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MÖSSBAUER EMISSION SPECTROSCOPY STUDIES OF TUNNELING CHEMICAL
RELAXATION
V. Goldanskii, R. Stukan
To cite this version:
V. Goldanskii, R. Stukan. MÖSSBAUER EMISSION SPECTROSCOPY STUDIES OF TUNNEL- ING CHEMICAL RELAXATION. Journal de Physique Colloques, 1980, 41 (C1), pp.C1-43-C1-50.
�10.1051/jphyscol:1980108�. �jpa-00219578�
JOURNAL DE PHYSIQUE Colloque C l , supplbment au n o 1, Tome 41, janvier 1980, page C 1-43
V.I. Goldanskii and R.A. stukan
I n s t i t u t e o f ChemicaZ Physics o f t h e Academy o f Sciences o f t h e USSR, Vorobjeuskoje Shausse, 2-b, Moscow, 117334, USSR.
Abstract
-
The method of Mgssbauer Emission Spectroscopy (MES) allows t o study the k i n e t i c s of chemical conversions ( e l e c t r o n and s p i n re- l a x a t i o n ) of' M6ssbauer e m i t t e r s i f the time of such conversionseC
i s comparable t o the life-time of l6asbauer l e v e l (
TC G ) .
Rateconstants of f a s t i n t e r i o n i c e l e c t r o n transf e r from 5 7 ~ e 2 " (HS-high s p i n s t a t e ) t o [ F ~ ( I I I ) ( c N ) ~ ] 3 - ( ~ ~ - l o w s p i n s t a t e ) i n the transf or- mation of !l!urnbull blue(TB) i n t o t h e Prussian blue(PB) were measured at 400-12 K by rapporteurs e t al. (Moscow-Helsinki group) and i t was found t h a t the r a t e of t h i s process reaches the low-temperature
p l a t e a u value below ca.50 K. The observations of the r a t e of s p i n re- l a x a t i o n (Hs-Ls) f o r various dipyridyl and phenantroline complexes of i r o n performed by Mains group a t 293-4 K a l s o have l e a d t o the revealing of low-temperature p l a t e a u of the r a t e of such conversions.
I n such a way the MES has opened new p o s s i b i l i t i e s of the s t u - d i e s of electron-nuclear tunneling which can be described on the base of the theory of the r a d i a t i o n l e s s e l e c t r o n t r a n s i t i o n s .
16ssbauer Emission Spectroscopy (MES) d e a l s with t h e e m i t t e r s of reso- nance
1(
-rays i.e. i t r e f l e c t s the s t r u c - t u r a l and dynamical p r o p e r t i e s of the atoms whose nuclei f i n d themselves i n the excited Mb'ssbauer s t a t e .The p o s s i b i l i t i e s of the study of r e l a x a t i o n a l changes of these p r o p e r t i e s a r e determined by the comparisoll be tween the life-time of Massbauer l e v e l
eM
andcharac t e r i s t i c r e l a x a t i o n time
2, .
A t T,..
<'$,
the r e l a x a t i o n proceeds mostly before the nuclear t r a n s i t i o n and theref ore the IzLrne-lntegral JbB ~ p e c tra(TIMES)
-
represent mainly the proper- t i e s of the e m i t t e r s which already have suffered the relaxation. Nevertheless the use of delayed coincidences c i r c u i t s with the r e s o l u t i o n timeq , < T ,
-i .e. the s t u d i e s of time-dif f e r e n t i a l ME s p e c t r a(TDMES)
-
opens a d d i t i o n a l p o s ~ l i b i l i t i e s of t h e s t u d i e s of f a s t r e l a x a t i o n , pro- c e ~ s e s .A t
?,.,>>%
the r e l a x a t i o n involves mainly the atoms with already deexcited nuclei i n W e i r ground s t a t e s , and t h e lVIES i s therefore deprived here of any a d d i t i o n a l informativi t y.
Thus, the most f avourable condition f o r the a p p l i c a t i o n s of the MES i n i t s
simplest TIMES v a r i a n t corresponds t o
T , " N ~ & .
Usual values of
tM
l i e within 10'~- 10-~Osec, the mosC developed case of 5 7 ~ e ( ~ 4 , 4 keV) corresponds t oh 'J 1 , 4 10-~sec, and the emission of re- sonance
[
-ray i s preceeded here by the K-cspture i n 5 7 with the f o m a t i o n of ~ ~ the short-lived( 2- 3 I2,5 nsec )I36,3 keV excited s t a t e ~ f and subsequent ~ ~ ~ eArticle published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1980108
c1-44 JOURNAL DE PHYSIQUE
emission of ca. 122 keV non-~Gssbauer f - r a y . Thus the use of delayed
d/
(122)( I 4 , 4 ) coincidences with the v a r i a b l e time of delay(TDBilES) opens here the pos- s i b i l i t y of the s t u d i e s of r e l a x a t i o n with c h a r a c t e r i s t i c times between
TP~2.EE
-
I O - ~ S ~ C andTp 3
Well-known are vsri ous chemical consequences of nuclear transformations
,
e.g, t h e "shake-off of the e l e c t r o n s h e l l s due t o the prompt change of nuc- l e a r charge and subsequent Auger-tran- s i t i o n s , Coulomb explosions of multiply iollised molecules, spot-heating, auto- ratti.olyeis e t c [I, 23, W s h a l l not e dis- c u s s here such processes (which a r e more- over usually completed before the popula- t i o n of I4,4 resonance Pe l e v e l ) and 57 w i l l r e s t r i c t ourselves j u s t by the che- mical relaxation.
That means t h a t we w i l l t r e a t the systems where the pre-bl$ssbauer nuclear conversion does not l e a d by i t s e l f t o the change of figands environment o r charge s t a t e of daughter ~ G s s b a u e r atoms
( 5 7 ~ e ) , which primarily a r e s t a b i l i z e d i n the same environment and valence s t a t e a s the parent ( 5 7 ~ o ) radioacfive atoms.
However some p a r t i c u l a r chemical (valence and s p i n ) s t a t e s being s t a b l e f o r the parent atom can w e l l be unstable f o r the daughter atom (with the e x c i t e d
~ g s s b a u e r nucleuer) and then the system w i l l tend towards the s t a b l e chemical
s t a t e i . e . i t w i l l undergo the chemical r e l a x a t i o n .
Two groups of chemical r e l a x a t i o n processes were found up t o now t o proceed with the l i f e - t i m e s comparable t o
ea
and t o be manifested theref ore i n MES:1,Change of the charge s t a t e of the daughter atom( Fe) i n compare t o the 57 p a r e n t atom ( 5 7 ~ o ) caused by the i n t e r i -
onic oxidation-reduction t r a n s f e r of elec;
trons,with the conservation of s p i n s t a t e a s e i t h e r the high-spin(HS)or the low- s p i n (LS) s t a t e
0-81.
2,Change of the s p i n s t a t e of the daughter atom( Fe) i n compare t o the 57 p a r e n t atom(*'~o) with the conservation
o f i t s charge s t a t e [9-161.
I. I n t e r i o n i c e l e c t r o n t r a n s f e r . A s i t i s w e l l known from the numero-
US absorption ~ $ s s b a u e r speotroscopy (US) d a t a ( s e e e.g,[g) the i n t e r a c t i o n s be-
tween HS f e r r i c and LS ferrocyanide s t a t - e s a s well as between HS f e r r o u s and LS f e r r i c y a n i d e s t a t e s l e a d t o the formation
of f e r r i f errocyani.de, Prussian blue (PB) Fe3+/l?e (XI) ( C E I ) ~ ] 4 - r a ~ e than of f e r r o - f erricyanide, Turnbull blue (TB)
F ~ ~ + / [ F ~ ( I I I ) ( c N ) ~ ] ~ - i.e. the e l e c t r o n i s promptly t r a n s f e r r e d from RS reducer
(Fez+ t o the LS o x i d i z e r ~ ~ e ( 1 1 1 ) ( c N ) ~ ] ~ - . The search f o r the short-lived TB by the methods of MES was based on the use of cobaltof erricyanide complexes 57~e2'/L~e(111) ( c N ) ~ ]
'-
a s Bournes i n TINrLES and T D ~ s (t=O-60 nsec) experiments.Preliminary e q e r i m e n t s with l a b e l - ed cobalticyanide sources
M ~ ~ / [ ~ ~ C O ( I I I ) 3- where
A ' + ITi2+. co2'.Cu 2 + , ~ e 3 + and with t h e 5 7 c o 2 + / ~ ~ e ( 1 1 ) i r n ) ~ ~ ~ - source have Indicated the formation af daughter 571?e atoms i n the same s t a t e s a s were parent 5 7 ~ o atoms [5,6]and
-
i n such away
-
they have demonstrated the elimina- t i o n of chemical a f t e r e f f e c t s of K-cap- t u r e i n 5 7 ~ 0 i n ME spectra.Cobaltof erricyanide 5 7 ~ 0 2 + / [Fe(111) ( c P ~ ) ~ ] 3- was used a s a source
€ind yellow blood sd.t IC4[Fe(11 ) ( c N ) ~ ] . 3 H20
-
a s an absorber i n f i r s t main experiments [3,4] .The r e s u l t s obtained at 77 K-
f o r both TIMES and TDMES(t = 0-60 nsec) v a r i a n t s
-
a r e presented i n Fig. I.Phe treatment of bES d a t a was based on the determination of the c o n t r i b u t i o n of broad ~ e doublet which could be ex- ~ + pected f o r the unstable TB, however w a s not observed i n absorption spectra.
Besides the change of the shape of s p e c t r a caused by the simple "steady- s t a t e w admixture of TB t o P B one could a l s o expect i n MES experiments the mani- f e s t a t i o n s of t i m e - f i l t e r i n g e f f e c t s
[17,18] a s well a s various d i s t o r t i o n s
with Helsinki group [B] (wiLh the
~ a ~ ~ ~ o ~ + [ ~ e (111)
(w)J
source).Figure I. ~ A s s b a u e r * emission s p e c t r a of cobaltof e r r i ~ ~ a n i d e s ~ ~ ~ o ~ + / ke(111) ( c N ) ~ ] ~ - a t 77 K. Upper: TIMES
(t= 0
-
00 ).
Lovrer: TDMES ( t t 0-60 naec 1.Harrow Fe3+ doublet and broad Fe2' doub- l e t a r e indicated.
(e.g. the broadening) of l i n e s caused by r e l a x a t i o n processes proceeding within
cr 6
[19-24.Nevertheless we have used f o r the crude estimate of the r a t e of e l e c t r o n t r a n s f e r the s i m p l i f i e d representation of the observed emission s p e c t r a by two undiatorted components
-
narrow ~ e (PB) ~ + and broad F'e2+ (TB) symmetric quadrupole/ /
doublets (supposing t h a t f pg= f T B ) v Under such asswnp ti on the f r a c t i o n of TB i n TDME s p e c t r a obtained with the g a t e of delayed
(Yb/
-coincidences fromt = 0 t o t E: f2 should be eaual to:
where
AZT;'
,K i s the r a t e constant of chemical t r a n s i t i o n ( TB-tPB),Po-
thei n i t i a l population of TB s t a t e .
'Nith the increasing 'ir the value of P should decrease approaching a t
e+
s,the value of PP, =Po x/(A+Y) c h a r a c t e r i s c t i c f o r TIMES measurements.
Results of such calculations of K values between 77 and 400 K a r e i l l u s t - r a t e d by the l e f t p a r t of the curve I a t Fig.2. Right p a r t of t h i s curve (baaed on the use of f o m u l a I ) and the curve 2 (based on the use of 1~akeleit~19]formu- l a s ) represent the d a t a obtained a t 77-12 K by TILIES method i n our j o i n t work
Figure 2. Temperature dep endenoe of the r a t e of TB(Turnbul1 blue) t o PB Prussian blue) t r a n s i t i o n . Rate cons- t a n t K i s given i n sec3.
Curve I
-
c a l c u l a t e d by the use of simp- l i f i e d formula: ,P = A/(A+)O from the d a t a of Refs. 3,4 ( l e f t p a r t ) and 8 ( r i g h t p a r t ) .Curve 2
-
c a l c u l a t e d by the use o f Kanke- l e i t f ormulas[19] from the data of Ref .%.A s i t can be seen Prom the Fig.2 the temperature dependence of the r a t e of e l e c t r o n t r a n s f e r from pe2+ t o Fe (XU) (Cf )6 i s gradually changing-f rom the Amheniu~l- type dependence above ca. 200 K ( 8 c t i v a ~ t i o n energy E reaches here the value of E ~ 0 , 0 2 5 eV) down t o the low-temperature p l a t e a u below ca. 50 K.
Such temperature dependence 09 the r a t e of e l e c t r o n t r a n s f e r i s t y p i c a l f o r the e l e c tron-nuclear tunneling which has a t t r a c t e d recently very w i d e attenkion
( s e e e.g. [22,23) ) and i s usually t r e a t e d i n terms of the theory of r a d i a t i o n l e s s e l e c t r o n t r a n s i ti ons
.
The p r o b a b i l i ty of a r a d i a t i o n l e s s e l e c t r o n t r a n s i t i o n Wif i s determined by the overlap of e l e c t r o n ( ) and nuclear v i b r a t i o n a l (
Yv
) wave f u n c t i o n s i n the i n i t i a l ( i ) and f i n a l ( f ) s t a t e s described-
respectively-
by the mat-r i x element of the e l e c t r o n t r a n s i t i o n
~t=I<t~ltIVt)l~
ana by the,
Franck-Condonfactor ~ s l ( ~ v ~ / ~ v ~ } / :
C1-46 JOURNAL DE PHYSIQUE
h
where L i s a t r a n s i t i o n operator such a s the non-adiabaticity operator and
J$
=
( k ~ p ) - ' i s the density of v i b r a t i-
onal l e v e l s i n the f i n a l s t a t e ( i t i s as- sumed t h a t the d i s s i p a t i o n of the h e a t of exothermic t r a n s i t i o n s i n s o l i d s i n the f o m of phonons proceeds very f a s t and
by no means can be t r e a t e d a s a rate-de- termining s t e p ) .
Figure 3. Scheme of e l e c tron-nuclear tunneling f o r e l e c t r o n t r a n s f e r from the donor(D) t o the acceptor(A).
a.The, tunneling of e l e c t r o n over the d i s t a n c e
!
under the b a r r i e r of t h e height Ee(levels i n D and A do not usually coin- c i d e ) .b. The displacement of nuclei over the distance d f o r the t r a n s i t i o n of the e l e c t r o n e ( ~ ) 4 e(A) i n d i c a t e d by ver- t i c a l arrow.
The scheme of e l e c tron-nuclear tun- neling i s shown a t Fig.3. The e l e c t m n p e n e t r a t i o n through the p o t e n t i a l b a r r t e r
of ,the width 1 and the height Ee i s accom- panied here by much amaller(d) b a r r i e r l e s s displacement of nuclei .However with the i n c r e a s i n g d, when the nuclear displace- ment strongly exceeds the amplitude of
the nuclear v i b r a t i o n s ( f o r the n-th vib- r a t i o n a l l e v e l of the harmonic o s c i l l a t o r ,
A ~ = V ! ~ C ~ ~ / M & "
where M i s n u c l e a r mass and &I-the c h a r a c t e r i s t i c vibra-t i o n a l frequency )
,
t h e p o t e n t i a l b a r r i e r appears f o r the nuclear t r a n s f e r too(see Fig. 41, and t h a t can r e s u l t i n t h e process of molecular chemical tunnel- i n g [23]. The wave f u n c t i o n s %(.y) a r e proportional t o exp(-x/ d ) ( f o r x S oC where a!=%/- and f o r
l>>d
thematrix element
: L
takes a f o m of the Gamov-type kunneli f a c t or:L:
3-u p ~ - ~ f -1k.3
where 1 (and depends on t h e shape of barrie;), m i s the e l e c t r o n mass.
" 1 /
Figure 4. Scheme of t h e tunneling displacement of the n u c l e i f o r t h e case of displaced ( i n both v e r t i c a l and horizon- t a l d i r e c t i o n s ) but u n d i s t o r t e d harmonic o s c i l l a t o r s . Transition heat i s indicated a s
A
E, a c t i v a t i o n energy-
a s EA.This expression f o r L; i s v a l i d f o r t h e low-temperature p l a t e a u while above
-
1t h e so-called "tunneling temperature"
12q T!,= (tc/~-,qiE'l) \ r w z
60 00fmyt (b)
t h e Arrhenius-type i s valid:
L:
Z=The wave functions LCv(&) a r e propor- t i o n a l t o exp
[- [&A)']
( f o r x>a
1,
andt h e r e f o r e t h e Franck-Condon f a c t o r a t d z A can be approximately expre~lsed a s
6 - e x p l - (=d/a)'.I ,
where 2 i s of t h e order of one.
Since the s t a t i s t i c a l l y averaged vibra- t i onal amplitude i n c r e a s e s with t h e tem- p e m t u r e
-
and f o r the harmonic o s c i l l a -t o r
(49
i s proportional t o T, the high-temperature behaviow? of the Franck- Condon f a c t o r s i s of drrhenius type f o r both b a r r i e r l e s s ( F i g . 3 ) and o v e r b a r r i e r (Fig .4 ) n u c l e a r displacement.With the decreasing temperature when 4 approaches the amplitude of zero-.
v i b r a t i o n s
4 , ,
t h e Pzanck-Condon f ac- t o r reaches a c e r t a i n minimum constantvalue ( a s the :L does) and t h a t r e s u l t s i n the appearance of the low-temperature p l a t e a u of the t o t a l rate(Wif) of the r a d i a t i o n l e s s e l e c t r o n t r a n s i t i o n .
For t h e simplest case of resonance nuclear t u n n e l i n g ( r \ ~ = 0 a t the Big.4).
the Franck-Condon f a c t o r takes a Gamov- type f o m ( s e e e.g.@!j]) and t h e "tunnel- i n g temperature" Tt which describes the gradual t r a n s i t i o n from the Arrhenius
(T
>
Tt ) t o tunneling ( T<
Tt ) regions f o r nuclear displacement would be e ual t oT + ~
= [ k h p c d ) V E T
20@/d (2)
f o r - - i r o n nuclei.
The s t r u c t u r e of f e r r i f errocyanide c r y s t a l s i s well-known and correeponds t o the d i s t a n c e of e l e c t r o n i n t e r i o n i c tunneling 1 d 5 0 A . The t y p i c a l energy of the charge t r a n s f e r from metal t o l i g a n d i n f irst-row t r a n s i t i o n metal complexes i s E,.v 4 eV 1163. Theref ore the Gamov- type tunneling f a c t o r f o r the parabolic b a r r i e r
( p = ~ E / 2
i s ca. 2,5.10-~.Meanwhile the t o t a l d e c e l e r a t i o n f a c t o r f o r the TB
-
PB conversion at the low-temperature plateau, where the r a t e con- s t a n t K
-
10~sec-', i s ca. 10'~. That means t h a t the contribution of the nucle- a r displacement (Franck-Condon f a c t o r ) t o such d e c e l e r a t i o n i s here p r a c t i c a l l y the same a s of-the e l e c t r o n tunneling:Fv N exp
l-(
~ d / dl 2
4 . 1 0 - ~The estimated value of ( a d / A o ) N 298 can be combined with t h e d a t a on t h e pro- b a b i l i t y of Mcssbauer e f f e c t f o r PB a t low temperatures : f'= exp
[-
(A,"/A~)J 2 0,6 where% =
0,148.
~ h u s
do r
0,18,
and I C ~ N 0 , 38.
This reasonable l a t t e r estimate together with E A % 0,025 eV would correspond i n t h e case of resonance nuclear displacement t o
Tt.&iOz
K and thus favours t h e conclusion t h a t j u s t t h e nuclear displacement r a t h e r than the e l e c t r o n t r a n s f e r i s t h e process which determines t h e appearance of t h e plateau i n t h e temperature dependence of t h e r a t e of TB-+PB conversion only below ca. 50 K and not a t higher temperatures(thermally a c t i v a t e d e l e c t r o n tunneling).
I n general t h e combination of t h e experimental d a t a on t h e plateau r a t e of
C1-47 chemical conversion (
ep - 1,
on f' -
value a t T 4 0 and on t h e temperature of t h e beginning of p l a t e a u can l e a d t o suf- f i c i e n t l y r e l i a b l e estimates of both and d.
2.Relaxation of s p i n s t a t e s . Relaxation of s p i n s t a t e s of i r o n
(Hs ~ L s ) w a s s t u d i e d by ~ i i t l i c h e t al.
by both TIMES p-15) and TDbES l16] me- thods f o r numerous dypiridyl and phenan- t r o l i n e complexes of f l ~ o l i s t e d i n the legend t o Fig. 5.
I
I
0 to0 2,oo T O K 300
Figure 5. Temperature dependence of the f r a c t i o n (
d
H S ) ~ J f HS(bigh s p i n ) s t a t e s of 5 7 ~ e 2 + complexes obtained from the ~ b ' s s b a u e r absorption s p e c t r a '(US)(dotted l i n e s ) and TIMES ( s o l i d l i n e s ) . 1 . [ ~ e ( 2 ~ 1 - p h e n ) ~
1
(C104)2. H20 1131.?.yPeCdlp~)~]2+ P41.
3. b e ( ~ h e n ) ~ I (ClO4I2 2 ~ ~ 0 k , 1 6 ] . 4 . f ~ e ( p r m ) ~ l (ClO4I2 l141.
5. p e ( 2 ~ ~ ~ - p h e n ) ~ ] (C104)2 [IO].
6. f ~ e ( 2 cH30-phen) 3] ( C104 H20
bd.
7. F e ( ~ h e n ) ~ (HCS)? 1261.
phen
-
I .IO-phenantroline; dipy-
2,2'-dipyridyl ; pmi
-
2-pgridinal-me thylimine.A l l coZ+ complexes represented i n Fig.5 b e e s t a b l e HS s t a t e s ( 'l?, ,Oh) while the ~ G s b a u e r absorption s p e c t r a
(MAS) of pe2+ complexes i n d i c a t e the exL- atence of t h r e e various c l a s s e s of such complexes:
1 ) Hs-state(weak ligand f i e l d ) i n the whole temperature i n t e r v a l 4-300 K
(curve I ) .
2 ) LS-state (strong ligand f i e l d ) a t 4-300 K(cumes 2,3,4)
3) Intermediate ligand f ield,more o r l e s s abrupt cooperative s p i n t r a n s i - t i on (cross-over)-f rom the domination of LS s t a t e t o the domination of HS s t a t e
C1-48 JOURNAL DE PHYSIQUE
a0 higher temperatures(curves 5,6,7).
NJSS method opens the p o s s i b i l i t y sf the c~bservation ef HHS
*
LS r e l a x a t i o n of 5 7 ~ e 2 * complexes since t h e gusdrupole daublet8 of LS s t a t e ('A, ) and of two HS s u b a t a t e s ( 5 ~ 1 , 5 ~ ) f e m e d by the s p l i t t i q g cf the (5~2,0h) HS s t a t e i n the f l e l d of D3 symetl.y k v e smewhat d i f f e r e n t is@- mer a h i i ts and qusdmpole s p l i t tings.The existence of the HS -c LS relaxa- t i o p of various 5 7 ~ e 2 + complexes i s i l l u - s t ~ 8 t e d i n Fig.5 by t h e excessive f rac- Oisncs (
d M s )
of HS s t a t e s i n MES a s com- pared with MAS. Moreever the d i f f e r e n c e s of-
(d,,s)Ms i n c r e a s e with the decreasing temperature demonstrating i n such a way that the s p i n-
r e l a x a t i o n r a t e i s temperature-
dependent.F i g w e 6. Temperature dependence of t h e m t e of s p i n r e l a x a t i o n ( H S a L S ) of 5 7 ~ e N .complexes. Curves 3.4.5.6. a r e ob- t d n e d by u s from the TIMES d a t a of G&- l i c h e t a l . (numbers of curves correspond t o the complexes l i s t e d i n the legend of Figure 5) by the simple treatment:
P
,
(LS)= h/O+
k1 .Curve 3a i s obtain- ed i n Ref. 16 by the use of Kankeleit C191 foyplu3as. Rate conskant K i s given i nsecw', N u e s of Ci (included t o avoid the overlap of curves) a r e equal to:
Ci = T , 2 (cumre 4 ) , I f c u r v e s 3 and 3 a), Q,S(curve 6) , ~ C o u w e 5 ) .
Such dependence i s shown i n Fig.6
-
f o u r curves a t t h a t f i g u r e have been ob- tained by u s from the TImS d a t a of Refs.
IO,I3,14,16 and the simplified expression
P,
= A ~ A + K ) ,curve 3a. rep roduced from Ref .I6 i s based on both TIMES and TDMES( % = 20,32,57,70,87 and I49 nsec) d a t a f o r [ ~ e (phen)
1
( C104 ) 2 H20 and on Kankeleit rIS]fomulas. 2 Again-
a s i n the abovedescribed case of i n t e r i o n i c e l e c t - ron t r a n s f e r (TB-PB)-
one can observe t h e gradual passage f mm the high- tempe- r a t u r e Arrhenius region (EzO,OI5 eV) t o the low-temperature plateau of s p i n re- l a x a t i o n r a t e .Figure 7. Lower a r t of the Tanabe- Sugano diagram of a d configuration i n
E
Oh symmetry. Two v a r i a n t s of H S A LS re- l a x a t i o n discussed i n Ref. I 6 correspond t o the t r a n s i t i o n s abd("horizontalN re- l a x a t i o n ) and abcd( ttverticallt 5 ~ 2 4'11, t r a n s i t i o n ) .
'Pwo v a r i a n t s of such r e l a x a t i o n a r e shown a t the Tansbe-Sugano diagram of a d 6 configuration i n Oh symmetry (Fig.7)
( s p l i t t i n g of 5 ~ a H S s t a t e i n t o two sub- s t a t e s i s not taken here i n t o account be- cause the t o t a l a r e a of two quadrupole
5 5
doublets ( A, and E) was used f o r the de- termination of t h e f r a c t i o n of HS s t a t e ) .
The h o r i z o n t a l r e l a x a t i o n along the abscissa a x i s (abd) i s t r e a t e d a s a con- sequence of the i n i t i a l formation of the p o s i t i v e l y charged phenantroline ligand
(due t o the a u t o r a d i o l y s i s ) with the i n - crease of the 3'e2+ - ' l i g a n d dietance (due t o the Coulomb repulsion) and correspon- ding weakening of the ligand f i e l d . Rela- xation i s caused i n t h i s case by the sub- sequent passing of an e l e c t r o n from the neighbouring C ~ ( p h e n ) ~ 2t complex t o a p o s i t i v e l y charged ligand and thus i t s r a t e can be described on the base -of the theory of r a d i a t i o n l e s s e l e c t r o n t r a n e i - t i o n s . Using the values of 1 ru 6 A 0 and Ee ~4 eV mentioned i n Ref. I 6 one can estimate here(from the r e l a x a t i o n r a t e a t the low-temperature p l a t e a u ) the d i s t a n c e of nuclear displacement as2d?2,5d20,25A 0
-
i n a f a i r l y c l o s e agreement with the d i r e c t determination UP the decrease of Fe-N distance i n LS a s compared with HS-
complexes (0,2
!
[27] 1.The v e r t i c a l r e l a x a t i o n (abcd) i s determined by the r a t e of strongly f o r - bidden slow ( A S = 2) t r a n e i tion:
5 ~ 2 + - 1 ~ 1 . The e l e c t r o n i s not t r a n s f e r r e d i n such s p i n t r a n s i t i o n s f o r any l a r g e d i s t a n c e s (i.e. here 1 <<d) and t h e r e f o r e one cannot speak about e l e c t r o n tunneling, However i t i s conserved the formal simi- l a r i t y of the expression f o r the t r a n s i - t i o n r a t e with the equation ( 2 )
-
matrixelement of the e l e c t r o n t r a n s i t i o n Le 2 should be replaced by the spin-orbit coup- l i n g matrix. element Vif 2 (see e .g.[28] )
.
A s long a s the spin-orbit coupling i r s a one-electron operator(which corres- ponds t o A S= 1 ), the
4s
= 2 t r a n s i - t i o n should be described by a secondorderterm s f the fform /
where { H ~ ~ ) i s the spin-orbit coupling i n t e g r a l , index C means the intermediate s t a t e , and A& i s the energy gap between tNs and e i t h e r i n i t i a l o r f i n a l s t a t e s . Fixing the abovementioned value of
2 d ~
0,25 (i.e. F V d Z.IO-~) one g e t s q u i t e reasonable value:V- P '
.v 7.1oU3
,i .e.{aso)
4 50-1 50 om-' a t A e a I eV.We had no i n t e n t i o n ts present a comprehensive survey of the MES s t u d i e s of chemical r e l a x a t i o n and r e s t r i c te d
ourselves by such conversiansl of i r o n coordination c onpounds wMc h could be t r e a t e d a s a kind of an electron-nucless tunneling.
Theyefore we have not discussed such r e c e n t i n t e r e s t i n g r e s u l t s a s the obser- v a t i o n of the time-dependent isomer s h i f t i n the ME s p e c t r a of 5 7 ~ o i m p u r i t i e s i n ZnS matrix l29) and the a p p l i c a t i o n af the hot luminescence theory, t o the t r e a t - ment of t h e ME s p e c t r a 1304.
W t e promising seem t o be the pros- p e c t s of MES a p p l i c a t i o n s t o b i o l o g i c a l
systems[22]. The f i r s t attempts of this kind were described recently by b a r Nath
(p.662 i n Ref. 22) i n connection j u s t t o the tunneling phenomena
-
namely t o the problems of molecular tunneling of Fe- atoms and l i g a n d s i n t h e conversions of heme-contdning proteins.We understand q u i t e c l e a r t h a t t h e abovementioned estimates of t h e d i s t a n c e s of nuclear displacement i n e l e c t r o n
-
nuclear tunneling processes and of spin- o r b i t coupling i n t e g r a l s i n slow s p i n t r a n s i t i o n s a r e very f a r from being r e a l - l y q u a n t i t a t i v e . Nevertheless we decided t o include t h e s e estimates i n our paper i n order t o demonstrate t h e general v a l i - d i t y of t h e treatment of a broad c i r c l e of M8ssbauer emission spectroscopy d a t a based on t h e theory of r a d i a t i o n l e s s e l e c t r o n t r a n s i t i o n s and on t h e concepts of various kinds of tunneling i n low- temperature chemical conversions i n s o l i d s .
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