Hyperfine Interactions 22 (I 985) 19-38
19
NUCLEAR ORIENTATION AND QUADRUPOLE INTERACTION E. H A G N
Physik-Department, Technische Universitat Mfinchen, D-8046 Garching, FRG
Abstract
In quadrupole-interaction nuclear-orientation experiments (QI-NO) the quadrupole interaction frequency VQ = e2qQ/h is determined from the angular distribution of Y-rays emitted in the decay of radioactive nuclei oriented at low temperatures as impurities in noncubic single-crystal matrices. This means that either the spectroscopic quadrupole moment Q of radioactive isotopes or the crystal electric field gradient eq can be determined from QI-NO experiments. Recent developments in QI-NO are discussed, especially with regard to the investigation of nuclei far from stability, with the following main topics: (i) Experimental aspects; (2) Quadrupole moments of short-lived nuclei; (3) Systematics of electric field gradients; (4) QI-NO with "new" host lattices, such as dichalcogenides; (5) Resonance techniques.
I.
Introduction
T h e e l e c t r i c q u a d r u p o l e i n t e r a c t i o n e n e r g y EQ = h v Q of a nucleus w i t h s p e c t r o s c o p i c q u a d r u p o l e m o m e n t Q in a n o n c u b i c e n v i r o n m e n t w i t h an e l e c t r i c f i e l d g r a d i e n t Vzz = eq is g i v e n by EQ = h v Q = e2qQ. The
quadrupole VQ
interaction (MHz)
The temperature g i v e n by TQ
TQ,
(mK)
frequency
= 24.180
x eq
for w h i c h
= 1.160
x eq
VQ
(1) is in u n i t s
( 1 0 1 7 V / c m 2) x Q
hVQ/kBT
of'MHz
given
(b).
= I, is in M i l l i - K e l v i n
( 1 0 1 7 V / c m 2) x Q
(b).
by (2)
(mK) (3)
F o r r a d i o a c t i v e nuclei, VQ can be d e t e r m i n e d w i t h Q I - N O e x p e r i m e n t s . T h i s i m m e d i a t e l y shows t h a t the a i m of Q I - N O s t u d i e s m a y be t w o f o l d (I) M e a s u r e m e n t of q u a d r u p o l e m o m e n t s of r a d i o a c t i v e n u c l e i u t i l i zing a m a t r i x , for w h i c h the E F G is known. (2) M e a s u r e m e n t of the EFG using radioactive isotopes with known quadrupole moments. For b o t h c a s e s it is a d e c i s i v e a d v a n t a g e t h a t the sign of the q u a d r u p o le s p l i t t i n g can be d e t e r m i n e d in a d d i t i o n to the a b s o l u t e magnitude. The first successfulQI-NO e x p e r i m e n t h a d b e e n r e p o r t e d by K a i n d l et al. [I]. F o r s e v e r a l e l e m e n t s as i m p u r i t i e s in (cubic) f e r r o m a g n e t i c Fe, Co or Ni a s m a l l q u a d r u p o l e i n t e r a c t i o n e x i s t s b e s i d e s a large m a gnetic hyperfine interaction. In f a v o r a b l e c a s e s this q u a d r u p o l e i n t e r a c t i o n c a n be m e a s u r e d w i t h the t e c h n i q u e of Q I - N M R - O N (quadrup o l e i n t e r a c t i o n r e s o l v e d N M R on o r i e n t e d n u c l e i ) , w h i c h m e a n s t h a t r e s o n a n c e p r e c i s i o n m a y be o b t a i n e d . T h e e x t e n s i o n of this m e t h o d u s i n g h c p - C o or h c p - G d as h o s t m a t r i c e s w i l l be d i s c u s s e d in sect.7.2.
~) J.C. Baltzer A.G., Scientific Publishing Company Printed in the Netherlands by Asco - Ommen
E. Hagn, Nuclear orientation and quadrupole interaction
20
G r o u n d state q u a d r u p o l e m o m e n t s of n u c l e i are i n t e r e s t i n g as they p r o v i d e a d i r e c t m e a s u r e of the n o n s p h e r i c i t y of the n u c l e a r charge distribution. The sign y i e l d s i n f o r m a t i o n on the n u c l e a r shape a n d / o r the g r o u n d state c o n f i g u r a t i o n . Recently, anomalous g r o u n d state c o n f i g u r a t i o n s in n e u t r o n d e f i c i e n t Ir and Ta i s o t o p e s c o u l d be i d e n t i f i e d w i t h Q I - N O [2-7]. Fig. 1 s h o w s a p e r i o d i c t a b l e of the e l e m e n t s in w h i c h the e l e m e n t s are m a r k e d w h i c h h a v e b e e n inv e s t i g a t e d w i t h QI-NO. The f i g u r e a l s o shows that the q u a d r u p o l e int e r a c t i o n of h e a v y Os, Ir, Pt and Au i s o t o p e s has a l r e a d y b e e n investigated with QI-NMR-ON spectroscopy. Up to n o w Q I - N M R - O N is limited to l o w - s p i n n u c l e a r states.
Periodic table of the elements Group IA
Villa IIA
IliA IVA VA VIA VIIA
Li
Be
Na
Mg IIIB IVB VB VIB VIIB
K
Co
Rb Sr
Sc
Ti
V
Cr Mn
r~Vlll~ Fe
Co
8
C
N
O
F
lIB AI rz Cu Zn Ga
Si
P
S
CI
Ar
As Se
8r
Kr
[
Xe
IB
Ni
Y Zr Nb Mo Tc Ru Rh Pd ~ g rC3d tin
c. 8o .o ".;
w ".'o
i~V 3,
%;
Ge
Sn !'SZb Te
TI Pb Bi %
Ne
rA't Rn
Fr Re 4c Lonthonides. Actin[des.
~
i
r~
:GI-NO
i
;,
L---] : (~]-NMR-ON
Fig. 1. Periodic table of the elements. Those elements are marked which have been investigated with QI-NO and QI-NMR-ON. The number of isotopes investigated is given besides the symbols. E l e c t r i c field g r a d i e n t s in n o n c u b i c m e t a l s are t h e o r e t i c a l l y n o t u n d e r s t o o d at present. E v e n the sign c a n n o t be p r e d i c t e d r e l i ably. Thus, as a f i r s t step, e x p e r i m e n t a l t r e n d s h a v e to be found. In this f i e l d Q I - N O has c o n t r i b u t e d v a l u a b l e i n f o r m a t i o n and w i l l p r o b a b l y c o n t r i b u t e in future. 2.
Basic
principles
2. I.
Quadrupole-Interaction
ented
T h e a n g u l a r d i s t r i b u t i o n of y - r a y s e m i t t e d in the d e c a y of o r i r a d i o a c t i v e n u c l e i is m o s t c o n v e n i e n t l y w r i t t e n as [8] W(e)
=
of Q I - N O
~ k
and Q I - N M R - O N
Nuclear-Orientation
Bk(hVQ/kBT) even
A k Pk (c~
Qk-
T h e p a r a m e t e r s B k d e s c r i b e the d e g r e e of o r i e n t a t i o n ; they the spin of the o r i e n t e d s t a t e and on VQ/T, w h e r e VQ is the q u o t e d q u a d r u p o l e s p l i t t i n g f r e q u e n c y d e f i n e d b e f o r e and T t e m p e r a t u r e of the system. T h e p a r a m e t e r s A k d e p e n d on the
(4) d e p e n d on usually is the characte-
E. Hagn, Nuclear orientation and quadrupole interaction
21
r i s t i c s of the n u c l e a r decay, t h e y are p r o d u c t s of the u s u a l a n g u l a r c o r r e l a t i o n c o e f f i c i e n t s U k and F k. T h e Pk(COSB) are L e g e n d r e p o l y n o m i a l s , e b e i n g the a n g l e b e t w e e n the q u a n t i z a t i o n axis (here the c - a x i s of the s i n g l e crystal) and the d i r e c t i o n of o b s e r v a t i o n . T h e Qk are s o l i d a n g l e c o r r e c t i o n c o e f f i c i e n t s ; t h e y are n o r m a l l y n e a r unity. In the " h i g h - t e m p e r a t u r e " region, h V Q << k B T , o n l y the k=2 cont r i b u t i o n in Eq. (3) p l a y s an e s s e n t i a l role, as the o r i e n t a t i o n par a m e t e r B 4 is t h e n m u c h s m a l l e r t h a n B 2. T h e n B 2 ( h V Q / k B T ) c a n be exp a n d e d in p o w e r s of h V Q / k B T , w h i c h y i e l d s B 2 = -cih~Q/kBT. H e r e c I is a p o s i t i v e c o n s t a n t t e d state, w h i c h is g i v e n by
depending
(5) on the
spin
I of the o r i e n -
~(I+1) ( 2 I + 3 ) } 1/2
cI =L ~ 5 ~ Y z 7 7 The y-anisotropy
is t h e n W(O)
given
by
- I = -c I A 2 P2(cosO)
h% Q2 kBT'
(6)
w h i c h s h o w s i m m e d i a t e l y t h a t o n l y the p r o d u c t A 2 V Q can be d e t e r m i n e d from QI-NO experiments. It s h o u l d be m e n t i o n e d t h a t an a l m o s t l i n e a r d e p e n d e n c e of the a n i s o t r o p y on I/T h o l d s in a r e m a r k a b l y l a r g e temp e r a t u r e range. Up to now, o n l y in few s p e c i a l c a s e s the o b t a i n e d h V Q / k B T v a l u e s w e r e large e n o u g h t h a t a d e v i a t i o n f r o m the l i n e a r b e h a v i o u r c o u l d be o b s e r v e d . T h i s m e a n s , h o w e v e r , t h a t o n l y the prod u c t A 2 V Q can be d e t e r m i n e d f r o m Q I - N O e x p e r i m e n t s . T h e a n g u l a r c o e f f i c i e n t A 2 can be p r e d i c t e d t h e o r e t i c a l l y o n l y in few e x c e p t i o nal cases, for w h i c h the d e c a y scheme, y - m u l t i p o l a r i t i e s and B - d e c a y t e n s o r r a n k s are known. T h e m o s t s e v e r e l i m i t a t i o n r e s u l t s f r o m the t e n s o r r a n k s of the S - d e c a y s , w h i c h can be p r e d i c t e d u n a m b i g u o u s l y o n l y for a l l o w e d aI = I and u n i q u e f i r s t f o r b i d d e n ~I = 2 t r a n s i tions. In all o t h e r c a s e s e x p e r i m e n t a l d a t a h a v e to be used. T h e experimental determination of A 2 c o e f f i c i e n t s c a n be p e r f o r m e d w i t h "magnetic"-NO experiments: H e r e the r a d i o a c t i v e i s o t o p e s are e m b e d d e d in a f e r r o m a g n e t i c m a t r i x , s u c h as Fe, Co, Ni, Gd. F r o m the lowtemperature y-anisotropy the m a g n e t i c h y p e r f i n e s p l i t t i n g f r e q u e n c y V M and the A2, 4 c o e f f i c i e n t s can be d e t e r m i n e d s i m u l t a n e o u s l y w i t h a least-squares f i t t i n g p r o c e d u r e . T h i s p r o c e d u r e is a p p l i c a b l e if the y-anisotropy is m e a s u r e d in such a l a r g e t e m p e r a t u r e r e g i o n t h a t the s t r u c t u r e of W(8) v e r s u s I/T ( d e p e n d i n g on u M) and the s a t u r a t i o n v a l u e of W(8) ( d e p e n d i n g on A k) can be d e t e r m i n e d i n d e p e n d e n t l y . As in m o s t c a s e s t h e p a r a m e t e r s d e d u c e d w i t h l e a s t - s q u a r e s fits are m o re or less c o r r e l a t e d , it is p r e f e r a b l e that V M is d e t e r m i n e d indep e n d e n t l y w i t h a n o t h e r t e c h n i q u e , such as N M R - O N . Up to n o w w e h a v e t a c i t e l y a s s u m e d t h a t 100% of the i m p u r i t y n u c l e i are s u b j e c t to o n e u n i q u e h y p e r f i n e i n t e r a c t i o n . O f t e n the ass u m p t i o n is m a d e t h a t a f r a c t i o n f is s u b j e c t to the full u n d i s t u r b e d h y p e r f i n e i n t e r a c t i o n , w h i l e t h e f r a c t i o n 1-f is s u b j e c t to a n e g l i g i b l y small, i.e., zero h y p e r f i n e i n t e r a c t i o n . It is o b v i o u s t h a t f has to be k n o w n for the i n t e r p r e t a t i o n of Q I - N O e x p e r i m e n t s . In this s e n s e it s h o u l d be s t a t e d t h a t o n l y the p r o d u c t f A 2 eQ V z z can be d e t e r m i n e d in Q I - N O e x p e r i m e n t s . We s h a l l c o m e b a c k to the p r o b l e m of l a t t i c e l o c a t i o n later.
E. Hagn, Nuclear orientation and quadrupole interaction
22
2.2.
Quadrupole-interaction
resolved NMR-ON
W i t h the Q I - N M R - O N t e c h n i q u e the l a r g e m a g n e t i c h y p e r f i n e intera c t i o n of r a d i o a c t i v e i s o t o p e s in a f e r r o m a g n e t i c h o s t l a t t i c e serves to get a h i g h d e g r e e of p o l a r i z a t i o n at t e m p e r a t u r e s of ~ 10 mK, w h i l e the s m a l l q u a d r u p o l e i n t e r a c t i o n s p l i t s the "pure" m a g n e t i c r e s o n a n c e into 2I s u b r e s o n a n c e s . T h e r e s o n a n c e f r e q u e n c y for t r a n s i t i o n s b e t w e e n s t a t e Im> and Im+1> is, a s s u m i n g that the m=I s t a t e lies l o w e s t in energy, g i v e n by ~;m ~ m+l = V M + AVQ
(m + I/2) + b
(I + K) B O
V M = Ig~NBHF/hl, VQ = e2qQ/h,
(7)
AVQ = 3VQ/[2I(2I-I)], b =
lg~N/hl
sgn(BHF).
H e r e V M is the " m a g n e t i c f r e q u e n c y " , i.e., the f r e q u e n c y that w o u l d be o b s e r v e d in the a b s e n c e of the q u a d r u p o l e i n t e r a c t i o n , VQ is the q u a d r u p o l e i n t e r a c t i o n f r e q u e n c y and ~V 0 is the q u a d r u p o l e s u b r e s o n a n c e s e p a r a t i o n . L e t us d e n o t e the s u b g e s o n a n c e that c o r r e s p o n d s to s u b l e v e l t r a n s i t i o n s b e t w e e n the e n e r g e t i c a l l y l o w e s t s u b s t a t e s as V I r e s o n a n c e , the n e x t as V 2 r e s o n a n c e , etc. T h e r e s o n a n c e e f f e c t for the q u a d r u p o l e s u b r e s o n a n c e "i" is g i v e n by A(i) (e) = Aw(i) (8) = A2 ~ B ~ i ) P 2 ( c o s e )
+ A4 A B ~ I ) P 4 ( c o s 8 ) "
(8)
T h e f o l l o w i n g f e a t u r e s d e s e r v e to be m e n t i o n e d : (I) As AB 2 and AB 4 are d i f f e r e n t in the g e n e r a l case, the r e s o n a n c e s p e c t r u m d e p e n d s on the a n g l e of o b s e r v a t i o n , i.e., for e=O O and 90 ~ d i f f e r e n t s u b r e s o n a n c e a m p l i t u d e s are e x p e c t e d if the k=4 c o n t r i b u t i o n to the T - a n i s o t r o p y is c o m p a r a b l e in m a g n i t u d e to the k=2 c o n t r i b u t i o n . (2) T h e r e l a t i v e s u b r e s o n a n c e a m p l i t u d e s d e p e n d on the t e m p e r a t u r e of the sample, the r f - a m p l i t u d e (and h e n c e on the e x t e r n a l m a g n e t i c f i e l d v i a the e n h a n c e m e n t f a c t o r for the rf-field) and on e x p e r i m e n t a l par a m e t e r s such as m e a s u r e m e n t time at a f i x e d f r e q u e n c y , if this m e a s u r e m e n t time is c o m p a r a b l e in m a g n i t u d e to the s p i n - l a t t i c e r e l a x a t i o n time. D e t a i l e d m o d e l c a l c u l a t i o n s for s p e c i a l s y s t e m s can be f o u n d in refs. [9,10]. If the s u b r e s o n a n c e s e p a r a t i o n can be r e s o l ved e x p e r i m e n t a l l y , the q u a d r u p o l e i n t e r a c t i o n is i m m e d i a t e l y f o u n d w i t h r e s o n a n c e p r e c i s i o n . If the s u b r e s o n a n c e s t r u c t u r e c a n n o t be res o l v e d t h e r e m a y be a d i f f e r e n t i a l r e s o n a n c e d i s p l a c e m e n t of the res o n a n c e c e n t e r s m e a s u r e d at 8 = O ~ and 8 = 9 0 ~ from w h i c h the q u a d r u p o le i n t e r a c t i o n f r e q u e n c y can be d e d u c e d . This f e a t u r e is d i s c u s s e d in d e t a i l in refs. [11,12]. Up to n o w Q I - N M R - O N has b e e n o b s e r v e d for 1 8 3 0 s F e [13], 186Ir in Ni [14], 1 8 8 I r in Fe and Ni [15], 192Ir in Fe and N~-[9], 194Ir in Fe and Ni [16], 189pt and 191pt in Fe [17], 198Au in Fe [10] and 199Au in Fe [18]. 3.
Experimental
aspects
F o r the e x i s t e n c e of an EFG a n o n c u b i c s y m m e t r y is n e c e s s a r y . A list of n o n c u b i c m e t a l s s u i t a b l e for Q I - N O is g i v e n in T a b l e I. It s h o u l d be n o t e d that s i n g l e c r y s t a l s h a v e to be used. Up to n o w the f o l l o w i n g m e t a l s h a v e b e e n u s e d s u c c e s s f u l l y in Q I - N O e x p e r i m e n t s : Be, Zn, Cd, In, Sb, Lu, Hf, Re, Os. U s u a l d i m e n s i o n s of the s i n g l e
E. Hagn, Nuclear orientation and quadrupole interaction
Table 1 List of noncubic metals suited for QI-NO experiments from ref. [19].) Metal
group
str.
c/a
Z a)
23
(c/a ratios taken
eqlatt [1015
eqlatt b) V/cm 2 ]
T=3OOK
T=OK
4Be
IIa
hcp
1.5667
2
+7.1
+7.0
12Mg
IIa
hcp
1.6236
2
+0.42
+0.44
21Sc
IIIb
hcp
1.5936
3
+2.1
+2.3
22Ti
IVb
hcp
1.589
4
+4.5
30Zn
IIb
hcp
1.8560
2
-14.8
-12.7
39Y
IIIb
hcp
1.5740
3
+2.3
+2.6
IVb
hcp
1.5931
4
+3.1
43Tc
VIIb
hcp
1.604
7
+6.5
44Ru
VIIIb
hcp
1.5835
4 c)
+6.5
+6.6
48Cd
Iib
hcp
1.8857
2
-11.9
-10.7
49In
IIIa
tcp
3
-1.5 d)
5oSn
IVa
tet
4
-1.7 e)
51Sb
Va
rhd
5
+5.O f)
71Lu
IIIb
hcp
1.5846
3
+2.2
72Hf
IVb
hcp
1.5822
4
+4.0
75Re
VIIb
hcp
1.615
7
+4.1
76Os
VIIIb
hcp
1.5799
4 c)
+6.7
81TI
Ilia
hcp
1.5984
3
+1.7
83Bi
Va
rhd
5
+4.0 g)
4oZr
+6.8
hcp: hexagonal closed packed; tcp: tetragonal closed packed; tet: tetragonal; rhd: rhombohedral. a) nominal valence b) extrapolated to T=OK with linear expansion data of ref. [20]. c) ref. [21]; d) ref. [22]; e) ref. [23]; f) ref. [24]; g) ref. [25]
c r y s t a l s are # 4 . . . 1 0 m m a n d a t h i c k n e s s 0 . 1 . . . 0 . 5 mm. For s u c h a p l a t e or f l a t d i s k t h e o r i e n t a t i o n of the c - a x i s c a n in p r i n c i p l e be chosen arbitrarily. In p r a c t i c e , the c - a x i s has in m o s t c a s e s b e e n oriented perpendicular to the d i s k p l a n e as such a g e o m e t r y f a c i l i a tes the p r o p e r a d j u s t m e n t of the c - a x i s ( q u a n t i z a t i o n axis) w i t h res p e c t to the p o s i t i o n of the d e t e c t o r s . T h i s g e o m e t r y h a s the d i s a d v a n t a g e t h a t for h i g h - Z c r y s t a l s s u c h as Lu, Hf, Re, Os a c o n s i d e r a b l e a b s o r p t i o n of l o w - e n e r g y T - r a d i a t i o n t a k e s p l a c e in the c r y s t a l itself. T h i s has the c o n s e q u e n c e t h a t l o w - e n e r g y y - r a y s e m i t t e d at 8=90 ~ i.e., p a r a l l e l to the d i s k p l a n e , are a t t e n u a t e d to a h i g h degree. (For an o r i e n t a t i o n of the c - a x i s p a r a l l e l to the d i s k plane, t h e m a x i m u m a t t e n u a t i o n of the l o w - e n e r g y T - r a d i a t i o n w o u l d o c c u r for
24
E. Hagn, Nuclear orientation and quadrupole interaction
8=O ~ which is more severe, as the accuracy obtainable is by a factor of 2 better for 8=0 ~ than for 8=90~ This could be avoided by using a single crystal for which the angle b e t w e e n the c-axis and the surface is 45 ~ . For this geometry 8=O ~ and 8=90 ~ would be e q u i v a l e n t with respect to the y - r a y attenuation. The main techniques for the p r e p a r a t i o n of single crystal samples containing radioactive isotopes as dilute impurities are in-situ preparation, diffusion, m a s s - s e p a r a t o r implantation and recoil-implantation. With the in-situ p r e p a r a t i o n the m a t e r i a l of the single crystal itself is used as target material for a proper n u c l e a r reaction, the main reactions being (n,y), (p,xn), (d,xn), (Q,xn), (HI,xn) and (y,n). I m p u r i t y - h o s t combinations with higher-Z impurities can easily be produced with (HI,xn) reactions. Here the type and energy of the heavy ions can be chosen in such a way that selected impurity isotopes can be produced. For the p r e p a r a t i o n of impurities with lower Z than that of the host m a t e r i a l h i g h - e n e r g y l i g h t - p a r t i c l e reactions can be used. These reactions are, however, not very selective. This is no general r e s t r i c t i o n as the NO technique itself is highly selective as long as the specific y - r a y transitions can be resolved. Thus spallation reactions could probably well be used for the p r e p a r a t i o n of "exotic" i m p u r i t y - h o s t c o m b i n a t i o n s w h i c h has not been p e r f o r m e d up to now. Sample p r e p a r a t i o n by d i f f u s i o n and r e c o i l - i m p l a n t a t i o n have a rather limited applicability. The sample p r e p a r a t i o n w i t h the recoili m p l a n t a t i o n technique, w h i c h has been used s u c c e s s f u l l y for m a n y " m a g n e t i c " - N O and N M R - O N experiments, cannot be applied for Q I - N O analogously. As single crystals cannot easily be p r e p a r e d w i t h a thickness of only several ~m, impurity isotopes produced by the beam in the single crystals p r o d u c e a too large y - r a y c o n t a m i n a t i o n background. This p r o b l e m could possibly be overcome by using heavy ions: First, the i m p l a n t a t i o n depth will be larger (in c o m p a r i s o n to light ions) b e c a u s e of the higher recoil momentum. Second, the p r o b l e m of c o n t a m i n a n t activities is less severe because of the higher energy loss of heavy charged particles p a s s i n g matter, by w h i c h the active "target" thickness of the single crystals will be r e d u c e d significantly. For QI-NO experiments on s h o r t - l i v e d nuclei far off stability, only m a s s - s e p a r a t o r - i m p l a n t a t i o n will be applicable. This means, however, that all problems c o n n e c t e d with the m a s s - s e p a r a t o r implantation will have to be studied with isotopes with longer half lives for w h i c h a l t e r n a t i v e sample p r e p a r a t i o n techniques can be applied. As the i m p l a n t a t i o n depth is only of the order of several h u n d r e d ~, the surface q u a l i t y of the single crystals will play an essential role. Moreover, the results on the h y p e r f i n e splitting may depend on the dose of the implantation, and the critical dose m a y be d i f f e r e n t for d i f f e r e n t i m p u r i t y - h o s t combinations. The same p r o b l e m applies for the lattice location of the impurity atoms, w h i c h is expected to be d e p e n d e n t on the type of i m p u r i t y - h o s t c o m b i n a t i o n and the dose of the implantation. Here a lot of p r e p a r a t o r y e x p e r i m e n t s have to be performed, and it should be m e n t i o n e d that the Bonn group investigates such problems s y s t e m a t i c a l l y [26]. In any case, relative m e a s u rements on two or more isotopes p e r f o r m e d s i m u l t a n e o u s l y will be important, as then unknown parameters such as the fraction on "good" lattice sites can be e l i m i n a t e d to a large degree. (See, e.g. disc u s s i o n on At in Be in sect. 4). If a s i m u l t a n e o u s m e a s u r e m e n t on two d i f f e r e n t isotopes is not possible, a precise k n o w l e d g e of the t e m p e r a t u r e of the single crystal is necessary. N o r m a l l y the t e m p e r a t u r e is d e t e r m i n e d with the help of a n u c l e a r o r i e n t a t i o n thermometer; often used t h e r m o m e t e r s
E. Hagn, Nuclear orientation and quadrupole interaction
25
are 54Mn, 57Co, 60Co in Fe or Ni. F o r t h e s e t h e r m o m e t e r s a m a g n e t i c f i e l d is n e c e s s a r y to o r i e n t the f e r r o m a g n e t i c d o m a i n s . T h i s m a y be a disadvantage, e s p e c i a l l y if a m a g n e t i c - f i e l d d e p e n d e n c e is to be m e a s u r e d . In this c a s e h c p - C o c a n be c h o s e n as h o s t m a t r i x . A 6OCoCo(hcp) t h e r m o m e t e r can be e a s i l y p r e p a r e d by n e u t r o n i r r a d i a tion--of a h c p Co s i n g l e c r y s t a l . A 5 7 C o C o t h e r m o m e t e r c a n be p r e p a red v i a the (y,2n) r e a c t i o n by irradiati-on of a s i n g l e c r y s t a l w i t h electron bremsstrahlung. T h e 5 8 C o a c t i v i t y , w h i c h is p r o d u c e d v i a (y,n), can be a l l o w e d to d e c a y b e c a u s e of its s h o r t e r h a l f life. As c o o l i n g d e v i c e s m o s t l y 3 H e / 4 H e d i l u t i o n r e f r i g e r a t o r s are used. T e m p e r a t u r e s of N5 m K can be a c h i e v e d in c o n t i n u o u s o p e r a t i o n . See, e.g. ref. [27]. If lower t e m p e r a t u r e s are n e c e s s a r y , a s e c o n d stage, m o s t l y o p e r a t i n g on the p r i n c i p l e of h y p e r f i n e e n h a n c e d n u c lear c o o l i n g of a v a n - V l e c k p a r a m a g n e t i c c o m p o u n d s u c h as PrNi 5, is c o u p l e d to the p r e c o o l i n g d e v i c e . W i t h s u c h an a s s e m b l y t e m p e r a t u r e s as low as ~2 m K h a v e b e e n o b t a i n e d up to now. It s h o u l d be m e n t i o n e d that r a d i o a c t i v e s e l f h e a t i n g d u e to the a b s o r p t i o n of y-, 8- a n d Xr a y s in the c r v s t a l s t h e m s e l v e s s t r o n q l y l i m i t s the o b t a i n a b l e final temperature, and t h a t t e m p e r a t u r e s a r o u n d 2..3 m K can be o b t a i n e d o n l y w i t h w e a k a c t i v i t i e s of s e l e c t e d i s o t o p e s . T h e l o w e s t t e m p e r a t u r e s in Q I - N O e x p e r i m e n t s h a v e b e e n o b t a i n e d by the O x f o r d g r o u p [3]: W e a k a c t i v i t i e s of 1 8 9 , 1 9 0 I r c o u l d be c o o l e d to 2 . 1 ( I ) m K . T h e s i n g l e c r y s t a l s a m p l e s are n o r m a l l y s o l d e r e d to the c o l d f i n g e r of the c o o l i n g d e v i c e . In o r d e r to e s t a b l i s h a g o o d t h e r m a l c o n t a c t u l t r a s o n i c s o l d e r i n g is n e c e s s a r y for s e v e r a l m a t e r i a l s such as Lu. E v e n w i t h u l t r a s o n i c s o l d e r i n g , t h e r m a l g r a d i e n t s b e t w e e n the c o l d f i n g e r and the s i n g l e c r y s t a l s a m p l e s h a v e b e e n o b s e r v e d . In o r d e r to e s t i m a t e the u n c e r t a i n t y c a u s e d by t h e r m o m e t r y it is u s e f u l to m e a s u r e the t e m p e r a t u r e at the s u r f a c e of the s i n g l e c r y s t a l s w i t h a s e c o n d i n d e p e n d e n t t h e r m o m e t e r , w h i c h has b e e n d o n e in several e x p e r i m e n t s . Up to now, l a r g e t e m p e r a t u r e g r a d i e n t s w e r e o b s e r v e d o n l y for Lu and Be. E s p e c i a l l y w i t h Be the p r e p a r a t i o n of a g o o d t h e r m a l c o n t a c t t u r n e d o u t to be d i f f i c u l t . F u r t h e r e x p e r i m e n t s w i t h d i f f e r e n t s o l d e r i n g m a t e r i a l s are d e s i r a b l e . 4.
Presentation
of e x p e r i m e n t a l
QI-NO
results
In t a b l e 2 the r e s u l t s of Q I - N O e x p e r i m e n t s p u b l i s h e d u n t i l A u g u s t 1984 are listed. T h e q u a n t i t i e s , w h i c h h a v e b e e n d e d u c e d , i.e., e i t h e r the s p e c t r o s c o p i c q u a d r u p o l e m o m e n t Q or the e l e c t r i c f i e l d g r a d i e n t eq, are u n d e r l i n e d . F o r an e x t e n s i v e d i s c u s s i o n on the c o n s i s t e n c y of Q I - N O d a t a we r e f e r to ref. [61]. H e r e o n l y s o m e s e l e c t e d c a s e s w i l l be d i s c u s s e d : 188ir : F r o m Q I - N O on 188 Ir in Re, M u r r a y et al. [3] d e t e r m i n e d t h e g r o u n d s t a t e q u a d r u p o l e m o m e n t of 188Ir to be +1.26(7) b. T h i s was b a s e d on the a s s u m p t i o n of I ~ = 2- for the 188Ir g r o u n d s t a t e and on an e s t i m a t e for t h e f i e l d g r a d i e n t of Ir in Re. R e c e n t l y , the g r o u n d s t a t e s p i n of 188Ir w a s e x p e r i m e n t a l l y d e t e r m i n e d to be I = I [15]. M o r e o v e r , t h e 188Ir g r o u n d s t a t e q u a d r u p o l e m o m e n t w a s m e a s u r e d w i t h Q I - N M R - O N in Fe a n d Ni to be Q(188Ir) = +0.54(2) b. A Q I - N M R - O N s p e c t r u m of 1 8 8 I r N i is s h o w n in F i g u r e 2. F o r I = 2, four q u a d r u p o l e s u b r e s o n a n c e s w o u l d be e x p e c t e d , w h i l e two r e s o n a n c e s are e x p e c t e d for I = I. T h i s e x a m p l e shows t h a t t h e s m a l l q u a d r u p o l e s p l i t t i n g m a y be a u s e f u l m e a n s for the d e t e r m i n a t i o n of g r o u n d s t a t e spins, too. T h e Q I - N O m e a s u r e m e n t of M u r r a y et al. [3] c a n n o w be u s e d to d e r i v e the E F G of I r R e w h i c h w a s n o t k n o w n e x p e r i m e n t a l l y up to now.
26
E. Hagn, Nuclear orientation and quadrupole interaction
Table 2 List of QI-NO results. Quantities deduced are underlined. Isotope
65Zn 69mzn
Host
In
Zn
5/2-
Zn
9/2-
TI/9 -
.Reaction
245d
n,T
13.8h
n,y
V [~t~z]
O -2.2(9)
Zn
6+
252d
m-i
IO9cd
Cd
5/2 +
1.2y
n,y
+3.40(34)
Q [b]
-O.O3 (i) a )
Ref.
[28] [29]
[3o]
-28(3) b) -44.0(4.4) -40(3)
[28] [31] +3.40(34)
+O. 50(6) a )
[32]
+67.2(1.9)
+1.68(11)
+1.65(IO) c)
[33]
+89(6) d) +110(4)
+6.6(7)
+0.69(7)
[35]
[36]
-41.5(2.1) 11OmAg
eq [1o 17 V/era2 ]
[34]
lllmcd
Be Zn
11/2
49m
m-i m-i
+43(16) -139(15)
-2.1(8) +6.8(1.O)
-O.85(9) -O.85(9)
]iSmcd
Cd
11/2-
43d
n,T
-50(14) d) -102(12)
+7.8(1.2)
-0.54(5)
[353
(-)2.2(8)
[36]
[34]
ll4mln
In
5+
5Od
n,y
-8.4(3)
(+)0.16(6)
[28]
122Sb
Sb
2+
2.7d
n,y
-32(2)
-2.8(3)
+0.47(3)
[37]
124Sb
Sb
3-
60.2d
n,y
-73(12)
-2.8(3)
+ 1.07 (20)
[37]
166~mi
Lu
2+
7.7h
Q,xn
-1440(100)
169yb
Lu
7/2 +
32.Od
~,xn
+280(30)
[38] [38] [39] C4o] [28] [40]
173Lu
Re
7/2 +
1.4y
~,xn
-1149(1OO)
-13.2(1.2)
+3.6(I)
176mLu
Lu
l-
3.7h
n,y
-128(16)
+3.6(5)
-1.47(I)
177Lu
Lu
7/2 +
6.7d
n,y n,y m-i m-i m-i
+144.3(6.O) e) +294(37) +3.6(5) +304(10) +3.71(14) +334(1OO) -180(5) -19(5)
n,~ m-i
+310(110) +392(42)
+3.71(14)
+4.2(7)
m-i m-i
-173(20) +211(10)
-2.6(5) +3.2(5)
+2.7(4) +2.7(4)
d,2n
+3-7 +50 u -90 +364(24) +604(75) -540(43)
+4 7+1"0 " -1.5 +5.6(9) +9.4(3) -8.3(8)
+2.7(4)
d,2n n,y ~,xn
+2.7(4) +2.7(4) +2.7(4)
[43]
177mLu 175Hf
Zn In Lu Be Zn
23/2 5/2
161d 7Od
Lu
+3.39(2) +3.39(2)
[32]
[32] [41] [41]
18OmHf
Hf Re Hf
8-
5.5h
n,T
+996(60)
+9.4(3)
+4.4(5)
173Ta
Lu
5/2-
3.6h
~,6n
-247(25)
+5.33(14)
-1.9(2)
175Ta
LU
[32] [32]
[37] [37] [42] [i] [39]
7/2 +
iO.5h
~,4n
+470(45)
+5.33(14)
+3.65(35)
178Taf) Re
1+
9.3m
a,xn
-103(10)
-6.55(13)
+0.65(6)
182Re
2+
12.7h
d,xn
-223(21)
-5.05(5)
+i .8(2) h)
[i] [7 ] [7 ] [44] [45]
12C,xn
+311(24)
+7.0(6) c)
+1.8(2)
[43]
Re Lu
E. Hagn, Nuclear orientation and quadrupole interaction
Isotope
Host
I
T1/2
Reaction
VQ [~{z]
27
Q [Iol~qv/cm2]
Ref.
[b]
182mRe
Re
7+
64h
O,xn
-502(30)
-5.05(5)
183Re
Re
5/2 +
71d
Re
3-
38d
186Re
Re
188Re
Re
I-
17h
9/2 +
13h
12C,xn Q,xn
+5.3(.5) -3.83(33)
+3.12(27)
[32] [43]
+3.12(27)
[29]
191Os
Lu Re Os
-262(24) -281(20) -390(33) -340(22) -IO4(14)g) -73(7) -66(10) -iO3(16)g) -44(20) +403(20) -289(10)
-5.05(5) -5.05(5)
184Re
diff a,xn diff S,xn n,y S,xn n,y n,y
9/2-
15.4d
n,y
-278(9) i)
-4.54(24)
+2.53(16)
[46]
193Os
Os
3/2-
31h
n,y
-96(15)
-4.54(24)
+O.87(!5)
[46]
184Ir
Re
5
3.Oh
O,5n
185Ir
Re
5/2-
14h
~,4n
-3.2(3) -3.6(2) k) -3.2(3) -3.6(2) k)
+2.2(4) +2.0(3) -2.0(3)
[4 ] [5 ] [4 ]
186Ir
Re
-2.5 (3)
5+
16h
~,3n
-3.6(2) k)
-2.54(16)
[5 ] [47] [3 ] [4 ] [2 ]
183
Os
i-
9Oh
+4.1(3) +2.1(2) h)
[44] [45]
+2.3(2)
[44]
[45] -5.05(5)
+2.8(2)
[44]
[45] -5.05(5) -5.05(5)
+0.60(6)
[44]
+0.54(9-~-h)) [32]
[45]
d,xn
-168(26) -175(26) -158(21) +219(20) +189(9) +218(11) +209(14) +175(10)
-3.OO(17)
-2.41(20)
2-
41.5h
~,xn
-107.8(3.3)
-3.6(2) k)
+1.26(7)
[3 ]
3/2 +
13d
~,xn d,xn
-85.9(3.6) -78(15)
-3.6(2) -3.OO(13)
i.O 1 ) +I.O8(21)
[3 ] [47]
4
12d
O,xn d,xn
-245(6) -203(9)
-3.6(2) k) -3.OO(13)
+2.85(14) +2.80(17)
[3 ] [47]
192Ir
Re Os Re Os Os
4-
74d
d,2n
-171(8)
-3.OO(17)
+2.36(11)
[47]
189pt
Os
3/2-
11h
~,n
+48(9)
191pt
Os
3/2-
2.8d
a,n
+39(6)
195mpt
Os
13/2 +
4.Od
a,n
-87(12)
195mAu%
cd
11/2-
30.28
diff
+395(18)
+1.57(23)
[48]
197mAun)
Cd
11/2-
7.68
diff
+350(58)
+1.51(28)
[48]
198Au
Zn Cd Zn Cd Be
2.7d
m-i m-i
+162(3) ~ ) +130(4) ~ )
3.1d
m-i m-i
+127(2) ~ ) +107(3) ~ )
13/2 +
4Oh
r-i
-52(8)
Be Zn Cd In Sb Re
13/2 +
24h
m-i m-i m-i m-i m-i m-i
-110(20) +480(20) +430(30) +104(5) +70(7) -110(15)
Be
5/2-
1.66h
m-i
-42(17) p)
188Ir 189Ir 19OIr
199Au 195mHg 197mHg
205
Po
Os Re
23/2 +
[17] [17] [17]
[49]
[49] [49]
[49] -3.1(6) +13.5(1.3) +12.1(1.4) +2.9(3) +2.0(3) -3.1(4)
+1.27(11)
[50]
+1.47(13) +1.47(13) +1.47(13) +1.47(13) +1.47(13) +1.47(13)
[51] [52] [52] [37] [53] [52]
[s4]
E. Hagn, Nuclear orientation and quadrupole interaction
28
Isotope
Host
I
n
TI/2
Reaction
VQ [MHz]
207po
Be Zn
5/2-
5.79h
m-i m-i
-70(20) p) +42(3)
208At
Be Zn
(6+ )
1.63h
m-i m-i
+144(32) q) -36.5(9.5) q)
209At
Be
9/2-
5.4h
r-i m-i m-i m-i m-i m-i
-208(23) r) +180(51) q) +147(18) s ) -41.6(4.5) q) -40. I(3.2) s) -IO.4(5) s)
5+
8.1h
r-i m-i m-i m-i
-138(I0~ r) +105(8) ) -29.4(1.3~ s) -7.5(5.0)-)
Zn Cd 21OAt
Be Zn Cd
eq [1017 V/cm 2]
Q [b]
Ref.
[54]
[5a] [55] [ss] [s6] [55] [55] [55] [55] [55] [56] [55] [55] [55]
a) recalculated using the EFG of ref. [57]. b) absolute value too small, probably because of thermometry; remeasured as -40(4) MHz [58']. c) recalculated. d) absolute value too small, probably because of faults in thermometry [59]. e) absolute value too small, possibly because of temperature gradients; see discussion in [32]. f) daughter of 178W(TI/2 = 22 d). g) absolute value too large, probably because of faults in thermometry. h) recalculated using the EFG of ref. [60]. i) spin-lattice relaxation observed. k) EFG deduced using a theoretical quadrupole moment for 189Ir. i) theoretical value. m) daughter of 195mHg (TI/2 = 40 h). n) daughter of 197mHg (TI/2 = 24 h). o) measured simultaneously; deduced Q(198Au)/Q(199Au) = +1.26(3). p) measured simultaneously; deduced Q(207po)/Q(2O5po) = +1.7(8). q) measured simultaneously; deduced Q(208At)/Q(209At) = +0.75(4). r) measured simultaneously; deduced Q(209At)/Q(21OAt) = +1.47(7). s) measured simultaneously; deduced Q(209At)/Q(21OAt) = +1.39(5).
197,198,199Au
:
QI-NO experiments o n 1 9 8 A u a n d 1 9 9 A u in C d a n d Zn h a v e b e e n r e p o r t e d b y H e r z o g e t al. [49]. T h e r a t i o o f q u a d r u p o l e moments, Q(198Au)/Q(199Au) = 1 . 2 6 ( 3 ) is in m o d e r a t e agreement with the ratio Q(198Au)/Q(199Au) = 1.37(3) known from QI-NMR-ON on 198,199AuFe [10, 18]. H o w e v e r , the absolute quadrupole moments of 198,199Au der-ived by Perscheid a n d H a a s [62], w h o r e p o r t e d a measurement of the EFG's o f A u in C d a n d Zn, Q ( 1 9 8 A u ) = 0.46(2)b Q(199Au) = 0.37(I)b, are strongly different from Q(198Au) = 0.76~4)b, Q(199Au) = 0.55(3)b, d e r i v e d b y R i e d i a n d H a g n [63] t a k i n g i n t o a c c o u n t t h e E F G o f A u F e measured with the spin-echo technique. These discrepancies are disc u s s e d in d e t a i l in ref. [63]; t h e m o s t p r o b a b l y explanation is a different l a t t i c e l o c a t i o n o f 1 9 7 A u in C d a n d Z n - in t h i s c a s e t h e
E. Hagn, Nuclear orientation and quadrupole interaction
29
mother isotope 197Hg was implanted - and of 198'199Au, w h i c h were implanted d i r e c t l y into Cd and Zn. I
I
I
I
41S00
41000
~-,
40500
o s
i
40000
P
39S00
39000
I
I
I
102
104
106
I 108
F r e q u e n c y (MHz) Fig. 2. QI-NMR-ON s p e c ~ of 188IrNi. The observation of two subresonanees proves the a s s i s t of I = I to the 188ir ground state, in contradiction to I = 2 adopted before. Taken frcm ref. [15]. 209,21OAt : The p r o b l e m of different lattice locations is most obviously" seen in the d i f f e r e n t results obtained from QI-NO on At isotopes: QI-NO experiments have been performed on 2 0 8 , 2 0 9 , 2 1 O A t B e prepared via m a s s - s e p a r a t o r i m p l a n t a t i o n by the Bonn aroup [55] and on 209,210AtBe p r e p a r e d via recoil i m p l a n t a t i o n - b y the Munich group [56] A d ~ e c t c o m p a r i s o n is thus possible for 209,21OAt The data VQ(209AtBe) = +147(18) MHz, VQ(21OAtBe) = +105(8) MHz for the mass ~ sep~stor-/-implanted samples [55] and-Ve(209AtBe) = -208(23) MHz, VQ( AtBe) = -138(10) MHz for the r e c o i l - i m p ~ n t e d samples [56] seem to be c o n t r a d i c t i n g totally; the ratio of q u a d r u p o l e interaction frequencies, and hence the ratio of q u a d r u p o l e moments, however, is similar, 1.44(8) [55] and 1.47(7) [56]. This means that the At isotopes are obviously s u b s t i t u t e d onto (at least) two d i f f e r e n t lattice sites, for which the sign of the EFG is different. The (small) integral q u a d r u p o l e splitting is d e t e r m i n e d by a partial cancellation of both contributions. In this w a y also the d i f f e r e n t signs can be understood: With the m a s s - s e p a r a t o r implantations, which were performed at t e m p e r a t u r e s b e l o w I K, the At isotopes are substituted to a larger degree onto those lattice sites for which V Q is positive,
E. Hagn, Nuclear orientation and quadrupole interaction
30
w h i l e l a t t i c e sites w i t h a m o r e n e g a t i v e VQ are f a v o u r e d in the recoil-implantation p e r f o r m e d at r o o m t e m p e r a t u r e . T h i s d e m o n s t r a t e s the n e c e s s i t y of s i m u l t a n e o u s m e a s u r e m e n t s of d i f f e r e n t i s o t o p e s : R a t i o s of q u a d r u p o l e m o m e n t s can be d e t e r m i n e d q u i t e r e l i a b l y , e v e n if the l a t t i c e l o c a t i o n of the i m p u r i t y i s o t o p e s is not k n o w n in dedail. 5.
Aspects The
of n u c l e a r
nuclear
spectroscopic
spectroscopic
quadrupole
quadrupole
moment
moments Q, w h i c h
is defined
as eQ = < I I I f d 3 X ~ N ( X )
(3z2 - r 2)
III>,
(9)
w h e r e ~N is the n u c l e a r c h a r g e d e n s i t y , is a d i r e c t m e a s u r e for the n o n s p h e r i c i t y of the n u c l e a r shape. O n l y for n u c l e i in the i m m e d i a t e v i c i n i t y of c l o s e d s h e l l s the s p e c t r o s c o p i c q u a d r u p o l e m o m e n t d e p e n d s on s i n g l e p a r t i c l e p r o p e r t i e s . For d e f o r m e d n u c l e i the q u a d r u p o ! e mom e n t d e p e n d s on c o l l e c t i v e p r o p e r t i e s , m a i n l y on d e f o r m a t i o n p a r a m e ters. In the f r a m e w o r k of the r o t a t i o n a l m o d e l the s p e c t r o s c o p i c quad r u p o l e m o m e n t Q is c o n n e c t e d w i t h the i n t r i n s i c q u a d r u p o l e m o m e n t Q~, w h i c h d i r e c t l y e n t e r s in B(E2) t r a n s i t i o n p r o b a b i l i t i e s , v i a the projection formula 3K2-I(I+I) (10) Q = Qo (I+I) (2I+3)' w h e r e K is the p r o j e c t i o n of the s i n g l e p a r t i c l e the s y m m e t r y axis of the (deformed) n u c l e u s . For s t a t e s K=I holds, and eq. (10) r e d u c e s to
Q = Qo
I(2I-I) (I+I) (2I+3)"
angular momenta "normal" g r o u n d
on
(11)
F r o m eq. (10) it is o b v i o u s t h a t the K q u a n t u m n u m b e r of a n u c l e a r s t a t e can be d e t e r m i n e d e x p e r i m e n t a l l y by the d e t e r m i n a t i o n of Q and Qo- " A n o m a l o u s " g r o u n d states, for w h i c h K 192 the e v e n - A Pt i s o t o p e s h a v e o b l a t e shapes. As the l i g h t Pt i s o t o p e s are e x p e c t e d to be d e f o r m e d w i t h p r o l a t e s h a p e s - t h e r e is no u n i q u e e x p e r i m e n t a l e v i d e n c e y e t - a p r o l a t e - o b l a t e phase transition is e x p e c t e d at A ~ 190. F o r the Pt n u c l e i in this t r a n s i t i o n region prolate-oblate s h a p e c o e x i s t e n c e m a y a l s o occur. R e c e n t Q I - N O m e a s u r e m e n t s on 1 8 9 , 1 9 1 p t (I" = 3/2-) a n d 7 9 5 m p t (I ~ = 13/2 + ) in Os [17] s h o w e d t h a t the g r o u n d s t a t e q u a d r u p o l e m o m e n t s of 1 8 9 , 1 9 1 P t w e r e n e g a t i v e . As the e x i s t e n c e of a n o m a l o u s g r o u n d s t a t e s for 1 8 9 , 1 9 1 p t c a n be r u l e d o u t w i t h g o o d a r g u m e n t s , n e g a t i v e i n t r i n s i c q u a d r u p o l e m o m e n t s and h e n c e an o b l a t e d e f o r m a t i o n of 1 8 9 , 1 9 1 p t c a n be c o n c l u d e d f r o m t h e s e e x p e r i m e n t s . This m e a n s t h a t the p r o l a t e o b l a t e p h a s e t r a n s i t i o n c a n n o w be l o c a t e d to o c c u r for A < 189.
E. Hagn, Nuclear orientation and quadrupole interaction
31
With o n - l i n e techniques, these experiments can easily be extended to lighter Pt isotopes. Such a p r o l a t e - o b l a t e phase transition had also be p r e d i c t e d to occur for Os around A ~ 192. QI-NO experiments on 191,193Os [46], together w i t h muonic X-ray data on the even-A stable Os isotopes, showed a slight decrease of the d e f o r m a t i o n with inc r e a s i n g mass number but no drastic change, i.e., for Os no prolateoblate phase transition occurs at A < 193. From systematic QI-NO and Q I - N M R - O N experiments on Ir isotcpes in the mass range A = 184-194 the following features were observed: The h e a v i e r isotopes 1 8 8 , 1 8 9 , 1 9 0 , 1 9 2 , 1 9 4 I r have "normal" ground states (K=I); the intrinsic q u a d r u p o l e m o m e n t s derived a c c o r d i n g to eq. (11) show a slight decrease with increasing mass number, i.e., a slight decrease of the (prolate) deformation. There is no evidence for a p r o ! a t e - o b l a t e phase transition, which can be understood because the d e f o r m a t i o n of the odd-even and odd-odd nuclei is more stable than for e v e n - e v e n nuclei. The light isotopes 184,185,!86Ir, however, have anomalous ground state c o n f i g u r a t i o n s [2-6]: The 185Ir ground state is the 5/2- member of the strongly d i s t u r b e d K=I/2- rotational band built on the ~I/2-[541] N i l s s o n state, i.e., InK = 5/2-I/2, w h i c h has been verified by the n e g a t i v e q u ~ d r u p o l e m o m e n t [4,5]. The 186Ir ground state is d e t e r m i n e d by the addition of a n e u t r o n in a I/2-[510] N i l s s o n state. By Coriolis m i x i n g of the K=O and K=I bands b u i l t up on the { , I / 2 - [ 5 4 1 ] ; V I / 2 - [ 5 1 0 ] } O + , I + states, the energy of the 5 + state is lowered below the band heads, i.e., the 1861r ground state consists m a i n l y of InK=5+O and 5+I components. Such a large d i f f e r e n c e between I and K is a b s o l u t e l y unexpected for a ground state, and has not been observed for any other nucleus up to now, but has been verified e x p e r i m e n t a l l y by the negative s p e c t r o s c o p i c q u a d r u p o l e m o m e n t [2,3]. Due to the similar B-decay p r o p e r t i e s of 1841r and 186Ir to levels in 184Os and 186Os e s p e c i a l l y the strong p o p u l a t i o n of the levels b e l o n g i n g to the K=O ground state r o t a t i o n a l band -, a similar ground state c o n f i g u r a t i o n had been p r e d i c t e d t h e o r e t i c a l l y for 184Ir. Here, however, a positive s p e c t r o s c o p i c q u a d r u p o l e m o m e n t was detected, the absolute m a g n i t u d e e x c l u d i n g a "normal" ground stat% c o n f i g u r a t i o n INK=5(+)5 [4-6]. A g a i n Coriolis mixing, m a i n l y caused by the I/2-[541] proton, is a s s u m e d to be responsible; the details on the neutron N i l s s o n state involved here are not clear at present, which is d i s c u s s e d in ref. [6]. This clearly d e m o n s t r a t e s that c o n f i g u r a t i o n a s s i g n m e n t s a c c o r d i n g to B-decay p r o p e r t i e s m a y fail completely, e s p e c i a l l y in this mass region, and that a direct m e a s u r e m e n t of the K q u a n t u m number allows more reliable a s s i g n m e n t s of ground state configurations. A similar situation exists for the light Ta isotopes: For 173Ta, an I~K=5/2-I/2 ground state c o n f i g u r a t i o n had been p r o p o s e d [64], w h i c h was r e c e n t l y c o n f i r m e d e x p e r i m e n t a l l y by a QI-NO measurement of the s p e c t r o s c o p i c q u a d r u p o ! e moment, which was found to be n e g a t i v e with a similar m a g n i t u d e as that of 185Ir [7]. For 174Ta, an a n o m a l o u s ground state c o n f i g u r a t i o n could thus be expected, w h i c h could be i n v e s t i g a t e d by a Q I - N O measurement. Because of the short half life, on-line techniques will be necessary. These selected examples show that v a l u a b l e n u c l e a r structure information can be o b t a i n e d from Q I - N O experiments, which, with the new on-line techniques, can be extended to i n t e r e s t i n g regions of s h o r t - l i v e d neutrond e f i c i e n t nuclei. 6.
Aspects
of electric
field
gradients
E s p e c i a l l y in recent years the study of EFG's has gained cons i d e r a b l e interest, m a i n l y b e c a u s e of the fact that no c o m p r e h e n s i v e t h e o r e t i c a l u n d e r s t a n d i n g of EFG's exists. The m o s t recent reviews
32
E. Hagn, Nuclear orientation and quadrupole interaction
of the situation can be found in refs. [65-68]. A c o m p i l a t i o n of q u a d r u p o l e interaction frequencies is given in ref. [69]. Here only those aspects will be c o v e r e d to w h i c h QI-NO has c o n t r i b u t e d and to which it may c o n t r i b u t e in future. Many EFG data result from m e a s u r e m e n t techniques, such as perturbed angular correlation, with w h i c h the sign is not accessible. The sign, however, is an e x t r e m e l y important quantity, as the total EFG is - in a simplified picture - the sum of two contributions, the ionic gradient eqion and the electronic field gradient eqel, w h e r e b y neither m a g n i t u d e nor sign of eqe I can be p r e d i c t e d theoretically. As leqell is of the same order of m a g n i t u d e as leqionl , it cannot be a n t i c i p a t e d a priori, w h e t h e r the two c o n t r i b u t i o n s add parallel or a n t i p a r a l l e l if the sign of the total EFG is unknown. Using the conventional parametrization eq = eqion + eqe I eqion =
(12)
(I - T ~ ) e q l a t t.
R a g h a v a n et al. [70,21] p r o p o s e d a "universal correlation" b e t w e e n the total EFG and the lattice g r a d i e n t eqlatt, w h i c h can easily be c a l c u l a t e d using lattice sum methods, a c c o r d i n g to w h i c h eq = K(I
- T ~ ) e q l a t t + eq
(13)
should hold in.general, w h e r e K ~ -2 is a "universal" constant, T ~ is the S t e r n h e i m e r factor of the impurity atoms and eq should take into account small c o r r e c t i o n s due to the individual p r o p e r t i e s of d i f f e r e n t i m p u r i t y - h o s t combinations. A c c o r d i n g to this c o r r e l a t i o n only n e g a t i v e EFG's w o u l d be expected for all h e x a g o n a l metals w i t h c/a < 1.6345, for w h i c h the lattice gradients are positive. Subsequently, many m e a s u r e m e n t s had been p e r f o r m e d to prove the u n i v e r s a lity of this correlation. However, in m o s t cases only the a b s o l u t e m a g n i t u d e of the EFG was determined, and the sign was g e n e r a l l y chosen in such a w a y that the s u b t r a c t i o n of the ionic part y i e l d e d an electronic c o n t r i b u t i o n fitting into this c o r r e l a t i o n scheme [65]. B a s e d on Q I - N O e x p e r i m e n t s on 177LuLu, from w h i c h a large positive E F G was found, Ernst et al. [40] r e e x a m i n e d the data leading to the "universal correlation". They argued that, to first approximation, the trends of pure systems should be viewed, and that impurity systems should be regarded in a second step. T a k i n g into account only the data on pure systems they p r o p o s e d that eq. (13) holds approximately, but the p r o p o r t i o n a l i t y c o n s t a n t should depend on the atomic group: K N -2 for Group K ~ +3 for Group
IIb, VIIb, IIIb, IVb.
VIIIb (14)
No p r e d i c t i o n s on impurity systems had been made in the f r a m e w o r k of this e x t e n d e d c o r r e l a t i o n [40]; e s p e c i a l l y the sign of i m p u r i t y - h o s t combinations, one b e l o n g i n g to G r o u p IIb, VIIb, VIIIb, the other to Group IIIb, IVb, could not be p r e d i c t e d a priori. S u b s e q u e n t Q I - N O m e a s u r e m e n t s on several d i f f e r e n t i m p u r i t y - h o s t c o m b i n a t i o n s led to the p r o p o s a l that the sign of the EFG is fixed by the sign of the EFG of the host lattice, i n d e p e n d e n t of the type of the impurity system [43]. Q I - N O m e a s u r e m e n t s on the inverse systems s u p p o r t e d also this p r o p o s a l [39]. W i t h one exception, 57FeTi [71], all p r e s e n t l y known signs of EFG's fit into this c o r r e l a t i ~ scheme. M o s t l y w i t h M 6 B b a u e r effect and a n g u l a r c o r r e l a t i o n techniques, m a n y EFG's have been d e t e r m i n e d for d i f f e r e n t i m p u r i t y - h o s t combina-
E. Hagn, Nuclear orientation and quadrupole interaction
33
t i o n s w h i c h f o l l o w the e x t e n d e d c o r r e l a t i o n in s i g n b u t n o t in magnitude. This m e a n s t h a t the c o n c e p t of a " u n i v e r s a l c o r r e l a t i o n " in the p r e s e n t f o r m is n o t a p p r o p r i a t e to i n c l u d e i m p u r i t y systems, s i n c e the t e r m e~. (13) t u r n e d out to be n o t a small c o r r e c t i o n as h a d b e e n assumed. This, h o w e v e r , is n o t v e r y a s t o n i s h i n g as no spec i f i c (electronic) p r o p e r t i e s of d i f f e r e n t i m p u r i t i e s are t a k e n into a c c o u n t in t h e s e c o n c e p t s . C o r r e l a t i o n s of the E F G w i t h the i m p u r i t y v a l e n c e h a d e a r l y b e e n o b s e r v e d by L e i t z et al. [72] and C o l l i n s [73]. S o a r e s et al. [53] p r o p o s e d a (linear) d e p e n d e n c e of the " u n i v e r s a l c o n s t a n t " K on the i m p u r i t y v a l e n c e . E F G d a t a on d i f f e r e n t i m p u r i t i e s in a Zn m a t r i x s h o w s u c h a l i n e a r b e h a v i o u r of K on the i m p u r i t y v a l e n c e [53]. R e c e n t d a t a on A g Z n [33] s e e m to fit w e l l into this scheme, too. It seems to be q u i t e r e a s o n a b l e that the e l e c t r o n i c f i e l d g r a d i e n t is p r o p o r t i o n a l to the n u m b e r of ("quasi-free") e l e c t r o n s at the impur i t y site. A s i m i l a r s y s t e m a t i c s w a s i n v e s t i g a t e d by H a g n et ai.[39] for d i f f e r e n t i m p u r i t i e s ("X") in Lu and Re. F o r XL__uu the b e h a v i o u r of K is s i m i l a r to t h a t for XZ__nn, a (linear) i n c r e a s e of K w i t h the i m p u r i t y v a l e n c e . F o r XRe, h o w e v e r , the o p p o s i t e b e h a v i o u r w a s observed: T h e e l e c t r o n i c field g r a d i e n t d e c r e a s e s w i t h i n c r e a s i n g valence, i.e., the n u m b e r of "outer" e l e c t r o n s . T h i s m e a n s t h a t the s i m p l e a r g u m e n t s l e a d i n g to a p r o p o r t i o n a l i t y b e t w e e n the e l e c t r o n i c f i e l d g r a d i e n t and the n u m b e r of v a l e n c e e l e c t r o n s is n o t a p p l i c a b l e in the g e n e r a l case. A s i m i l a r t r e n d h a d a l s o b e e n o b s e r v e d by W o r t m a n n et al. [74]. T h e y a r g u e that e q i o n m a y be an a r t i f i c i a l p a r a m e ter for i m p u r i t y systems, s i n c e the local v o l u m e and the local lattice distortion (c/a ratio) at the i m p u r i t y site are not known. Recent measurements of the E F G ' s of d i f f e r e n t i m p u r i t i e s in Os s h o w e d an e v e n m o r e c o m p l i c a t e d b e h a v i o u r of the e l e c t r o n i c f i e l d g r a d i e n t on the i m p u r i t y v a l e n c e [38], w h i c h s u p p o r t t h e s e a r g u m e n t s . At this p o i n t a c r i t i c a l c o m m e n t on the p r o b l e m of l a t t i c e l o c a t i o n s h o u l d be made: M o s t of t h e s e E F G ' s h a v e b e e n d e t e r m i n e d w i t h " i n t e g r a l " t e c h n i q u e s , Q I - N O or u n r e s o l v e d M 6 B b a u e r s p e c t r o s c o p y . For the anal y s i s it is a l w a y s a s s u m e d t h a t the i m p u r i t y n u c l e i are s u b s t i t u t e d o n t o r e g u l a r l a t t i c e sites w i t h a f r a c t i o n of f=1 (1OO%). ( S o m e t i m e s it is a s s u m e d t h a t a f r a c t i o n f<1 of n u c l e i is s u b j e c t to the full u n d i s t u r b e d h y p e r f i n e i n t e r a c t i o n w h i l e the rest, l-f, is s u b j e c t to no h y p e r f i n e i n t e r a c t i o n ) . T h i s a s s u m p t i o n has b e e n p r o v e n for several s e l e c t e d c a s e s w i t h the d i f f e r e n t i a l angular correlation technique. H o w e v e r , a g e n e r a l i z a t i o n c a n n o t be j u s t i f i e d by p h y s i c a l a r g u m e n t s . E s p e c i a l l y for i m p u r i t y s y s t e m s for w h i c h the m e t a l l u r g i c p r o p e r t i e s or the a t o m i c r a d i i of the i m p u r i t y and the h o s t are s t r o n g l y d i f f e r e n t one can i m a g i n e t h a t the i m p u r i t y n u c l e i are part i a l l y s u b s t i t u t e d o n t o i n t e r s t i t i a l sites w h e r e the E F G m a y be ent i r e l y d i f f e r e n t , e v e n the sign. F o r e x a m p l e , the E F G of Hg on inters t i t i a l s i t e s in Be is by a f a c t o r of ~ 10 l a r g e r t h a n the E F G on substitutional sites [51]. T h i s m e a n s t h a t e v e n a s m a l l f r a c t i o n of i m p u r i t y n u c l e i on i n t e r s t i t i a l sites m a y i n f l u e n c e s t r o n g l y the "total" E F G m e a s u r e d w i t h i n t e g r a l t e c h n i q u e s , and t h a t this "total" E F G d o e s n o t r e p r e s e n t the E F G on s u b s t i t u t i o n a l sites. As this f r a c t i o n w o u l d be e x p e c t e d to be d i f f e r e n t for d i f f e r e n t i m p u r i t y e l e m e n t s , a w r o n g c o r r e l a t i o n of the E F G on, e.g., the i m p u r i t y valence c o u l d be e x t r a c t e d f r o m the "total" EFG's. T h e E F G ' s at the t r a n s i t i o n - e l e m e n t i m p u r i t y 193Ir in the h e x a g o n a l t r a n s i t i o n m e t a l s Sc, Y, Lu, Ti, Zr a n d Hf h a v e b e e n i n v e s t i gated with M6Bbauer effect measurements by F o r k e r and K r u s c h [75]. L a r g e E F G ' s w e r e found, n o t f i t t i n g i n t o any c o r r e l a t i o n scheme. T h e E F G of IrS__cc, leqi = 4 2 . 9 ( 1 1 . 0 ) x 1017 V / c m 2, is the l a r g e s t v a l u e e v e r o b s e r v e d at a n o n - r a r e - e a r t h i m p u r i t y in a n o n - c u b i c m e t a l .
E. Hagn, Nuclear orientation and quadrupole interaction
34
Forker and K r u s c h argue that the d e n s i t y of states at the Fermi energy of the host and the electronic structure of the impurity are of m a j o r importance for the EFG in t r a n s i t i o n - m e t a l alloys. However, as melted samples were used in these experiments, it cannot be excluded to my opinion that i n t e r m e t a l l i c compounds are formed leading to such high EFG's. Thus no definite conclusions should be drawn at present. It w o u l d highly be d e s i r a b l e to m e a s u r e more EFG's w i t h d i f f e r e n t i a l m e a s u r e m e n t techniques and more effort should be made for the development of the technique of n u c l e a r q u a d r u p o l e r e s o n a n c e on oriented nuclei. It should be m e n t i o n e d that the d i f f e r e n t i a l t e c h n i q u e of level m i x i n g r e s o n a n c e on o r i e n t e d nuclei (LMR-ON) may be well a p p l ~ cable in special cases for the precise d e t e r m i n a t i o n of the substitutional EFG. 7.
Recent
developments
7. I.
N e w m a t r i c e s for Q I - N O
In the p r e c e d i n g it has been pointed out that ratios of quadrupole splittings and hence ratios of s p e c t r o s c o p i c q u a d r u p o l e m o m e n t s can be d e t e r m i n e d reliably with QI-NO. The o b t a i n a b l e a c c u r a c y strongly depends on the absolute m a g n i t u d e of the o b s e r v e d y - a n i s o tropies. This means that matrices with EFG's as large as p o s s i b l e are desirable. Moreover, m a s s - s e p a r a t o r i m p l a n t a t i o n should be avoided, if possible, in order to get rid of the surface q u a l i t y problems. (If two ~ s o t o p e s are implanted, which is in general not be done simultaneously, d i f f e r e n t areas m a y be hit for the d i f f e r e n t isotopes, not g u a r a n t e e i n g the same average EFG). For in-situ preparations the p o s s i b i l i t i e s u s i n g n o n - c u b i c m e t a l s as targets are limited. Thus other m e t a l l i c compounds with large EFG's w o u l d be of interest. Recently it had been proposed that d i c h a l c o g e n i d e s m i g h t be good m a t r i c e s for QI-NO [76]. For 2H-TaS 2 a large EFG (> I x 1018 V / c m 2) had been observed with PAC [77]. A l t h o u g h there are two inequivalent (substitutional) sites, for which the EFG is slightly different - the l o w - f r e q u e n c y - s i t e EFG is axially asymmetric, ~ = 0.35, w h i l e the h i g h - f r e q u e n c y EFG is axially symmetric -, such m a t r i c e s could be well suited for QI-NO. In the first Q I - N O e x p e r i m e n t s on 182Ta in 2H-TaS 2 [76] y - a n i s o t r o p i e s up to 30% were observed, which, however, was only about half of the value expected taking into account the k n o w n EFG and a r e a s o n a b l e estimate of the a u a d r u p o l e moment of 182Ta. In subsequent e x p e r i m e n t s it was found'that the too small y - a n i s o t r o p i e s were due to lattice location. (The first samples had not been annealed after the n e u t r o n irradiations). U s i n g singlecrystal samples w h i c h were annealed after the i r r a d i a t i o n and singlecrystals for w h i c h the 182Ta activity was i n c o r p o r a t e d during the c r y s t a l growing c o n s i s t e n t q u a d r u p o l e splittings were obtained, ~ = -11OO(1OO) MHz, from w h i c h the s p e c t r o s c o p i c q u a d r u p o l e m o m e n t 182Ta could be d e d u c e d to be +2.6(3) b [78]. (The r e l a t i v e l y large error is m a i n l y due to the yet unknown h e a t - c o n d u c t i v i t y properties of 2H-TaS2; ratios of q u a d r u p o l e splittings could be determ i n e d w i t h much improved accuracy). These e x p e r i m e n t s showed that matrices of d i c h a l c o g e n i d e s are well suited for QI-NO. In addition, such c o m p o u n d s have i n t e r e s t i n g p r o p e r t i e s per se, such as an anisotropy of the s u p e r c o n d u c t i n g critical fields and thus an a n i s o t r o p y in the heat conductivity, w h i c h can be i n v e s t i g a t e d with QI-NO. 7.2.
"New" m a t r i c e s for Q I - N M R - O N
Up to now q u a d r u p o l e
resonance
on o r i e n t e d
nuclei
(NQR-ON)
has
E. ttagn, Nuclear orientation and quadrupole interaction
35
n o t b e e n o b s e r v e d . An a l t e r n a t i v e a p p r o a c h is q u a d r u p o l e i n t e r a c t i o n r e s o l v e d N M R on o r i e n t e d n u c l e i (QI-NMR-ON) u s i n g a f e r r o m a g n e t i c n o n - c u b i c h o s t m a t r i x . T h e m a g n e t i c i n t e r a c t i o n s e r v e s to get a h i g h d e g r e e of p o l a r i z a t i o n and a l a r g e e n h a n c e m e n t f a c t o r for the r a d i o f r e q u e n c y field, w h i l e the e l e c t r i c f i e l d g r a d i e n t s p l i t s the r e s o n a n c e i n t o a set of 2I s u b r e s o n a n c e s . The m o s t a t t r a c t i v e h o s t m a t e r i a l s are h c p - C o and h c p - G d . F i r s t e x p e r i m e n t s on 6 O C o C o ( h c p ) s h o w e d a O ~ - 90 ~ r e s o n a n c e d i s p l a c e m e n t , b u t no r e s o l v e d q u a ~ u p o l e subres o n a n c e s t r u c t u r e . T h e u s e of h c p - C o for m a s s - s e p a r a t o r implantation of h e a v y e l e m e n t s s u f f e r s f r o m the f a c t t h a t h c p - C o c a n n o t be a n n e a led at t e m p e r a t u r e s > 4 3 0 ~ as it u n d e r g o e s a h e x a g o n a l - c u b i c p h a s e t r a n s i t i o n . T h u s Gd, d e s p i t e of the c o m p l i c a t e d m a g n e t i z a t i o n b e h a v i o u r , m i g h t be a b e t t e r m a t r i x . F o r e x a m p l e , the q u a d r u p o l e s u b r e s o n a n c e s e p a r a t i o n for 1 9 8 A u G d is e x p e c t e d to be ~ 50 MHz at a m a g n e t i c h y p e r f i n e s p l i t t i n g of N 180 MHz. As no N M R - O N r e s o n a n c e h a d et b e e n o b s e r v e d in a Gd host, f i r s t e x p e r i m e n t s w e r e p e r f o r m e d on 11InGd, for w h i c h the s m a l l q u a d r u p o l e s u b r e s o n a n c e s e p a r a t i o n of I MH--~ f a c i l i a t e d the o b s e r v a t i o n of the N M R - O N r e s o n a n c e , w h i c h w a s e x p e c t e d at > 300 M H z [79]. 1 1 1 I n was i m p l a n t e d w i t h 350 kV i n t o a Gd s i n g l e c r y s t a l w i t h the m a s s s e p a r a t o r at K o n s t a n z . F i r s t the r e s o n a n c e w a s m e a s u r e d w i t h the u n a n n e a l e d s a m p l e in e x t e r n a l m a g n e tic f i e l d s O < B o < 4 kG. T h e z e r o - f i e l d h y p e r f i n e s p l i t t i n g , d e d u ced by e x t r a p o l a t i o n to B o = O a s s u m i n g a l i n e a r d e p e n d e n c e of the r e s o n a n c e f r e q u e n c y on Bo, w a s f o u n d to be 340.5(5) MHz. (Because of the u n r e s o l v e d q u a d r u p o l e i n t e r a c t i o n and the f i e l d - d e p e n d e n t a n g l e b e t w e e n the m a g n e t i z a t i o n and the c - a x i s of the s i n g l e c r y s t a l dev i a t i o n s f r o m the l i n e a r b e h a v i o u r b e t w e e n the a v e r a g e r e s o n a n c e freq u e n c y a n d the e x t e r n a l f i e l d m a y be e x p e c t e d ) . The o b s e r v e d l i n e w i d t h s , w h i c h w e r e a l s o f o u n d to s h o w a (small) d e p e n d e n c e on B o,
y
I
I
I
I 330
I 335
I 340
-0. 680 T-I
9 -~ Z
-0. 682
0
Z
-0. 684
-0. 686
Frequency (MHz) Fig.3. NMR-ON spectrum of 1111nGd. The well observable NMR-ON signal indicates that G d m i g h t be a good matrix for QI-NMR-ON on heavy impurities. Taken from ref. [79].
E. Hagn, Nuclear orientation and quadrupole interaction
36
v a r i e d b e t w e e n N 6 and ~ 8 MHz. A f t e r a n n e a l i n g the s a m p e for 1 h o u r at 6 5 0 ~ further measurements were performed. The line widths were r e d u c e d to 3 - 4 M H z and the z e r o - f i e l d h y p e r f i n e s p l i t t i n g w a s f o u n d to be 339.3(7) MHz. F i g u r e 3 s h o w s a N M R - O N s p e c t r u m of the a n n e a l e d s a m p l e . T h e d i f f e r e n c e in the z e r o - f i e l d h y p e r f i n e s p l i t t i n g s of the u n a n n e a l e d and the a n n e a l e d s a m p l e is a r e m a r k a b l e result. To my o p i n i o n it is a g e n e r a l e f f e c t t h a t the c e n t e r of r e l a t i v e l y b r o a d N M R - O N r e s o n a n c e s do n o t r e p r e s e n t the t r u e s u b s t i t u t i o n a l h y p e r f i n e s p l i t t i n g , i.e., the h y p e r f i n e s p l i t t i n g t h a t w o u l d be o b s e r v e d w i t h a h i g h l y d i l u t e sample. T h i s m e a n s t h a t the a c c u r a c y of the N M R - O N m e t h o d m a y by lost, and t h a t a g a i n o n l y r a t i o s of hyp e r f i n e s p l i t t i n g s can be m e a s u r e d w i t h r e s o n a n c e p r e c i s i o n . (See, e.g., the d i s c u s s i o n in ref. [63]). H o w e v e r , t h e s e m e a s u r e m e n t s h a v e s h o w n t h a t the N M R - O N t e c h n i q u e is w e l l a p p l i c a b l e to Gd s i n g l e c r y stal s a m p l e s , w h i c h m e a n s t h a t the q u a d r u p o l e s p l i t t i n g s for h e a v y e l e m e n t s s h o u l d be m e a s u r a b l e w i t h r e s o n a n c e p r e c i s i o n . (The q u a d r u p o l e s p l i t t i n g is e x p e c t e d to be not a f f e c t e d by l a r g e - l i n e - w i d t h effects). 8.
Conclusions
T h e m e t h o d s of Q I - N O and Q I - N M R - O N are w e l l a p p l i c a b l e to det e r m i n e r a t i o s of q u a d r u p o l e s p l i t t i n g s and h e n c e r a t i o s of n u c l e a r s p e c t r o s c o p i c q u a d r u p o l e m o m e n t s . The p r e c i s i o n , a l b e i t m u c h less t h a n the p r e c i s i o n o b t a i n a b l e w i t h o p t i c a l m e t h o d s , e.g. l a s e r s p e c t r o s c o p y , is s u f f i c i e n t for the d e r i v a t i o n of v a l u a b l e n u c l e a r s t r u c t u r e i n f o r m a t i o n . A d e c i s i v e a d v a n t a g e is the f a c t t h a t the sign of q u a d r u p o l e m o m e n t s can be d e t e r m i n e d in a d d i t i o n to the a b s o l u t e m a g n i t u d e . T h e s a m e f e a t u r e h o l d s t r u e for e l e c t r i c f i e l d g r a d i e n t s . E s p e c i a l l y the m e a s u r e m e n t s of the s i g n s of E F G ' s of p u r e - a n d impur i t y - s y s t e m s h a v e r e v e a l e d n e w a s p e c t s on the s y s t e m a t i c s of E F G ' s , w h i c h are n o t at all u n d e r s t o o d t h e o r e t i c a l l y at p r e s e n t . F o r a b e t ter u n d e r s t a n d i n g of E F G ' s Q I - N O m e a s u r e m e n t s can a l s o c o n t r i b u t e in future. It w o u l d be a d e c i s i v e a d v a n t a g e if n u c l e a r q u a d r u p o l e r e s o n a n c e on o r i e n t e d n u c l e i c o u l d be o b s e r v e d as t h e n the p r o b l e m of lattice location would disappear, which may obscure experimental t r e n d s k n o w n at p r e s e n t o n l y f r o m i n t e g r a l m e a s u r e m e n t t e c h n i q u e s . Acknowledgements I w o u l d like to t h a n k Dr. for d i s c u s s i o n s . T h i s w o r k w a s
E. Zech, R. E d e r s u p p o r t e d by the
and K.-H. E b e l i n g BMFT, Bonn, FRG.
References [i] [2] [3] [4] [5] [6] [7] [8]
[9] [iO] [II] [12] [13]
G. Kaindl, F. Bacon and A.J. Soinski, Phys. Lett. 46B(1973)62. H. Ernst, E. Hagn, U. Schneider and E. Zech, Phys. Lett. 86B(1979)154. D.W. Murray, A.L. Allsop and N.J. Stone, Hyp. Int. 7(1980)481. E. Hagn, H. Kleebauer and E. Zech, Phys. Lett. I04B(1981)365. A.L. Allsop, V.R. Green and N.J. Stone, Hyp. Int. 12(1982)289. E. Hagn and E. Zech, Hyp. Int. 14(1983)97. R. Eder, E. Hagn and E. Zech, Phys. Lett. 133B(1983)44. S.R. de Groot, H.A. Tolhoek and W.J. Huiskamp, in Alpha-, beta- and gammaray spectroscopy, ed. K. Siegbahn, vol. 2 (North-Holland, Amsterdam, 1968) p. 1199 ff. E. Hagn, K. Leuthold, E. Zech and H. Ernst, Z. Phys. A295(1980)385. E. Hagn and E. Zech, Phys. Rev. B29(1984)I148. E. Hagn, Phys. Rev. B25(1982)1521. E. Hagn and E. Zech, Phys. Rev. B25(1982)1529. E. Hagn and E. Zech, Z. Phys. A295(1980) 345.
E. Hagn, Nuclear orientation and quadrupole interaction
[14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31]
[32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] [43] [44] [45] [46] [47] [48] [49] [50] [5[] [52] [53] [54] [55] [56] [57] [58]
37
E. Hagn and E. Zech, Z. Phys. A297(1980)329. R. Eder, E. Hagn and E. Zech, to be published. E. Hagn, H. Kleebauer, M. Zahn and E. Zech, Z. Phys. A306(1982)73. R. Eder, E. Hagn and E. Zech, this conference E. Hagn and E. Zech, Z. Phys. A307(1982)159. W.B. Pearson, "A Handbook of lattice spacings and structures of metals and alloys", volume 2, (Pergamon Press, Oxford, 1967). American Institute of Physics Handbook, D.E. Gray, ed., (McGraw-Hill, New York, 1972). P. Raghavan, N. Kaufmann, R.S. Raghavan, E.J. Ansaldo and R.A. Naumann, Phys. Rev. B13(1976)2835. F.W. de Wette, Phys. Rev. 123(1961)103. T. Butz, private communication. E.H. Hygh and T.P. Das, Phys. Rev. 143(1966)452. M. Krusius and G. Picket, Sol. Stat. Comm. 9(1971)[917. P. Berzog, this conference. G. Eska, this conference. W.D. Brewer and G. Kaindl, Hyp. Int. 4(1978)576. H. Ernst, thesis, TU Munich, 1979, unpublished. P. Herzog, H.-R. Folle and E. Bodenstedt, Hyp. Int. 3(1977)361. J. Geenen, C. Nuytten, D. Vandeplassche and L. Vanneste, Annual Report, Instituut voor Kern- en Stralingsfysika, Kathilieke Universiteit Leuven, 1979, p. I11. D. Oertel, A. Kettschau, W.D. Brewer and L. Vanneste, Z. Phys. A310(1983)233. E. van Walle, D. Vandeplassche, C. Nuytten, J. Wouters and L. Vanneste, Phys. Rev. B28(1983) 1109. S.S. Rosenblum and W.A. Steyert, Phys. Lett. 53A(1975)34. H. Ernst, E. Hagn and E. Zech, Phys. Lett. 93A(1983)357. P. Herzog, K. Freitag, M. Reuschenbach and H. Walitzki, Z. Phys. A294 (1980) 13. P. Herzog, K. Freitag, M. Reuschenbach and H. Walitzki, P. Herzog, private communication. E. Hagn and E. Zech, this conference. E. Hagn, M. Zahn and E. Zech, Phys. Rev. B28(1983)3130. H. Ernst, E. Hagn, E. Zech and G. Eska, Phys. Rev. B19(1979)4460. P. Herzog, K. Freitag, C.-D. Herrmann and K. Schl6sser, Z. Phys. 54B([983)31. H. Ernst, E. Hagn and E. Zech, J. Phys. F9(1979) 1701. H. Ernst, E. Hagn and E. Zech, Phys. Rev. B22(1980)2248. E. Hagn, M. Zahn and E. Zech, Hyp. Int. 15/16(1983)105. H. Ernst, E. Hagn and E. Zech, Phys. Rev. C23(1981)1739. H. Ernst, E. Hagn and E. Zech, Nucl. Phys. A332(1979)41. U. Schneider, Diplomarbeit TU M~nchen, [980, unpublished. I. Berkes, G. Marest, J. Sau, H. Sayouty, P. Put, R. Coussement and G. Scheveneels, Hyp. Int. 15/16(1983)233. P. Herzog, K. Freitag, H. Hildebrand, M. Reuschenbach and H. Walitzki, Z. Phys. A314(1983)215. E. Hagn, H. Kleebauer, M. Zahn, E. Zech and S. Jonsson, unpublished. K. Krien, F. Reuschenbach, J.C. Soares, P. Herzog, H.-R. Folle, B. Perscheid, R. Trzcinski and K. Freitag, Hyp. Int. 7(1980)401. P. Herzog, K. Krien, J.C. Soares, H.-R. Folle, K. Freitag, F. Reuschenbach, M. Reuschenbach and R. Trzcinski, Phys. Lett. 66A(1978)495. J.C. Soares, K. Krien, P. Herzog, H.-R. Folle, K. Freitag, F. Reuschenbach, M. Reuschenbach and R. Trzcinski, Z. Phys. B31([978)395. P. Herzog, H. Walitzki, K. Freitag, H. Hildebrand and K. Schl6sser, Z. Phys. A311(1983)35[. M. Reuschenbach, thesis, Universit~t Bonn, 1981, unpublished. E. Hagn, S. Jonsson, C. Trautmann and E. Zech, Hyp. Int. 15/16([983)245. W. Potzel, T. Obenhuber, A. Forster and G.M. Kalvius, Hyp. Int. 12(1982)135. P. Herzog, private communication.
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E. Hagn, Nuclear orientation and quadrupole interaction
[59] W.A. Steyert, private communication to P. Herzog, quoted in [36]. [60] M. Stachel and H.E. B6mmel, Appl. Phys. A30(1983)27. [61] E. Hagn, in "Low-Temperature Nuclear Orientation", eds. H. Postma and N.J. Stone (North-Holland), in press. [62] B. Perscheid and H. Haas, Hyp~ Int. 15/16(1983)227. [63] P.C. Riedi and E. Hagn, Phys. Rev. B, in press. [64] B. Harmatz, D.J. Horen and Y.A. Ellis, Phys. Rev. C12(1975)IO83. [65] E.N. Kaufmann and R.J. Vianden, Rev. Mod. Phys. 51(1979)161. [66] E.N. Kaufmann, Hyp. Int. 9(1981)219. [67] R. Vianden, Hyp. Int. 15/16(1983)189. [68] W. witthuhn and W. Engel, "Electric quadrupole interactions in noncubic memals", in "Hyperfine Interactions of radioactive nuclei", ed. by J. Christiansen, (Springer, Berlin, Heidelberg, New York, Tokyo, 1983). [69] R. Vianden, Hyp. Int. 15/16(1983)1081. [70] R.S. Raghavan, E.N. Kaufmann and P. Raghavan, Phys. Rev. Lett. 34(1975) 1280. [71] G. Wortmann and D.L. Williamson, Hyp. Int. i(1975)167. [72] W. Leitz, W. Semmler, R. Sielemann and Th. Wichert, Phys. Rev. B14(1976)5228. [73] G.S. Collins, Hyp. Int. 4(1978)523. [74] (G. Wortmann, B. Perscheid, G. Kaindl and F.E. Wagner, Hyp. Int. 9(1981)343. [75] M. Forker and K. Krusch, Phys. Rev. B21(1980) 2090. [76] S. Fabry, T. Butz, E. Hagn, A. Lerf and E. Zech, Hyp. Int. 15/16(1983)863. [77] T. Butz, A. Hflbler, A. Lerf and W. Biberacher, Mat. Res. Bull. 16(1981)541. [78] S. Fabry, Diplomarbeit, TU M~nchen, 1984, unpublished. [79] R. Eder, E. Hagn, E. Zech and G. Schatz, to be published.