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Chemical binding in silicate minerals Part III. Application of energy calculations to the prediction of silicate mineral stability
Qeochimica
et Cosmorhimira
_&eta, 1986,
Vol.
30, pp.
323 to 339.
Pergamon Press
Ltd.
Printed inNorthern Ireland
Chemical binding in silicate minerals Part III. Application of energy calculations to the prediction of silicate minerd-stability M. SLAUGHTER Crystallography Laboratory, Department of Geology University of Missouri, Columbia (Received
19 April
1965; in revised form 4 September
1965)
Abstract---Combining Coulomb energies with appropriate corrections makes possible quantitative prediction of stability relations of minerals. Melting and decomposition temperatures of some minerals including corundum and quartz have been calculated from the binding energies. Agreement between calculated and observed melting points of minerale is exceptionally good when covalency, radius-ratio, and coordinationeffect correctionsare made to the melting points determined from Coulomb binding energies. Thermal stabilities of some phyllosilicates are predicted semiquantitatively. Calculated energies show that the stability of montmorillonite with respect to other phyllosilicatea in most low-tempemture geochemical environments is probably the result of hydration of the inter-layer space. Also, when small amounts of magnesium are present in a silicate system montmorillonite is the phase which minimizes the total energy of the system. INTRODUCTION IN Parts I and II of this series, a model and methods
have been set forth for calculating and using energies for deducing physico-chemical properties of silicate and oxide minerals at low and high temperatures. In this paper the model and energy calculations are used to illustrate several different types of geochemical applications. Melting points of several oxides are calculated assuming complete ionic binding and the assumptions used in the simple model of Part I. The thermal stability of alpha and beta quartz is determined to illustrate the use of the model for predicting polymorphic transitions. The dehydroxylation temperatures of some phyllosilicates are related to structure and composition. And the low-temperature stability of montmorillonite in Wyoming bentonites is considered using both calculated and experimental free energies of formation. THE APPLICATION OF ENERGIES TO THE CALCULATION OF MELTING POINTS
Calculation of melting temperatures of several minerals illustrates the use of binding energies in determining the thermal properties of minerals, and demonstrates to what extent covalency can be ignored in the consideration of mineral reactions. Coulomb energies of the compounds whose melting points are to be determined are listed in Table 1, with calculated minimum or pairing and observed cation-anion and anion-anion distances, respectively. The calculated values R,, in Table 1 are equal to sums of cation and anion pairing radii for NaCl-type structures, or have been derived from equation (12), Part I, for non-NaCl type structures, and represent the 323
89
60 63
2.014, 2.72(B)
._- ...-.-.---I.95 , 2*70(A)
2.67, 2.70 2.31, 2.70 2.25, 2.78 2.04, 2.78 2.28, 2.78 2.072, 2.78 f-945, 2.70
1.865, 2.78
1.861, Pi%
1.610, 2-78
ICI? NaF NasO M& CaO Fe@ &fgFzb
TiOah
4G3
p-&O,”
a Fe,.,, 0 N Fe&&, Fe$&O. b Struoture of RAWR (1956). c Structure of YOUNG (1963). d Energy adjusted to n = 7.0
1+9&w.), 1 x 2.50 1 x 2.72 I+94(av.), 2.595(av.)
2.672, 2.72 2.314, 2.72 2.407, 2.78 2.106, 2.7& 2.406, 2.78 2.150, 2.78 2 x 1,997 , 1 x 2.577 I >: 1.98
51
92 91 82 73 79 55 86
Per cent ionic character
RBn Observed
IzAB,
Calculated
.--
1841.1
1450.3
94.7”
217.1 250.7 347.5 1101.7 984.8” 1103@J 403.4
-
480.7
575.6
551.8”
228,9(223)d kcal mole-l aniorr2 183*8 207.5 233,7 593.6 614.6d 333.6d 298.1
____.
-- Coulomb energy Ionic covalent
288~0(280)~
Ionic
for calculation of melting t.emperatures
Solid ---_LiF
Table 1. IMa
Chemical binding in silicate minerals-III
325
mimim~ cation-anion approach distances for the particular structural configuration. Calculated values of Rnn are simply twice the pairing anion radii of Table 2, Part I. Observed values of BdB or RBB are crystal distances measured at room temperature. Multiple cation-anion distances are listed and multiplied by the relative frequency of each. Where all anion-anion distances are not the same, the number of anions per anion at the given distance is the multiplying factor; all other anion distances in the structure are greater than twice the anion radius. The values of percent ionic character listed in Table 1 were determined using Pauling’s formula : Amount of Ionic Character = 1 - exp - 4(X:, - X,)2 where X is the electronegativity. Coulomb energies are expressed as the energy of one formula weight divided by the number of anions in the formula. Coulomb energies have been computed from published values of the Madelung constants. The covalent-ionic Coulomb energies were calculated from Madelung constants employing the cation charges as determined from the appropriate electronegativity differences. The results of melting point calculations are presented in Table 2 with radiusratio, coordination, and polarization correction listed separately. To contrast the melting temperatures calculated for the ionic-covalent model the melting temperat~es were also ~alcula~d assuming complete ionicity of bonds. These results are also presented in Tables 1 and 2, The calculated melting temperat~es of the io~c-covalent model with co~ections for radius-ratio and other effects agree s~prisingly well with the observed melting temperatures, particularly considering the number of approximations. It may be worth noting that the assumption that all radius-ratio and coordination effects are eliminated with fusion, would require the melting points of compounds to be invariant with changes in composition of the system. An alternative expedient is to introduce a proportionality constant into the calculation of melting points to make the elimination of radius-ratio and coordination effects during fusion incomplete. Introducing a fractional reduction in the corrections will not affect the calculated melting points of the pure minerals. However, fusion temperatures of specific species will vary when the composition of the system is not the same as that of the mineral. The reason for the variable melting points is that radius-ratio and other effects in the liquid phase do vary with com~sition. ALPHA AND BETA QUARTZ TRANSITION
One test of the method proposed in Part I is the ability to use the method to predict transition temperatures of polymorphs which differ very little in binding energies. The CouIomb energy of /?-SiO, was determined from the published Madelung consent. The binding energy of a-SiO, was estimated to be about equal to the energy of @-SiO,. The coordination corrections employed the parame~~ of Yoa~a and
5578 4957
5473 1869 8050 742% 9542
MgO CaO
Fe0 MsFz TiO, *‘zOz B-SO, r-SO,
324°C’
19 555
1296 1606
1269 210 2550 1162 0 0
1115°C
1038 1179
3450 3547
1800 1597 3209 333% 2742 -2742
temperatures
0°C’ 0 0 0 0 0 183 1544 2423 5460 -I
235°C 152 373 637 1035 400 169 887 425 (t 0
minerals
0°C’ 0 0 0 0 0 0 349 llr0 --
0°C: 0 0 0 0 0 125 512 886 1312 1172
0 0 112 ni0 -. .-
0 0
0 0
0°C’
AT Polarization IonicIonic covalent -.-______~
of’ selected
--AT ~‘oordination Ioniccovalent, ionic ___-
2. MelGng
-AT X.adinz+ratio Ionic: Ionic covalent -----.-.
* From Coulomb energy. 7 Melting temperature of cristobalitcx. $ \vWKS and BLOCK (1963).
1194°C
1058 1572
LiF
Ionic
NaF Na@
________--._
Ioniccovalent .- _~___
Initial*
Table
2813 2512 1400 1303 1902 2027 1547 1570
4282 3351 4204 1456 4306 3843 4202
-
-
1024°C’ 806
Ionic
1039°C ( 1017
loniccovalent
Final
1263 1840 2050 1713f (16lO)g
2800 2570 1370
992°C’ 897
-._.
Observed
$ 0 g S
.z %
Chemical binding in silicate miner&-111
327
POST (1962) for a-SiO, and the structure of YOUNG(1963) for /?-SiOz. Results are given in the last row of Table 2. The “melting” temperat~es of a-SiOz and &SiOz are physically meaningless, Silica, however, differs from most of the structures of Table 2 in that it is an “open” structure in which small rotations of tetrahedra preserve the essential structure but change the individual Coulomb and repulsive interactions. In calculating the “melting” temperature, the interactions of first anion-axon and cation-axon neighbor interactions were accounted for. However the a- and &silica structures can open in the liquid state by rotation of tetrahedra so that second neighbor anion-anion and first neighbor cation~ation interactions at high thermal vibration levels have a smaller elect on the energy. For second neighbor i~lteractions at higher vibration levels, the chief increase in interaction energy should result from anion-anion, overlap repulsion. As the z- and @W& structures open with increasing temperature, ~larization energy is lost (raising the melting point), while second neighbor cations become further apart as the Si-0-Si bond angle increases from about 150 to 180’. Table 2 lists calculated corrections and the final calculated and observed upper limits of thermal stability of a x- and /?-SiO,. The calculations are based on an average Si-O-Si angle of 150 and lii23 for a- a.nd P-quartz respectively. THERMALSTABEITYOF PYROPHYLLITE, TALC ANDOTHERPHYLLO~ELICATE~ A number of phyIlosilicate phases including p~ophyIlite and talc occur in the system SiO~-MgO-~~O~-~~O. Several important papers on this system are available, among these being that of ROY and ROY ( 1955) who present data convenient for relating calculated energies to experimentally determined equilibrium phases. The paper of Rou and ROY will, therefore, be taken as the primary source of information to which reference will be made in this paper. The electrostatic binding and overlap repulsion energies have been computed for various models of pyrophyllite, talc, and montmorillonite. The structures assumed basic for the computation of the Coulomb energy of pyrophyllite and talc were determined from X-ray data first by CRUNER(1934) and later by HENDRICKS(1938). CRUNESdetermined the placement of the octahedral ions in pyrophylli~ and talc to be as shown in Fig. l(a) and the octahedra1 oxygen and hydroxyl atoms for the lower half of the cell as in Fig. l(b). Silicons without their tetrahedral oxygens are shown in Fig. l(c). Cell parameters, space groups and atomic coordinates employed for energy computations are given in Tables 4 and 5. The montmo~llo~te structure model was constructed from that of p~ophylli~ by random substitution of one Mg+* for one of the eight AlfS ions occupying the Al sites in pyrophyllite. The charge imbalance was restored by placing _iliiof an Mg+a atom in a special position of the interIayer space; this position is marked with an “x” in Fig. l(c). The structures of the phyllosilicates are in general not accurately known; however, it should be possible to make at least qualitative estimates of the thermal stability of p~ophyllite, tale, and some other three-layer phyllosilica~s. The energy values are given in Table 6. The Coulomb energy-derived temperatures has been
corrected for the fact that the energy is that of an unrefined structure. An approximate correction factor for refinement was found by multiplying the energy of pyrophyllite by the ratio of the energy of the refined muscovite structure of RADOSLOVICH (1960) to that of the unrefined structure of JACKSON and WEST (1933), i.e. 1.006. Radius-ratio and coordination corrections were made from the RADOSLOVICHstructure of muscovite and the STEINFINK (1962) structure of phlogopite, without aluminum substitution in the tetrahedral layer. The results of calculations for yyrophyllite and talc are given in Table 7. PYROPHYLLITE
G
a.
I
b.
C. Fig. 1. Projection of part of atomic positions in pyrophyllite-solid circles are in upper half of cell. (a) Aluminum positions (b) oxygens and hydroxyls surrounding aluminums in (a)-circles with dots are OH’s; (c) Silicon positions.
All coordination and radius-ratio corrections were made in the manner of the calculations for quartz. The Si-0 correction for pyrophyllite includes both the coordination and polarization correction. The Si-0-Si angle employed in the Si-Si coordination correction was 130 and 131” for pyrophyllite and talc respectively. The final calculated dehydroxylation temperatures are rough, because the structures are not refined. The dehydroxylation temperature for talc is too high by about 80°C. Had not the data from a partially refined structure such as muscovite been used the errors might have been 30-40 per cent in determination of coordination corrections. Specifically the effect of magnesium in the octahedral layer of talc is to expand both the octahedral layer and the tetrahedral layers relative to the expansion by
Chemical binding in silicate minerals-III
329
Table 3. Upper limit of thermal stability of SiO, at low pressure AT Correction
-o-o
1st neighbor coordination coordination 2nd neighbor coordination
Si-0 o-o
a-SiOs
&SiOs
-1172°C
- 1547%
0
+ 235
- 438 + 385 - 920 2742°C -2145 597 573
Polarization Si-Si coordination Initial Total AT Final Observed
- 237 + 400 - 770 2742°C - 1859 883 867
Table 4. Cell parameters and space groups
Pyrophyllite Talc Montmori~onit~
a
b
5.16A 5.28 5.16
&9OA 9.15 8.90
C 1864A 18.92 1864
B
S.G.
100” 100” 100”
C 2/o c 2/c C 2/c
Table 5. Coordinates of atoms in py~phy~ite, talc, montmorillonite
Atom
Al@%) Six Si, 00, 0% OT, % Or, OH
H
Pyro.,
Talc, *
Mont.?
X
Y
2
0.333 0.167 o-000 0.167 0.500 0.084 0.084 0.333 -0.167 -0.164
0.000
o-000 O-261 -0.239 0.203 0.203 0.025 -0.475 0.275 0.203 0.203
* Mg at 0.000, O+OOO, O*OOO. t M2+ at 0.500, 0.350, 0.250.
0,143 0.143 0.058 0.058 0.176 0.176 0.176 O-058 0.110
* kcal~mole.
OH 0 H $@+z
-0.633 -1.023 0‘390
“828.5
2657.9
-_
2814.5
43.6
175.9
2644.7
~
71.6
175.8
166.9
I- 1 so25
OT*
173.4
169.6
234.7
165.0
161.1
246.3
- 1.025
I.145
410.3 598.6 597.6 234.9
0%
-
372.2 607.5 606.4 246.5
Wf0.39
-1.025
02
1‘900 2,050 2.050 - 1,145
HtO.00
-Ec*jiosi
Pyrophyllite
0%
0
Si, Si, 0 01
Al
Chg.
-
1282.5
110.5
160.0
l64.3
164.3
164.3
7&O 142‘8 141.8 161.4
EB*/ion
_.-.
-- 0,730 - 1.120 0.390
2761.4
2750.6
94.6
162.3
-~ 1.025 170.7
169.X
169.3
161.5 161.3
276.X
398.8 611.5 609.8 276.6
J$-W3+
288*0
358.1 620.0 618-3 288.2
H+o.oo
Talc -E&on
- 1.026
- 1.025
- 1.234
1.46 2.05 2.05 - 1.243
Chg.
..__123!?.9
117.9
136.8
142.4
142.4
162.4
138.1 129.2 128.2 162.7
E&n
._.
.
2837.7 ~__. _._
U-8 12.7
170.1
186.5
.- 1.025 -- 1.040 .- 1,054 0,390 OG.83 0.225
179.2
175,Y
229.1
408.8 594.5 592.5 229.3
Rig
2862.S
16.0
4.5d
172.9
190.5
181.7
179-3
232.1
415.2 592.5 590.4 232.3
Na,
Xontmorillonitc -E&on
.- 1,025
1.845 2.050 2.060 ,-1.158 - 1.172 - 1~158 - 1.172 -L.O25
Chg.
Table 6. Calculated coulomb and repukive enrrgiw of ~~~~~phyllit,e~t,alc xnd lnontmorillonitc
::
164.3 169 3 111.6
---1300.; 1351~0
16.!>
i.3
2 3
F K F 164.7 1653
164.3 164.7
162.3
79.0 142.8 141.8 162.7
Mg,Ka
E&on
Chemical binding in silicate minerals-111 Table 7. Dehydroxylation
temperature
of pyrophyllite
331 (P) and talc (T)
R “Bond”
Ohs.* (P)
0~O~(lst %-%I OTSi Si-Si O,-Si O,,-Al O,,-Al OH-Al %1-O,, %a-%2
OH-OH O,,-OH (),-OH K-OT
neighbors) (2nd neighbors)
2.68,
-AT Calc.
(T)
(M/PHI t
A
~+v_JA(av.1
(T)
(P) 2.78
A
(P)
(1’)
575°C 135 60 -702 1281 1226 3 63 120 94 120 130 27 119 0 3 26 62 60
(WPH) 349°C
165
2.70, 1.60, 2.87, 1.64, 1.94, 2.108 1.99, 2.108 1.93, 2.034 2.39, 2.78 2.76, 2.78 2.51, 2.73, 2.68, 3.06
2.78 1.62 3.20 1.64, 1.84, I.940 1.84, I.940 1.62 1.947 2.78 2.78 2.78 2.78 2.78 2.78 2.78 2.75 Total
-AT
55 i86ti(P)
1693(T)
Initial ionic-covalent “melting” temperature-2465°C (P). Initial temperature corrected for lack of refinement--2479°C (P). Final dehydroxylation temperature-(247Q-1868)“C = 611°C (P). * Muscovite (RADOSLOVICH, 1960) and phlogopite (STEINFINX, 1962) distance. t Muscovite and phlogopite where they differ appreciably from pyrophyllite and talc.
aluminum in the octahedral layer of pyrophyllite. The expanded structure at higher vibration levels has a smaller overlap repulsion and therefore is thermally stable to higher temperatures. The expansion effects are reinforced by slightly higher ionicity in talc. In addition to predicting that talc is stable to higher temperatures than pyrophyllite, one may also predict that any Mg-trioctahedral phyllosilicate should be stable to higher temperatures than Al-dioctahedral equivalents. Biotite would be predicted to be stable to higher temperatures than muscovite and phlogopite to higher temperature than biotite. Applying the partial ionic octahedral layer model to two-layer phyllosilicates, increasing amounts of aluminum in the octahedral layers should tend to decrease the upper thermal limit of stability in the following sequence : serpentine, amesite, kaolinite. Each of these predicted relations compare favorably with the data of ROY and ROY and other similar data. The higher temperature range of thermal stability of minerals such as muscovite and phlogopite relative to pyrophyllite and talc is due to differences in Crst and second neighbor oxygen coordination effects in the tetrahedral layers. In phlogopite and muscovite there is one aluminum substituted in every fourth silicon position. The Coulomb energy difference and the resulting thermal stability differences between the tetrahedrally substituted and the unsubstituted phyllosilicates is small. Aluminum, when substituted for silicon reduces the coordination effects in the tetrahedral layer, thereby raising the thermal range of stability. Employing tetrahedral
332
M. HL_~UC+HTER
O-O distances of muscovite, calculated for phlogopite and hedral corrections. Adding temperatures of pyrophyllite assumed to be negligible.
approximate corrections for coordination effects were muscovite and were included with dioctahedral-trioctaappropriate corrections to the observed dehydration gives the dehydration temperatures of Table 8, PE2,, is
Table 8. Dehydroxylation temperatures of some phyllosilicates Observed DTA* Pyrophyllite Muscovite Talc Phlogopite
640°C 763 900 1120
Equilibriumt 590 f”C 715 720 *
Calculated 610°C 781 899 1070
* Kiefer, 1949; beginning of dehydroxylation (D.T.A.). t Data from DEER, HOWIE and ZUSSMAN(1962).
The substitution of two aluminum atoms for two of the four silicons probably accounts for the relatively high thermal stability of chlorite. The stabilizing effect of tetrahedral aluminum in chlorite seems to be partially counter-balanced by weak electrostatic binding in the brucite-like layer. Table 9. Dehydroxylation temperature of pyrophyllik with ionic octahedral layer “Bond” ___~ OF-O, O!r-0, OpSi Si-Si O,--Si O,-Al O,,-Al OH-Al Ocli-001 OrJz-00, OH-OH O,,-OH O,,OH Total AT Initial temperature Dehydroxylation temperature
__hT 575” + 155°C 65 --702 1281 45 223 285 321 208 6 40 104 120 -2651°C 3542°C 891°C -
No covalency in the octahedral layer of pyrophyllite gives the calculated upper limits of thermal stability of Table 9. The calculated values do not agree with the observed values as well as the model in which covalency in the octahedral layer is compensated for by decreasing the octahedral charges. Increasing ionicity much above the values from PAULINO’S formula will not improve calculated decomposition temperatures.
Chemical binding in silicate minerals-III
333
As the charge on the octahedral oxygena increases, the total electrostatic binding energy increases, largely due to the greater magnitude of the potential at Al and Si sites. Hence, the total binding energy of both the octahedral and tetrahedral layers is larger for three-layer silicates than two-layer silicates because of the relatively low charge on the oxygens of the hydroxyl layers of two-layer silicates. Based both on the binding energy differences and radius-ratio-coordination effects, the high temperature limits of stability of three-layer versus two-layer silicates should then be following: pyrophyllite > kaolinite ; talc > serpentine ; chlorite > amesite (‘1?). Qualitative agreement of these predicted conclusions with experimental data of ROY and ROY is good. THE STABILITY OF BENTONITICMONTMORILLONITE AT Low TEMPERATURES The bentonites found in the Cretaceous rocks of the Western Interior of the United States may be typified by the bentonites of Wyoming (SLAUBHTER and EARLEY, 1965). From mineralogical evidence, the bentonites were formed by the alteration of volcanic ash (glass) of average composition equivalent to latite (or monzonite) or quartz latite (Table 10). The alteration products in the bentonites are chiefly montmorillonite, with a few weight percent of zeolites, and small amounts of kaolinite and silica. The montmorillonites have about 8Na and _S(Mg + Ca) as exchange ions (WILLIAMS et al., 1954). Silica is sometimes found precipitated in the beds immediately overlying bentonites. The field evidence indicates the alteration process took place after deposition of the ash in waters ranging from brackish to marine compositions. The pH range seems to have been about neutral to slightly alkaline. Since the alteration appears to have taken place soon after deposition the temperature of alteration could have been as low as 15’C and probably not higher than 40°C. Table 10. Chemical data on monzonite and montmorillonite (a) Monzonite*
Gram-ions
Analysis
Gram charges
Combined? gram charge
Gram charges $ factor 11.0314
Ions per unit of glass
SiO,
57.44
Si
0.9564
36266
36256
42.2017
Si
Fe,%
3.26 16.39 3.48 3-12
FE?+ Al Fe2+ Mg
O-0484 0.3216 0.0410 o-0774
0.1230 O-9648 1 0.0968 0.1548
1.0878
12.0000
Al
4*0000
0.2516
2.7755
Mg
1.388
0.4110
4.5339
M+t
4.534
*1,0, Fe0 MgG
Na20
3.44
Na
O*lllO
0.1110
K2O CaO
4.37 5-81
K Ca
0.0928 0.1036
0.0928I 0.2072
H,O+ TiO,
0.63 0.92
H,O-
0.24
0
-
-
-
61.5111
0
10.550
30.756
* Monzonite glass. t Al ions are equivalent to all Al and Few ions, and univalent metal ions M+ include Ca. $ Arbitrarily based on 12 charges for 4 aluminum atoms. 6
334
31.
SLAUGHTER
Table 10 (cr,nt.) (b) Montmorillonit~e~ Ions per unit cell
i(
C’ombined ions per unit cell11
_.~~~~ _~~
7.731
Si Al Fe3+
Si
7.731
0.035
Al Fe3+ Mg Na K
Al
3.795
3.166 0.234 0.360 1 0.508
Mg
0.508
0.6641 O.OllJ
MA
0.675
5 Montmorillonite, Clay Spur, Wyoming. 11Based on 20 oxygens, 4 hydroxyls per unit cell. 7 M+-Alkali metal ions.
Given the above geochemical condition is it possible to rationalize montmorillonite as the most abundant stable phyllosilicate phase resulting from alteration of volcanic ash at low temperatures ? A complete treatment of montmorillonite stability will not be attempted, but enough of the problem will be elucidated to illustrate the application of energy calculations for low temperature systems. Table 11. Calculated energies of some silicates and oxides (1 -
--E, &A&.0, + 2Si0, + iH,O Pyrophyllite jMg0 + 2Si0, + $H,O Talc Mg-montmorillonite &,Al,O, + &MgO + &Na,O 2Si0, + &H,O Na-montmorillonite
+
c/7.0)
-2E,
-AFf*
2836.5 kcaljmole 2828.5 2860.5 2954.1 2837.7 2828.9
0.857 0.857 0.866 0.866 O&56 0.858
4861.8 kcal 4848.2 4954.2 5116.6 4858.1 4854.3
1253.6 kcal 1250.1 1277.4 1319.3 1252.7 1251.7
2862.5
0.855
4894.8
1262.1
* Free energy of formation of 3 moles ~0.2578
x
%EM.
Results of calculation of Coulomb and repulsive energies of pyrophyllite, talc, montmorillonite, are listed in Table 6. The Coulomb energies, E,, with an appropriate charge on the hydrogen site were used for deducing low temperature properties. The repulsive energies of Table 6 are those for the completely ionic approximation. The calculated energies of minerals related to these in Table 6 are given in Table 11; the values of E, were calculated from the equation
E, =
E&l
-
c/7.0)
Since E, is approximately proportional to A( AF,), the differences in free energy of formation, values of E, of Table 11 are scaled on free energies of formation of Al,O, + 4Si0, + H,O. Some of these scaled values are plotted in Fig. 2 with observed values of AF,. The value of AF, of SiO, used is 204.75 kcal per mole. The agreement between observed and calculated differences in AF, is very good, althoughtherearesomedifferences between theexperimental andcalculatedenergies.
Chemical binding in silicate minerals-III
335
The calculated differences seem to be accurate enough for deducing mineralogical stability relations. In the system represented by the components on Fig- 2, p~ophyl~te (P) is not a stable phase with respect to its oxides. The line connecting the AF, of pyrophyllite and AF, of talc (T) represents the energy of a single mixed pyrophyllite talc phase.
1260
_ 1280 T I iz G 4 I& 9 1300
xKQ 1320
i_.-.--*
_l
Pyrophyllite
Fig. 2. Free energy of formation of pyrophyllite (P), talc (T), magnesium montmorillonite (Mg-M), their oxides, kaolinite + quartz (KQ) and serpentine f quartz (SQ) (estimated). [Z1---calculated, X--experimental.
This mixed phase is not stable with respect to its oxides unless the amount of magnesium in the octahedral layer corresponds to that of about 10 per cent talc component. The hypothetical magnesium montmorillonite (Mg-M) is stable neither with respect to its oxides nor the mixed pyrophyllite-talc phase. Instability results from removal of ions from the large-potential octahedral sites to the small-potential sites of the interlayer space. The AF, of serpentine + quartz is estimated. Figure 3 represents an expanded portion of Fig. 2 with additional energy values. Stability relations of the non pyrophyllite-talc combinations of minerals of Fig. 3 are deduced by adjusting free energy values to the pyrophyllite-talc oxide line by adding or subtracting free energy values to compensate for compositional differences. Subtracting the free energy of formation of one mole of water from the kaolinite plus quartz (KQ) value places the stability of kaolinite plus quartz about 2 kcal below that of equivalent oxides of p~ophyllite. Excess water in the system is aesumed. The energy values of sodium saturated montmorillonite (Na-M) and its oxides have been adjusted to the oxide energy of the appropriate proportions of pyrophyllite and talc. All adjusted values are encircled in Fig. 3.
336
ill. SLAUGHTEII.
Although the Mg-montmorillonite is very definitely less stable than kaolinite plus quartz plus serpentine, placing Ng in the interlayer space has a particular advantage in that Mg with its very large l~ydration energy can stabilize the structure through absorption of water into the interlayer space. Estimates of the energy of hydration for the Mg-montmorillonite arc as follows: the amounts of energy available to do work of expansion are about 10 kcal for hydration of the oxygen surface and 57-63 kcal for hydration of the Mg ions. The energy required is about 17 kcai to overcome 1240
1260
1280 Mg-NH.0
1290 Pyrophyllile
u Talc a Pyrophyilite
Fig. 3. Free energy of formation of combinations of silicates equivalent of Mg-M-magnesium montmorillonite, pyrophyllite to & talc, 4 pyrophyllite. Na-M-sodium montmorillonite, P-pyrophyllite, XC--kaolinite, Q--quartz, Free energies for compositions not P to T-talc, A-analcite, S-serpentine. tT, %P are adjusted so that their oxide free energies coincide with the oxide line of P and T; adjusted values are encircled. n--calculated, ~~xperimental. Experimental values of kaolinite from REESEMAN and KELLER (1965) ; pyrophyllite
value determined by REESEMAN.
(‘oulomb forces during expansion and 18 kcal to overcome London forces. The lowering of the energy of montmorillonite through hydration is about 31-37 kcal. The estimation of Coulomb energy term is based on the surface energy of 4600 ergs/ cm2 for muscovite (BRYANT, TAYLOR and GUTSHALL, 1963). The value of the hydration energy of Mg@ is the value from -AaH, (escape of ions from water), i.e. -467 to --510 kcal/mole (MOELWYX-HUGHES, 195'7, p. 848), -AFescape will be somewhat less, but -AH, should serve as a good approximation.
337
Chemical binding in silicate minerals-III
The hydration stabilization of Mg-montmorillonite is sufficient to prelude the formation of kaolinite, talc, or serpentine plus silica phase for the composition of the system near that of the hypothetical Mg-montmorillonite. Hydration stabilization accounts very well for the large montmorillonite field observed by ROY and ROY in the MgO-Al,O,-SiO,-H,O system at low temperatures. Sodium montmorillonite, without hydration, is not stable with respect to other components. More stable than sodium montmorillonite is the combination kaolin&e + quartz + analcite + (serpentine or Mg-montmorillonite). For rocks of the composition of the bentonites the minerals predicted from Fig. 3 are summarized in Table 12. The composition and assemblage 2 corresponds most closely to that found in Wyoming bentonites. Table 12. Minerals expected from bentonite source rock with variation in Mg,Na content
1. 2. 3. 4. 5.
Mg
N&X
a* a -
a a vat -
Predicted minerals Mg-Montmorillonite > kaolinite + quartz Na,Mg-Montmorillonite > analcite > kaolinite Analcite + kaolin% + quartz Analcite > kaoline + quartz Kaolinite + quartz
3_ quartz
* Relatively abundant. t Very abundant.
The influence of pH has not been considered. The main effect of differences in pH in the limited range expected in the natural system will be to shift the relative and more amounts of phases. A low pH will favor less montmorillonite-analcite kaolinite-quartz. Potassium in the system introduces the possibility of illite, whereas Ca favors montmorillonite and zeolite since its hydration properties are similar to Mg. PROBLEMSIN APPLICATIONOF ENERGY CALCULATIONS In employing PAULING’S formula for amount of ionic character in a bond it has been assumed that the formula is correct to within a few per cent. If the assumptions that have been employed in calculating decomposition temperatures are approximately correct, then PAULINB’S formula is also approximately correct for oxygen compounds with small metal cations. However DAILEY and TOUTNES(1955) have shown that the alkali halogenides and other gaseous diatomic molecules have ionicities far in excess of ionicities predicted from strict application of PAULINO’S formula. Obviously if PAULINQ’S formula gives ionicities far from the real values for the alkali halides, melting points calculated with use of PAuLmo’s formula should not be correct. Instead of calculating melting temperatures using ionicity,. one may calculate ionicity using the observed melting temperatures. The ionicity of nine alkali halides have been calculated from their melting temperatures in just the reverse manner of calculation of decomposition temperatures. In making the calculation, the ionicities Pauling’s standard of LiF, NaF and KF are determined from Pauling’s formula. radii were used as pairing radii for all calculations. The radius-ratio corrections of LiCI, LiBr, LiI and NaI allowed for energy required to increase cation-anion distances for non-paired interactions. Results are presented in Table 13 with ionicities
338
M.SL_~~~~~TER
derived by other methods. The closest match to the melting point ionicities are those derived from quadrupole coupling constants as measured from microwave spectra of the diatomic molecules, which are the most accurate experimental values for ionicities. The estimation of ionicities of the alkali halides seems sufficiently good to indicate that the general method of calculations of transition temperatures and stabilities of minerals should give good results if the bonds are ionic enough (i.e. 50 per cent or more ionic) and if the ionicity can be determined reasonably closely. In view of the possible difficulty in estimating the ionicity it might be expedient to use MgO, CaO, etc., as standards for finding the ionicity to be used in calculating Table 13. Ionicity of alkali halides Solid meltin@ points LiCl N&l KC1 LiBr NaBr KBr LX NaI KI
95 94 96 98 97 95 106 97 97
Microwaveb
Gaseous molecule DipoleC 1 _ moment
90 5 0.03* 97 * 0.03* 100 95 91 99 90 87 97
73 75 82 61 77 .55 76
,-on%S,
_.TB)Z
63 67 76 55 59 63 43 47 51
a Calculated from observed melting point with ionicities of LiF, NaF, 1 _ ~--O~WX~--S~)* 1*&g KF calculated with PAULINQ’S Formula: PAULINQ’B standard radii. b Derived from experimental values of nuclear coupling constants of the diatomic molecules by DAILEY and TOWNES (1955). c Calculated in manner of PAULINE (1960) from dipole moments of diatomic molecules (HONIG et al., 1954). * Estimated from curve of DAILEY and TOWNES (1955).
the properties of complex silicates. This tack is not very good, however, for it then must be accepted that assumptions concerning the independence of covalency with phase etc., are correct. In conclusion it appears unsafe to extend the calculation of ionicities and application of energy calculation beyond the oxides and silicates without first checking the feasibility of extension. CoNCLUsIoN
In the three parts of this series a scheme has been developed which enables one to calculate some stabilities of silicate and oxide minerals at low and higher temperatures. The information derived by such calculations may have qualitative or semiquantitative application. The calculations, once programmed, are simple and can be handled on a small computer. The methods and computations can be extended to much more complicated problems such as stability relations when pressure, temperature, and composition are variable. This extension is now underway. Needless to say, the model can and should be improved and modified. What has been offered in these papers is only a start toward a more than speculative approach to molecular solid-state geochemistry.
Chemical binding in silicate minerale-
339
REFERENCES B-Y R. (1963) Heats of formation of gehlenite and talc. U.S. Bureau of Mine-3 Rept. 8251, 10 p. BAUR W. H. (1956) tfber die Verfeinerung der Kristallstructurbe&immung oiniger Vertreter dea Rutiltype: TiO,; SnOz, GeO, und MgF,. Actu. Cry&. 9, 616. BRYANTP. J., TAYLORL. H. and GUTSHI+LL P. L. (1903) Cleavage studies of lamellar eolids in various gas environment@. Tmn8. of the Tenth National Vacuum Symposium. p. 121. DAILEY B. P. and TOWNESC. H. (1955) The ionic character of diatomic molecules. J. Chem. Phys. $X3, 118. DEER W. A., HOWIE R. A. and ZUSSMANJ. (1962) Rock Forming Minerala, Vol. 3. John Wiley. GRUNERJ. W. (1934) The crystal structure of talc and pyrophyllite. 2. K&t. 88, 412. HE,-RICKS S. B. (1938) On the crystal structure of talc and pyrophyllite. 2. Kriet. 99, 264. HONIG A., MANDELM., STITCH_M.L. and TO‘WNESC. H. (1964) Microwave spectra of the alkali halides. Phya. Rev. 96, 629. JACKSONW. W. and WEST J. (1933) The crystal structure of muscovite. 2. Ktit. 85, 160. KIEFER C. (1949) Deshydration thermique des mineraux phylliteux. C.R. Acad. Sci., Paris &39, 1021. MOEL~YN-HUQHESE. A. (1967) Phyeicu.2 Chemietry. p. 1295. Pergamon Press. PAULISQL. (1960) Nature of the Chemicul Bond. Cornell Universit,yPrees. PAULINE L. and HENDRICKS8. (1932) The crystal structurea of hematite and corundum. J. Amer. Chem. Sot. 47, 781. R~OSLOVICH E. W. (1960) The structure of muscovite. Acta. Cry&. 18,919. REEBMANA. L. and KELLER W. D. (1966) Apparent standard free energies of formation of selected clay minerals calculated from dissolution data. Proceedings of the Fourteenth National Conference on Claya and Cluy Miner&. Pergamon Prese (in press). ROY D. M. and ROY R. (1955) Synthesis and stability of minerals in the system MgO-Al,O,SiO,-H,O. Amer. Min. 40, 147. SWU~ETER M. and EARLEYJ. W. (1966) The mineralogy and geological aigniflcanceof Mowry bentonites, Wyoming. cfwl. Sot. Amer. Special paper a, 118 p. STEMFINKH. (1962) Crystal structure of a trioctahedral micaphlogopite. Amer. Min. 47, 886. WILLIAMSF. J., EL~LEYB. C. and WE-IT D. J. (1964) The variations of Wyoming bentonite beds aa a function of the overburden. Proceeding8 of the Second ~National Conference on Claye and Cluy Miner&. p. 141. Pergamon Press. YOUNO R. A. (1962) Mechanisma of the Phase transition in quartz. Engineering Exp. Stat., Georgia Inst. of Tech. Pub. Yomo R. A. and POSTB. (1962) Electron density and thermal effects in alpha quartz. AC&. Cry&. 15,337.
et Cosmorhimira
_&eta, 1986,
Vol.
30, pp.
323 to 339.
Pergamon Press
Ltd.
Printed inNorthern Ireland
Chemical binding in silicate minerals Part III. Application of energy calculations to the prediction of silicate minerd-stability M. SLAUGHTER Crystallography Laboratory, Department of Geology University of Missouri, Columbia (Received
19 April
1965; in revised form 4 September
1965)
Abstract---Combining Coulomb energies with appropriate corrections makes possible quantitative prediction of stability relations of minerals. Melting and decomposition temperatures of some minerals including corundum and quartz have been calculated from the binding energies. Agreement between calculated and observed melting points of minerale is exceptionally good when covalency, radius-ratio, and coordinationeffect correctionsare made to the melting points determined from Coulomb binding energies. Thermal stabilities of some phyllosilicates are predicted semiquantitatively. Calculated energies show that the stability of montmorillonite with respect to other phyllosilicatea in most low-tempemture geochemical environments is probably the result of hydration of the inter-layer space. Also, when small amounts of magnesium are present in a silicate system montmorillonite is the phase which minimizes the total energy of the system. INTRODUCTION IN Parts I and II of this series, a model and methods
have been set forth for calculating and using energies for deducing physico-chemical properties of silicate and oxide minerals at low and high temperatures. In this paper the model and energy calculations are used to illustrate several different types of geochemical applications. Melting points of several oxides are calculated assuming complete ionic binding and the assumptions used in the simple model of Part I. The thermal stability of alpha and beta quartz is determined to illustrate the use of the model for predicting polymorphic transitions. The dehydroxylation temperatures of some phyllosilicates are related to structure and composition. And the low-temperature stability of montmorillonite in Wyoming bentonites is considered using both calculated and experimental free energies of formation. THE APPLICATION OF ENERGIES TO THE CALCULATION OF MELTING POINTS
Calculation of melting temperatures of several minerals illustrates the use of binding energies in determining the thermal properties of minerals, and demonstrates to what extent covalency can be ignored in the consideration of mineral reactions. Coulomb energies of the compounds whose melting points are to be determined are listed in Table 1, with calculated minimum or pairing and observed cation-anion and anion-anion distances, respectively. The calculated values R,, in Table 1 are equal to sums of cation and anion pairing radii for NaCl-type structures, or have been derived from equation (12), Part I, for non-NaCl type structures, and represent the 323
89
60 63
2.014, 2.72(B)
._- ...-.-.---I.95 , 2*70(A)
2.67, 2.70 2.31, 2.70 2.25, 2.78 2.04, 2.78 2.28, 2.78 2.072, 2.78 f-945, 2.70
1.865, 2.78
1.861, Pi%
1.610, 2-78
ICI? NaF NasO M& CaO Fe@ &fgFzb
TiOah
4G3
p-&O,”
a Fe,.,, 0 N Fe&&, Fe$&O. b Struoture of RAWR (1956). c Structure of YOUNG (1963). d Energy adjusted to n = 7.0
1+9&w.), 1 x 2.50 1 x 2.72 I+94(av.), 2.595(av.)
2.672, 2.72 2.314, 2.72 2.407, 2.78 2.106, 2.7& 2.406, 2.78 2.150, 2.78 2 x 1,997 , 1 x 2.577 I >: 1.98
51
92 91 82 73 79 55 86
Per cent ionic character
RBn Observed
IzAB,
Calculated
.--
1841.1
1450.3
94.7”
217.1 250.7 347.5 1101.7 984.8” 1103@J 403.4
-
480.7
575.6
551.8”
228,9(223)d kcal mole-l aniorr2 183*8 207.5 233,7 593.6 614.6d 333.6d 298.1
____.
-- Coulomb energy Ionic covalent
288~0(280)~
Ionic
for calculation of melting t.emperatures
Solid ---_LiF
Table 1. IMa
Chemical binding in silicate minerals-III
325
mimim~ cation-anion approach distances for the particular structural configuration. Calculated values of Rnn are simply twice the pairing anion radii of Table 2, Part I. Observed values of BdB or RBB are crystal distances measured at room temperature. Multiple cation-anion distances are listed and multiplied by the relative frequency of each. Where all anion-anion distances are not the same, the number of anions per anion at the given distance is the multiplying factor; all other anion distances in the structure are greater than twice the anion radius. The values of percent ionic character listed in Table 1 were determined using Pauling’s formula : Amount of Ionic Character = 1 - exp - 4(X:, - X,)2 where X is the electronegativity. Coulomb energies are expressed as the energy of one formula weight divided by the number of anions in the formula. Coulomb energies have been computed from published values of the Madelung constants. The covalent-ionic Coulomb energies were calculated from Madelung constants employing the cation charges as determined from the appropriate electronegativity differences. The results of melting point calculations are presented in Table 2 with radiusratio, coordination, and polarization correction listed separately. To contrast the melting temperatures calculated for the ionic-covalent model the melting temperat~es were also ~alcula~d assuming complete ionicity of bonds. These results are also presented in Tables 1 and 2, The calculated melting temperat~es of the io~c-covalent model with co~ections for radius-ratio and other effects agree s~prisingly well with the observed melting temperatures, particularly considering the number of approximations. It may be worth noting that the assumption that all radius-ratio and coordination effects are eliminated with fusion, would require the melting points of compounds to be invariant with changes in composition of the system. An alternative expedient is to introduce a proportionality constant into the calculation of melting points to make the elimination of radius-ratio and coordination effects during fusion incomplete. Introducing a fractional reduction in the corrections will not affect the calculated melting points of the pure minerals. However, fusion temperatures of specific species will vary when the composition of the system is not the same as that of the mineral. The reason for the variable melting points is that radius-ratio and other effects in the liquid phase do vary with com~sition. ALPHA AND BETA QUARTZ TRANSITION
One test of the method proposed in Part I is the ability to use the method to predict transition temperatures of polymorphs which differ very little in binding energies. The CouIomb energy of /?-SiO, was determined from the published Madelung consent. The binding energy of a-SiO, was estimated to be about equal to the energy of @-SiO,. The coordination corrections employed the parame~~ of Yoa~a and
5578 4957
5473 1869 8050 742% 9542
MgO CaO
Fe0 MsFz TiO, *‘zOz B-SO, r-SO,
324°C’
19 555
1296 1606
1269 210 2550 1162 0 0
1115°C
1038 1179
3450 3547
1800 1597 3209 333% 2742 -2742
temperatures
0°C’ 0 0 0 0 0 183 1544 2423 5460 -I
235°C 152 373 637 1035 400 169 887 425 (t 0
minerals
0°C’ 0 0 0 0 0 0 349 llr0 --
0°C: 0 0 0 0 0 125 512 886 1312 1172
0 0 112 ni0 -. .-
0 0
0 0
0°C’
AT Polarization IonicIonic covalent -.-______~
of’ selected
--AT ~‘oordination Ioniccovalent, ionic ___-
2. MelGng
-AT X.adinz+ratio Ionic: Ionic covalent -----.-.
* From Coulomb energy. 7 Melting temperature of cristobalitcx. $ \vWKS and BLOCK (1963).
1194°C
1058 1572
LiF
Ionic
NaF Na@
________--._
Ioniccovalent .- _~___
Initial*
Table
2813 2512 1400 1303 1902 2027 1547 1570
4282 3351 4204 1456 4306 3843 4202
-
-
1024°C’ 806
Ionic
1039°C ( 1017
loniccovalent
Final
1263 1840 2050 1713f (16lO)g
2800 2570 1370
992°C’ 897
-._.
Observed
$ 0 g S
.z %
Chemical binding in silicate miner&-111
327
POST (1962) for a-SiO, and the structure of YOUNG(1963) for /?-SiOz. Results are given in the last row of Table 2. The “melting” temperat~es of a-SiOz and &SiOz are physically meaningless, Silica, however, differs from most of the structures of Table 2 in that it is an “open” structure in which small rotations of tetrahedra preserve the essential structure but change the individual Coulomb and repulsive interactions. In calculating the “melting” temperature, the interactions of first anion-axon and cation-axon neighbor interactions were accounted for. However the a- and &silica structures can open in the liquid state by rotation of tetrahedra so that second neighbor anion-anion and first neighbor cation~ation interactions at high thermal vibration levels have a smaller elect on the energy. For second neighbor i~lteractions at higher vibration levels, the chief increase in interaction energy should result from anion-anion, overlap repulsion. As the z- and @W& structures open with increasing temperature, ~larization energy is lost (raising the melting point), while second neighbor cations become further apart as the Si-0-Si bond angle increases from about 150 to 180’. Table 2 lists calculated corrections and the final calculated and observed upper limits of thermal stability of a x- and /?-SiO,. The calculations are based on an average Si-O-Si angle of 150 and lii23 for a- a.nd P-quartz respectively. THERMALSTABEITYOF PYROPHYLLITE, TALC ANDOTHERPHYLLO~ELICATE~ A number of phyIlosilicate phases including p~ophyIlite and talc occur in the system SiO~-MgO-~~O~-~~O. Several important papers on this system are available, among these being that of ROY and ROY ( 1955) who present data convenient for relating calculated energies to experimentally determined equilibrium phases. The paper of Rou and ROY will, therefore, be taken as the primary source of information to which reference will be made in this paper. The electrostatic binding and overlap repulsion energies have been computed for various models of pyrophyllite, talc, and montmorillonite. The structures assumed basic for the computation of the Coulomb energy of pyrophyllite and talc were determined from X-ray data first by CRUNER(1934) and later by HENDRICKS(1938). CRUNESdetermined the placement of the octahedral ions in pyrophylli~ and talc to be as shown in Fig. l(a) and the octahedra1 oxygen and hydroxyl atoms for the lower half of the cell as in Fig. l(b). Silicons without their tetrahedral oxygens are shown in Fig. l(c). Cell parameters, space groups and atomic coordinates employed for energy computations are given in Tables 4 and 5. The montmo~llo~te structure model was constructed from that of p~ophylli~ by random substitution of one Mg+* for one of the eight AlfS ions occupying the Al sites in pyrophyllite. The charge imbalance was restored by placing _iliiof an Mg+a atom in a special position of the interIayer space; this position is marked with an “x” in Fig. l(c). The structures of the phyllosilicates are in general not accurately known; however, it should be possible to make at least qualitative estimates of the thermal stability of p~ophyllite, tale, and some other three-layer phyllosilica~s. The energy values are given in Table 6. The Coulomb energy-derived temperatures has been
corrected for the fact that the energy is that of an unrefined structure. An approximate correction factor for refinement was found by multiplying the energy of pyrophyllite by the ratio of the energy of the refined muscovite structure of RADOSLOVICH (1960) to that of the unrefined structure of JACKSON and WEST (1933), i.e. 1.006. Radius-ratio and coordination corrections were made from the RADOSLOVICHstructure of muscovite and the STEINFINK (1962) structure of phlogopite, without aluminum substitution in the tetrahedral layer. The results of calculations for yyrophyllite and talc are given in Table 7. PYROPHYLLITE
G
a.
I
b.
C. Fig. 1. Projection of part of atomic positions in pyrophyllite-solid circles are in upper half of cell. (a) Aluminum positions (b) oxygens and hydroxyls surrounding aluminums in (a)-circles with dots are OH’s; (c) Silicon positions.
All coordination and radius-ratio corrections were made in the manner of the calculations for quartz. The Si-0 correction for pyrophyllite includes both the coordination and polarization correction. The Si-0-Si angle employed in the Si-Si coordination correction was 130 and 131” for pyrophyllite and talc respectively. The final calculated dehydroxylation temperatures are rough, because the structures are not refined. The dehydroxylation temperature for talc is too high by about 80°C. Had not the data from a partially refined structure such as muscovite been used the errors might have been 30-40 per cent in determination of coordination corrections. Specifically the effect of magnesium in the octahedral layer of talc is to expand both the octahedral layer and the tetrahedral layers relative to the expansion by
Chemical binding in silicate minerals-III
329
Table 3. Upper limit of thermal stability of SiO, at low pressure AT Correction
-o-o
1st neighbor coordination coordination 2nd neighbor coordination
Si-0 o-o
a-SiOs
&SiOs
-1172°C
- 1547%
0
+ 235
- 438 + 385 - 920 2742°C -2145 597 573
Polarization Si-Si coordination Initial Total AT Final Observed
- 237 + 400 - 770 2742°C - 1859 883 867
Table 4. Cell parameters and space groups
Pyrophyllite Talc Montmori~onit~
a
b
5.16A 5.28 5.16
&9OA 9.15 8.90
C 1864A 18.92 1864
B
S.G.
100” 100” 100”
C 2/o c 2/c C 2/c
Table 5. Coordinates of atoms in py~phy~ite, talc, montmorillonite
Atom
Al@%) Six Si, 00, 0% OT, % Or, OH
H
Pyro.,
Talc, *
Mont.?
X
Y
2
0.333 0.167 o-000 0.167 0.500 0.084 0.084 0.333 -0.167 -0.164
0.000
o-000 O-261 -0.239 0.203 0.203 0.025 -0.475 0.275 0.203 0.203
* Mg at 0.000, O+OOO, O*OOO. t M2+ at 0.500, 0.350, 0.250.
0,143 0.143 0.058 0.058 0.176 0.176 0.176 O-058 0.110
* kcal~mole.
OH 0 H $@+z
-0.633 -1.023 0‘390
“828.5
2657.9
-_
2814.5
43.6
175.9
2644.7
~
71.6
175.8
166.9
I- 1 so25
OT*
173.4
169.6
234.7
165.0
161.1
246.3
- 1.025
I.145
410.3 598.6 597.6 234.9
0%
-
372.2 607.5 606.4 246.5
Wf0.39
-1.025
02
1‘900 2,050 2.050 - 1,145
HtO.00
-Ec*jiosi
Pyrophyllite
0%
0
Si, Si, 0 01
Al
Chg.
-
1282.5
110.5
160.0
l64.3
164.3
164.3
7&O 142‘8 141.8 161.4
EB*/ion
_.-.
-- 0,730 - 1.120 0.390
2761.4
2750.6
94.6
162.3
-~ 1.025 170.7
169.X
169.3
161.5 161.3
276.X
398.8 611.5 609.8 276.6
J$-W3+
288*0
358.1 620.0 618-3 288.2
H+o.oo
Talc -E&on
- 1.026
- 1.025
- 1.234
1.46 2.05 2.05 - 1.243
Chg.
..__123!?.9
117.9
136.8
142.4
142.4
162.4
138.1 129.2 128.2 162.7
E&n
._.
.
2837.7 ~__. _._
U-8 12.7
170.1
186.5
.- 1.025 -- 1.040 .- 1,054 0,390 OG.83 0.225
179.2
175,Y
229.1
408.8 594.5 592.5 229.3
Rig
2862.S
16.0
4.5d
172.9
190.5
181.7
179-3
232.1
415.2 592.5 590.4 232.3
Na,
Xontmorillonitc -E&on
.- 1,025
1.845 2.050 2.060 ,-1.158 - 1.172 - 1~158 - 1.172 -L.O25
Chg.
Table 6. Calculated coulomb and repukive enrrgiw of ~~~~~phyllit,e~t,alc xnd lnontmorillonitc
::
164.3 169 3 111.6
---1300.; 1351~0
16.!>
i.3
2 3
F K F 164.7 1653
164.3 164.7
162.3
79.0 142.8 141.8 162.7
Mg,Ka
E&on
Chemical binding in silicate minerals-111 Table 7. Dehydroxylation
temperature
of pyrophyllite
331 (P) and talc (T)
R “Bond”
Ohs.* (P)
0~O~(lst %-%I OTSi Si-Si O,-Si O,,-Al O,,-Al OH-Al %1-O,, %a-%2
OH-OH O,,-OH (),-OH K-OT
neighbors) (2nd neighbors)
2.68,
-AT Calc.
(T)
(M/PHI t
A
~+v_JA(av.1
(T)
(P) 2.78
A
(P)
(1’)
575°C 135 60 -702 1281 1226 3 63 120 94 120 130 27 119 0 3 26 62 60
(WPH) 349°C
165
2.70, 1.60, 2.87, 1.64, 1.94, 2.108 1.99, 2.108 1.93, 2.034 2.39, 2.78 2.76, 2.78 2.51, 2.73, 2.68, 3.06
2.78 1.62 3.20 1.64, 1.84, I.940 1.84, I.940 1.62 1.947 2.78 2.78 2.78 2.78 2.78 2.78 2.78 2.75 Total
-AT
55 i86ti(P)
1693(T)
Initial ionic-covalent “melting” temperature-2465°C (P). Initial temperature corrected for lack of refinement--2479°C (P). Final dehydroxylation temperature-(247Q-1868)“C = 611°C (P). * Muscovite (RADOSLOVICH, 1960) and phlogopite (STEINFINX, 1962) distance. t Muscovite and phlogopite where they differ appreciably from pyrophyllite and talc.
aluminum in the octahedral layer of pyrophyllite. The expanded structure at higher vibration levels has a smaller overlap repulsion and therefore is thermally stable to higher temperatures. The expansion effects are reinforced by slightly higher ionicity in talc. In addition to predicting that talc is stable to higher temperatures than pyrophyllite, one may also predict that any Mg-trioctahedral phyllosilicate should be stable to higher temperatures than Al-dioctahedral equivalents. Biotite would be predicted to be stable to higher temperatures than muscovite and phlogopite to higher temperature than biotite. Applying the partial ionic octahedral layer model to two-layer phyllosilicates, increasing amounts of aluminum in the octahedral layers should tend to decrease the upper thermal limit of stability in the following sequence : serpentine, amesite, kaolinite. Each of these predicted relations compare favorably with the data of ROY and ROY and other similar data. The higher temperature range of thermal stability of minerals such as muscovite and phlogopite relative to pyrophyllite and talc is due to differences in Crst and second neighbor oxygen coordination effects in the tetrahedral layers. In phlogopite and muscovite there is one aluminum substituted in every fourth silicon position. The Coulomb energy difference and the resulting thermal stability differences between the tetrahedrally substituted and the unsubstituted phyllosilicates is small. Aluminum, when substituted for silicon reduces the coordination effects in the tetrahedral layer, thereby raising the thermal range of stability. Employing tetrahedral
332
M. HL_~UC+HTER
O-O distances of muscovite, calculated for phlogopite and hedral corrections. Adding temperatures of pyrophyllite assumed to be negligible.
approximate corrections for coordination effects were muscovite and were included with dioctahedral-trioctaappropriate corrections to the observed dehydration gives the dehydration temperatures of Table 8, PE2,, is
Table 8. Dehydroxylation temperatures of some phyllosilicates Observed DTA* Pyrophyllite Muscovite Talc Phlogopite
640°C 763 900 1120
Equilibriumt 590 f”C 715 720 *
Calculated 610°C 781 899 1070
* Kiefer, 1949; beginning of dehydroxylation (D.T.A.). t Data from DEER, HOWIE and ZUSSMAN(1962).
The substitution of two aluminum atoms for two of the four silicons probably accounts for the relatively high thermal stability of chlorite. The stabilizing effect of tetrahedral aluminum in chlorite seems to be partially counter-balanced by weak electrostatic binding in the brucite-like layer. Table 9. Dehydroxylation temperature of pyrophyllik with ionic octahedral layer “Bond” ___~ OF-O, O!r-0, OpSi Si-Si O,--Si O,-Al O,,-Al OH-Al Ocli-001 OrJz-00, OH-OH O,,-OH O,,OH Total AT Initial temperature Dehydroxylation temperature
__hT 575” + 155°C 65 --702 1281 45 223 285 321 208 6 40 104 120 -2651°C 3542°C 891°C -
No covalency in the octahedral layer of pyrophyllite gives the calculated upper limits of thermal stability of Table 9. The calculated values do not agree with the observed values as well as the model in which covalency in the octahedral layer is compensated for by decreasing the octahedral charges. Increasing ionicity much above the values from PAULINO’S formula will not improve calculated decomposition temperatures.
Chemical binding in silicate minerals-III
333
As the charge on the octahedral oxygena increases, the total electrostatic binding energy increases, largely due to the greater magnitude of the potential at Al and Si sites. Hence, the total binding energy of both the octahedral and tetrahedral layers is larger for three-layer silicates than two-layer silicates because of the relatively low charge on the oxygens of the hydroxyl layers of two-layer silicates. Based both on the binding energy differences and radius-ratio-coordination effects, the high temperature limits of stability of three-layer versus two-layer silicates should then be following: pyrophyllite > kaolinite ; talc > serpentine ; chlorite > amesite (‘1?). Qualitative agreement of these predicted conclusions with experimental data of ROY and ROY is good. THE STABILITY OF BENTONITICMONTMORILLONITE AT Low TEMPERATURES The bentonites found in the Cretaceous rocks of the Western Interior of the United States may be typified by the bentonites of Wyoming (SLAUBHTER and EARLEY, 1965). From mineralogical evidence, the bentonites were formed by the alteration of volcanic ash (glass) of average composition equivalent to latite (or monzonite) or quartz latite (Table 10). The alteration products in the bentonites are chiefly montmorillonite, with a few weight percent of zeolites, and small amounts of kaolinite and silica. The montmorillonites have about 8Na and _S(Mg + Ca) as exchange ions (WILLIAMS et al., 1954). Silica is sometimes found precipitated in the beds immediately overlying bentonites. The field evidence indicates the alteration process took place after deposition of the ash in waters ranging from brackish to marine compositions. The pH range seems to have been about neutral to slightly alkaline. Since the alteration appears to have taken place soon after deposition the temperature of alteration could have been as low as 15’C and probably not higher than 40°C. Table 10. Chemical data on monzonite and montmorillonite (a) Monzonite*
Gram-ions
Analysis
Gram charges
Combined? gram charge
Gram charges $ factor 11.0314
Ions per unit of glass
SiO,
57.44
Si
0.9564
36266
36256
42.2017
Si
Fe,%
3.26 16.39 3.48 3-12
FE?+ Al Fe2+ Mg
O-0484 0.3216 0.0410 o-0774
0.1230 O-9648 1 0.0968 0.1548
1.0878
12.0000
Al
4*0000
0.2516
2.7755
Mg
1.388
0.4110
4.5339
M+t
4.534
*1,0, Fe0 MgG
Na20
3.44
Na
O*lllO
0.1110
K2O CaO
4.37 5-81
K Ca
0.0928 0.1036
0.0928I 0.2072
H,O+ TiO,
0.63 0.92
H,O-
0.24
0
-
-
-
61.5111
0
10.550
30.756
* Monzonite glass. t Al ions are equivalent to all Al and Few ions, and univalent metal ions M+ include Ca. $ Arbitrarily based on 12 charges for 4 aluminum atoms. 6
334
31.
SLAUGHTER
Table 10 (cr,nt.) (b) Montmorillonit~e~ Ions per unit cell
i(
C’ombined ions per unit cell11
_.~~~~ _~~
7.731
Si Al Fe3+
Si
7.731
0.035
Al Fe3+ Mg Na K
Al
3.795
3.166 0.234 0.360 1 0.508
Mg
0.508
0.6641 O.OllJ
MA
0.675
5 Montmorillonite, Clay Spur, Wyoming. 11Based on 20 oxygens, 4 hydroxyls per unit cell. 7 M+-Alkali metal ions.
Given the above geochemical condition is it possible to rationalize montmorillonite as the most abundant stable phyllosilicate phase resulting from alteration of volcanic ash at low temperatures ? A complete treatment of montmorillonite stability will not be attempted, but enough of the problem will be elucidated to illustrate the application of energy calculations for low temperature systems. Table 11. Calculated energies of some silicates and oxides (1 -
--E, &A&.0, + 2Si0, + iH,O Pyrophyllite jMg0 + 2Si0, + $H,O Talc Mg-montmorillonite &,Al,O, + &MgO + &Na,O 2Si0, + &H,O Na-montmorillonite
+
c/7.0)
-2E,
-AFf*
2836.5 kcaljmole 2828.5 2860.5 2954.1 2837.7 2828.9
0.857 0.857 0.866 0.866 O&56 0.858
4861.8 kcal 4848.2 4954.2 5116.6 4858.1 4854.3
1253.6 kcal 1250.1 1277.4 1319.3 1252.7 1251.7
2862.5
0.855
4894.8
1262.1
* Free energy of formation of 3 moles ~0.2578
x
%EM.
Results of calculation of Coulomb and repulsive energies of pyrophyllite, talc, montmorillonite, are listed in Table 6. The Coulomb energies, E,, with an appropriate charge on the hydrogen site were used for deducing low temperature properties. The repulsive energies of Table 6 are those for the completely ionic approximation. The calculated energies of minerals related to these in Table 6 are given in Table 11; the values of E, were calculated from the equation
E, =
E&l
-
c/7.0)
Since E, is approximately proportional to A( AF,), the differences in free energy of formation, values of E, of Table 11 are scaled on free energies of formation of Al,O, + 4Si0, + H,O. Some of these scaled values are plotted in Fig. 2 with observed values of AF,. The value of AF, of SiO, used is 204.75 kcal per mole. The agreement between observed and calculated differences in AF, is very good, althoughtherearesomedifferences between theexperimental andcalculatedenergies.
Chemical binding in silicate minerals-III
335
The calculated differences seem to be accurate enough for deducing mineralogical stability relations. In the system represented by the components on Fig- 2, p~ophyl~te (P) is not a stable phase with respect to its oxides. The line connecting the AF, of pyrophyllite and AF, of talc (T) represents the energy of a single mixed pyrophyllite talc phase.
1260
_ 1280 T I iz G 4 I& 9 1300
xKQ 1320
i_.-.--*
_l
Pyrophyllite
Fig. 2. Free energy of formation of pyrophyllite (P), talc (T), magnesium montmorillonite (Mg-M), their oxides, kaolinite + quartz (KQ) and serpentine f quartz (SQ) (estimated). [Z1---calculated, X--experimental.
This mixed phase is not stable with respect to its oxides unless the amount of magnesium in the octahedral layer corresponds to that of about 10 per cent talc component. The hypothetical magnesium montmorillonite (Mg-M) is stable neither with respect to its oxides nor the mixed pyrophyllite-talc phase. Instability results from removal of ions from the large-potential octahedral sites to the small-potential sites of the interlayer space. The AF, of serpentine + quartz is estimated. Figure 3 represents an expanded portion of Fig. 2 with additional energy values. Stability relations of the non pyrophyllite-talc combinations of minerals of Fig. 3 are deduced by adjusting free energy values to the pyrophyllite-talc oxide line by adding or subtracting free energy values to compensate for compositional differences. Subtracting the free energy of formation of one mole of water from the kaolinite plus quartz (KQ) value places the stability of kaolinite plus quartz about 2 kcal below that of equivalent oxides of p~ophyllite. Excess water in the system is aesumed. The energy values of sodium saturated montmorillonite (Na-M) and its oxides have been adjusted to the oxide energy of the appropriate proportions of pyrophyllite and talc. All adjusted values are encircled in Fig. 3.
336
ill. SLAUGHTEII.
Although the Mg-montmorillonite is very definitely less stable than kaolinite plus quartz plus serpentine, placing Ng in the interlayer space has a particular advantage in that Mg with its very large l~ydration energy can stabilize the structure through absorption of water into the interlayer space. Estimates of the energy of hydration for the Mg-montmorillonite arc as follows: the amounts of energy available to do work of expansion are about 10 kcal for hydration of the oxygen surface and 57-63 kcal for hydration of the Mg ions. The energy required is about 17 kcai to overcome 1240
1260
1280 Mg-NH.0
1290 Pyrophyllile
u Talc a Pyrophyilite
Fig. 3. Free energy of formation of combinations of silicates equivalent of Mg-M-magnesium montmorillonite, pyrophyllite to & talc, 4 pyrophyllite. Na-M-sodium montmorillonite, P-pyrophyllite, XC--kaolinite, Q--quartz, Free energies for compositions not P to T-talc, A-analcite, S-serpentine. tT, %P are adjusted so that their oxide free energies coincide with the oxide line of P and T; adjusted values are encircled. n--calculated, ~~xperimental. Experimental values of kaolinite from REESEMAN and KELLER (1965) ; pyrophyllite
value determined by REESEMAN.
(‘oulomb forces during expansion and 18 kcal to overcome London forces. The lowering of the energy of montmorillonite through hydration is about 31-37 kcal. The estimation of Coulomb energy term is based on the surface energy of 4600 ergs/ cm2 for muscovite (BRYANT, TAYLOR and GUTSHALL, 1963). The value of the hydration energy of Mg@ is the value from -AaH, (escape of ions from water), i.e. -467 to --510 kcal/mole (MOELWYX-HUGHES, 195'7, p. 848), -AFescape will be somewhat less, but -AH, should serve as a good approximation.
337
Chemical binding in silicate minerals-III
The hydration stabilization of Mg-montmorillonite is sufficient to prelude the formation of kaolinite, talc, or serpentine plus silica phase for the composition of the system near that of the hypothetical Mg-montmorillonite. Hydration stabilization accounts very well for the large montmorillonite field observed by ROY and ROY in the MgO-Al,O,-SiO,-H,O system at low temperatures. Sodium montmorillonite, without hydration, is not stable with respect to other components. More stable than sodium montmorillonite is the combination kaolin&e + quartz + analcite + (serpentine or Mg-montmorillonite). For rocks of the composition of the bentonites the minerals predicted from Fig. 3 are summarized in Table 12. The composition and assemblage 2 corresponds most closely to that found in Wyoming bentonites. Table 12. Minerals expected from bentonite source rock with variation in Mg,Na content
1. 2. 3. 4. 5.
Mg
N&X
a* a -
a a vat -
Predicted minerals Mg-Montmorillonite > kaolinite + quartz Na,Mg-Montmorillonite > analcite > kaolinite Analcite + kaolin% + quartz Analcite > kaoline + quartz Kaolinite + quartz
3_ quartz
* Relatively abundant. t Very abundant.
The influence of pH has not been considered. The main effect of differences in pH in the limited range expected in the natural system will be to shift the relative and more amounts of phases. A low pH will favor less montmorillonite-analcite kaolinite-quartz. Potassium in the system introduces the possibility of illite, whereas Ca favors montmorillonite and zeolite since its hydration properties are similar to Mg. PROBLEMSIN APPLICATIONOF ENERGY CALCULATIONS In employing PAULING’S formula for amount of ionic character in a bond it has been assumed that the formula is correct to within a few per cent. If the assumptions that have been employed in calculating decomposition temperatures are approximately correct, then PAULINB’S formula is also approximately correct for oxygen compounds with small metal cations. However DAILEY and TOUTNES(1955) have shown that the alkali halogenides and other gaseous diatomic molecules have ionicities far in excess of ionicities predicted from strict application of PAULINO’S formula. Obviously if PAULINQ’S formula gives ionicities far from the real values for the alkali halides, melting points calculated with use of PAuLmo’s formula should not be correct. Instead of calculating melting temperatures using ionicity,. one may calculate ionicity using the observed melting temperatures. The ionicity of nine alkali halides have been calculated from their melting temperatures in just the reverse manner of calculation of decomposition temperatures. In making the calculation, the ionicities Pauling’s standard of LiF, NaF and KF are determined from Pauling’s formula. radii were used as pairing radii for all calculations. The radius-ratio corrections of LiCI, LiBr, LiI and NaI allowed for energy required to increase cation-anion distances for non-paired interactions. Results are presented in Table 13 with ionicities
338
M.SL_~~~~~TER
derived by other methods. The closest match to the melting point ionicities are those derived from quadrupole coupling constants as measured from microwave spectra of the diatomic molecules, which are the most accurate experimental values for ionicities. The estimation of ionicities of the alkali halides seems sufficiently good to indicate that the general method of calculations of transition temperatures and stabilities of minerals should give good results if the bonds are ionic enough (i.e. 50 per cent or more ionic) and if the ionicity can be determined reasonably closely. In view of the possible difficulty in estimating the ionicity it might be expedient to use MgO, CaO, etc., as standards for finding the ionicity to be used in calculating Table 13. Ionicity of alkali halides Solid meltin@ points LiCl N&l KC1 LiBr NaBr KBr LX NaI KI
95 94 96 98 97 95 106 97 97
Microwaveb
Gaseous molecule DipoleC 1 _ moment
90 5 0.03* 97 * 0.03* 100 95 91 99 90 87 97
73 75 82 61 77 .55 76
,-on%S,
_.TB)Z
63 67 76 55 59 63 43 47 51
a Calculated from observed melting point with ionicities of LiF, NaF, 1 _ ~--O~WX~--S~)* 1*&g KF calculated with PAULINQ’S Formula: PAULINQ’B standard radii. b Derived from experimental values of nuclear coupling constants of the diatomic molecules by DAILEY and TOWNES (1955). c Calculated in manner of PAULINE (1960) from dipole moments of diatomic molecules (HONIG et al., 1954). * Estimated from curve of DAILEY and TOWNES (1955).
the properties of complex silicates. This tack is not very good, however, for it then must be accepted that assumptions concerning the independence of covalency with phase etc., are correct. In conclusion it appears unsafe to extend the calculation of ionicities and application of energy calculation beyond the oxides and silicates without first checking the feasibility of extension. CoNCLUsIoN
In the three parts of this series a scheme has been developed which enables one to calculate some stabilities of silicate and oxide minerals at low and higher temperatures. The information derived by such calculations may have qualitative or semiquantitative application. The calculations, once programmed, are simple and can be handled on a small computer. The methods and computations can be extended to much more complicated problems such as stability relations when pressure, temperature, and composition are variable. This extension is now underway. Needless to say, the model can and should be improved and modified. What has been offered in these papers is only a start toward a more than speculative approach to molecular solid-state geochemistry.
Chemical binding in silicate minerale-
339
REFERENCES B-Y R. (1963) Heats of formation of gehlenite and talc. U.S. Bureau of Mine-3 Rept. 8251, 10 p. BAUR W. H. (1956) tfber die Verfeinerung der Kristallstructurbe&immung oiniger Vertreter dea Rutiltype: TiO,; SnOz, GeO, und MgF,. Actu. Cry&. 9, 616. BRYANTP. J., TAYLORL. H. and GUTSHI+LL P. L. (1903) Cleavage studies of lamellar eolids in various gas environment@. Tmn8. of the Tenth National Vacuum Symposium. p. 121. DAILEY B. P. and TOWNESC. H. (1955) The ionic character of diatomic molecules. J. Chem. Phys. $X3, 118. DEER W. A., HOWIE R. A. and ZUSSMANJ. (1962) Rock Forming Minerala, Vol. 3. John Wiley. GRUNERJ. W. (1934) The crystal structure of talc and pyrophyllite. 2. K&t. 88, 412. HE,-RICKS S. B. (1938) On the crystal structure of talc and pyrophyllite. 2. Kriet. 99, 264. HONIG A., MANDELM., STITCH_M.L. and TO‘WNESC. H. (1964) Microwave spectra of the alkali halides. Phya. Rev. 96, 629. JACKSONW. W. and WEST J. (1933) The crystal structure of muscovite. 2. Ktit. 85, 160. KIEFER C. (1949) Deshydration thermique des mineraux phylliteux. C.R. Acad. Sci., Paris &39, 1021. MOEL~YN-HUQHESE. A. (1967) Phyeicu.2 Chemietry. p. 1295. Pergamon Press. PAULISQL. (1960) Nature of the Chemicul Bond. Cornell Universit,yPrees. PAULINE L. and HENDRICKS8. (1932) The crystal structurea of hematite and corundum. J. Amer. Chem. Sot. 47, 781. R~OSLOVICH E. W. (1960) The structure of muscovite. Acta. Cry&. 18,919. REEBMANA. L. and KELLER W. D. (1966) Apparent standard free energies of formation of selected clay minerals calculated from dissolution data. Proceedings of the Fourteenth National Conference on Claya and Cluy Miner&. Pergamon Prese (in press). ROY D. M. and ROY R. (1955) Synthesis and stability of minerals in the system MgO-Al,O,SiO,-H,O. Amer. Min. 40, 147. SWU~ETER M. and EARLEYJ. W. (1966) The mineralogy and geological aigniflcanceof Mowry bentonites, Wyoming. cfwl. Sot. Amer. Special paper a, 118 p. STEMFINKH. (1962) Crystal structure of a trioctahedral micaphlogopite. Amer. Min. 47, 886. WILLIAMSF. J., EL~LEYB. C. and WE-IT D. J. (1964) The variations of Wyoming bentonite beds aa a function of the overburden. Proceeding8 of the Second ~National Conference on Claye and Cluy Miner&. p. 141. Pergamon Press. YOUNO R. A. (1962) Mechanisma of the Phase transition in quartz. Engineering Exp. Stat., Georgia Inst. of Tech. Pub. Yomo R. A. and POSTB. (1962) Electron density and thermal effects in alpha quartz. AC&. Cry&. 15,337.