Chapter 1

Introduction

Electron Pararnuynct~c Resotlance ( t P R ) is defined as the form of

spectroscopy conccmctl tvith ~n~crowav~.- induced transitions between

m a g n c t i ~ cnurgy levels ol'clcctrons 11,rving a net spin (i.e., unpaired electrons)

anlI i ~ r h ~ [ . ~ i ; I I I ~ I I ~ ; I I I I I ~ ' I I I L , I I I L I I I I h1,1\1 C ~ I I ~ I I ~ O I I ~ ~ these systems have S = Ii?

hut 5 call be an) \aIuc li.i1111 1:2 to 7 2 i l l incrclncnta of 112. When the spin is

odd, I.c., lor CXUIIIPIC. S - 1 2 . .<:2 111. 5 2 . ipcctra are easily obtained at room

[cmperaturc. Howcvcr it ~ l i c iplli is CLCII, 1.e.. for example, S = I . 2 or 3, then

the possibil~ty of obtdlnlng speclrd u ~ l l depend upon a number of

c~rcumstnnces that arc usu~ll! 1101 I1ieV: tllus the EPR of even spin systems is a

very specializ,ed unc. E P R specrrosiopy is capable of providing molecular

structural dciails inazcc\hihle by orher ; in~l$~caI tools. EPR has been

successfully spp l~ed In suili i i ~ \ e ~ . z c Li~scipl:nrj ds biology. phys~cs, geology.

chemistry, medical sclellcc. lnattrlal science. anthropology, to name but a

few. Solids. liqulds and gtise, arc dl1 . ~ ~ i t s b ~ b l c to EPR. B) utilizing a variety

of special~zed lcchniquca (sucll as splri-rrapptng, spin-labeling, ESEEM and

ENDOR) in conjunction ~ ~ t h EPR. rcscdrchers are capable of obtaining

detailed inibrlnatlon about many Loplca of scientific interest. For example,

chemical kinetics, electroil txchangc, clcciruchemical processes, crystalline

S t U c t u ~ , fundament;ll cjuantum t1ieor.y. catalysis, and polymerization

reactions habe all bculi studied ~ ~ t h great success. Possible systems

encountered in biology are:

1. Organic radicals:

Quinones. Redox, Prusthctic groups (Flavin, amino acids).

Chlorophyll'. R~~d~at ln i l Damage (amino acids, purines and

pyriniidines). Spin L~hclh rtc..

2, Inorganic radicals (S = 112):

OX. NO

3. Rletals:

Fe S = 1 3 . [lo\\ >pin Fc(lll), FeS clusters]

S = I jFcliV))

S = 9 2 [intmnediatc spln Fe(lfl)]

S 2 [kclll)]

S - 5 2 [ll!gh >PI11 Fc. (Ill)]

Cu (11) S - I ?

Mn(I1) S = 5 7

Mu(\') S - I 2

Cu(l1) S = I 2 . 3 2

Ki(1, Ill) S= I 2

The detection of EPR sgnals from !metal-ions in proteins can provide the

ibllowing infurniat~un:

1 ) Identiiicnt~on iifrlic prcsence til'a mcral ioc: Confirmation that the EPR

signal bclongs ti) a ~xirhcula~ metal ion can 5ometimes he done by

mcusurcnicnl ~>l'riucIt.ar 1i)pc1 l int a l i .n .d (see h r l o ~ ) .

2 ) By t b l l o ~ iny the ch.ingus in l l i ~ , ~~xidntion stalc of rhe metal ion.

3) Identification of the metal ion and the surrounding ligands.

4) Quantifying the concentration of paramagnetic centre.

The technique of' ciectron param~gnetic resonance was discovered in

1944 by Zavo~sky [I j In thc coursc ~il'invesligation of electron paramagnetic

energy absorption by pararnagnetlc oieral salts. Since its discovery, EPR

spectroscopy has becomc a most important and dominant tool for quantitative

structural infonnat~on o i the elrctron~c and spatial configuration of

pararnagnetlc centers. Thc maln advantage of this spectroscopy is that a small

percentage of paramagner~c impurity present in a bulk diamagnetic host lattice

can bc studied In dctail. Thc appli~~ition and theory of t h ~ s spectroscopy is

discussed in detail in a nuniber of text books [2-81. Nowadays, EPR has

become an important tool In csumatiny the ages of fossils [9], in imaging etc.

Electrons in molecular systems, by virme of their spin and orbital

motion, have spin magnetic moment 11, and orbital magnetic moment PI given

by

p5 = -(2.00?3 e! 11 4mn) S

111 = - ( I el h 1 4m) L -----[I. 11

where S and L are thc spln and orb~t~ll angular momenta in units of h12n and

e is the ma~mitudc of tiit. electron~i charge. The factor 2.0023, known as

free-electron gyomagnetic ratio. ariscs out of the 'anomalous' Zeeman effect

and can be derived fi.0111 Diras's r~Iatl\~iitic wave mechanics and includes a

correction of +0.0023 due to relati\~stic mass variation [10,1 I]. The total

effectlve magnetlc moment p, whlch is the vector sum of the spln magnetlc

moment and orb~tal magnetlc moment, therefore, can be expressed as

p = pb + 1) = -[)e ( 2 0023S - L) -----[I 21

where pe - I e hi4;im, is known as the Rohr mdgneton For a free electron

(rarely found in pract~cal systems, except In cases such as conduction

electrons or In S states), the orbltal contr~but~on becomes zero. Hence, the

interaction energy, In an applled magnetlc field (B) is glven by

E = -213B.S o r - g p B S -----[I .3]

For free electrori Yyatems, thc spln iiiomenta are quantized along the apphed

field dXl5 w ~ t h 7 components Sr = t l 2b That 1s the time Independent

component$ o t the preceasirly \p:n \r i tors Ile either parallel or anti-parallel to

the direct~on of ~ h c dppl~i'd d c ilelii B Thus only two energy states are

posslble for a frec electron at i gPBSz dbout the unpenurhed energy level. as

shown In Flbure I I Transltlons berueen thcse le\els are posslble when the

system is subjected to 611 oscillat~np elrctromagnet~c field It can be eastly

shown that the net paranlagnetlc moment @resent as a result of Boltrmann

dlstnbutlon) precesses about the euterndl field axis w ~ t h an angular velocity

to glven by o = - I el B:lm, tcnned .la the Larmor precession frequency. A

smdll rotatlng mabmetlc 5eld Bl rotating In the sdrne sense as the net

rnagnetlzallon vector cdu\c\ exchange of energy between ~tself and the system

of splns causlng transitions to occur br..ween the Zeeman states I.e., at

resonance w ~ l = - el B;2m Expenmentally, microwave field replaces the

rotdtlng field B I The alternating field cdn be shown to be equ~valent to the

Energy

h

I I I

Magnetic I field [B]

_h I ,,,,ti,

Bo

Figure 1.1: Schetnatic representation of thc resonance condition in the

frequency mode.

rotatlng field as far as EPR and KMR are concerned The requirement that the

osc~llatlng field should bc appl~ed pcrpcnd~cular to the statlc external field has

been proved using qudnrum n ~ e ~ h ~ i n ~ ~ \ whlch also throws l~ght on the

select~on rules for mnbmetlc dipole translt~ons According to the well-known

result of the t~me-dependent pcnurhdt~on theory [l2], the t~me-~ndependent

transltlon probah~l~ty la pruport~onal to the q u a r e of the absolute value of the

transltlon moment P given by

P = < ~ l ' v l ! + , > ' -----[I 41

where < i+~, and 1 ~1 ; dre the in~tial dnd final state vectors and V IS the tlme-

independent part ot the p c ~ ~ u i h a ~ l o n that conneLts these states In EPR. y, and

y , ~orres~,onll ro Ms value\ dnd ~i B1, = 2Blcoccot and V = gp Bl.S, then

P = < ~ , V ~ + I , > = = <-1.2 gPBlSi+1,2>'

= gp[< -1 '2 B z S z l ~ 1/2> T c -li2BxSx+1!2> +

< -112 B ~ S ~ ~ T I ! ~ > ] ' ----[I 51

Slnce the first term in square brackets IS zero, BI parallel to the axls of

qudnt~zation will be lneffect~ve Also when B I la perpend~cular to the a x ~ s of

quantlzatlon, the operators Sx and Sy lead to w, = y,=l and hence the

s e l e ~ t ~ o n ~ u l e AMs - i l Howe~er in tnplet spln ground states, ~t can be

shown that transltlons can occur at low fields with BI parallel to the axis of

quant~zat~on In general, unpa~red electrons In transltlon metal complexes do

possess orb~tal angular momentum The cpln and orb~tal angular momenta

couple to g v c a resultant angular momentum J. w ~ t h (25-1) degeneracy The

J values range from L+S to L-S The energy levels In a magnetic field B

are glven by

The correspond~ng g-factors, known ns the Lande g- factors are gven by

with J = I L-S / for less than half-filled d-shell and J = I L r S for more than

half-filled shell

The effect~vcnesa of the coupllng of the spln and orbital motion,

however, depends of the exacr nature of the envlronment of the paramagnetic

Ion Surround~ng ionlc charges, bonded ligands e tc , produce a strong

electrostat~c field and the spin-orb11 coupling wlll breakdown due to the

'quenching' of the orbital angular niomentuin Thus EPR systems can be

divided ~ n t o three maln carcgones I c . ueali-iield, intermed~ate field and

strong field cases In the plcscnr thesis, some first row transition ions are

studled In divalent environment and ~liesc fall under the intermediate crystal-

field clas?. wherc the crystal-tield ipllttlng dnd spin-orb11 coupling compete

Thus the g-factors would be neither 2 0023 nor the one given in Lande

equation, but wlll depend on the symmetry and strength of the crystalline

electnc field and the orientation of the external tield with respect to the axes

of the crystal field

EPR 1s scnsitlve to the changes In symmetry of the envlronment.

Apart from this, a number of interact~ons modify and spllt the energy levels of

the unpalred electron The former causes a shift In the center of grav~ty of the

spectrum, where as the latter Influences the fine structure In favorable

circumstances, a detalled analyslq of thc EPR spectrum leads to a very

accurate d e t e m ~ n a t ~ o n of bondlng pmmeters and the electronic structure of

the ground state, not eastly posslble In many other types of spectroscopy A

general cons~deratlon of the Interaction involved in the case of a paramagnetic

specles (wlth panlcular emphas~s on transition metal ions) In a crystal field 1s

formulated in terms of general~zed Hamlltonlan A consequence of th~s ,

lnvolvlng only spln-operators, 1s the spln-Hamllton~an, whlch is an art~ficlal,

though pract~cai concept IS dcscnbed ~ubsequently

The spln Ham~ltonlan conslats of vanous terms. whlch have been

ansen due to d~tferenr type, u! lnteractlons between electron spln wlth elther

the applled magnetlc field or nuclear spln or another electron spln and the

nuclear s p ~ n either w ~ t h the applled maLmeric tield or another nuclear spln

The ongln and tmponance of these interactluna are ment~oned below

Zeeman Interaction: 3fiz,,

T h ~ s anses due to the interaction of the external magnetlc field with

the apln and orbltdl magnetlc momenta of the electrons and nuclear spln

magnetlc moment and IS ylven by

Z z e e = P (L + 2 5 ) B - gn P n B INI, -----[I 81

where p, 1s the nuclear mabaeton and 1, are the vanous magnetlc nuclear

spins. The first term is known as the electron Zeeman Interacbon. The

second term, which is the nuclear Zeeman interaction, causes to a high degree

of approximation, merely a constant shifi of all the energy levels and is of

minor importance in EPR. except in cases where the hyperfine coupling is

much smaller than the nuclear Zeemaii interaction.

Spin-Orbit Interaction: 21 s

This represents thc coupllng between the magnetic momenta arising

fiom the spin and orb~tal motion of the unpaired electrons and can be written

as:

'%?is = Il,i 81.1 1, S h -----[I .9]

If we neylcct the electron spin and 'other-orbit' interaction, then the above

term can be given in terms of the one-electron spin-orbit coupling constants E,,,

Within the Russel-Saunders scheme, rhc interaction reduces to

:H)Ls = 7.L.S ----[I. 111

where A is the spin-orbit coupling constant of the ion and is a function of the

effective nuclear charge. For more than half-filled shells, A is negative and

for less than half-filled shells, it is positi1.e. In the spin-Harniltonian

formalism, the effect of spin-orbit coupllng is assimilated into 'the fictitious'

spin concept (vide infra).

Spin-Spin Interaction: Xss

When more than one unpaired electrons are involved in the systems

with ground state triplet or higher spln multiplicity, direct dipole-dipole

interactions among these spins lead t o the splitting of the spin-states via the

spin-spin interaction given by

When the external ma~metlc ticid 1s niuch stronger than the magnitude of spin-

spin coupling constant. the above vector dot products can be expanded to give

Xiss = (gp)' (3cos20 -1) Sj. ~k ----[1.13] rijI

Here 6 is the angle between the external field and the vector joining Sj and Sk.

Hyperfine Interaction: :@$I

This is a zero-fieid type interadion connecting the electronic mabmetic

momenta and the asso~iatcd nuclear ma~metic momenta. This consists of an

isotropic Fermi contact term for s-type spin-densities and a pure dipole-dipole

type interaction described b) a tenhor due to unpaired p, d, f type spin-

densities. The interaction is written as:

The first tern descr~bes an interaction of two point-dipoles and the second

containing the Dirac delta function, whlch when integrated wirh the wave

function vanishes exccpt at r , = 0 corresponds to the isotropic interaction.

Thus, in the non-relativistic approximation, only s-orbitals can contribute to

isotropic coupling to the concerned nuclei.

In a more rigorous Treatment, interactions between the orbital magnetic

moment and the nuclear spin moment also have to be taken into account.

Again, this can be effectively taken into account in the spin Hamiltonian

formalism.

Nuclear Quadrupole Interaction: 3iio

This interaction is relevant only to systems having nuclei with spin I

tl and arises as a result of the interaction of the nuclear electric quadrupole

moment with thc clcctric licit1 gradient at the nucleus due to the surrounding

electrons. It is expressed as

ZQ = I,, [e2~,;21, (21,-I)] [r',,.l,.(l,+l) -3(rg.1,)*] r-',)

where Q is the nuclear electnc quadrupole moment.

Spin Hamiltonian:

Most EPK data can be described in terms of "Spin-Hamiltonian'

invoicing smaller number of tcnns by use of an effective fictitious spin

without a detalled knowledge of spin-orbit coupliny, the magnitude of crystal

field splitting, etc.

In Dyad operator notation, the Spin-Harniltonian can be expressed as

c V s = P , B , g . S + l . A . S * S . D . S + l . Q . I + ..... ----[1.16]

where g, A, D and Q are second rank tensors, whose principal axes need not

coincide. These correspond to the electronic g-tensor, hyperfine tensor, zero-

field tansor and quadrupole coupling constant tensor respectively.

The concept of fictitious spin will be discussed in a more detailed way.

Just like in the case of a quantum state described by J splits it into ( 2 J t l )

levels in an external field, a system designated with the fictitious spin S' splits

into (2S'+1) lcvcls and transitions arc allowed between these according to the

selection rules. Thc only diffcrence bctwecn the true spin S and fictitious S' is

that the latter defines the efttctive spin-angular momentum endowed due to

any orbital contribution. Whereas the spin-only g-factor would deviate from

this due to admixture of higher lying dates into the ground state via spin-orbit

coupling and hcncc cfScct~\cly t&es into account of the effect of crystal field

terms and spin-orbit tern1 of'rhe generalized Hamiltonian. Since the isotropic

g-i:dctor of a free electron is moditied into a tensor when orbital momentum is

nor completely quenched In the principal axls system of the g-tensor, the

Hamiltonian is written as

3P = P (BxgxtS, + B,vg!,S, + B,guS,) ----[I. 171

If the tensor is cylindrically symrnetnc. g,, = g, = g~ = g and B x x = B, = BU

= B, then

And ~f the tensor i, ax~ally symmetnc

Z = P[B,g S i* g,(BxS, BvS,)I

Likewise, the hyperfine terms whlch cons~st of a d~polar part and lsotroplc

part are wntten generally aa

X = Ax, I x Sx - A!, 1, S, + A n Iz S, ----[I 201

If the unpdlred elcctron 15 purely ?-type, then

2 = a 11, S, and = (8x13) gpg,P, I ~J(o)! ----[I 211

where I y ~ ( 0 ) ' 17 thc s q u a d ampl~tude of the unpalred s-electron dens~ty at

the nucleua lsotrop~c hyperfinc Interaction anses due to (a) d~rect unpalred

sp~n-dens~ty In an s-orh~tal or In a moleculdr orb~tal (M 0 ) w ~ t h s-orb~tal

contnbutlon, (b) sp~n-poldr~~atlon, due to ~sot;op~c hyperfine coupllng In an

lsolated paramdbnetlc atom or Ion. i\here the electron 1s In a p or d orb~tal

arlac? wo poldi~/dt~tin ot c o ~ c \-electrons, (c) also configuration lnteractlon

between d b~ound state M 0 orbrtdl w~th no s-orbital contnbutlon and states

uvth fin~te a-orb~tal contribution

D~polar coupllng a n x i out ot polnt d~pole lnteractlon between p or d

orblral w ~ t h the nucleus ~ n d toliows a (3 cos28-1) Xanat~on p e n by

311d - g~g,~,(3cos'0-1) ( ~ l ( r ' ) ) ----[I 221

In p' or di h ~ g h apln ~onfiguratlon, due to aphencal charge d~stnbut~on,

d~polar-couplmg van~shei Also In pdramagnetlc systems In solut~ons, where

the system tumbles rdpldiy. ~t averages to zero, helng represented by a trace-

less tensor

The s p a of the expenmental pnnc~pai values of the hyperfine tensor

cannot be Inferred from EPR apectra However, a sens~ble cho~ce (often made

easier, if the isotropic coupling can he independently determined) can always

be made with the ratio of unpaired p and s densities in simple free-radicals

depends on the hybridization and hence leads to an estimation of bond angles

[ 6 ] . Often hyperfine coupling to ligand-magnetic nuclei in transition metal

complexes, when the unpaired electron 'formally' occupies a metal orbital and

orbital can lead to an estimate of the covalence of the metal ligand bonds.

In systems wlth Inore than one unpaired electron, the spin-degeneracy

is removed even in the absence of external magnetic field by second spin-

orbital coupling known as the zero-field interaction. This is also a dipolar

type interaction and expressed in the spin Haniltonian as

ZSS = D[s,'-I/~ S(S-I)] - E(s,' - s:)

= D ~ ~ s , , ~ rD!!SP? -Dusu: ----[I ,231

The D,,'s are the principal values ot' the D-tensor and E is an asymmetry

parameter depending on rhr deviarlot~ ui' the D-tensor from axial symmetry.

The relative mayl tude of D and gpB is to be noted in any perturbation

treatment of the spin-Hamiltonlm.

The quadmpolar rcnn in the spin-Hamiltonian is quite

analogous to the zero-field terms and is give by

20 = ~ ~ ~ 1 , ' - Q ~ ~ I ! ' ~~i~

=Q'[I,! -1!3 1 (l+i)] -Q" [I,?-I,'] ----[I ,241

where Q,,'s are the principal values of the quadrupole coupling constant

tensor. Here, Q' is similar to D and Q" to E. The quadmpolar interaction

affects the EPR spectrum in two ways. Firstly, since there will be a

competition between the electric field gradient at the nucleus and the

hyperfine field to quantize the nuclear spin-angular momentum about their

respective axis, the / m p ' s are no longer good quantum numbers: hence the

selection rule AMs = ?I, Am1 = 0, is no longer valid and 'forbidden'

transitions with Am1 = 11, f2 become allowed. Secondly, q u a d ~ p o l a r effects

cause the intensities of normal transitions and hqperfine spacing to become

unequal, the latter showing progressive increase or decrease from the ends

towards the center. in slngle crystals, especially when the external field is

perpendicular to the s,mmetry axis, the analysis becomes difficult due to the

preaence of intense forbidden tranaittons [15]. In the present thesis, we have

examined some first row transition ions in tlistorted octahedral environments.

I:ro~ii our rcuulth. ~ l i c clti,~tIrt~l)olai' cl'fccts kcem to bc small and a complete

analysis of the spectra a i th the inclusion of quadrupolar terms has not been

attempted.

An important theorem. which helps to predict the observability of EPR

spectrum, is Kramer's theorem [I31 which states that a purely electrostatic

field c2n nevcr rcducc the degencracy of the system, if it has an odd number

of electrons. Such degencracy as remains (generally two-fold) can be lifted

only by an extemai magnetic field. Another concerned theorem is the one due

to Jahn and Teller [I41 according to ~ h i c h any symmetric non-linear molecule

with an orbitally degenerate ground state undergoes such a distortion as to

remove the degeneracy including spin-degeneracy, limited only by Krarner's

theorem. Excitcd states may still be only a few hundred cm" above, leading

to short spin-lattice relaxation time (vide injra). Thus octahedral complexes

with d3, high spin dS and d7 give narrow EPR lines at room temperatures. The

other dn system (S>I) must be studied at low temperatures except in cases

where ground state is orbitally non-dcyenerate.

An appropriate choice of the spin Hamiltonian based on the symmetry

of the paramagnetic species often leads to a correct solution of the spin

Hamiltonian parameters such as g, A, D, Q etc. The parameters are also

derived theoret~cally from the knowledge of the ground state molecular orbital

and optical spectroscopic data w~th the use of perturbation theory. The

methodology of obtainirig M.0, coi.i'ficients from the observed magnetic

rcsonancc porilinctcrs OULC bccn dcsc~ihcd in dctail in the literature [16,17]. It

I > possible, i n f;l\orahlu case>, thcrcfore to obtain bonding parameters for

transition metal complexes from EPR data.

Crystal field parameters for d electrons:

Both dl and d' systems have a single unpaired electron in the

outermost d-orbital and hence, give rise ro 'D in the free ion state. The energy

level splitting for dl and d" systems IS the same but the ordering of the energy

levels is inverted tbr both Ions in any symmetry like octahedral, tetrahedral,

square planar etc. In octahedral symmetry, six ligands are arranged

octahedraily around tho central d-metal ion and it is clear that the repulsive

forces exened by the ligands would be strongest along the directions of the X,

Y and Z- axes, because in Oh field all ligands are aligned along X, Y and Z-

axes. We know that dx'-i2 and d: orbitals (known as e, set) of the d-metal

ion are aligned along the X, Y and 2- axes respectively and the remaining d,,,

d, and d,, orbitals (known as tzg set) are directed along lobes between the X,

Y and Z- axes. In other words, in 01, field, the repulsion effects on orbital eg

will be more than on the tr, set. As a result, the 'D term splits into e, and tz,

levels in Oh field. Fibures 1.2 and 1.3 show the splitting of d-orbitals under

various symmetry environments of the metal ion. In the case of d9 electron,

where the t2, level is lower, then in the Oh field, the two levels have the

cnergles

< t!, I Voc, I > - - 4Dq

< c, 1 v,,, 1 e, z = 6Dq

The energy difference between thesc two levels is 10 Dq, where Dq is a

measure of the interaction of the ion with the crystal field and is usually

treated as a semi-empirical parameter wh~ch can be obtained from the

experimental results. 'The Dq value in any complex depends on the

geometrical shape, the nature of rhe central metal ion and the nature of the

ligands, The Dq value for an octahedral complex is greater that that of for a

tetrahedral complex within the same ligands, which are at the same distance

from the central ion. This is because of the geometrical shape and also the

number of ligands present in the complex 1211. Dq also depends on the

effective charge (Z,I~) and the valency of the central metal ion. This effect is

probably due to the fact that the central metal ions with higher charge will

polarize the ligands more effectively. The ligand field effects contribute more

A A (cube) = -8/9 b(oct)

& Dq(cube) = -819 Dq(oct)

A(tetr)= -4@ A ( ~ c t ) Dq (tetr) = -419 Dq (oct)

N

Octahedron Cube Tetrahedron

Figure 1.2: Schematic representation of the splitting of d-orbitals under

various crystal field s)mmerries.

Figure 1.3: Crystal field splitting of the d-orbitals in (a) octahedral (b)

octahedral with tetragonal distortion (c) square planar and (d) distorted square

planar.

to the vanatlon In D ralue for d glven central Ion and a gtven geometry A

llgand exenlng a strong field w~l l gi\e a low Dq value

Honever, many complexes seem to possess symmetry lower than

octahedrll Devlat~ons from octahcdrdl symmetry are usually treated as

perturbations on the hlgh symmetry and would cause spl~nlng In the

degenerate levels da shown In F l y r e 1 3 In the present Investlgatlon, the

symmetry of the metdl Ion\ In all the latt~ces 1s lower than octahedral In such

d \ltu~tlon, the ground hurt 15 not purclq due to a s~ngle d-orb~tal, because, the

orbital contnbutlon to the cpln Ham~ltonlnn IS due to the mixlng of the excited

stdte wdvc iunitivn with the ground ';tare through sp~n-orb11 coupllng

Therefore, in the most generdl i~tudtlon, the b~ound state IS the h e a r

ioli?hlnntion (it ,111 fi\i riihlt.ll\ k ~ t h o u t rc\ortlng to any \ynimctrq

~onalderatlons, the coetiii~enti of thc d-orbitals and hence the b~ound state

i 4 n be cal~ulnted ualng thc procedur~ de~cioped by Swalen et a1 [22] They

used the cxper~mcn~dllq ohsened g-~alues to detenn~ne the five coeffic~enta

of the Krdmers doublet There Are only three g-values dnd a normal~zat~on

cond~t~on to detcnnine f i ~ e cocitii~cnts The fifth equation 1s obtalned by

ri>su~il~~lg t l i ~ ioctt i~lcnt\ oi tlic (I, , JIKI d,, nrbltals to be c q u ~ l

Ilclaxntion [IX]:

In the spln Hamllton~an formal~sm outllned above, the paramagnet~c

entltles are considcrcd na In isolation Such Ideal system of 'non-~nteract~ng'

splns is hardly ever dttalnablc In practlce The lnteract~ons among

d # b d n g spins spoil the coherent precession of the net magnetization

vlstor &out B, leading to time-independent transitions. Also the systems of

spins an energetically coupled to the 'lattice' via spin-orbit lattice interaction

which affects the life-time of the excited state by transfemng the energy to

lattice via radiationless processes. In an exact solution of the dynamics of the

energy transfer between the microwave field and the magnetic dipoles, these

two processes have to be tnken into account [19].

The spin-lattice relaxation, or the longitudinal relaxation (TI),

measures the efficiency wtth which the spins can transfer their energy to the

surrounding medium. The energy of the magnetic dipoles is not conserved in

this process and leads to the establishment of spin populations governed by

Boltzmann distribution.

The spin-spin relaxation or transverse relaxation time (T2) is a measure

of the raae a! which the asiembly of spins comes to internal equilibrium at a

given temperature, and bears no immediate relationship to the lattice

temperature. The energy of the system is conserved in this process. The spin-

spin relaxation controls the natural width of resonance when complication

from 'saturation' does not occur.

In ideal paramagnetic systems, the Tz process leads to very broad

resonance and often these may be even beyond detection. Usually,

paramagnetic compounds are doped into isomorphous diamagnetic host-

lattices to reduce the dipolar broadening. The spin-lattice relaxation is more

of a property of the individual system and can be altered only by temperature

vanatlon Due to the presence of local tluctuatlng magnetlc d~poles, not all

the splns In an ensemble have the same Ldrmor frequency In other words,

even ~f phase coherence of all spins is achleved by some external perturbat~on,

very soon thls coherence will decay (I e , the phases of the sptn become

randomized) w ~ t h charactenstlc first order kinetlcs This process, which IS

respons~ble for natural llne w~dth or resonance absorpt~on, 1s known as the

spln-spln or transverse reldxat~on tlme, T2 NOW, we wtll ISC CUSS the factors

responsible for llne w~drh in sollds and 11qu1di

L ~ n e widths in Solid,

There are lour poss~ble tdctors thdt ~ontnbute to the Ilne w~dth of EPR

absorption llnes for solid samples

a Anisotropy of g factor and hpertine lnteractlon or spln - spln

lnteractions

b Intera~tlon v ~ t h magnetlc dlpole of netghbonng electronic and

nucledr splns

c Exc~lange InterdLtion with neighboring unpalred electrons

d Spin - l a t t ~ ~ r . dnd spln - bplll relaxation tlmes (TI and T2)

One or more of these tdctors may be major contributors to the w~dth and shape

of the absorption 11ne The first IS Important only for powder samples In

w h l ~ h the smdl ~rystdls have a random onentarton If the anlsotropy In g and

the hypertine interaction or the presence of zero field spllttmg are the main

factors In determining the llne wldth, the powder will have a wldth and shape

determined by these parameters. In this case, the method needed to obtain

narrower lines is to use single crystals rather than powder. If a single crystal

study is not possible, information about g and the hyperfine interaction can be

obtained from the broad powder spectrum.

The second factor can be a significant one, since the magnetic field

produced by an electron at a distance of 0.4 nm is approximately 60 mT.

Since the field of a magnerlc dipole depends on the third power of distance, a

si~nplc way to reducc thc broadening is to study in an isomorphic crystal,

which is dialnabmetic. The magnetic nuclear ,pin in the compound can also

produce broadening. I f the neighboring ele:tron spins are close enough to

have their orbital overlap appreciably, an exchange interaction will occur

between the splns. When this interaction is greater than kT, it primarily

influences the line shape of thc EYR spectrum. if the exchange interaction is

large, the effect is similar to what ac expect if the electrons are free to move

throughout the crystal. The electron sees an average of all local sites in the

crystal, giving rise to narroa lines in which all the interactions are averaged

out. This exchange narrowing is a common occurrence for solid free radicals,

which often have sharp EPR lines. S~nce the exchange interaction is strongly

dependent on the distance between the magnetic lines, it is not present is

magnetically dilute systcms.

The time constant associated with the role of transfer of energy of the

crystal lattice is cclllcd the spin-lattice relaxation time (TI). For the systems

where the spins are strongly coupled to the vibration modes (short TI), the

lifetime of a given magnetic state is short resulting in an uncertainty in the

energy, which manifests as a broad-spectrum line in the EPR spectrum. This

particular broadening mechanism is strongly dependent on temperature so that

line broadened in this manner can be sharpened by lowering the temperature

of the sample. Extremely short TI often occur when the ion has an electronic

excited state only a few cm-' above the ground state. In these cases, it is often

necessary to measure the EPR spectrum at liquid-helium temperatures.

Line widths in Liquids

In liquid solutions. the concentration of the transition metal ions is

kept small enough so that the magnetic dipole interaction and exchange

interaction can be minimized. Thus (a) and (d) are the only important

contributions to the absorption line width. (a) is important only when the

tumbling rate for the ion and any attached ligands is not rapid enough to

average out any aniaotropv. The frequency of the tumbling must be longer

than the width of the absorpt~on line to have all the anisotropies averaged out.

In some cases, the tumbling rate is not sufficient to obtain complete averaging

and hence one observes broad 11nes.

It is to bc notcd hcrc that space-averaged and time-averaged species

will give different EPR spectra. In the case c,f paramagnetic species in

solution, each entity exhibits a time-averaged response. This will give rise to

a narrow EPR 11ne. On the other hand, a powder can be considered as a space-

averaged species. In this case, each center contributes its own resonance

position, depending on the orientatlon and the result is a broad line.

Magnetically and chemically inequivalent sites:

A paramagnetic system with anisotropic g and A tensors will give rise

to EPR resonance depending on the orientatlon of the magnetic field B with

respect to the tensor axes. In single crystals, depending on the space group

and the number of molecules per unit cell (Z), there will be several different

spatial orientations of the paramabmetic sites. Species that are chemically

identical (i.e., they are described by identical spin Hamiltonian parameters)

but are spatially oriented differently are referred to as magnetically distinct

sites. It is also possible that due to charge compensation process [20] in the

lattice, depending upon different relative contigurations of the 'radical

vacancy' directions, there exists rnany different sets of spin Hamiltonian

parameters (although these may differ only slightly). The species themselves

would be expected to be identical H hen the charge-compensating vacancies

are not taken into account. Such sites are referred to as chemically distinct

sites. These chemically distinct sites are necessarily magnetically distinct,

whereas the converse need not necessarily hold. In the present thesis,

chenlically and mabvetically different sites in the case of powder spectrum of

VO(11) doped in cadmium sodium phosphate hexahydrate have been identified

(discussed in detail in Chapter 5).

In the present thesls, slngle irystal EPR studies of VO(l1) doped In

d~amagnetlc host lattl~os, such a. Mapeslum Ammonlum Phosphate

Hexahydrate, Cadmlum Potass~um Phosphate Hexahydrate and Cadm~um

Sodlum Phosphdre Hexahydrate ha\e been undertaken and the results are

discussed In detall In Pan .4, as Chapters 3, 4 and 5 respectively EPR results

of paramagnctrc Ion\ I I I paramngnetlc host latt~ces arc presented In Pan B,

whrch contalns Chapters 6. 7 , 8 and 9 S~ngle crystal EPR studies of VO(I1)

doped in Heialm~dazole Cobalt Sulphate are presented In Chapter 6. Chapter

7 contalns the EPR rcsulis due to Mn(I1) doped Into Cobalt Sod~um Sulphate

Hexahydrate Further, s~ngle crystal EPR results of NI(II) lmpunty In

Hrxd1m1da7ole Cobalt Y ~ t r ~ r e l'srr~hqdrate are d~scussed In Chapter 8

F~nally in Chapter 9. the results on the s~ngle crystal EPR studles of Cu(l1)

doped In Coblit Amrnc~nluni Phosphate hexhydrate have been d~scussed All

the dlamabnetlc host systems have becn studled at room temperature. whereas

\,anable temperdturc EPR ,tud~es arc a150 carned out to calculate the spln-

lattice relaxat~on tlmes for pararnapetlc host iattlces

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