Electrical and dielectric investigations of the conduction processes in KY3F10 crystals

Article abstract of DOI:10.1088/0953-8984/10/23/016

Dielectric constant and ac and dc electrical conductivity measurements have been performed in single crystals of the flourite compound KY₃F₁₀, in the temperature range 100 to 770 K. The dielectric response shows both dipolar and char

Full text of DOI:10.1088/0953-8984/10/23/016

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J. Phys.: Condens. Matter 10 (1998) 5161–5170. Printed in the UK
PII: S0953-8984(98)88374-4
Electrical and dielectric investigations of the conduction
processes in KY3F10 crystals
A P Ayala†, M A S Oliveira†, J-Y Gesland‡ and R L Moreira†
† Departamento de F´ısica, ICEx, Universidade Federal de Minas Gerais, CP 702, 30123-970
Belo Horizonte (MG), Brazil
‡ Universite´ du Maine—Cristallogenese, 72025 Le Mans Ce´dex 09, France
Received 13 October 1997, in final form 13 January 1998
Abstract. Dielectric constant and ac and dc electrical conductivity measurements have been
performed in single crystals of the fluorite compound KY3F10, in the temperature range 100
to 770 K. The dielectric response shows both dipolar and charge carrier contributions. The
electrical conductivity varied more than 11 orders of magnitude and showed the existence of
two thermally activated processes, with activation energies of 1.71(1) eV and 1.17(1) eV, for
the higher and lower temperature regions, respectively. The conduction mechanisms have been
discussed in terms of the different conduction pathways for the fluorine vacancy motion in the
crystal.
1. Introduction
Interest in KY3F10 crystals arises since materials containing the Y3+ trivalent rare earth ion
in a non-centrosymmetrical site are very suitable as hosts for build up solid state lasers
[1–3]. This crystal presents the fluorite-type structure (MF2) belonging to the cubic Oh5
˚
spatial group (Fm3m), with a = 11.54 A and two structural units per primitive cell [4–6].
The ionic groups [KY3F8]2+ and [KY3F12]2− alternate along the three crystallographic axes,
forming the multiple face centred cell (Z = 8), characteristic of the fluorite structure (figure
1). In the [KY3F8]2+ motif, the fluorine ions, represented by F2, form a cube (like in
CaF2), while in the [KY3F12]2− motif the twelve F1 ions form a cube-octahedral cluster.
2
2
Some characteristic interatomic distances are: F1–F1 = 2.6879 A, F –F = 2.4949 A,
˚
˚
1
2
˚
˚
K–F = 3.2033 A and K–F = 2.8363 A. These values show that the KY3F10 structure
is very closely packed, the interatomic distances being approximately the sum of the ionic
radii involved.
From the electrical point of view, fluorite structures show high electrical conductivities at
high temperatures, so that they can be classified as solid electrolytes [7–10]. In general, the
high conductivity values attained at elevated temperatures come from a diffuse (or Faraday)
phase transition to a fast conducting phase. The conduction mechanism is due to the
appearance of anion Frenkel defects in the structure, allowing easy vacancy mobility. While
Faraday transition has not been observed in KY3F10, previous investigations concerning the
fluorine ion mobility present some discrepancies and misinterpretations, as discussed below.
Toshmatov et al studied this crystal using NMR and ac electrical conductivity [7]. They
observed two thermally activated processes, one of them by NMR (600 to 750 K) and the
other by ac conductivity (600 to 1000 K). These processes presented migration enthalphies
of 1.1 eV and 1.5 eV respectively. The authors associate them with different conduction
c
0953-8984/98/235161+10$19.50 ꢀ 1998 IOP Publishing Ltd
5161

5162
A P Ayala et al
Figure 1. Crystalline structure of KY3F10. Unit cell (left) and structural motifs: [KY3F8]2+
2−
and [KY3F12
]
(right). The fluorine ions occupy the polyhedron vertices.
pathways in the crystal. Later, a Raman scattering investigation was accomplished by
Mortier et al between 40 and 950 K [2]. The results presented in their work were consistent
with the Fm3m crystallographic structure of KY3F10, which showed it to be stable in all
the temperature ranges investigated. As expected for ionic conductors, the Raman line
widths increased at high temperatures. From this dependence Mortier et al obtained values
for the activation energies ranging from 0.2 to 0.4 eV, which is of the same order of that
expected for a Faraday conductor. Motivated by the important discrepancies between these
results and by the lack of systematic studies on the electrical behaviour of KY3F10, we have
performed a detailed experimental investigation of the ac and dc electrical conductivities of
this material, between 100 and 770 K. The results presented in this work allow us to give
a better picture on the conduction mechanism of this crystal.
2. Experimental procedures
Good quality KY3F10 crystals were grown by the Czochralski technique. YF3 was first
synthesized by NH4HF2 fluorination of Y2O3 (5-nines grade, Shin-Etsu). Single crystals of
KY3F10 were pulled from a stoichiometric melt of 3YF3 + KF (Suprapur grade, Merck),
in a platinum crucible, along the [110] direction. The boules are easily cleaved along the
{111} planes.
In view of the dielectric investigations, several plates were cut following the easy
cleavage planes (typical surface area = 50 mm2; thickness = 0.80 mm). Then, ac dielectric
measurements were performed along the [111] direction, using an HP4192A impedance
analyser in a parallel configuration (capacitance, conductance), as functions of frequency
(10 Hz to 10 MHz) and temperature (100 to 770 K). The oscillation level was kept at
1.0 V rms. Silver paste electrodes were used to connect the samples to the holders in
either a home made controlled furnace under nitrogen atmosphere or an evacuated Janis
cryostat. The measurements were carried out either isothermally or under a continuous
linear heating/cooling rates (2.0 K min−1). Four-point dc conductivity (current measured
with a Keithley 617 electrometer, for an applied voltage of 1.0 V and heating/cooling rates
of 2.0 K min−1) complements the data between 330 and 550 K.

Conduction processes in KY3F10 crystals
5163
3. Results
The temperature dependence of the real part of the dielectric constant (ε0) of KY3F10, given
in figure 2, shows a rather normal behaviour of an ordinary ionic crystal: ε0 remains constant
over a large temperature interval and becomes increasingly higher for higher temperatures.
The latest effect is still more pronounced for lower frequencies. Indeed, the dielectric
response has a contribution from the mobile ions, which leads to some sample polarization
√
(εi∗onic = jσ∗(ω)/ω, with σ∗(ω) ∝ (jω)00, where n 6 1, j = −1, ε∗ is the complex
dielectric permittivity and σ∗ the complex electrical conductivity) [10, 11].
Figure 2. Temperature dependence of the dielectric constant of KY3F10, for some chosen
measurement frequencies.
Let us now investigate the behaviour of the real part of the electrical conductivity σ(ω),
versus temperature. As can be observed in figure 3, σ becomes increasingly frequency
independent for higher temperatures, which can be interpreted as a consequence of the
increasing jump frequency of the carriers [10] (the charges become increasingly free to move
[12]). In addition, this figure indicates clearly the increasing of the electrical conductivity
with temperature.
Since we have established the frequency independence of σ at higher temperatures, we
can try to determine the activation energy of the conduction mechanism. Thus, we present in
figure 4 a classical Arrhenius plot (log(σT ) against 1/T ) for the ac electrical conductivity
data. The straight line representing the low frequency limit allows the determination of
an intrinsic activation energy of 1.68(1) eV, for temperatures above 550 K. Note that,
for increasing frequency, the separation of the measured conductivity from this ‘static
limit’ line becomes larger. This is well compatible with the model outlined above for the
jump conduction in solids [10]: for frequencies above the characteristic jump frequency,
the charge carriers behave as dipole-like relaxators, bringing an additional (extrinsic)
contribution to the measured conductivity.

5164
A P Ayala et al
Figure 3. Frequency dependence of the electrical conductivity of KY3F10, for various
temperatures, between 375 and 649 K.
Figure 4. Arrhenius plot for the ac electrical conductivity of KY3F10, for the same frequencies
as figure 2.
Since the intrinsic conductivity should be obtained for ω → 0, we used the classical
Argand plot in order to verify the validity of the data treatment of figure 4. Our results are

Conduction processes in KY3F10 crystals
5165
Figure 5. Arrhenius plot for the static series conductance (Rs−01) obtained from the Argand
diagrams (Xs versus Rs) shown in the inset of the figure. The radii of the circles (Rs0/2)
decrease with increasing temperature.
Figure 6. Comparison between ac and dc electrical conductivities, obtained for KY3F10 crystal.
given in figure 5. In the inset of this figure we exemplify the Argand diagrams, where Xs
and Rs are respectively the series reactance and resistance of the sample, calculated from
the measured (parallel) ε0 and σ. Note that the diagrams form complete semi-circles, with
radii equal to Rs0/2, where Rs0 is the static series resistance (equal to the inverse of the

5166
A P Ayala et al
Figure 7. Arrhenius plot for the overall electrical conductivity of KY3F10, obtained from
combined ac and dc data.
sample static series conductance). Thus, the plot of T/Rs0 as a function of the reciprocal
temperature should give the activation energy of conduction mechanism. As shown in
figure 5, the obtained results are satisfactory for temperatures above 550 K, leading to
an activation energy of 1.63(1) eV, roughly equivalent to that obtained on the previous
treatment of log(σT ) against 1/T . Nevertheless, the results below 550 K are affected by
the measurement limit of the apparatus, i.e. the measured conductance becomes out of range.
The straight line below 500 K corresponds to the saturation of the impedance analyser. The
same behaviour is observed in figure 4, for the lowest frequency data.
The saturation of σ(ω, T ) for low frequencies and temperatures occurs because the
sample becomes highly resistive. Thus, this allows us to make dc electrical measurements
without destroying the intrinsic properties of the sample (i.e., dry electrolysis is avoided).
The results, obtained with the four-point method between 350 and 550 K, are presented in
figure 6, in comparison with those obtained by the ac technique. We note that the curve
for the static measurement matches very well the ‘intrinsic’ ac conductivity, i.e., the lowest
frequency ac conductivity limit. Note that the combined data show 11 orders of magnitude
of variation of the intrinsic conductivity, between 330 and 770 K.
We present now an overall analysis of the intrinsic electrical conductivity (figure 7). The
temperature variation of σT above 330 K is well described by the sum of two thermally
activated processes. Then a non-linear least squares fit was made using the following
expression:
ln(σT ) = A − 1H1/kT + ln[1 + B exp(−(1H2 − 1H1)/kT )].
(1)
In this way, the electrical conductivity appears to be characterized by (i) a higher
temperature process, above 550 K, with a migration enthalpy (1H) 1.71(1) eV which is

Conduction processes in KY3F10 crystals
5167
slightly higher than the values obtained above; and (ii) a lower temperature process, with
an activation energy of only 1.17(1) eV.
4. Discussion
The observation of two thermally activated conduction processes in KY3F10 is well
compatible with the existence of distinct paths for the vacancy movement in the crystal.
In order to analyse the possible conduction paths it is convenient to consider separately
the two structural units: [KY3F8]2+ (RF8) and [KY3F12]2− (RF12). In the first one, the
ions F2 occupy the vertices of a cube, in a similar arrangement to CaF2, while in RF12
the fluorine (F1) form a cube-octahedron. As can be observed in figure 1, the yttrium
atoms placed in the centre of the motif faces prevent conduction in the directions of the
crystallographic axes. Then, we note that the movement of the fluorine vacancies cannot be
along regular lattice sites, but rather through interstitial sites as in CaF2. This determines
that the conduction paths are in the [110] direction, through interstitial sites located in the
edges of each motif. To explain the possible conduction mechanisms, only the interstitial
site neighbourhood is redrawn in figure 8. These sites are in the middle of two concentric
octahedra, one of them determined by four F2 and two F1; the other has a plane of four
Y and two K. Based on this picture different possibilities for the vacancy (V·F ) filling can
be proposed [7, 13]: (a) FxF1 ↔ V·F1 ; (b) Fx ↔ V·F2 ; (c) Fx ↔ VF· 2 ; (d) Fx ↔ V·F1
2
F1
F2
(each possibility means the exchange betweFen one kind of fluorine ion and one kind of
fluorine vacancy). Toshmatov et al [7] suggested that the jumps (c) and (d) have the higher
diffusion energies. Nevertheless, in their analysis of the more probable paths, they only
consider the inner motif movements, which do not contribute to electrical conductivity, for
which long-range motions are required. In fact, the macroscopic conduction process should
be divided in two steps: inner motif movements and jumps between motifs (equivalent
or not). In the isostructural RbBi3F10, Matar et al [13] determined that the inner motif
movements require very low energies (0.17 eV). This allows us to conclude that the ionic
conductivity in these crystals is dominated by the jumps between motifs. Following this
reasoning and considering that the conduction pathways are through interstitial sites, we
propose that only three thermally activated processes would produce net charge diffusion in
these compounds, and thus would contribute to the electrical conductivity. These processes,
whose detailed discussion is presented below, would be:
(i) FxF1 ↔ V·F1
;
(ii) FxF2 ↔ VF· 1 conjugated with FFx 1 ↔ V·F2
;
(iii) FxF2 ↔ V·F2
.
Let us now discuss our model, which describes the main qualitative features of the ionic
conductivity in KY3F10. Since this crystal presents two non-equivalent fluorine ions, the
fluorine vacancy concentrations can be written as:
f
j
[VF· j ][Fi0 ] = NN0zj e−βG
[VF· ] = [VF· 1 ] + [VF· 2
]
f
f
2
f
1
[V·F ][F0i] = NN0 e−βG1 (z1 + z2 e−β(G −G )).
(2)
As usual, β = (kT )−1, N and N0 are the numbers of fluorine and interstitial sites
respectively, [V·Fj ] and [Fi0 ] correspond to the numbers of Fj vacancies and interstitial
fluorines F0, zj is the fraction of Fj ions and Gjf is the Frenkel pair formation energy. In
i
a pure crystal, the charge neutrality requires that [V·F ] = [Fi0 ]. Thus, the ionic conductivity

5168
would be given by:
σ(T ) =
A P Ayala et al
4q2
X
0
[F0i]di2νi e−βg
+
σj (T )
(3)
kT
j
where the first term describes the fluorine interstitial conduction and the summation
corresponds to the three different processes for the V·F1 and VF· 2 diffusion, as discussed
above (σ1: FxF1 ↔ VF· 1 ; σ2: FxF2 ↔ VF· 1 coupled with FFx 1 ↔ VF· 2 ; and σ3: FFx 2 ↔ VF· 2 ).
Since the structure is closely compacted the simple interstitial fluorine diffusion (F0i ↔ Vix)
is not possible. Then, these ions could only diffuse by more complex processes such as
an intersticialcy mechanism (F0i ↔ FFx ↔ Vxi ), but these processes are less probable and
require more energy than vacancy diffusion. Thus, the first term of equation (3) can be
neglected and the conductivity is entirely determined by vacancy diffusion, following the
conduction pathways proposed above. The terms corresponding to the vacancy movement
can be written as:
4q2
[V·F1 ]d121ν1 e−βg
11
σ1(T ) =
σ2(T ) =
kT
4q2
ꢀ
ꢁ
[V·F1
[V·F2
]
]
2
d12 ν1
2[V·F2 ]d221ν2 e−βg 1 + 2
(4)
12−g21
e−β(g
)
21
2
kT
ν2
d21
4q2
2[V·F2 ]d222ν2 e−βg
22
σ3(T ) =
kT
where dij and gij are the average displacements and migration energies for jumps between
Fi and Fj sites and νj the Fj mobility.
In order to discuss the different conduction pathways we can benefit from previous data
obtained with the NMR technique. The measurements of Toshmatov et al in this compound
and the observations of Matar et al in the isostructural RbBi3F10, showed that the F2 ions
have higher internal mobility than the F1 ones. This fact has a direct consequence in the
electrical conductivity because even the V·F1 vacancies, lying near the interstitial sites, are
easily filled by F2 ions and diffuse through RF8 motifs better than through RF12. Then,
the processes (ii) and (iii) which involve the F2 ions are more efficient than the process
(i). The conduction in the process (ii) is determined by the σ2 expression in (4) and some
considerations can be made about this expression. From equation (2) the ratio between
f
f
the numbers of fluorine vacancies is [V·F1 ]/[V· 2 ] = z1/z2 e−β(G −G )
. If the vacancy
1
2
formation energies are approximately equal, thisFratio will be approximately z1/z2 ≈ 3/2.
Furthermore, d12/d21 ≈ 1 and, since F2 ions have higher mobility than F1, the ratio ν1/ν2
is lower than one. Then, the term in parenthesis in the expression of σ2 will be close to
one and this contribution to the conductivity will have approximately a simple exponential
behaviour characterized by the energy g21. Therefore, the direct analysis of the expressions
does not allow us to associate the different processes to the measured migration enthalpies
(each case is characterized, or approximately characterized, by a simple exponential term).
Let us consider again figure 8, where the proposed conduction processes are indicated
by arrows. Note that the simple process FxF2 ↔ VF· 2 involves larger interatomic distances
x
through the interstitial (F2–F2 = 5.2609 A) than the FF1 ↔ VF· 1 exchange (F1–F1
=
˚
˚
2.7842 A). We remark also that the three conduction pathways are all in the same average
direction [110]. However, we notice that the fluorine octahedron is contracted in the
direction that connects the F1 ions (figure 8). In this way, the F1 obstruct partially the
diffusion path FxF2 ↔ VF· 2 , favouring the exchange FFx 1 ↔ VF· 2 . Thus, process (iii) requires
outward movements of the F1, allowing the passage of the F2 ions (this is viable because

Conduction processes in KY3F10 crystals
5169
Figure 8. Atomic distribution in the interstitial site neighbourhood. The arrows correspond to
the proposed conduction paths.
the RF12 cube-octahedron is less compact than the RF8 cube). Therefore, two kinds of
V·F2 diffusion can occur: in one of them the FFx 2 ↔ VF· 2 diffusion is assisted by the
FxF1 ↔ V·F2 exchange (process (ii)), while in the other one, the F1 participation is only by
releasing space for the FxF2 ↔ VF· 2 interchange (process (iii)). Thus, we suppose that the
latest process involves higher diffusion energy than others since it requires an interstitial
environment relaxation. If this assumption holds and considering that processes (ii) and (iii)
are more efficient than (i), we propose that the measured high temperature process would
be that of type (iii) (σ3). For lower temperatures, when this process would become less
efficient, the coupled migration (ii) (σ2) would still permit vacancy migration through the
RF8 motifs. However, from our measurements, we cannot separate this mechanism from
the process (i), because the small distance between the F1 ions (for which there are no ions
obstructing the exchange) could compensate its lower mobility. Therefore, at intermediate
temperatures, the conduction would be through the more efficient process (ii) or by a mixed
conduction between processes (i) and (ii). Finally, at still lower temperatures only the first
process (i) would survive, since it corresponds to the pathway with the smallest interatomic
distances. This situation could not be observed in our measurements, due to the high
electrical resistance attained by the samples at low temperatures.
The observation of (at least) two conduction processes in KY3F10 helps us to understand
the discrepancies found by previous authors using different techniques: the conductivity
values and activation energy of 1.5 eV found by Toshmatov et al [7], by electrical
measurements above 600 K, are compatible with our higher energetic process. The same

5170
A P Ayala et al
authors found an activation energy of 1.1 eV below 600 K from the NMR line narrowing;
this should correspond to our second measured process. Finally, Mortier et al [2] observed
a very low activation energy (0.2 to 0.4 eV) through the line width broadening of some low
frequency Raman bands. This effect was observed in a relatively wide temperature range
(room temperature up to 950 K). This very low value can be reinterpreted considering that
the vibrational modes are strictly perturbed by the vacancy movement within each motif.
In fact, the energies observed by Mortier et al are compatible with the NMR results in
RiBi3F10, where Matar et al obtained an energy of 0.17 eV, for the local movements of the
fluorine vacancies.
5. Conclusion
Ac electrical conductivity measurements of KY3F10 show: (i) a frequency dependent
charge carrier contribution to the dielectric response at higher temperatures; (ii) a dipole-
type relaxation (extrinsic) contribution to the electrical conductivity, mainly at lower
temperatures and higher frequencies; (iii) an intrinsic ac contribution (higher temperatures,
lower frequencies). The combination of the intrinsic ac conductivity data with the dc ones
reveals the presence of two conduction processes, associated with the different pathways
for the fluorine vacancy conduction in the crystal.
Acknowledgments
We thank Professor J F Sampaio for many helpful discussions and for a critical reading of
the manuscript. This work has been partially supported by the Brazilian (CNPq, Finep and
FAPEMIG) and French (CNRS) government agencies.
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