Ionic radii and optical susceptibilities in the halite-type alkali halides

Optical properties of ionic crystals are often described in terms of an approach based on the additivity rule. The approach assumes that the electronic polarizability assigned to each ion remains unchanged in all crystals containing this ion and that the electronic polarizability of the crystal is the sum of the polarizabilities of individual ions. If a crystal possesses the cubic symmetry, the optical susceptibility is related to polarizabilities of its constituent ions by the Clausius-Mossotti relation. The concept of additivity is very useful and there exist several sets of additive polarizabilities e. g. /1 to 3 1 . However, the additivity rule, which implies that the polarizability of a given ion remains constant in different crystals holds only in an approximate manner, even within the same crystal family. Theoretical values of electronic polarizabilities obtained employing different theoretical approaches predict also polarizabilities which change from crystal to crystal /2, 4 to 9/.The electronic polarizabilities are of great interest as related to ionic sizes (see, for example / 4 , lo/). Analogously to ionic polarizabilities, the additivity rule of ionic radii is often taken into consideration. However, as in the case of additive ionic polarizabilities one can observe the failure of this approach. Studies of X-ray determined electron density maps proved that within the alkali halides the radii change from crystal to crystal (see, for example values listed in /11/). Theoretical values of ionic radii obtained for alkali halides are also individual crystal dependent /12, 131.The aim of this note is to report the correlation between the polarizability ratio a / a where ac and aa are the polarizabilities of cation and anion, respectively, and the ratio of cation to anion radii rc/ra. It is usually assumed that the polarizability of cations is essentially unaffected by its environment while the polarizability of an anion Varies considerably as it is paired with different cations. Therefore, to derive aa it seems reasonable to subtract ac from the total molar polarizability . Recently, Johnson and Subbaswamy have computed polarizabilities of alkali halides in a local-density approximation scheme 181. The calculations have c a' ) U1. W6lczafiska 219, PL-93-005 Lodz, Poland. ') This work was carried out under Research Project CPBP 01.06,6.04

Correlation between Electronic Polarizabilities of Ions and Ratio of Their Radii in Alkali Halides

Kucharczyk

1990

Analysis of Ionic Radii, Second Neighbour Interactions, and Electronegativity Difference for Ionic Crystals

Singh¹

1990

Values of ionic radii are determined using the additivity rule and experimental information on X-ray diffraction and electron density measurements for NaCl crystals. The calculated values of ionic radii are found to produce the nearest-neighbour interionic separations close to the experimental values in I-VII, 11-VI, and 111-V compounds. In order to demonstrate the suitability of the calculated radii the interionic distances in tri-atomic compounds are also predicted. The second-neighbour overlap repulsive interactions and electronegativity differences are discussed in terms of ionic radii. The calculated radii are found to correlate very well with the electronegativity differences.Mit der Summenregel und experimentellen Informationen iiber Rontgenbeugungs-und Elektronendichtemessungen werden die Werte der Ionenradien fur NaC1-Kristalle bestimmt. Es wird gefunden, daB die berechneten Werte der Ionenradien Ionenabstande der nlchsten Nachbarn hervorrufen, die in den I-VII, 11-VI-und 111-V-Verbindungen nahe bei den experimentellen Werten liegen. Um die Eignung der berechneten Radien zu demonstrierm, werden auch die Interionenabstande in Dreierverbindungen vorhergesagt. Die abstoBenden Uberlappungs-Wechselwirkungen und die Elektronegativitatsdifferenzen zweiter Nachbarn werden mit den Ionenradien diskutiert. Es wird gefunden, daB die berechneten Radien sehr gut mit den Elektronegativitatsdifferenzen korrelieren.

An Empirical Correlation of Electron Density with Optical Susceptibility and Ionicity in Partly Ionic Diatomic Crystals

Kucharczyk

1993

Self Cite

The bond-charge interpretation of the Penn model and Phillips-Van Vechten theory [l to 31 has been applied to different optical phenomena in crystals (see, e.g. references in [4, 51). According to this approach the long-wavelength optical susceptibility is given by where up is the plasma frequency, C and E, are the heteropolar and homopolar constituents of the effective energy gap, respectively, and A is a correction factor. In ANBsPN compounds C is expressed as) exp (e), -k R where rcr and rp are the distances from the AN and B8-N atom to the centre of gravity of the bond charge, respectively, Z , and Z , denote the numbers of valence electrons, R = r, + r p is the bond length, k, is the Thomas-Fermi screening wave number, and the factor b is introduced to account for the deficiency of the free electron model [3, 61. The homopolar term depends on R as E, = A,R-S, with s 2.48. In the theory the ionicity of crystals is described by the parameter fi = C'/(C' + E;).The aim of this note is to discuss the relationship between the position of the bond charge and the refractive data in partly covalent diatomic crystals. Previously, Wemple [7] noted that the values of C and E , obtained employing the expression for A given by Penn had to be revised. Therefore in our calculations we have also checked how the choice of A effects these parameters.In the Penn model the optical susceptibility of the crystal originates from transitions from the valence to the conduction band or to the exciton state. Thus individual ionic polarizabilities have no well-defined meaning. However, a factor D has been introduced in (1) to account for the excitations of core electrons [3]. According to this picture the optical susceptibility stems from the excitations which are both interionic and intraionic in nature.