Theoretical analysis of the kinetics of low-temperature defect recombination in alkali halide crystals
We analyzed carefully the experimental kinetics of the low-temperature diffusion-controlled F, H center recombination in a series of irradiated alkali halides and extracted the migration energies and pre-exponential parameters for the hole H centers. The migration energy for the complementary electr...
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| Cite this: | Theoretical analysis of the kinetics of low-temperature defect recombination in alkali halide crystals / V.N. Kuzovkov, A.I. Popov, E.A. Kotomin, A.M. Moskina, E. Vasil'chenko, A. Lushchik // Физика низких температур. — 2016. — Т. 42, № 7. — С. 748-755. — Бібліогр.: 59 назв. — англ. |
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irk-123456789-1291952018-01-17T03:04:47Z Theoretical analysis of the kinetics of low-temperature defect recombination in alkali halide crystals Kuzovkov, V.N. Popov, A.I. Kotomin, E.A. Moskina, A.M. Vasil'chenko, E. Lushchik, A. Low-Temperature Radiation Effects in Wide Gap Materials We analyzed carefully the experimental kinetics of the low-temperature diffusion-controlled F, H center recombination in a series of irradiated alkali halides and extracted the migration energies and pre-exponential parameters for the hole H centers. The migration energy for the complementary electronic F centers in NaCl was obtained from the colloid formation kinetics observed above room temperature. The obtained parameters were compared with data available from the literature. 2016 Article Theoretical analysis of the kinetics of low-temperature defect recombination in alkali halide crystals / V.N. Kuzovkov, A.I. Popov, E.A. Kotomin, A.M. Moskina, E. Vasil'chenko, A. Lushchik // Физика низких температур. — 2016. — Т. 42, № 7. — С. 748-755. — Бібліогр.: 59 назв. — англ. 0132-6414 PACS: 61.72.Cc, 61.82.Ms, 64.70.pv http://dspace.nbuv.gov.ua/handle/123456789/129195 en Физика низких температур Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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Low-Temperature Radiation Effects in Wide Gap Materials Low-Temperature Radiation Effects in Wide Gap Materials |
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Low-Temperature Radiation Effects in Wide Gap Materials Low-Temperature Radiation Effects in Wide Gap Materials Kuzovkov, V.N. Popov, A.I. Kotomin, E.A. Moskina, A.M. Vasil'chenko, E. Lushchik, A. Theoretical analysis of the kinetics of low-temperature defect recombination in alkali halide crystals Физика низких температур |
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We analyzed carefully the experimental kinetics of the low-temperature diffusion-controlled F, H center recombination in a series of irradiated alkali halides and extracted the migration energies and pre-exponential parameters for the hole H centers. The migration energy for the complementary electronic F centers in NaCl was obtained from the colloid formation kinetics observed above room temperature. The obtained parameters were compared with data available from the literature. |
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Kuzovkov, V.N. Popov, A.I. Kotomin, E.A. Moskina, A.M. Vasil'chenko, E. Lushchik, A. |
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Kuzovkov, V.N. Popov, A.I. Kotomin, E.A. Moskina, A.M. Vasil'chenko, E. Lushchik, A. |
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Kuzovkov, V.N. |
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Theoretical analysis of the kinetics of low-temperature defect recombination in alkali halide crystals |
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Theoretical analysis of the kinetics of low-temperature defect recombination in alkali halide crystals |
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Theoretical analysis of the kinetics of low-temperature defect recombination in alkali halide crystals |
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Theoretical analysis of the kinetics of low-temperature defect recombination in alkali halide crystals |
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Theoretical analysis of the kinetics of low-temperature defect recombination in alkali halide crystals |
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theoretical analysis of the kinetics of low-temperature defect recombination in alkali halide crystals |
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Low-Temperature Radiation Effects in Wide Gap Materials |
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Theoretical analysis of the kinetics of low-temperature defect recombination in alkali halide crystals / V.N. Kuzovkov, A.I. Popov, E.A. Kotomin, A.M. Moskina, E. Vasil'chenko, A. Lushchik // Физика низких температур. — 2016. — Т. 42, № 7. — С. 748-755. — Бібліогр.: 59 назв. — англ. |
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Физика низких температур |
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Low Temperature Physics/Fizika Nizkikh Temperatur, 2016, v. 42, No. 7, pp. 748–755
Theoretical analysis of the kinetics of low-temperature
defect recombination in alkali halide crystals
V.N. Kuzovkov1, A.I. Popov1, E.A. Kotomin1,2, A.M. Moskina1,
E. Vasil'chenko3, and A. Lushchik3
1Institute of Solid State Physics, 8 Kengaraga Str., Riga LV 1063, Latvia
E-mail: kuzovkov@latnet.lv
2Photochemistry Center, Russian Academy of Sciences Str., Moscow 1199911, Russia
3Institute of Physics, University of Tartu, 1 W. Ostwald Str., Tartu 50411, Estonia
Received April 25, 2016, published online May 25, 2016
We analyzed carefully the experimental kinetics of the low-temperature diffusion-controlled F, H center re-
combination in a series of irradiated alkali halides and extracted the migration energies and pre-exponential pa-
rameters for the hole H centers. The migration energy for the complementary electronic F centers in NaCl was
obtained from the colloid formation kinetics observed above room temperature. The obtained parameters were
compared with data available from the literature.
PACS: 61.72.Cc Kinetics of defect formation and annealing
61.82.Ms Insulators (radiation effects in ..)
64.70.pv Colloids.
Keywords: alkali halides; defect; diffusion; reaction; ionizing radiation.
1. Introduction
It is generally accepted that radiation instability of the
majority of alkali halide crystals (AHCs) is determined
by the creation of interstitial-vacancy (i–v) pairs of
Frenkel defects (FDs) in an anion sublattice via the de-
cay of self-trapping excitons or the recombination of
conduction band electrons with self-trapped holes (Vk
centers), i.e., the so-called excitonic and electron-hole
(e–h) mechanisms of FDs creation (see [1–8] and refer-
ences therein). About 95% of such anion FDs are short-
lived ones (10-11−10-1 s) [3–7,9–11], while the accumu-
lation of so-called long-lived structural defects which are
stable for hours, days and months plays a crucial role in
radiation-induced material degradation, therefore, being
a limitation for many applications [12–16]. It is experi-
mentally proved that low-temperature irradiation leads to
the creation of two types of FD pairs: a classical Frenkel
pair is defined as a positively charged anion vacancy (va,
α center) and an interstitial halide ion ( ,ai
− I center),
while a pair of neutral FDs consists of an F center (an
electron trapped by an anion vacancy, vae) and an H cen-
ter (a dihalide molecule 2X − located in one anion site,
0 )ai [1–9,17–19].
It is generally accepted that the energy of various radia-
tion-induced electronic excitations (EEs) in AHCs is partly
transformed into F–H pairs, while α–I pairs are formed
due to the tunnel recharging of primary close F–H or due
to the recharge of F and H centers into α and I with the
participation of e–h pairs. On the other hand, the spectra of
stable F–H and α–I pair creation by vacuum ultraviolet
(VUV) radiation measured in a number of AHCs using
highly sensitive luminescence methods do not totally coin-
cide, and the formation of primary α–I under certain condi-
tions is not excluded [2,20–24].
F, H as well as α and I centers manifest themselves as
typical bands of radiation-induced optical absorption (see,
e.g., [19]). Interstitials in the form of H centers are detecta-
ble by the electron paramagnetic resonance (EPR) method
that provides direct information about microstructure and
surrounding of a paramagnetic center [25–29]. However,
both these methods can be used only at rather high concen-
tration of FDs, i.e., after “integral” x-irradiation. On the oth-
er hand, the creation of small amount of F–H and α–I pairs
© V.N. Kuzovkov, A.I. Popov, E.A. Kotomin, A.M. Moskina, E. Vasil'chenko, and A. Lushchik, 2016
Theoretical analysis of the kinetics of low-temperature defect recombination in alkali halide crystals
by, VUV radiation that selectively formed various intrinsic
EEs in a thin crystal layer was also detected using lumines-
cent methods [20–23,26,30]. The so-called α luminescence,
the stimulation spectrum of which coincides with the α ab-
sorption band, can be taken as a measure of radiation-
induced α centers (α–I pairs), while a typical tunnel lumi-
nescence can be considered as a measure of F–H pairs, that
undergo radiative recharging under stimulation within the F
absorption band. The use of low-dose VUV irradiation al-
lowed to realize the creation regime of isolated FDs pairs,
when the average distance between primary F–H pairs con-
siderably exceeds the interdefect distance within FDs pairs
[23,26,30].
At liquid helium temperature, radiation-induced stable
F–H and α–I pairs consist of immobile defects, while in-
terstitials (at first I centers and then H centers) easily be-
come mobile with the temperature rise up to ~20−40 K and
recombine with F centers remaining immobile even highly
above room temperature. The thermal annealing of radia-
tion-induced F–H and α–I pairs in AHCs was experimen-
tally investigated in details by means of various versions of
thermoactivation spectroscopy. Measuring the intensity
(light sum) of typical photostimulated luminescence, sev-
eral stages of the annealing of F–H or α–I pairs were re-
vealed in VUV-irradiated AHCs. In x-irradiated AHCs, the
pulse annealing curves of the EPR signal of the H centers
as well as the annealing of typical optical absorption bands
of FDs were measured as well. In addition, a number of
peaks of thermally stimulated luminescence usually ac-
companies the thermal annealing.
If the recombination occurs between defects within spa-
tially separated (isolated) pairs, the annealing stages are
connected with the migration distance of a mobile defect
toward its complementary counterpart in the pair. In x-irra-
diated AHCs, the situation is more complicated because
besides F–H or α–I pairs, complex groups of spatially cor-
related defects, for instance F–I–Vk triplets, are also
formed during irradiation (see, e.g., [2,17,31–33]). The
formation of such and similar defect triplets/groups was
detected in KBr, NaCl, and LiF even under low-tem-
perature VUV irradiation, when an exciting photon is able
to form simultaneously two-three spatially close EEs (via
the multiplication process), which undergo transformation
into various defect groups [32–34]. Under such irradiation
conditions, the certain annealing stages of a certain defect
can be connected with the mobility of other defects and
their interaction with the partners from a defect group. As a
result, a rise stage was detected at the annealing of para-
magnetic H centers in x-irradiated KBr and KCl crystals
due to a secondary reaction I + Vk → H within a F–I–Vk
triplet [22,23,25,26].
It is worth noting that the average interdefect distance
FHr within F–H pairs depends on the elementary mecha-
nism of their creation and, respectively, a type of irradiation.
If the exciting photons form anion excitons, the value of
FHr is larger than that for F–H pairs photocreated via e–h
recombination. The annealing of F–H pairs is accompanied
by several peaks of thermally stimulated luminescence con-
nected with different migration distances (number of jumps)
of a mobile H center toward a complementary immobile F
center.
By means of highly sensitive luminescent methods, it is
possible to select F–H (and α–I) pairs with a certain value
of .FHr For instance, tunnel recharging (F–H → α-I trans-
formation) occurs in F–H pairs with larger values of FHr
(by a few interanion distances) under additional F-stimu-
lation–optical excitation of the existing F centers. The rela-
tive amount of H centers that undergo such recharging can
be determined by direct EPR method [23,25,26].
The microstructure of paramagnetic H centers in five
investigated AHCs is rather different. In NaCl, H centers
are oriented along <111> crystallographic directions, while
in KCl, RbCl, KBr, and RbBr crystals the orientation is
along <110>. H center can be only approximately consid-
ered as a dihalide molecule 2X − located in one anion site.
There is additional hyperfine interaction of 2X − with two
more neighbor anions along [110], i.e., strictly, an H center
is 3
4 .X − This fact is obtained from the analysis of EPR
spectrum (and it’s spin-Hamiltonian). The value of such
superfine interaction 2X X X− − −− − is high in KBr, RbBr
and KCl, but is very weak in RbCl [25]. These circum-
stances (orientation and superfine interaction) influence the
initial separation of F and H centers formed as an F–H pair
and, as a result, the thermal stability of these pairs (and
especially α–I pairs formed at a subsequent tunnel rechar-
ging of F–H).
Concluding, only a detailed complex analysis of the da-
ta received by all the above-mentioned versions of thermo-
activation spectroscopy allowed to select the annealing
stage connected with the recombination of a becoming
mobile interstitial with its counterpart from a FDs pair. The
purpose of the present paper is to compare the experi-
mental results available in the literature on the recombina-
tion of radiation-induced mobile H interstitials with immo-
bile F centers at low temperatures in the series of alkali
halides (NaCl, KCl, RbCl, KBr, RbBr) with the quantita-
tive computer simulations of these diffusion-controlled
processes. Despite numerous experimental studies of the
kinetics of primary defect annealing upon temperature in-
crease, obtained by a number of optical and magnetic
methods, very little quantitative information is available on
the defect migration energies and their pre-exponential
factors. These parameters are necessary for the prediction of
the kinetics of possible secondary reactions and, in general,
material radiation stability. Previous studies performed on
KCl and KBr crystals were focused mostly on spatially cor-
related defect pairs (F–H and α–I) [11,35–38], while this
paper deals with the recombination kinetics of spatially un-
correlated complementary defect pairs.
Low Temperature Physics/Fizika Nizkikh Temperatur, 2016, v. 42, No. 7 749
V.N. Kuzovkov, A.I. Popov, E.A. Kotomin, A.M. Moskina, E. Vasil'chenko, and A. Lushchik
2. Method
Numerous experimental studies provide data on the
changes of radiation defect concentration versus heating
(annealing) temperature caused by mobile defect encounter
and recombination. Usually, the temperature in these ex-
periments is a linear function of time. As mentioned above,
our purpose is to extract the key diffusion parameters —
migration energy and pre-exponential factor from the ex-
perimental data for alkali halides.
Change of F, H defect concentration in the bimolecular
recombination is described by the standard kinetic equation
( )
( ) ( ) ( )F
F H
dn t
K t n t n t
dt
= − , (1)
where K(t) is the recombination rate.
Assuming equal F and H concentrations 0/Fn n =
0/ Hn n C= = with initial concentration n0, this reads
2
0
( ) ( ) ( )dC t K t n C t
dt
= . (2)
Thus, the defect concentration decay is
0
0
1( )
1 ( )
tC t
n K t dt
=
+ ∫
, (3)
where the diffusion-controlled reaction rate K is propor-
tional to the mutual diffusion coefficient D [39]
4K DR= π (4)
and, thus, depends exponentially on the defect migration
energy Ea, D = D0 exp(–Ea/kT), whereas R is the recombi-
nation radius. In our case of F, H defects, Ea is the migra-
tion energy of a more mobile defect (an H center). Finally,
assuming the temperature increase with the heating rate
β(t), one gets the following relation for the concentration
decay
0
/ 1
0 0
1
1 4 ( e ( )
i
a B
i T
E k T
T
C
n D R T dT− −
=
+ π β∫
. (5)
In most experiments, β(t) = β = const and we get two con-
trol parameters: the migration energy Ea, and pre-
exponential factor
0 0 /X n D R= β . (6)
We fitted below these two key parameters, Ea and X to
the available experimental kinetics by means of the least
square method. The typical value of X ~ 108 K–1 could be
estimated using the commonly known basic parameters:
n0 = 1017 cm–3, D0 = 10–3 cm2·s-1, R = 10–7 cm, the con-
stant heating rate β ~ 0.15 Ks–1. The estimates of the F, H
migration energies in alkali halides available from the lit-
erature are summarized in Table 1.
3. Main results
3.1. NaCl
There are several available studies of the H center re-
combination kinetics in NaCl crystals. The annealing
kinetics curves obtained in the temperature range around
35 K using both EPR [26] and optical absorption method
[48] are shown in Fig. 1 by symbols, while solid lines
present the results of our simulation. The values of the
simulated migration energy, Ea = 0.05−0.09 eV agree
well with those known for the H centers from the litera-
ture (see Table 1). Please note several annealing stages in
the optical measurements [48]: the first one is caused by
the thermal annealing of correlated F, H centers, the se-
cond one is due to recombination of uncorrelated defects,
and, lastly, the third stage, presented as a small peak at
about 40 K, is related to the delocalization of an H center
from a metal impurity trap (i.e., thermal destruction of HA
centers). As Fig. 1(b) shows, the fitting curve only partly
covers the last stage, reduces the curve slope and, there-
fore, causes the lowering of the value of the estimated
migration energy. The EPR data [26] from Fig. 1(a) are
free from this problem (signals from H and HA centers
can be separated) and thus, the estimated value of
Ea = 0.09 eV looks more reliable. The parameter X is
large in both cases, as expected for the regular diffusion
in a single crystal.
Table 1. Activation energy Ea (in eV) assigned to H center
migration
This work Other studies Reference
LiF − 0.13 40
– – 0.11 41
– – 0.138 42
KBr 0.087−0.10 0.090 43
– – 0.081 44
RbBr 0.065 0.08 45
CsBr − 0.035 45
KCl 0.12 0.075 43
– – 0.12−0.13 46
NaCl 0.089 – –
– – 0.08 47
– – 0.09−0.17 (theor) 47
RbCl 0.078 – –
KI − 0.075 45
750 Low Temperature Physics/Fizika Nizkikh Temperatur, 2016, v. 42, No. 7
Theoretical analysis of the kinetics of low-temperature defect recombination in alkali halide crystals
3.2. KCl
The H center annealing kinetics observed above 45 K
(see Fig. 2) is characterized by the slightly higher migra-
tion energy of 0.12 eV, as compared to the NaCl case,
while the large X factor is qualitatively similar. It is worth
noting that a small increase stage at 40−45 K is due to the
H center formation because of the α–I pair annealing at
lower temperatures. The energy estimate is close to that
evaluated by Kolk [46] and considerably larger than that
assigned by Ueta [43].
3.3. KBr
The analysis of I center thermal annealing (via recom-
bination of mobile I centers with still immobile α centers)
is shown in Fig. 3. The experimental points are taken
from Ref. 49, and the simulation (solid line) is performed
for the second stage around 15 K — annealing via uncor-
related defect recombination and suggests quite low mi-
gration energy of Ea = 0.026 eV for the I centers. On the
other hand, analysis of the optical absorption annealing
for the F, H centers in the same KBr crystal [48] around
40 K (see Fig. 4) yields similar energies for both defect
annealing kinetics (0.087 and 0.10 eV) since in both cas-
es just an H center is a mobile recombining partner. The-
se values of Ea are close to previous estimates by other
authors (see Table 1). As one can also see, a fraction of
F centers survives the recombination since some of mo-
bile H centers undergo trapping by metal impurities with
the formation of HA centers and, thus, avoid their recom-
bination with the F centers. Note that a simple relation
for the destruction temperature Td of the HA centers as a
function of the difference in the radii for a host cation and
impurity in KBr and KCl crystals has been presented and
theoretically justified in [50].
Fig. 1. The annealing kinetics of the H center concentration as
measured in a NaCl single crystal by means of the EPR (■, ac-
cording to Ref. 26) or optical absorption (●, [48]). The solid line
is theoretical fitting. The obtained migration energy Ea and pre-
exponential factor X are shown in a legend (see text for details).
Fig. 2. The annealing kinetics of radiation-induced H centers in
KCl measured by the EPR method (■, according to Ref. 26), solid
line presents the result of the present simulation.
Fig. 3. The annealing kinetics of radiation-induced I centers in a
KBr crystal after simulation (solid line) or as measured via the ther-
mal annealing of the optical absorption band according to Ref. 49.
Low Temperature Physics/Fizika Nizkikh Temperatur, 2016, v. 42, No. 7 751
V.N. Kuzovkov, A.I. Popov, E.A. Kotomin, A.M. Moskina, E. Vasil'chenko, and A. Lushchik
3.4. RbCl
The H center migration in RbCl [26] (see Fig. 5(a)) is
characterized by the energy of 0.078 eV, slightly lower
than in two other chlorides, KCl and NaCl. The pre-
exponential factor X is also smaller. To our knowledge,
this is the first estimate for the H center migration energy
in RbCl.
3.5. RbBr
The H center migration energy of 0.065 eV in RbBr
(see Fig. 5(b)) derived from the pulse annealing of the EPR
signal of H centers [26] is lower than that in both KBr and
RbCl crystals (see Table 1). It is a reasonable result be-
cause the lower H center migration energy is, the larger is
the overlap of two nearest anions that depends on radii of
both cations and anions. The previous estimate of Ea was
considerably higher. The pre-exponential factor X is also
smaller than that in KCl.
3.6. NaCl at high temperatures
All the above-discussed low-temperature annealing ki-
netics allowed us to obtain the migration energies for the H
centers, which become mobile at temperatures when elec-
tronic F centers are totally immobile. In order to get infor-
mation on the F center motion, one has to analyze the ki-
netics caused by the mobile F centers. It is known that
mobile F centers produce more complex defects containing
the dimer (M centers), trimer (R), tetramer (N) F aggre-
gates and finally, metal colloids [16,51–53]. Such kinetics
were studied in the electron-irradiated NaCl crystals in
particular [54]. It was shown that the F center concentra-
tion decay above 400 K is accompanied by a simultaneous
growth of the colloid X absorption band. In this case, the
main mechanism of colloid formation is the mutual en-
counter of mobile F centers and their aggregation caused
by an elastic attraction, which can be characterized by the
interaction energy ε for the nearest neighbor defects. The
relevant theory and computer program were described ear-
lier [52,53,55,56] and successfully applied to the kinetics
of colloid formation under intensive electron irradiation of
CaF2 [57] and LiF [58] as well as for thermochemically-
reduced MgO and Al2O3 [16,52,56,59].
Figure 6 depicts the calculated annealing kinetics of F
centers for different values of Ea and simultaneous tem-
perature-induced growth of the concentration of colloids
consisting of different number of defects (N0) in a NaCl
crystal. According to Fig. 6(a), the best agreement with
experimental data (given by filled squares according to
Ref. 54) is achieved for the F migration energy of
Ea = 1.13 eV which is close to the previous estimates
[16]. It is commonly accepted that the peak energy and
halfwidth of the X-absorption band of metal colloids de-
pend strongly on colloid size: very small colloids possess
broad structureless bands, whereas the well-pronounced
experimental optical band obtained in Ref. 54 and pre-
Fig. 4. (Color online) The annealing kinetics of radiation-induced
F, H centers in KBr measured via the thermal annealing of optical
absorption bands related to F (■) or H (○) centers [48]. Solid
lines shows the result of present simulation.
Fig. 5. (Color online) The annealing kinetics of radiation-induced
H centers in RbCl (a) and RbBr crystals (b) measured by the
pulse annealing of the EPR signal [26] or as the result of the pre-
sent simulation (solid curves).
752 Low Temperature Physics/Fizika Nizkikh Temperatur, 2016, v. 42, No. 7
Theoretical analysis of the kinetics of low-temperature defect recombination in alkali halide crystals
sented in Fig. 6 definitely corresponds to large-size col-
loids. We assume here the Poisson distribution of colloids
in size. Figure 6(b) shows that the best agreement with
experimental data is achieved assuming that each colloid
contains at least N0 = 20 defects.
Lastly, Fig. 7 demonstrates the influence of the attrac-
tion energy between F centers ε on the temperature de-
pendence of an average number of defects within a colloid
N0 as well as on the temperature dependence of the con-
centration of colloids with N0 =0. The latter dependences
manifest a peak shape (see Fig. 7(b)) due to a sharp in-
crease in the number of defects within a colloid at low-
temperature side and the prevalence of many-defect-
containing colloids on the high temperature side. The latter
causes the decrease of the colloid concentration (decrease
of X-band intensity): many small colloids are transformed
into several large colloids, and this process is called as
Ostwald ripening [51]. When F centers do not attract each
other (ε = 0), neither F center aggregation nor metal col-
loid formation occurs. For a weak attraction (curves 1 and
2 in Fig. 7(a)) the number of defects in colloids increases,
however, already for ε = 0.05 eV only relatively small col-
loids are formed (N ~ 10). These small colloids are not
transformed into larger ones due to a strong defect binding
within each colloid.
Thus, practically, the range of the attraction energies cor-
responding to the experiments is quite narrow, 0.02–0.03 eV.
Further calculations of the colloid concentration variation
with temperature for these attraction energies (see Fig. 7(b))
clearly demonstrate that only ε = 0.02 eV provides the results
close to the experiment, whereas higher values of ε (curves 2
and 3) give broad peaks as well. Thus, the analysis of the
colloid band formation in NaCl allows to obtain the F center
migration and attraction energies with a quite high accuracy.
4. Conclusions
We have estimated for the first time the migration ener-
gies of the H centers in a series of alkali halides as well as
of the F centers in NaCl, which are important parameters
for phenomenological analysis of radiation-induced pro-
cesses in these materials. Note that our estimates are much
more precise compared to the previous ones (see Table 1)
based on a simple assumption of the first- or second-order
reaction. Analysis of the pre-exponential factor X charac-
Fig. 6. (Color online) The calculated annealing kinetics (solid
lines) of the F center concentration for different values of Ea (a)
as well as the growth of the colloid concentration with the certain
defect number N0 (b, see text for details) in a NaCl crystal. The
experimental points are taken from Ref. 54 and are shown by
filled squares and open circles.
Fig. 7. (Color online) The calculated temperature dependences of
the average number of defects within a colloid (a) and of the con-
centration of colloids with a certain N0 = 0 (b) for different attrac-
tion energies ε between F centers in a NaCl crystal.
Low Temperature Physics/Fizika Nizkikh Temperatur, 2016, v. 42, No. 7 753
V.N. Kuzovkov, A.I. Popov, E.A. Kotomin, A.M. Moskina, E. Vasil'chenko, and A. Lushchik
terizing the radiation-induced material disordering will be
presented in a separate paper.
We are greatful to Prof. Cheslav Lushchik for valuable
and stimulating discussions. A.I. Popov and A. Moskina
would like to thank the support of Latvian research program
IMIS2, while E. Vasil'chenko and A. Lushchik thank the
Estonian Research Council−Institutional Research Fundings
IUT02-26. E.A. Kotomin acknowledges the Russian Science
Foundation (project 14-43-00052) for provided support of
the present study of radiation defecrs.
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1. Introduction
2. Method
3. Main results
3.1. NaCl
3.2. KCl
3.3. KBr
3.4. RbCl
3.5. RbBr
3.6. NaCl at high temperatures
4. Conclusions
|