The Hunting of the Snark :An Agony in Eight Fits By Lewis Carroll With nine illustrations by Henry Holiday SEE: http://ebooks.adelaide.edu.au/c/carroll/lewis/snark/
Yonghe Zhang ionocovalent theory applications (19) Zhang Lewis acid strengths predicted Pyridine Compositions SYNTHESIS AND CHARACTERIZATION OF MIXED OXIDES CONTAINING COBALT,COPPER AND IRON AND STUDY OF THEIR CATALYTIC ACTIVITY THOMAS MATHEW CATALYSIS DIVISION NATIONAL CHEMICAL LABORATORY, PUNE , INDIA 2.4.4 .4. Correlation between theoretical and experimental results In the following an attempt has been made to correlate experimental results with theoretical (empirical) quantities. According to Lewis definition, acidity and basicity are electron accepting and electron donating properties that could contribute to the formation of a covalent bond. Larger the electronegativity, the stronger the electron accepting power can be considered as a first approximation . According to Sanderson the electronegativity of the metal ion would be expected to change linearly with its charge. Later Zhang has proposed a numerical scale for the acid strengths Z of cations and he defined it as Z = P - 7.7Xz + 8 (7) where P andXz are the polarizing power and electronegativity of the ion respectively. The advantage of such a scale is the predictive power for thermochemical and physical properties that obviously depend on the nature of the chemical bond established between the acid cation and the basic anion. In the case of inorganic compounds, this bond is called iono-covalent, meaning that this bond involves simultaneously electrostatic force (ionic part) and covalent forces resulting from the combination of atomic orbitals. To express this duality, for a given cation, Zhang took into account (a) the polarizing power and (b) the electronegativity for the covalent part. He calculated the polarizing power, electronegativity and acid strength of various cations and it is note d that the acid strength of cations relevant to our compositions are in the order Fe3+Fe2+Co2+Cu2+Cu+. When an organic molecule like electron donating pyridine adsorbs on the surface, cations get reduced due to charge transfer. Thus the easily reducible metal ions like Cu2+ undergo fast reduction to Cu+ and hence the stability of metal ion-pyridine complex decreases. From the acid strength of various cations it is clear that reduced Cu+ has very poor acidity. In other words, for a given ligand, corresponding stability constants of metal ions are in the order Fe3+ Co2+ Cu2+ and hence the acidity of these ions also follow the same order, as shown earlier. J. Kijenski and A. Baiker, Catal. Today, 5 (1989) 1. R.T. Sanderson, Inorganic Chemistry, Reinhold: New York , p. 136 (1967). Y. Zhang, Inorg. Chem., 21 (1982) 3889.
Yonghe Zhang ionocovalent theory applications (15) A Relation between Zhang Lewis AcidStrengths and Dopant Elements Marcel et al. established a relation between the Zhang Lewis acid strength of the dopant element and its scattering cross section ： LSn 4+ /LGe 4+ QGe 4+ /QSn 4+ : In fact, we have recently shown(2,3,4) that the ideal doping cation must have a low electronegativity and a small ionic radius (r) associated with high effective nuclear charge (Z*). Indeed , such a cation having high value of Z*/r 2 will polarize the electron cloud of oxygen 2p6 valence band more strongly, thereby screening its charge so as to weaken it as a scattering center. Moreover, a low electrronegativity for the dopant cation accounts for a weak interaction between the conduction band electrons and the dopant cation. Zhang established an empirical equation relating the Lewis acid strength of the cation, L its electronegtativity, and the Z*/r 2 value as L = Z*/r 2 7.7X + 8.0 (1) Under such a circumstance, a high L value of the doping cation necessarily means a reduced scattering effect (and thereby a reduced scattering cross section) of the doping cation with regard to the conduction band electrons. Therefore, when the factor dominating the mobility is the scattering of electrons from the ionized donor centers, higher (lower) mobilities will occur for semiconductors doped with donor elements having higher (lower) L values (2,3,4). Following this guideline, it appeared that the use of Ge4+ as a doping element in ITO (partially or totally substituted to Sn4+) could induce an enhancement in the mobility since L Ge 4+ = 3.06 L Sn 4+ = 1.62 (2) Consequently , we can obtain the following expression after simple transformation Q Ge 4+ /Q Sn 4+ = 0.55 (3) It is interesting to note that for similarly heavily doped ITO and IGO (such as f and k) the value obtained above is close to the ratio calculated based on the Lewis acid strengths . Using relation (2) we get L Sn 4+ /L Ge 4+ = 0.53 (4) This result confirms the expected close relation between the scattering cross section of the dopant ion and its Lewis acid strength. It appears that when the factor dominating the mobility is the scattering of electrons from the ionized donor centers, L roughly varies inversely as Q. We note here that the concepts we have put forward also apply for other degenerate oxides having a predominant ionic-bond character as we have recently investigated. C. Marcel, J. Salardenne, S. Y. Huuang, G. Campet, and J. Portier, Active and Passive Elec.Comp.1997, Vol. 19, 217-223 S. J. Wen, G. Campet, J. Portier and J. Goodenough Mat.Science and Eng. , 1992, B. 14, 115. G. Campet, S. D. Han, S. J.Wen, J. P. Manaud, J. Portier, Y. Xu and J. Salardenne, Mat. Sci. and Eng. , B (accepted for publication 1995). S. J. Wen, doctoral thesis, University of Bordeaux I, 1992. Y. Zhang. Inorg. Chem., 1982, 21, 3886, 3889 .
Yonghe Zhang ionocovalent theory applications (11) Zhang Electronegativity Derived Brown Lewis Acid Strengths Brown derived an alternative Lewis acid strength S a from Zhang electronegativity X z . : The average Lewis-acid strengths given in Table 2 can be seen to increase with the electronegativity. The correlation between the two quantities is shown in Fig.4 using the Zhang (1982) electronegativities that are specific to oxidation state. The line corresponds to the equation X z = 1.118S a + 0.771 which can be rewritten as S a = 1.18 X z -0.653 where X z is Zhang electronegativity, which gave S a a solid definition and physical significance. I.D. Brown, Acta Cryst. B, 44, 545-553, 1988 Y. Zhang, (1982). Inorg. Chem., 21, 3886.
Yonghe Zhang ionocovalent theory applications (7). I. Methods Zhang's Scale for Strengths of Lewis Acids Published in ACS: Y. Zhang, Inorg, Chem.,21 (1982)3889
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