Jack 1. Lambert Kansas State University Manhattan
Spinel Models for Demonstrating Crystal Field Stabilization
W h e n chemistry students arc first introduced to ligand field theory, the instructor usually finds it desirable to be able to prove the existence of ligand field or crystal field stabilization energy in simple systems. The "double-humped" curves for the hydration energies of divalent and trivalent fourth period transition metal cations have been used by Orgel (1) and other authors of recent textbooks of inorganic chemistry as examples demonstrating ligand field stabilization. Both Orgel and Wells ( 2 ) , also used the normal spinel structure of hausmannite, Mn80a,and the "inverse" spinel structure of magnetite, FeaOn,to demonstrate the comparative "site-preference energies" of octahedral and tetrahedral sites in a close-packed lattice of anions. The anomalous hydration energy curves of transition metal cations can readily be understood by chemistry students who have had physical chemistry or one of the more rigorous courses in freshman chemistry; but unfamiliarity with ionic lattice structures as complicated as the spinels precludes more than a partial underst,anding of the spinel examples. Lattice models or
City, hlo., for kri.20 per gross. V h r k balls of t,llis type are dltainillde from the Emo Protlncls Cm, 6.5 North Second St,., I'l~iladelphio(i, P:L.,9t $rill ~ C grws P few l.l~e"/,-in. Irnlls and % . I 5 per gmss Cr the '/An. 1n:~lls.
Fig. 1 o. t o y e r rtructure ond charocteriatic pottern of cofionr in the lattice, with the unit cell indicated by inked line..
Fig. Ib.
their photographs can I)c a valuable instruction aid in such cases. Models represcntativc of Mn30rand Fe,Or were constructed of table tennis and cork balls. The normal spinel structure was based on the projection and drawing of half a unit cell of spinel, MgAI2O4,in Wyckoff (3). Table tennis halls of suitable grade for model construction can be purchased for approximately 4'/z cents each if purchased wholesale in gross lots.' Composition cork ballsZof '/,-and 5/8-in.diameters represent the divalent and trivalent cations. The radius ratios are approximately correct when the ll/r-in. diameter table tennis halls are used to represent the oxide ions. Experimental values for the ionic radii are
The smaller cork balls were spray painted a flat black to differentiate them from the natural tan colored larger cork halls. Duco Cement is fast-drying adhesive that bonds the balls into strong, rigid stnrctures. Figure 1shows the layer strncture of Mn304,a normal spinel structure with the octahedral sites occnpied by Mn3+ions (black) and tetrahedrally coordinated N1n2+ ions (natural cork) situated between the layers. The unit cell of the normal spinel-type structure is indicatd hy the i11kt.d liws in Figure l a . Thirty-two 02-, sixtern Mn3+,and eight Mn2+ions lie within the iwit
Some model with top loyer removed.
Fig. 1 c. Some model with the two uppermost loyerr removed.
Model of the normal spinel structure of MnrOl. Note that adjocent and dternate layers are not ruperimpomble, but tho1 every flfth loyer is ruperimpomble. The large while spheres represent OP;the rmoll block cork b d i r Mn", m d the larger cork balls Mnzt.
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I, January 1964
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cell. 1':acIi succeeding layer shows the clraractcristic cross-hatch arrangement of the rows of trivalent ions and the regular pattcsn spacing of the divalent ions. The oxide ions are described as "nearly" close-packed in cuhic arrangement, but the horizontal layers shown arc not the close-packed abcabc . . . layer arrangement of the cubic structure. Those layers lie a t an angle of tiso measured from the horizoutal in the modcl, in a plaue perpeudicular to the face of the model which fronts toward the lower left hand corner of thc photograph. The inverse spinel structure of FesOI in Figure 2 has the same layer arrangement of anions but oue half of the trivalent cations have exchanged places with the divalent cations, preserving the same general arrangcment of anions and cations that characterizes the spinels. The unit cell is again indicated by lines in Figure 2a. If n anions am close-packed in either cubic or hexagonal arrangement, there are n number of holes surrounded by six anions (octahedral sites) and 2n number of holes surrounded by four anions (tetrahedral sites). I11 the spinels, one-half of the octahedral sites and oneeighth of the tetrahedral sites are occupied. During formation of the solid spinel compouud, the cations will seek the sites of lowest energy in the lattice of oxide anions. The oxide ions produce a "weak" crystal field which is unahle to effect spin-pairing of the d electrons in any of the manganese or iron cations. As a result, the cations having the dQonfiguration are indifferent to the crystal fields, while those having d4 and d6 configurations are stabilized in both the octahedral and tetrahedral sites but to different degrees. Table 1shows the crystal field stabilization energics (CFSE) for the cations in the two types of holes and the excess stahilization cnergy in kcal/mole for the octahedral over the tetrahedral sites. It must be remembered that the magnitude of Dq varics from element to clement for cations of the same valmce, and even more sharply for cations of the same elcment having different valmces. In the two spinels,
Fig. 20. Layer rtructure ond choracterirtic pattern of rations in the lattice, with the unit cell indicated.
Fig. 2b.
the crystal fields of the oxidc ions call he cousidcrcd virtually identical. I n the normal spinel s t r u c t u ~of~ MnaOa,liigure 1, the Mn3+ions are so stabilized in the octahedral sites that the Mn2+ ions must of necessity reside in tetwhedral sites. In the inversc spinel structure of Fe,Oi, Figure 2, the Fez+ ions are stabilized in the octahedral sites, so one-half of the Few ions must occupy the tetrahedral sites. The fraction of trivalent cations displaced to the tetrahedral sites may vary from zero in a normal spinel to 0.5 in an invcrsc spinel. This parameter is tcrmed X aud may vary between zero and 0.5 in "random" spinels. In inverse and random spinels, tla: positions of the divalent cations in the octahedral positions are not necessarily regular, so the inverse spinel model of Fe304is highly idealized. Although many liberties were taken with the geomctries of the structures, some of the physical properties of MnsOnand Fe:,04become apparent upou examination of the models. Both compounds are black, as are most compounds containing cations of the same metal in two oxidation states. The hardness of magnetite is 5.5-6.5 on the Moh scale compared to 5.0-5.5 for hausmannite. This would be expected if the layers of oxide ions are drawn together more tightly hy the smaller trivalent Ye3+ ion in the tetrahedral sites in magnetite thau are those in hausmannite hy largcr divalcnt Mn2+ion in comparable sites. The densities,
Table 1.
d"
Crystal Field Stabilization Energy for the Cations in the W e a k Field of Oxide Ions. Enwss OrtaTetraOSK" hedral h&al (lid/ Ion (Ilq) (Dq) A nralo)
" Jhx.css OSI': is rlctined ss thc cxress st,ahilis:~tirmoncrgy tl~:ti. t,he p n r t , i n h r x t i m sehieves in nctnhcdrul sitce as eornpnrcd t , ~ totri~hcdrelsites.
Same model withtop layer removed.
Fig. 2'. Same model with the two uppermost layers removed.
Model of the inverle spinel structure of Fei04. Note the exchange of positions of divalent ond trivalent cations in c o m p o r i ~ nwith their poritions in the normal spinel rtrvctvre (Fig. 11. Adjacent and alternate loyerr ore not ruperimposoble, but every fifth layer is ruperimporoble. The l a r g e white spheres represent Oz-,the m a l l blackcork bolls Fe3+, and the l o r g e r m r k bolls Fdi.
42 / Journal of Chemical Educafion
5.16-5.18 for magnetite compared to 4.714.85 for hausmannite, follow from the same argument. The model of Mn304is very similar to that shown by Wyckoff for spinel. In both the drawing and the model, the Mn2+ ions are not exactly tetrahedrally coordinated but rather contact a pair of adjoining oxide ions in each layer. To have achieved true tetrahedral coordination would have introduced separations between rows of table tennis balls in the layers and would have made the construction of the model difficult. Also, there is no reason to believe that the oxide ions lie in perfectly flat layers. The layers may be puckered to achieve a more correct coordination geometry for both the octahedral and tetrahedral sites. Still further liberties were taken in the construction of the Fe304 model. The same fault exists for the tetrahedrally coordinated Fe3+ ions as existed for the Mnl+ ions in the Mna04model. Further, to crowd the large Fe2+ ions into the octahedral sites in the table
tennis ball layers, four holes were countersunk 90' apart equatorially around the 3/r-in. cork balls to make them fit. In other words interpenetration, or covalency, was arbitrarily introduced for structural reasons, but it must be remembered that a degree of covalency undoubtedly does exist for all the cations with oxygen. Acknowledgment
The author wishes to thank Dr. R. Dean Dragsdorf, Department of Physics, Kansas State University, for his advice on the lattice structures of the spinels. Literature Cited ( 1 ) ORGELL. E., "An Introduction to Transition-Metal Chemistry. Ligand-Field Theory," John Wiley & Sons, Inc., New York. 1960. DD. 77-8. , $., ' ' S t m ~ t u r dInorgrtnio Chemistry," 3rd ed., (2) ~ E m s A. Oxford University Press, 1962, pp. 48740. R. W. G., " C r y ~ t dStructures," Vol. 11, Inter(3) WYCKOFP, science Publishers, Inc., New York, 1957, Chapter YIII, illustration page 6 .
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