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T. YOKOKAWA AND 0. J. KLEPPA
was taken as 90°K. which gave T ' M as 80°K. The potential barrier B' was 800 cal. (mole of 0,)-1. The entropy change at 300"K., obtained from an integration of curve A, gave 8.5 gibbs (mole of 0 2 ) - 1 , while curve B gave 3.7 gibbs (mole of Oz)-l. The experinzentalchange of entropyat 300'K. is 3.6 gibbs (moleof OZ)-'. Curve C is a plot of the entropy change obtained from an integration of curve B. The fit of curves B and C to the experimental heat capacity and entropy change data on the basis of a mole of chemisorbed O2 is surprisingly good. However, it must be emphasized that use of eq. 20 has no known theoretical justification, and it is used in an entirely empirical manner. (The introduction of 7'0 is some-
what analogous to the introduction of the Weiss A into the equation for magnetic susceptibility, 11, = C / ( T A ) .)
If the assumption is made that the oxygen is atomically chemisorbed, and that only a fraction of it, about 50%, occupies sites with barriers which can become sufficiently lowered through cooperative interactions, then the heat capacity data can also be fit using the empirical method embodied in eq. 20 and 21. The same empirical method may be applied to hindered rotational degrees of freedom which involve co(For calculating hindered operative interactions. rotational heat capacities and associated entropy changes. the tables given by Pitzer are u~eful.'~)
A Calorimetric Study of the Transformation of Some Metastable Modifications of Alumina to a-Alumina
by T. Yokokawa and 0. J. Kleppa Department of Chemistry and Institute jot- the S t u d y of Metals, T h e University of Chicago, Chicago, Illinois 60697 (Received J u n e $6, lQ64)
The heats of solution, in a lead-cadmium-borate melt a t 705O, of a-alumina (corundum) and of several metastable modifications of aluminum oxide have been investigated. From the measured heats of solution we obtained the following enthalpies of transformation: Al2O3(r) = Alz03(a),AH = -5.3 kcal./mole; A1203(~)= Al,Os(a), AH = -3.6 kcal./ mole; hl,03(6) = A1203(a), AH = -2.7 kcal./mole.
Introduction Crystalline alumina (A1203) is known to occur in a series of different structural modifications. Among these only the a-modification (corundum) is thermodynamically stable. The various metastable forms are denoted p, y,8, K, 7,e, x and have been characterized by X-ray powder diagrams only. The conditions under which they form are not well understood. Characteristically they are obtained on the ignition of aluminum compounds, and the appearance of a particular phase depends on a variety of factors such as imT h e Journal of Physical Chemistry
purity content, temperature, particle size, quenching speed, etc.' All the various metastable modifications can be converted to the stable corundum form by ignition a t sufficiently high temperatures. The conditions required for complete conversion change from one sample t(J another. We have found no reliable information in the published literature on the heat of transformation of the (1) See, e.g., M. Plummer, J . A p p l . Chem. (London), 8 , 35 (1958); 8 , 44 (1958).
H.P. Roothsby, ibid.,
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TRANSFORMATION OF METASTABLE ~ ~ O D I F I C A T I O X OF S ALUMINA TO ALUMINA
various metastable forms to the stable corundum modification. This is not surprising since the conversion process is quite sluggish. Also corundum digsolves only with great difficulty in calorimetric solvents near room temperature. Thus the heat of transformation cannot be obtained from conventional solution calorimetry. We were alerted to the interesting problems associated with the energy of transformation of the metastable aluminas to corundum through two considerations. On the one hand it has been noted on many occasions that the end product in the combustion calorimetry of aluminum compounds sometimes is a mixture of corundum with differing amounts of a metastable form.2 As a consequence there is at times some uncertainty associated with the adopted value of the heat of combustion of aluminum. On the other hand, we have recently become interested in the thermodynamics of spinel formation, and it is known that one of the metastable forms of alumina (yA1203) has a defect spinel s t r u c t ~ r e . ~ I n the present communication we report the results of a calorimetric study of the heats of solution of a-, y-, 6-, and K-alumina in a lead-cadmium-borate melt a t 705’. From these results we have derived the heats of transformation of these metastable modifications to the a-form.
12Hz0, Jlerck reagent grade). A sample of aA&03 (Baker’s Analyzed reagent) was used as a reference material. This oxide was sifted, and the finest material (-200 mesh) was used in our experiments in order to achieve a fast dissolution reaction. Finally, through the courtesy of Drs. G. T. Armstrong and R. C. King of the Xational Bureau of Standards, we obtained a small sample of 6-A1203,which had been obtained as a reaction product in a bomb-calorimetric study of A14C3. The samples of metastable alumina, contained in a platinum crucible, were heated in air. Most ignitions were carried out in a muffle furnace suitable for temperatures up to 1200O. In addition, two samples of alumina-A were ignited in a high frequency induction furnace at 1350 and 1450’. After each stage of heat treatment the samples were examined by X-ray powder diffraction, and the phase(s) present identified by comparison with patterns reported in the l i t e r a t ~ r e . ~ The calorimeter was the same, and the experimental procedures similar to those adopted by Yokokawa and Kleppa5 in their recent calorimetric study of the Pb0-V206 system. The only significant modification in procedure involved the method for adding the solid sample to the melt at 705’. In the present work the solid powder was contained in a shallow platinum spoon which was maintained before the reaction just above the surface of the melt. Dissolution of the sample was facilitated by moving the spoon up and down in the melt a few times. The temperature of the calorimeter was maintained at 705 f 2’ throughout the present work. Calibration was achieved by dropping small pieces of gold wire into the calorinieter from room temperature. The calibrating heat effects were computed from the heat content equation for gold given by KelleyS6 Small corrections were applied for the heat generated in the mixing operation and for the heat pickup of the gold pieces during the drop. The solvent was renewed after each two consecutive solution experiments. I n the concentration range used (up to 150 mg. of A1~03/40g. of solvent) we observed no concentration dependence of the heat of solution.
Experimental and Materials The solvent used in the present work was prepared from reagent grade lead(I1) oxide, cadmium(I1) oxide, and boric acid, in the ratio 9Pb0 :3Cd0 :4B203. Forty grams of this mixture was melted down prior to each run in a platinum dish. Near the liquidus temperature (about SOOO) this melt is very viscous. However, it is quite fluid a t 700°, and a t this temperature it dissolves alumina a t a satisfactory rate. In our early work we attempted to use a pure lead borate solvent of composition 3Pb0. Bz03, which melt has been used for the growing of single crystals of various oxides. However, we found that this melt attacked our gold and platinum containers. Results and Discussion Our alumina samples were prepared from three different starting materials. One sample (alumina-P) We present in Fig. 1 a graph of the experimental was obtained by ignition of aluminum hydroxide, values of the heat of solution (kcal./mole of Alz03) which was precipitated from an aqueous solution of aluminum nitrate (Nerck reagent grade, total non(2) G. T. Armstrong and R. C. King, private communication. volatile impurities
