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Optical Energy Gaps in the Monoclinic Oxides of Hafnium and Zirconium 2.
and Their Solid Solutions'
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by J. G. Bendoraitis and R. E. Salomon Department of Chemistry, Temple University, Philadelphia, Pennsylvania 19122 (Received June 2, 1966)
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Zirconiuin and hafnium are perhaps the most similar pair of elements with respect to chemical and physical properties. Their compounds are similar in crystal structure, melting point, and solubility. The monoclinic oxides of zirconium and hafnium, in particular, have nearly identical unit cell dimensions,2 with the following lattice parameters: a = 5.1454, b = 5.2075, c = 5.3107 8.,/3 = 99" 14' k0.05 for ZrOz, and a = 5.1156, b = 5.1722, c = 5.2948 p = 99" 11' i 0 . 0 5 for HfOz. The isomorphous character of these oxides has been demonstrated by the formation of homogeneous solid solutions in all proportion^.^ It was of interest to determine the extent of the difference in the optical energy gap of these oxides. Among other things, the energy gap is expected to be sensitive to the type of bonding in the lattice. Although the exact nature of the bonding is not well understood, crystal field studies applied to the optical spectra of the Cr+3 ion doped into the monoclinic lattice of ZnOz suggest significant covalent contribution^.^ The estimate is based on the ratio of the Racah B parameters of the Cr+3ion in the lattice to that of the free ion. I n recent years, diffuse reflectance spectroscopy has been applied as a convenient technique for estimating the width of the energy gap in systems which are not amenable to investigation by transmission measurements.61' It was felt that the diffuse reflectance spectra of HfO,-ZrOz solid solutions could be used to demonstrate orbital overlap, since such solutions would be expected to have a behavior which is intermediate between that of a solid solution of weakly interacting organic molecules and strongly interacting atoms in a metallic d o y . Experimental Section Low hafnium zirconium oxide, obtained from the TAM Division of National Lead. Co., and hafnium oxide, obtained from Alfa Inorganics, Inc., were purified by forming insoluble chelates with mandelic acid? Impurities which might mask the onset of the intrinsic oxide absorption in the ultraviolet region were removed in this manner. The diffuse reflectance spectra of the purified oxides are shown in Figure 1.
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The Journal of Physical Chemistry
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SOLUTION
MECHANICAL MIXTURE
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Figure 2. Diffuse reflectance spectra of a mechanical mixture of solid solutions of 40 mole $7, zirconium oxide in hafnium oxide.
Solid solutions of the oxides were prepared by ignition of the mixed mandelates. Weighed portions of the purified oxides were dissolved in molten sodium bisulfate. After cooling, the resulting melts were dissolved in dilute HC1 (1:10). The mixed mandelates then precipitated upon the addition of mandelic acid. These (1) This work was supported in part by the Socony Mobil Oil Co., Inc., and the U. S. Atomic Energy Commission, Contract No. AT(301)-2775, and is from the Ph.D. thesis of J. G. Bendoraitis to be submitted to the Graduate School, Temple University. (2) J. Adam and M. D. Rogers, Acta Cryst., 12,951 (1959). (3) C. E. Curtis, L. M. Doney, and J. R. Johnson, J . A m . Ceram. Soc., 37,458 (1954). (4) J. F. Meehan, Ph.D. Thesis, Temple University, 1965. ( 5 ) D. L.Wood, 3. Ferguson, E. Knox, and J. F. Dillon, J. C h m . Phys., 39, 890 (1963). (6) P. D.Fochs, Proc. Phys. SOC.(London), 69,70 (1956). (7) A. L. Companion, J. Phys. Chem. Solids, 25, 357 (1964). (8) W. B. Blumenthal, "Chemical Behavior of Zirconium," D. Van Nostrand Co. Inc., New York, N. Y.,1958.
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precipitates were filtered, washed, and dissolved in dilute ammonium hydroxide to minimize contamination by foreign ions. The mandelates were reprecipitated by the addition of HC1, filtered, and ignited at 1000” for periods ranging from 1 to 100 hr. Typical ignition times were 20 hr. X-Ray powder diffractometer studies showed the resulting solid solutions to be homogeneous and they were invariant in both their optical and X-ray spectra after heating for 1 hr. at 1000”. No evidence of a superlattice structure was observed in the diffraction patterns. 5.6 0
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- E G - I VALUES - EG-II VALUES
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Figure 3. Variation of the optical energy gap with composition in solid solutions of hafnium and zirconium oxides.
Spectra were determined with a Cary Model 14 recording spectrophotometer equipped with a ring collector reflectance attachment calibrated against MgC08 (220-700 mp). Reflectance measurements relative to the standard are given in units of optical density, . ~ ~ L Jspectra . where O.D. = log ( R M ~ C O ~ / R ~Typical of a 40 mole % mechanical mixture of ZrO2 in Hf02 and the corresponding solid solution are shown in Figure 2. Results The energy gap is taken as the intercept of the extrapolated linear portion of the absorption edge (region of strong optical absorption) with a base line corresponding to the region of minimum absorption. A band gap obtained in this manner for rutile has been shown by CompanionQto be in good agreement with values obtained by transmission measurements. This value is essentially the minimum width between the valence and conduction bands and does not necessarily agree with values based on the long wave length limit of photoconductivity. Such extrapolations, in our case, lead to two values (E.G.-I and E.G.-11) of the energy gap depending on the choice of the region of minimum
absorption in the presence of contributions from impurities. The difference in the values of the energy gap obtained in this manner is normally of the order of 0.02 e.v. The observed variation in the energy gap over the concentration range extending from pure Hf02 (5.55 e.v.) to pure Zr02 (4.99 e.v.) is shown in Figure 3. The variation with composition more nearly resembles the behavior of metallic alloys1° rather than mechanical mixtures or solid solutions of organic molecules. The nonlinear dependence of band gap on composition can be explained as due to appreciable cation-cation orbital overlap in the solid solution. In the tight binding approximation, the band gap of a solid can be expressed as a linear combination of matrix elements connecting neighboring atomic orbita1s.l1 The coefficients of these matrix elements depend, among other things, on the crystal symmetry and, for the case of alloys, the degree of order and the composition. I n the case of completely disordered alloys, the coefficients of matrix elements connecting functions localized on neighboring cations and anions would be proportional to the mole fraction, whereas the coefficients of matrix elements connecting functions on neighboring cations would be proportional to the square of the mole fraction; i.e., the number of cation-cation pairs is proportional to the square of the mole fractions. The deviation from linearity of the curve in Figure 3 indicates that the matrix element connecting functions centered on adjacent cation sites is of appreciable magnitude, if the tight binding approximation is appropriate. It is often important to know the magnitude of the extinction coefficient for the purpose of making spectral assignments. I n the case of ZrO2, diffuse reflectance spectra may be compared with transmission spectra measurements made with stripped anodic films12 in which one can ascribe the large extinction coefficients below 250 mp to transitions from the valence to the conduction band.13 The d u e n c e of the lattice parameters on the energy gap is not known, although the lattice spacing in these solutions appears to vary linearly with composition (Vegard’s law). ~
(9) A. L. Companion and R. E. Wyatt, J . Phys. Chem. Solids, 24, 1025 (1963). (10) J. C.Wooley and J. Warner, Can. J. Phys., 42, 1879 (1964). (11) F. Seitz and D. Turnbull, “Solid State Physics,” Vol. 1, Academic Press, Inc., New York, N. Y.,1955. (12)R. E. Salomon, W. M. Graven, and G. B. Adams, J . Chem. Phys., 3 2 , 310 (1960). (13) R.E.Salomon, G. B. Adam, and W. M. Graven, J . Electrochem. SOC.,110, 1163 (1963).
vohme 69,Number 10 October 1966
