DONALD L. FRESH AND J. STUART DOOLING
3198
in the Raman effect. Due to the low symmetry of the molecules, all combination and overtone frequencies are permitted. Therefore, several weak bands observed in the infrared and Raman spectra could not be uniquely assigned, but a few reasonable assignments
are given in Tables I and 11. The data do not justify a detailed discussion of these assignments. Acknowledgment. We wish to thank Mr. Harold Klapper for recording the nmr data and the National Science Foundation for support of this research.
Kinetics of the Solid-State Reaction between Magnesium Oxide and Ferric Oxide
by Donald L. Fresh’ and J. Stuart Dooling Department of Chemistry, Catholic University of America, Washington, D. C.
(Received M a y 5 , 1966)
The reaction between equimolar amounts of intimately mixed powders of magnesium oxide and ferric oxide at elevated temperatures to form magnesium ferrite was studied considering the variables of temperature, time, and particle size of the oxide powders. The reaction mixtures were analyzed by X-ray diff ractometry employing a spectrogoniometer. After a rapid initial reaction period, which was attributed to surface diffusion, the reaction was expressed by Jander’s diffusion equation. The controlling process was the diffusion of the oxide components through the ferrite product layer. The solid-state reaction rate constants were calculated, and the temperature dependence of the rate constants was studied. Activation energies were found to be 117 kcal/mole.
Introduction Although solid-state reactions were recognized during the 1800’s and early 19OO’s, as evidenced by work of Faradayj2 Spring,3 and C ~ b b very , ~ little was done toward understanding the mechanisms until after 1910. Some of the earliest quantitative work on the kinetics of solid-phase reactions was done by H e d ~ a l l Tam,~ mann,E and Jander.? Jander conducted experiments on the solid-phase reaction between crystalline solids and concluded that the square of the thickness of the reaction layer of the new-formed product is proportional to time. The differential equation representing the reaction is
Equation 1 states that the rate of thickening of the product layer is inversely proportional to the thickness of the layer, y, a t time, t. The product layer may be The Journal of Physical Chemistry
considered as a diffusion barrier which tends to retard the reaction as the layer thickens. A number of experimental methods have been employed in following solid-state reactions. Chemical analytical techniques meet with only limited use when the reactions do not involve a change in chemical composition but merely a change in crystalline configuration. This is the case in the reaction MgO
+ Fe203+MgFe201
(1) General Precision Inc., Librsscope Group, Glendale, Calif. (2) M. Faraday and J. Stodart, Quart. J . Sci., 9, 319 (1820). (3) W. Spring, 2. Physik. Chem., 2, 535 (1888). (4) J. Cobb, J . SOC.Chem. Ind., 29, 69, 250, 399, 608, 799 (1910). (5) J. A. Hedvall, “Reaktionshahigkeit Fester Stoff,” J. Barth Co., Leipeig, 1938. (6) G. Tammann, Z . Anorg. Allgem. Chem., 1 1 1 , 78 (1921); 123, 196 (1922); 149,21 (1925). (7) (a) W. Jander, ibid., 163, 1 (1927); 166, 31 (1927); 214, 55 (1933); (b) W. Jander, Z . Ver. Deut. Ing., 80, 506 (1936).
KINETICSOF
THE
3199
SOLID-STATE REACTION BETWEEN R4gO AND Fe203
Although X-ray diffraction, principally camera techniques, has been used for a number of years to measure crystalline structures, only recently have methods been available that provide the degree of accuracy required to follow a reaction of this type quantitatively.
uniform by microscopic examination. This examination also showed that the original size of the coarse particles had not been reduced by the mixing operation. ~
~~
Table I : Particle size of Reaction Specimens
Experimental Section The particle method, as applied in this study, includes the following experimental steps: selection and preparation of the reactant oxides; preparation of large particles of XgO by comminuting and sizing; preparation of the reaction specimens by intimately mixing the two oxides and compacting the mixtures into disk shapes; heat-treating the shapes; preparation of the heat-treated shapes for X-ray diffraction analysis by pulverizing to fine powders; and analysis by X-ray diffractometry. For the finely divided ferric oxide, Grade 2199 of the C. E(. Williams Co., Easton, Pa., was selected on the basis of purir,y and particle size. A spectrographic analysis of the material indicated a purity of 99.2% and an electron micrograph of the material showed the particles to be in the vicinity of 0.05 1.1. A high purity (99.5%) “optxal fused grade” of magnesium oxide in the form of large crystals (5- to 50-mm diameter) available from the Sorton Co. of Worcester, Mass., was used as the source of the other reactant particles. In order to obtain the various coarse particle-size ranges, the large crystals of magnesium oxide were comminuted into three particle-size ranges. An upper limit of about 0.25-mm cross-sectional dimension was felt sufficiently large to guarantee that complete reaction mould not occur even after exposure to high temperatures for long periods of time. The ranges of 177 to 210, 88 to 805, and 44 to 53 p were then selected on the basis of available Tyler Standard Sieves. Crushing was accomplished between two hardened steel plates on a mechanical press. A slow stream of dry argon was introduced into the crushing assembly and into containers used in all subsequent steps to minimize hydroxide and carbonate formation. Three reaclion specimen types were prepared by combining equimolar amounts of each of the particlesize ranges of magnesium oxide with the finely divided ferric oxide as shown in Table I. The weighed amounts of each of the two oxides were placed in glass jars with plastic screw caps and were shaken to promote dry mixing. Additional mixing was performed by shaking after the addition of stainless steel balls. Xext, an amount of anhydrous ethanol, sufficient to produce a good mixing consistency, was added and the jars and balls were again shaken and then revolved on a ballmill roller until a mixture was obtained that appeared
Specimen no.
1 2
3
ME0
FegOs
1 mole 44-53 p 1 mole 88-105 p 1 mole 177-210 p
1 mole 0.05 p 1 mole 0.05 p 1 mole 0.05 p
Rapid drying was accomplished by placing the jars under heat lamps while gently blowing argon into each jar to remove the alcohol vapor. The drying was rapid enough to minimize preferential settling of heavy particles in the slurries. The specimen powders were pressed into disks in order to force the particles closer together and thereby obtain a higher degree of intimacy between the reactants and to provide a convenient shape to facilitate handling during the heat-treating step. Disks, with dimensions 5-mm thickness by 17.5” diameter, were formed with 10,000 kg of force. The three reaction disks (plus individual MgO and Fe208disks and crucibles of powders for use in preparing X-ray standards) were placed in procelain boats lined with platinum foil in preparation for heat treatment. A preheating furnace was used to heat the boats of specimens before placing them in the heattreating furnace. This served to prevent any drastic lowering of the temperature in the heat-treating furnace and permit rapid attainment of the desired peak temperatures. At the completion of the heat-treatment period, the boats of specimens were removed from the furnace and rapidly cooled by air quenching. Electronic measuring and controlling apparatus maintained the zone used in the heat-treating furnace within *2” of the desired value. The reaction specimens were fired at four temperatures (1000,1100,1200, and 1300”) for seven periods of time (0.25, 0.5, 1, 2 , 4, 8, and 20 hr) . X-Ray diffraction was used to follow the reaction by measuring the amount of ferric oxide remaining in a specimen. The ferric oxide crystal provides a strong diffraction line that receives no interference from the patterns of the other constituents in the way of line superposition or adjacency. The intensity of this ferric oxide line was measured in each specimen and the amount of reactant remaining was thereby determined. Apparatus utilized was a Norelco difVolume ‘70, Number 10
October 1966
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DONALD L. FRESH AND J. STUART DOOLING
fractometer with high-angle goniometer, Geiger tube detector, counting circuit, and recording potentiometer. Since only one diffraction line was of concern, a scanning range of just a few degrees was employed. The strongest ferric oxide line occurs at 42” 20 with an Fe K&radiation. To apply the powder technique, the sample must be composed of fine, randomly oriented particles. The disks were ground in agate mortars until they passed through a 44-p sieve. To obtain a statistical value, each powdered specimen was packed in the X-ray sample holder three times and each packing was analyzed twice. The six-line intensities were then averaged to obtain the value for the specimen. The powder technique was employed rather than a solid specimen disk. Two reasons are cited. First, if the surface of a disk were analyzed, only a very narrow outer film of the specimen would be “seen” due to the limited penetration of the X-ray beam. Second, due to the presence of large MgO particles in the original mixture of the reaction specimens, a situation would result where a large particle of MgO would become coated via surface diffusion and appear to the X-rays as a large particle composed completely of the surface coat. Such a large particle must be crushed, thereby exposing all portions of the particle and giving a representative picture of the specimen. Standard specimens were employed to calibrate the X-ray equipment by obtaining a calibration plot of counts per second against weight fraction of ferric oxide and also eliminating the effect of any variation in crystallinity resulting from the different firing schedules. This permitted the intensity of each reaction specimen to be directly converted to a ferric oxide weight fraction. These standards were prepared by mechanically combining three pulverized constituents (MgO, Fe203, and fired hlg Fez04) so that the 1 : 2 ratio of -Ilg/Fe existed in all standards, and so that the weight fraction [h9gFe2O4]/[(MgO) (FezOZ)] varied from 0 to 1 among standards. The pulverized oxide constituents had previously been heat treated under the various temperature and time ranges of this study.
+
Results Before discussing the results, it is desirable to establish whether the experimental data may be considered as descriptive of the reaction of both oxides and of the formation of ferrite and not just descriptive of the reaction of ferric oxide, as the unreacted ferric oxide was the only constituent quantitatively measured. This point requires consideration since magnesium ferrite is one of a number of materials which might not rigidly obey The Journal of Physical Chemistry
the law of fixed proportions. In general, members of the spinel family may gain or lose some constituents within certain limits and still retain their lattice structures. Such materials may be thought of as ordered solid solutions. It would be possible to obtain a definite answer if one could quantitatively determine the amount of magnesium oxide and magnesium ferrite along with the ferric oxide. Unfortunately, no satisfactory method was available for accurately measuring these two constituents in mixtures of the three. Attempts were made to dissolve the unreacted magnesium oxide preferentially and to determine the quantity present by chemical means. A method outlined by Bussen, Schustesius, and Ungewisss which had been used with the magnesium aluminate reaction did not prove chemically feasible with the magnesium ferrite. Although ferric oxide may be analyzed quite accurately by X-ray diffraction, it is difficult to determine the presence of magnesium oxide and magnesium ferrite in this system quantitatively. This is due to the following reasons. (1) Because of the low scattering power of magnesium, its contributiorl to the diffraction pattern of a compound in which it occurs is not great (compared to that of iron, for instance). (2) Since weight fraction determines the intensity of the lines, the magnesium oxide line suffers because of the low weight fraction present in an equimolar mixture of magnesium oxide and ferric oxide. (3) The strong diffraction lines of magnesium oxide and magnesium ferrite receive interference through superposition by other lines. (4) Since the newly formed ferrite is not well crystallized, broadening of the lines occurs and greatly reduces the ability to determine the amount of ferrite product present accurately. A separate study was conducted to investigate the nonstoichiometry of the product and so ascertain whether the reactants combine in equimolar proportions. The product of a series of reactions, each involving a different ratio of magnesium oxide to ferric oxide, was analyzed. The results revealed that only a narrow composition range exists where either oxide will enter the spinel lattice, and that the reaction product could be considered as essentially equimolar. Further, under the reaction conditions employed, there are no significant side reactions that would alter the stoichiometry of the reaction. Therefore, the data obtained by analyzing the unreacted ferric oxide by X-ray diffraction actually describe, under the specified reaction conditions, the (8) W. Bussen, C. Schustesius, and A. Ungewiss. Ber. Deut. Keram. Ges., 18, 433 (1937).
KINETICS OF
THE
SOLID-STATE REACTION BETWEEN MgO AND Fez03
1.0
From the standpoint of the quantitative consideration of reaction kinetics, the reaction was found to follow chiefly the diffusion equation
0.9 P
.g 0 5
