Solid State Ionics 93
( 1997) 85-93
Effect of grain boundaries on the low-temperature ionic conductivity of polycrystalline RbAgJ, and Ag,SBr G. Staikova’*, M. Nold”, W.J. Lorenza, A. Froeseb, R. Speckb, W. Wiesbeckb, M.W. Breiter’ “Institute of Physical Chemistr?, and Electrochemistry, University of Karlsruhe. D- 76131 Karlsruhe. Germany ‘Institute of Microwave Techniques and Electronics, University of Karlsruhe. D- 76131 Karlsruhe, Germany ‘Institute of Technical Electrochemistry. University of Vienna, A- 1060 Vienna, Austria
Received 15 July 1996; accepted I October
Abstract The influence of grain boundaries on dc and ac conductivities of polycrystalline RbAg,I, and Ag,SBr was studied in the temperature range 15 K < T < 298 K using low-frequency EIS and high-frequency waveguide measurements. A change of the ion conduction mechanism is found at a transition temperature in the range 60 K < T, < 90 K. The conductivity behaviour shows that at T < T, the ion transport occurs preferentially along paths at the grain boundaries with very low activation energy, whereas the conventional conduction through the grains and across grain boundaries dominates at T > T,. A long-time relaxation effect is observed around the transition temperature (T = T,). This effect is attributed to a subsurface superionic transition leading to a formation of a subsurface superionic phase at the grain boundaries. The analysis of experimental results shows that the temperature-independent high-frequency ac conductivity observed at T < 100 K can be explained by a model involving a Debye relaxation of Ag + ions in preferred sites with an appropriate distribution of relaxation times. Keywords: New universality;
1. Introduction It is well established that the ionic transport in polycrystalline solids depends strongly on their microstructure [ 1 - 131. In different model approaches the total ionic conductivity is usually considered as consisting of a component due to intragranular or bulk contributions and a second component due to contributions of grain boundaries. The knowledge of bulk and grain boundary contributions to the ion *Corresponding author. 0167-2738/97/$17.00 01997 Elsevier Science B.V. All rights reserved PII SO167-2738(96)00496-l
silver iodide; Silver sulfide bromide
transport in polycrystalline superionic conductors is of great importance for the application of these materials as solid electrolytes in different electrochemical energy storage, energy conversion and sensor devices. At normal and elevated temperatures most of the polycrystalline superionic conductors have a considerably lower ionic conductivity than that of the corresponding single crystals [l-13]. In this case the conduction along the grain boundaries is negligible and the conductivity behaviour of polycrystalline materials is usually explained in terms of an ion
G. Staikov et al. I Solid State tonics 93 (1997)
transport through the grains and across grain boundaries. These processes are thermally activated and are usually described by the so-called ‘hopping’ models considering the ion transport as an ionic motion by successive ion hops between discrete lattice positions [ 14,151. Recent results obtained on different superionic conductors and frozen aqueous electrolytes’ in the temperature range 15 K < T < 150 K showed that below a transition temperature T, the ionic conductivity becomes nearly temperature independent, i.e. it is characterized by a vanishing activation energy [16-281. The activation energies of the thermally activated ion transport processes occurring above T, were found to be in good agreement with literature data. The low-temperature conductivity behaviour of different superionic conductors below a transition temperature T, is not yet well understood. In a previous paper  the change of the ion conduction mechanism below T, had been attributed to an ion transport along grain boundaries and/or other inhomogeneities in real superionic conductors. The aim of this paper is to discuss the role of grain boundaries in ion transport processes in superionic conductors at low temperatures on the basis of new results obtained by low- and high-frequency conductivity measurements on polycrystalline RbAg,I, and Ag,SBr with different microstructures. Only polycrystalline samples were used because phase transitions of first-order and higher order destabilize the corresponding single crystals with decreasing temperature.
2. Experimental 2.1. Preparation
The starting material was synthesized by melting a stoichiometric mixture of AgI and RbI in a nitrogen atmosphere at 593 K. The resulting product was quenched and powdered.
‘Aqueous electrolytes such as HCIO, X 5.5 H,O crystallize at low temperatures into a unique phase with a clathrate structure  and serve for electrochemical measurements comparing solid/ liquid and solid/solid interfaces [24-271.
Three different polycrystalline samples were prepared from this material in the following ways: (i) Pressed samples: the material was pressed at 8 X lo6 Pa. (ii) Quenched samples; the material was molten at 493 K and quenched into a silver-coated metallic vessel. (iii) Pressed- or quenched-annealed samples: the samples of types (i) and (ii) were annealed under vacuum for one day at 443 K and cooled down to room temperature within 40 min. 2.2. Preparation
The synthesis of the starting material was carried out by melting a stoichiometric mixture of Ag,S and AgBr under vacuum at 1073 K. The resulting product was quenched and powdered. The following three different polycrystalline Ag,SBr samples were prepared: (i) Quenched samples: the material was molten at 1048 K and quenched into a silver-coated metallic vessel. (ii) Quenched-annealed samples: the samples of type (i) were annealed under vacuum for 1 day at 553 K and cooled down to room temperature within 40 min. (iii) Pressed-annealed samples: the material was pressed at 5 X lo* Pa and subsequently annealed at 423 K under vacuum for 1 week. 2.3. Determination
of the grain size
The microstructure of polycrystalline samples was determined by standard procedures consisting of successive polishing, etching and microstructural analysis. In the case of RbAg,I, samples the selective etching of the grain boundaries was achieved by a chemical treatment with propanol or acetone, while for Ag,SBr a thermal treatment of polished samples at 700 K for 1 min was found to be effective. The microstructural analysis was performed using a computer-aided camera system: Olympus Cue 2 Super VS. Typical examples of the observed microstructures are shown in Fig. 1. The average grain size D of polycrystalline samples varied in the range 4.5 km-45 km for RbAg,I, and 10 km-100 urn for Ag,SBr.
G. Staikov et al. I Solid State Ionics 93 (1997) 85-9-T
were inserted as reference electrodes within the samples during the pressing or quenching procedure. Waveguide measurements were only performed on polycrystalline RbAg,I, samples in the frequency range 19 GHz
3. Results and discussion 3.1. DC conductivity
Fig. 1. Microstructures of polycrystalline Quenched-annealed sample; (b) quenched
2.4. Low- and high-frequency measurements
Ionic conductivities were determined by low-frequency electrochemical impedance spectroscopy (EIS) measurements and high-frequency waveguide measurements in the temperature range 15-298 K. The temperature of the samples was controlled with an accuracy of kO.1 K using a liquid helium-based cryostat (Cryophysics, model LTS-22-DRC 91 C). Two- and four-probe EIS measurements of polycrystalline RbAg,I, and Ag,SBr samples were carried out in the frequency range 1 mHz
The experimental results obtained by two- and four-probe EIS measurements were found to be in good agreement. A comparison between impedance spectra measured on a pressed-annealed Ag,SBr sample by two- and four-probe techniques is shown in Fig. 2. The slightly depressed semicircles in the impedance spectra observed at relatively high frequencies are directly related to the ionic conductivity of the superionic conductor. The low-frequency part of the impedance in the case of the two-probe measurement is connected with the contribution of both electrode/ superionic conductor interfaces. The ionic dc conductivities were determined from the impedance data corresponding to the depressed high-frequency semicircles using a non-linear fit procedure . Figs. 3 and 4 show the temperature
Re (Z) I GCl cm
Fig. 2. Impedance spectra of a quenched Ag,SBr sample (D= 10 pm) at T= 106 K. q =Four-probe EIS measurement, 0 = twoprobe EIS measurement.
G. Staikov et al. I Solid State lonics 93 (1997)
lo3 T-’ /
Fig. 3. Temperature dependence of the dc conductivity of a pressed RbAgJ, sample (D =4.5 pm) obtained by four-probe EIS measurements.
103 T-’ I K-’
perature range 60-90 K the dc conductivities measured by cooling and heating of the samples show a hysteresis. The extent of this hysteresis strongly depends on the time needed for EIS measurements at different temperatures during one cooling-heating cycle in the temperature range 15-90 K. The temperature was changed in 4 K step intervals and was adjusted with a cooling or heating rate \dT/dt] = 0.033 K min-‘. In the following, only the conductivity data obtained from EIS measurements during the heating cycle will be discussed. The observed hysteresis of the conductivity in the temperature range 60-90 K (Figs. 3 and 4) indicates the occurrence of a phase transition. A bulk phase transition should cause a jump in the specific heat or the thermal expansion coefficient of the Ag,SBr and RbAg,I, materials. However, specific heat measurements of RbAg,I, do not give evidence for a bulk phase transition in the temperature range 60-90 K . As no such measurements exist for Ag,SBr, the thermal expansion coefficient of this material was measured in the temperature range lo-200 K (Fig. 5). The results clearly show the P-r phase transition taking place at Tp_, = 126 K but also do not indicate any bulk phase transition in the temperature range 60 K < T < 90 K. Thus, the conductivity behaviour observed in this temperature range is most probably related to a phase transition occurring at grain boundaries, which will be discussed below. EIS measurements on samples with a different microstructure showed a significant influence of the grain size on the impedance spectra [30,3 11. Typical
Fig. 4. Temperature dependence of the dc conductivity of a pressed-annealed Ag,SBr sample (D = 100 urn) obtained by twoprobe EIS measurements. 1O-3
dependence of the dc conductivities of polycrystalline Ag,SBr and RbAg,I, samples obtained by twoand four-probe EIS measurements, respectively. The /3-r phase transitions taking place at T, _y = 126 K for Ag,SBr and T,_, = 121.9 K for RbAg41S result in jumps in the corresponding dc conductivities. An unusual conductivity behaviour is observed, however, at temperatures T < 100 K. With decreasing temperature below a transition temperature T, the dc conductivity rises again reaching a nearly temperature-independent value. In the transition tem-
-5 10 10
Fig. 5. Temperature dependence of the thermal expansion cient of a pressed-annealed Ag,SBr sample.
G. Staikov et al. I Solid State Ionics 93 (1997) 85-93
Re (Z) /GO cm
Fig. 6. Impedance spectra of a quenched Ag,SBr sample measured by a four-probe technique at T= 50 K. 0 = before annealing (D = IO pm), 0 = after annealing (D = 40 pm).
results obtained by four-probe measurements at T = 50 K are presented in Fig. 6. It is seen that after annealing the conductivity of a quenched Ag,SBr sample significantly decreases. The effect of sample preparation on the dc conductivity of polycrystalline Ag,SBr and RbAg,I, is illustrated in Figs. 7 and 8. In the temperature range 15 K < T < 90 K the experimental results show a significant influence of the average grain size D on the dc conductivity indicating that the ion transport along the grain boundaries dominates. The weak temperature dependence of the dc conductivity
Fig. 8. Temperature dependence of the dc conductivities of differently prepared Ag,SBr samples obtained by four-probe EIS measurements. 0 = quenched sample (D = 10 km), 0 = quenchedannealed sample (D = 40 pm).
shows that this process is still thermally activated but is characterized by a very small activation energy. A thermally activated ion transport process is usually described by uddcT = A exp(-E,lkT)
where uddcis the total dc conductivity and E, is the corresponding activation energy. In the case of a polycrystalline solid with a dominant ion transport along grain boundaries the preexponential factor A in Eq. ( 1) depends not only on the grain boundary properties but also on the sample microstructure and can be generally expressed by A=gA*
Fig. 7. Temperature dependence of the dc conductivities of differently prepared RbAg,I, samples obtained by four-probe EIS measurements. A = pressed sample (D = 4.5 pm), 0 = quenched sample (D = 12 pm), 0 = quenched-annealed sample (D = 45 km).
where g is a geometric factor related to the volume fraction of the grain boundaries and A* is a materialspecific constant. In the simplified ‘brick layer model’ [6-9,131 a polycrystalline solid is considered to be composed of cubic grains with a side D, separated by flat grain boundaries with a thickness d. For d +Z D the volume fraction of the grain boundaries is 3(dlD) and the geometrical factor in Eq. (2) is g =2(dlD). The values of the preexponential factors A and the activation energies E, determined from the experimental data obtained in the temperature range 15 K< T < 70 K are summarized in Table 1. For
G. Staikov et al. I Solid State lonics 93 (1997) 85-93
Table 1 Influence of sample preparation on the average grain size D and the preexponential factor A and activation energy Ea of crdCin the temperature range 15 K-CT<70 K Superionic conductor
quenched quenched-annealed pressed-annealed
D (Pm) 4.5 12 10 40 100
A (fi-’ cm-’ K)
2X 1om9 5x lo-”
5x lomh 3x10-’
RbAg,I* the pressed/tempered and quenched/tempered samples showed the same microstructure and average grain size (D =45 km). It was impossible, however, to determine a finite dc conductivity of these samples in the temperature range 15 K< T< 70 K since the sample impedance was in the same order of magnitude as the input impedance of the experimental setup. The results in Table 1 show that the grain size D of the samples does not significantly affect the E, values but strongly influences the preexponential factors A, in agreement with Eqs. (1) and (2). It is reasonable to assume that in this temperature range the grains and the grain boundaries in polycrystalline Ag,SBr and RbAg,I, have relatively ordered Agfion sublattices so that the conduction through the grains is negligible and the ion transport occurs preferentially along paths at the grain boundaries characterized by a low activation energy and low charge carrier density. The ion transport paths with low activation energy appear in the transition temperature range and can be related to a slow local reorganization of the AgC-ion sublattice at the grain boundaries. The long-time relaxation effect observed in the low-frequency EIS measurements in the temperature range 60 K
than that along grain boundaries. In other words, the dc conductivity paths along grain boundaries, which are effective in the temperature range 15 KC T <60 K may be progressively interrupted by the formation of SSP with increasing temperature. After the complete conversion of grain boundaries in SSP the ion transport through the grains and across grain boundaries dominates and the dc conductivity increases again with increasing temperature. This hypothesis is schematically illustrated in Fig. 9 and can explain the observed dc conductivity behaviour in the temperature range 60-90 K (cf. Figs. 3, 4, 7 and 8). 3.2. AC conductivity Previous waveguide measurements of polycrystalline RbAg,I, samples showed that the high-frequency ac conductivity, uaac, becomes temperature independent at T
conductivity paths with low activation energy
conventional conductivity paths with high activation energy
subsurface superionic phase (SSP)
Fig. 9. Schematic representation of the proposed mechanism in the transition-temperature range.
G. Staikov et al. I Solid State Ionics 93 (1997)
and pd is the dipole moment resulting from an occupied and an unoccupied site. For a thermally activated transition of a charge carrier between two preferred sites the relaxation time r can be expressed by r = vi’expz
Fig. 10. Temperature dependence of the high-frequency ac conductivities of differently prepared RbAg,I, samples obtained by waveguide measurements. A = pressed sample (D = 4.5 pm, f= 19 GHz), 0 =quenched sample (D = 12 pm, f= 32 GHz), 0 = quenched-annealed sample (D =45 km, f= 32 GHz).
also strongly depend on the sample microstructure [3 1,341. The uaC plateau increases with decreasing grain size confirming a preferential ion transport along grain boundaries. The experimental results shown in Fig. 10 can be explained on the basis of the ac conductivity approach proposed by Pollak and Pike  and Elliott . In this approach the dielectric response of a solid to the applied alternating field is assumed to be Debye-like, i.e. the polarization caused by the transition of a charge between two preferred sites decays on the removal of the exciting field following firstorder kinetics with a relaxation time r. The corresponding frequency dependence of the total ac conductivity o_(w) of a polycrystalline solid with a dominant ion transport along grain boundaries is given by
where g is the geometric factor related to the volume fraction of the grain boundaries (cf. Eq. (2)), co is the free space permittivity and w =2n-f. The susceptibility x(O) can be described by 
vi x(O) = 3Eok7where n is the spatial density
(4) of the charge carriers
where V, is the attempt frequency and EL is the corresponding activation energy. Following the paper of Pollak and Pike , it can be assumed that the grain boundary inhomogeneities lead to a uniform distribution of activation energies in the limits Ei, and Ei2, which is described by a distribution function P’(Ei) = (EL2 - Ei, )- ’ = P = const. According to Eq. (5) such a distribution of activation energies corresponds to an exponential distribution of relaxation times r(Ei) in the limits T, and r2. Using Eqs. (3)-(5) the ac conductivity can be expressed by EL
- arctan(w.r, )]
is the distribution constant. where P = (Ei2 -Ei,)-’ A temperature-independent ac conductivity follows from Eq. (6) for high frequencies w> > 1/r2: u&o)
This result is in good agreement with the experimental data of Fig. 10 in the temperature range T-C 100 K. The values for Ei2, E:, and g obtained by a fit of experimental results with Eq. (6) are shown in Table 2, where the dipole moment pd was calculated using a jump distance x0 =0.23 nm and the Ag+-ion density was assumed to be n = 1.15X 10” cmp3. The frequency dispersion of the ionic conductivity a(w) obtained by the low- and high-frequency measurements of quenched polycrystalline RbAg,I, samples is shown in Fig. 11. At T= const. the conductivity qualitatively follows a relation u(W) = UdC+ cwp with p = 1 according
(8) to the so-called
G. Staikov et al. I Solid State Ionics 93 (1997) 85-93
Table 2 Fitting parameters RbAg,I,
g, E:, and E:, obtained
by fitting of temperature-independent
Pressed (D = 4.5 pm) Quenched (D = 12 urn) Quenched-annealed (D = 45 p,m)
a,, data in Fig. 10 with Rq. (6)
(2%1)X 10-l (1-c0.5)x10~’ (523)X 1o-4
121 lrtl 121
40210 40210 40210
ty’ proposed by Nowick . In Eq. (8), C is a material-specific constant and w =2d A quantitative analysis was not possible due to the lack of experimental data in a wide frequency range caused by the present status of the EIS and waveguide measurement techniques. The improvement of electronic devices is in progress to fill this gap.
the transition temperature range can be related to a local reorganization of the Ag+-ion sublattice at grain boundaries. Around the transition temperature (T==T,) the results show a long-time relaxation effect, which might be attributed to a subsurface superionic transition (SST) and the appearance of a subsurface superionic phase (SSP) at the grain boundaries. The formation of SSP domains leads to a progressive interruption of ion transport paths with low activation energy so that at T >T, the conventional conduction through the grains and across grain boundaries becomes dominant. The analysis of experimental results shows that the temperature-independent high-frequency ac conductivity observed at T < 100 K can be explained by a model involving the Debye relaxation of Ag+-ions in energetically nearly equivalent sites with an appropriate distribution of relaxation times. The observed change in the ion transport mechanism results in a finite dc and ac ionic conductivity at T-=C 100 K, which is of great importance for the application of superionic conductors as solid electrolytes in the low-temperature electrochemistry and for the development of new electrochemical energy or sensor devices operating at low temperatures [34,39].
The low-temperature dc and ac conductivity behaviour of polycrystalline RbAg,I, and Ag,SBr with different microstructures shows a change of the ion conduction mechanism at a transition temperature in the range 60 K< T,<90 K (cf. Fig. 9). At T< T,the ion transport preferentially occurs along paths at grain boundaries with negligibly small activation energy. The appearance of these preferential paths in
The authors gratefully acknowledge the financial support of this work by Deutsche Forschungsgemeinschaft (DFG contract No. Wi 1044/1-l and Wi 1044/l-3) and the helpful discussions with Prof. H. v. Lohneysen, University of Karlsruhe. The authors also thank Dr. C. Meingast from the Research Center Karlsruhe for thermal expansion coefficient measurements of Ag,SBr.
log (f / Hz)
Fig. 11. Frequency dispersion of the conductivity o-(f) of a quenched RbAg,I, sample (Do= 12 pm). O=EIS measurements (1 mHz5js 10 kHz), 0 = waveguide measurements (19 GHz 5 f532 GHz).
G. Staikov et al. I Solid State lonics 93 (1997) 85-93
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