UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

An M.O. study of the stereochemistry and energy of three-repeat single silicate chains Roussy, Marie Monique 1982

You don't seem to have a PDF reader installed, try download the pdf

Item Metadata

Download

Media
[if-you-see-this-DO-NOT-CLICK]
UBC_1982_A6_7 R69.pdf [ 1.9MB ]
[if-you-see-this-DO-NOT-CLICK]
Metadata
JSON: 1.0052532.json
JSON-LD: 1.0052532+ld.json
RDF/XML (Pretty): 1.0052532.xml
RDF/JSON: 1.0052532+rdf.json
Turtle: 1.0052532+rdf-turtle.txt
N-Triples: 1.0052532+rdf-ntriples.txt
Original Record: 1.0052532 +original-record.json
Full Text
1.0052532.txt
Citation
1.0052532.ris

Full Text

M.O. STUDY OF THE STEREOCHEMISTRY AND ENERGY OF THREE-REPEAT SINGLE SILICATE CHAINS by MARIE MONIQUE ROUSSY B.Sc, McGill University, 1978 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in THE FACULTY 'OF GRADUATE STUDIES DEPARTMENT OF GEOLOGICAL SCIENCES We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA September 1982 Marie Monique Roussy, 1982 > In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y available for reference and study. I further agree that permission for extensive copying of t h i s thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. I t i s understood that copying or publication of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of G e o l o g i c a l Sciences The University of B r i t i s h Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 Date September 3rd. 1982 DE-6 (3/81) i i ABSTRACT Hypothetical three—repeat single chains consisting of regular SiO« tetrahedra were generated with a computer program to study the possible conformations and their t o t a l potential energy by the CNDO/2 molecular o r b i t a l method. Calculations were r e s t r i c t e d to those chains with /Si-O-Si between 110° and 180° with an average of 140° and /(O-O-O) between 90° and 180°. In addition, successive pairs of tetrahedra in each chain were r e s t r i c t e d to either single or double—eclipsed or staggered conformation. Those chains with the largest d(Si—Si) and at least one staggered pair of tetrahedra have a lower energy. These are not, as yet, observed in nature presumably because their packing does not accomodate the i n t e r s t i a l cations. i i i TABLE OF CONTENTS ABSTRACT i i LIST OF TABLES iv LIST OF FIGURES v ACKNOWLEDGEMENT v i I. INTRODUCTION 1 11 . THE CNDO/2 METHOD 2 1 . THEORY 2 2. CNDO/2 APPROXIMATION 3 3. CNDO/2 PARAMETRIZATION 4 III . MODELS OF THREE-REPEAT CHAINS 6 1. DESCRIPTION OF CHAIN CONSTRUCTION 6 2. DESCRIPTION OF FIXED PAIRS 6 IV. CLASSIFICATION OF CHAINS 8 1. DEFINITION OF SYMBOLS 8 2. REPRESENTATIVE CHAINS 11 V. DISCUSSION OF ENERGY CALCULATIONS '13 1. SINGLE CHAIN SELECTION 13 2. RESULTS OF ENERGY CALCULATIONS 18 3. PACKING OF CHAINS 23 VI. CONCLUSION 27 VII. REFERENCES 29 i v LIST OF TABLES Table Page I. Unique settings for the rotation angles <j> 2 , 9 2 , <fr 3 and 6 3 that y i e l d double or single—eclipsed and staggered pairs. 10 II. Summary of symbols used in describing three—repeat single chains. These represent a l l the possible comformations of the double or single—eclipsed and staggered pairs of tetrahedra in a chain. 12 II I . L i s t of three—repeat chains composed of two fixed pairs of tetrahedra. The pair quoted in parantheses represents the closest approximation to the standard orientation of the t h i r d and fourth tetrahedra. The /Si-O-Si vary between 120° and 180° with an average of 140°. The /(0-0-0) b r vary between 90° and 180°. 14 IV. /Si-O-Si and /(O-O-O) for bustamite (B) and wollastonite (W) . b** 17 V LIST OF FIGURES Figure Page Origin a l configuration of the three—repeat chain showing 2/m point group symmetry and the same cluster after rotation by angles C 2 = 40°, 4> 2 = 35°, 0 2 = 30°, f 3 = 40°, (j> 3 = 10° and 0 3 = 45°. 7 Double—eclipsed, single—eclipsed and staggered pairs of tetrahedra with energies -137.9974, -137.9977 and -137.9983 A.U. respectively. 9 Three segments of the same chain whose energies are -256.172, -256.170 and -256.170 A.U. respectively. 19 Total energy (A.U.) against average d(Si—Si) (A), those chains with the largest d(Si-Si) have the lowest energy. 21 Total energy (A.U.) against average d(Si—Si) (A) for each group of chains. ' 22 Wollastonite (Buerger and Prewitt,1961) and i t s closest approximation with t o t a l energy -256.158 A.U. 24 Chains containing a combination of double or single—eclipsed pairs with energies -256.164, -256.163 and -256.163 A.U. respectively. 25 Chains containing a staggered pair of tetrahedra with either a double or single eclipsed or another staggered pair. Energies are -256.165, -256.167 and -256.164 A.U. respectively. 26 v i ACKNOWLEDGEMENT I am grateful to Dr E.P support throughout this study, grant 67-7061. Table II was compiled from King. I also thank Mr. Gord i l l u s t r a t i o n s in the text. Meagher for his guidance and This work was supported by NSERC data calculated by Ms. Irene Hodge for draughting a l l the 1 I. INTRODUCTION Only one type of three—repeat single s i l i c a t e chain is found in nature in the minerals wollastonite, bustamite, the pectolite—serandite series, s c h i z o l i t e and sorensonite. From a study of the role of octahedral cations in the packing of tetrahedral chains in each of the above minerals, except sorensonite, Ohashi and Finger (1978) found that only small changes in the comformation of the chains occur as a function of chemical variations. The purpose of th i s study is to define the di f f e r e n t types of three—repeat single chains which are stereochemically possible and to determine their r e l a t i v e energy. E a r l i e r work on two—repeat chains by Meagher (1980) has shown that the potential energy of those chains with bridging Si—O—Si angles, /Si—O—Si, between 125° and 150° and bridging oxygen angles, /(O—O—O)^ , between 125° and 180° i s lower than that of chains with any oter conformations. Meagher found that the chains of lowest energy are those with both /Si-O-Si approaching 135°. The /(0-0-0) b r i s apparently less important in determining the energy of these chains. This study was therefore limited to those three—repeat single s i l i c a t e chains with /Si-O-Si between 110° and 180° with an average of 140° and /(0-0-0) f c r between 90° and 180°, thus reducing the number of chains to be considered. To further reduce the number of chains and to f a c i l i t a t e their i d e n t i f i c a t i o n each was looked upon as composed of three pairs of tetrahedra that were either single or double—eclipsed or 2 staggered. II. THE CNDO/2 METHOD 1. Theory The t o t a l energy E of an atomic cluster i s given by the Schrodinger equation function. This equation cannot be solved for many—electron problems. The Hartree-Fock Operator, F, (Hartree, 1928 and Fock, 1930) i s an appproximation of the Hamiltonian given by where H i s ca l l e d the one—center or core Hamiltonian and represents the attr a c t i o n between an electron in the i— t h molecular o r b i t a l and the nuclei in the cl u s t e r . The terms Jt'j and K^j describe the two—electron interactions. J V J' i s the coulomb integral representing the repulsion between two electrons in the i— t h and j—th molecular o r b i t a l s respectively. K^j i s the exchange integral representing the decrease in energy associated with two electrons having the same spin. The t o t a l wave function is an antisymmetrized product of molecular o r b i t a l s which Roothan (1951) represents by a linear combination of n atomic o r b i t a l s , S , (LCAO) H l f = E l\> ( 1 ) where H i s the Hamiltonian Operator and is the to t a l wave F = Ht + J^' - 1/2K^ (2) (3) 3 For orthonormal atomic o r b i t a l s ^ , <|>̂  the overlap matrix is given by sn- = f $r ( s ) ^ ( s ) a r ( s ) ( 4 ) where dT is the volume element associated with electron s. The best approximation of the energy of an atomic cl u s t e r , i , is given by the Variation Theorem. J l//*Hy/dT E = <L (5) the c o e f f i c i e n t s c^p that correspond to the minimun energy must s a t i s f y the set of simultaneous equations 5 CM> 0 (6) where ( i s a solution to the secular equation | F f f - ES p^| = 0 (7) 2. CNDO/2 Approximation The Complete Neglect of D i f f e r e n t i a l Overlap (CNDO) method was introduced by Pople, Santry and Segal in 1965. The overlap associated with the electron repulsion between molecular o r b i t a l s with d i f f e r e n t p r i n c i p a l quantum number i s assumed to be negligable, i . e . , '(s) Ifj (s) r; T 1 Vj/*(t) Vj/(t) dT 5 dTT = 0 a j j i c , * (8) for i # j and k ± 1 In addition the corresponding overlap integrals are neglected in the normalization of the molecular o r b i t a l s . The remaining 4 electron—repulsion integrals of the form (s) r.V 4>,*> (t) dr* d7:- = (9) are evaluated. This term represent the average interaction between valence electrons assumed to belong to a s—type o r b i t a l on atoms a and b respectively 3. CNDO/2 Parametrization Each diagonal matrix element H cn be separated into a one—center and a two—center contributions of the form where = U£" - £ V^ b (j^on a (10) un = -1/2 ( i j + A ; ) - ( z - * - ) r- (11) and 1/2 ( Ii. + A ) is the Mulliken d e f i n i t i o n of electronegativity,where I is the ionization potential and A is the electronic a f f i n i t y associated with <^ . Z^ i s the core charge of atom a. U^i represents the t o t a l energy of an electron belonging to the atomic o r b i t a l <^ centered on atom a. The term V„,J> given by v«cfc = zfe *o.l (12) which represents the interaction of any valence electron on atom a with the core of atom b. For two atomic o r b i t a l t on atoms a and b respectively the off-diagonal matrix element H^j becomes 5 Htj = Ay = / U s+k (is) where / - ^ t j i s c a l l e d the resonnance i n t e g r a l . The bonding parameter / ^ l i s given by Ai= 1 /2K( + ) ( 1 4 ) where K = 0 . 7 5 i f either a or b i s a second row element ./̂ L and /^y are found by b e s t — f i t t i n g to f u l l SCF calculations for small molecules. To summerize, diagonal elements of the Hartree—Fock matrix take the form *u = u t - : < p „ * - 1/2 p - ) K~ + X, [-Q^A + ( z b - >] ( 1 5 ) The net charge, , is given by Q b = zf> - pt,b ( 1 6 ) where the gross electronic population on atom b, Pj, b, is given by and the density matrix, pp|,r i^^given by p f > = 2 S ( 1 8 ) The quantity -Q represents the effect of the potential due to the t o t a l charge on atom b. The penetration integral, zb X^t - represents the difference between the potentials due to the valence electrons on the core of the neutral atom b. The off-diagonal elements take the form F c j - A ^ S p ^ - 1 / 2 p f>^ (19) A l l calculations were carried out with the program CNINDO (Dobash, 1974) with the parametrization of Pople and Segal ( 1 9 6 5 ) for the f i r s t row elements and that of Santry and Segal 6 (1967) for the second row elements. I l l . MODELS OF THREE-REPEAT CHAINS 1. Description of chain construction A computer program was written that calculates any four—membered, three—repeat chain st a r t i n g with the coordinates of three tetrahedra expressed as a function of the Si—0 bond length, d(Si—0). In the o r i g i n a l configuration, both /Si—O-Si equal 180° and the cluster has the point symmetry 2/m. Fig 1 shows an atomic cluster before and after rotation including reference and rotation axes. The f i r s t tetrahedron remains fixed at a l l times. The second tetrahedron is free to rotate about the y—axis by an angle (f 2. A counterclockwise rotation by an angle £ 2 brings the four non—bridging oxygen atoms on the f i r s t and second tetrahedra into a double—eelipsed pair, a clockwise rotation brings them into a single—eclipsed pair. Either a clockwise or a counterclockwise rotation about the -Si—0 bonds by angle <̂> 2 and © 2 respectively create a staggered pair. The th i r d tetrahedron i s also rotated by an angle £ 3 about y'—axis which i s the previously rotated y—axis and by angles ^ 3 and © 3 about i t s own Si-0 bonds. The fourth tetrahedron i s added by translating the f i r s t tetrahedron along a vector connecting the non-bridging oxygen atoms on the. f i r s t and t h i r d tetrahedra. 2. Description of the fixed pairs  8 In order to simplify the i d e n t i f i c a t i o n of the types of three—repeat chains each i s looked upon as composed of three pairs of tetrahera. Fig 2 shows three standard orientations between the members of a p a i r . It i s double—eclipsed i f two oxygen atoms on each tetrahedron in an eclipsed conformation move closer to each other with narrowing /Si—O-Si or single—eclipsed i f only one oxygen atom on each tetrahedron moves s i m i l a r l y . The pair i s staggered i f one tetrahedron is rotated so that one oxygen atom resides on the plane bisecting one of the /0—Si—0 on the other tetrahedron and these three oxygen atoms move toward each other with narrowing /Si-O—Si. No va r i a t i o n of the above types are considered for the f i r s t and second pairs of tetrahedra in a chain since these can be fixed by keeping the rotation angles ? 2, 4> 21 <J> 3 and & 3 constant. Table I shows the choice of unique settings for the rotation angles >̂ 2, O 2> <̂> 3 and 0 3 that y i e l d s double or s i n g l e — e c l i s e d and staggered pa i r s . The t h i r d pair of tetrahedra in a chain depends on the translation of the f i r s t tetrahedron so intermediate types are possible. IV. CLASSIFICATION OF CHAINS 1. D e f i n i t i o n of symbols Each of the pairs of tetrahedra described in the previous chapter is i d e n t i f i e d by a l e t t e r ; D for double-eclipsed, S for single-eclipsed and St for staggered. Furthermore the DOUBLE ECLIPSED PAIR SINGLE ECLIPSED PAIR STAGGERED PAIR r e s p e c t i v e l y 10 Table I. Unique settings for the rotation angles 2 1 0 2, 3 and O 3 that y i e l d double or single-eclipsed and staggered pa i r s . F i r s t pair Second pair ^ 2 0 2 ^ 3 © 3 Double—eclipsed pairs 0° 0° 0° 0° 0° 120° 120° 0° Single—eelipsed pairs 60° 60° 60° 60° 60° 180° 180° 60° Staggered pairs 0° 60° 0° 60° 0° 180° 60° 0° 180° 0° 60° 0° 11 relationship of the bridging oxygen atoms from which the chain w i l l be extended, i . e . , a l l oxygen atoms other than 0, on Figure 2, with respect to the Si—0—Si plane of the pair i s described by a number. On Figure 2 0 b n i s always oxygen atom 0,. These symbols are summerized in Table I I . These symbols can be grouped into four categories, as follows. The symbols D,, S, and St, represent the case where both bridging oxygen atoms are in the Si—0—Si plane of a given pair . The symbols D2, S 2, S t 2 and S t 5 refer to the case where one of the bridging oxygen atom is not in the Si—0—Si plane of a given pair. The last two categories include the pairs in which both bridging oxygen atoms are off the Si—0—Si plane of a given p a i r . The symbols D 3, S 3 and S t 3 designate the case where the bridging oxygen atoms are both on the same side of the Si—O—Si plane while the symbols Da, S„ and St„ refer to the case where the bridging oxygen atoms are on either side of t h i s plane. 2. Representative chains The work of Meagher (1980) and Newton and Gibbs (1980) indicates that nearest neighbour interactions are most important in determining the comformation of bridging s i l i c a t e tetrahedra. Accordingly, to decrease the number of chains to be considered only those chains with adjacent tetrahedra having /Si—0—Si and /(0—0—0 ) ^ which f a l l into the region of minimum energy as defined by these authors w i l l be computed. The following r e s t r i c t i o n s were imposed on the chains. The /Si—O—Si are 12 Table I I . Summary of symbols used in describing three-repeat single chains. These represent a l l the possible comformations of the double or single-eclipsed and staggered pairs of tetrahedra in a chain. Symbols Choice of 0 i t r — br Double—eclipsed pairs D, 0 2 and 0 7 D 2 (a) 0 7 and either 0 3 or 0„ D 2 (b) 0 2 and either 0 6 or 0 7 D 3 (a) 0„ and 0 5 D 3 (b) 0 3 and 0 6 D 4 (a) 0 3 and 0 5 D, (b) 0« and 0 6 Single—eclipsed pairs S, 0 2 and 0 5 S 2 (a) 0 5 and either 0 3 or 0„ 5 2 (b) 0 2 and either 0 6 or 0 7 5 3 (a) 0 3 and 0 6 S 3 (b) On and 0 7 S a (a) 0 3 and 0 7 S„ (b) 0« and 0 6 Staggered pairs St, 0„ and O 5 S t 2 0 5 and either 0 2 or 0 3 S t 3 (a) 0 2 and 0 7 S t 3 (b) 0 3 and 0 6 St« (a) 0-2 and 0 6 St„ (b) 0 3 and 0 7 S t 5 0« and either 0 6 or 0 7 13 between 110° and 180° with an average of 140°. The /(0-0-0). vary between 90° and 180°. The shortest d(0-0)^i, r i s 2.63 A i . e . , the d(0—0) in a regular tetrahedron where the Si—0 bonds are equal to the sum of ionic r a d i i (Shannon and Prewitt, 1969). A l i s t of three—repeat chains composed of two fixed pairs as described above is given on Table I I I . Table IV shows a l i s t of /Si-O-Si and /(0-0-0) b r, for wollastonite (Buerger and Prewitt, 1961) and bustamite (Peacor and Buerger, 1962). The series p e c t o l i t e ( C a 2 N a H S i 3 0 9 ) - serandite(Mn 2NaHSi 30 9) (Prewitt, 1967; Takeuchi, Kudoh and Yamanska, 1976) and s c h i z o l i t e , a manganoan p e c t o l i t e , (Ohashi and Finger, 1978) are not included because of the presence of OH" group in the chain. The presence of a water molecule forming a hydrogen bridge with oxygen atoms bonded to the s i l i c o n atom precludes taking sorensonite, Na„SnBe 2(Si 30 9).2H 20, (Metcalf—Johansen and Hazell, 1976) into account as well. A l l of these compounds have a very narrow range of /Si—O—Si and /(0-0-0) b . The /Si-O-Si are between 135° and 160° with an average between 142° and 145°. The /(0-0-0 ) b r, are between 121° and 156° with an average between 140° and 149°. V^ DISCUSSION OF ENERGY CALCULATIONS 1 . Single chain selection To select the possible chains the computer program steps through (* values for predetermined values of (|> and 0 . The 14 Table I I I . L i s t of three-repeat chains composed of two fixed pairs of tetrahedra. The pair quoted in parentheses represents the closest approximation to the standard orientation of the th i r d and fourth tetrahedra. The /Si-O-Si vary between 120° and 180° with an average of 140°. The 7(0-0-0). vary between 90° and 180°. ~ b r / S i - O - S i /(O-O-O) b r DT-Dz-CSt,) 145.00 150.00 122.53 D 2 - D 2 - ( D 2 ) 140.00 140.00 138.82 D 2 - D „ - ( D 2 ) 145.00 145.00 131.57 D , - S 2 - ( S t , ) 150.00 145.00 123.08 D 2 - S , - ( S 2 )' 120.00 179.88 121.16 D 2 - S 2 - ( S t 3 ) 130.00 140.00 152.32 D 2 - S 3 - ( D 2 ) 145.00 140.00 133.01 D 2 - S „ - ( D 2 ) 145.00 145.00 130.67 D a - S „ - ( D 2 ) 145.00 145.00 130.96 D , - S t , - ( S t , ) 135.00 130.00 155.53 D , - S t , - ( S 2 ) 130.00 125.00 166.87 Dj-St^-tD,) 135.00 150.00 132.23 D 2 - S t 2 - ( S 2 ) 125.00 145.00 151.47 144.47 147.09 143.78 142.17 142.18 143.56 117.22 144.87 150.27 139.47 123.19 122.62 128.37 109.47 140.92 135.74 119.33 161.33 144.87 119.99 149.78 144.87 176.61 148.27 117.22 176.61 119.44 135.00 159.47 155.53 137.06 164.47 147.32 139.11 150.36 166.83 1 32. 1 1 90.23 136.62 15 Table I I I . (continued) /Si-O-Si D 2 - S t 3 - ( S t 1 ) 145.00 135.00 139.71 D 2-St,-(St 5) 135.00 160.00 124.05 D 2-St 5-(S 2) 150.00 135.00 135.94 D 3-St,-(St,) 135.00 150.00 137.79 D„-St5-(D„) 130.00 130.00 161.00 S 2 - S 2 - ( S t 5 ) 140.00 140.00 140.53 S 2-S„-(D 2) 150.00 150.00 122.67 S 2 - S t 3 - ( S t 3 ) 145.00 150.00 124.85 S 2-St ( (-(D 1 ) 135.00 165.00 119.97 5 2- S t 5 - ( S 2 ) 140.00 140.00 141.06 5 3 - St,-(S 2) 140.00 140.00 141.57 S , - S t 1 - ( S t 5 ) 135.00 140.00 147.45 S , - S t 3 - ( S t , ) 165.00 135.00 119.34 S a-St 4-(D 1) 135.00 165.00 120.14 S„-St 5-(St 5) 135.00 140.00 143.93 /(o-o-o)bf. 144.87 106.28 139.81 141.29 149.74 167.55 147.09 148.50 132.66 135.00 91.18 133.12 105.30 149.67 133.87 119.13 119.13 146.45 172.26 127.15 134.16 123.19 113.55 110.72 115.00 167.03 115.56 119.13 146.88 120.00 119.19 145.55 119.41 135.00 179.14 135.53 159.30 106.30 120.33 174.75 167.03 161.73 174.75 146.88 144.04 16 Table I I I . (continued) /Si-O-Si / ( 0 - 0 - 0 ) St , - s t 155.00 St !-St 2- 130.00 St ,-St 3-135.00 St ,-St«- 135.00 St ,-St s- 135.00 St 2 - S t 3 -145.00 St 2-St,- 145.00 St 2 - S t 5 -120.00 St 3-St«-1 20.00 St 3 - S t 5 -150.00 -(D2) 130.00 -(D2) 165.00 •(D2) 140.00 •(D,) 150.00 •(D2) 140.00 •(S2) 140.00 •(D2) 125.00 •(DJ 179.88 •(St, ) 179.88 •(St,) 150.00 St,-St«-(St 5) 130.00 170.00 St«-St 5-(D 2) 125.00 145.00 S t 5 - S t 5 - ( D 2 ) 150.00 150.00 134.47 122.92 147.45 137.79 142.06 133. 18 151.37 120.00 120.00 120.72 121.50 151.37 120.00 155.00 130.00 155.00 130.00 107.46 144.61 135.00 108.94 153.93 135.00 154.10 147.82 135.00 146.88 167.23 90.23 108.94 100.97 144.60 132.86 151.76 149.58 120.00 137.51 128.68 120.00 120.00 141.86 113.55 125.16 137.06 171.35 145.34 132.86 144.60 151.73 141.86 141.86 137.51 17 J. Table IV. /Si-O-Si wollastonite (W). and for bustamite (B). and B/ Ca-B1 Mn--B1 Fe--B2 /Si2-07-Si3 7si1-08-Si3 /Si1-09-Si2 1 35 1 35 160 .59° .80° .80° 138.15° 136.19° 155.47° 139. 1 34. 159. 1 7° 95° 91 ° 1 37. 1 34. 1 62. 50° 01 ° 49° * ** AVE/Si-O-Si 1 44 .06° 143.25° 1 44. 68° 1 44. 67° /09-07-08 709-08-07 707-09-08 1 53 1 48 1 22 .33° .87° .74° 156.27° 150.17° 126.75° 1 54. 1 48. 123. 30° 84° 05° 1 55. 1 46. 121 . 15° 37° 94° AVE/(0-0-0) b r 141 .65° 144.40° 1 42. 06° 141. 15° wi Mn--W1 Fe--W1 Para -W /Si1-07-Si3 7si2-08-Si3 /Si1-09-Si2 1 39 1 40 1 49 .24° .18° .14° 1 39. 1 40. 1 50. 37° 08° 54° 139. 1 39. 151 . 18° 88° 1 1 ° 140. 1 40. 149. 24° 42° 33° AVE/Si-O-Si 142 .85° 1 43 . 33° 1 43. 39° 1 44. 33° /O9-07-08 709-08-07 707-09-08 1 55 1 56 1 32 .37° .67° .00° 1 55. 1 56. 131. 02° 37° 41 0 1 54. 1 56. 1 30. 72° 25° 99° 1 56. 1 55. 1 32. 46° 84° 30° AVE/ (0—0—0) b f m 1 48 .01 ° 147. 60° 147. 32° 1 48 . 20° * /Si1-07-Si3 ** /Si2-08-Si3 1 Osashi and Finger (1978) 2 Rapoport and Burnham (1973) 3 Peacor and Prewitt (1963) • Trojer (1968) 18 steps were usually 5° increments. The chains for each set of angular values was then checked to determine that the. /Si—0—Si and /(0—0—0) b r % s a t i s f i e d the previously mentioned angular r e s t r i c t i o n s . Energy calculations were then undertaken for 61 out of aproximatively 182,000 chains generated. Over one half of these chains also have the smallest possible difference between their individual /Si—O—Si and therefore the largest average d ( S i - S i ) . As shown on Figure 3 an i n f i n i t e three—repeat chain can be represented by three segments each one consisting of three symmetry non—equivalent tetrahedra. However the fourth tetrahedron was included to more f u l l y describe a l l the atomic interactions. It i s also necessary to ascertain that these three segments have comparable energies; i . e . The second and t h i r d neighbour interactions are r e l a t i v e l y small. The largest variation in energy between two segments of the same chain shown on Figure 3 is 0.001 %. In a l l cases hydrogen atoms were appended to the non—bridging oxygen atoms at a distance of 0.95 A and with /Si-O-H of 180°. The resulting S i „ 0 1 3 H 1 0 cluster i s neutral. 2. Results of energy calculations It can be shown that for chains with average /Si—O-Si equal to a constant those chains with a l l /Si—O—Si equal to the average have the largest d ( S i — S i ) . The t o t a l energy of chains Figure 3. Three segments of the same chain whose energies are 7256.172, -256.170 and -256.170 A.U respectively. 20 can then be related to the /Si-O-Si through the d ( S i - S i ) . Figure 4 shows a plot of t o t a l energy against the average d(Si—Si) in the c l u s t e r . The t o t a l energy varies between -256.168 and -256.147 A.U. While the average d(Si-Si) ranges from 2.93 to 3.04 A. A weak negative correlation exists between these two as indicated by the regression equation with regression c o e f f i c i e n t 0.63. E = 267 (42) - 0.142 (14) d(Si-Si) R2 = .63 For t h i s population of chains with average /Si—0—Si approximatively equal to 140°, those with a l l three /Si—O—Si close to the average generally have lower energy than those with /Si-O—Si covering a wider angle. Figure 5 shows six plots of t o t a l energy vs average d ( S i — S i ) . The top row includes chains with combinations of double and single—eelipsed p a i r s . Since the spacing between every other bar on the v e r t i c a l scale i s of the same order of magnitude as the discrepancy between calculations on the dif f e r e n t segments of the same chain; no s t a t i s t i c a l l y s i g n i f i c a n t trend can be observed from the diagram for the chains with a double and a single—eelipsed pair or those with two single—eelipsed pairs. A l l diagrams in the f i r s t row contain very few points r e f l e c t i n g geometry constraints on these chains. The chains composed of double and single—eclipsed pairs and those composed of two single—eclipsed pairs have a narrower range of average d(Si—Si) than the chains composed of two double—eelipsed pairs. The second row includes chains composed of combinations of ' 1 1 1 1 1 l i l t 2-83 2.97 3.00 3.04 AVERAGE d(Si-Si) A F i g u r e 4. T o t a l energy (A.U.) a g a i n s t average d ( S i - S i ) (A) , t h o s e c h a i n s w i t h the l a r g e s t d ( S i - S i ) have the l o w e s t energy. [ the s p a c i n g on the h o r i z o n t a l a x i s i s 0.012 A the i n a c c u r a c y r e f l e c t s the r o u n d - o f f e r r o r ] -8M.147 3 4 >. .IM a s s 3 .1*1 o D-D D-S • i i i i i i > i » s-s i i i t i "S i i i i i i i i » •Ml 147 >. .164 O a s ^ .Ml .1H D-St •V s-st aas M T «JOO AVEfUUM d(tt-H) A 1 I » I I I St-St i i i i i u r AVERAOf 4UU-80 A AVERAOK dlH-SU A Figure 5 . Total energy (A.U.) against average d(Si-Si) (A) , for each group of chains. [ the spacing on the horizontal axis i s 0 . 0 1 2 A the inaccuracy r e f l e c t s the round-off error ] 23 one staggered pair with either a single or a double—eclipsed pair or another staggered pair. A l l of these combinations have a larger number of chains. The f i r s t two diagrams show a range of d(Si—Si) between 2.97 and 3.03 A. However in the f i r s t case the energy varies between -256.163 and -256.147 A.U. While in the second case i t varies between -256.168 and -256.147 A.U. Although chains consisting of a staggered pair and either a double or a single—eclipsed pair cover the same range of average d(Si—Si) the l a t t e r group has chains with a lower energy. In both cases the chains with the highest energy has one /Si—O—Si less than 110°. The la s t diagram shows a range of average d(Si—Si) between 2.93 and 3.03 A with energy varying between -256.164 and -256.152 A.U. The two chains with the higest energy are those with two /Si—O—Si equal to 120°. In this case the range of average d(Si—Si) is wider than in the previous examples. Although a combination of single and staggered pairs y i e l d chains with the lowest energy i . e . -256.167 A.U. Any combination including at least a staggered pair of tetrahedra tend to have a lower energy than a chain containing no such pai r . Figure 6 shows the wollastonite chain and the chain generated which i s closest in comformation. Figures 7 and 8 i l l u s t r a t e the chains with the lowest energy in each of the six groups of theoretical chains 3. Packing of chains WOLLASTONITE - D 2 - St 4 F i g u r e 6. W o l l a s t o n i t e (Buerger and P r e w i t t , 1 9 6 1 ) and i t s c l o s e s t a p p r o x i m a t i o n w i t h t o t a l energy -256.158 A.U. D 2 - D 2 - D 2 D 1 -S 2 -St 4 S 2-S 2-St 5 F i g u r e 7. Chain s c o n t a i n i n g a c o m b i n a t i o n of double or s i n g l e - e c l i p s e d p a x r s wath e n e r g i e s -256.164, -256.163 and -256.163 A.U. r e s p e c t i v e l y . D 2 - St3 - St., S 2 - S t 4 - D 2 S t 1 - S t 3 - D 2 F i g u r e 8. Chai n s c o n t a i n i n g a s t a g g e r e d p a i r of t e t r a h e d r a w i t h e i t h e r a double or s i n g l e e c l i p s e d or a n o t h e r s t a g g e r e d p a i r . E n e r g i e s a r e -256.165, -256.167 and -256.164 A.U. r e s p e c t i v e l y . 27 Liebau (1980) defined the stretching factor of a chain as C ^ A M I , I f = 1 c P where I i s the length of the chain, I t i s the length of the tetrahedral edge and p i s the p e r i o d i c i t y . The stretching factor of odd repeat chains is larger than that of even repeat chains. It appears to be related to the electronegativity and the r a d i i of the i n t e r s t i t i a l cations. A regression of t o t a l energy against the stretching factor for the theore t i c a l chains gives a regression c o e f f i c i e n t of 0.01 showing that no cor r e l a t i o n exist i . e . , there i s no tendency for a straighter chain to have a lower energy. Of those low energy chains generated in this study only the S 2—St„ —(D 2) and S 3 —St,—(D 2) chains appear unlikely to lend themselves to close packing. A further study is required to determine i f the remaining chains can be packed such that i n t e r s t i t i a l cations can be coordinated in a c r y s t a l chemically reasonnable manner. VI. CONCLUSION The t o t a l energy of three—repeat chains i s influenced by two factors. F i r s t , chains with the largest d ( S i - S i ) , i . e, those with a l l three /Si—O-Si equal to 140° have the lowest energy. Secondly, chains with at least a staggered pair of tetrahedra also have a lower energy than those with no such pai r . This is 28 in keeping with the. fact that for pairs of tetrahedra with a constant /Si—O—Si the staggered conformation has a lower energy than either the single or double—eclipsed pa i r s . It i s noteworthy that the two lowest energy two—repeat chains are the sodium s i l i c a t e type which is composed of two pairs of staggered tetrahedra and the pyroxene type which i s composed of two pairs of single—eclipsed tetrahedra. Under the geometric r e s t r i c t i o n s of this study there exist three—repeat chains d i f f e r e n t from the one type found in nature and the energy of a number of these chains i s as low or lower than that of the closest approximation to the wollastonite type. In the group of two—repeat chains those of lowest energy happen to pack in such a way as to accommodate i n t e r s t i t i a l cations. In the three—repeat chains there appear to be many low energy chains which cannot pack together such as to provide suitable s i t e s for i n t e r s t i t i a l cations. Further investigation i s necessary to determine i f i t i s possible to optimize both the average d(Si—Si) and the bonding requirements of the i n t e r s t i t i a l cations for chains di f f e r e n t from the wollastonite type. No corre l e t i o n was found between the stretching factor and the energy of three—repeat chains indicating no tendency for straighter chains to have lower energy. 29 REFERENCES Buerger, M.J and C.T. Prewitt, 1961, The c r y s t a l structure of wollastonite and p e c t o l i t e ; Proc N.A.S 47,1884-1888. Dobash, P.A, 1974, Quantum Chemistry Program Exchange No. 141 (available from QCEP, Indiana University, Bloomington, Indiana 47410). Dewar, M.J.S., 1969, The molecular o r b i t a l theory of organic chemistry: McGraw-Hill. Fock, V., 1930, Naherungsmethode zur Lozung des quantenmechanischen Mehrkorperproblems: Z. Physik, 61, 126-146 Hartree, D.R., 1927, The wave mechanics of an atom with a non- coulomb central f i e l d Part I . Theory and methods: Proc. Cambridge P h i l . S o c , 24, 89-110. Liebau, F., 1980, The influence of cations properties on the comformation of s i l i c a t e and phosphate anions: In Structure and bonding in c r y s t a l s II. [ eds O'Keeffe, M. and A. Navrotsky. ] Acadamic Press Inc 197—232. Meagher, E.P., 1980, Streochemistry and energies of single two—repeat s i l i c a t e chains: Am. Mineral. 65, 746-755. Metcalf—Johansen, J. and Hazell, R.G., 1976, The c r y s t a l structure of sorensonite, Na„SnBe 2(Si 30 9)2H 20: Acta Cryst B32 , 2553-2556. Newton, M.D. and G.V. Gibbs, 1980, Ab I n i t i o calculated calculated geometries and charge d i s t r i b u t i o n s for HySiOi, and H 6 S i 2 0 7 compared with experimental values for s i l i c a t e s and siloxanes: Phys. Chem. Minerals 6, 221-246. Ohashi,Y. and Finger, L.W.,1978, The role of octahedral cations in pyroxenoids c r y s t a l chemistry. I. Bustamite, wollastonite, and the p e c t o l i t e — s c h i z o l i t e — s e r a n d i t e series: Am. Mineral. 63, 274-288. Peacor, D.R. and M.J. Buerger, 1962, Determination and refinement of the c r y s t a l structure of bustamite, CaMnSi 20 6: Z. K r i s t . JJ_7, 331-343. Peacor, D.R. and Prewitt, C.T., 1963, Comparison of the c r y s t a l structures of bustamite and wollastonite: 48, 588-596. Pople, J.A, and Beveridge, D.L., 1970, Approximate molecular o r b i t a l theory: McGraw-Hill. 30 D.P. Santry and G.A. Segal, 1965, Approximate self—consistent molecular o r b i t a l theory. I. Invariant procedures: J . Chem. Phys., 4_3, S129-S135. and G.A. Segal, 1965, Approximate s e l f - consistent molecular o r b i t a l theory. I I. Calculations with complete neglect of d i f f e r e n t i a l overlap: J. Chem. Phys. 43, SI 36—SI 51. Prewitt, C.T. and M.J. Buerger, 1963, Comparison of the c r y s t a l structures of wollastonite and p e c t o l i t e : MSA Special Paper J_ , 293-302. 1967, Refinement of the structure of pe c t o l i t e , Ca 2NaHSi 30 9: Z. Kris t 125, 298-316. Roothan, C.C.J., 1951, New developments in molecular o r b i t a l theory: Rev. Mod. Phys. 23, (2), 69-89. Rapoport, P.A. and C.W. Burnham, 1973, Ferrobustamite: The cr y s t a l structures of two Ca, Fe bustamite-type pyroxenoids: Z. K r i s t . 138, 419-438. Santry, D.P. and G.A. Segal, 1967, Approximate s e l f - consistent molecular o r b i t a l theory. IV. Calculations on molecules including the elements sodium through chlorine: J. Chem. Phys. 47_, 158-174. Shannon, R.P. and C.T. Prewitt, 1969, Ef f e c t i v e ionic r a d i i in oxydes and fluori d e s : Acta Cryst. B25, 925—946. Takeuchi, Y.,Y. Kudoh and T. Yamanaka, 1976, Crystal chemistry of the serandite—pectolite series and related minerals: Am. Mineral. 6J_, 229-237. Trojer, F.J., 1968, The c r y s t a l structure of parawollastonite: Z. K r i s t . 127, 291-308.

Cite

Citation Scheme:

    

Usage Statistics

Country Views Downloads
United States 3 0
China 3 4
City Views Downloads
Beijing 3 4
Ashburn 2 0
Mountain View 1 0

{[{ mDataHeader[type] }]} {[{ month[type] }]} {[{ tData[type] }]}
Download Stats

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0052532/manifest

Comment

Related Items