LIGAND HYPERFINE INTERACTIONS
IN OXYHALIDES OF PENTAVALENT
CHROMIUM, MOLYBDENUM AND TUNGSTEN
2336
C10065
60021
LIGAND HYPERFINE INTERACTIONS
IN OXYHALIDES OF PENTAVALENT
CHROMIUM, MOLYBDENUM AND TUNGSTEN
P R O E F S C H R I F T
TER VERKRIJGING VAN DE GRAAD VAN DOCTOR IN DE TECHNISCHE WETENSCHAPPEN AAN DE TECH-NISCHE HOGESCHOOL DELFT, OP GEZAG VAN DE RECTOR MAGNIFICUS IR. H. R. VAN NAUTA LEMKE, HOOGLERAAR IN DE AFDELING DER ELEKTRO-TECHNIEK, VOOR EEN COMMISSIE UIT DE SENAAT
TE VERDEDIGEN OP WOENSDAG 9 DECEMBER 1970 TE 16.00 UUR
DOOR
JOHANNES TRUDO CORNELIS van KEMENADE scheikundig ingenieur geboren te Eindhoven
/ ƒ ^- 4'i3<^
/o o\ Ac- c;A 1970Aan mijn ouders
C O N T E N T S
Chapter I INTRODUCTION 7
Chapter II THEORY 17
2.1 Spin Hamiltonian 17
2.2 Calculation of spectra from the spin
Hamiltonian 25
2.3 Comparison of powder spectra and single
crystal spectra 31
Chapter III EXPERIMENTAL 32
3.1 Choice and structure of host lattices 32
3.2 Preparation of the single crystals 36
3.3 Morphology of the crystals 38
3.4 Choice of rotation axes and rotation
techniques 't2
3.5 Comparison between the EPR spectra of
frozen solutions and of powdered crystals '*7
3.6 Accuracy of orientation and its effect on
the spectra 'tS
3.7 Signs of the HFS parameters A8
3.8 Simulation of spectra 50
Chapter IV EPR SPECTRA OF THE OXYFLUORIDES 51
4.1 K2SnFg.H20 host lattice 51
4.2 (NH4)2GeF6 host lattice 57
4.3 Comparison of the results 67
Chapter V EPR SPECTRA OF THE OXYCHLORIDES AND OXYBROMIDES 69
5.1 The M0OCI5 ion 69
5.2 The MoOBrs ion 76
5.3 The WOCI5 ion 80
5.4 The WOBr" ion 82
5.5 Discussion of the results 83
6
Chapter VI INTERPRETATION OF EPR DATA IN TERMS OF
BONDING COEFFICIENTS
6.1 Internal check on the consistency of the
data obtained
6.2 Comparison with data of other authors
6.3 Calculation of bonding coefficients from
9// . gj_.
^11 ,
and Aj_
6.4 Calculation of orbital coefficients from
LHFS parameters
Chapter VII EXTENDED HÜCKEL CALCULATIONS
CHapter VIII FINAL CONCLUSIONS AND REMARKS
Appendix CALCULATION OF MATRIX ELEMENTS OF DIPOLAR
HYPERFINE INTERACTION
Samenvatting
CHAPTER I - INTRODUCTION
The nature of the bonding in molecules, ions or radicals has been studied since the early days of chemistry. A nowadays generally accep-ted description of it is given by the Molecular Orbital theory formula-ted about kO years ago. In this description the mu1ti-electron wave function of the molecule is composed of one electron wave functions il).. The i|). are expressed as a L^inear Combination of Atomic O^rbitals
(LCAO-MO)
é . = Ec .dl. ^1 j r I
The orbital coefficients c. of the atomic orbitals 6. can be calculated
I I
using the variation principle. In small molecules from the first row of the Periodic System the necessary integrals can be evaluated by using high speed computers and satisfactory results are obtained. The calcu-lation of all necessary integrals in molecules containing a number of atoms is very tedious, so approximations, often of an empirical nature, have to be used to evaluate the greater part of required integrals. To check the feasibility of the approximations made in such calculations the calculated data can be compared with experiment. The following pos-sibilities are available to make this check.
a) The energy levels can be related to the optical spectrum.
b) The variation of energy with internuclear distance can be related to the IR and Raman spectrum.
c) The charge distribution can be related to chemical shifts in the NMR spectrum.
d) The orbital coefficients can be related to data from the electron paramagnetic resonance spectrum.
In this thesis the last technique will be used to derive the or-bital coefficients from experimental data, which will be compared with those obtained from theoretical calculations.
Electron Paramagnetic Resonance (EPR) is, as its name suggests, restricted to molecules or ions which contain one or more unpaired electrons.
8
Two interactions are important in this technique: a) Zeeman effect.
This effect is the interaction between the magnetic moment of the unpaired electron and the external magnetic field. This term is des-cribed by the g tensor which reflects the symmetry of the complex. The deviation from free-electron behaviour is governed by the spin-orbit coupling. The magnitude of the g tensor components depends on the or-bital coefficients of molecular oror-bitals of the ground state and a num-ber of excited states.
b) Hyperfine Structure (HFS).
This is the magnetic interaction between the unpaired electron and the nuclear spin of one of the atoms in the complex. It is a dipole-dipole interaction and so is proportional to 1/R^, where R is the dis-tance between the electron and the nucleus involved. Mostly a distinc-tion is made between the nuclear spin of the central atom and the nuclear spin of the ligand atoms.
1. Central atom Hyperfine Structure (CHFS).
This term gives the interaction with the nuclear spin of the central atom. The magnitude of the A tensor describing this effect is mainly governed by the coefficients of the atomic orbitals of the central atom in the ground state molecular orbital of the unpaired electron.
2. Ligand Hyperfine Structure (LHFS).
This term gives the interaction with the nuclear spin of ligand atoms. The magnitude of the a tensor describing this effect is mainly govern-ed by the coefficients of the atomic orbitals of the ligand in the ground state molecular orbital of the unpaired electron.
So in principle this technique can provide us with rather detail-ed knowldetail-edge about a number of orbital coefficients.
In organic chemistry orbital coefficients are generally derived from the proton hyperfine structure in the EPR spectra of radicals pre-pared by adding or subtracting an electron from the stable molecule. The agreement between the coefficients obtained from EPR spectra and those derived by theoretical calculations is quite good, justifying to
a certain extent the use of the simple HCi'ckel treatment for the des-cription of the chemical bond in these compounds.
In inorganic chemistry most EPR work has been done on compounds of transition metal ions, where one or more unpaired electrons are present in many of the frequently occurring valency states.
The first class of compounds extensively studied with the aim to describe the chemical bond between transition metal ion and ligands consists of the octahedral hexahalides of metals of the first transi-tion series. From the EPR data the fractransi-tions of unpaired spin density f , f , and f in the s, a bonding p and TT bonding p orbitals could be
7 k~ 4 4
-deduced. Typical examples are the 3d' ions CoFg , CoBre and CoJg in KMgF3, CdBr2 and CdJ2 studied by Windsor, Griffiths and Owen (1) and the 3d^ ion MnFg in ZnF2 studied by Clogston et at (2).
Another group of compounds which has received much interest in the last decades as to the elucidation of the chemical bond by means of EPR consists of complexes of the type MOX5 in which M = Cr, Mo, or W and X = F, CI, or Br. These complexes were first prepared (3) at the end of the 19th century or in the beginning of this century. The struc-ture of these ions is octahedral-1ike but with the oxygen atom at a somewhat shorter distance to the central atom M than the X ligands. In fig. 1.1 this structure is given together with the axes used. The struc ture of the blue V 0 ( H 2 0 ) 5 S 0 L , belonging to this type was first
deter-z-ox»
mined by Sgarlata et at {h) . Later the structure of Cs2CrOCl5, CS2M0OCI5, and CS2WOCI5 also gave this configuration of the MOX5 group with a point group of C ( 5 ) . All complexes are nd^ systems and so contain 1 u n -paired electron.
An excellent review of earlier experimental studies of this type of ions has been given by Mitchell ( 6 ) .
The Molecular Orbital energy level diagram of this type of ions has been calculated by Gray and Hare (7) and is given in fig. 1.2. In this calculation TT bonding was neglected, but this does not very much
r-1 / 1 1 / / / / , ' /I '1 j
-S]
^1 °1 —\ %\
/I'^f \\^
\\\ \ ,\* \s(0)vnr:.-F i g . 1.2 M o l e c u l a r O r b i t a l energy l e v e l diagram o f M0OCI5 as c a l c u l a t e d by Gray and Hare ( 7 ) •
a f f e c t t h e o r d e n i n g o f t h e e n e r g y l e v e l s . The u n p a i r e d e l e c t r o n i s i n an a n t i b o n d i n g m o l e c u l a r o r b i t a l o f b2 symmetry. W i t h TT b o n d i n g i n c l u -ded t h i s o r b i t a l i s composed o f t h e t r a n s i t i o n m e t a l d o r b i t a l and
xy
It bonding p orbitals of the k equatorial ligands. A pictorial drawing
F i g . 1.3 P i c t o r i a l drawing o f the b2 o r b i t a l .
O r b i t a l c o e f f i c i e n t s of t h i s o r b i t a l w i l l be derived from the EPR data. The o r b i t a l c o e f f i c i e n t s o f the empty a n t i - b o n d i n g o r b i t a l s formed from the metal d o 9, d , and d o r b i t a l s can also be c a l c u
-x'^-y^ x z ' yz
l a t e d . A l l bonding o r b i t a l s are f u l l y occupied and are not d i r e c t l y involved in EPR r e s u l t s . Of course, the chemical bond is more charac-t e r i z e d by charac-the bonding charac-than by charac-the a n charac-t i - b o n d i n g o r b i charac-t a l s . F o r charac-t u n a charac-t e l y , there is a close r e l a t i o n between c o e f f i c i e n t s of the a n t i b o n d i n g o r -b i t a l s and those o f the corresponding -bonding o r -b i t a l s . This may -be i l l u s t r a t e d by a simple example.
Consider a molecule in which j u s t two atomic o r b i t a l s <(> j and 412 combine t o molecular o r b i t a l s ii.. The energy level diagram is given ir f i g . l.^t. The two r e s u l t i n g molecular o r b i t a l s are of the f o r m :
F i g . 1 . ^ Energy l e v e l diagram o f a molecule in which o n l y 2 atomic o r b i t a l s combine.
i|j = 3(^2 ~ bcfii
<i) = C(j)i + d(})2
(anti-bonding o r b i t a l ) (bonding o r b i t a l )
12
If just one of these orbital coefficients a, b, c, or d is known the others can be calculated from the orthonorma 1 i ty of I|J and ip .
a2 - 2ab.S + b2 - 1 c2 + 2cd.S + d2 = 1
ad - be + (ac - bd) S = 0 in which S is the overlap inte-gral < (1)1 I 412 >.
This thesis will be dedicated to this type of MOX5 compounds. The central ions Cr(V), M o ( V ) , and W(V) will be used in a number of combi-nations with F, C I , or Br as ligands. The approach presented in this thesis can be divided in three parts:
1. Derivation of orbital coefficients from experimentally deter-mined g and A tensor.
The experimental values given by a number of authors for g and A ten-sor in these ions are in good agreement with each other. Some of these authors have used these parameters to calculate bonding coefficients. This rather optimistic approach will be analyzed critically now. It turns out that such a calculation is rather complicated and contains a number of parameters for which independent estimates have to be availa-ble. The approximations used in the derivation of formulas relating g and A tensor to bonding coefficients will be checked carefully and the
influence of variations in the parameters used on the calculated bon-ding coefficients will be evaluated.
2. Experimental determination of LHFS parameters.
Thus far there is little agreement about the magnitude of the LHFS pa-rameters. Most studies used the technique of quickly freezing a solution of the ions in the corresponding concentrated hydrohalic acid. From such a spectrum which is composed of contributions of all possible orientations LHFS data can be estimated. As is evident from the diffe-rences between the data given by various authors the results depend a great deal on the interpretation of the spectrum.
To solve many of these problems it was decided to prepare single crystals of suitable diamagnetic host lattices into which the ions could be incorporated. This would enable us to determine all LFHS parameters unamb iguously.
Garif'yanov and co-workers (8) were the first who discovered the existence of LHFS in these ions. In a number of publications they gave their results on CrOFs, M0OF5, and WOF5.
Kon and Sharpless (9) determined aj_ "^ from the splittings in the frozen glass spectrum of MoOBrs ^nd WOBrs.
Dowsing et at (10) also investigated the MoOBrs '°n. They ignored
the non-equivalence of x and y components of the LHFS tensor and con-cluded a| = a?.
Verbeek in his thesis (11) and publications (12) gave the EPR spectra of CrOFs and M0OF5 and determined from them four LHFS parameters a , aj_, aj_, and aj_ . These data contain inconsistencies which show up on calculating aj_^ from a, and a_i_, and the isotropic <a> from aj_, aj_, and a .
z
3. Interpretation of LHFS data in terms of bonding coefficients. To investigate the various proposed interpretations of the LHFS data
it is our intention to calculate all terms which can contribute to the
LHFS data exactly without making a-priori assumptions of their
magni-tude. These terms are:
a) The contribution of the d orbital. xy
b) The contribution of the IT bonding p orbitals of the ligands. c) The cross term of a and b.
d) The second order effects caused by spin-orbit coupling.
Thus far only incomplete treatments are available. Kon and Sharpless (9) gave an interpretation entirely based on the TT bonding ligand p orbi-tals. Verbeek (11) based his interpretation on the contribution of the d orbital to the LHFS terms.
xy
While the investigations described in this thesis were in pro-gress a paper by Manoharan and Rogers (13) was published in which they
A Since for the field in the xy-plane only two Independent LHFS para-meters are needed and all authors have different conventions about the assignment of signs or the choice of a and a , in table 1.1 all
3 " X y'
values are given without a sign while the smallest splitting is deno-ted by aj_ and the other by a^. All other symbols have their usual mea n i ng.
u
gave the LHFS parameters of M0OF5 and M0OCI5 as determined from EPR
spectra of these ions incorporated into single crystals of diamagnetic
host lattices. Their interpretation of the results was based on the
contribution o f the TT bonding ligand p orbitals and an extra term from
the
a
bonding ligand p orbitals mixed in the ground state by
configu-ration interaction. In table 1.1 all previous data on the LHFS in these
ions a r e presented.
Table 1.1
LHFS parameters from literature
1 1,. 2
I on
ajj'
aj_
CrOFs
CrOFs
CrOF"
M0OF5
M0OF5
M0OF5
22
2k25
30
27
22.5
ko
43
^0
55
60.1
59.6
S
-23
-23
-<a>
6
-6.A
11
-12.2
ref.
( 8)
(11)
(13)
(18)
(11)
(13)
M0OCI5 - 6.0 - - (13)
MoOBrs < 6 39.5 < 6 - (9)
MoOBrs 40 40 < 3 - (10)
WOF5 42 64 - - (18)
WOBrs < 6 40 < 6 - ( 9 )
* All hyperfine parameters in Oersted.
To have an experimental approach in which many factors could be
compared we tried to prepare all ions of Cr, Mo, or W with the ligands
F, Cl, or Br. These ligand nuclei all possess a nuclear spin differing from zero as can be seen from table 1.2 where all nuclear properties of the atoms used are given. It was possible to prepare and incorporate into a diamagnetic host lattice the following ions: CrOFs, MoOFs, MoOCls, MoOBrs, WOF5, and WOBrs.
Table 1.2
Some properties of nuclei*
Atom Isotope Abundance I g g /g n ni n2
F
Cl
Br
Cr
Mo
W
19
35
37
79
81
53
95
97
183
100.0 1/2 5.255
75.524.5
50.5
49.5
3/2
3/2
3/2
3/2
0.5473
0.4555
1.3995
1.5083
9.55 3/2 0.3157
15.70 5/2 O.39I6
9.45 5/2 0.3794
14.4 1/2 0.230
1.172
0.928
.032
ARatio of hyperfine component to unsplit line = >„. . \ 1i^n-A^
Cr = 0.0264 Mo = O.O56O W = 0.0841 * From ref. (27a)
A theoretical introduction to the methods of investigation to be used is given in chapter II. In this chapter the disadvantages of using frozen glass spectra are discussed and the necessity of using diamagnetic host lattices is proved. The experimental techniques used
in growing, handling and orienting single crystals are given in chapter III.
16
In chapter IV the EPR spectra of the oxyfluorides are presented followed in chapter V by the EPR spectra of the oxychlorides and oxy-bromides. The theoretical expressions outlined in chapter II which relate the parameters of the spin Hamiltonian to bonding coefficients, are used in chapter VI to derive a qualitative scheme of bonding in these complexes. In this chapter a comparison is made between the
ear-lier published interpretations and the method presented in this the-sis. Slightly out of the scope of the experimental approach of this thesis but essential for an evaluation of the results in a theoreti-cal context is the extended Huckel treatment of the complexes studied. These calculations are given in chapter VII. In chapter VIII a survey and evaluation is given of the results of this thesis.
CHAPTER II - THEORY
2.1 Spin Hamiltonian
The spin Hamiltonian is the basic frame of reference of all expe-rimental EPR work. Relations between parameters of the spin Hamiltonian and bonding coefficients can be derived using the theory given by Abragam and Pryce (14). A recent and consistent application of this
theory to complexes of the type MOX5 has been given by DeArmond et at
(15). They have calculated expressions for g,,and gj_, representing the Zeeman interaction, and for A,, and A_|_, representing the interaction be-tween the unpaired electron and the nuclear spin of the central atom. So far nobody has given an accurate derivation of the LHFS parameters, re-presenting the interaction between the unpaired electron and the nuclear spin of the ligand atoms. In this chapter LHFS parameters will be rela-ted to bonding coefficients applying the same principles.
For a better understanding of the approximations and limitations of this derivation the principal steps in the calculation of the Zeeman and CHFS terms are given below. Then the extension to LHFS terms is considered.
The MOX5 ions exhibit C symmetry and as a consequence of this the eigenfunctions of the Hamiltonian are basis functions of irreducible representations of this group.
The Hamiltonian is given by:
Z ,
Ü = -L Y. - \ L. - -^— + Y. - ! — (1)
^ I r . . . r . .
1 y ly K j ij
in which i runs over the electrons and p over the nuclei of the system. As the complexes to be studied contain one unpaired d electron in addi-tion to closed electron shells, the symmetry of the total wave funcaddi-tion is identical to that of the single electron wave function of the un-paired electron. It is possible to describe this wave function as a
linear combination of atomic orbitals. A restriction will be made to the
valence orbitals of the ion viz. nd, (n+l)s, (n+l)p of the transition
18
representations of the symmetry group C can be constructed using the transformation properties of these atomic orbitals. A classification of all orbitals or orbital combinations into the representation they span
i s g iven in table 2.1.
Table 2.1
Classification of Atomic Orbitals
into the Irreducible Representations of the Group C.
Symmetry Transition metal orbitals Ligand orbitals
Ai s s^ P P5 z z d^2 S" pO z sl+s^+s^+s"* P^+P^+Pz+Pz P''+D2-D^-D'* '^x *^y *^x ^y A , pl-p2-p3+p4 Z Ky F^ Ky K^ d,2_ 2 sl- s2 + s3-s'* x'-y^ P^ -p2+n3-p'* '^Z *^Z ^T. ^Z pi _p2_p3+p't '^x '^y '^x '^y d pl+n2-p3_p't xy '^y '^x '^y '^x (d .d ) (pO, pO ) x z ' yz '^x' ^y (P , P ) ( P ^ p5) (Sl-S3),(s2-Si,) (pl-p3),(p2-p^) (pl+p3),(p2+p^) (P;+P5).(P^PX)
In an LCAO description of this complex the resulting molecular
orbitals are filled with electrons. Gray and Hare (7) calculated the
Molecular Orbital energy level diagram of the representative M0OCL5 ion
which was given in fig. 1.2. In this energy level diagram the unpaired
electron is placed in an orbital of bj symmetry.
In the derivation of spin Hamiltonian parameters perturbation
theory is applied with the perturbation Hamiltonian of the unpaired
electron
5(r)i.s
+ 6^ (ï+g^s).H
(2a)
(2b)
g [(?-§-.i ^3(f..s-).(r.i)
^ 8 T ^ ( ^+ 9 e 9 n ^ ^ n
^^"-^
^
^'l
^
T^'r^O^
'
'^^^^^n
' "^^
(Zc)
In this perturbation treatment spin operators are treated as
non-commu-ting constants and only integrals involving the other operators are
evaluated over the radial and angular parts of the orbitals to obtain
an energy expression which only contains spin operators and the
exter-nal field H. The order of magnitude of these terms is:
-1
(a) (b) ( c ) 100 - 2000 cm 0 . 3 - 1.2 cm 0 - 0 . 0 2 cmSo these terms are small compared with the separations between the
dif-ferent energy levels which are 10,000 cm or more. In the perturbation
treatment a basis is chosen consisting of the ground state B2 and the
excited Bj and E states arising from the B2 state by promoting the
un-paired electron into bj and e Molecular Orbitals. For these states the
Hamiltonian (1) is diagonal.
With the use of table 2.1 the molecular orbitals needed in this
treatment can be constructed. They are:
|b2> =
|bi> =
d >
-xy
'xy
h I *x2-y2'
e > =
e d > -
E '(3)
yz
20
in which the <!>' s are the proper combinations of ligand orbitals.
In the construction of the $'s a problem arises since it is evident
from table 2.1 that the * 9 9, $ , and $ are not unambiguous.
j^/_yz» xz yz ^
The general expression for them is:
*x2.y2 = Ci(sl-s2+s3-s'*) + C2(p^-p2-p3+pJ;) = i (spl-SpJ+Sp3-spj)
*xz = d l ( P ° ) + d 2 ( p 5 ) + d3(p^-p|)
(k)
% Z = ''l^P?) ""
'^2(P5J+ d3(p2-p^)
Until the present time all authors have chosen dj = 1, d2 = ds = 0 for
the $ but no justification has been given for it. The effect of this
choice will be discussed in chapter VIII.
The ground state is denoted by |0> and the excited states by |n>.
The first order energy is simple <0|5|0>. In the calculation of these
matrix elements the following assumptions are made:
1. Al1 integrals involving
E,{r)
between transition metal functions and
ligand functions are neglected.
2. All integrals involving r which contain ligand functions are
ne-glected .
In chapter VI the effect of these assumptions on the final results will
be discussed.
Since <0|T|0> = 0 this yields:
/1\ - .
W^
'
= g„6„H.S +62P {+ 4/71 S^ - 2/7(1 S^ + I S„) + Kl.S} (5)
1 - 3 I
in which P = g g 6 6 <0 r 0>.
^e^n e n ' '
The isotropic term in
H'
gives In this scheme no contribution to
the first order energy since the orbitals involved have zero density
at the nucleus. In experiments an isotropic term is found. It is
ex-plained by considering the polarization of the inner s electrons by the
unpaired electron in such a way that a net spin density at the central
atom nucleus is produced. Its calculation falls beyond the scope of the
present work. As usual the magnitude of the effect is described by <P,
In second order only combinations of l.s and other terms:
<0|a|n> <n|b|0>/(E -E ) and <0|a|n> <n|c|0>/(E -E ) are considered II II n o n o since the f.s term is much greater than the other terms, and the term <0|a|n>2/(E -E ) gives no terms in the spin Hamiltonian. This yields:
"^'^ = ^ j e e " i S j ' (^'ij - 3^j)Silj (6) i n w h i c h A . . = -2 I < O k ( r ) f . | n > < n | f . | 0 > / ( E -E ) IJ ^^Q l<i ^ ,1 1 j l V n o^ A ' = - 2 I < 0 | 5 ( r ) ? . | n > < n | ? . / r 3 | 0 > / ( E - E - ) (7) IJ n?«0 ' ' J ' n o ' u . j = - i e . . „ Z < 0 k ( r ) ï |n> <n I r, r . / r ^ | 0 > / ( E - E ^ ) IJ I km pijiQ m' k J ' ^ n o '
The suffixes i,j, etc. refer to the Cartesian coordinates x, y, z. E.. = ± 1 as ikm represents an even or an odd permutation of xyz, and is zero if any pair of i, k or m are the same.
Combining (5) and (6) and evaluating the various matrix elements a spin Hamiltonian is obtained
H . = g,,6 H S + g,6 (H S + H S ) +A , , I S + A,(S I + S I ) spin ^// e z z ^-L^e x x y y' // z z -1- x x y y' in whi ch = 2.0023 - 2(2X6261 - XiB26i).
V/
(262B1 - 261B2S, - 262Bis. - B1S2)/(E. - E. ) 02 D]^ Dl D 2 g , = 2.0023 - 2X^B2e(B2e - B2e'S - E B ^ S , ) / ( E - E, ) -^ m ^ ^ e D 2 e b 2 A / / = + P { 6 2 ( < + ' * / 7 ) + 2.0023 - g / / + 3 / 7 ( 2 . 0 0 2 3 - g j (8)+ 6 / 7 X ^ B 2 E ' S ^ + eB2S^^WE^ - Ej^^) + 2 (X^62Bi - Xi&{$2) .
(2B2B1S^^^ + 2BiB2Sj^^ + 6 ; B 2 ) / ( E ^ - £^^ ) }
+ P { B 2 ( < - 2 / 7 ) + 11/14 ( 2 . 0 0 2 3 - g j . ) + 11/7X B2e ( B 2 E S ^ + eB2S, ) / ( E ^ - E, ) }
22
in which
X is the spin-orbit coupling constant of the transition metal, m
Xj is the spin-orbit coupling constant of the ligand atom, S, , S, , and S are group overlap integrals.
bj 02 e
These expressions are those obtained by DeArmond et at (15). If in
these equations Bi> B2> and E are set equal to 1 and 6i, B2> and E ' to zero, these equations reduce to the simple crystal field expressions
given by Gray et at (l6).
Kon and Sharpless (17) have extended the basis functions for the perturbation treatment by also considering the state arising from a pro-motion of an electron from the filled bj orbital to the b2 orbital. This
is the lowest "charge transfer" state in the optical spectrum. Taking this state into consideration adds an extra term to g ., and A,,.
9// = g// + (2B2BiX^ + B2BiAi) (2B26I + i-i^z)/t^Z^b _^ ^
V / = V ^ ' ' ( 8 B i X ^ B2')/AE,b_^^,^
In chapter VI these formulas are used to calculate the bonding coeffi-cients from the observed spin Hamiltonian parameters.
Thus far the extension of this approach to the problem of LHFS parameters has not been given in a similar consistent way. The inter-action between the unpaired electron and a ligand nuclear spin is given
+ g^enH.? (10) in which r' is now the distance of the electron to the ligand nucleus.
Applying the same perturbation treatment as before to this term yields first and second order energy expressions. It is convenient to
discuss the isotropic and anisotropic part of H" separately. The first
order energy expression of the anisotropic part of ff" is given by:
W^^^ = -g g B B <0|(r26.. - 3r.r.)/r51o> S.?. (11) ^e^n e n ' 1j 1 J 1 J
Abbreviating -g g B B (r26.. - 3r.r.)/r^ as Dip., and remembering that e n e n ij i j ij
|0> = B2|d > - B2I* > this integral <0|Dip..|0> splits up in three parts: <0|Dip,j|0> = B | D , J - 2B2B2 DP,J + Bz^ Pjj (12) in which D.. = <d lDlp..|d > IJ x y I '^ 1J I x y
DP.. = <d iDip..1$ > (13)
IJ xy' IJ' xy P.. = < $ |Dip..|$ > IJ xy' '^ IJ ' xyIn the calculation of the CHFS term only the first term was im--3
portant since Dip., depends on r which is for the CHFS the distance of the electron to the central metal nucleus. Since B2 's small com-pared to B? and for an electron in <!> the distance to the central
me-'^ xy
tal atom is rather great compared to this distance for an electron in the d orbital, it seems justified to neglect the second and third term in the calculation of the CHFS term. For the LHFS this is no lon-ger justified since none of these terms can be neglected beforehand using the same arguments. So all three terms are calculated exactly using the atomic wave functions of the central metal and the ligands. The details of this calculation are given in Appendix I.
The second order energy is given by a similar formula as the one for the CHFS:
W^'^ = (A'.'. - 3u:.) §,?, (14)
ij 'J I J in which
'^ij = - 2 5: <0U(r)i.|n> <n|T r' |0>/(E -E^)
n^O J (15) "ij = -iE., I < O k ( r ) f |n> <n|r, r./r5|0>/(E -E„)
i k m , - ' ^ ' m ' k j ' ^ n o '
n^O •'
These terms can be represented by aa. = A".. - 3u... The evaluation of these terms is postponed to chapter VI where the effects of it are d i scussed.
24
The results can be summarized in the form of an extra term to be
added for each ligand nucleus k to the spin Hamiltonian.
/ . = a "^l "".S + a '^i" "".S + a '^i "".S (]6)
spin XX X X yy y y zz z z
i n wh ich
a '' = B2D'' - 2B2B2 DP"" +B22p'* + aa""
XX 2 X '^ ^ X "^ X Xa
^
= B 2 D ^ - 2B262 DP'' + Bz^P*" + aa*" (17)
yy 2 y
'^^
y y y
a •* = B2D'' - 2B2B2 DP*" + B22p'' + aa'^
zz 2 z ^ ^ z
'^ z z
in which the D , DP , and P are the results of the calculation given
i n Append ix I.
The isotropic term is proportional to the spin density at the
ligand nucleus. Orbitals of bz symmetry have a nodal plane at the ligand
nucleus, so this spin density is zero. Beyond the scope of this approach
but important is the fact that the unpaired electron polarizes the inner
shells in such a way as to produce a net spin density at the ligand
nucleus. This polarization for an electron in an np orbital is given by
< P. So this term is proportional to 62^*^ P- The second order terms
np
t- r
-^ np
do not contribute to the isotropic a.
The isotropic value is very sensitive to the overlap of orbitals
and the exact form of the radial part of the wave functions as was
dis-cussed by Freeman and Watson (I8). The isotropic term is most
convenient-ly denoted by <a>. The final spin Hamiltonian parameters are obtained by
adding up the isotropic and anisotropic parts.
a = a + <a>
X XXa' = a ' + <a>' (I8)
y yy
a = a + <a>
z zz
The extension to more ligands is simple:
H . = I
a'ï's + a'i's + a'ï's (19)
From the symmetry of the complex it is clear that: al = a2 X y al = a2 y X al = a2 ^z ^z
For the fifth
a5 = a5 X y s ax ^ = ^// = a3 = X = , 3 .
. a | .
axial
= a f
a;;
= a i = a^
< = ^ ^ ^
^^ = ^z igand the sy (20) (21)This nomenclature will be used throughout this thesis. The advantage of this choice is that a is the LHFS component in the xy plane in the direction along the F-M bond and a the component perpendicular to this bond axis.
2.2 Calculation of spectra from the spin Hamiltonian
After having derived a spin Hamiltonian the next step is to cal-culate the spectra arising from it for a given orientation of the mag-netic field. The eigenfunctions and eigenenergies of this spin
Hamiltonian must be calculated for a given direction of the external magnetic field, with respect to the x, y, and z axis of the complex, denoted by (0,<|>) as shown in fig. 2.1. This can be done in two ways:
1. Transforming the spin Hamiltonian to a new coordinate system in which the new z axis is parallel with the external magnetic field. Assuming gB H to be much bigger than A.I.S., one can apply an approxi-mation which yields a formula for the resonance field H which is
in-' r dependent of <i> for axial symmetry:
hv = g(0)BgH^ + M . A ( Q ) . M . = - I , - 1 + 1 . . . +1 (22)
The derivation of this formula can be found in many textbooks (19). The expressions for g and A as a function of (o) are:
g(0) = (g2 cos2e + g?_sin2e)^ , ^
// -^ (23) A(0) = (g^,A2 cos20 + g2j^ls\n^ey/g{Q)
26 - I f F i g . 2.1 O r i e n t a t i o n o f H w i t h respect t o MOX5 i o n . In t h i s a p p r o x i m a t i o n t h e LHFS i s not t a k e n i n t o a c c o u n t . I f t h i s t e r m i s t r e a t e d i n a s i m i l a r way terms a i ( 0 . * ) ( M ! + M ^ + a2(0,<t>)(M? + M^) (24)
should be added to formula (22).
Also the selection rule AM. = 0 for the nuclear spin should hold. Evaluation of the effect of the LHFS terms in the Hamiltonian shows that such simple formulas are only valid if the magnetic field is orien-ted along one of the principal axes of the a tensor. For an arbitrary direction of the magnetic field the simple formulas are not even good approximations. This is due to the circumstance that the nuclear spin feels the effect of the external field (nuclear Zeeman term) and the effect of the field due to the electron spin (LHFS t e r m ) .
The magnitude of these two effects is: a) Hyperfine interaction 20 - 60 x 10 cm
b) Nuclear Zeeman interaction 5 x 1 0 cm for l^F at 3'»00 Oersted, and they are of the same order of magnitude. The direction of the ex-ternal field and the field produced by the electron spin at the nucleus do not have the same direction due to the differences between a , a ,
x y and a . Due to this effect the quantum number M. is no longer a good quantum number and the selection rule AM. = 0 becomes meaningless. The effect of it is that "forbidden" transitions occur. This effect is
dis-cussed by Trammel
et at
(20) and Baker
et at
(21). To deal with this
effect quantitatively a more exact approach must be used as described
below.
2. Solving the eigenvalue problem exactly. The eigenvalues of the
spin Hamiltonian and the corresponding eigenfunctions having been
ob-tained, the resonance frequencies and the intensities of them can be
calculated and in this way all resonance fields are found. The spin
Hamiltonian is simplified by neglecting the CHFS terms since most
cen-tral atom isotopes have no nuclear spin. If the cencen-tral atom isotope
does have a nuclear spin (table 1.2) the effect of this is simply to
split each line into (21+1) equidistant lines.
In a general approach the functions used in this problem are
pro-duct functions, é = Im > |m-!> |m.> lm.>
^ ' s ' I ' I ' I
in which the |m > and |m.> are spin functions. The quantization of the
electron spin is only determined by the external magnetic field as can
be seen by the magnitude of the different terms in the spin Hamiltonian
below. The four ligand nuclear spins have no direct interaction with
each other, so it is possible to deal with them separately and to
ob-tain the final spectrum by combining their splittings and multiplying
their intensities. In this approach the problem is simplified to the
following spin Hamiltonian:
^ = 9 / / ^ " z ^ ^ ^x^e ('^x^x ^ \ ^ ^ ^3°° "^ lo'Vm"^)
k - k - k - k - k - k - - 4 - 1
+ a'^rs + a'^rs + a'^rs ( 40 X 10 cm ) 25)
z z z X X X y y y i ^ •"
^ 9nSn(Hj^ - H^?;; - H^l^^ ( 10 x l O ' ^ m ' ^ )
in which k denotes the ligand for which the calculation is done. The
order of magnitude of the various terms is also indicated.
The eigenfunctions of this spin Hamiltonian are expressed as a
linear combination of product functions Im >|m.> where |m > and |m.> are
r ' S ' I ' S ' I
electron and nuclear spin functions with eigenvalues m , m. of S and I
'^ ^
S ' I z z
So Ü/. = Z C..|d).> in which the |<t).>'s are Im >|m.>.
1 j Jl ' J ' J ^ 'k
28
I . k k H.. - E. 6.. I I I J I i j <^.\H^\^.>. k k 0 must be solved, in which H.. is given by H..IJ ^ ' IJ
So the problem is to diagonalize the matrix H... This matrix is
IJ
of size (2S+l)(2l+l) which is 4 for fluor as a ligand and 8 for chlorine or bromine as ligands and it has complex elements for an arbitrary d i -rection of the field. This problem is best solved with the use of a computer. In the program a constant field H satisfying hv = g(0)BH is used and the obtained energies can be converted to field values satisfying AE = hv.
The next step is to calculate the intensities of transitions b e -tween these energy levels. These intensities are proportional to P, , = <^, |v|4) > in which |i(j,> and |i(j.> are eigenfunct ions and V is the Hamiltonian d u e to the rf-field perpendicular to the external field H : V = g B ^ H , . S + g ^ B ^ H , . l .
In the same computer program which diagonalized the H.. matrix the transition probabilities P., of all transitions with AE = hv w e r e calculated. Since the ligands can be divided into two sets of equivalent pairs, this matrix had to be diagonalized two times instead of four t imes.
T h e results of this diagonalization yield the following spectra: 1. I = J (Fluorine).
For H along the x or y axis a splitting of a from one pair of ligand nuclei and a subsequent splitting a from the other pair gives a 9"
line spectrum with intensity ratios 1 2 : 1
For H along the z axis five lines with intensity ratios 1 : 4
2 : 1 .
6 : 4
2 3 4
Fig. 2.2 a Spectrum for H along x or y a x i s ; I = J. b Spectrum for H along z a x i s ; I = J.
caused by an equal splitting a from each of the four equatorial ligand nuclei are obtained. These spectra are given in fig. 2.2.
2. I = 3/2 (Chlorine or Bromine).
For H along the x or y axis 49 lines with splittings a and a are obtained with intensity ratios 1 : 2 : 3 : 4 : 3 : 2 : 1 and a subsequent splitting of each 1ine in 1 : 2 : 3 : A : 3 : 2 : 1. For H along the z axis an equidistant 13-line spectrum is obtained with separation a., and intensii
10 : 4 : 1.
splitting of each 1ine in 1 : 2 : 3 : A : 3 : 2 : 1. For H along the
ara 1- Ï nn -.^
and intensity ratios 1 : 4 : 10 : 20 : 31 : 40 : 44 : 40 : 31 : 20 :
From the above given discussion it is evident that
ai(0,0) = a2(0,0) = a^
ai(90,0) = a2(90,90) = a^ (26)
ai (90,90) = a2(90,0) = a^
and A(0) = A^^ A(90) = Aj_.
The splitting due to the fifth ligand is assumed to be smaller than the linewidth. Its effect is of course simply a splitting of each line into two components with separation a^*^, aj_ , a,, if the field is along x , y, or z axis.
From this diagonalization and from the symmetry of the problem it
is clear that for i) = 45° all ligand nuclei are equivalent, so aj = a2
for these orientations and this gives 5 equidistant lines with intensity ratios 1 : 4 : 6 : 4 : 1 i f l = J and 13 equidistant lines with intensity ratios 1 : 4 : 10 : 20 : 31 : 40 : 44 : 40 : 31 : 20 : 10 : 4 : 1 if I = 3/2 if "forbidden transitions" are neglected.
For the three orientations of H along x, y or z axis no "forbidden" transitions appear. For other orientations of the field sometimes more than (21+1) hyperfine components for each ligand nucleus have a non-zero intensity. As an illustration of this the results for
_ \ MoOFs are given in fig. 2.3, using the value of the parameters of this
30
by s u c c e s s i v e s t e p s o f 5 d e g r e e s . The " f o r b i d d e n " t r a n s i t i o n d e n o t e d a ' i s g i v e n i f t h e i n t e n s i t y o f t h i s t r a n s i t i o n i s more t h a n 3% o f t h e s t r o n g e s t t r a n s i t i o n . From t h e s e r e s u l t s f i g . 2 . 4 was c o n s t r u c t e d where t h e c a l c u l a t e d s p e c t r u m i s p l o t t e d a g a i n s t <i>. Here o n l y t h e v a l u e s o f a j and a2 a r e used and t h e " f o r b i d d e n " t r a n s i t i o n s a{ and 82 a r e n e -g l e c t e d .
F i g . 2.3 Spectrum c a l c u l a t e d from s p i n Hamiltonian for magnetic f i e l d in the xy p l a n e . M0OF5, only i n t e r a c t i o n s w i t h 1igand no. 1 .
60-
«I-•UO -120 Too ^ b ^60~
F i g . 2.'t C a l c u l a t e d spectrum o f M0OF5 ions ve. if; 0 = 9 0 ° . F i e l d v a l u e s in Oe r e l a t i v e t o resonance f i e l d w i t h o u t LHFS.
In s p e c t r a f r o m t h e s e ions i n s o l u t i o n a l l a n i s o t r o p i c e f f e c t s a v e r a g e o u t and t h e s p e c t r u m can be d e s c r i b e d by a s i m p l e H a m i l t o n i a n :
i n which <g> = ( g / / + 2 g J / 3 <A> = (A^^ + 2Aj_)/3
< a ' > = (a^ + a ; + a ; ) / 3 ^^S)
2.3 Comparison of powder spectra and single crystal spectra
In a powder spectrum or a spectrum from a quickly frozen solu-tion of a paramagnetic ion all orientasolu-tions of this ion with respect to the field have equal probability. So the spectrum observed is the sum of the spectra of all orientations and will be rather complex. A number of techniques have been used (22) for the problem how to get
information from these spectra. They all make use of the fact that peaks in the powder spectrum correspond to orientations where a reso-nance line reaches an extremum. In the absence of LHFS interaction this technique workes quite well and yields approximate values for g and A tensor.
If LHFS is present this is not necessarily true as is evident from fig. 2.4 giving the position of resonances as a function of 4i. The outermost transitions do not reach extremum values for <t) = 0° or 90°, but for ()) = 45°. So from the peaks in the powder spectrum a and a are not obtained but something like a (90,45). By comparison with the values obtained from single crystals it will be demonstrated in chapter VI that in this way several authors have been led to erroneous data derived from powder spectra.
In a single crystal spectrum 0 and ^ are known precisely and by choosing appropriate values for them all spin Hamiltonian parameters can be obtained directly. Only two orientations are needed:
1 . 0 = 0 ° ^ g^/, A//, a^
2. 0 = 90° ^ = 0° or 90° - gj_, A_^, a^. ay.
By measuring also other orientations viz. (90,45) the observed split-tings can be compared with the results of a diagonalizat ion of the spin Hamiltonian matrix using the observed values of g/;, gj_, a , a , and a . This gives a direct check upon the accuracy of the parameters and can be used to solve more difficult spectra where it is not possi-ble to obtain a and a from the (90,0) spectrum.
32
CHAPTER III - EXPERIMENTAL
3.1 Choice and structure of host lattices
Since the MOXs complex is octahedral-1ike the host lattice should contain a similar group which can be replaced by the MOXs complex. In this thesis the host lattices used contain a M,Xg group. Also a M/OXs group could be u s e d , but there are very few compounds containing such a group. A comparison of ionic radii and the known or estimated bond dis-tances in the MOX5 complexes - given in table 3-1 - shows that the only suitable diamagnetic tetravalent ions are Ge "*" and Sn . Assuming ana-logous alignment of MOX5 and M.Xg g r o u p s , the MOX5 complex can substi-tute for the M.Xg group in six different w a y s , since the distribution of the M0 axis over the three different XM,X directions gives 6 d i f -ferent orientations of the MOXs complex. T o avoid too complicated spectra it is necessary for all the M , X ~ groups in the host lattice to have their X-M,-X directions parallel with each other.
Table 3.1
Distances in the MOX^ complexes
CrOFs M0OF5 MoOC15 MoOBrs WO F 5 WOCI5 WOBrs
M-0
1.65 1.75 1.75 1.75 1.75 1.75 1.75 M-F eq 1.70 1.85 2.12 2.30 1.85 2.12 2.30 M-F ax 1.75 1.90 2.17 2.35 1.90 2.17 2.35 Referencea
a
a + ba
a
a + ba
a. Estimated using bond distances in corresponding compounds listed in
(44).
Using the above considerations crystals of the type M„M,X, in which
M is K, Rb, Cs, or NH^
Mpi is Ge or Sn
X is F, C I , or Br
were chosen. It proved to be necessary to avoid big cations as Rb or Cs since this resulted in a total random orientation of the MOX5 group in the crystal, giving an EPR spectrum of single crystals similar to the EPR spectrum of a powder. After some trial and error the following crystals have yielded good results:
a) K2SnFg.H20 and (NHi^)2GeFg for the oxyfluorides. b) (NH4)2SnClg and K2SnCl6 for the oxychlorides. c) (NH4)2SnBrg for the oxybromides .
In all these structures the M.Xg groups are octahedral-1ike, but small deviations from the ideal octahedron are present in some cases. The three different X-M.-X directions will, however, be referred to as "octahedral" directions, and the MXg group as an octahedron.
1. K2SnFg.H20 structure.
This structure was unknown at the start of our investigations. It was determined by Beemster (23). The elementary cell is orthorhombic with space group D2j+.The point symmetry at the Sn atom is 2. In this struc-ture the three Sn-F directions are not equivalent by symmetry. A draw-ing of this structure is given in fig. 3.1. All octahedra have their axes parallel with each other. Since the octahedral directions are not equivalent they are denoted by 1, 2 , and 3. In fig. 3-2 these three directions are drawn with respect to the crystal axes. Direction 1 is parallel with the b axis. Directions 2 and 3 lie in the ac plane and bisect the angles between the a and c axis. The cell dimensions and
interatomic distances are:
a = 13.7'»2 A° Sn-F = 1 .94 A° b = 17.643 A°
3k
• ' © O O
Hp K F Sn
F i g . 3-1 KzSnFg.HjO s t r u c t u r e . b F , ' • *F iSnF"
J-2
— O I *F F i g . 3-2 O r i e n t a t i o n o f o c t a h e d r a l d i r e c t i o n s o f SnFg group w i t h r e s p e c t t o c r y s t a l l i n e axes o f K2SnFg.H20. 2 . (NHit)2GeF6 S t r u c t u r e . I n t h i s s t r u c t u r e w i t h space g r o u p 0 ^ . ( 2 4 ) t h e GeFg g r o u p s a r e a l m o s t p e r f e c t o c t a h e d r a . The p o i n t symmetry a t t h e Ge atom i s 3m. The p a c k i n g o f t h e s e o c t a h e d r a and t h e ammonium i o n s i s l a y e r l i k e and shown i n" This drawing and the (NHi,)2GeFf, and K2PtCl6 ones were computed by the program "ORTEP" CiS). I am indebted to Mr. F.E. van der Vloot who programmed them.
fig. 3.3. The three octahedral directions of each GeFg group are equi-valent by symmetry and all groups have their Ge-F directions parallel with each other. These directions are found to make an angle of 54°44' with the c axis, corresponding with a regular octahedron, and their projections on the a-a plane are perpendicular to one of the a-axes. The cell dimensions and interatomic distances are:
a = 5.85 A° Ge-F = 1.77 A" c = 4.775 A°
F
uy\
Ge
Fig. 3.3 (NHi,)2GeF5 structure.
3. K2PtCL6 structure.
In this cubic structure with space group 0^ (25) the PtClg unit is a perfect octahedron. The point symmetry at che Pt atom is m3m. These octahedra and the potassium atoms are distributed over the elementary cell as the Ca and F atoms in CaF2. A drawing of this structure is gi-ven in fig. 3-'*. All PtCLg octahedra have their octahedral axes paral-lel with the cubic axes. The host lattices used - which are isomorphic to K2PtClg - have the following cell dimension and interatomic distances.
K2SnClg a = 10.002 A° Sn-Cl = 2.40 A° (NH4)2SnCl6 a = IO.O6O A° Sn-Cl = 2.40 A° (NH4)2SnBr6 a = 10.59 A° Sn-Br = 2.60 A°
36
The deviations from a perfect octahedron in K2SnFg.H20
and (NHL,)2GeFg are small. The X-ray determined structure gives angles of 89-91° between the three distinct X-M,-X directions.
Manoharan and Rogers (13) used different host lattices: K2NbOFs.KHF2 for M0OF5 and
(NH4)2lnCl5.H20 for M0OCIÏ
but these host lattices do not contain octahedrons. DeArmond et at (15) used the same host lattice as Manoharan and Rogers (13) for the M0OCI5
ion, but they did not observe any LHFS.
3.2 Preparation of the single crystals
The salts used in the single crystal preparation were prepared as follows:
1. K2SnFg.H20.
Potassiumstannate, K2Sn(0H)g was dissolved in an excess of concentrated hydrofluoric acid. When it was dissolved completely, the solution was gently heated to evaporate the solvent.
2. (NH4)2GeF6.
concen-trated hydrofluoric acid. A small residue remained undissolved. The so-lution was filtered and the theoretical amount of NH^F.HF dissolved in concentrated hydrofluoric acid was added. This solution was treated as the K2SnFg.H20 solution to obtain the salt.
3. (NH4)2SnClg, K2SnCle, and (NH4)2SnBr6.
SnCli^ or SnBri^ were dissolved in the corresponding concentrated acid. To this solution, a solution of (NHij)Cl, KCl , or (NH4)Br in the same concentrated acid was added. The resulting solution was treated as above to obtain the salt.
To purify the salts they were recrysta11ized twice from water. All crystals were powdered and X-ray photographs proved them to have the
indicated structure. The concentrated acids used were: HF 3 8 ^ = 19 N
HCl 40% = 13 N HBr 38% = 9 N
Two techniques have been used to obtain single crystals. In both methods a saturated solution of the salt in the corresponding acid was prepared first.
The first method was slow evaporation of the solution at room tem-perature under vacuum. The second method was slow cooling of the satura-ted solution from 40° to room temperature in a few days. K2SnFg.H20 and
(NHi4)2GeFg single crystals were prepared by the first method. (NHL,)2SnCl g, K2SnCl6, and (NHij)2SnBrg single crystals were prepared by the second me-thod.
To incorporate the various MOX5 ions the following techniques were used :
a. Chromium ions.
Since Cr is reduced by hydrofluoric acid, K2Cr207 was added to the solution of the host lattice (approximately 2 grams/100 ml solution) and the reduction to the pentavalent state took place in one or two days. After 7 to 10 days reduction to the trivalent state was complete and the solution had turned green. So only crystals grown in the first 3 or 4 days were used. It proved to be very difficult to incorporate this ion and only a few crystals containing this ion could be prepared.
38
The crystals contained, due to this effect, varying amounts of Cr . b. Molybdenum ions.
Since M0OF5, M0OCI5, and MoOBrs are very stable in solutions of the strong corresponding acid, standard 1 M. solutions of these complexes were prepared by reducing a solution of molybdic acid in the corres-ponding acid with metallic tin. Approximately 1-10 ml of this solution were added to 100 ml of the host crystal solution.
c. Tungsten ions.
Since WOF5, WOCI5, and WOBrs reoxidize very quickly to the hexavalent state, the complex was reduced constantly by adding small amounts of metallic tin to the host crystal solution containing this complex.
For all ions the concentration of the paramagnetic ion in the solution was changed to obtain the dilution leading to the sharpest lines in the EPR spectrum. The amount of paramagnetic ions in each crystal was determined by emission spectroscopy*.
The results are:
ION HOST LATTICE % BY WEIGHT % MOLAR
CrOFs C r O F s M0OF5 M0OF5 WO F 5 MoOC15 WOCI5 M o O B r s W O B r l K2SnFg.H20 ( N H j 2 G e F g K2SnFg.H20 (NH4)2GeFg (NH4)2GeFg K2SnClg (NH4)2SnClg (NHi,)2SnBrg (NH4)2SnBr6 < 0 . 0 1 0.03 < 0 . 0 1 0 . 0 6 - 0 . 1 0 0 . 0 8 < 0 . 0 1 0 . 5 0 . 1 - 0 . 3 0 . 8 < 0 . 0 6 0 . 1 3 < 0 . 0 3 0 . 0 9 - 0 . 1 5 0 . 1 0 < 0 . 0 4 1 .00 0 . 6 0 - 1 . 7 5 2 . 7 5
3.3 Morphology of the crystals
Many crystals needed to be rotated around specific axes; each crystal could have been oriented by X-ray techniques, but this would have required about one day for each crystal. So a way was sought to make use of the morphology of the crystals. This morphology was de-termined for some crystals using only the point symmetry of the
crys-•'• I am indebted to Mrs. M.A. Koper of the Laboratorium voor Instrumentele Analyse, T.H. Delft, who did these analyses.
tal (K2PtClg type) or by determining the orientation of the crystal axes with respect to the crystal faces (K2SnFg.H20 and (NHi+)2GeFg) by X-ray techniques. The following results were obtained:
1. K2SnFg.H20 crystals.
These crystals had the form of long needles approximately 10-20 mm long and 2-5 mm thick. X-ray analysis showed that the c axis was parallel with the needle axis, and the needle faces were {110} and {111}. Some-times a small {010} face was visible. This is in accordance with the data given in Groth (26).
2 . (NHit)2GeFg c r y s t a l s .
These crystals were small hexagonal plates with the c-axis perpendicu-lar to the plate. X-ray techniques showed the a axes to be parallel with the side faces of the plates. The size of the crystals was 4x8x8 mm.
3. KaPtClg type.
Crystals of this structure crystallized in three distinct ways: a) Cubes with only {100} faces.
b) Octahedrons with only {111} faces.
c) A mixture of a) and b) with {100} and {111} faces. (NH4)2SnClg and K2SnClg were always of type c . (NH4)2SnBrg was mostly of type a .
The size of these crystals varied from 2x2x2 mm to 6x6x6 mm.
A photograph of the crystals is given in fig. 3.5 and the ideal shape showing the morphology is drawn in fig. 3.6.
The K2SnF6.H20 morphology was checked with an optical goniometer by measuring the angles between all the faces of the crystal. The mea-sured angles were in perfect agreement with the ones calculated from the unit cell dimensions.
Knowing this morphology it is possible to rotate the crystal about any specific axis with respect to the M.Xg group, since the orienta-tion of this M, X~ group with respect to the crystal faces is known. An ambiguity occurs in the case of the (NHtj)2GeF6 crystal due to the 6-fold screw ax is.
40
Fig. 3.5 Photographs of single crystals used a. KjSnFg.HjO c. (NH^jjSnBrg b. (NH4)2GeF6 d. (NH^)2SnCl6
(001)
V
/ (001) nil) (d)Fig. 3.6 Ideal shape of single crystals used
a. K2SnF5.H20 d. K2PtCl6 combination of type a and b b. (NH^jjGeFg e. KjPtCle type b.
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3.4 Choice of rotation axes and rotation techniques
As was pointed out in chapter II one can obtain all parameters of the spin Hamiltonian from just two EPR spectra:
a) H along the z axis, (0,0) spectrum
b) H along the x or y axis, (90,0) spectrum.
To measure these two specific orientations the following method was used. All host lattices contain MXg groups which have their three octahedral directions parallel. Assuming for the moment that the paramagnetic ion will substitute in such a way that the x, y and z axes of the complex
are along these octahedral directions, then for an arbitrary direction of the field with respect to the three octahedral axes three different spectra (0i ,<j>i), (02, 412), and (03, cfs) - one for each octahedral direction which is occupied by the M-0 axis of the complex - will be observed. The orientation of the field with respect to these three oc-tahedral directions can be given by denoting the angles 0. and ^. of the field with respect to the MOX5 complexes: (Sj , cjii) + (02, 1^2) "*"
(03.
«t-a)-To observe the (0,0) and (90,0) spectra the field must be paral-lel with one octahedral direction, since then 1/3 of the ions have the z axis parallel with the field and 2/3 of the. ions have the x or y axis parallel with the field. So the rotation axis has to be perpendi-cular to one of the octahedral directions. Two choices for this rota-tion axis were used:
a. The rotation axis is an octahedral direction.
The EPR spectrum is now symmetric upon a 90° rotation and the following interesting spectra can be observed:
1. H along one of the other two octahedral directions gives 1 x (0,0) + 2 X (90,0) spectrum.
2. H rotated 45° from 1 gives 1 x (90,45) + 2 x (45,0) spectrum. b. The rotation axis is the bisector of the angle between two oc-tahedral directions and perpendicular to the third one:
This will yield the following interesting spectra:
1. H along the third octahedral direction gives 1 x (0,0) + 2 x (90,0) spectrum.
2. H rotated 90° from position 1 gives 1 x (90,45) + 2 x (45,0) spec-trum.
3. H rotated 54°44' from position 1 gives 3 x (54°44',45) spectrum.
The advantage of the first rotation axis is that only for posi-tions 1 and 2 of H two spectra (0i , (jji) and (02, it>2) become equivalent, which proved to be a very sharp criterion to get these orientations exactly.
The second rotation axis has two advantages:
a) Two of the three spectra - (0^ , (tn), and (02, <J>2) " are identical for all orientations of H which gives a less complicated overall spectrum.
b) It is possible to obtain an orientation for which all three spectra " (01. «t»!), (02, <l'2) . and (03, (t>3) - are identical.
The general method of orienting these crystals consisted of glue-ing them on perspex rods in which sometimes specific angles were cut. These perspex rods were of size 4x150 mm for X-band and 2x11 mm for Q.-band measurements. The Q-band rods could also be used for X-band work. Each crystal was glued on the perspex rod in such a way that the axis of rotation was parallel with the rod. The details of these orien-tations are given below for each crystal type:
1. K2SnFg.H20.
Rotation around the a-axis was achieved by glueing the crystal with the (110) and (110) faces in the corresponding angle (103°50') cut into the rod (fig. 3.7a). Rotation around the b axis was achieved by glue-ing the crystal with the (110) and (110) faces in the correspondglue-ing angle (76°10') cut into the rod (fig. 3.7b). Rotation around the c axis was achieved similar to the rotation around the a axis, but here the angle was cut in the parallel direction of the rod (fig. 3.7c).
2. (NH4)20eFg.
The first rotation axis gave some difficulties because of the fact that the octahedral directions of the GeFg groups are not uniquely re-lated to the morphology. These octahedral directions make an angle of 54°44' with the c axis and their projections on the a-a plane are per-pendicular to the a axis. But there is still an ambiguity since these
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Fig. 3-7 Orientation of single crystals on perspex rods a. K2SnF5.H20 around a axis b. K2SnF5.H20 around b axis
c. K2SnF5.H20 around c axis d. (NHi,)2GeFg around a Ge-F direction e. (NH4)2GeFg around bisector of two Ge-F directions
f. K2SnClg around an Sn-Cl direction (100)
g. K2SnCl6 around bisector of two Sn-Cl directions (Oil) h. (NHi,)2SnBr5 around an Sn-Br direction (100)
projections can be chosen in two ways which differ by a 60° rotation around the c axis, as is indicated in fig. 3.8. So the crystal was placed with the (OOOl) face on a rod whose top face made an angle of
Fig. 3.8 Ambiguity in the orientation of the octahedral directions of the GeFg group with respect to crystal faces of (NHi,)2GeF6.
35°26' with the rod axis. The crystal was glued on this rod with one (1010) face downward as shown in fig. 3.7d.
Always one crystal was used, cleaved perpendicular to the c axis and the two pieces were taken, using {1010} faces which differed by a 60° rotation. Proceeding in this way it is certain that one of the two pieces has one of the octahedral directions parallel with the rod axis. The right piece was selected by checking both pieces for the 90° symmetry, upon rotation around the rod axis.
The second rotation axis was much easier to obtain by simply glue-ing the crystal with a (0001) face on a rod given in fig. 3.7e, with a point of the hexagon downward.
3. (NH4)2SnClg or K2SnClg.
These crystals are octahedra, so rotation around a cube axis was ob-tained by cutting in a rod the sharp angle between two {111} faces which is 70°32' and glueing the crystal in this angle (fig. 3.7f). The
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I09°28' which is the obtuse angle between two {111} faces and glueing the crystal in this angle (fig. 3.7g).
4. (NH4)2SnBrg.
The octahedral directions of the SnBrg group are parallel with the cube axes, so the first rotation was achieved by glueing the crystal with a {100} face on the end face of the perspex rod, (fig. 3.7h). The second rotation axis was obtained by glueing the crystal with a {100} face on a rod in which an angle of 90° was cut (fig. 3.7i).
The crystals on the rods were rotated in two different ways: for (1-band the rods were placed in a hole drilled in the bottom of the Q.-band cavity. Rotation was accomplished by rotating the magnet. Cooling was obtained by placing the cavity in liquid nitrogen using a
polyethy-lene bag to prevent liquid nitrogen from leaking into the cavity. A specially constructed one-angle rotation unit was used for the X-band.
It was made of a rigid cylinder screwed on top of the X-band cavity. The perspex rods were mounted in a rotatable Vernier on the top of the cylinder. Cooling was obtained by placing a Dewar in this cylinder and
fig. 3-9 Part of two-angle rotation unit showing the second axis of rotation.
f i l l i n g i t w i t h l i q u i d n i t r o g e n . The EPR spectrometers used were Varian V 4500 - 10 A and Varian E 3 * . Rotation around two perpendicular axes was obtained by using a rod i n which a small perspex c y l i n d e r could be
rotated as shown in f i g . 3.9- The c r y s t a l was placed in t h i s small per-spex c y l i n d e r . The accuracy o f the r o t a t i o n around the f i r s t a x i s was about 1 5 ' .
Rotation around the second axis was less accurate due t o the very small size of the c y l i n d e r . The accuracy was about 2 ° .
3.5 Comparison between the EPR spectra of frozen solutions and of
powdered crystals
To v e r i f y the assumption that indeed the MOX5 'ons had entered the host l a t t i c e the EPR spectra of q u i c k l y frozen s o l u t i o n s of these
ions in the corresponding strong acids were measured t o o b t a i n the " g l a s s " spectrum. As an example i n f i g . 3.10a the " g l a s s " spectrum o f MoOBrs is g i v e n . I t should be compared w i t h the spectrum of powdered c r y s t a l s of {NH4)2SnBrg doped w i t h MoOBrs 9'ven in f i g . 3.10b, also measured at l i q u i d n i t r o g e n temperature. The shape of both spectra is very s i m i l a r . This behaviour was found f o r a l l ions except WOCI5, the c r y s t a l spectra mostly being somewhat sharper than the f r o z e n s o l u t i o n s p e c t r a .
F i g . 3.10 Comparison o f spectrum o f f r o z e n s o l u t i o n s w i t h spectrum o f powdered c r y s t a l s T = 77°K
a . Q u i c k l y f r o z e n s o l u t i o n o f MoOBrj in c o n c e n t r a t e d HBr b. Powdered c r y s t a l s o f (NH|,)2SnBrg c o n t a i n i n g MoOBrj The spectrometers used were calibrated by measuring the magnetic field with an NMR probe. T h e field sweeps were calibrated using a O.OIM solution of MnCl2 '" water or a solution of NOSO3 in w a t e r .
