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a-Radiation Detected Li Diffusion in the Fast Ionic Conductor Li3N.

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Annalen der Physik. 7. Folge, Band 42, Heft 2, 1985, S. 169-174
J. A. Barth, Leipzig
@-RadiationDetected Li Diffusion in the Fast Ionic
Conductor Li,N
By B. BADER,
P. HEITJANS,
H. ACKERMANN,
P. FREILANDER,
G. KIESE,A. SCHIRMER,
H.-J. STOCKMA", and C. VAN DER MAREL
Fachbereich Physik der Philipps-Universitat, Narburg, Institut Laue-Langevin, Grenoble, France
Dedicated to W . Walcher on occasion of his 75th birthday
Abstract. The method of /%radiationdetected nuclear magnetic resonance (,9-NMR) was applied
to *Li in a 7Li,N single crystal. From NMR signals and spin-lattice relaxation rates the activation
enthalpies for two distinct Li+ diffusion processes were deduced. Ultraslow diffusion corresponding
to ionic jump rates down to 0.1 s-l was observed. It could be confirmed that the static electric field
gradients a t the two inequivalent Li sites have opposite signs.
Untersuchung der Li-Diffusion im schnellen Ionenleiter LiaN mit &-Strahlungsnachweis
Inhaltsiibersicht. I m 7Li,N-Einkristall wurdo der Sondenkern 8Li durch Kernresonanz mit
p-Strahlungsnachweis (B-NMR) beobachtet. AuB NMR-Signalen und Spin-Gitter-Rslaxationsraten
wurden die Aktivierungsenthalpien fur zwei unterschiedliche Li+-Diffusionsprozessegewonneh. Es
wurde ultralangsame Diffusion mit Ionensprungraten bis hinab zu 0,1s+ nachgewiesen. Es konnte
bestiitigt werden, dal3 die statischen elektrischen Feldgradienten an beiden nichtiiquivalenten LiPlatzen verschiedene Vorzeichen haben.
1. Introduction
Oriented radioactive nuclei and particles attract increasing interest as a tool in
condensed matter research (see e.g. [l, 21). Besides other methods B-NMR is now an
established technique in this respect. It uses ,!?-activeprobe nuclei which are produced
and polarised simultaneously by a nuclear reaction. The probe polarisation and its
change due to external and internal electromagnetic fields are monitored via the directional asymmetry of the ,!?-decayradiation. In this way static and dynamic properties
of a variety of solid and liquid systems were studied (see [3] for a review).
I n the work reported here the probe nuclei were produced by capture of polarised
thermal neutrons. In this case the risk of radiation damage is the least of all in-beam
methods and no bulk radiation damage of the sample occurs even for the case of insulators
at low temperatures. Thus one is able to investigate also purely intrinsic properties for
many compounds. Here, we are concerned with ionic diffusion in Li,N which we mainly
studied by measuring spin-lattice relaxation (SLR) of the B-emitter sLi
= 0.8 s).
The SLR time TIis strongly influenced by the diffusive motions if - at a certain temperature T - the internal fields induced by the ionic jumps fluctuate with a rate of the
order of the Larmor precession frequency in an external field B. Detailed diffusion studies by the neutron-activation B-NMR technique were done in Li metal [4] and binary
170
Ann. Physik Leipzig 43 (1985) 2
Li alloys [ 5 ] . I n these systems which have cubic structure diffusion is isotropic. Li,N,
on the other hand, has a layer structure and may be regarded as a model substance for
the study of non-isotropic, low-dimensional diffusion.
Fig. 1 shows the crystal structure of Li,N which consists of alternating hexagonal
Li,N and Li layers perpendicular to the c-axis with Li ions labelled Li(2) and Li(l),
respectively [6]. Three Li+ diffusion processes have been found up to now. Investigations
by conventional NMR detected an i n t r a l a y e r process confined to the Li,N layers and
a n i n t e r l a y e r process consisting of Li jumps betweenLi(1) and Li(2) sites ((1* 2)jumps) [7]. Further, X-ray [8] and ionic conductivity [9] measurements were interpreted
in terms of a third process, interlayer diffusion parallel t o the c-axis involving only Li(2)
sites.
N
Fig. 1. Crystal structure of Li,N. c = 0.194 nm, L = 0.213 nm
2. E5perimental
The experiments were performed at the High Flux Reactor Grenoble using the InBeam NMR Spectrometer S6. Polarised ,&active % nuclei were produced in the 7Li,N
crystal by capture of polarised thermal neutrons. The flux of polarised neutrons, having
a degree of polarisation of more than 90%) was 5x l o 7
s-l. The 8Li polarisation P
was monitored via the asymmetry of the ,&radiation with respect to the external magnetic field B. P was measured either in a time-integral way with continuous neutron activation in order to observe NMR spectra or in a time-differential way with pulsed neutron
activation which allows direct determination of SLR times (see [3] for details). The Li,N
single crystal which was grown by the Czochralski method [lo] using 99.9% isotopically
pure 7Li had a volume of 0.6 cm3.
3. Quadrupole Split NMR Spectra
Due to the noncubic symmetry of the crystal structure static electric field gradients
(EFG) exist. They couple t o the quadrupole moment of the BLinuclei (I = 2, Q = 32 mb)
which gives rise to quadrupole split spectra. Below T % 250K two sets of four well
resolved resonance lines, arranged symmetrically around the Larmor frequency uL(see
Fig. 2, upper part), were detected. The corresponding coupling constants are 1 e2q(')Q/h1
= 455(5) kHz and ]e2q(2)Q/h
I = 220(3)kHz. They can be assigned t o %i residing on
Li(1)- and Li(2)-sites, respectively. This assignment agrees with that from conventional
NMR measurements on 7Li [7]. The principal axis of the axially symmetric EFG tensor
which belongs to the largest component q ( l ) or q(') is aligned along the c-axis. Above
T m 320 K the resonance lines begin to broaden and disappear. Above T w 570 K a
new spectrum appears consisting of four lines with a drastically reduced coupling con-
*
B. BADER
et al., Li Diffusion in Li,N
171
stant of le%&/hl= 2.0(3)kHz. This effect was first measured by NMR on ‘Li [7] and was
ascribed t o rapid (1-+ 2)- and (2 -+ 1)-jumps. For reasons of detailed balance, the
respective jump rates W(12)and W(21)are related by W(12)= 2W(21)since there are
twice as much Li(2)- as Li(1)-sites. If the jump rates are much greater than the differences
of corresponding quadrupole frequencies a t bhe two Li-sites the static coupling constants are averaged by the jumps. Assuming opposite signs of the static EFG’s, in the
l 1
caseof 8Li the averaged value I eqQ/h I = &
le2q(’)&/hl
is expected. This agrees with the measured value 2.0(3) kHz.
2 (e2q(2)&/hlI
I = 5(6) kHz
rf -scheme
+
+ i
I
0
,
t
1
.
1
^
4
I
I
1
m
I
mm(21~L~21111i2) (11
111
EFG-signs
equal
Li(1)
opposite
Li(2) Lit11
--
Li(21
Pig. 2. Upper part: Schematic representation of the resonance lines of the two quadrupole split
spectra versus the frequency. (1) sLi(l)-spins, (2) *Li(2)-spins, oL Larmor frequency. The arrows
indicate the irradiated rf-transition frequencies
Lower part: The five m-levelsfor I = 2 of sLi(l)and sLi(2);vertical arrowA: coupling by rf transitions,
horizontal arrows: coupling by (1 cf 2)-jumps
Besides this indirect proof B-NMR allows to directly measure the opposite signs of
the EFG’s. To this end the radiofrequency (rf) scheme shown in Fig. 2 was applied a t
T M 320 K where the eight static resonance lines are still apparent. A t this temperature
the interlayer jumps are fast compared to l/ts but much slower than the differrences
of corresponding quadrupolefrequencies of Li(1)and Li(2). We assume that a 8Linucleus
jumping between the sites Li(1) and Li(2) does not change its quantum state m (m =
2, ... , -2). Due t o the coupling of the corresponding m states by the rapid jumps, the
irradiation of either a rf transition frequency in the 8Li(l)level scheme or the corresponding one in the BLi(2) level scheme influences the 8Li polarisation, averaged over the
nuclear lifetime tp,in the same way. Now, one saturates three out of the four transitions of theaLi(1) and additionally one transition of the 8Li(2) system as indicated in
Fig. 2. The influence of the fourth rf field on the 8Li polarisation depends on the
relative sign of the EFG’s a t the two sites. I n the case of opposite signs all m-states
are coupled (Fig. 2, lower right part) and the polarisation is completely destroyed. In
the case of equal EFG signs only the two upper and the three lower m-states are coupled
(Fig. 2, lower left part) and part of the polarisation is retained. Experimentally the
former case was found.
Ann. Physik Leipzig 42 (1985) '1
172
4. Spin-Lattice Relaxation Measurements
The temperature dependence of the SLR rate is shown in Fig. 3. Transients P(t) of
the polarisation behave quite differently in the three temperature ranges to be distinguished. At T > 300 K (range I) P ( t )is single-exponential. At 180 K < T < 300 K (range 11)
P(t) changes significantly to a two-exponential behaviour (Fig. 4). I n this T-range the
8Li(l)and 8Li(2)spins relax single-exponentially with different SLR times Tc,')and Tf).
500 300
</<'Ii
r\
4
1
200
I
I1
I
150 125
1 K
I
Ill
.I ,.
I !
101
I
-
1
I
I
I
&i
I
7
1oo -
10'
Fig. 3. Temperature dependence of the SLR of 8Li in Li,N a t B = 300 mT and c I( B
1
A: -measured without rf-irradiation
T;)
o,.:
i.e.
1
T(,2),
~ ( 1=
)
1
0, ~
measured with irradiation of the resonance frequencies of 8Li(l),sLi(2)respectively,
( 2=
)
0
Fig. 4. Transient P(t)of sLi in Li,N a t T = 239 K and B = 300 mT. The full line represents a twoexponential fit to the data yielding two relaxation times
R . BADERet al., Li Diffusion m Li,S
173
This was shown in the following way. The polarisation of either spin sort, i.e. P (' ) or
P ( z )was destroyed during a Tl-measurement by irradiating the four resonance frequencies of the corresponding quadrupole split spectrum. One is then left with the polarisation
of the other sLi-spin sort. The transients P(')(t)and Pc2)(t)measured in this way were
single-exponential. At T < 180 K (range 111)the transients P(')(t)and P(2)(t)approach
each other. Here they can better be fitted by P(t) = Po exp
instead of P(t) =
Po exp (-W1).
(-fc)
5. Discussion of Spin-Lattice Relaxation
I n the T-range I1 the different temperature dependences of the SLR of Li(1)- and
Li(2)-nuclei can be explained by the presence of two diffusion processes: Relatively fast
intralayer diffusion involvingLi(2)-sitesonly and slow (1+ 2)-jumps. Let R(')=R(l)(B,T)
and R(2)= R(2)(B,T ) be the SLR rates a t Li(1)- and Li(2)-sites, respectively, due t o
intralayer diffusion. The transient behaviour of the polarisations P ( l )and P ( 2 can
) then
be described by the master equation system
p w = -(R(') + WW)) pcu + WC"). p m ,
(1)
p(2)= W(W p(1)- (R(2' + W(21)) pcz).'
.
I n the case of selective rf irradiation, i e. if P(*)= 0 or PC2)= 0, we get with
WlZ)= 2W21) for the two relaxation rates
W
=
The best agreement of Eqs. (2) with the relaxation data is achieved by setting R(')(B, T )
m 0 in the whole T range 11. This means that the intralayer diffusion depolarises only
the sLi-spins a t Li(2)-sites,and the diffusion is confined to the Li,N-layers. Furthermore
it follows l/Til) = W(T) so that the (1-+ 2)-jumprate W(T) is directly obtainedfroni
the transient P(')(t).This is supported by the fact that TI') was found to be independent
of the direction and the value of B. It was possible to observe jumprates down to
W = 0.09(1) s-l at T = 227 K, corresponding t o ultraslow diffusion. Assuming l/Tl
B-%-l, as predicted e.g. by the BPP theory [ l l ] for low temperatures, and using
z ~ e x (E/kT)
p
the activation enthalpies E,,
.= 550(50) meV for the (1*+ 2)-jumps and
E , = 250(50) meV for the intralayer diffusion were obtained. It should, however, be
noted that a B-dependence R(2) B-" not with 01 = 2 but 01 = 0.5 ...0.6 was found in
the whole T-range 11. This weak B-dependence cannot be explained by siniple twodiniensional models either [12, 131. So the microscopic nature of the intralayer diffusion
still remains unclear.
I n the T-range I the jumprate W comes into the order of magnitude of the Larnior
frequency wL. Thus an especially efficient SLR mechanism is established since the sLi
spins juinp between sites possessing EFG values which differ both in magnitude and
sign. A fit assuming the relation l/Tl -7, as it follows froin the BPP theory for high
temperatures, yielded the activation enthalpy E,, = 570(30) meV. This value agrees
with the El,-valueobtained in the slow-diffusion regime (T-range 11).
I n the T-range I11 a n interpretation is still lacking. It should however be remarked
that a exp (- ft/T,) behaviour of P(t)together with a very weak B- and T-dependence
of T I was also found in a Li-silicate glass [14]. Indication for glassy properties of crystalline Li,N showed upbefore in acoustic and dielectric nieasurenients at very low temperatures [ 151.
-
-
174
Ann. Physik Leipzig 42 (1985) 2
We are grateful t o W. KRESSfor the loan of the crystal and for characterising measurements and to W. KRESS,R. MESSER, and A. SEEGER
for helpful comments. This work
is sponsored by The Bundesministeriuni fur Forschung und Technologie.
References
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[2] YANAZAKI,
T.; NAGAMINE,
K. (Eds.): Muon Spin Rotation and Associated Problems, Proc. of
the Yamada Conf. VII. In: Hyperfine Interactions 17-19 (1984).
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H. ; HEITJANS,
P.; STOCKMA", H.-J. : ,9 Emitters and Isomeric Nuclei as Probes
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A. ; ACKERMANN,
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H.-J.:
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W. ;
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[8] SCHULZ,
H.; THIEMANN,
K. H.: Acta Cryst. A 35 (1979) 309.
[9] NISHIDA,K. ; ASAI, T. ; KAWAI,S. : Sol. State Comm. 48 (1983) 701.
[lo] SCHONHERR,
E.; MULLER,G.; WINKLER,E.: J. Cryst. Growth 43 (1978) 469.
[ll] BLOENBERGEN,
N.; PURCELL,E. M.; POUND,
R. V.: Phys. Rev. 73 (1948) 679.
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pp. 141-174.
[13] AVOGADRO,
A.; VILLA,M.: J. Chem. Phys. 66 (1977) 2359.
[14] HEITJANS,P.; BADER,B. ; STOCKMA", H.-J.; DORR,K.; KIESE, G.; &4CKERMANN,H.; FREILANDER,
P. ; MULLER-WARMUTH,
W. ; MEISE-GRESCH,
G. : Hyperfine Interactions 15/16 (1953)
697.
T.; v. SCHICKFUS,
M.; HUNKLINGER,
S.; JACKLE,
J.: Sol. State Comm. 35 (1980)
[16] BAUNANN,
587.
Bei cler Redaktion eingegangen am 7. Dezember 1984.
Anschr. d. Verf.: P. HEITJANS,
H. ACKERMANN,
H.-J. STOCKMANN
Fachbereich Physik der Philipps-Universit,at
Renthof 5
D-3550 Marburg
B. BADER,P. FREILANDER,
-4.SCHIRMER
Institut Laue-Langevin, B.P. 156
F-38042 Grenoble-Cedex
G. KIESE
Leybold-Heraeus, Postfach 510 760
D-6000 KO111 51
C. V A N DER MAREL
Physics Lab., University of Groningen
Melkweg 1
NL-9718 EP Groningen
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