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On the propagation of electromagnetic waves in a plasma with heavy positive and negative ions
Volume 19, number 7
PHYSICS LETTERS
a l l s u r f a c e s a r e e n t i r e l y diffuse, (2) t h e r e is no phonon-phonon s c a t t e r i n g , and (3) any effect of r o t o n e x c i t a t i o n is ignored. Then in the f i n a l exp r e s s i o n for A1 the c l a s s i c a l m o m e n t u m per p a r ticle P was r e p l a c e d by (3Pphc)4N where N i s the n u m b e r of phonons p e r cm~, c is the velocity_of sound, and Pph is the phonon density in g/cm-3. The smoothed liquid-4He data for this e x p e r i m e n t a r e given in table 1. We have c o m p a r e d A / ( e x p e r i m e n t a l ) with Lxl (calculated f r o m eq. 2) below 0.55OK. The c a l c u l a t e d v a l u e s for LXl might be expected to be higher than the e x p e r i m e n t a l v a l u e s s i n c e eq. (2) a s s u m e s only diffuse behavfour. A l o g a r i t h m i c plot of the smoothed e x p e r i m e n t a l v a l u e s of LXl below 0 . 6 ° K is shown i n fig. 1. The slope of this " l i n e " y i e l d s a t e m p e r a t u r e dependence of T 4.o a0.1 for Lxl and for the phonon d e n s i t y s i n c e ~ l aPPh" This is in e x c e l l e n t a g r e e m e n t with the Landau e x p r e s s i o n for phonon density d i s c u s s e d by Atkins [3]. The p r o b a b l e e r r o r in the m e a s u r e d v a l u e s of A / i n c r e a s e s f r o m about 2 p e r c e n t at 0.55°K to about 6 p e r c e n t at 0.38°K. E x p e r i m e n t a l v a l u e s of A / a r e given in table 1 f r o m 0 . 6 ° K to 0.925°K w h e r e n e i t h e r equation is applicable. Above 0.95°K, eq. (1) y i e l d s v a l u e s of 7/n which a r e between the e x p e r i m e n t a l v a l u e s of Zinov' eva [4] and Woods and Hallett [5] but within the e x p e r i m e n t a l e r r o r of the l a t t e r . References 1. R.W.H.Webeler, Ph.D.Thesis, UniVersity of Cincinnati (1961). 2. R°W.H.Webeler and D.C.Harnmer, Physics Letters 15 (1965} 233.
15 December 1965 Iq vlt:,-7
A{
.3
.4
.5
.6
T, ~K
Fig. 1. Logarithmic decrement in 4He. 3. K.R. Atkins, Liquid helium (The University Press, Cambridge, England, 1959) p. 681 4. K.N.Zinov, eva, Soviet Phys.-JETP 4 (1957} 36. 5. A.D.B.Woods and A.C.Hollis Hallett, Can.J.Phys. 41 (1963) 596. 6. R.H.Sherman, S.G.Sydoriak and T.R.Roberts, J. Res. Nat. Bur. Standards 68A (1964} 579. 7. P.J.Bendt, R.D.Cowan and J.L.Yarnell, Phys. Rev.113 (1959} 1391.
ON T H E P R O P A G A T I O N OF ELECTROMAGNETIC WAVES AND NEGATIVE IONS IN A P L A S M A W I T H H E A V Y P O S I T I V E
*
J. TEICHMANN ** D~parternent de Physique, Universit~ de Mont~'6al, Montreal, Canada -Received 12 November 1965
The propagation of s m a l l signal e l e c t r o m a g netic waves in m u l t i c o m p o n e n t p l a s m a s with s e v * Work supported by the National Research Council of Canada. ** On leave of absence from the Institute of Plasma Physics, Prague, Czechoslovakia. 534
e r a l s p e c i e s of positive ions has been studied e l s e w h e r e [1-5]. Some e x p e r i m e n t a l r e s u l t s show that in m a n y l a b o r a t o r y p l a s m a s , e s p e c i a l l y with heavy ions such as Cs and C1, a s u b s t a n t i a l n u m b e r of negative ions o c c u r s [6, 7]. The p u r p o s e of the following note is to c l a r i f y some p e c u l i a r i t i e s in propagation c h a r a c t e r i s t i c s in such p l a s m a . In
Volume 19, number 7
PHYSICS LETTERS
15 December 1965
a c o l d c o l U s i o n l e s s and infinite p l a s m a containing e l e c t r o n s , p o s i t i v e and n e g a t i v e i o n s of d i f f e r e n t c h a r g e - t o - m a s s r a t i o , s u b m e r g e d in a h o m o g e neous magnetostatic field a simple three-fluid magneto hydrodynamic model is used for classif i c a t i o n of waves. G e n e r a l l y , the d i s p e r s i o n e q u a tion N2(w) = 0, double v a l u e d in r e s p e c t to N 2, w h e r e N i s the r e f r a c t i v e index, h a s r + 1 z e r o s and p o l e s when r i s the n u m b e r of p l a s m a c o m p o nents, r e g a r d l e s s on t h e i r c h a r g e s and m a s s e s . The o r d e r i n g of t h e s e z e r o s (cutoff f r e q u e n c i e s ) and p o l e s (anomalous d i s p e r s i o n f r e q u e n c i e s ) d e pends a l s o on the r a t i o of m a s s e s and d e n s i t i e s of p o s i t i v e and n e g a t i v e ions. T h e r e f o r e , the d i s p e r s i o n equation h a s in the p l a s m a under c o n s i d e r a tion s o m e new b r a n c h e s . If we i n t r o d u c e the notation 8 = h i _ / h i + for the r a t i o of ion d e n s i t i e s , 7 = m i + / m i . , ~t = m i + / m e f o r the r a t i o of m a s s e s of p o s i t i v e , n e g a t i v e ions and e l e c t r o n s , then u n d e r the a s s u m p t i o n of q u a s i n e u t r a l i t y , the r e f r a c t i v e i n d i c e s f o r the p r i n c i p a l m o d e s a r e given by (Y. = ~ . /co, X = ~ 2 . / ~ 2 ) : 1+ el+ i+ pl+
/~R = 1 - Xi+([l + Ji(l-8) - ~IYi+](1 + Yi+)'l(1 - ~IYi+)-I 4 +
87(i-7ri+)-i~, (17
o
=
2N~NL
(N2R + N 2"-1 I_)
"
The low frequency part of the C M A d i a g r a m for Cs +, CI- plasma (7 > 1) is plotted in fig. 1 for various values of 8. The high-frequency region is influenced very little by negative ions for m i >> m The fuil lines are cutoffs for extraordinary, left and right hand polarised waves and resonances for left and right polarised waves; the dotted lines are resonances for extraordinary waves. The ordinary wave cutoff, not plotted, follows from (1). Since the position of this cutoff depends on 8 and 7, the presence of negative ions affects greatly for large 8 and 7 < 1 the width of transparent region for frequencies above the electron gyrofrequency [8]. The negative ions influence noticeably the propagation of right-hand polarised and extraordinary waves. For parallel propagation and co > lWci_ I the negative ions give rise to a new stop-band, the width of which grows with concentration. For frequencies above the cutoff line a new right-polarised wave, which m a y be called the negative ion wave, propagates. Rs phase velocity diminishes with frequency. For frequencies, given by --
r.
I+
= (i-8)b,+~) - i + o ( ~ -2)
e
(~.)
'o.2
'o.3
x~
Fig. 1. CMA diagram for plasma with Cs+and Cl-ions.
= i - x i + [ ~(i- 8) + i +8~] , N L2 ( Y i + ) = N 2 ( - Y i + ) ,
Ni
b.,
•
the p h a s e v e l o c i t y e q u a l s the v e l o c i t y of light. The n e g a t i v e ion b r a n c h g o e s to infinity at w = I ~ c e I. The next b r a n c h of the d i s p e r s i o n equation s o l u tion d e s c r i b e s the u s u a l f a s t e l e c t r o m a g n e t i c wave. F o r p e r p e n d i c u l a r p r o p a g a t i o n and f o r > ~ci+ a f a s t m a g n e t o a c o u s t i c wave p r o p a g a t e s up to the l o w e s t h y b r i d r e s o n a n c e , which i s due to the p r e s e n c e of n e g a t i v e ions. F o r s u f f i c i e n t l y l a r g e X ~ t h e r e follows a wide r e g i o n of nonp r o p a g a h o n which ends at the cutoff line EX=RH=0, the p o s i t i o n of which s h i f t s with g r o w i n g ~ into the h i g h f r e q u e n c y r e g i o n . F o r f r e q u e n c i e s above t h i s cutoff a n e g a t i v e ion e x t r a o r d i n a r y wave with l e f t p o l a r i s a t i o n p r o p a g a t e s up to the s e c o n d h y b r i d r e s o n a n c e . F o r p l a s m a with low c o n c e n t r a tion t h e r e i s a r e l a t i v e l y Harrow r e g i o n of non p r o p a g a t i o n above the f i r s t h y b r i d r e s o n a n c e , the s e c o n d one t a k e s p l a c e for f r e q u e n c i e s above the n e g a t i v e ion g y r o f r e q u e n c y . F o r s o m e p l a s m a p a r a m e t e r s , a l l t h e s e e x t r a o r d i n a r y w a v e s have t h e i r p h a s e v e l o c i t y equal to the v e l o c i t y of light. F o r l o w X i + and f o r Y? = ( 1 - 8 ) ( ~ - ~ ) " l + O(~ -~') 1+
(3)
the n e g a t i v e ion e x t r a o r d i n a r y wave i s l i n e a r l y p o l a r i s e d . The line (37 c u t s the c o m m o n point of 535
Volume 19, number 7
PHYSICS LETTERS
i n t e r s e c t i o n of EX=RH=0 and EX=~o l i n e s ; this is c h a r a c t e r i s t i c of p l a s m a with n e g a t i v e ions and y > 1. At this point, the d i s p e r s i o n r e l a t i o n has a s i n g u l a r solution. The r e l a t i o n (3) d e f i n e s a l s o the c r o s s o v e r f r e q u e n c y of the 1st o r d e r , w h e r e N 2 = N 2 At this value of y.2 a l i n e a r l y p o l a r i s e d R L" 1-{w a v e may propagate along and normal to the magnetic field. The frequencies, givenby (3) are at the same time the crossover_ ~ frequencies of the 2nd order, where N~ = N~. The strong interaction between these waves may thus be expected. It should be noted, that the whistler propagation occurs at two different frequencies. The case y < 1 has been treated elsewhere [8].
57Fe
15 December 1965
The author is g r a t e f u l to Mr. R. T. Horwood for his kind a s s i s t a n c e in obtaining the n u m e r i c a l r e sults. 1. C.O. Hines, J. Atmospheric Terrest. Phys. 11 (1957) 36. 2. S.J.Buchsbaum, Phys. Fluids 3 (1960) 418. 3. V.L.Yakimenko, Zh.Tekh. Fiz.32 (1962) 117. 4. M.A.Ginsburg, Geomagnetism Aeronomy 3 (1963) 610. 5. R.L. Smith, N. Brice, J. Geophys. Research 69 (1964) 5029. 6. G.G. Cloutier, C. Richard, RCA Victor Report 7-811-6 (1963). 7. S.Von Goeler, T.Ohe, N.D'Angelo, Report MATT357 (1965). 8. J.Teichmann, Bull.Am.Phys.Soc., to be published.
QUADRUPOLE I N T E R A C T I O N AND SUPERPARAMAGNETISM OF Fe 2+ IN CRYSTALS OF MgO * D. J. SIMKIN **, P . J . F I C A L O R A and R. A. BERNHE1M DeparDnent of Chemistry, Whitmore Laboratory The Pennsylvania State University, University Park, Pennsylvania Received 12 November 1965 i
When a s i n g l e c r y s t a l of MgO is doped with a r e l a t i v e l y high c o n c e n t r a t i o n of Fe 2+ (18.3 weight %) its r e c o i l l e s s g a m m a r a y a b s o r p t i o n s p e c t r u m [1] is found to exhibit a 57Fe q u a d r u p o l e i n t e r a c tion as shown in fig. 1. At low c o n c e n t r a t i o n s of Fe 2+ (1.5%) only a s i n g l e line is o b s e r v e d having a width of 0.54 + 0.05 m m / s e c and o c c u r i n g at an i s o m e r shift of 0.84 ± 0.05 m m / s e c with r e s p e c t to a 57Co s o u r c e in c o p p e r m e t a l . Since the MgO l a t t i c e is cubic, the n u c l e a r e l e c t r i c q u a d r u p o l e interaction must a r i s e from lattice distortions of s o m e kind. This note e x p l o r e s the n a t u r e of the l a t t i c e d i s t o r t i o n s which s e e m to r e s u l t f r o m a s y s t e m a t i c c l u s t e r i n g of i r o n ions r a t h e r than a r a n d o m d i s t r i b u t i o n of c r y s t a l i m p e r f e c t i o n s . The c r y s t a l s c o n s i d e r e d h e r e w e r e f a b r i c a t e d [2] by p r o l o n g e d h e a ti n g and a n n e a li n g of single c r y s t a l s of MgO c o a t e d with a s l u r r y of F e O in a c o n t r o l l e d C O - C O 2 a t m o s p h e r e f u r n a c e at 1300°C. The p a r t i a l p r e s s u r e of oxygen of 10 -8.5 m m Hg i n s u r e s that the p h a s e c o m p o s i t i o n of the s y s t e m l i e s along the F e O - M g O join. N e v e r t h e l e s s , the f o r m a t i o n of minute a m o u n ts of Fe 3+ is unavoidable, e s p e c i a l l y at high i r o n c o m p o s i tions. The c h e m i c a l a n a l y s e s of the two c r y s t a l s r e s u l t e d in an i r o n c o m p o s i t i o n in weight p e r c e n t
536
f
13C
? o_ 125 z
?, u
20
/ I
i
-2
-I
I
0 VELOCITY m m / s e c
I
2
Fig. 1. The room temperature M~ssbauer spectrum of a single crystal of MgO doped with 18.3% Fe 2+ and 0.19% Fe 3+ exhibiting a 57Fe quadrupole splitting of 0.63 -+0.005 m m / s e c and in isomer shift of 0.86 ~0.005 m m / s e c r e l ative to a 57Co in copper metal source. The line widths of the components of the spectrum are approximately 0.6 m m / sec. * This work was supported in part by the National Science Foundation. ** National Science Foundation Cooperative Fellow, 1965-1966.
PHYSICS LETTERS
a l l s u r f a c e s a r e e n t i r e l y diffuse, (2) t h e r e is no phonon-phonon s c a t t e r i n g , and (3) any effect of r o t o n e x c i t a t i o n is ignored. Then in the f i n a l exp r e s s i o n for A1 the c l a s s i c a l m o m e n t u m per p a r ticle P was r e p l a c e d by (3Pphc)4N where N i s the n u m b e r of phonons p e r cm~, c is the velocity_of sound, and Pph is the phonon density in g/cm-3. The smoothed liquid-4He data for this e x p e r i m e n t a r e given in table 1. We have c o m p a r e d A / ( e x p e r i m e n t a l ) with Lxl (calculated f r o m eq. 2) below 0.55OK. The c a l c u l a t e d v a l u e s for LXl might be expected to be higher than the e x p e r i m e n t a l v a l u e s s i n c e eq. (2) a s s u m e s only diffuse behavfour. A l o g a r i t h m i c plot of the smoothed e x p e r i m e n t a l v a l u e s of LXl below 0 . 6 ° K is shown i n fig. 1. The slope of this " l i n e " y i e l d s a t e m p e r a t u r e dependence of T 4.o a0.1 for Lxl and for the phonon d e n s i t y s i n c e ~ l aPPh" This is in e x c e l l e n t a g r e e m e n t with the Landau e x p r e s s i o n for phonon density d i s c u s s e d by Atkins [3]. The p r o b a b l e e r r o r in the m e a s u r e d v a l u e s of A / i n c r e a s e s f r o m about 2 p e r c e n t at 0.55°K to about 6 p e r c e n t at 0.38°K. E x p e r i m e n t a l v a l u e s of A / a r e given in table 1 f r o m 0 . 6 ° K to 0.925°K w h e r e n e i t h e r equation is applicable. Above 0.95°K, eq. (1) y i e l d s v a l u e s of 7/n which a r e between the e x p e r i m e n t a l v a l u e s of Zinov' eva [4] and Woods and Hallett [5] but within the e x p e r i m e n t a l e r r o r of the l a t t e r . References 1. R.W.H.Webeler, Ph.D.Thesis, UniVersity of Cincinnati (1961). 2. R°W.H.Webeler and D.C.Harnmer, Physics Letters 15 (1965} 233.
15 December 1965 Iq vlt:,-7
A{
.3
.4
.5
.6
T, ~K
Fig. 1. Logarithmic decrement in 4He. 3. K.R. Atkins, Liquid helium (The University Press, Cambridge, England, 1959) p. 681 4. K.N.Zinov, eva, Soviet Phys.-JETP 4 (1957} 36. 5. A.D.B.Woods and A.C.Hollis Hallett, Can.J.Phys. 41 (1963) 596. 6. R.H.Sherman, S.G.Sydoriak and T.R.Roberts, J. Res. Nat. Bur. Standards 68A (1964} 579. 7. P.J.Bendt, R.D.Cowan and J.L.Yarnell, Phys. Rev.113 (1959} 1391.
ON T H E P R O P A G A T I O N OF ELECTROMAGNETIC WAVES AND NEGATIVE IONS IN A P L A S M A W I T H H E A V Y P O S I T I V E
*
J. TEICHMANN ** D~parternent de Physique, Universit~ de Mont~'6al, Montreal, Canada -Received 12 November 1965
The propagation of s m a l l signal e l e c t r o m a g netic waves in m u l t i c o m p o n e n t p l a s m a s with s e v * Work supported by the National Research Council of Canada. ** On leave of absence from the Institute of Plasma Physics, Prague, Czechoslovakia. 534
e r a l s p e c i e s of positive ions has been studied e l s e w h e r e [1-5]. Some e x p e r i m e n t a l r e s u l t s show that in m a n y l a b o r a t o r y p l a s m a s , e s p e c i a l l y with heavy ions such as Cs and C1, a s u b s t a n t i a l n u m b e r of negative ions o c c u r s [6, 7]. The p u r p o s e of the following note is to c l a r i f y some p e c u l i a r i t i e s in propagation c h a r a c t e r i s t i c s in such p l a s m a . In
Volume 19, number 7
PHYSICS LETTERS
15 December 1965
a c o l d c o l U s i o n l e s s and infinite p l a s m a containing e l e c t r o n s , p o s i t i v e and n e g a t i v e i o n s of d i f f e r e n t c h a r g e - t o - m a s s r a t i o , s u b m e r g e d in a h o m o g e neous magnetostatic field a simple three-fluid magneto hydrodynamic model is used for classif i c a t i o n of waves. G e n e r a l l y , the d i s p e r s i o n e q u a tion N2(w) = 0, double v a l u e d in r e s p e c t to N 2, w h e r e N i s the r e f r a c t i v e index, h a s r + 1 z e r o s and p o l e s when r i s the n u m b e r of p l a s m a c o m p o nents, r e g a r d l e s s on t h e i r c h a r g e s and m a s s e s . The o r d e r i n g of t h e s e z e r o s (cutoff f r e q u e n c i e s ) and p o l e s (anomalous d i s p e r s i o n f r e q u e n c i e s ) d e pends a l s o on the r a t i o of m a s s e s and d e n s i t i e s of p o s i t i v e and n e g a t i v e ions. T h e r e f o r e , the d i s p e r s i o n equation h a s in the p l a s m a under c o n s i d e r a tion s o m e new b r a n c h e s . If we i n t r o d u c e the notation 8 = h i _ / h i + for the r a t i o of ion d e n s i t i e s , 7 = m i + / m i . , ~t = m i + / m e f o r the r a t i o of m a s s e s of p o s i t i v e , n e g a t i v e ions and e l e c t r o n s , then u n d e r the a s s u m p t i o n of q u a s i n e u t r a l i t y , the r e f r a c t i v e i n d i c e s f o r the p r i n c i p a l m o d e s a r e given by (Y. = ~ . /co, X = ~ 2 . / ~ 2 ) : 1+ el+ i+ pl+
/~R = 1 - Xi+([l + Ji(l-8) - ~IYi+](1 + Yi+)'l(1 - ~IYi+)-I 4 +
87(i-7ri+)-i~, (17
o
=
2N~NL
(N2R + N 2"-1 I_)
"
The low frequency part of the C M A d i a g r a m for Cs +, CI- plasma (7 > 1) is plotted in fig. 1 for various values of 8. The high-frequency region is influenced very little by negative ions for m i >> m The fuil lines are cutoffs for extraordinary, left and right hand polarised waves and resonances for left and right polarised waves; the dotted lines are resonances for extraordinary waves. The ordinary wave cutoff, not plotted, follows from (1). Since the position of this cutoff depends on 8 and 7, the presence of negative ions affects greatly for large 8 and 7 < 1 the width of transparent region for frequencies above the electron gyrofrequency [8]. The negative ions influence noticeably the propagation of right-hand polarised and extraordinary waves. For parallel propagation and co > lWci_ I the negative ions give rise to a new stop-band, the width of which grows with concentration. For frequencies above the cutoff line a new right-polarised wave, which m a y be called the negative ion wave, propagates. Rs phase velocity diminishes with frequency. For frequencies, given by --
r.
I+
= (i-8)b,+~) - i + o ( ~ -2)
e
(~.)
'o.2
'o.3
x~
Fig. 1. CMA diagram for plasma with Cs+and Cl-ions.
= i - x i + [ ~(i- 8) + i +8~] , N L2 ( Y i + ) = N 2 ( - Y i + ) ,
Ni
b.,
•
the p h a s e v e l o c i t y e q u a l s the v e l o c i t y of light. The n e g a t i v e ion b r a n c h g o e s to infinity at w = I ~ c e I. The next b r a n c h of the d i s p e r s i o n equation s o l u tion d e s c r i b e s the u s u a l f a s t e l e c t r o m a g n e t i c wave. F o r p e r p e n d i c u l a r p r o p a g a t i o n and f o r > ~ci+ a f a s t m a g n e t o a c o u s t i c wave p r o p a g a t e s up to the l o w e s t h y b r i d r e s o n a n c e , which i s due to the p r e s e n c e of n e g a t i v e ions. F o r s u f f i c i e n t l y l a r g e X ~ t h e r e follows a wide r e g i o n of nonp r o p a g a h o n which ends at the cutoff line EX=RH=0, the p o s i t i o n of which s h i f t s with g r o w i n g ~ into the h i g h f r e q u e n c y r e g i o n . F o r f r e q u e n c i e s above t h i s cutoff a n e g a t i v e ion e x t r a o r d i n a r y wave with l e f t p o l a r i s a t i o n p r o p a g a t e s up to the s e c o n d h y b r i d r e s o n a n c e . F o r p l a s m a with low c o n c e n t r a tion t h e r e i s a r e l a t i v e l y Harrow r e g i o n of non p r o p a g a t i o n above the f i r s t h y b r i d r e s o n a n c e , the s e c o n d one t a k e s p l a c e for f r e q u e n c i e s above the n e g a t i v e ion g y r o f r e q u e n c y . F o r s o m e p l a s m a p a r a m e t e r s , a l l t h e s e e x t r a o r d i n a r y w a v e s have t h e i r p h a s e v e l o c i t y equal to the v e l o c i t y of light. F o r l o w X i + and f o r Y? = ( 1 - 8 ) ( ~ - ~ ) " l + O(~ -~') 1+
(3)
the n e g a t i v e ion e x t r a o r d i n a r y wave i s l i n e a r l y p o l a r i s e d . The line (37 c u t s the c o m m o n point of 535
Volume 19, number 7
PHYSICS LETTERS
i n t e r s e c t i o n of EX=RH=0 and EX=~o l i n e s ; this is c h a r a c t e r i s t i c of p l a s m a with n e g a t i v e ions and y > 1. At this point, the d i s p e r s i o n r e l a t i o n has a s i n g u l a r solution. The r e l a t i o n (3) d e f i n e s a l s o the c r o s s o v e r f r e q u e n c y of the 1st o r d e r , w h e r e N 2 = N 2 At this value of y.2 a l i n e a r l y p o l a r i s e d R L" 1-{w a v e may propagate along and normal to the magnetic field. The frequencies, givenby (3) are at the same time the crossover_ ~ frequencies of the 2nd order, where N~ = N~. The strong interaction between these waves may thus be expected. It should be noted, that the whistler propagation occurs at two different frequencies. The case y < 1 has been treated elsewhere [8].
57Fe
15 December 1965
The author is g r a t e f u l to Mr. R. T. Horwood for his kind a s s i s t a n c e in obtaining the n u m e r i c a l r e sults. 1. C.O. Hines, J. Atmospheric Terrest. Phys. 11 (1957) 36. 2. S.J.Buchsbaum, Phys. Fluids 3 (1960) 418. 3. V.L.Yakimenko, Zh.Tekh. Fiz.32 (1962) 117. 4. M.A.Ginsburg, Geomagnetism Aeronomy 3 (1963) 610. 5. R.L. Smith, N. Brice, J. Geophys. Research 69 (1964) 5029. 6. G.G. Cloutier, C. Richard, RCA Victor Report 7-811-6 (1963). 7. S.Von Goeler, T.Ohe, N.D'Angelo, Report MATT357 (1965). 8. J.Teichmann, Bull.Am.Phys.Soc., to be published.
QUADRUPOLE I N T E R A C T I O N AND SUPERPARAMAGNETISM OF Fe 2+ IN CRYSTALS OF MgO * D. J. SIMKIN **, P . J . F I C A L O R A and R. A. BERNHE1M DeparDnent of Chemistry, Whitmore Laboratory The Pennsylvania State University, University Park, Pennsylvania Received 12 November 1965 i
When a s i n g l e c r y s t a l of MgO is doped with a r e l a t i v e l y high c o n c e n t r a t i o n of Fe 2+ (18.3 weight %) its r e c o i l l e s s g a m m a r a y a b s o r p t i o n s p e c t r u m [1] is found to exhibit a 57Fe q u a d r u p o l e i n t e r a c tion as shown in fig. 1. At low c o n c e n t r a t i o n s of Fe 2+ (1.5%) only a s i n g l e line is o b s e r v e d having a width of 0.54 + 0.05 m m / s e c and o c c u r i n g at an i s o m e r shift of 0.84 ± 0.05 m m / s e c with r e s p e c t to a 57Co s o u r c e in c o p p e r m e t a l . Since the MgO l a t t i c e is cubic, the n u c l e a r e l e c t r i c q u a d r u p o l e interaction must a r i s e from lattice distortions of s o m e kind. This note e x p l o r e s the n a t u r e of the l a t t i c e d i s t o r t i o n s which s e e m to r e s u l t f r o m a s y s t e m a t i c c l u s t e r i n g of i r o n ions r a t h e r than a r a n d o m d i s t r i b u t i o n of c r y s t a l i m p e r f e c t i o n s . The c r y s t a l s c o n s i d e r e d h e r e w e r e f a b r i c a t e d [2] by p r o l o n g e d h e a ti n g and a n n e a li n g of single c r y s t a l s of MgO c o a t e d with a s l u r r y of F e O in a c o n t r o l l e d C O - C O 2 a t m o s p h e r e f u r n a c e at 1300°C. The p a r t i a l p r e s s u r e of oxygen of 10 -8.5 m m Hg i n s u r e s that the p h a s e c o m p o s i t i o n of the s y s t e m l i e s along the F e O - M g O join. N e v e r t h e l e s s , the f o r m a t i o n of minute a m o u n ts of Fe 3+ is unavoidable, e s p e c i a l l y at high i r o n c o m p o s i tions. The c h e m i c a l a n a l y s e s of the two c r y s t a l s r e s u l t e d in an i r o n c o m p o s i t i o n in weight p e r c e n t
536
f
13C
? o_ 125 z
?, u
20
/ I
i
-2
-I
I
0 VELOCITY m m / s e c
I
2
Fig. 1. The room temperature M~ssbauer spectrum of a single crystal of MgO doped with 18.3% Fe 2+ and 0.19% Fe 3+ exhibiting a 57Fe quadrupole splitting of 0.63 -+0.005 m m / s e c and in isomer shift of 0.86 ~0.005 m m / s e c r e l ative to a 57Co in copper metal source. The line widths of the components of the spectrum are approximately 0.6 m m / sec. * This work was supported in part by the National Science Foundation. ** National Science Foundation Cooperative Fellow, 1965-1966.