A Thermochemical Note on the Bonding in Metallic Crystals R. J. Tykodi Southeastern Massachusetts University. North Dartmouth, MA 02747 The bonding in metallic crystals has been dealt with in terms of hand theory ( I ) and in terms of covalent bonds resonating among nearest neighbor positions (2).I wondered what light the newer compilations of thermodynamic data (3. 4 ) could shed on the hondine in metallic cwstals. and I compiled the results displayel below for t i e me& of HumeRothery's Class I (5)for which data are available. Consider the following two processes for a metal (M) of Class 1a t 25 'C and 1bar:
where "mol-set-'" means "for the set of mole numbers given bv the stoichiometric coefficients in the dimlaved reaction " equation" (6). The ouantitv A,H0 is twice the e n t h a-l ~ - vreauired . for a metal atbm in ac&stal to escape from its crystalline environment into the gas phase. The quantity A* is the hond enthalpy of the corresponding diatomic molecule in the gas phase. I call the ratio A I H ~ I A the~effective ~ O bond number, Ef.B.N., of a metal atom in its crystalline environment: the enthalpy required to escape from the crystalline environment is a certain numher (Ef.B.N.) times the enthalpy required to escape from a covalent bond-to escape from the crystal, the metal atom must overcome an "enthalpy harrier" eauivalent to that of hreakine the reouired numher (H.B.N.) of covalent bonds. In the table are shown A4H0.AIHo. EtB.N. (AIH~IATH'). and t h e ~ r ~ s t a l c o o r d i n a t ni ~; nm b e r ( ~ . ~ .fo;tl;e ) metalsof Class I for which data are availahle (3.4) at 25 OC and 1 bar. Because of the extreme weakness of the bonds in diatomic molecules formed from the alkaline earth elements, the correnponding effective hond numhers are of little relevance to the bonding in crystals of those elements. Note that the average effective hond numher for crystals with coordination number R (alkali metals) is 3.2 andexcluding the alkaline earth elements-that the corresponding average value for coordination numher 12 is 4.5. In terms of the thermuchemical auantities considered above, the crystalline environment of an atom of a metal of Clasa I is eauivalent to that of an atom covalentlv bonded to three to eight other atoms.
.
306
Journal of Chemical Education
The thermochemical results displayed above should be of interest to anyone contemplating a Pauling-like (2) treatment of the bonding in metallic crystals in terms of resonating covalent bonds. Literature Cited 1. West, A. R. Solid Stote Chemistry and Its Apnlicotiom; Wiiey: Cbiehestm, 1984, Chapter 14. 2. Pauling, L. The Notwe of the ChomicolBond, 31d ed: Comdl: Ithsca, 1980.Chapter 11. 3. Wagman. D. D.:Euaoa. W . H.: Parker. V B.; Schumm. R H.; Halow, I.; Bailey, S. B.: TheNBS Tobkr o1Chomicol Thermodvwnriefiooertiea:J.Phva. . . . Chem.R#l.D.~oto 1982,11,Suppl.No. 2. 4. Chase.M. W.;Dauies,C.A.:Doamey,J.R;Frurip.D.J.;MeDonald.RA.:Syverud,A N.; JANAF Thwmochemhol Tablea, 3rd ad.: J. Phyr. Chem. Ref.Doto 1981.14. Suppl. No. 1. 5. H u n r R o t h e w , W.: RBynor. G.V. The Structure afMefols and Alloys. 4th 4.;Inatitute of Me* london, 1962. 6. T y k d i , R. 3. Chom. Enp. Neu. 19SE.B8,66(. 23.6.hune). 3.
Thennochemical CharacterI.tlcs ot Class I Metals at 25 'C and 1 bar
