buckingham potential. However, it is of interest to also consider this material as a mixture of 2K + , Na + , and Figure 3 shows the two options in a thermochemical cycle diagram.…”

Section: ■ Madelung Energies Of Complex Ionsmentioning

confidence: 99%

Simple Route to Lattice Energies in the Presence of Complex Ions

Glasser

2012

Inorg. Chem.

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Lattice energies for ionic materials which separate into independent gaseous ions can be calculated by standard Born-Haber-Fajans thermochemical cycle procedures, based on the energies of formation of those ions. However, if complex ions (such as sulfates) occur in the material, then a sophisticated calculation procedure must be invoked which requires allocation of the total ion charge among the atom components of the complex ion and evaluation of the attractive and repulsive energy terms. If, instead, the total ion charge is allocated to the central atom of the complex ion (with zero charge on the coordinated atoms), to create a "condensed charge ion" (having zero self-energy), then a straightforward calculation of the electrostatic (Madelung) energy, E(M)', correlates well with published lattice energies: U(POT)/kJ mol(-1) = 0.963E(M)', with a correlation coefficient, R(2) = 0.976. E(M)' is here termed the "condensed charge" electrostatic (Madelung) energy. Thus, using the condensed charge ion model, we observe that a roughly constant proportion (∼96%) of the corresponding lattice energy arises from the electrostatic interaction terms. The above equation permits ready evaluation of lattice energies for ionic crystal structures containing complex ions, without the necessity to estimate any of the problematic nonelectrostatic interaction terms. A commentary by Prof. H. D. B. Jenkins substantiating this analysis is appended.

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Section: ■ Madelung Energies Of Complex Ionsmentioning

confidence: 99%

Simple Route to Lattice Energies in the Presence of Complex Ions

Glasser

2012

Inorg. Chem.

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“…In this current work, and for illustrative purposes, we have chosen the method due to Ewald 4,5 . 6,7,8 In this model, of rigid spheres, in the case of a MX type crystal, the distance…”

Section: The Coulombic Potentialmentioning

confidence: 99%

“…, , NaLnBr Cs NaLnCl Cs NaLnF Cs , 6 2 NaLnF Rb and 6 2 KLnF Cs in the m Fm3 space group. A substantial amount of theoretical models have been analyzed and several computing simulations have been undertaken to estimate the reticular energies and the corresponding heat of formation for these crystals.…”

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confidence: 99%

On the theory of interaction potentials in ionic crystals

Acevedo¹,

Soto-Bubert

2008

J. Phys.: Conf. Ser.

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Abstract. The aim of this research work is to report a more comprehensive and detailed study of both, the intermolecular and intramolecular potencial functions with reference to the various families of the elpasolite type crystals. The cohesive energy has been thought as a sum of three terms; the long range (Coulombic), the Born and the van der Waals contributions to the total energy. The Born-Mayer-Buckingham potential 1 has been employed in all of these current studies and a number of convergence tests are analyzed from a formal viewpoint. Our work has been focused to the following systems: theoretical models have been analyzed and several computing simulations have been undertaken to estimate the reticular energies and the corresponding heat of formation for these crystals. To achieve this goal, a Born-Haber thermodynamic cycle has been introduced in our model. It is shown that the calculated energy values are reasonable and follow the expected trend along the lanthanide series in the periodic chart. We also discuss the advantages and disadvantages of the current and proposed generalized model. The most likely sources for improvement are discussed in detail. New convergence tests as well as some master equations have been introduced to study the various diagonal contributions to the total energy.

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“…In a pioneer work, Madelung 5 put forward a model to estimate the constant named after him, modeling the ionic crystal as periodic array of alternate charges in two and three dimensions covering the whole physical space. There have also been alternative schemes due to other workers to pursue the same objective 6–9 . Some of these research efforts are as follows:…”

Section: Introductionmentioning

confidence: 99%

“…In the above identity, “” stands for the mean value of the electric dipolar polarizability corresponding to the i th-atom, “” is the electron mass and “N” is related to the concept of an effective number of electrons involved 3,21–25…”

Section: Introductionmentioning

confidence: 99%

A Calculation Model of the General Theory of Interaction Potentials for Stoichiometric Lanthanide Type Crystals: Applications to the Cs2KLnCl6 System

Trescastro-López

Shanavas

Acevedo

2019

Sci Rep

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This article aims to develop a generalized model calculation model to be applicable to the general theory of interaction potentials with reference to the stoichiometric elpasolite type crystals. In this study, we have chosen to report both a theoretical model and a calculation strategy to undertake semi empirical calculations of thermodynamic properties, such as reticular energies and heats of formation for the series of systems such as: Cs2KLnCl6. We have also carried out quite a number of calculations for a variety of systems such as: Cs2NaLnF6, Cs2NaLnCl6, Cs2NaLnBr6, Rb2NaLnF6 and Cs2KLnF6 in the Fm3m space group since we aim to check the strengths and weaknesses of our model calculations. We have analyzed a substantial number of approximate theoretical models and have carried a formidable amount of computing simulations to estimate the reticular energies and the corresponding heat of formation for these type of crystal using a semi empirical model. We made use of the thermodynamic cycles of Born-Haber so as to get a broad view with reference to the accuracy of our semi empirical theoretical models. The problem itself is quite challenging since we have focused our attention upon trivalent lanthanide ions in the first inner transition series of the chemical elements: (Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu). There are a significant amount of outstanding research works published in the literature with reference to structural analysis, one photon spectroscopy, vibrionic intensity model calculations and generalized models to deal with these kind of complex crystals. The calculated energy values associated with these observables seems to be most reasonable, and these follow the expected trends, as may be expected on both theoretical and experimental grounds. Both, the advantages and disadvantages of the current model calculations, have been tested against other previous calculations performed for this type of complex systems. It is of a paramount importance, the results obtained and reported in this article with regards to convergence tests as well as some master equations derived to account for the various contributions to the total energy. The Born-Mayer-Buckingham potential is carefully examined with reference to these lanthanide type crystals Cs2KLnCl6. Finally but not at last, the most likely sources for improvement are carefully discussed in this work. We strongly believe that there is enough room for improvement and have therefore initiated a new research program of activities tackling systems of well-known optical and structural properties.

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The Madelung Function of Elpasolites

Cited by 3 publications

References 0 publications

Simple Route to Lattice Energies in the Presence of Complex Ions

Simple Route to Lattice Energies in the Presence of Complex Ions

On the theory of interaction potentials in ionic crystals

A Calculation Model of the General Theory of Interaction Potentials for Stoichiometric Lanthanide Type Crystals: Applications to the Cs2KLnCl6 System

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