Quantum properties of nanoscale metallic Li colloids formed by electron irradiation in LiF

Article abstract of DOI:10.1016/j.ssc.2003.09.003

We present experimental results on the nucleation of nanoscale metallic lithium colloids, of well-controlled diameter (2-5 nm), in MeV electron-irradiated LiF single crystals. Conduction electron spin resonance experiments show a clear-cut quantum effect in these colloids: the spin susceptibility follows a mixed Curie-Pauli law, characteristic for tiny metallic particles in which the mean level spacing is comparable to kT. The behavior of the spin relaxation times (T₁ and T₂) is presented and a discussion of quantum size effect in small metallic particles is proposed.

Full text of DOI:10.1016/j.ssc.2003.09.003

Solid State Communications 128 (2003) 329–333
www.elsevier.com/locate/ssc
Quantum properties of nanoscale metallic Li colloids formed by
electron irradiation in LiF
*
F. Beuneu , P. Vajda
´
Laboratoire des Solides Irradi e´ s, CNRS-CEA, Ecole Polytechnique, route de Saclay, F-91128 Palaiseau, France
Received 9 July 2003; received in revised form 5 August 2003; accepted 2 September 2003 by B. Jusserand
Abstract
We present experimental results on the nucleation of nanoscale metallic lithium colloids, of well-controlled diameter (2–
nm), in MeV electron-irradiated LiF single crystals. Conduction electron spin resonance experiments show a clear-cut
quantum effect in these colloids: the spin susceptibility follows a mixed Curie–Pauli law, characteristic for tiny metallic
5
particles in which the mean level spacing is comparable to kT: The behavior of the spin relaxation times (T and T ) is presented
1
2
and a discussion of quantum size effect in small metallic particles is proposed.
q 2003 Elsevier Ltd. All rights reserved.
PACS: 61.46. þ w; 61.72.Ji; 75.20.En; 76.30.Pk
Keywords: A. Nanostructures; D. Radiation effects; E. Electron paramagnetic resonance
1
. Introduction
gives an exceptionally good ESR signal. Van den Bosch [9]
measured the static magnetic susceptibility of neutron-
irradiated and gamma-irradiated LiF crystals. He attributed
the temperature-independent paramagnetic part to the
presence of metallic lithium. Taupin [10], on similar
samples, observed by X-ray diffraction and ESR the
presence of two kinds of colloids: one type, called
‘platelets’, is particularly interesting, as she claimed that
they show a QSE behavior. Watts and Cousins [11] worked
again with neutron-irradiated LiF, but thought they were not
in the full QSE regime. Finally, Stesmans and Wu [12],
again with similar samples, reported the absence of QSE in
their signals.
The creation of small metallic colloids in insulating
compounds—in particular by irradiation—is a very inter-
esting research domain, much explored during the last
decades [1]. Among many others, we made our own
contribution by irradiating with MeV-electrons two lithium
ionic compounds, namely Li O [2–5] and LiF [6,7]. We
2
obtained, depending on the compound and the irradiation
conditions, metallic colloids of various sizes, as shown by
ESR (electron spin resonance). In Li O, in particular, two
2
families of colloids were obtained, one in the 10-mm range,
the second much smaller, but still with bulk magnetic-
susceptibility properties, without any quantum size effect
Colloid creation by radiolysis is not the only possibility.
Gen and Petinov [13] prepared Li particles with diameter of
(
QSE).
Very small metallic colloids or clusters were studied [8]
6
0–600 nm, by an aerosol in argon, and observed a size
by several authors, in particular using ESR, often well in the
QSE regime. Lithium particles were very popular, because
they are quite easy to nucleate and also because lithium
dependence of the ESR signal. With a similar technique,
Saiki et al. [14] also obtained size-dependent signals. Borel
et al. [15] nucleated very small Li particles in a CO
and observed QSE properties by ESR.
2
matrix
*
Corresponding author. Tel.: þ33-1-69-33-47-47; fax: þ33-1-
Among ESR-work done on other systems, let us mention
here the studies of small Mg particles created by evaporation
69-33-30-22.
E-mail
addresses:
francois.beuneu@polytechnique.fr
[
16,17] as well as the interesting metal–insulator transitions
(F. Beuneu), peter.vajda@polytechnique.fr (P. Vajda).
0038-1098/$ - see front matter q 2003 Elsevier Ltd. All rights reserved.
doi:10.1016/j.ssc.2003.09.003

330
F. Beuneu, P. Vajda / Solid State Communications 128 (2003) 329–333
in Na colloids observed in doped NaCl after neutron
irradiation [18].
As will appear in the discussion below, the above data
are not always very coherent. In the present paper, we
address the problem of QSE in nanoscale metallic clusters
by creating Li colloids with electron-irradiation in LiF
crystals: the procedure enables the well-controlled nuclea-
tion of colloids of diameter in the nanometer range, as well
as the evolution of their size under heat treatment.
2
. Experimental details
Single crystals, in the shape of small parallelepipeds with
thickness below 1 mm, have been uniformly irradiated by
.5-MeV electrons from our Van de Graaff accelerator, with
Fig. 1. ESR spectrum of an irradiated LiF sample, taken at room
temperature. The dashed line corresponds to a Lorentzian fit. Signal
2
a current of the order of 20 mA/cm , and fluences about
2
9
intensity, in arbitrary units: 4:0 £ 10 ; linewidth: 75.4 G; g ¼
2
C/cm . The samples were wrapped in a 10mm thick copper
2:0032:
1
foil and irradiated in a liquid-hydrogen bath at 21 K. The
electron beam was parallel to a (100) axis. The energy loss
of 2.5 MeV electrons in the Cu foil is less than 15 keV and
the beam dispersion of the order of a few degrees; thus, the
effect on the defect production in LiF can be considered as
negligible.
value, g ¼ 2:0023 ^ 0:0002; which is a good first indication
for the presence of metallic lithium. By comparison with the
signal of Fig. 1, most of the F-center intensity is lost, while a
small part of it corresponds to F-center aggregates, which
are metallic precipitates.
ESR spectra were obtained on a computerized Bruker
ESR 200D spectrometer operating at X-band (9.5 GHz),
equipped with an Oxford ESR 900 cryostat working from 4
to 300 K. The maximum power is levelled at 200 mW. The
lines were fitted with a Lorentzian shape, yielding
automatically all data, e.g. intensity, linewidth, g-factor:
The linewidth corresponds to the half-width at half-
Fig. 2 shows the temperature variation of the ESR
linewidth for four annealing temperatures. It is roughly
independent of measuring T; but clearly decreases with
increasing Tann; except for 400 8C where it increases again
(mean value 17 G). Its absolute value, between 25 and 10 G,
is quite large for pure metallic lithium, for which the
linewidth can be as small as 0.03 G. In Fig. 3, we show the
temperature variation of the line intensity, which is
proportional to the paramagnetic susceptibility of the spins
involved. As is clear from Fig. 3(b), this susceptibility
follows a law which is intermediate between the Curie law
for isolated spins ð1=TÞ and the Pauli law for conduction
electrons in a bulk metal (no T variation). With increasing
maximum of the integrated signal, which gives 1=gT (g is
2
the gyromagnetic ratio).
3
. Results
After irradiation, the samples gave a very broad ESR
signal due to isolated F-centers (Fig. 1). This is fully
coherent with our earlier observations in Li O: when
2
irradiated at low temperature [2], only F-centers but no
colloids were found. We concluded that the creation of
metallic colloids was only possible if the elementary defects
were mobile during irradiation, a condition fulfilled for
T * 200 K. In the case of our LiF samples, we wanted to see
if the F-centers could coalesce after irradiation through heat
treatments, giving rise to metallic precipitates. We
performed isochronal anneals of 1 h in air, with a
temperature increment of 50 8C.
Beginning with Tann ¼ 200 8C; the signal was strongly
modified, becoming a narrower line, with a simple
Lorentzian shape. This signal could be observed until Tann
¼
400 8C; where it was still visible but with a very small
intensity. The temperature variation of the properties of this
line was very interesting: the g-factor took the free-electron
Fig. 2. ESR linewidth versus temperature of the same irradiated LiF
sample after 1 h anneals at different temperatures. X: 200 8C; W:
250 8C; S: 300 8C; £ : 350 8C.

F. Beuneu, P. Vajda / Solid State Communications 128 (2003) 329–333
331
Fig. 3. ESR line intensity, in the same arbitrary units as in Fig. 1, of the same irradiated LiF sample after 1 h anneals at different temperatures: (a)
versus temperature or (b) versus inverse temperature. X: 200 8C; W: 250 8C; S: 300 8C; £ : 350 8C. The data are fitted by the empirical law:
x ¼ x =tanhð4kT=dÞ:
0
Tann; the behavior gradually shifts from a predominant Curie
character to a predominant Pauli one.
Classically, the two relevant spin relaxation times, T1
inhomogeneous saturation, which they attributed to the
size distribution of the metallic particles.
(
spin–lattice) and T (spin–spin), are equal in metals, due to
2
the rapid momentum relaxation around the Fermi surface
19]. In our case, where the small size of the colloids can
strongly affect the momentum relaxation, it is interesting to
4
. Discussion
[
The spin susceptibility behavior shown in Fig. 3(b) is
check the law T ¼ T ; by performing r.f.-power saturation
1
2
very similar to the model presented by Denton et al. [20],
who calculate, in the random matrix theory framework, the
susceptibility of very small metallic particles. When the
number of atoms N in the particle decreases, the mean
electronic level spacing, d; increases, until kT & d: In such a
case, it is normal to get departure from the Pauli law; in the
extreme case kT p d; one gets a near-zero susceptibility if
N is even and a Curie law if N is odd. The temperature
region where the susceptibility of an assembly of metallic
particles shifts from the Curie to the Pauli law permits to
determine the number N:
measurements. The results of such an experiment are shown
in Fig. 4, for a sample annealed at 350 8C. The signal peak-
to-peak amplitude is plotted against the square root of the
relative (to the maximum spectrometer power) r.f. power,
Prel ¼ P=Pmax: The low temperature spectra appear to be
very saturable (non-linear behavior of the plot), while the
saturation is less pronounced as T increases, and is no longer
observable above 70 K. The saturation has a typical
inhomogeneous behavior. Borel et al. [15] observed
Considering that there must be statistically the same
number of even and odd particles, we found that the
empirical formula x ¼ x =tanhð4kT=dÞ is a good fit for the
0
total spin susceptibility (even and odd particles) in the grand
canonical model as shown in Fig. 2(b) of Ref. [20]. We used
this law to fit the experimental ESR intensity data versus
temperature, as exemplified in Fig. 3(b), where the ESR
intensity versus 1=T is given after four different anneals; the
fits show that the model of Denton et al. is well followed.
The coefficient x0 corresponds to the Pauli limit of the
susceptibility (for T ! 1). The global metallic content of
the irradiated LiF sample can be deduced from it and is
given in Table 1: it is seen to decrease during annealing,
which we interpret by a re-dissolution of metallic colloids in
the matrix, possibly by chemical recombination with
fluorine bubbles.
Fig. 4. Saturation of ESR line peak-to-peak amplitude of an
irradiated LiF sample annealed at 350 8C, versus the square root of
the relative r.f. power Prel ¼ P=Pmax: X: 4.6 K; W: 10 K; S: 30 K;
The most interesting parameter extracted from this fit is
the mean energy spacing between electronic levels, d; which
is given in Table 1 in temperature units (K). The d value is
£
: 50 K. The data are fitted by the empirical law: h ¼ h
pffiffiffiffiffiffiffiffiffiffi
Â
0
arctanð P =P Þ:
rel sat

332
F. Beuneu, P. Vajda / Solid State Communications 128 (2003) 329–333
Table 1
Parameters deduced from the ESR intensity after anneals at Tann: The metal concentration c (in dimensionless volume units), the mean energy
level separation d; the number N of atoms per particle, the mean diameter d of the particles (taken as spherical) and the value of the spin
relaxation probability at the surfaces e are given
23
26
Tann (8C)
c ( £ 10
)
d=k (K)
N; number of atoms/particle
Diameter d (nm)
e ( £ 10
)
2
2
3
3
4
00
50
00
50
00
3.8
646.5
380.8
227.5
101.5
30.2
114
193
1.7
2.0
2.4
3.1
4.6
6.7
5.8
2.6
2.1
323
5.5
0.86
0.25
724
5.5
2430
11.6
strongly decreasing with annealing, which means that the
mean size N of the Li colloids, directly related through d ¼
with widths around 1 G, never observed in the present
experiments.
4
4
E =3N; is increasing; E ¼ 4:74 eV (T ¼ 5:51 £ 10 K) is
Eigler and Schultz [23] gave a comprehensive discussion
of the question of spin relaxation on surfaces in metals. In
the case of our colloids, the inhomogeneous character of the
lines prevents from attributing the whole linewidth to
surface relaxation, but only some part of it. However, in a
semi-quantitative effort to estimate surface relaxation, we
shall arbitrarily assume that colloids are spherical and that
the whole ESR linewidth is due to surface relaxation. Thus,
we can deduce a value for the so-called e parameter, which
describes the spin-flip probability during electron scattering
by a surface, given by e ¼ 4d=½ð1 þ B Þv T ꢀ in the limit
F
F
F
the Fermi energy of lithium. The values of N are given in
Table 1; if we arbitrarily consider the particles as spherical,
we can estimate values for the diameter d of these particles
in the same Table.
We must now address the problem of the influence of
QSE on the ESR linewidth. The key paper on this subject is
that by Kawabata [21]. This author found two relevant
parameters for the emergence of QSE: in the case when both
"v=d and "=T d are much lower than unity (v is the ESR
microwave frequency), he predicts (‘quantum limit’) that
2
0
F 2
the linewidth will be given by "v=d £ 1=gT : In such a
2
when e is small; B < 20:2 is the first Landau spin
0
regime, the line should considerably narrow when reducing
the colloid size. We do not observe such an effect (see Table
7
parameter, v ¼ 5:48 £ 10 cm/s is the Fermi velocity, and
F
d is the particle diameter. Values obtained for e are given in
Table 1. One may remark that these e data show little
variation with the colloid size and are in order-of-magnitude
agreement with typical values in the literature [11–14],
which supports our conclusion that no QSE is present in our
linewidth data. The 400 8C value is quite a bit higher: at this
temperature, most colloids are dissolved and their shape
could be particularly far from being spherical.
1
and Fig. 2), even though we are clearly in Kawabata’s
quantum limit: in temperature units, "v < 0:46 K, and
23
"
=T < 10 K.
2
One possible explanation for the breakdown of QSE is
given by Tanaka and Sugano [22], who studied by computer
simulations and by an analytical approach the energy-level
statistics of small metallic particles. They showed that their
surface roughness is a key parameter for the statistics of the
energy levels: the level repulsion is much reduced for
smooth surfaces. In that case, the level degeneracy remains
high around the Fermi level, preventing the relaxation to be
quenched when d increases. This feature is invoked by
Kimura and Bandow [17] to account for the lack of QSE
narrowing in their ESR data on Mg particles. In our case, it
is highly probable that the surfaces of the colloids, in close
relation with LiF lattice planes, are quite smooth.
The saturation phenomenon appears when the r.f.
2
2
1
1 2
magnetic field H is such that g H T T * 1: We define
1
the saturation power, Psat; as the power for which the plot is
no longer linear in Fig. 4 (see the legend). This power is very
temperature dependent, as seen in Fig. 5; this variation is
fitted by the form Psat ¼ P expð2T =TÞ; which takes the
0
0
asymptotic value Psat ¼ P for T ! 1: From this, one can
0
easily extract a value for the high-T limit of T :
1
2
8
T ¼ 1:3 £ 10 s. The latter can be compared to
However, we must remark that some authors have indeed
reported QSE in their ESR linewidth data. Gen and Petinov
1
29
T ¼ 5:2 £ 10 s, taken from linewidth data for Tann
¼
2
2
3
508C (< 11 G in Fig. 2): it is not too far from the T ¼ T
[
13] and Saiki et al. [14] both claim their linewidth data to
1
law in the non-quantum regime. The other parameter
be in the QSE regime, but the size of their particles is rather
large and does not satisfy Kawabata’s criterion; however,
their Li particles, due to the preparation procedure, are
probably much less smooth than ours. More surprising is the
discrepancy with Taupin’s results [10], because her
procedure is closer to ours; however, her samples were
heavily neutron-irradiated at temperatures much higher than
ours. She observed QSE in platelets which gave ESR lines
obtained from the fit in Fig. 5 is the value T ¼ 44:9 K,
0
which is of the same order of magnitude as d=k ¼ 101:5 K
(see Table 1). We arrive to a model in which T2 is T-
independent and not influenced by QSE; this spin–spin
relaxation appears to be due in majority to the classical
relaxation on the surfaces of the colloids. On the opposite,
QSE assumes its full role for T ; which increases
1

F. Beuneu, P. Vajda / Solid State Communications 128 (2003) 329–333
333
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subsequent anneals permit to nucleate very small metallic
particles, with a well-controlled size in the nanometer range,
and that this size increases with the annealing temperature.
The spin susceptibilities of these colloids clearly show
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than the mean energy level spacing. The ESR linewidth is
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1