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Far-infrared absorption due to U-centres in cerium halides
Solid State C o m m u m c a t m n s ,
Vol. 11, pp 1 7 1 9 - 1 7 2 1 , 1972.
Pergamon P r e s s .
P r i n t e d m Great B r i t a i n
F A R - I N F R A R E D ABSORPTION DUE TO L'-CENTRES IN CESIUM HALIDES P N Ram and Bal K A g r a w a l P h y s : c s Department, Un!verstt~ of A l l a h a b a d , A l l a h a b a d , India
(Received 21 September 1972 b)' q R !/erma)
The i m p u r i t y - i n d u c e d far-infrared a b s o r p t i o n due to 6~-centres (Hi o n s ) m band mode reglon of c e s m m h a h d e s has been c a l c u l a t e d using a d e f e c t model which has e a r l , e r been found to e x p l a m the m f r a , e d l a t t i c e a b s o r p t i o n expenmm, t s . E x p e r i m e n t s are required to be performed m far l ~ r a r e d r e g m n to d e t e c t the p r e d i c t e d a b s o r p t m n
I INTRODUCTION THE F A R - I N F R A R E D a b s o r p t i o n m e a s u r e m e n t s b? S m v e r s 1 on KI c r y s t a l s c o n t a m m g L-centres showed the p o s s t b z h t y o{ some s t r u c t u r e m a b s o r p tion by m-band F~,~ modes D e t a i l e d e x D e n m e n t a i and t h e o r e t i c a l s t u d m s of m-band a b s o r p t i o n due to (u-centres m p o t a s s i u m h a h d e s have been made by ~oI1 et al 2 T h e s e l n v e s t t g a t , o n s w e r e , ! a t e r on, e x t e n d e d to s o d m m h a h d e s by Macpherson and Tlmusk 3 So far no measurement of a b s o r p t m n due to U - c e n t r e s m-band mode r e g m n h a s been reported m the c a s e of c e s t u m h a h d e s although d e t a i l e d e x p e n m e n t a J s t u d m s of the a b s o r p t i o n of the l o c a l modes of H- and D- c e n t r e s have been made by Mltra arid h!s c o w o r k e r s a and more r e c e n t l y by O l s o n and Lynch s In the present communication, we prese~,t the c a l c u l a t e d far infrared a b s o r p t i o n m the band mode region of c e s i u m h a h d e s produced by U - c e n t r e s (H-)
2 THEORY
(nL
-
2) 2 4-r~'
9n(a,)
p\e*'-
c~O_ (_~ _ ~2)2
[ i
t0o(z) =V
8
16
16\ 2
[~-l-_ t'' +~77 t ~ -~-7 t3~ 8 t, \'(~1_ ~t_) ~
- -
4\2 } t,~ \'(~L ~I_ )
~t_
'
t2~
(2)
where t w are the matrix elements of the matrix in the F,,~ irreducible representatmn In writing the above T-matrix only nearest-nelghbour tnteractmn has been considered. The T matrix is determmed by
t(z) = p(~)
The i m p u r i t y - r e d u c e d infrared a b s o r p t i o n in a s o h d of C s C I s t r u c t u r e isS (~)
is velocity of hght and [I Is volume of an umt cell. The quantity ~ ( = M. W_/M_ - ~I-) is the reduced m a of the two tons m tbe umt cell, M- and ~I_ being the masses of the alkali and halide ions, respectlvely p is the fractlonal concentratlon of the Impurlt~ m the crystal, '~ is the number of unit cells and e ~ is the effective change of anion ~'o denotes the transverse optmal frequenc} of the host lattice The element of T matrix is given by
[I - g(z) p(z~)]-',
(3)
where p(~,z) and g(z) are the perturbatmn and Green's functmns matrices m the Impurity space of single defect, respectively
Im to~ (z) , 3 C A L C U L A T I O N AND R E S U L T S
(1)
The infrared a b s o r p t i o n due to 6 ' - c e n t r e s h a v e been c a l c u l a t e d by using e q u a t i o n (1) for a impurity
where r ~ and n(~) are refractive mdmes at Mgh frequencies and at frequency ~, respectively, c 1719
1720
L-CENTRES
-I
C~Cl 4
IN C E S I U M H A L I D E S
~
frequenc~ s~
The v a l u e s of the G r e e n ' s f u n c n o n s
appropriate for a negatl~el~ charged lmpunt~ in c e s i u m h a h d e s ha~e been c a l c u l a t e d r e c e n t l y ~ T h e e f f e c t l ~ e charge e ~ has been taken to be e q u a l to S z l g e t l e f f e c t l , , e charge ez the host cr~stal
0
C~8,
E' ~
12
c o n c e n t r a t : o n Df 0 l m o ! e m In the c a i c u l a t : o ~ ~ e ha~e ut~hzed the chapge m c e n t r a l force const an t determined e a r h e r b~ L-cent:e l o c a h z e d
I
-I
%'oi ii, No
r
t~ 121
0
-I
I
,
I 20
J
160 I
Fte~uenc F (Cm-~)
FIG 1 R e a l part of r e s o n a n c e denominator DE1, (z) in F,,o ~rreducible r e p r e s e n t a t m n
]
ToLCsa,) 5
"4 o3
~ {C$I)i--a
Fre~uenc 9 (CRY')
FIG 2 Calculated absorptmn spectra in (a) CsCI H- 0 Imole %, i = - 0 8 5 8 x 1026sec -2, Co) CsBr H- 0 Imole %, k : - 0 384 >, I02~ sec -2, and (c) Csl H- 0 Imole %, ,\ = - 0 18 i0 2~ sec -z A represents the central force constant change
The real part of the r e s o n a n c e denominator for the three s ~ s t e m s has been p!otted m F!g 1 One may o b s e r v e that no r e s o n a n c e mode appears b e l o ~ r e s t r a h l e n frequenc~ m all ".he three s ~ s t e ~ : 1 e CsC1 H-, CsBr H- and CsI H- The c a l c u lated far infrared t a t t m e a b s o r p n o n ha~e been shown m F i g 2 In C s C l H - , there is an appreciable a b s o r p u o n b e t w e e n the reglon 5 0 - 7 5 c - In C s B r the L -centre g i v e s s l g n l f : c a n t absorption b e t w e e n 45 and 6 5 c m - ' and there occurs a sharp peak near 6 0 c n In CsI H-, there does not occur any a p p r e c i a b l e absorptlop before r e s t r a h ! e absorptmn The e x p e r i m e n t a l m e a s u r e m e r t s m far mfrarec region are e x p e c t e d to r e ~ e a l l a t t . c e absorption m CsBr and CsCI -lckpowled~e~,:e~s - Th e authors are thankful to the C o u n m l ot S c l e n t l h c and Industrial R e s e a r c h , Ne~ D el h l for h n a n c l a l asslstar~ce
Vo[ Ii, No. 12
6-CENTRES
IN C E S I U M H A L I D E S
1721
REFERENCES 1
SIEVERS A J , Lo',~ Tep,~eratL~re P ; o s l c s LEd~ted b~ DAUNT ] G , EDWARDS D O , \ I I L F O R D F . ] and YAQUB ~,I ,), LT9, Pt B, p 1170 Plenum P r e s s , New York (1965) ~ O L L JR, E ] , GETHINS T and TI'vlUSK T , C m z a d
]
Ph,,s
46, 2 2 6 3 (1968)
3
MACPHERSON R ~{ , TIMUSK T , C a n a d
4
'vlITRA S S and BRADA Y , P / n s 178, 1492 (1969)
5
OLSON C G and LYNCH D ~ , P;z; s
Re~
6
RAM P N and AGRAWAL B A L K , ]
Ph< s
7
RAM P N and A G R A W A L B A L K , S o h d S t a t e C o m m u n
8
AGRAWAL B A L K
9
RAM P N , D P h i l T h e s i s , u n p u b h s h e d A l l a h a b a d U m v e r s t t y (1972)
Re~
]
Ph~s
48, 2917 (1970)
145, 62 (1966), DOTSCH H and MITRA S S , P h ~ s B4, 1990 (1971) Che,z,
and RAM P N , Ph>'s Re~
Sohds
33, 957 (1972) 10, 1111 (1972), ~b¢d
l l, 93 (1972)
B4, 2774 (.1971), tbCd BS, 2335 (1972)
L ' a b s o r p t l o n mfra-rouge-@lotgne c a u s 6 e par des lmpuretes et dfie aux c e n t r e s - 0 (ions H - ) dans ia region en b a n d e d e s halog@nes de c e s m m , a ete c a l c u l e e a l ' a l d e d'un modele de d6faut qm a~alt e x p h q u e les e t u d e s e x p e r i m e n t a l e s f a l t e s sur le r 6 s e a u d ' a b s o r p n o n rafts-rouge I1 est n e c e s s a l r e de falre d e s e x p e r l e n c e s darts la regton mfra-rougee l o : g n e pour pou~o~r d e t e c t e r l ' a b s o r p t t o n e n w s a g 6 e
Re~
Vol. 11, pp 1 7 1 9 - 1 7 2 1 , 1972.
Pergamon P r e s s .
P r i n t e d m Great B r i t a i n
F A R - I N F R A R E D ABSORPTION DUE TO L'-CENTRES IN CESIUM HALIDES P N Ram and Bal K A g r a w a l P h y s : c s Department, Un!verstt~ of A l l a h a b a d , A l l a h a b a d , India
(Received 21 September 1972 b)' q R !/erma)
The i m p u r i t y - i n d u c e d far-infrared a b s o r p t i o n due to 6~-centres (Hi o n s ) m band mode reglon of c e s m m h a h d e s has been c a l c u l a t e d using a d e f e c t model which has e a r l , e r been found to e x p l a m the m f r a , e d l a t t i c e a b s o r p t i o n expenmm, t s . E x p e r i m e n t s are required to be performed m far l ~ r a r e d r e g m n to d e t e c t the p r e d i c t e d a b s o r p t m n
I INTRODUCTION THE F A R - I N F R A R E D a b s o r p t i o n m e a s u r e m e n t s b? S m v e r s 1 on KI c r y s t a l s c o n t a m m g L-centres showed the p o s s t b z h t y o{ some s t r u c t u r e m a b s o r p tion by m-band F~,~ modes D e t a i l e d e x D e n m e n t a i and t h e o r e t i c a l s t u d m s of m-band a b s o r p t i o n due to (u-centres m p o t a s s i u m h a h d e s have been made by ~oI1 et al 2 T h e s e l n v e s t t g a t , o n s w e r e , ! a t e r on, e x t e n d e d to s o d m m h a h d e s by Macpherson and Tlmusk 3 So far no measurement of a b s o r p t m n due to U - c e n t r e s m-band mode r e g m n h a s been reported m the c a s e of c e s t u m h a h d e s although d e t a i l e d e x p e n m e n t a J s t u d m s of the a b s o r p t i o n of the l o c a l modes of H- and D- c e n t r e s have been made by Mltra arid h!s c o w o r k e r s a and more r e c e n t l y by O l s o n and Lynch s In the present communication, we prese~,t the c a l c u l a t e d far infrared a b s o r p t i o n m the band mode region of c e s i u m h a h d e s produced by U - c e n t r e s (H-)
2 THEORY
(nL
-
2) 2 4-r~'
9n(a,)
p\e*'-
c~O_ (_~ _ ~2)2
[ i
t0o(z) =V
8
16
16\ 2
[~-l-_ t'' +~77 t ~ -~-7 t3~ 8 t, \'(~1_ ~t_) ~
- -
4\2 } t,~ \'(~L ~I_ )
~t_
'
t2~
(2)
where t w are the matrix elements of the matrix in the F,,~ irreducible representatmn In writing the above T-matrix only nearest-nelghbour tnteractmn has been considered. The T matrix is determmed by
t(z) = p(~)
The i m p u r i t y - r e d u c e d infrared a b s o r p t i o n in a s o h d of C s C I s t r u c t u r e isS (~)
is velocity of hght and [I Is volume of an umt cell. The quantity ~ ( = M. W_/M_ - ~I-) is the reduced m a of the two tons m tbe umt cell, M- and ~I_ being the masses of the alkali and halide ions, respectlvely p is the fractlonal concentratlon of the Impurlt~ m the crystal, '~ is the number of unit cells and e ~ is the effective change of anion ~'o denotes the transverse optmal frequenc} of the host lattice The element of T matrix is given by
[I - g(z) p(z~)]-',
(3)
where p(~,z) and g(z) are the perturbatmn and Green's functmns matrices m the Impurity space of single defect, respectively
Im to~ (z) , 3 C A L C U L A T I O N AND R E S U L T S
(1)
The infrared a b s o r p t i o n due to 6 ' - c e n t r e s h a v e been c a l c u l a t e d by using e q u a t i o n (1) for a impurity
where r ~ and n(~) are refractive mdmes at Mgh frequencies and at frequency ~, respectively, c 1719
1720
L-CENTRES
-I
C~Cl 4
IN C E S I U M H A L I D E S
~
frequenc~ s~
The v a l u e s of the G r e e n ' s f u n c n o n s
appropriate for a negatl~el~ charged lmpunt~ in c e s i u m h a h d e s ha~e been c a l c u l a t e d r e c e n t l y ~ T h e e f f e c t l ~ e charge e ~ has been taken to be e q u a l to S z l g e t l e f f e c t l , , e charge ez the host cr~stal
0
C~8,
E' ~
12
c o n c e n t r a t : o n Df 0 l m o ! e m In the c a i c u l a t : o ~ ~ e ha~e ut~hzed the chapge m c e n t r a l force const an t determined e a r h e r b~ L-cent:e l o c a h z e d
I
-I
%'oi ii, No
r
t~ 121
0
-I
I
,
I 20
J
160 I
Fte~uenc F (Cm-~)
FIG 1 R e a l part of r e s o n a n c e denominator DE1, (z) in F,,o ~rreducible r e p r e s e n t a t m n
]
ToLCsa,) 5
"4 o3
~ {C$I)i--a
Fre~uenc 9 (CRY')
FIG 2 Calculated absorptmn spectra in (a) CsCI H- 0 Imole %, i = - 0 8 5 8 x 1026sec -2, Co) CsBr H- 0 Imole %, k : - 0 384 >, I02~ sec -2, and (c) Csl H- 0 Imole %, ,\ = - 0 18 i0 2~ sec -z A represents the central force constant change
The real part of the r e s o n a n c e denominator for the three s ~ s t e m s has been p!otted m F!g 1 One may o b s e r v e that no r e s o n a n c e mode appears b e l o ~ r e s t r a h l e n frequenc~ m all ".he three s ~ s t e ~ : 1 e CsC1 H-, CsBr H- and CsI H- The c a l c u lated far infrared t a t t m e a b s o r p n o n ha~e been shown m F i g 2 In C s C l H - , there is an appreciable a b s o r p u o n b e t w e e n the reglon 5 0 - 7 5 c - In C s B r the L -centre g i v e s s l g n l f : c a n t absorption b e t w e e n 45 and 6 5 c m - ' and there occurs a sharp peak near 6 0 c n In CsI H-, there does not occur any a p p r e c i a b l e absorptlop before r e s t r a h ! e absorptmn The e x p e r i m e n t a l m e a s u r e m e r t s m far mfrarec region are e x p e c t e d to r e ~ e a l l a t t . c e absorption m CsBr and CsCI -lckpowled~e~,:e~s - Th e authors are thankful to the C o u n m l ot S c l e n t l h c and Industrial R e s e a r c h , Ne~ D el h l for h n a n c l a l asslstar~ce
Vo[ Ii, No. 12
6-CENTRES
IN C E S I U M H A L I D E S
1721
REFERENCES 1
SIEVERS A J , Lo',~ Tep,~eratL~re P ; o s l c s LEd~ted b~ DAUNT ] G , EDWARDS D O , \ I I L F O R D F . ] and YAQUB ~,I ,), LT9, Pt B, p 1170 Plenum P r e s s , New York (1965) ~ O L L JR, E ] , GETHINS T and TI'vlUSK T , C m z a d
]
Ph,,s
46, 2 2 6 3 (1968)
3
MACPHERSON R ~{ , TIMUSK T , C a n a d
4
'vlITRA S S and BRADA Y , P / n s 178, 1492 (1969)
5
OLSON C G and LYNCH D ~ , P;z; s
Re~
6
RAM P N and AGRAWAL B A L K , ]
Ph< s
7
RAM P N and A G R A W A L B A L K , S o h d S t a t e C o m m u n
8
AGRAWAL B A L K
9
RAM P N , D P h i l T h e s i s , u n p u b h s h e d A l l a h a b a d U m v e r s t t y (1972)
Re~
]
Ph~s
48, 2917 (1970)
145, 62 (1966), DOTSCH H and MITRA S S , P h ~ s B4, 1990 (1971) Che,z,
and RAM P N , Ph>'s Re~
Sohds
33, 957 (1972) 10, 1111 (1972), ~b¢d
l l, 93 (1972)
B4, 2774 (.1971), tbCd BS, 2335 (1972)
L ' a b s o r p t l o n mfra-rouge-@lotgne c a u s 6 e par des lmpuretes et dfie aux c e n t r e s - 0 (ions H - ) dans ia region en b a n d e d e s halog@nes de c e s m m , a ete c a l c u l e e a l ' a l d e d'un modele de d6faut qm a~alt e x p h q u e les e t u d e s e x p e r i m e n t a l e s f a l t e s sur le r 6 s e a u d ' a b s o r p n o n rafts-rouge I1 est n e c e s s a l r e de falre d e s e x p e r l e n c e s darts la regton mfra-rougee l o : g n e pour pou~o~r d e t e c t e r l ' a b s o r p t t o n e n w s a g 6 e
Re~