-1-
THE EFFECT OF CATION SUBSTITUTIONS
ON THE PHYSICAL PROPERTIES
OF TRIOCTAHEDRAL MICAS
-by
Robert Miller Hazen
SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY
June, 1971
Signature of Author .-.-...... Department of Earth and Planetary Sciences, May 8, 1971
Certified by ...... ' M v , . . *. 4oW ar.:4. •.•.r..-.t..... Thepis Supervisor
.- /11 - ..
Accepted by ..... (.../.. vuW'"r.Y'/Y...... Chairman, Departmental Committee Lindgren on Graduate Students ABSTRACT -2-
The Effect of Cation Substitutionp on the Physical Propertiep of Trioctahedral Micas
by
Robert Miller fazen
Submitted to the Department of Earth and Planetary Sciences in partial fulfillment of the requirement for the degree of Master of Science June, 1971
Unit cell dimensions and refractive indices have been determined for synthetic hydrous trioctahedral micas in which each of Co+ 2 , Cu+ 2 , Fe+ 2 and Ni+ 2 completely occupies the oc- tahedral sites. Zn and Mn micas with excess aluminum have also been synthesized,.but syntheses of pure Zn+2 , Mn+2 , Cd+ 2 and Pb+2 micas were not successful. Tetrahedral substitutions of B+3, Fet3 and Ga+3 for Al+ 3 and Ge 4 for Si+4 ; and inter- layer cation substitutions of Rb+, Cs+, NH4+ and Na+ for K+ provide additional data on linear relationships that exist between ionic radii (Shannon and Prewitt) and unit cell edges, and between ionic radii cubed and unit cell volumes of these micas. The influence of substitutions on the unit cell are such that octahedral substitutions predominantly affect the a-dimension, interlayer substitutions the c-dimension, and tetrahedral substitutions affect both dimensions.
Tetrahedral and interlayer cation substitutions of a wide range of ionic radii were found to form stable micas. However, octahedral cations of greater than 0.78 A average ionic radius do not form stable trioctahedral micas of the form KR3+ 2AlSi3OlO0(OH)2. The instability of such micas is shown to be due to the misfit of smaller tetrahedral layers onto a larger octahedral layer. The composition of natural biotites are explained on the basis of this model. In addi- tion, quantitative predictions of the amount of Fe+ 3 in octa- hedral and tetrahedral positions in synthetic annite were made, and have been confirmed by M6psbauer and analytical chemistry techniques. A nomogram is conptructed in which, for any given composition of a hydrous trioctahedral mica, the relative stability of the mica may be determined.
Thesis Supervisor: David R. Wones Title: Associate Professor of Geology TABLE OF CONTENTS -3-
TITLE PAGE 1
ABSTRACT 2
TABLE OF CONTENTS 3
ACKNOWLEDGMENTS 5
INTRODUCTION 6
Table 1--Previous studies 7
MICA COMPOSITIONS STUDIED 8
EXPERIMENTAL TECHNIQUE 9
Table 2--Chemicals Used 11
Table 3--Mica Synthesis Experiments 14
UNIT CELL PARAMETERS 20
Table 4--Unit Cell Parameters of Synthetic Micas 21
OPTICAL DATA 23
Table 5--Optical Properties of Synthetic Micas 25
SOURCES OF ERROR 26
RELATIONS BETWEEN CELL PARAMETERS AND IONIC RADII 29
Figure 1--Monoclinic bm vs. octahedral cation radius-- 31 Figure 2--c m vs. interlayer cation radius 33 Figure 3--Volume vs. ionic radii cubed for R + 2 35
+ + 3 - Figure 4--Volume vs. ionic radii cubed for R and R 37 Figure 5--d001 vs. b 39
SUBSTITUTIONS AND STABILITY 41
Figure 6--Octahedral layer compression 43
Figure 7--T vs. ionic radius R+ 2 46
Figure 8--Tetrahedral layer rotation 48
Figure 9--a vs. ionic radius R+ 2 51 -4-
OCTAHEDRAL CATION DISTRIBUTION IN NATURAL MICAP 53
Figure 10--R+ 2 coposition in natural mwicap 54
THE COMPOSITION OF ANNITE 56
PREDICTION OF TRIOCTAHEDRAL MICA STABILITY 58
Figure 11--a vs. cation radius R+ 2 59
Figure 12--Nomogram of cosa vs. ionic radii vs. dt 61
FUTURE STUDIES 63
REFERENCES 65
APPENDIX A--The Stability of Hydrous Trioctahedral Micas 70 and their Related Hydroxides
Introduction 70
Experiments and Data 71
Preliminary Conclusions 71
Table A-l--Stability experiments 72
Table A-2--Cell Parameters of oxides and hydroxides 74
APPENDIX B--Selected Computer d-spacings for synthetic 76 Micas
VITA -5- ACKNOWLEDGMENTS
I wipsh to expreps my great appreciation to Prof. David
R. Wones for his many hourp of advice and guidance. Not only
did he provide the initial outline for this ptudy, but he
also maintained close contact as the study progressed, thus adding direction and enthusiasm to my efforts.
I would also like to thank Messrs Robert Charles, Joseph
Chernosky , Yves Pelletier, and Dr. David Hewitt for aiding me in many aspects of laboratory techniques and maintenance.
Many hours of labor were saved through their suggestions and aid.
Many thanks are also due to Prof. Charles W. Burnham,
Prof. Charles T. Prewitt, Dr. Hiroshi Takeda, and Dr. James Munoz for their stimulating discussions and many helpful comments.
This investigation was supported by National Science
Foundation grants GAll09 and GA13092 to Prof. David R. Wones. -6-
Introduction
Trioctahedral micas are subject to a wide variety of cation substitutions. Several authors have demonstrated that such substitutions have a profound effect on both the physical properties and the stabilities of these layer sili- cates (Hatch et al., 1957; Wones, 1963b; Klingsberg and Roy,
1957). A list of several recent studies on synthetic hydrous trioctahedral micas is given in Table One. While data is now available for a dozen such mica end-members, there has been little attempt tb systematically examine changes in mica properties with composition. The present study is an attempt to quantitatively define the effects of a wide range of cation substitutions on the physical properties of hydrous triocta- hedral micas. TABLE 1. Previous Studies of Synthetic Hydrous Trioctahedral Micas
Composition Emphases of Study References Physical Properties & Stability Yoder & Eugster (1954) KMg AISi30 (OH) 3 2 Stability Wones (1967) Structure Steinfink (1962)
& Physical Properties Eugster & Wones (1962) KFe 3 AISi3O0 (OH) 2 Stability Stability & Physical Properties Wones, Burns & Carroll (1971) Wones (1963) K(Mg,Fe) AISi 0 (OH)2 Physical Properties 3 3 1 0 Stability Wones & Eugster (1965)
Physical Properties Wise & Eugster (1964) KMg3 FeSi 3 O1 0 (OH) 2 Physical Properties Wones (1963a) KFe 3FeSi30 1 0 (OH) 2 Physical Properties Eugster & Wright (1960) KMg3 BSi 3O1 0 (OH) 2 Physical Properties Stubicon & Roy (1962) Klingsberg & Roy (1957) O (OH) Stabilities only KMg9 GaSi 3 1 0 DeVries & Roy (1958) KNi 3 AISi 3 0 1 (OH) 2 Unit Cell Parameters Frondel & Ito (1966) KZn 3 AISi 3 0 1 0 (OH) 2 KMn3AiSi 30 1 0 (OH)2 Physical Properties Carman (1969) NaMg 3 AISi 3O1 0 (OH) 2 Physical Properties Eugster & Munoz (1966) Nh 4 Mg3 AISi 3 010(OH) 2 -8-
. Mica Compositions Studied
The hydrous magnesian trioctahedral mica, phlogopite
KMg3AlSi 3010 (OH)2' was used as the reference composition in this study. Attempted 100% octahedral substitutions for Mg+ 2 +2 +2 +2 +2 +2 +2 +2 included Mn ,Co ,N ,Cu ,Zn ,Cd , and Pb . Data of Wones (1963b) on the Fe+2 mica annite, and synthetic bio- tites on the join phlogopite-annite, have also been employed.
Tetrahedral cation substitutions were Ga + 3 , Fe + 3 , and B for
Al+ 3 , and Ge+ for Si +; while substitutions into the inter- layer cation K position include Rb , Cs , Cu , and Ag . In addition, Na+ phlogopite data of Carman (1969) and NH+ phlo- gopite data of Eugster and Munoz (1966) have been used in this study. Finally, a number of double 100% cation substi- tutions into the phlogopite structure were studied, including ferriannite-KFe 3erant-~+2Fe+3Si3 3 0(OH) 10 2 (data of Wones, 1963a), nickelous ferriphlogopite-KNi 3FeSi 3020 (OH)2,' cobaltous ferri- phlogopite-KCo 3FeSi 300 (OH)2 and sodium-zinc phlogopite-
NaZn AlSi33 0 (OH) 2 Experimental Technique
A complete list of chemicals and their lot numbers used
in starting material preparation will be found in Table Two.
Cobaltous hydroxide was prepared by the T.A. Edison precipi-
tation method (U.S. Patent # 1,167,484) in which ammonium hy-
droxide is added to a cobaltous sulfate solution. The preci-
pitate of Co(OH)2 is washed five times in deionized and dis- tilled water, and then dried at 100*C for 4h. y-alumina was
0 prepared by heating AlCl 3 226H0 for lh. at 750 C. The silicat glass was cleaned both magnetically and in acid, and fired at
800°C for 2h. before using. K-O-2SiO was prepared by D.R. 2 2
Wones from cleaned SiO 2 glass and KHCO3 after the method of Schairer and Bowen (1955). Starting materials of five types were used: I) Oxide Mix
2) K2Si 20 s plus oxides 3) KA1Si30. gel plus R+ 2 oxide or hydroxide
+ 2 4) KFeSi30 8 gel plus R oxide or hydroxide
5) Mica gel
All gels were prepared by titration of standardized nitrate
solutions. The solution-mixes were dried and fired as de-
scribed by Shaw (1963). Oxide mixes were prepared by weighing
and mixing dried oxides or hydroxides, and then grinding in
an agate mortar until homogeneous.
Charges were sealed with excess deionized and distilled
water, or 30% H O solution in Au or Ag Pd 1/8" x 1/2" 2 2 80 20 -10- capsules. In several runs oxygen fugacities were controlled by the solid buffer technique of Eugster (1957). Standard cold seal hydrothermal pressure apparatus was used in all runs (Tuttle, 1949). Pressure measurements are believed accurate within 1%, and the error in temperature is within ±3C. All runs were rapidly quenched (2 minutes) in a cool water bath.
X-ray powder diffraction examination of all runs was performed on a Picker diffractometer using Cu K radiation, and data was collected on a servoriter strip chart recorder.
Both CaF2 (Baker's Analytical Reagent lot #91548; annealed
3X at 800°C for lh.; a = 5.4620 ±.0005) and BaF2 (Baker's lot #308; annealed 2X at 800 0C for lh.; a = 6.1971 + .0002) were employed as internal standards. Least squares unit cell refinements were performed on the Appleman, Handworker and Evans program. Optical data was obtained using a Zeiss binocular polarizing microscope with a white light source. Determination of mica indices of refraction were accomplished with Cargille's Index of Refraction Liquids, which are ac- curate to within ±.0005. All x-ray diffraction and optical work was performed at room temperature (240 ± 1C). TABLE 2. Chemicals used in starting material preparation
Chemicals used in oxide mix preparation
Formulae Manufacturer (& Grade)* Lot Number
SiO 2 glass Corning (lump cullet) 7940
GeO 2 (trigonal) Fisher 786604
AICI 3 *6h 20 Mallinkrodt 15961X
Fe203 Fisher 762942 B203 BO 2 3 J.T. Baker 39315 MgO Fisher 787699
MnO K & K 10868
CoSO 4 *7H 20 Mallinkrodt n.d.
NiO Matheson, Coleman & Bell CB918 NX345
CuO Mallinkrodt X40588
ZnO Baker & Adamson B354
CdO Baker & Adamson A244X364J
Ni (OH) 2 K & K 16214
NH 4 (OH) J.T. Baker 24037 KHCO 3 J.T. Baker 21537 TABLE 2. Continued
Formulae Manufacturer (& Grade)* Lot Number
K (OH1 J.T. Baker 14890 Ag20 K & K 17692 Cu20 Fisher n.d.
Additional chemicals used in gel preparations
"Ludox"** Dupont (High Silica) n.d.
Ag Metal Fisher 71096
Cu Metal Baker & Adamson N-023
Zn Metal Merck 40678
Pb Meta I Fisher (8/1000" foil) n.d.
Ga Metal J.T. Baker (99.999%) n.d. J.T. Baker 30158 KNO3 J.T. Baker 33275 NaNO 3 K & K 18088 RbNO 3 K & K 7824 CsNO 3 TABLE 2. Continued
Formuale Manufacturer (& Grade)* Lot Number
Mg(NO 3 ) 2* 6H20 Ma llinkrodt 37012 27357 Mn(NO3) 2 Mallinkrodt (50% solution) 26829 Al (NO 3 3 9H 2 0 Mallinkrodt
Cr(NO 3 3" 9H20 Mallinkrodt 795204
*All chemicals reagent grade unless noted. **Dupont Ludox was analyzed by F. Frey. Solids after drying and firing at 300 0C
include by weight SiO 2 = 99.0% and Na20 = 1.0%. TABLE 3. Mica Synthesis Experiments
Micas of the form R Mg AISiOl 3 0 (OH) 2 + + R R ionic Run PT H 0 T(OC) Duration Starting Capsule Products cation radius (A ) (in kbals) (t+30) (hours) Materials Buffer
K 1.38 M#1l 2.0 800 gel Au 100% phlogopite + Rb 1.49 M#105 2.0 700 140 gel Au Rb-phlogopite, Forsterite, & RbAISi20
M#98 2.0 300 340 gel Au do. plus glass
Cs 1.70 M#106 2.0 700 140 gel Au Cs-Phlogopite, Forsterite, & CsAISi206 340 M#99 2.0 300 gel Au Forsterite, CsAISi20 6 & glass
Ag 1.15 M#46 2.0 310 48 gel Au Silver Metal & gfas$
M#67 2.0 540 48 gel Pt do.
M#90 2.0 600 72 Mg AISi Au Silver Metal, Chlor;e gl plds & glass Agp
Cu+ 0.96 M#122 2.0 630 96 Oxide Mix Au Cu20, Talc & unknown TABLE 3. Continued
Micas of the form KR 3+2AISi 3 0 1 0 (OH) 2
++ . R R ionic Run T(oC) Duration Starting # PT= PH 2 0 Capsule Products cation radius (A). (in kbars) ( 30) (hours) Materials Buffer
Mg+2 0.720 M#1I 2.0 800 70 gel Au 100% Phlogopite 2 Mn+ 0.83 M#13 2.0 450 96 Oxide Mix & Au a-Mn20 ; y-Mn2 0 3 & sana ine K2Si 2 0 5 gel
M#18 2.0 280 216 Reduced Au MnO; Mn(OH)2 & glass Oxide Mix
M#19 2.0 362 120 Reduced Au Tephroite, Kalsitite & Oxide Mix Leucite
M#32 2.0 603 120 Gel Au Mn(OH) 2 & Manganophyl- lite
M#62 2.0 725 72 Gel Au y-Mn203 & Sanidine
M#86 2.0 540 96 Reduced Gel Au Braunite, Tephroite Sanidine & <10% Mica
M#84 2.0 580 670 Reduced Gel Au Braunite & Sanidine 1.0 kb M#91 500 336 M#32 Ag-Pd Mn(OH) 2 & Manganophyl- CH 4 lite M#92 1.0 kb 500 336 Gel Ag-Pd Tephroite, Kalsilite & CH Leucite 4 M#117 1.0 kb 600 96 MnO plus Ag-Pd Tephroite, Kalsilite & Kfs gel Leucite CH4 ul
~I~L~ _1 _____ TABLE 3. Continued
2 R+z R+ ionic Run# PT = PH20 T(oC) duration Starting Capsule Products cation radius (A ) (in kbars) (*30) (hours) Materials Buffer
+ 2 Co 0.745 M#114 2.0 750 48 Co(OH) 2 Au 100% Cobaltous plus Phlogopite gel
SR#12 1.0 710 48 Co(OH) 2 Au 100% Cobaltous plus Phlogopite gel
SR#34 0.2 880 48 SR#12 Au CoO, Co Olivine & Leucite
Ni + 2 0.69 M#7b 2.0 600 145 Oxide mix Au 100% Nickelous plus K2Si20 5 Phlogopite gel
M#115 2.0 750 48 Ni(OH) plus Au 100% Nickelous gei Phlogopite 2 Cu+ 0.73 M#29 2.0 600 120 Gel Au 80% Cupric Phlogopite, glass and minor uni- dentified #
M#49 2.0 703 96 Gel 50% Cupric Phlogopite, glass and unidentified phase
M#77 2.0 260 215 Gel Cupric Phlogopite, Cu- Pyroxene & Muscovite
I TABLE 3. Continued
R+2 R ionic Run PT = PH 2 0 T(OC) Duration Starting 0 # ° Capsule Products cation radius (A ) (in kbars) (2I3 ) (hours) Materials Buffer
+ 2 Zn 0.75 M#8 2.0 600 145 Oxide mix Au Willemite, Kalsilite & K 2 Si 205 & Leucite M#17 2.0 280 215 Oxide mix Au Willemite, Mica & & K2Si205 minor Leucite M#61 2.0 725 72 Gel Au Willemite, Kalsilite & Leucite
M#94 2.0 530 50 Gel Au Willemite, Mica & Leucite
M#101 2.0 500 290 Gel Au Willemite, Mica & Leucite
0.95 M#9 2.0 600 145 Oxide mix Au Cd-Olivine & Leucite & K2Si205
M#22 2.0 385 360 Reduced Au Cd-Olivine & Sanidine Oxide mix
1.18 M#57 2.0 650 290 Gel Au Pb 4 SiO 6 & unknown
M#66 2.0 410 170 Gel Au K2Pb 4Si8 021' Sanidine & Pb 30 4
H
_ _ Table 3. Continued
+ 3 PT PH R R + 3 ionic Run 2 0 T(OC) Duration Starting Capsule Products cation radius (A) # (in kbars) (-30) (hours) Materials Buffer
Micas of the form KM R+ 3 Si310(OH) 2
+ 3 Al 0.39 M#1 2.0 800 Gel Au 100% Phlogopite
0.12 M#30 2.0 603 120 Oxide Mix Au 50% Boron Phlogopite, & Glass K 2Si 2 0 5 M#108 2.0 720 120 Oxide Mix Au 95% Boron Phlogopite & K2Si205 3 Ga+ 0.47 M#46 2.0 310 45 Gel Au 40% Gallium, Phlogopit% Ga20 , unknown 0, & glasa
M#109 2.0 720 120 Gel Au 100% Gallium Phlogopite
+ 3 Fe 0.49 M#100 2.0 500 265 Oxide Mix Au 100% Ferri-Phlogopite & X 2 SiO 5 M#107 2.0 720 120 Oxide Mix Au 100% Ferri-Phlogopite & K2Si205
M#111 2.0 690 215 Oxide Mix Au 100% Ferri-Phlogopite & K2Si20 5 Cr + 3 (IV) n.d. M#44 2.0 700 96 Gel Au Cr 0 , Forsterite & uningwn
M#72 2.0 410 Gel Au Cr 20 3, Forsterite & glass I co
~ I 1_~1_ TABLE 3. Continued
+ 4 P T =P R+4 R ionic Run H 2 0 T(OC) Duration Starting Capsule Products cation radius (A*) # (in kbars) (±30) (hours) Materials Buffer
Micas of the form KMg3AIR3+4O 1 0 (OH) 2
Si + 4 0.26 M#l 2.0 800 Gel Au 100% Phlogopite
4 Ge + 0.40 M#63 2.0 725 Oxide Mix Au 100% Ge-Phlogopite
of the form KR 010(OH) Micas 32FeSi Au 100% Ferri-phlogopite Mg+2 0.72 M#100 2.0 500 265 Oxide Mix & K2 Si 2 0 5 M#107 2.0 720 120 Oxide Mix Au 100% Ferri-phlogopite & K2Si205
M#111 2.0 690 215 Oxide Mix Au 100% Ferri-phlogopite & K Si205
No+2 0.69 M#123 2.0 700 24 Ni (OH) 2 & Au 100% Nickelous KFeSi 3 08 Ferri-phlogopite Gel
+ 2 Co 0.745 M#127 2.0 700 24 Co(OH) & Au 100% Cobaltous Ferri- KFeSi3 8 phlogopite Gel
~L~ ______-20-
Unit Cell Parameters IM unit cell dimensions and volumes, as well as molecular weights and calculated densities, for synthetic hydrous tri- octahedral micas of this and other studies are listed in Table Four. Smith and Yoder (1956) have shown that trioctahedral micas often possess an ideal pseudo-trigonal unit cell, de-
' fined by am = bm/NrJ and m = 99054 . The conversion from the monoclinic IM to trigonal 3T cell is accomplished by at = am and ct = 3 cm.sin$s. Of the micas examined, only sodium and boron phlogopites depart appreciably from these ideal relations.
Crowley and Roy (1960) have demonstrated that pressure of formation does not significantly affect unit cell parameters of phlogopite. Similarly, synthetic micas examined in this study showed no systematic variations of cell parameters with temperature or pressure. However, Eugster and Wright (1966) have noted that the physical properties of boron phlogopite appear to vary with temperature and pressure of formation.
Also, Carman (1969) has clearly documented the tendency of sodium phlogopite to hydrate below 800 C. Thus, sodium and boron phlogopiteonce again depart from the ideal case. It should be noted that sodium and boron phlogopites have the smallest cell dimensions of all micas studied. TABLE 4. Unit Cell Parameters of Synthetic Hydrous Trioctahedral Micas
Micas of Known Composition
a (AO) bm (AO) cm (AO) Pcalc. 3 Run# or Composition m F.r Vol (Ao ) GFW gm/cm Reference
KMg3A1Si OI0 (OH)2 5.315±.001 9.204±.002 10.311±.003 99054' ±4 497.0±0.6 417.3 2.79 M#1 5.314 ±.001 9.208 ±.002 10.314±.005 99054' ±2' 497. 0±1. 0 Wones (1966) 5.314 ±.01 9.204 ±.02 10.314±.005 99054' 5 0 + 497.0±1. Yoder & Eugster (1954) Na Mg A1Si 3 301 0 (OH)2 5.265±.008 9.203 ±.006 9.994 ±.001 97045' ±8 479. 8 ±0 .8 401.2 2.78 Carman (1969) 1 + NF4 5.311±.008 9.224±.004 10.443±.007 99042 504.2 396.2 2.61 Eugster & Munoz (1966) + Rb 5.34 ±.01 9.24 ±.02 10.48 ±.05 99 54 ' 510.0 463.6 3.02 M#105 2 + ' Cs 5.37 ±.01 9.30 ±.02 10.83 +.05 99054 516.8 510.8 3.18 M#17y6 2
2 KCo~ AISi 3 O1 0 (OH)2 5.340 ±.001 9.240 ±.005 10.345±.002 990581'±2 502.8±0.3 521.1 3.44 M#114 ' 5.341±.001 9.240±.002 10.347±.002 99054 1 503.3 SR#12 2 -+2 5.303 ±.005 9.172±.001 10. 286±.002 99056'±31 493.1±. 5 M#7b 5.297±.003 9.175±.003 10.281±.004 99050'±3 ' 492.3±.3 520.5 3.51 M#115 n.d. n.d. 10.17 n.d. n.d. Klingsberg & Roy (1957) 5.334±.001 9.238±.002 10.314±.004 99054 ' 498.8±.4 535.0 3.56 M#29 2 5.330±.001 9.234±.002 10.316±.003 99056'1±2' 497.8±.2 M#49 Fe+2 e3 5.401±.01 9.347±.005 10.297±.01 10Go 10'±12'1 511.7 511.9 3.32 Wones (1963b) 5.397±.001 9.348±.002 10.316±.005 99054'± 512.0 Wones, Burns & Carrol (1971) 2 (FeMg) 3 -Mole % Fe ). 169 5.339±.006 9.230± .001 10.311±.002 99050'+4' 500.6 Wones (1963b) 0.250 5.333± .002 9.242±.001 10.312±.001 99*56'1i ' 500.6 10.293±.006 99038'±6' 502.6 0.352 5.349±.005 9.260±.002 99057'+4 ' 0. 450 5.343± . 007 9.276±.001 10.312±.003 503.4 I\ 0.550 5.358±.003 9.285+.003 10.297+.002 1000' ±1' 504.5 H 0.765 5.373± .01 9.312± .003 10.297±.009 10003' ±6' 507.3 0.880 5.389±.003 9.335±.002 10.322±.004 990581±4' 511.4
P rm(_ ~ ~CO~ ~P~ TABLE 4. Continued
am (AO) 0 Pcalc 3 Run # or 3sition b (A*) Cm (A ) 3 Compo m m Vol (A) GFW gm/cm References KMg3B 3 S i 0 (OH) 5.29U. 002 9.177±.001 10.246±.002 98034 ' ±4' 491. 9±.2 401.1 2.77 M#108 5.321. 01 9.165±.02 10.29 ±.01 100010'-10' 496.5 Eugster & Wright (1960) 5.310 9.150 10.234 1000 8' 489.5 Stubicon & Roy (1962) ' G +3 5.327±. 002 9.218±.005 10.359±.002 99049'1±21 501.2±.3 460.0 3.05 M#109 n.d. n.d. 10.26 n.d. n.d. Klingsberg & Roy (1957) + 3 Fe 5.354±.001 9.273±. 002 10.316±.004 99054'1 505.0±.2 446.1 2.93 M#107 2 ' 5.358±. 003 9.276±. 003 10.321±.004 99058'1±41 505.2±.3 M#111 3 ' 5.34 ±.01 9.28 ±.005 10.35 ±.01 99055'+10 505.6 Wise & Eugster (1964) .002 9.341i .004 10.600±.002 99o54' 526.1+1.0 550.8 3.48 M#63 2 KMg3 AlGe+4 0 (OH) 2 5.393± 5.387± .002 9.378± .02 10.593± .003 99043'1±2' 525. 5±1.0 550.8 M#68 ± ' 519.9 540.76 3.45 Wones (1963a) KFe 3+2Fe+3Si 0 (OH)25.430 .002 9.404± .005 10.341±.006 10004'±10 3 1 0 ' 5.335± .005 10.332±.006 99055'±10 1 501.5± .08 549.34 3.63 M#123 KNi Fe i3010(OH) 2 9.237± .005 5.368±.001 9.329±. 002 10.346±. 002 99050'-+5' 510.1+.04 550.00 3.58 M#127 KCo3Fe+3Si30 1 0 (OH)2 Synthetic Micas of Unknown Composition R+ 2 Cation & Extra Phases + 2 ' Zn 5.31 ±.02 9.205±.01 10.25± .05 9s050' ±101 492.5±1. 0 M#17 ' Willemite 25% in 5.30 3±.004 9.214±.005 10.285±.003 9c041't±3 495.4±.4 M#94 all runs 5. 32 8.002 9.226 ±.002 10.312±.004 99059'±1' 498.9±.2 M#101 , 4 Willeriite reported 5.32 5±.005 9.210 ±.005 10,210 990501±10' 493.0±+1.0 Frondel & Itc (1966) from all runs + 2 Mn 5.27±.01 9.20±.02 10.17±.03 99050'+10 ' MM#22 912 6 ' MN(CH) 2 25% 5.31±.01 9.21±.01 10.31±.01 990451± 503 ±3 in all runs ' Tephroite reported 5.32±. 01 9.394±.01 1b.32±.01 99050'±10 Frondel & Itc (196- in all runs 1. X-ray diffraction performed at 1300 C. 2. iM unit cell calculated from ideal 3T cell data. a,=at, bm=/?-at, cm= ct/3*sin 99054 ', a 99-541 3. Mbss auer analyses of ferriphlogopites by W. Burns reveals 5 to 15% Fe+ 2 in all runs. 4. Unit cell parameters calculated on the Appleman, Handworker & Evans Program by this author from Frondel & Ito (1966), Table 7, p. 1421.
______-23-
Optical Data
Indices of refraction for synthetic hydrous trioctahedral micas of this and other studies are found in Table Five. Due to the psuedo-trigonal habit of these micas, y=8 , and thus two refractive indices are definitive. Other optical para- meters considered include birefringence B =y -a and the ob-
_ 32 = + served mean refractive index n = /&7 . While syn- thetic crystallites seldom exceeded 20p in size, thus making
2V determination difficult, all observed 2V O . Micas are colorless except for those containing cations of the transi- tion metal series. Intense pleochroism was observed only in iron-bearing trioctahedral micas, whereas faint pleochroism was noted in cobalt and copper phlogopites.
A useful, but seldom used optical property is the speci- fic refractive energy K, defined by K = n-1/p where n is the mean refractive index and p the density. Gladstone and Dale (1864) demonstrated that K for liquids may be calculated from the formula: K = k (PI/100) + k2 (P2 /100) + etc., where kj, k2 , etc. are the specific refractive energies of the com- ponents of the liquids and P1 , P2,, etc. are the weight per- centages of these components. H.W. Jaffe (1956) applied the rule of Gladstone and Dale to minerals, treating oxides as the components of the minerals. Jaffe obtained reasonable agreement between observed and calculated n in this manner.
However, it is interesting to note that the calculated n for hydrous silicatesydisplayed consistent positive deviations from considered in Jaffe's study -24- observed n. Deviations ranged from a low of -.001 to as high as +0.064 for the twenty-five hydrous-silicates discussed.
Similarly, synthetic hydrous micas of this study dis- play consistently positive deviations of cal:c. from nobs..
Only annites display a negative deviation, and positive de- viations as high as +0.087 are noted. It would thus appear that the value cited for k(H 20) by Larsen and Berman (1934) of 0.034 cannot be applied directly to water in the silicate minerals. A significantly smaller value for k(H20)is implied by the above data. Another source of error in the calculated
K for silicates may result from erroneous k values for transi- tion metals. Jaffee (1956) notes that k(Fe 20 3) varies from
0.290 in silicates to 0.404 in oxides. It thus appears that k for transition metals may be lowered considerably in a silicate environment. However, k values for copper, cobalt, nickel, etc. are known only for the oxide environment. This may, in part, explain the anomalously high values for n cal- culated. It seems that further refinement of k values are needed before the rule of Gladstone and Dale may be effective- ly applied to silicate minerals. TABLE 5. Optical Properties of Synthetic Hydrous Trioctahedral Micas - 2 - 3 Deviation Color, Pleochroism & Compositon a B1 nobs ca lc Run# or 1I obs AI other remarks Reference KMg A1Si30 (OH) 1.550 .002 .002 3 1 0 2 1.587 0.037 1.575 1.586 +0.011 Colorless, 2V=00 M#1 1.550 .002 .001 1.581 0.031 1.571 +0.016 Wones (1966) 1.548 .003 0 1.588 .003 0.040 1.575 +0.011 " 2V 0 Yoder & Eugster (1954) Na+ 1.545 .003 .004 1.569 0.024 1.561 1.581 +0.020 Colorless Carman (1969)4 Rb 1.540 .01 1.575 .01 0.035 1.560 + 1.647 +0.087 Colorless M#105 Cs 1.570 .01 1.605 .01 0.035 1.590 1.601 +0.011 Colorless +2 M#106 Fe3 1.633 .002 1.700 .002 0.067 1.678 1.667 -0.011 Pleochroic: Wones (1963b) 1.636 .002 1.690 .002 0.055 1.672 -0.005 X = Red or yellow-brown Z = light green Co3 +2 Wones & Carroll (1971) .002 1.668 .002 N+2 1.607 0.061 1.648 1.688 +0.040 Pale Purple to Lavendar M#114 1.614 .002 1.675 .002 0.061 1.654 1.702 +0.048 Medium green 2V=0O M#115 n.d. 1.652 .004 Klingsberg & Roy (195 1.588 1.630 ;7) .004 0.042 1.616 1.690 +0.074 Medium blue M#29 1.549 .002 1.580 .002 0.031 1.570 1.581 +0.011 Colorless M#108 1.546 .002 1.568 .002 0.022 to 3 1.560 +0.021 Eugster & Wright (1960) Ga+ .003 1.558 1.598 .003 0.040 1.585 n.d. n.d. Colorless M#109 n.d. 1.598 3 Klingsberq & Roy (1957) Fe .002 0.041 1.601 1.642 .002 1.628 1.656 +0.028 Pleochroic: M#111 1.600 .001 1.642 .001 0.040 1.629 X = reddish-brown Ge +4 +0.027 Wise & 3ugster (1964) 1.596 1.646 1.623 Z = pale orange Fe3+2 L- 3 .003 .003 0.050 n.d. n.d. Colorless M#63 1.705 .005 1.748 .003 0.043 1.734 1.711 -0.023 n.d. Wones (1963a) +2 +3 .005 1.760 1.715 .005 0.0 1.745 1.787 +.042 x=red-brown M#127 3 + Fe3 z= pale purple 1.730 .005 1.770 .005 0.040 1.757 1.799 +.042 x=red-brown M#123 z=pale green 1. B =y- a
3 3. Icalc. = P'k + 1, where p = density in gm/.m and k = specific refractive energy after the rule of Gladstone and Dale (1864).
4. Indices of refraction determined on mica heated to 800 C and immediately placed into oil. 5. Recent Mossbauer work reveals appreciable Fe '3 in all synthetic annites.
----~- - ---.I-, -e --..~--,,.....I... ,, -26- Sources of Error
The majority of trioctahedral micas pynthepized repre-
sent 100% reaction from starting materialp, and are thus ag- sumed to be of ideal composition. However, rubidium and
cesium phlogopitep represented only =20-25% of the reactants
in those runs. These micas are thought to approximate ideal
composition on the basis of the observed trioctahedral x-ray
patterns and the predicted unit cell parameters. Due to dif-
ficulties in standardizing gallium in nitrate solution, the gallium phlogopite gel may be slightly difficient in Ga+ 3
explaining why a maximum reaction of only 95% was obtained. Another .possible source of error in the assumed compositions
was revealed through Mbssbauer studies of iron-bearing phlo-
gopites. Roger Burns pas shown a minimum of 10% Fe++33 in all annites, and from 5 to 15% Fe+ 2 in ferriphlogopites. Thus, one might also expect multiple valence states in Ni, Co and Cu- bearing micas. Seifert and Schreyer (1971) have demonstrated +2 the presence of Mg+ 2 in tetrahedral coordination in Mg-rich synthetic trioctahedral micas. However, the assumption is made that all R+2~cations in this study are in octahedral co- ordination unless noted otherwise.
In the investigqatiodn'byFrondel and Ito (1966), and in this study, end-member zinc phlogopite KZn 3AlSi 3 01 0 (OH)2 wap not achieved. In all experiments in which mica was pro- duced, .25% willemite-Zn 2 SiO 4 with minor leucite and/or glass were also present. While the mica is clearly zinc- bearing, having cell parameters and indices of refraction higher than phlogopite, the excess willemite is evidence of less than three Zn +2 atoms per mica formula unit. Neumann (1949) has well documented the great preference of zinc for tetrahedral coordination. Thus, one possible explanation for such a zinc-poor mica is that the zinc enters the tetra- hedral layer, while aluminum fills the three octahedral sites;
1 +3 +2 +4 i.e., KA (Zn ,Si 2 )30 1 0 (OH)2 . A structural study of the natural zinc mica hendricksite from Franklin, New Jersey, would aid in an understanding of zinc's role in the layer silicates.
Synthesis of end-member manganese phlogopite-KMn3 AlSi 3 010- (OH)2 was also unsuccessful. Frondel and Ito (1966) report that tephroite-Mn 2SiO 4 is present as a major phase in all mica-bearing runs, while in the present study pyrochroite-
Mn(OH)2 accompanies the mica phase. Thus, while the unit cell parameters of the mica are greater than those of phlogo- pite, there are fewer than three manganese atoms per mica formula unit. Burns (1970, p. 43) has demonstrated from absorption spectra evidence that the distorted octahedral site of the phlogopite structure may stabilize manganese in the plus-three valence state. Furthermore, natural mangano- phyllites invariably contain aluminum in more than 10% of the octahedral sites. Therefore, the manganese-poor mica synthesized in this study may represent a solid solution be- tween the components KMn +2AlSi+2 0 (OH) + KMn +3AlSi3+3 0 (OH) 3 33 10 2 2 3 10 2
+ KAl2 AlSi 300 (OH) . Further study on natural manganophyl- lites isto needed define the extent of Mn+3/ M+2 substitution lites is needed to define the extent of Mn / Mn substitution -28- in the mica's distorted octahedral sites. -29-
Relations between Cell Parameters and Ionic Radii
There exist several systematic relations between unit cell parameters and ionic radii of substituting cations.
For example, the cell dimensions am, bm and cm are each pro- portional to the Shannon and Prewitt (revised 1970) ionic radii of cations substituting into the tetrahedral, octahe- dral or interlayer positions. This relation is clearly de- monstrated by Figure One of bm vs. octahedral cation ionic radii. The single exception to this rule is that of cm vs. interlayer cation ionic radii (Fig. #2). The distinct nega- tive curvature has been explained by Prewitt as the result of increasing coordination number of the interlayer cation with increasing ionic radii of this cation. For a given cation, an increase in coordination number is accompanied by a decrease in effective ionic radii. As expected, unit cell volumes are linearly related to the cube of the substi- tuting cations' ionic radii for octahedral and tetrahedral substitutions, and display a slight negative curvature in the interlayer case (Figs. #3 and #4).
It is of interest to consider how bm (the cell dimension within the mica layers) varies with respect to d0 0 1 (the di- mension perpendicular to the layers) for each type of cation substitution. A plot of bm vs. d001 (Fig. #5) demonstrates that octahedral, tetrahedral and interlayer cation substitu- tions have differing effects on the size and shape of the unit cell. For example, octahedral substitutions have a profound influence on bm, while d0 0 1 remains virtually constant. The +2 near-vertical plope of the R line is a result of this fact. On the other hand, interlayer cation substitutions alter the thickness d0 0 1 of the layers, while having a 3 much smaller effect on b R+ and R tetrahedral substi- m. tutions influence both bm and d 001 . It should be noted that these observations agree with the theoretical predictions of Takeda and Morimoto (1970). -31-
Figure #1--Monoclinic bm unit cell dimension vs. ionic
radius of the octahedral cation for micas of +2 the form KR3 A1Si30 (OH)2. Black dots represent biotites on the join phlogopite--
annite synthesized by Wones (1963b). 32-'
0.78
0.7
CUC
2u+
0 0.70
Ni+ 2 bm cc Ionic
0.66
9.20 9.24 9.28 bnmA 0 -33-
Figure #2--Monoclinic cm unit cell dimension vs. ionic
radius of the interlayer cation for micas of
the form R +Mg3AlSi3010 (OH) 2. -34-
1.60
1.40
n,0z 0 H<1 z0
1.20 wX w z -1.00 1.0
10.0 10.2 10.4 . 10.6 10.8 Cm in A -35-
Figure #3--Monoclinic unit cell volume vs. ionic radius
of the octahedral R+ 2 cation cubed, for micas +2 of the form KR2 AlSi3 O1 0 (OH)2 . Black dots represent biotites on the join phlogopite--
annite synthesized by Wones (1963b). IIYPP-~------
of*
O0 Mg*
WONES 0.35 - IM UNIT CELL VOLUME ) o (1 9 6 3) OO0.35 *WONE S (19 63)
4 90 500 510 IM UNIT CELL VOLUME (As)
I -37- -37,
Figure #4--Monoclinic unit cell volume vs. the cube of
the interlayer+ R+ cation radius for micas of the form R Mg 3AlSi 301 0 (OH)2 , and vs. the cube of the tetrahedral R+ 3 cation radius for micas of the form KMg 3R+3Si 30 1 0 (OH)2. -38-
to *4
C 4.0 w cm
S3.0 a
2.0
0
I I Fe+ 3 TEl RAHEDRAL CATION G+3A m SUBSTITUTIONS -,-I 3 a KMg 5 F' Si 30 10 (OH) 2
0.6 Al
S0.3 BAI+ 3
0 z 0 cme 4k Bj __ I c 490 495 500 505 IM UNIT CELL VOLUME Figure #5--Monoclinic interlayer spacing d001 vs. mono-
clinic b m cell dimension. The four lines represent micas of the form KMg3AIR+4010 (OH)2 KMg3Al 3 010 (H 2, +3 +2 KMg 3 R Si30 1 0 (OH) 2 , KR AlSi 0 (OH) and
R+Mg 3 AlSi30 1 0 (OH)2" ------sl-~---~-
s 9.4-- 1?*4 * 2 R-0+4
I o R +R * Fe+2 Go 4
*
* R 9.3
E + Rb oCo f . Co3 C2 A (NH4)* Wones (1963) ,..s...... u,Eugster8 Mun Phlogopite.o o,. 9.21 4..No+ Carman (1969) SB 2Ni 10.0 10.2 10.4 10.6 dool = Cm-s in, m (A) Substitutions and Stability Interlayer and tetrahedral cation substitutions demon- strate that a wide range of ionic radii are possible in these positions. Interlayer cations vary from sodium (ionic radius = 0.98 A*) to cesium (1.70). Tetrahedral cations from boron (0.12) to iron III (0.49) form stable micas. However, octa- hedral cations seem far more restricted in their ability to substitute into the phlogopite sturcture. No R 2 ation of radius greater than iron II (0.78), including lead (1.18) cadmium (0.95) and manganese (0.83), was found to form a sta- ble mica. Furthermore, Eugster and Wones (1962) have demon- +2 strated that the Fe mica annite is far less stable than phlogopite. Thus, it appears that the stability of triocta- hedral micas may be in part a function of the octahedral cation's ionic radius. It is well known that in phlogopite the ideal AlSi tetrahedral layer is larger than the Mg 3 layer (Radoslovich and Norrish, 1962). If the trioctahedral mica is to be sta- ble, then these two layers must coincide, either by expansion of the octahedrtyaiong a and b or by contraction A m m of the tetrahedral layer along a and b . Radoslovich m m and Norrish suggest four ways to accomplish this: 1) Altering bond lengths of the ideal layers, 2) tetrahedral layer tilting or corrugation, 3) octahedral layer flattening, or 4) tetrahedral layer rotation. -42- The altering of bond lengths is energetically far more difficult than altering bond angles. Thup, while such dis- tortions have been noted in dioctahedral mica structure studies (Takeda and Burnham, 1969), bond stretching or con- traction is assumed to be a minor effect. Tetrahedral tilting or corrugation is also well documented by Takeda and Burnham in their study of dioctahedral fluor-lithionite. However, these authors believe that tilting of tetrahedra will be minimized when all three octahedral positions are filled. Donnay, Donnay and Takeda (1963) have demonstrated that the octahedral 001 projection may conform to the larger tetra- hedral layer by octahedral layer flattening (See Fig. #6). In this way bond lengths are preserved while bond angles are altered. The amount of compression may be represented by the angle P, which has the value 54044 ' in an ideal octahedron. If the assumptions are made that: 1) there is no tetrahedral tilting or corrugation (i.e., basal oxygens in each tetrahedral sheet are coplanar), 2) 001 projections of tetrahedra are equilateral tri- angles, and 3) am = bm/ , then q is a simple function of the mean octahedral bond length d and cell dimension b : sin Y = /3Y/d The mean octa- om bmn o . hedral bond length for Mg-(O,OH) and Fe - (O,OH) are given by Donnay, Donnay and Takeda (1963) as 2.07 A* and 2.12 Ao -43- Figure #6--Expansion of the octahedral 001 projection by octahedral layer compression. OC TAHEDRAL LAYER COMPRESSION S= Arc sin (b/3 *Tdo.) boa 3. do * E 001 Projections B Ideal Octahedron: Flattened Octahedron: Y = 54P44 ' Y> 54044 Y Axis Projections _ ~i~ __f_~l__I_~____~___ 1_ _lll_____~__~____F_ IFI1-- ~----__.~~__sl1~_l____I ~___1_-__-_1~~----~~~~.. .~11111111~ -45- respectively. Mean bond lengths for other octahedral cations maybe calculated by interpolation. Thus, knowing bm , we can calculate T for each octahedral layer substitution. In. Figure #7, T is plotted vs. octahedral cation ionic radius. As ionic radius increases, the value of T is noted to de- crease slightly. Thus, larger octahedral cations require less site flattening to expand the 001 octahedral projection. While octahedral layer flattening is a real effect in hydrous trioctahedral micas, this structural parameter does not ex- plain the instability of 100% octahedral substitutions of cations larger than iron II. Tetrahedral layer rotation is a fourth means of fitting the non-equivalent octahedral and tetrahedral layers (see Fig. #8). Donnay, Donnay and Takeda (1963) have shown that by rotating each tetrahedron through an angle a about an axis perpendicular to the 001 plane, the effective size of the tetrahedral sheet is reduced. Structure studies by Steinfink (1962) and others reveal values for a may be greater than 100 in natural micas. Thus, in phlogopite the strain between octahedral and tetrahedral layers may be released primarily through tetrahedral layer rotation. If the conditions assumed by Donnay, Donnay and Takeda (1963) for octahedral layer flattening are correct, then a is defined by the mean tetrahedral bond length dt and the cell dimension bm: cop Q = b/4*4.-dt . The mean tetrahedral bond length for the AlSi layer is known to be 1.643 ± .002A0 from studies of muscovite (Guven, 1967 and Burnham and Figure #7--Octahedral layer compression angle T vs. ionic radius of the octahedral R+ 2 cation in micas +2 of the form KR2 AlSi30 (OH)2. Black dots represent biotites on the join phlogopite-- annite synthesized by Wones (1963b). -47- I I I m~+1 0.78 0 * 0 Co~2 0.74 - LC U+2 n, 0 0-2 0.70 1- Ni+2 * Wones (1963) 0.661- I I I I 580 590 600 P = Arc sin (bm / 3V-do ) 48- Figure #8--Contraction of the tetrahedral 001 projection by tetrahedral layer rotation. _ _~ _~_~ ~ ~ TETRAHEDRAL LAYER ROTATION Or a = Arc cos (b/42dt) S= 30 D cru~ar~-UI------_lr-~~~~Il I------1 ~~_ ---cr.PI-Y~-~----r~naaanr~arn*n~---aq\- _ 1. -50- Radoslovich, 1964), biotite (Franzini, 1963) and fluor- phlogopite (McCauley, 1968). With this value of dt, and the known values of bm, a plot of R+ 2 ionic radius vs. a has been constructed for micas of the form KR 3 2A1Si O02(OH) 2 (see Fig. #9). As the octahedral cation ionic radius increases to 0.76 AO, a approaches the critical value of 0*. For octa- hedral cations of ionic radius greater than f0.76 AO, the tetrahedral layer cannot expand further by rotation. It might therefore be expected that hydrous trioctahedral micas with an AlSi tetrahedral layer would not be stable for an octahedral layer3octahedral cation of radius greater than about 0.76 A0 . Figure #9--Tetrahedral layer rotation angle a vs. ionic radius of the octahedral R+ 2 cation for micas +2 of the form KR3 2A1Si 3O1 0 (OH)2 . Black dots represent biotites on the join phlogopite-- annite synthesized by Wones (1963b). -52- ! I I 0Fe+2 0.78 - 0 * •0 - ._- Cu Cu42 + + N -0.70 0z Ni * Wones (1963) 0.66 I oI 100 00 50 S= Arc cos (bm/4r- d t) -53- Octahedral Cation Diptribution tn Natural Micasp Foster (1960) has plotted the octahedral cation distri- bution for over 200 natural phlogopites, biotites and pidero- phyllites (Fig. #10). As the iron II content of these micas increases, so does the octahedral aluminum content. Trivalent aluminum in R+ 2 sites requires a corresponding substitution of aluminum for silicon in the tetrahedral layer. Thus, alu- minum has the dual effect of increasing the size of the tetra- hedral layer, while decreasing the effective octahedral cation radius. The maximum observed effective octahedral ionic rad- ius, for the most iron-rich, aluminum-poor specimens, is 0.74 A0 . Similarly, manganophyllites are known with almost 20% MnO substituting for MgO (Jakob, 1925), resulting in an effec- tive octahedral ionic radius of 0.74 A0 . Thus, while octahe- dral cations in natural micas of the form KR 2AlSi3 010 (OH)2 0° approach the critical the ionic radius of 0.76 A A, 3approach,tethey arer noto ob-b served to exceed this value. -54- Figure #10--The composition of the octahedral layer of more than 200 natural phlogopites, biotites and siderophyllites from Foster (1960). ~_I______1~1_ __ /2 ~-7~7 I 10 v * Siderophyllitesand S lepidomelanes + 90 80 70 60 50 40 30 20 0 + 3 2 P+ 90 so70 60 50 40 30 20 10-- Fc- (+ ) I _ ~ The Composition of Annite Synthetic annite was noted to be the only hydrous tri- octahedral mica of the form KR3 +2AlSi30 1 0 (OH)2 which appears to have an average octahedral ionic radius greater than the critical Value of 0.76 AO. Eugster and Wones (1962) have demonstrated that trivalent iron (VI ionic radius = 0.63 A0 ) may substitute for octahedral divalent iron (0.78 A*) in annite as expressed by the oxyannite reaction: +2 +3 +H 2 KFe 3+ AlSi3 0 10(OH) 2- K(Fe +2Fe2 +3) AlSi 0 2+ H. An annite with 212 mole percent octahedral Fe (i.e. Q,18 mole percent oxyannite) has an average octahedral cation radius of 0.76 A0 , and it was thus predicted that even the most reduced synthetic annites may have appreciable oxyannite content. Subsequent study by Wones, Burns and Carroll (1971) employing Mssbauer and analytical chemistry techniques have confirmed that at least 10 mole % of octahedral iron in all synthetic annnites is in the trivalent state. It therefore appears that octahedral cation size restrictions, resulting from the misfit between octahedral and tetrahedral mica layers, may have a profound effect on the valency of iron in annite. From Fig. #MR it can be seen that for synthetic biotites of high iron content, tetrahedral rotation (i.e., a ) is zero. Therefore, from Donnay, Donnay and Takeda (1963): cos a = 1 = bm/4-e4 .dt for these micas. However, Wones (1963b) has shown that values for bm increase -57- with increasing Fe content, in these high-iron biotites. It must therefore be assumed that d is also increasing in order to maintain the relation bm/dt = 4'f for these micas. One possible way to increase the mean tetrahedral bond length dt is by substitution of Fe +3 for Al +3 in the tetra- hedral layer. Since bm for annite = 9.348 AQ, then dt = 9.348/4q2 = 1.652 A*. Donnay, Donnay and Takeda (1963) have suggested a value of 1.68 A0 for d of the FeSi tetrahedral t3 3 layer, as opposed to the smaller 1.643 A0 mean tetrahedral bond length for an AlSi 3 sheet. Therefore, dt = 1.652 im- plies a composition of (Fe0 2 , Al e) Si3 (i.e. 7% total iron is trivalent and in tetrahedral sites) for annites' tetrahedral layer. Indeed, M05ssbauer studies by Burns (see Wones, Burns and Carroll, 1971) confirm that 6.5% total Fetetrahedral is Fe+3 Fe is tetrahedral Fe -58- Prediction of Trioctahedral Mica Stability It has been phown that bm is proportional to the octa- hedral cation ionic radius (Fig. #1). But we know that cos a is proportional to bm/dt . Therefore, cos a is proportional to octahedral ionic radius/dt. This linear relation is de- +2 monstrated in Figure #11, a plot of cos a vs. R ionic radii for varying mean tetrahedral bond length dt. The line for an AlSi 3 tetrahedral layer (dt = 1.643) has been developed previously (Fig. #9). Donnay, Donnay and Takeda (1963) sug- gest a value of dt = 1.68 AQ for the FeSi 3 tetrahedral layer, line on and this value has beenNi+ used2 to+2 obtaino+2 a secondF+2 Figure #11 defined by Ni, Mg + 2 , Co2 and Fe 2 ferri-phlogo- pites. By noting that these two lines are parallel, and by calculating additional mean tetrahedral bond lengths from data of Shannon and Prewitt (rev. 1970), additional lines can be drawn for the BSi 3 , GaSi 3 and AlGe 3 tetrahedral layers. The resulting nomogram is found in Figure #12. The inter- section of any line with cos a = 1.00 defines the critical octahedral cation radius for a hydrous trioctahedral mica with a mean tetrahedral bond length corresponding to that line. Thus, if the composition of a hydrous trioctahedral mica is known, systematic relations between composition and ionic radii enable us to predict unit cell dimensions, structural parameters, and even the stability of the mica. -59- Figure #11--Cosine of the tetrahedral layer rotation angle a vs. octahedral cation radius for + 2 micas of the form KR 3 (AlSi3 )O100 (OH)2 [d = 1.643 A0 ] and of the form KR+2(FeSi) t [t 3 3) 0 01 0 (OH)2 [dt = 1.68 A ]. -60- 7 a: .970 .980 .990 1.000 bm /41 d, (= Cos ex) -61- Figure #12--A nomogram for cos a vs. octahedral R+ 2 cation radius vs. mean tetrahedral bond length dt for all hydrous, potassic, tri- octahedral micas. 0.84 00tOBO v< .80 S0.76 S 0.72 0.68 -O.70 0.68 0.94 0.96 0.98 1.00 bm /4-V -d t (= COS a) 4 - ~ ~ ~ ~ -~ ~ ----- ~--- ~ ---b /~l_~l~la~_..v'---~~.~-.------dt (=cos~ cx) ~ ~ JI- 'r - FUTURE STUDTES Several future studies are suggested by the present work. Of primary importance is the need for a structure determination of a hydrous trioctahedral mica. While nearly pure specimens of natural hydrous phlogopite exist (Foster, 1960), no x-ray crystal structural study of such a mica has been published. Structure studies of natural Zn and Mn micas would enhance our understanding of both mica structure and the role of Zn and Mn in these hydrous silicates. It is well known that transition metal cations may induce site distortions in silicates. Examinations of the absorption spectra of Ni, Cu, Co, Fe and Mn-bearing micas might provide information regarding the nature and extent of such distortions. The greatest difficulty in performing x-ray and spectral single crystal work on synthetic hydrous micas is that such crystallites rarely exceed 20P in diameter. A technique for growing larger crystals under hydrothermal conditions would benefit both this and many other researches. Several alter- ations in the standard hydrothermal apparatus might facili- tate single crystal growth. The use of higher ratios of H20 to starting material might increase mobility of solids while decreasing the number of nucleation sites. A larger volume of starting materials, requiring a larger capsule, might also aid in macrocrystal development. A third tech- nique for increasing crystallite size might be to super- -64- impose a directional stress onto the hydrothermal system. Such a directional stress field might lower the surface free energy of large crystals. As mentioned previously, the refractive energies of water and transition metals in silicates are not well known. A systematic study of hydrous silicate indices of refraction vs. composition would enable more meaningful applications of the rule of Gladstone and Dale. The present study by no means has considered all pos- sible end-member micas. Rather, it demonstrates the vast number of synthetic micas, of both end-member and inter- mediate compositions, that may be produced with relative ease. Future studies on the effects of cation substi- tutions on the physical properties of dioctahedral micas and fluor-trioctahedral micas would enhance our present understanding of the sheet silicate structure. Indeed, the method of cation substitution in silicate minerals can provide useful information about virtually every silicate structure. -65- Referencep Barnes, H.L, and W.G. Ernst (1963) Xdeality and ionization in hydrothermal fluids: The system MgO-H20-NaoH'. Amer. Jour. Sci., 261, 129-150.. Burnham, C.W. and E.W. Radoslovich (1964) Crystal structures of coexisting muscovite and paragonite. Carnegie Inst. Wash. Yearb., 63, 232-236. Burns, R.G. (1970) Mineralogical Applications of Crystal Field Theory. Cambridge University Press, Cambridge, England, 2 2 4p. Carman, J.H. (1969) The study of the system NaAlSiQ-Mg 2SiO4 - 0 0 SiO2 - H20 from 200 to 5000 bars and 800 C to 1100 C and its petrologic applications. Ph.D. Thesis, Penn. State Univ. 290p. Crowley, M.S. and R. Roy (1960) The effect of formation pres- sure on sheet structures - a possible case of Al-Si ordering. Geochim. Cosmochim. Acta, 18, 94-100. DeVries, R.C. and R. Roy (1958) The influence of ionic sub- stitution on the stability of micas and chlorites. Econ. Geol., 53, 958-965. Donnay, G., J.D.H. Donnay and H. Takeda (1964) Trioctahedral one-layer micas. 3r. Prediction of the structure from composition and cell dimensions. Acta Cryst., 17, 1371-- 1381. Edison, T.A. (1916) U.S. Patent #1,167,484. Chem. Abstracts, 10, 725. Eugster, H.P. (1957) Heterogeneous-reactions involving -66- oxidation and reduction at high preppures and temperatures. J. Chem. Phyp., 26, 1160. Eugster, H.P. and J. Munoz (1966) Ammonium micap: Popsible sources of atmospheric ammonia and nitrogen. Science, 151, 683-686. Eugster, H.P. and D.R. Wones (1962) Stability relations of the ferruginous biotite, annite. J. Petrol., 3, 82-125. Eugster, H.P. and T.L. Wright (1960) Synthetic hydrous boron micas. U.S. Geol. Survey PP400, B441-B442. Figlarz, M. and F. Vincent (1968) Sur la deshydmtation de l'hydroxyde .de cobalt Co(0H)2. C.R. Acad. Sc. Paris, 266, 376-378. Foster, M.D. (1960) Interpretation of the composition of Trioctahedral micas. U.S. Geol. Survey PP 354-B, 11-46. Franzini, M. (1963) On the crystal structure of biotite. Zeit. Krist., 119, 297-309. Franzini, M. (1969) The A and B mica layers. Contrib. Mineral. Petrol., 21, 203-224. Frondel, C. and J. Ito (1966) Hendricksite, a new species of mica. Amer. Mineral. 51, 1107-1123.' Gladstone, J.H. and T.P. Dale (1864) Researches on the re- fraction, dispersion, and sensitiveness of liquids. Phil. Trans. Roy. Soc. London, 153, 337-348. Given, N. (1967) The crystal structure of 2M, phengite and 2M muscovite. Carnegie Inst. Wash Yearb. 66, 487-492. Hatch, R.A., R.A. Humphrey, W. Eitel and J.E. Comeforo (1957) Synthetic mica investigations. IX. Review of progess -67- from 1947-1955, U.S. Bureau of Minep, Rept. Inv. 5337. Jaffe, H.W. (1956) Application of the rule of Gladptone and Dale to minerals. Amer. Mineral., 41, 757-777. Jakob, J. (1925) Beitrage zur chemischen konstitution der glimmer. I. Mitteilung: die schwedischen manganophylle. Zeit. Krist., 61, 155. Klingsberg, C. and R. Roy (1957) Synthesis, stability and polytypism of mickel and gallium phlogopite. Amer. Mineral., 42, 629-634. Larsen, E.S. and H. Berman (1934) The microscopic determina- tion of the nonopaque minerals. U.S. Geol. Surv. Bull., 848, 266p. McCauley, J.W. (1968) Crystal structures of the micas KMg 3- AlSi30 2 0F2 and BaLiMg 2AlSi 3Oo1 0 F2 . Ph.D. Thesis, Penn. State Univ., 180p. Neumann, H. (1949) Notes on the mineralogy and geochemistry of zinc. Mineral. Mag., 28, 575-581. Pistorius, C.W.F.T. (1962) Thermal decomposition of the hy- droxides of cobalt and nickel to 100 kilobars. Zeit. fur P. Chem., 34, 287-294. Prewitt, C.T. (1971) Private Communication. Radoslovich, E.W. (1960) The structure of muscovite, KAl 2- (Si3Al)O0,(OH) 2 . Acta Cryst., 13, 919-932. Radoslovich, E.W. (1962) The cell dimensions and symmetray of layer lattice silicates. II. Regression relations. Amer. Mineral., 47, 617-636. Radoslovich, E.W. and K. Norrish (1962)The cell dimensions -68- and symmetry of layer lattice pil4catep. I. Some struc- tural considerations. Amer. Mineral., 47, 599-616. Schairer, J.F. and N.L. Bowen (1955) The pyptem K 20-AI 20 3- Si0 2 . Amer. Jour. Sci., 253, 681-746. Seifert, F. and W. Schreyer (1971) Synthesip and stability of micas in the system K 20-MgO-SiO 2 - H20 and the relations to phlogopite. Contrib. Mineral. Petrol., 30, 196-215. Shannon, R.D. and C.T. Prewitt (1970) Revised values of effective ionic radii. Acta Cryst., 26, 1046-1048. Shaw, H. (1963) The four-phase curve sanidine-quartz-liquid- gas between 500 and 4000 bars. Amer. Mineral., 48, 883- 896. Smith, J.V. {'ed.] (1967) X-ray Powder Data File. American Society for Testing and Materials, Philadelphia, Pa. Smith, J.V. and H.S. Yoder (1956) Experimental and theoretical studies of the mica polymorphs. Mineral. Mag., 31, 209- 235. Steinfink, H. (1962) Crystal structure of a trioctahedral mica: phlogopite. Amer. Mineral., 47, 886-896. Stubicon, V. and R. Roy (1962) Boron substitution in synthe- tic micas and clays. Amer. Mineral. 47, 1166-1173. Takeda, H. and C.W. Burnham (1969) Fluor-polylithionite: 2 A lithium mica with nearly hexagonal (Si2 s0)ring. Mineral. Jour., 6, 102-109. Takeda, H. and N. Morimoto (1970) Crystal chemistry of rock- forming minerals. I. Structural studies of micas. Jour. Cryst. Soc. Japan, 112, 231-248. -69- Tuttle, O.F. (1949) Two pressure vesppels for splicate-water ptudies, Geol. Soc. Amer. Bull., 60, 1727-1729. Van My, M. le (1964) Etude microcalorimetrique dep hydrates de cuivre et de nickel. Bull. Soc. Chem. France, 3, 545- 549. Wise, W.S. and H.P. Eugster (1964) Celadonite: Synthesis, thermal stability and occurrence. Amer. Mineral., 49, 1031-1083. Wones, D.R. (1963a) Phase equilibria of "ferriannite," KFe 3 Fe 3 0 10 (OH)2 . Amer. Jour. Sci., 261, 581-596. Wones, D.R. (1963b) Physical properties of synthetic bio- tites on the join phlogopite-annite. Amer. Mineral., 48, 1300-1321. Wones, D.R. (1967) A low pressure investigation of the sta- bility of phlogopite. Geochim. Cosmochim. Acta, 31, 2248-2253. Wones, D.R., R. Burns, and B. Carroll (1971) Stability and properties of annite.(abs.):Trans. A. G. U., 52, 369-370. Wones, D.R. and H.P. Eugster (1965) Stability of biotite: Experiment, theory and application. Amer. Mineral., 50, 1228-1272. Yoder, H.S. and E.2..E.ugster (1954) Phlogopite synthesis and ptability range. Geochim. Cosmochim. Acta, 6. 157-185. -70-. APPENDTX A--The stability of hydrou§ trioctahedral micap and their related hydroxidep. Introduction It has been demonstrated that mica stability is closely related to the ionic radius of the octahedral cation. Rado- slovich (1963) and others have noted that the octahedral layer of trioctahedral micas possesses a structure analagous to that of brucite--Mg(OH) 2 . Therefore, in conjunction with studies on the physical properties of hydrous trioctahedral micas, stability relations of nickel and cobalt micas and hydroxides are now being determined. While this work is not finalized, a preliminary report follows. Several studies on the stabilities of hydrous triocta- hedral micas and their related hydroxides have been pre- sented by previous investigators. Brucite--Mg(OH) 2 sta- bilities have been examined by several authors, the most frequently cited being that of Barnes and Ernst (1963). The hydroxide stabilities of cobalt and nickel have been determined by Pistorius (1962) for pressures from 5 to 100 kilobars. Van My (1964) and Figlarz and Vincent (1968) pro- vide additional data on these stabilitiep. AS mentioned previously (see Table One), several authors have examined stabilities of hydrous trioctahedral micas of the form KR32AlSi3010(OH)2.+2 The most important of these studiep are, for Mg+ 2 , Yoder and Eugster (1954) and Wones (1967); for Fe+ 2 , Eugster and Wones (1962) and Wones, Burns & Carroll (1971); and for Ni + 2 , Klingsberg and Roy (1957). Experiments and Data All stability experiments were performed in standard hydrothermal pressure apparatus as previously described. A partial list of synthesis experiments and resulting stability points thus far completed may be found in Table A-1. Slow quenching of pure CoO, Co(OH) 2' NiO and Ni(OH) 2 from stability curve temperatures and pressures revealed no development of other phases. It is therefore assumed that no anomalous phase development took place in fast-quenching of these sta- bility determination experiments. In order to determine thermodynamic properties of the hydroxides and oxides of cobalt and nickel, the unit cell volumes of these substances have been redetermined (see Table A-2). While volume and cell parameters of CoO, Co(OH) 2 and NiO are in close agreement with those reported in the ASTM File (Smith (ed.), 1967), those of Ni(OH) 2 are somewhat lower than ASTM values. Future work will consider this discrepancy more carefully, and determinations of the cell parameters of Ni(OH) 2 formed at a range of temperatures will be performed. Preliminary Conclusions Data of Pistorius (1962) and of this ptudy agree that Co(OH) 2 and Ni(OH)2 dehydrate at much lower temperatures than Mg(OH) 2, but are certainly more stable than Fe(OH) 2 -72r TABLE A-l--Stability Experiments a . Cobalt Hydroxide Dehydration: Co(QH) 2 coCoO + R2 0 Pressure Temperature Duration Reactants Products (bars) (Oc)(.. (hrs.) 200 208 CoO CoO + Co(OH) 2 200 214 Co (OH) 2 CoO CoO 2000 240 CoO + Co(OH) 2 Co CoO 2000 244 (OH) 2 Stability Points: (200 ± 2 bars, 211 ± 3 0C) (2000 ± 20 brs, 242 ± 2 C) (5 ±1 kbars, 258 ±10 0C) (15 ±1 kbars, 297 ± 5 C) (27 ±1.5 kbs, 308 10 C) (50 ±2.5 kbs, 315 ± 50C) b. Nickel Hydroxide Dehydration: Ni(OH)2 + NiO + H20. Pressure Temperature Duration Reactants Products (0C) (bars) (hrs.) 200 265 NiO NiO + Ni(OH) 2 200 270 Ni (OH) 2 NiO NiO 2000 275 Ni (OH) 2 2000 280 Ni(OH) NiO 2 + Ni(OH) 2 2000 285 48 Ni(OH) 2 NiO Stability Points: (200 ±2 bars, 268 ± 3 0C) (2000 ±20 brs, 280 ± 5 C) 1(5± 1 kbars, 295 ± 50C)* (16 ±1 kbars, 325 ±100C) (31.5 ±1.5 kb, 330 ±15 0C) (50 ± 2.5 kb, 338 ±12 0C) (100 ± 5 kb, 345 ± 50C) ,--Data of PistoriuP (1962) -73r Table A-l--Continued c. Cobalt Mica Dehydration; KCo 3A1Si 3Q 1 0 (QH)2 CoQ + Co2 SiO 4 + KA1Si 2 06 Pressure Temperature Duration Reactants Products (bars) (°C) (hrs.) 100 790 48B Gel Co Mica 100 795 48 Gel Co Mica, CoO, Co2SiOCO2 si044 & Leucite 100 802 32 Co Mica CoO, Co2 SiO 4, & Leucite 205 825 46 Gel Co Mica 205 880 39 Gel CoO, Co 2 SiO 4, & Leucite 300 875 48 Gel CoO, Co2SiO41 & Leucite Stability Points: (100 ±1 bars, 796 ±6 0C) (205 ±2 bars, 850 ±200C) -74- Table A-2--Cell parameterp and hkl dspacing for the Oxidep and Hydroxidep of Cobalt and Nickel a. Oxides: CoO This StudNiO hkl This Study ASTM File This Study ASTM File ill111 2.4599 2.460 2.4108 2.410 200 2.1295 2.130 2.0881 2.088 220 1.5059 1.5062 1.4766 1.476 311 1.2840 1.2846 1.2596 1.259 222 1.2298 1.2298 1.2059 1.206 a (A )' 4.2595 4.260 4.17665 4.1769 Vol. (A) 3 77.281 77.31 72.859 72.872 b. Hydroxides: Ni (OH) 2 hkl This Study ASTM File This Study ASTM File 001 4.654 4.66 4.638 4.605 100 2.755 2.76 2.706 2.707 101 2.368 2.38 2.336 2.334 102 1.776 1.78 1.758 1.754 110 1.594 1.60 1.563 1.563 ill 1.506 1.51 1.481 1.480 103 1.352 1.36 a (Ao) 3.182 3.179 3.125 3.126 c (A 0 ) 4.653 4.649 4.628 4.608 ) Vol. (A 3 40.795 40.688 39.15 38.97 Brucite--Mg(OH) 2 : a = 3.147 A b = 4.769 A 3 Vol = 40.9026 A -75- which is metastable at laboratory condition§. Furthermore, Co(OH) 2 has a slightly lower thermal ptability than Ni(OH)2 . < < This relative pequence of ptabilitiep: Fe(OH)2 Co(OH) 2 Ni(OH) 2 < Mg(OH)2 , is identical to the order of stabilities +2 +2 .+2 +2 seen in Fe , Co , N+ and Mg micas. Therefore, we may conclude that the factors which control the qualitative (if not quantitative) aspects of hydroxide stabilities may also strongly influence trioctahedral mica stabilities. Ionic radii, crystal field stabilization, and oxidation potential of the octahedral cation are all known to affect the pressure-temperature stability of micas. Furthermore, octahedral cations affect the dehydration products of micas. While nickel and cobalt phlogopite react to form monoxide plus olivine plus leucite, Mg-phlogopite reacts to form kalsilite plus olivine plus leucite, and annite dehydrates to sanidine and magnetite! Clearly, the differences in AVrx n for the decomposition of these four micas will affect the pressure stabilities. Accuratedeterminations of a vari- ety of mica dehydrations will aid in our understanding of these controls on the stability of micas. APPENDIX B--Selected computer d-spacing output for synthetic micas. On the following pages are computer output d-spacings for the micas listed below: Formulae Run Number KMg 3AlSi 3 01 0 (OH)2 Ml Ni3 M7b Cu3 M49 Co3 Ml14 Zn3 Ml01 Mn3 M91 KMg 3 B Si 3 0 1 0 (OH) 2 Ml08 Ga M109 3 Fe+ Mll KMg 3 AlGe 3 0 1 0 (OH) 2 M68 w I v w %0N IN i V V %JN Vi V I i C x: --- C' _v opv "1 4 40" -1 00 -' .9 0C n0 w'j& 4r FI I.- ) C) 0 1 4-3 C.i "r 7Ci J - 4 C -j c0 I uI I~w 'r,1JJ _jJ r '\JI' J .r-- J. '-, : 41-j-4-Q 1 J~ NJ -0% 10 _ 4 %nC CD 4 -4'4 '41 0 J ' 7GI ! &) C ) * 4 . e ' J 0 U ' . ' U ' o ,C Oi 0)Q 0 C, ) 0 0 0C). 0 0 C .0- 0 0 O C o C .V 0 j *.3 c 'jC) .t 0 0 -' P n3 I C- 0 0 U n ' . 1 '1 P Ir .11;"1 Ir ,P PI I x %. kI P U P , 1 k , 1nJ r ' l ' ,' "% I_ X.' ,- IP ,: C) 0, c3 C) )r n tI)o)n<-0,nrrn .n> - )n1 nn-r 1r n c" Z _ i r 0 0 . r- n ne - ) C)L.C C,, 0 0 0 C C , 0 10( C- C, n r C ) n c , C " j 0 U C ' C ' C) C, C)0 ' C7 1 C) n l 0C c)) 1 ' 1 0 S 19 ' 4.4 4- 4IJ -" -1 ,X '4-0 - . 4 -.nw v '11L. " )0 L:-~ % "- 1 P w J j -'4 - 4 ' - 4) .7 P' n Q 4 3 aI1 NJC)- 4 - ~' j- 4 - n - '4 w N 1 . m %C1 t ' i I . ' &~.1 '4 Xi j U) C ) lN) 00 llyL~v~'-^yyy-)P~gli~$*ilplrUIIIYLuY s -r~-~-, . .I _ ~ ~~~_~~~~_~_~~~~ _~~___ r)~lP~LLIEie~irC~i~~4U~i~?YIW1S~t~h~~ Y"'~ '.8 .I .4 3. '7.3. N - 0.0 ~ -J a ~I ~~ a ~iia ~ ~ a ~ a a t ~ a N j aa a aI PO 0 t-,&0 .jn 00 I 'S I a - N 'A 'A P - N 03 -i NP. P- 41 Z, 0--N t.w vN NJ-W0 0 N 41 W0'w0%. A0 0NN... O0 J.C. NUJ, ll-3,N V "1 5- . rN W NMN Ci4SN J- b ~~ ~ ~ ~~ ~ ~ ~ ~ ~ ~NJf.iJC..bN.%.'b..)).~N.LJNi..--' ~ ~N0 ~ 0-- ~ ~ ~ ~ ~ ~ 1 NJ tv5- wj..J.J3WW %0N 0 ) ...... N...... 5- -S.4p . 0.71 --. 7 -L - .. -J - i C) -. -J- 4 - 4 41J-6 0. a. .6 04 0 - O - 7 ON N N N T N 0, j- V- V03.1.1.3 .3 .0 - .0 l.J5-3 3 146- to .1 7'0 30 w N .00C 0 Nb 41 4.3 -J, w~ ,2- . ~4. J. 'D- n..0 0 1N0-. 3.0A- NO V N _j N 2- -' .-'U~ .0.0m.14 0 ). 7- -: & PIC*A1. J, .11a, 0A .1%." w 'Z -J J0.-C , u.4w - 0% D .. 4 . O c M ' w) -) MV W )4mm- )0 1j j: j X 10 w ,wa DA -J j_ 4 p4 .p 1 j% fl JP J " " ji 11.V 12.. 3 Cn L. 7- n .5 N 0.0 31. N r~* 100 0 .3A 7 41,) 0 l - 0 ~ -.1 m.a-.4 o0Q-JC)O 00 0 N- S- J .3 S- 41 - 3.'r0 .i1Jl,%nv . I .A 'A%" u n 0 n0 elWl.0 1 0n 141- P.33. "5 I-l s-- "" s-- 0. lo 4) 'oaC 0 o.7 0 N to0: C.. 0)C C)l(0 0. 0 0 0 .. C 0 0 Q.. 0 0 0 n0Q Sd n0))0 %1C) 0r.C) ) C C C) 0) . I,4 I N 000000 cr. w 4. IN O W L.. IFZ Vi L8AP 'i . 7.. Zy.41v02-J J i N.~-- 0 U ' 0 0.U. .0.-O 0'b ..A'N 0 .0 -I- ... J03'Aa 'a - w3 Ki:7 0.2'0 M-JN'U A33-. Kii) - a.3,. A ' - (-;C) .3I Ns -4 N- Ou .A 0- ZJ NJ b N 0a %p-C0 - 0.3 LO 10%PJ4-J0140.- IA U 0-J W - ) .3.3.IV 7 J~J .14 3.'. IV .t-t-2 .. 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It D eD ew -j -J C%'C A M' tieN A ru C% 0 -jo f b w : %t D 0 %n %i I nn-j 0 f~dWAn c llr% ws %A ww M0%A -& ,yl'I .0 %*%"cow4 s 6-P-P- NCAw- % , j - J- , a 4)w v-4- N n -e- - Q a men n 0 n m n lm #% #- M%". t NM r 4C ib 4I U.a o % - ,x 0 n Ih e Ut j-t0 'b4.W,0UM0A0AU'.%U'he AU'0 A l %ONI n lft p W^Fj 4.s - -MI N -O.'S-b a~ot%. 4 0 .O -%'N 4 0 FmUow''kj . S .0- A-0%Ut.- 0% AkU'h" on . 1 Nm0. m '- uS 0 , ab J. tv Ab'0 I I .10 'A 7 77 030 -3 Q103 1o10'304 )- 3D00A 0D0. j 0 000 . 0 0 D 3 . e).0 0 0 oo 00 0 0 00 0.3 k0 00 . 4 0~0003)0 3300000000~ '0 00 0 00 3 030 Zp2 00-a -00 0 U 0ac 0 a0 000 0 0 0 0 0 C2 0 0 0 0 00 0 0 0 00 0 0 0 0 0 0 00.1 0Q 0 0 0 0 0 0 0 0 0 0 0 0,; 30 Q 300) . 0 0 0 0 0 e3 0;0 0 0 0 0 00Q002 0 0 000 0 -a a 5 00t Un .U'. o .0 al ev e- '0 in a' 4. 40 4 C.S0 . Q0 O0 UP 0 0* U'o 4 U 4, -4 U' .0 Oa N0 a0 M 34 N ul j -J A %P'A Ut0' 4, 0kv 4 .0 Aa~N sO %j .0 -N e-0 .- 90 W 0 4 -1 - 0. .N.. J~~04WS 0, * 0 a %A Go C %A400 0- Q 0 w- 0 ws o 0 0 PL *~ 0 CR .. .3x' us.d~.4- O.sW*O N4- utA(Y-0w 01J- -J40 1 . CD04, 'e,4. a- N 40 %x w''U 4 4 " 4 .U.-4-M 4 w0 t ' 0 010W u.0 4.*0 0 ,0 .0 w W0 0 M .4. Z. o,-s. 0QgO* 4 rv0 %"U'0 w M jW4.0 0U' lI- - 4 VA %.04 -j -4 41V 4pt 0 4. 4.44- 1 - - . C %'0-4.0 41 1.4 1P.0 N u S.0 4s-c .g. s-., r- MtI~.WWO04U'044. I 4.$S0WoW- 4. t-0 N0 WO J N - .J00W 00004 WU0,D.04400U) O0044 .j 00ON 4 b CD4. 4. -00N Np-U UtWfuSUSO W Z~43S 1 1 :3~~% 0l 00 00 4 0 i 0 5. 0. 3 0 3 C %P. p C, NJ S 0. 0, 3o 0 P 0 -- - NJNJNJNJNJ 4% -V * . D q 7b P *f C) 41. A'-4 4 41 A P' 4' 4-Q.0 -I .-P - 4 4 J- 04 4' 4. .,4 'NJ - 15 0M - - V -. 0j j.-- I J, 0 a v 0 z w, j J I, II B B B ii B B I I ~41~21J-J~41'JJWJNJ .J'JNJ NJ~V j~JJ4JP - 1 - .1 NJ NJ V 4' '4J1 J.4' , J- - N '.4NJN -2-4'1N 4 S. A,, 44 W 4. ' vJ 4 4- j.I .3p1, ~..'- I ? J. § JV-N ,V .4- 44'I-N 1 4 1- NJ 1.. qji ~~~~~~J~~ JN JN ~JN JN ~JN 4JN - vJ -VJN -j JN vJ vJ jAJ' IN N J v 3. . 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A. vi 3 44 3 3 . % ~ d SA 0 .3 o 0 0 %#A 06 P- 0 0 -. 3 -87- VITA The author was born in Rockville Center, Long Island, New York on November 1, 1948. He graduated with high honors from Ridgewood High School, Ridgewood, New Jersey where he concentrated in science and music. He entered the Massachu- setts Institute of Technology in September of 1966, and sub- sequently enrolled in the five-year Masters degree program in the Department of Earth and Planetary Sciences. In addition to his scientific studies, the author has studied trumpet privately for four years with AndreCome of the Boston Symphony Orchestra. He has been principle trum- pet of the M. I. T. Symphony Orchestra for five years, and has appeared as soloist with the M. I. T. Concert Band, Sym- phony Orchestra, and many other groups in more than a dozen states. Among the author's academic awards are the Harvard Alumni Award (1965), the New Jersey Science Teachers' Award (1966), Outstanding Musician--New York State Music Festival (1966), and the Phi Sigma Kappa Foundation Award (1968). He is a member of Sigma Xi, Phi Lambda Upsilon, and Baton hon- orary societies. Professional experience includes summer work with Iso- topes, Inc. of Westwood, New Jersey (1968) and as field assistant for the United States Geological Survey (1970). Next year the author will continue hip studies at Harvard University, and will receive for a second year a National Science Foundation Fellowship. -88- The author was married to Margaret Joan Hndle on August 9, 1969,