Ionic conductivities of calcium-phosphate glasses
J. Martin, D. Budina, J. Zakel, M. Schäfer and K.-M. Weitzel
Fachbereich Chemie, Physikalische Chemie, Philipps Universität Marburg
35032 Marburg, Germany
[email protected]
The transport of potassium and rubidium ions through glasses
containing the respective alkali ion as mobile species has been
investigated by means of bombardment induced ion transport
(BIIT) and impedance spectroscopy (IS). The conductivities as
well as the activation energies derived from the two approaches
are in agreement lending further support to the recently
developed BIIT approach.
Ion conductivity; electrodiffusion
I.
INTRODUCTION
Recently, we have developed a new technique, which
allows to induce and to measure ion transport through a wide
range of materials under conditions of a single
sample/electrode contact. The technique was termed
bombardment induced ion transport (BIIT) since the ion
transport of interest was induced by shining a continuous ion
beam at a sample surface [1]. Attachment of the ions to the
surface causes a surface potential and a surface charge density.
A grounded metal electrode connected to the backside of the
sample ultimately defines a potential gradient across the
sample, which is inherently also accompanied by a
concentration gradient. These gradients induce ion transport
through the sample which is detected as a current at the
backside electrode. So far we have demonstrated the viability
of the BIIT approach for ion conducting glasses [2] as well as
polymer films [3]. If the focus of interest is on the macroscopic
conductivity of an ion conducting glass, the choice is to employ
the same alkali ion for bombardment which is the carrier of
charge transport in the glass. This intuitive condition is
meaningless when investigating alkali ion transport through a
polymer film, which does not contain the alkali ion in the
beginning. In that case the BIIT experiment (when operated for
a sufficiently long time) will lead to the formation of an
electrodiffusion profile [4]. Such a diffusion profile does not
evolve if e.g. a potassium ion conducting glass is bombardment
with a potassium ion beam. However, if we bombard a sodium
ion conducting glass with a potassium ion beam, an
electrodiffusion profile evolves for the sodium which is
replaced by the potassium ions [5]. Since under such conditions
potassium ions and sodium ions coexist over a spatial zone
spanning on the order of 100 nm, one hopes that such
experiments may contribute to the understanding of the mixed
alkali effect [6-8].
Ultimately one would aim at experiments on a type of glass
for which two variants can be prepared, one conducting alkali
ion A1 and one conducting alkali ion A2. Consequently one
can think of two different BIIT experiments, i. one where the
ion conducting glass is bombarded with the same alkali ion,
which would yield the conductivities, and ii. the cross-wise
bombardment with the respectively other alkali ions which
would yield the diffusion profiles. It is the aim of the current
contribution to set the stage for the first part of the challenge,
part i.
In order to reach the goal stated above, we need to identify
a glass system, which first of all is chemically and
mechanically stable and secondly ensure that the relevant
conductivities are within the accessible detection range. As
such a glass system we have identified the calcium-phosphate
glasses, which have attracted interest because of the potential
for medical application [9]. These glasses can be prepared with
alkali ions of our choice, which will ultimately be the mobile
species in that glass.
II.
EXPERIMENTAL APPROACH
The BIIT experiments have been performed under high
vacuum conditions at a working pressure of less than
2·10-6 mbar. The setup consists of a thermionic ion emitter (1),
a system of electrostatic lenses (L1-L6) used for guiding the
ions and the sample holder (3) including the sample (2). A
sketch of the setup is given in Fig. 1.
As thermionic emitter a synthetic leucite (KAlSi2O6) or Rbleucite (RbAlSi2O6) pellet is used that is heated to about
850 °C. The leucite has been mixed with molybdenum in a
ratio of 1:4 to improve the emission properties of the emitter. In
front of the emitter, a strong electric field of -2 kV/cm abstracts
the ions and leads to a continuous ion beam such that ion
currents up to 2 µA can be reached.
3
L0
2
1
L1
L2
PC
L3
L4
A/DConverter
L5
Amplifier
Figure 1. Scheme of the experimental setup.
L6
The kinetic energy of the ions is determined by setting
appropriate voltages to the repeller lens L0. The subsequent
lens system focuses and guides the ions toward the glass
sample position where the ions impinge on the glass surface.
By slowly increasing the repeller voltage, direct implantation
of the ions is avoided. The ions are softly attached to the front
side of the glass sample and give rise to a concentration and a
potential gradient across the glass [1,2]. The ion current
flowing through the glass is detected at the backside of the
glass via a glued metal electrode, subsequently A/D converted
and processed in a computer. After some seconds a quasi
stationary situation establishes where the ion current detected at
the backside electrode becomes time independent. Under these
conditions, the same amount of carriers is attached to the glass
surface as is neutralized at the backside electrode and the
potential at the glass surface is determined by the kinetic ion
energy. The ion currents discussed in this manuscript are
recorded in this limit. The specific conductivity can finally be
determined by recording the current at the detection electrode
as a function of the kinetic ion energy. At low kinetic ion
energies a linear increase of the ion current as a function of the
kinetic ion energy is observed with a slope that is given by the
resistance of the glass. Eventually, the specific conductivity is
calculated by taking into account the glass thickness and the
bombarded area of the sample.
The AC impedance spectroscopy (IS) measurements have
been performed in a temperature range between 30 °C to
240 °C controlled by a Novocontrol Quadro Cryosystem.
Additionally, a Novocontrol Alpha-AK impedance analyzer
has been used to control the applied voltage and the ac
frequency. The voltage applied has been 0.5 V (rms) while the
AC frequency has been set to values between 0.01 Hz and 1
MHz. Ultimately, the DC plateau is analyzed for deriving the
conductivity of the sample.
The glass samples with the composition xCaO·(55-x)
M2O·45P2O5 (M = K, Rb and x = 20, 30) were synthesized by
mixing stoichiometric amounts of CaCO3 (Grüssing),
(NH4)2HPO4 (Grüssing, 99%) and K2CO3 (Sigma-Aldrich,
99.0%) or Rb2CO3 (ChemPur, 99.0%), respectively. The
carbonates were dried for 24 h at 120 °C. After mortaring the
educts in an agate mortar, the educts were mixed for 45 min.
Subsequently, the mixture was melted in a Pt/10% Rh crucible
for 1 h at 950 °C and subsequently heated for 2 h to 1200 °C.
The resulting melt was poured in a stainless steal mold which
was preheated at a temperature about 50 K below the glass
transition temperature of the system. The potassium glasses
were relaxed about 30 K below the glass transition temperature
for 10 h. The rubidium glasses were relaxed 8 K below the
glass transition temperature for 15 h. Due to the constant P2O5
content of 45% and a [O]/[P] ratio of 3.1, the glasses we
produced are assigned to the group of polyphosphate glasses
[10].
After cooling, the sample was cut into cylindrical slices of
about 900 µm thickness using a high-precision cutting machine
(Struers Accutom-5). Each side of the disc was lapped using
SiC (Logitech PM5) and subsequently polished (LaboPol-5).
The polishing procedure was performed in three steps with
decreasing grain size of the polishing compound (Kemet, 3KD-C3, 1-KD-C3, ¼-KD-C2).
The thermo analysis of the glass samples has been carried
out using a differential scanning calorimeter (Mettler-Toledo,
DSC 1 – Sensor: HSS7). To this end, some milligrams of the
sample material have been mortared in an agate mortar and
were subsequently pressed into an aluminum crucible. As
reference an identical aluminum crucible has been used. Both
crucibles have been heated twice between 100 °C and 500 °C
at a rate of 10 K/min and were subsequently cooled. The
experiments have been carried out under a nitrogen
atmosphere.
The density of the glasses was obtained by applying the
Archimedic principle. In order to determine the mass of the
sample a high precision balance (Mettler-Toledo, XS105
DualRange) has been used. The accuracy of the balance is
±0.02 mg. The glass density has eventually been determined
using a pycnometer (Brand) with an accuracy of ±0.001
mg/cm³. Every glass density has been determined three times.
The standard deviation of these measurements has been ±0.06
mg/cm³.
III.
RESULTS AND DISCUSSION
In order to characterize the investigated glasses, the glass
transition temperature and the mass density ρ of each glass has
been measured. The results are given in table 1 where also the
calculated alkali ion density ρ(M) is given. For completeness,
the thickness d of the glass sample that is used in the BIIT
experiment is given.
One obtains that the glass transition temperature increases
with increasing CaO-content. This observation is reasonable as
the CaO acts as a network modifier oxide and links the
phosphate chains. The larger the amount of CaO, the more
cross links are present between the phosphate chains [11]. The
cross links stabilize the glass and lead to a higher viscosity and
eventually to a higher glass transition temperature. The mass
density of the glasses can be motivated by comparing the
densities of the educts [12,13]. For the potassium glasses, the
K2O has a lower mass density (2.35 g/cm³) than the CaO (3.34
g/cm³). In the case of the rubidium glasses the situation is
converse. Here, the RbO2 has the higher mass density
(4.00 g/cm³). As a consequence, it is expected that the mass
density of the potassium glasses should increase with
increasing CaO content while the mass density of the rubidium
glasses is decreasing with increasing CaO content. As table 1
shows the measured glass densities follow the expected trend.
From the mass density and the stoichiometry of the glass it is
possible to calculate the mobile ion density of the glasses, e.g.
the density of the alkali ion.
TABLE I.
Glass
SAMPLE THICKNESS, GLASS TRANSITION TEMPERATURE AND
ION-DENSITY OF THE GLASSES.
d (µm) Tg (°C)
ρ (g cm-3)
ρ(M) (cm-3)
Ca20K
799
338
2.498±0.01
9.75E+021
Ca30K
535
401
2.56±0.01
7.35E+021
Ca20Rb
955
318
3.07±0.06
9.22E+021
Ca30Rb
571
418
2.914±0.004
6.89E+021
It is found that the ion density in the rubidium glasses is
about 5 percent lower than the mobile ion density in the
potassium glasses. Hence, we can conclude that the rubidium
widens the glass structure compared to the potassium glasses
most probably due to its larger ion radius.
One of the most important quantities that characterize the
ion transport through a glass is the specific conductivity.
Generally, all mobile charge carriers of the glass contribute the
specific conductivity. For the current glass system the ionic
conductivity is known to be much larger than the electronic
conductivity in the investigated temperature regime.
Additionally, from Time-of-Flight Secondary Ion MassSpectrometry investigations on bombarded calcium phosphate
glasses, it is known that the calcium ions are basically
immobile [5]. As a consequence, the alkali ion is the only
charge carrier that significantly contributes to the conductivity.
Often, the specific conductivity of a glass obeys an Arrhenius
law
σ
spec
=
σ0
T
⎛ E act ⎞
⎟,
⎝ k BT ⎠
⋅ exp ⎜ −
(1)
where Eact is the activation energy and kBT is the
Boltzmann’s constant times the temperature. The constant σ0
contains the mobility of the ions and the mobile ion density. In
order to connect the structure information to the ion transport
properties of the glasses, we detect the specific conductivity of
the glasses as a function of the sample temperature using two
independent techniques, the BIIT and the IS.
In the framework of the BIIT technique, we bombard the
glass with the alkali ion species that is native to the glass, i.e. a
CaXK glass is bombarded with K+ ions and a CaXRb glass is
bombarded with Rb+ ions. The temperatures applied during the
BIIT experiments were between 35 °C and 125 °C. The
repeller voltage was varied between 15 V and 100 V. The ion
current that reached the glass surface was about one order of
magnitude higher than the maximally detected backside
current, which guaranteed that the bombarded glass surface
was homogeneously charged [1,2]. The sample thicknesses are
listed in table 1.
ln( σT ( KScm-1) )
-5.0
BIIT Ca20K
BIIT Ca30K
IS Ca20K
IS Ca30K
-10.0
Figure 2 shows the specific conductivity of the two
potassium glasses in an Arrhenius plot. The specific
conductivities measured via BIIT (filled symbols) are
compared to respective data from IS (open symbols). Very
good agreement between the two methods is observed both in
terms of absolute conductivity as well as in term of the
activation energy, which is derived from the slope of the
curves. For the Ca20K, we find Eact(BIIT) = 0.84 eV ± 0.02 eV
and Eact(IS) = 0.91 eV ± 0.02 eV. For the Ca30K glass, we find
Eact (BIIT) = 0.96 eV ± 0.02 eV and Eact(IS) = 1.04 eV ±
0.02 eV. The fact that the IS value for Eact is larger than the
BIIT values is connected to the temperature range extending to
significantly higher values for the IS setup. In all measurements
we observe a slight increase of the activation energy with
increasing temperature. Although an interesting detail, this is
not at the heart of the current investigation.
At 100 °C, the conductivity of the Ca20K is about two
orders of magnitude larger than the conductivity of Ca30K
(compare table 2). This difference is partially due to the larger
density of alkali ions in the Ca20K (compare table 1). On the
other hand, the potassium ion density in the Ca30K is only
about 25 percent lower than that in the Ca20K glass. Hence, the
different ion density can explain only a small fraction of the
conductivity difference. Most of the difference originates from
the different diffusion coefficients in the two glasses. The
Ca30K glass has the higher CaO content and thus exhibits
more cross links. These cross links lead to a less flexible glass
structure such that structure is hardly modified if an ion jumps
from side to side. In contrast the Ca20K structure may respond
more flexible to jumps of the ions such that the activation
energy for the ion transport is lower in this case. Additionally,
as the Ca20K shows less cross links there may be more paths
for the ion movement available. Both effects lead to a larger
diffusion coefficient in the case of Ca20K. Here, the diffusion
coefficients can be calculated from the specific conductivities
using the Einstein relation
D=
σ spez ,
(2)
q ρ(M)
where q is the ion charge. The values derived for the
diffusion coefficient are given in table 2.
In a second step, specific conductivities have also been
measured for the corresponding rubidium glasses. The results
are shown in Fig. 3, again in the form of an Arrhenius plot,
where the data detected via BIIT are shown as filled red
symbols while the open black symbols represent the IS data.
TABLE II.
-15.0
-20.0
-25.0
1.6
2.0
2.4
2.8
1 / T (1000 / K)
Figure 2. Arrhenius plot for the CaXK glasses
3.2
k BT
2
SPECIFIC CONDUCTIVITY AND DIFFUSION COEFFICIENT OF THE
CAXK AND THE CAXRB-SERIES. ALL DATA AT 100 °C.
Glass
σspec (Scm-1)
D (cm²s-1)
Ca20K
1.19E-10
2.44E-15
Ca30K
1.70E-12
4.65E-17
Ca20Rb
1.75E-10
3.80E-15
Ca30Rb
3.92E-13
1.14E-17
ln( σT / ( KScm-1 ) )
-5.0
BIIT Ca20Rb
BIIT Ca30Rb
IS Ca20Rb
IS Ca30Rb
-10.0
-15.0
case the cations have to overcome a higher energy barrier to
jump to the next cation site.
From the ion density and the specific conductivity the
diffusion coefficient in each glass could be determined. The
diffusion coefficients are smaller for larger CaO content which
may be explained by the higher degree of cross linking of the
phosphate network. This effect is obviously stronger in the
rubidium glasses most likely due to the larger ion radius of
rubidium compared to potassium.
For the future we plan to complement the investigation
presented here with a cross-wise BIIT experiment where the
rubidium conducting glasses are bombarded with potassium
ions and vice versa. This is the subject of ongoing work.
-20.0
-25.0
1.6
2.0
2.4
2.8
3.2
1 / T ( 1000 / K )
Figure 3. Arrhenius plot for the CaXRb glasses
The conductivity of Ca20Rb is shown as triangles while the
Ca30Rb data are presented at squares. We observe again very
good agreement between the IS and the BIIT measurements.
For Ca20Rb, we find an activation energy of
Eact(BIIT) = 0.80 eV ± 0.02 eV and Eact(IS) = 0.84 eV ±
0.02 eV. For the Ca30Rb glass, we find Eact (BIIT) = 1.05 eV ±
0.04 eV and Eact(IS) = 1.04 eV ± 0.02 eV. Similar to the
potassium glass the increase of the CaO concentration leads to
higher activation energies. However, for the rubidium glasses
this effect is even stronger than for the potassium glasses. The
reason might be that rubidium ions have a larger ion radius and
a more rigid glass structure may inhibit the ion transport of the
larger ions more effectively. This interpretation is supported by
the diffusion coefficient of Rb+ in the Ca30Rb which is about 4
times smaller than that of K+ in Ca30K (compare table 2). In
the less cross linked Ca20M glasses an opposite effect is
observed. Here, the rubidium glass shows a larger diffusion
coefficient. One could speculate that in the case of a weakly
cross linked glass the larger rubidium ion radius leads to an
effective widening of the glass structure such that the ion
transport is supported. The lower activation energy is also
fostering this interpretation.
IV.
SUMMARY
We have investigated the transport of potassium ions and
rubidium ions through calcium-phosphate glasses containing
varying amounts of the respective alkali ions as mobile species.
Conductivities as well as activation energies have been
determined by means of BIIT and IS. Results from the two
techniques are in good agreement. Additionally, the mobile ion
densities in the glasses have been calculated via the mass
density and the stoichiometry of the glasses.
Investigating the temperature dependent specific
conductivities, we were able to determine the activation energy
for the DC transport of the ions. In both series of alkali
conducting glasses an increasing amount of CaO leads to larger
activation energies. With decreasing density of the mobile ions
the average separation of these cations increases, which leads
to a less strong overlap of the coulomb potential [14]. In this
V.
ACKNOWLEDGMENT
We gratefully acknowledge fruitful discussions with Prof. B.
Roling as well as the possibility to use equipment of his group.
Financial support has been provided by the DFG.
VI.
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