Behavior of some elements during magmatic crystallisation

Geochemiu& notes

664

der Elements. Slw@sr Nor&e v. M. (lW7) GozDscm VMW-AM. MO, ~~.-~~. El. I. GOLDSCHMIDT V. M. (196%) t?es&m&@/, p. 489. Oxford Uuivsrsity Press. I&Y I& II. (lQ66) C&&gu8 of M&es&x (3rd edition), pp. 680-626. Th5 British Museum (N8td Hietory}, London. Public&ion No. 464. IIUOEESD. J. (1963) Pa Neubron.&MU+&, Chap. 4. Addison-Wesley. EEMP D. M. and Smaawea A. A. (1969) The determin&ion of vsmxlium iu rocks zud meteorites by neutron-e&iv&ion suslysis. Ana& C%n. Ada S, 397-410. bGLUERT G., Bos~n J. and mu?! J, (195%) Astivefion analysis of vsmuliuxnin high 811Oy steela u&g merqpne aa instaudsrd. Ad. Ckim. Acta lB, 100-107. Lovum~a J. F. (1967) Tempsr&ures snd pressures within 9 typic& parent meteorite body. &xhirn. Caa+no&~. A&a l& 263-261. N~CHIPOR~K W. aad C!EODO~ A. A. (1969) The conoentrations of vanadium, chromium, iron, sob&, uiokel, copper, zinc end srsenio iu the meteoritic iron sublde nodules. J. G&&I& Res. 64,246 l-2403. WAS%BN J. T. (1967) Private communiostion. WAMON J. T. and KIXE~BZZH J. (1967) The .ehemicsl a&v&%&ion of iron meteorite+--II. Irons end pnllasites with germznium con~ntr6tio~ between 8 and 100 ppm. Qeoohkm. Codim. A+ Sl, 2066. WIPSTG. B. (1963) Crploulatedfluxes end or088 se&ions for TRIGA msotors. General Atomio Report GA-4361,176 pp.

PAUL E. DAHON Depzrtmsnts of Geochronology and Geology, The University of Arizona, Tumon, Arizona 86721

(Rsaeid

4 &x&e?

1967; aceepksdda ret&eii&rtn 2 Jcb?&~w 1968)

&h&6&--Followiug soncap@ first iutroduosd by PA~IXNC?,8 simple equation can be derived for prediotion of single bond energies for distomic mol~ules. For transition elementa an sdditiod term must be added to aoaouut for cry&d ii&d &&ilization. When allowance is m&e for multiple bonds, this equation provides B quzntitetive substitute for Goldschmidt’s rulss. It has the added advantage of &so inuorpor&ing the influenotaof elestronegstivity dif%renCefI. A BECENT paper in this joxzrmd, NOcxorJ3S (1966) haf8 painted out the &m&g&y and inadequzey of Goldsnbmidt’s rules add he baa propossd sn &ern&ive zpproaeh to the perem& problem of prsdi&ng the b&&or of elements during fractions1 sryst8tlisztion of a w. This paper wss of psrtioular interest to me bus% during the past 8~vsrsl years, I heve bssn following 8 eimiler line of m9sonmg in Bosdemiofeatures in geosbemistry end in trzoe element studies (DAXON et al., 1964,1966). l3ri&ly, Noondr+ns(1966) propozss en sppratrohto the problem that iuvolvee the calculation to tb qq~~xia~~& totel bond energy (Fr). The total bond of a number whioh energy is oompossd of three pscts which BW the oovslent oontribution (V,), the iouis msonzxuoe contribution ( V,), end the arystal field s~bilisstion energy ( V,) :

IN

vp = vo -t- v, t

v,.

+ ContributionNo, 132, Univzrsity of Arizona Apogrem in aeodhronology.

ill

Geochemical

notes

665

SOCKOLDS uses SANDERSON's (1960, pp. 31-52) formula for calculating the covalent energy, McClure’s (CURTIS, 1963, Table 4, p. 394) estimate of the crystal field stabilisation energy and the following formula for the single bond ionic resonance energy: 265Aa v1 = R

(2)

’

where A is the electronegativity difference between cation and anion and R is the bond length. The single bond energy is then multiplied by the formal charge of the cation (valence) to obtain the total multiple bond energy. If valid, this relationship has the virtue of considering charge, radius and electronegativity simultaneously, thus incorporating Goldschmidt’s approach with RIN~WOOD’S (1955) and FYFE’S (1951) emphasis on the importance of electronegativity. Unfortunately, 26.5A2 is PATJLINQ’S extra ionic energy and, consequently, dividing by the bond length not only makes the equation dimensionally invalid but results in too small an ionic resonance energy. PAULINE (1960) has shown that the ratio of the experimental electric dipole moment to the electric dipole moment calculated for a rigid ionic structure is given by the following relationship :

$*

=

(1

-

e-o.*sq.

r

(3)

He refers to this ratio as the amount of ionic character. If it is assumed that the bond length remains constant, then the lower values of pexp relative to prigid can be ascribed to the transfer of a fraction of the formal charge from cation to anion. If e is the formal charge and e’ is the effective charge, then:

p =

2 =$ =

(1

_

e-o~*u~),

and consequently, e’ = Fe

(5)

where P is, by definition, identical to the expression on the right hand side of equation 3 as indicated in equation 4. The single bond ionic resonance energy can then be calculated from the following equation :

Jr‘

=

!c!t!~ = 33op R

(6)

where 330 Kc&/mole is the ionic bonding energy of a rigid molecule with bond length of 1 A. Table 1 shows the results of some calculations of V, and V, using values of electronegativity That exception is the use of 1.83 and bond length from Nockold’s paper with one exception. instead of 1.9 for the electronegativity of Mn2+. The total bond energy, V,, is obtained from equation 1, making allowance for multiple bonds by multiplying the single bond ionic energy, V,, and the single bond covalent energy, Vo, by the formal charge on the cation Z,. The difference in the two values of total energy, V,, given in Table 1, is entirely due to use of the different values of ionic energy (equation 2 vs. equation 6). The column headed “ % Ionic” in Table 1 is obtained by dividing the multiple bond ionic energy (2, x V,) by the total energy, V,, and, of course, multiplying by 100. F is calculated directly from equation 3. It can be seen from the table that the relative total energies are similar to those of NOCKOLD’S, but equation 6 yields higher V8heS of V, and values closer to F for the per cent of the total bond energy which is ionic. Except for Ni2+, Co2+ and Fe2+, which involve crystal field stabilisation, the calculated fractional ionic character is within 10 per cent of F. I have chosen the transition elements for comparison because crystal field energies are involved, and the other elements were chosen because of their diadochy with Ca2+ or K’-+ in

Geoohemioal notes

666

Table 1. Bonding energie%of X-0 Bond X-O

VI Thispaper Koalfmole

V, Thiapaper Kcal/mole

VJ ~OCKO&DS

Kcal[mole

Vr NOCKOLDS

Kcal[mole

bonds 9: Ionic P x 100 This paper _l..-.---_---_-"^..

-_

-..a*_ ?,,’ To&

KOC+K~I,~S _-.. _".

Ni”---0 co’+---0 FE@---0 niin~-o .ZnZ+---0 C&B+---0 K&r+--0 SW---0 Al*---0 cu*+-0 A&+-O K1+--0

74 37 37 39 49 42 84 86 39 63 35 34 80

59 34 34 35.5 44 37 66 69 37 51 33 31 F.5

232 203 189 185 I84 180 236 117 388 336 81 74 105

202 197 183 178 174 170 200 100 480 300 79 71 !I0

68 47 47 49 57 51 78 79 45 tit) 47

64 37 39 42 53 47 71. 74 48 56 43

4!)

46

76

58 3s 37 itt $1 ,II 41 66 69 a9 51 42 44 ‘72

Rbl+--0 c!s’+-O TY*+--0 Sr~+--O Baz+--0 Pb2+-0

76 72 45 80 76 30

62 60 37 68 62 28

99 93 82 223 209 142

85 81 74 191 186 138

8:! 82 60 79 80 47

7: 77 55 $2 ;3 42

7;i 7.1: 50 68 69 $1

r&3+--0

82

feldspars. The predicted order of substitut.iorr of the transition elemtintu Or Mg”+ dunng fractional crystalhsation is in good agreement with observation: cation:

V, Kcalsjmole:

MgZ+ 3%Ni2” :, (‘OW

v,‘W A M!lW r xii” -

232 > 203 > 189 _I 185 t

1% ,a 180.

In the aase of solid solution for Ca2+ in plagioclasn: cation pair: V,, Kcaljmole:

~%2+~13+

r N&1T‘ji4+ .I_&l+siQ

> L\gi-~~W-

576 > 505 :a 469 :z 462.

In the osse of solid solution for K’+ in potash fekispars: cation pair:

V,, Kcaljmole :

559 > 545 > 493 :> 487 > 481 > 478 > 470 > 462.

Thus the predictions of behavior of elemonta are in good accord with observation when tha total bond energy method, euggeeted by NOC~OLDS (iB66), is modified by the sub~titutioi~ of Bquation 6 for Nockolds’ method of caloulatiug the ionio resonance energy. The advantages of equation 6 are that it can be derived fkom fundamental principles, yields reasonable results, and does not violate dimensional restriotions, Furthermore, because it has b&n deIno~t~t~ that 3 is a good measure of the fiaotional ionic contribution to the total bond energy, divi&on of V, by E” yields a good approximation to the sum of oovalent energy plus ionic energy. Thus, equation 1 oan be expressed as follows:

Geoohemical

notes

567

Equation 7 is a quantit,ative expression incorporating Goldschmidt’s rules mod&d to include olectronegativity and crystal field stabilisation energy. It has the advantage of allowing an unequivocal estimation of the relative importance of the different factors involved in diadochy . A systematic analysis of solid solution relationships shows that the nature of the solid solution is determined primarily by the radius of the end members, whereas melting temperatures of the pure end members are determined in large part by the total bond energy. Continuous ascending type solid solutions do not generally form when the difference in the radius of the cation end members exceeds 20 per cent. When the cation radius difference exceeds 20 per cent, solid solutions with minima tend to form. For example, Nal+ and Ca2+, which have almost identical cation radii, form a continuous ascending type solid solution. The Ca2+A1” (572 Kcal/mole) pure end member (m.p. = 1550°C) melts at a much higher temperature than the = 112O’C). On the other hand, when Na’TNa1+Si4+ (505 Kcal/mole) pure end member (m.p. snbstitutos for K’+, the approximately 26 per cent difference in cation radii results in a solid solution series with a minimum. In this case, the melting temperatures are not very different. The pure potash end member melts at 1170°C (K I+ Si 4+ = 493 Kcal/mole) and the pure sodic end member melts at 1120” (Na1+Si4+ = 505 Kcal/mole). h’OCXOLDS has presented a very powerful approach to the problem of the behavior of elements during magmatic crystallisation. I believe that the calculations can be significantly improved by use of the equation’for ionic resonance energy derived in this note. REFERENCES CI!HTIS C. D. (1963) Applications of the crystal-field theory to the inclusion of trace transition Geochim. Cosmochim. Acta 28,389~403. elements in minerals during magmatic differentiation. D.4MON P. E. et al. (1964) Correlation and chronology of ore deposits and volcanic rocks. Annual Progress Report No. COO-689-42 to U.S. Atomic Energy Commission. DAMON P. E. et al. (1965) Correlation and chronology of ore deposits and volcanic rooks. Annual Progress Report So. COO-689-50 to U.S. Atomic Energy Commission. FIFE W. S. (1951) Isomorphism and bond-type. Alner. Mine&. 36, 538-542. NOCKOLDS S. R. (19G6) The behavior of some elements during fractional crystallization of magma. Geochim. Cosmochim. Actn 30, 267-278. Cornell University Press. I’AI.LING L. (1960) The Nature of the Chemical BonrE (3rd edition). Rr~owoor~ A. E. (1955) The principles governing t,race-element distribut,ion during rnagmat,ic differentiation. Part I. Geochim. Cosmochim. ilcta 7, 189-202. SAXDERSON R. T. (1960) Chemicul Periotlicity. Remhold.