On the occurrence of metallic character in the periodic table of the

Sep 1, 1983 - A Visually Attractive “Interconnected Network of Ideas” for Organizing the Teaching and Learning of Descriptive Inorganic Chemistry...
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On the Occurrence of Metallic Character in the Periodic Table of the Elements Peter P. Edwards University Chemical Laboratory, Lensfield Road, Cambridge CB2 lEW, United Kingdom M. J. Slenko Baker Laboratory of Chemistry. Cornell University. Ithaca. NY 14853 Prior to Sir Humphry Davy's discovery and isolation of sodium and potassium in 1807, the established metals (iron, lead, gold, silver, etc.) were identified as high-density elementa possessing hallmark physical properties of brilliant lustre, malleability, ductility and elasticity (1, 2). Davy's monumental discovery (3)posed a major and fundamental dilemma to this classification of metals since hoth sodium and potassium possessed all the physical and chemical properties of the known metals, but had exceptionally low densities (2). Indeed, that Erman and Simon (. 4.) in 1808 went so far as to DroDose . . sod~umand potassium he termed "mrtnll~~i[ls"-meaning r2l " t h ~ i rthat are like metalsn-tc indicatr that thrv rwcml~lr metals only in certain respects! In his second ~ a k e & nLecture to the Royal Society (1), Davy also addressed the controversial question as to whether the newly discovered elements sodium and potassium could justifiably he called metals. Davy remarked ( 1 ) t h a t . . . "The great number of philosophical persons to whom this question has been put, have answered in the affirmative. They agree with metals in opacity, lustre, malleability, conducting powers as to heat and electricity, and in their qualities of chemical combination." At the nresent time such characteristics are indeed still widely utilized as the hasii of our iyskmilrrmtion of inorganic chemirtrv within rhe framework of the periodic system; viz, the classification of the elements into metals and nonmetals (5-9). In their simple limits, the characterization of these two canonical states generally relies either upon the physical properties of the element in i b condensed state (conductivity,

crystal structure, etc.), or via its chemical properties in aqueous solution. For example, a general chemical definition (8)of a metal (which may well require amendment in the near future) (10-12) is that of an element which, in solution, displays cationic behavior. The vast majority, some 80% of the naturally occurring elements, satisfy these criteria for metallic character and these elements comprise the entire s-, d-, and f-blocks and Dart of the D-block of the oeriodic table. In rontrmt, nonmetals are, in this nmtext, relatively sparse and are confined to rhe rieht-hand side of the ~ c r i o d i table c (Fir. 1).Thus the group of30 or so elements o i the p-block sir& is composed of hoth metals and nonmetals. In Figure 1,we identify metallic elements in their solid and liquid states a t normal atmospheric pressure (hatched). Four elements are semiconducting in the solid state, hut become metallic when molten (Si, Ge, Se, and Te, cross-hatched). A most striking feature (8.9, 131ofthis partirular area of the periodic tahlr is the almost d~nrunaldrmarc,ation s r r ~ a rating metals from nonmetals. For example, it was noted q& some time ago ( 1 4 ) that metallic structures cease a t carbon, silicon, and germanium in the first three periods, and a t antimony and polonium in the fourth and fifth periods. Similar Emor's Nan: M. J. Sienko. m - a h d *is paps received the 1983 ACS Award in Chemical Educationat the Seattle Nations1ACS Meeting this past March. The JOURNALcongratulatesDr. Sienko and joins ACS in recognizing his many contributions to chemical education.

p-block

a-block

rq-q

d-block

I n nn

.. ~i~~~~ 1. A this classification.

...

table of the elements. In the interests of Clarity for the presentation of Figure 3, the lanthanids and actinide elements have been omitted from

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conclusions as to the extent of metalliclnonmetallic status in the p-block series can also be drawn from considerations of elemental conductivities 161 ~~-~~~ . . or via the chemical hallmarks of the elements in aqueous solution (8). The diaeonal dividine line runs throueh boron. silicon. arsenic, tellurium, and astatine. On the basis of the definitions outlined above. elements to the rieht of this demarcation are nonmetallic and those to the left a r e predominantly metallic-hut. in certain contexts,. eermanium, antimonv. and .. pnlunium are t ~ ~defined st us semi-metab. Of the elemcnts on the other s d e of the di\.idinr line. twrm and siliron are n w . metals while arsenic, tellurium, and (probably) astatine are semi-metals. In this communication we attempt to rationalize the occurrence or location of metallic behavior in the periodic table in wrms ot'lltc ocornw p r o p ~ r l k -which amfer metall~cstatus to elements il.51.Our fundamrntal tenet ia that the n h n e occupied by an isolated atom in the gas phase, when coupled with the normal density of that element in the condensed state, is of paramount importance in dictating whether the valence electrons of the material are localized or itinerant. Stated in simple terms: if the mutual polarization of an atom by the remaining atoms in the condensed phase is sufficiently strong-that is, when the individual atoms are sufficiently large, or theirdensity sufficiently high-the valenceelectrons are set free and the svstem acauires metallic status. This simple, conceptual idealinking atomic properties, density, and the metallic state was recoenized hv K. F. Herzfeld (15) in 1927, and probably eveh earlier by D: A. Goldhammer in 1913 (16)'. Possihlv because of the verv ranid advances in auantum phisics and chemistry around that period, this attractive idea based on atom size was lost for some considerable time ( 1 7. 18). We now outline the main features of Herzfeld's treatment for determining which elements are metallic, which are nonmetallic, and which are borderline in the condensed state (15). ~~

~

~~

Denslty and Metallic State Consider an element in the condensed state, be it liquid or solid. An atom or molecule is placed in a Lorentz cavity in the system (19). We must now inquire "What is the internal electric field experienced by one particular atom arising from the other atoms in the system?". Under the influence of an the resultant local electric field external macroscopic field (El, a t the reference atom is given by the well-known Lorentz expression (20) 3, = E + (4/3)sP = E + (4/3)nNp (1) where P is the volarization of the surroundine medium (renresenting the total electrostatic dipole moment per unit volume of material), D is the electric dipole moment of an atom or molecule, and N is the number of atoms or molecules per

..... . cm:j

On classical yroundi Herzfeld argucutd r l i j that ~ the equation ~ l motion f i d the valence clrcirons In an i\olorcd orurn would

where f is the rlumbrrof hound 1vdenceJ elcvtrons and u, IS their characteristic freauencv. At the tinitt. densitiri oneencounters in the condeised state, eqn. (2) must he replaced by The net result is that the characteristic freauencv uo of the bound electrons, representing a measure of the force holding the valence electrons in the isolated atom or molecule, is diminished a t finite densities to the value (15) u = "011 - (RIV)1112

(4)

where V is the molar volume in the condensed state (under 692

Journal of Chemical Education

ambient c o n d i t i ~ n sand ) ~ R is the molar refractivity of the gaseous atomic state. Here R = (4/3)Laa, where L is the Avogadro number and a is the polarizahility. If we have IRI (RIVI , ~ ~ . =. 1.~. then the resultant force on the valence electron vanishes. The electron becomes itinerant and the svstem takes on metallic characteristic$! The previous statements may also he recast in slightly different form in terms of the venerable Lorentz-Lorentz or Clausius-Mossotti relationships (19,21,22)

where n is the index of refraction, nz represents the dielectric constant (E,,) arising from the electronic polarizability, and d is the elemental density. Now it is clear that the quotient (n2 - l)/(n2 2) cannot be larger than 1. However, Herzfeld argued that if we start with a substance of large refractive index (polarizahility) in the gaseous state and compress it, increasing the density such that the ratio (RIV) reaches unit, then for (RIVI = 1

+

a condition onlv realized when n is infinite (23)! 'l'hus a pcdar~estion,ur dit.lrctric c a ~ ~ i t r o p 15 h rimticipatcd, and this mesni that the \.alenee clectrons, uhwh hefore had been quasielastically hound to their respective atoms or ions, are now set free via mutual wlarization and the solid becomes a metallic conductor. In Herzfeld's original, simple approach (15) the parameter R is treated as a constant for all densities up to the onset of metallic character. We can therefore safely predict (23) a nonmetal to metal transition when the condition V = R is fulfilled. Such a transition can be affected experimentally by i n r r e n h y the normal d e n s ~ t UC s the s\stem t t , r t.x;imple, by prc~ssure.ivncentratirm. etc.1 until metalliza~ionand rheassocinted "dielectric catastronhe" (viz. n" -) occur The nonmetal-to-metal (NM-M) transition in condensed svstems has been the subiect of intensive ex~erimentaland theoretical investigation 6y physicists and chemists over the nast two decades (24-26). A wide varietv of ex~erimental techniques ranging from transport property measurements to maenetic vroverties have been e m.~ l o.v e dto studv the . . NU-hItransitim in n-tyl~edoped i r m ~ c m d u c t o r (i 2 i ,2.51, transition metal oxidez (271, alkali atoms in inert matrices tAr (281, WOa (29), etc.), and metal-ammonia (30) and related solutions (31.32). The dielectric vroverties of the host material appear to he of cardinal import&ce in determining the binding energy of the localized electrons for the isolated species in the low electron-density limit (33,341. In this context, there has recently been considerable interest directed to the question of the variation of the background dielectric constant with electron concentration N (35)9, as N approaches the critical concentration, N,, a t the NM-M transition (36). Castner et al. (37) and Capizzi e t al. (38) give results from capacitance measurements on n-type doped silicon a t various donor concentrations which reveal the onset of a possible

'

This criterion for distinguishing metals from nonmetals may, in fact. be much older, going back to D. A. Goldhammer in 1913. We define, for our purposes, ambient conditions as the normal density of the liquid or solid at 1 atm pressure eilher at rwm temperature (lor solid-state materials) or at the melting point for molecular liquids (e.g.. liquid hydrogen at -259.14 'C). FM. me purposes of discusion of me doped semicwKluctor systems and sodium-ammoniasolutions. we assume that each donor or solute atom prwuces one electron upon subst!rut!on or olsso utlon on me host mah r or so vent Tnere .s cons derable evmence (see references(25. 3 11 to suggest that tn s is moeed !he case

tallization of elemental and molecular hydrogen, the solid rare Eases, and even the alkali halides-all with remarkable succrs5. A spectacular dppli(xtiot~, l i the simple 111.r~1eld criterim wqn. 1.511is in thc wnrid~rstiund t h imixrtsnr ~ cc~oversim of molecular- to metallic-hydrogen. On the basis of the measured refractive index of liquid hydrogen a t -252.80 "C, Ross (23) utilized the Herzfeld criterion to predict a metallization onset in condensed hydrogen a t a density of 1.02 glcm". The recent ex~erimentsof Hawke et al(44) a t Berkelev now reveal that hydrogen hecmnes metnlltc ar a density ut' r t ~ t r t ~1.M t g,vm ' nnd a calculated pressure d a b o u t 200 (;Pa. ur 2 MIwr. Bergpen 1451has similarly utilized the metallrzntrm criterion 10 successfullv mrdict .T. for n-tvne .. .. Si and (k.~h.ctron-hde droplets, metal atoms in'rare gas matrices, and even the supercritical alkali metals. We therefore follow Herzfeld (15) and suggest that the following simple criterion is a necessary and sufficient condition for predicting nonmetallic or metallic character in the condensed state. ~

-

.-u

-lo5

, I

u

-a w

-

10-I

lo0

lo1

Mole Percent Sodium

.-

~

RIV 2 1 (metal) RIV

101 1oI6

I

loi7

1olq

1oI8 Concentrotion of Dopant (cm3)

Figure 2. Dielectric catastrophe for two systems exhibiting a polarization ca. tastropheatthe NM-M transition. @)The real part of the microwave frequency (10 GHZ) dielecnic constant versus sadium concentration in fluid sodiumammonia solutions IRe~rintedwith oermissian from ref.1431. Caovrioht 1968. ~~. American Inst lute 01 Phyncs I !ol The stallc ale ectr c constant as a f.nct on of excess aonor concentrallan 01 S dopea * In P. IReprmIed wlth permiss on from re1 t37) COoyright 1975. Amencan InrtlMe 01 Pnyslco 11" baminotances. the approximate location of the NM-M transition is indicated polarization catadtmphe in the dielectric constant as N, is apprunched from the tnsulatina state. More recent work hy Hess et al. I N 1 on silicon dur~edwith .~hosnhorus also reveal . giant dielectric constants at the approach to the NM-M transitions. Similar results have also been reported for amorphous Au-Si alloys (401, n-type Ge (41, 42), and sodium-ammonia solutions (43). In Fteure 2 we show t v ~ i c a l results from measurements on $odiumyammonia solutioG(43) a t 298K. and ~hosnhorus donors in silicon a t temneratures . . beluw I K ( 1.2). Both systems obviously shuwa ver!:lnrgeenhanrement in the dielectric constant as the NM-M transition is approached. The reader is referred to a recent article (36) . . bv . T. G. Castner for a comprehensive review of the current experimental and theoretical situation. In summarv, the experimental data certainly lend credence to the ~ e r z f e l didEa uf .Y, at the an imwndinr phrization catastrophe 1%) as.Y metaliic onsit: The Herzfeld criterion (eqn. (5)) predicts that a material will show metallic behavior if its molar volume is reduced below the value R, the molar refractivity obtained a t standard tte.. low density) conditions. This criterion, at varying Irvels dctmtplextty. has nou, heen appliecl it wide rangeofswrtns in order t u t~rcdictthe exhihitine induced .M-Nhl traniir~,~ns critical experimental conditions for the onset of metallic character. For example, M. Ross (23) has employed the criterion to predict the required volume reduction for the me-

.

< 1 (nonmetal)

(7)

Just how well the overall features of the periodic classification of the elements conform to this simple criterion can he seen by referring to Figure 3 which shows the data (46j4for the naturally occurring elements a t their normal densities. As a representative example we consider the elements of Group VIIA. All the halogens have (RIV) < 1, and consequently, we expect nonmetallic behaviour a t ambient conditions. Moving down the group, (RIV) increases. This is consistent with the established picture of increasing polarizability (6-8.47) of atoms leadine, a t normal (ambient) densities, to thetmnsition to thesolid material n t IJand,at higher densi. ties, 10 the metallic state. (In fact. t t i 4 well estal~iillhedthat liquid iodine a t normal densities exhibits various traits of metallic character) (48). In contrast, the group IA elements all have (RIV) > 1and metallic character is predicted for all the members. Note that the Herzfeld metallization criterion (23) predicts the conditions for the onset of metallic character. It does not, however, tell us anything about the actual conductivity variations in agroup for which all members have (RIV) > 1.The resistance of a metal arises from the scatterine of hieh-velocitv conduction electrons from the thermal vibrations of the lattice. Irregularities in the electrical conductivities of elements are successfully accounted for in terms of the differences in lattice characteristics and band occupancies (6,49), but any further consideration is beyond the scope of this article. Groups IIIA-VIA of the periodic table are perhaps the most interesting. These elements effectively straddle the dividing line between localized-and itinerantelectron behavior. One might even suggest that these elements may take on the appellation "transition elements"! Two features of these elements are particularly apparent in the approach to the transition region from the nonmetallic side (RIV < 1). The first in Figure 3, shaded circles represent eiements for which both R and V are known experimentally. in general. densities were obtained from references (46%) and (9).Molar refractivities were caicuiatad from measurements of the refractive index for the vapor at 0 "C and 1 atm pressure, or for the particular condensed state system under ambient conditions set out in footnote 2 (18);for example, liquid hydrogen at -259.14 OC. For certain of the eiements, e.9.. the alkali metals Li-Rb, atomic poiarizabiiities are also known with some precision; see reference (46b). For these situations we estimate R via R = (413)Laa. For certain eiements. R is now known explicitly from experimental to the eiements with larae measurements. In oarticuiar. this awlies ,, enthaioies of atomisation: . -~ ~. for examole. .~ . W. In these situations R wasagain calculated from the above expresson. but now. tho atomtc polarizablllty was obla nea horn me relativ~stc ca,cdat#onsfor the lsoiated atom wavefunction (see, for example, reference ( 4 6 ~ )An ) . extensive tabulation of this sort is given in reference (46d).

-

7

-

~~

~

Volume GO

~

~~~

~

~

~

~~

Number 9

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693

THE METALLIZATION

OF ELEMENTS

-

NON-METALS

Figure 3.The metallilatlan of elements under the ambient conditions Imposed on this planet. The figure shows the ratlo (RI V) for elements of the s-,d-, and pbiock 01 the periodic table. Here R is the molar refractivity and V is the molar volume (see text). The shaded circles represent elements for which both R and Vare known experimentally. The open circles are f w elements of which only Vis known experimentally. The sources of data are outlined in ref. (46) and footnote 4.

is the marked tendencv to form stable diatomic molecules, or more complicated entities (e.g., Sg, Se4, Sea, As4)-as exemplified by the success of the (8 - N ) rule for elemental structures (14). Similar clustering phenomena are indeed well recognized in other svstems traversing the NM-M transition (24-56). The secondaspect concernsthe extremely large dielectric constants found, for example, in the group VA "semimetals". As indicated in the recent review by B. K. Chakraverty (50,51), and the earlier work of J. B. Goodenough (521, both facets are entirely symptomatic of the socalled "narrow-band" transition region separating the three simple canonical states, namely, metals, Mott (ionic) insulators, and covalent insulators. Within the present simple scheme it is also possible to understand the fundamental origin of the well-established diagonal relationship (47) separating elemental metals from nonmetals in the p-block series (Fig. 1). It is well known (53) that R, the molarrefractivity of the isolated, gaseous species is in fact related to the actual total volume occupied by the atoms or molecules themselves. When this actual volume R becomes much larger than the auailable volume V in the condensed state. a transition to a metallic state of smaller volume h~comesneressarv 1291. I)r. ].inus I'aulmg 1541 hus recentls"~.o i n t e dout that the cube root of the molar rviractivity, a gas phase property, is tantamount to an approximate measure of the radius of the outermost valence electrons in the atom. If it is approximately equal to the cube root of the molar volume in the condensed state, then the outer orbitals from one atom will overlap with those from an adjacent atom, and unless there are filled shells, covalent bonds will he formed. If there is a metallic orbital, the covalent bonds will show unsynchronized resonance (54,55), and the system will exhibit metallic properties. Much more work remains to he done in linking the HerzfeldIPauling ideas of the metallic state, and the complimentary Mott view of the transition between the two limiting electronic regimes.

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In somewhat similar vein, the transition to diatomic and polymeric states in condensed media (Fig. 3) may well be generally symptomatic of the impending transition to the metallic state under the more stringent conditions (RIV > 1) achieved a t higher densities. The disparity between estimated volumes for certain isolated (gas-phase) atoms and their counterpart* in the condensed state has indeed been recognized for some considerable time as being symptomatic of interatomic bonding in the solid state (6). That this diagonal demarcation exists even for the canonical states of the p-block elements themselves (47), stronelv the fundamental im~ortanceof the atomic -.sueeests "" size in dictating whether an element exhibits metallic or nonmetallic behavior a t its normal densitv in the condensed state. Here, the well-recognized orbital construction of individual atoms as one ~ r o c e e d sacross the deriodic table gives rise to insufficient orbital-overlab to the metallic state. The well known diagonal relationship in simple chemical properties (6-9, 47) (salt hydration, covalency, thermal instabilities, etc.) for several elements in the periodic table similarly originates in the incidence of the two Fajan's rules (56) in which the ionic size is perhaps the most important feature. The Metallizatlon Onset We have suggested a simple rationalization for the occurrence of metallic character in the periodic table of the elements. In an attempt to highlight the fundamental importance of the atomic properties in dictating metallic or nonmetallic character in the condensed state, we have resurrected and applied the original Herzfeld criterion ( 1 5 ) in its most literal sense. In this form, the molar refractivity, R , is treated as a constant for all densities up to the metallization onset. One feature which a more rigorous approach would have to take into account is the possible variation in R as a result of (mi-

croscopic) interatomic interactions in the approach to the metallic state. Indeed. one sten towards this tvne of selfconsistent approach i s that deGeloped recently-by Castner (57). However, as Berggren (45) has previously pointed out with such elaboration, the present criterion may well lose its immediate and attractive simplicitv. Indeed, the present aoplication (Fig. 3) suggests that evedin its simplest form (e& (7)) the original Herzfeld criterion does indeed give a reasonable firscorder description of the metallization i f elements under ambient conditions imposed on this planet. The two fundamental properties which appear to he of paramount importance in this context are the volume occupied by an isolated atom in its gaseous (low density) form, and the normal (electron) density of the element in the condensed state. The importance of these two parameters in dictating the metallization of two component systems (e.g., doped semiconductors. solutions., etc.) has also been - - - ~ - ~ ~ ~ , metal-ammonia recognized for some time (24,25). In this context Sir Nevill Mott (331 first introduced the idea that the transition from nonm&llic to metallic behavior in these systems might occur abruptly a t a critical concentration N , given by

is ap licable over a range oisome 10Inin .V, tor equivalently. 600 l i n Dohr radii!. nrwided (I; is ohtained from a realistic wave-function for th;isolated donor state. The experimental data are given in Figure 4. Equation (6) can also be written in the general form (37,58) for the dielectric constant r,

+ % 81Na)Ill-

% 4liNa)

4liN,a = 3 Writing the polarizability of the hydrogen-like donor states as 9

n = - (&)3 2

~

~~~~

where a; is an effective (Bohr) radius of the isolated donor or solute state, and C is a constant, typically of the order 0.25. From an extensive analysis of experimental data for the doped semi-conductors, we have recently found (34)that a particular (scaled) form of the Mott criterion, namely

= I1

19) The critical composition for a polarization catastrophe will occur when E

(10)

this occurs when (37.58) N:%; = 0.38

111)

a value not too dissimilar to that found em~iricallv(0.26 f O . r m from our recent snalysis of the experimental results. In Mott's oriainal work 133) the transition from metallic. to nonmetallic sktus in a simple array of hydrogen-like atoms takes place when the (ionic) potential of an electron-cation pair (M+,e-) becomes insufficiently screened via the itinerant-electron gas. Each atom now "captures" its own valence electron, anti a bound, nonconducting state results. Approached from the nonmetallic side, a similar transition occurs if the binding energy of an electron-cation aggregate (M+,e-) is reduced to zero. This is completely equivalent to a polarization, or dielectric catastrophe a t N,, when the (normal) electron-cation Coulomb potential, K (r) = (-e21r) is now replaced by where c is the effective dielectric constant, and r is the electron-cation separation. At the critical density N , for metallization, f(NJ

-

and thus the valence electron is ionized from its parent site, and hence acquires metallic status. More sophisticated treatments (36,57) for the dielectric catastrophe result in a condition for metallization which represents the experimental data more closely. This, coupled with our use of the simple Herzfeld criterion in rationalizing the periodic table itself, lend some credibility to the idea of a simple, universal relation for predicting the onset of metallic character in condensed phases.

-

Log [critical concentration, n c ] ~ c r n - ~ )

Figure 4. Leprlthrnic plot of ewective radlus a;, 01 lhlocslized~lechonstate vs. nitical concentrationfw metaillzatlon. N,, in a variety of systems. Closed cimles represent twocomponent, condensed state systems. Open circles represent experimentaldata for the supercrifialalkali metals. Tlw solid line represents N:"& = 0.26 Figure taken from Edwards. P. P. and Slenko. M. J.. J. Amer. Chem. Soc.. 103. 2967 (1981).

Acknowledamenis We thank numerous culleagues for helpful discussions on the subiect matter of this article. In narticular. we wish to thank sir Nevill Mott and B. K. ~hakravertyfor their considerable assistance in the transition from chemistry to physics; and J. B. Goodenough, A. D. Buckingham, Sir J. Lewis, and A. G. Sharpe for their invaluable assistance in the transition back again. The support of the NSF, AFOSR, SERC, and NATO is gratefully acknowledged. We also thank Dr. Linus Pauling for a most helpful correspondence.

London, 1832.

141 Ermsn,P . and Simon.P. L.,Gilberl'8Annnlen.28.131 11608):etted i n r d (21. ( 5 ) Ephrsim,F.,"lnoreanicChemistry~6fhed.,Oliver and Boyd. London, 1954.

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161 Phillips. C. S. G., and Williamr. R. J. P.. "Inorganic Chemistry." Oxfird llniverrity Press, New Ymk, 1966. !?I Cutton. F. A . and Wilkinson. G.. "Advanced Inorganic Chemistry." John Wiley and sons. New York. 1980. I81 Pnrrirh. R. V.. "The M ~ t a l l i cElemenfr." I.ongmsn, Lundon and New Yurk. 1977. 191 Cmper, D. i:. "The . Periodic Tahle." 4th ed.. Ruftprwnrthr, Londun. 1968. IIOi Dye, J. L..Anleiil C h r m In1 Ed. Enel.. 18,587 119791. I l l 1 Peer. W.J..and Ls~uuski..l..I.. J. Am?? Chrm S m . lW,6260(1978). 1121 Edwards. P. P.. i:uv. S. C.. Hnlfon. 0.. and McFarlane. W..J Chem Soc. Chem. CO~~~.,Z~II~S~I~~II. 1131 Huheey,d. E.."lnorgenicChemistry."Hsrper and Row. New York. 1978. I141 Hume-Rothory. W.."AfomieThouryb~r Students of Meullurg?." I n s t i t u t e d Metals. Mmug?sphend ReponSeriesNo. 3. 194L (16) H e d e l d . K. F..Phys. R r o . 29,701 119271. 1161 Goldhammer. D. A,. " D i a w r a h und Absnrption des Lichtes." Teuhner. Leiprig,

Mntt. N. F. Philmr May., 6.287 (196l1. Edwards. P P. and Sienke M. J.. P h v r Re&,.,R17.257511978) See Raferenrrs 125,261. Castner,T.G.. Phibr. M o g . 842,643 119791. Castnrr.T.1;. Lee. N. K..Ciplorssk. C;. S.. and Salinger, G. 1.. P h i . A n . L r l t r . 3 4 . ,,a7

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