Defect chemistry and transport characteristics of β-AgI

Defect chemistry and transport characteristics ofb-AgI

J.-S. Leea,* , S. Adamsb, J. Maiera

aMax-Planck-Institut fu¨r Festkorperforschung, Heisenbergstr. 1, D-70569 Stuttgart, GermanybMin.-Kristallographisches Institut, Universita¨t Gottingen, Goldschmidtstr. 1 D-37077 Go¨ttingen, Germany

Received 27 December 1999; accepted 9 February 2000

Abstract

The defect chemistry and d.c. transport characteristics ofb-AgI are reconsidered by taking into account (i) two structurallydifferent interstitial positions, (ii) short-range interactions via associations, (iii) anisotropy of the wurtzite structure, (iv) long-range defect-defect interactions via Coulomb forces, and (v) formation of highly conducting layers perpendicular to thec-axisvia a disordered interface structure with stacking faults. Besides microstructural characterization the analysis relies on the ionicconductivity data by impedance spectroscopy with conventional as well as micro-electrodes, and utilizes recent reports on thedefect concentration and defect energies ofb-AgI by molecular dynamics simulations and on AgI:Al2O3 composites. Staticvalence sum calculations were performed to elucidate the ion conduction pathways and related migration barriers.q 2000Elsevier Science Ltd. All rights reserved.

Keywords: Wurtzite structure; D. Defects; D. Transport properties; Conduction pathways; Stacking faults

1. Introduction

AgI is certainly one of the most studied solid electrolytes:the superionic conductivity of the high-temperaturea-AgIwith the quasi-molten cationic sublattice characterized bylow-activation energies (,0.1 eV) inspired an intensivesearch and study for fast ionic conductors in different AgI-based systems [1]. The low temperatureb-AgI is a moderatesilver electrolyte. Like for other silver halides Frenkeldisorder has been made responsible for the cation transport[2–7]. Yet, concerning the defect chemistry ofb-AgI stillmuch controversy exists in the literature. This is partly dueto the anisotropy of the hexagonalb-AgI (wurtzite structure)[2,4,7] and is further complicated by the existence ofanother polymorph viz.g-AgI (sphalerite structure) [3,6,8].

In the present work defect chemistry and transportmechanisms ofb-AgI are readdressed. Experimentallydetermined conductivities of single crystalline as well asof different polycrystalline specimens are given a satisfac-tory phenomenological description, which is furthersupported by recent MD results [9,10] and by valence sum

calculations. The role of an interface-enhanced conductionmechanism is discussed in view of our recent results onAgI:Al 2O3 composites [11,12].

2. Experimental

Single crystals ofb-AgI were grown from AgI-HI solu-tion by slowly evaporating the solution at 408C for severalweeks following Ref. [2]. As-grown thin plates (ca. 0:7 ×0:7 × 0:03 cm3� were used for thec-axis conductivitymeasurements whereas theab-plane conductivity wasmeasured for both as-grown truncated dihexagonal pyra-mids (electrode contact geometry ca. 0:2 × 0:5 × 0:6 cm3�(Type I, Single) andcleaved crystals (ca. 0:25× 0:25×0:15 cm3� (Type II, Single).

Pellets of polycrystalline AgI were prepared by pressingthe reagent powder (Alfa, 99.999%) uni-axially at 5400 kg/cm2 into discs of diameter 0.6 cm followed by sintering thepellets at temperatures below the melting point (Type I,Poly). Another type of polycrystalline specimen, in thefollowing termed ‘Type II, Poly,’ was prepared by meltingthe powder at 6008C, grinding and pressing it into pellets.

In the temperature range of220 to 1508C impedancespectra were recorded by a HP4192A or a Solartron1260 using pasted silver electrodes. In the case of the

Journal of Physics and Chemistry of Solids 61 (2000) 1607–1622

0022-3697/00/$ - see front matterq 2000 Elsevier Science Ltd. All rights reserved.PII: S0022-3697(00)00020-2

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* Corresponding author. Present address: Center for Microstruc-ture Science of Materials, Seoul National University, Seoul 151-742, South Korea. Tel.:1 82-2-880-8862; fax:1 82-2-887-8164.

E-mail address:[email protected] (J.-S. Lee).

microelectrode measurements cleaved platelets werepositioned on a sapphire plate on top of a hot chuck. Theimpedance was measured between the counter electrode anda silver coated tungsten tip (tip radius 1mm). For details ofthe microelectrode measurement the reader is referred toRefs. [13,14]. Extremely high impedances up to 1012 Vcould be measured reliably using a home made impedanceconverter [15] connected to a Solartron 1260.

Usually, the first heating curves for the polycrystallinepellets were irreproducible because of the existence ofmetastableg-AgI and/or dislocations in the freshly pressedspecimens, but otherwise the reproducibility of everyconductivity curve was confirmed through repeatedtemperature cycles above thea/b transition temperaturefor polycrystalline specimens and below the transitiontemperature for single crystalline specimens and by apply-ing different heating and cooling rates. For single crystallinesamples, there remains an uncertainty of the absolute valuesof ^10–15% because of the difficulty in determining theexact cell constant.

3. Results

Fig. 1 gives an overview of the conductivity curves for thevarious types of AgI samples in the Arrhenius representa-tion. Curves (a), (c), (d) and (f) refer to single crystalline AgIspecimens measured below thea/b transition temperatureand Curves (b) and (e) are for polycrystalline specimens.

Curve (a) for the conductivity along thec-axis (k c) exhi-bits continuously increasing activation energyE over thewhole temperature range: between room temperature and,908C Ek is roughly 0.7 eV. Above that temperature, theapparent activation energy rises to values exceeding 1 eV,while the curve flattens below room temperature.

The conductivity perpendicular to thec-axis (' c) wasmeasured using two variants of specimens, and strikinglydifferent behaviors were observed:

1. Two opposite sides of the hexagonal pyramidal crystalwere polished plane-parallel along thec-axis (Type I,Single). The electrode contact area was smaller thanthe polished area and the lateral sides of the crystallitesconsist of the as-grown (0001) and�10�11� planes. Anactivation energy (E') of 0.38 eV characterizes theArrhenius regime below,408C (curve (c)) for such asample.

2. Crystallites, however, cleaved exactly along theab-planeexhibited a distinctly lower value for the activationenergy viz.Es

' � 0:29 eV (curve (d)) and higher abso-lute values of the conductivity below,208C even thoughmeasured in the same crystallographic direction asabove. Note that in comparison to (1) now the twolarge lateral surfaces arecleaved ab-planes, which adjoindirectly the faces pasted with silver electrodes.

Conductivity values from the microelectrode measure-ment on the cleavedab-plane (open squares, (f) in Fig. 1)were estimated according to the relation

s � 1pd

1R

�1�

from the measured resistance of the impedance spectra (R)and from the microscopically observed size of pointcontacts of ca. 4mm (d). The conductivity values aresubstantially higher than the ones just discussed.

Polycrystalline specimens prepared without meltingprocess (Type I, Poly) (curve (b)) are characterized by acti-vation energy (and also absolute conductivity) values whichare intermediate between values for the two crystallographicdirections of the single crystal e.g. 0.47 eV below,408C.Polycrystalline specimens made via melting process (TypeII, Poly) exhibit an activation energyEs

' � 0:29 eV below,658C (curve (e)), which is the same as for the' c conduc-tivity of the cleaved single crystalline AgI (Type II, Single)below ,208C. The absolute conductivity values are muchhigher than those of Type I polycrystalline specimen (curve(b)) and comparable to those measured by microelectrodeson the cleavedab-plane (curve (f)).

J.-S. Lee et al. / Journal of Physics and Chemistry of Solids 61 (2000) 1607–16221608

Fig. 1. Overview of conductivity curves as a function of tempera-ture: (a) single crystalline AgI along thec-axis; (b) normal poly-crystalline AgI (Type I, Poly); (c) as grown single crystalline AgIperpendicular to thec-axis (Type I, Single); (d) cleaved singlecrystalline AgI perpendicular to thec-axis (Type II, Single); (e)polycrystalline AgI from melting (Type II, Poly); (f) microelectrodeconductivity on the cleavedab-plane of single crystalline AgI.

Throughout this paper the term ‘Type II’ is reserved forthe specimens which exhibit an activation energy of0.29 eV, both for single crystalline AgI and polycrystallineAgI. Unlike Type I samples, Type II specimens exhibitsurface- or interface-dominated transport characteristics asdiscussed later.

Figs. 2 and 3 display our results for the single crystal-line samples k c and ' c, respectively, in comparisonwith the impedance spectroscopy data of Cava and Riet-man [7] (which covered only the temperature range aboveroom temperature) as well as with earlier single frequencydata on pure and Cu-doped samples by Cochrane andFletcher [4] and Govindacharyulu et al. [5]. The coinci-dence of most data over a large temperature rangecontrasts the large discrepancies in the reported (apparent)activation energies and the transport mechanisms. Themajor source of these discrepancies is obviously thepronounced curvature of the Arrhenius plots over anextended temperature range. The variation of the slopeas well as its anisotropy is seen more clearly in Fig. 4where local slopes of the Arrhenius representations for the

data of Figs. 2 and 3 are converted into activation energyvalues.

The activation energy curve along the hexagonalc-axis( k c) in Fig. 4(a) exhibits different regimes: (i) belowapproximately2208C the activation energy is 0.45 eV;(ii) with increasing temperatures the activation energyrises in the temperature range from220 to 208C. Sincethe exact location and extension of this range varies slightlydepending on the (purity of the) sample, the regression curve(bold line) probably overestimates the extension of the tran-sition region; (iii) the increase in the activation energy issucceeded by a 0.73 eV plateau. Conductivity data byCochrane and Fletcher [4] on samples with different impur-ity contents suggest that this plateau should represent intrin-sic values: Open circles and squares in Fig. 4(a) (k c) referto nominally pure and Cu-doped samples, respectively. Theplateau extends to the lowest reported temperatures for thesample of a higher purity. (iv) Between 908C and the phase

J.-S. Lee et al. / Journal of Physics and Chemistry of Solids 61 (2000) 1607–1622 1609

Fig. 2. Single crystal conductivity data along thec-axis direction( k c): filled small symbols represent impedance data from this work(B) and from Cava and Rietman [7] (X), while hollow symbols referto earlier single frequency data:W, A from Cochrane and Fletcher[4], K, L from Govindacharyulu et al. [5].

Fig. 3. Single crystal conductivity data perpendicular to thec-axisdirection (' c): filled small symbols represent impedance data fromthis work (B) and from Cava and Rietman (with sealing) [7] (X),while hollow symbols refer to earlier single frequency data:A fromCochrane and Fletcher [4],K from Govindacharyulu et al. [5]. Theinset (' Sc) displays the conductivity of the cleaved single crystal-line AgI (Type II, Single) from this work (B), the single crystal datawithout sealing from Cava and Rietman [7] (X), and microelectrodeconductivity on theab-plane of AgI.

transition temperature of 1478C the activation energy againrises continuously with temperature up to nearly 1.2 eV.

The most prominent feature of the corresponding varia-tion of E with temperature perpendicular toc-axis in Fig.4(b) (' c), compared withk c, is the absence of the 0.73 eVplateau. The activation energy of 0.38 eV remains almostunchanged up to 408C. Above 408C, the activation energyincreases continuously like thek c conductivity. The lowtemperature activation energy is also in accordance withconductivity data given in Ref. [5] for a Cd-doped AgIcrystal. The reported average activation energy of 0.52 eVcan be reanalyzed yielding 0.41 eV above2208C androughly 0.58 eV below2208C. The latter may includecontributions from impurity-vacancy association. In viewof the significantly lower impurity concentration, this kindof association should not occur in the nominally pure AgIcrystals throughout the covered temperature range.

A different type ofE' vs.T behavior is displayed in Fig.4(b) (curve' S). The plot includes the three data sets in theinset of Fig. 3 i.e. the measurements on the cleaved singlecrystals (Type II, Single), microelectrode data on theab-plane as well as the data set from Cava and Rietman for

the specimen without sealing treatment [7]. In contrast to theprevious report [7], we did not find that sealing influencedthe conductivity of cleaved single crystals (curve (d) in Fig.1). For all the samples the activation energy in the low-temperature range remains as low as,0.3 eV up to about408C. Above that temperature the activation energy risescontinuously with temperature as for the other types ofsamples.

It is to be noted that not only activation energy but alsoabsolute conductivity appears to be essentially the same inthe two crystallographically distinct directions above 1008C,although the crystallographic anisotropy of the wurtzitestructure persists up to the phase transition toa-AgI at1478C.

4. Discussion

4.1. Defect chemistry ofb -AgI

Frenkel disorder of the cations is generally assumed forb-AgI as for the other silver halides [2–7]. Unlike AgCl andAgBr, in which the Frenkel pairs represent Ag interstitials innominally unoccupied tetrahedral sites and Ag vacancies innominally occupied octahedral sites of the rocksalt struc-ture,b-AgI crystallizes in the wurtzite structure as outlinedin Fig. 5 (l.h.s.). The hexagonal close packing of the iodineions in the wurtzite structure offers three crystallographi-cally distinct sites for cations, i.e. two sets of tetrahedralsites and one set of octahedral sites. The two types of tetra-hedral sites form isolated pairs as shown in Fig. 5, in whichdark tetrahedra (Ag) represent the regularly occupied silversites while the face-sharing light tetrahedra (T) are regularlyunoccupied. The defective species may thus be specified asvacancies in the normally occupied tetrahedral sites�V 0Ag�;interstitials in the normally unoccupied tetrahedral sites(AgT

z ) and interstitials in the octahedral sites (AgOz ). There-

fore the defect chemistry can be approximately treated interms of the two Frenkel equilibria, viz.

AgAg 1 VO O AgzO 1 V 0Ag KO � �V 0Ag��Agz

O� �2�

AgAg 1 VT O AgzT 1 V 0Ag KT � �V 0Ag��Agz

T� �3�The respective standard enthalpies have been recentlyassessed in a MD study to beDOH8 � 0:55 eV andDTH8 �1:2 eV [9,10].

While the octahedral interstitials (AgOz ) can be unambigu-

ously identified, the configurations involving the vacancies(VAg

0) and tetrahedral interstitials (AgTz ) require a more

detailed definition. Silver ions in the regular tetrahedralsites AgAg can easily hop into the neighboring vacant tetra-hedral site resulting in the configuration (V0Ag AgT

z ).

AgAg 1 VT O �V 0AgAgzT� K 0T � ��V 0Ag��Agz

T��; �4�Owing to the short distance of only 1.9 A˚ between thecenters of the regular Ag site and the tetrahedral vacancy,


Fig. 4. Variation of the activation energy (a) along thec-axis (k c)from the data of Fig. 2, (b) perpendicular to thec-axis (' c) fromthe data in Fig. 3, and from the data in the inset (' Sc) of Fig. 3. Theinset displays the average curves together.

the configuration (V0Ag AgTz ) represents a dipolar, effectively

neutral associate rather than a usual (separated) Frenkel pairdescribed by Eq. (3). Recent MD simulations [9,10]suggested a formation enthalpy of onlyDT

0H8 � 0:1 eV orless for the associates, i.e. an association enthalpy of theisolated defects ofDassH8 � DTH8 2 DT

0H8 � 21:1 eV:For the following discussion it proves helpful to write

down the tetrahedral pairs explicitly, i.e. to write

�AgAgVT�1 �AgAgVT�O �AgAgAgTz�1 �VAg

0VT�: �5�for the tetrahedral Frenkel equilibrium and

�AgAgVT�O �V 0AgAgTz� �6�

for the formation of dipoles.The MD study in Refs. [9,10] indicates that

[(V 0AgAgTz)] @ [V 0Ag] < [AgO

z] @ [AgTz] over the whole

stability range ofb-AgI except for the premelting high-temperature regime in which [(V0AgAgT

z )] and [V0Ag] are ofthe same order of magnitude. Charge neutrality requires[AgO

z] 1 [AgTz] � [V 0Ag] and thus for dilute situations

[AgOz] � �VAg

0� � ��KOp

and [AgTz ]� KT=

��KOp

.

4.2. Transport pathways inb -AgI

In addition to the defect chemistry of the mobile species, aconsideration of transport mechanisms in view of crystalstructure seems essential to account for the anisotropicconductivity of b-AgI. Possible silver jumps among the

three different types of sites are indicated on the l.h.s. ofFig. 5: jumps between face-sharing octahedra along thek caxis which can be continued along the octahedral channels;jumps between face-sharing tetrahedra alongc-axis whichare confined to a short distance within isolated pairs; finallyjumps between face-sharing tetrahedra and octahedraperpendicular toc-axis which can be continued on theab-plane.

As demonstrated for a variety of other compounds, inparticular silver conductors, bond-valence sum calculations[16] can be employed to construct a semi-quantitative modelof possible diffusion paths [17,18]. This technique relies onsimple empirical bond-length bond-valence correlationsand the assumption that the ion transport should followpathways along which the deviationDV � V 2 Videal ofthe bond-valence sum V for a mobile ion from its formalvalence Videal remains as small as possible.

The top part of the r.h.s. in Fig. 5 displays a three-dimen-sional (3D) network of possible pathways in terms of anisosurface of constant bond-valence sum mismatchDV.The shape of the Ag sites in this representation is consistentwith the anharmonic thermal displacement study describedin Ref. [19]. The connecting necks of the bond-valenceisosurfaces correspond to the common triangular planesfor neighboring sites in the crystallographic representation.The bottom part of the r.h.s. displays a cross-section of thebond-valence isosurface perpendicular to thec-axis. Owingto the low-valence sum for the center of the octahederal site


Fig. 5. (l.h.s.) Schematic structure of the hexagonal close packing of the iodine ions: a channel consisting of face-sharing octahedral sites alongthec-axis, isolated pairs of face-sharing tetrahedral sites and a close-packedab-pane of alternating tetrahedral and octahedal sites face sharingwith each other are shown. Three different kinds of hopping between face-sharing sites such as between two octahedra, between two tetrahedra,and between tetrahedron and octahedron are designated. (r.h.s.) A valence sum pseudopotential isosurface depicting the various Ag conductionpathways. The bottom part of the r.h.s. displays a slice of the isosurface alongc-axis. The yellow (violet) color stands for the valence sum larger(smaller) than the equilibrium value. The violet isosurface surrounding the octahedral sites shows that the very central region of the octahedralsites is unfavorable for silver ions to be occupied.

(with valence mismatch barrierDV < 20:35� the verycentral region of the octahedral sites is unfavorable for silverions to be occupied.

The bond-valence isosurface in Fig. 6(a) withDV � 0:01demonstrates that the tetrahedral sites are equilibrium posi-tions for silver ions. With increasingDV, octahedral sitesare connected atDV � 0:082 (Fig. 6(b)) and the tetrahedralsites are connected via octahedral sites atDV � 0:114 (Fig.6(c)). The isosurface in Fig. 6(d) (same as the r.h.s. above inFig. 5) represents the valence sum mismatch ofDV � 0:125at which the tetrahedral pairs are also directly connectedwith each other. From these considerations three differentkinds of conduction pathways for the successful long ranged.c. transport can be distinguished: pathways (I) consistingof alternating tetrahedra and octahedra essentially in theab-plane (' c), pathways (II) consisting of face-sharing octa-hedra along thec-axis direction (k c) and pathways (III)which lead to a migration in both crystallographic directions( k c and ' c) in that they include a short distance migrationwithin tetrahedral site pairs along thec-direction and amigration ' c via octahedral sites.

Besides visualizing potential ion conduction pathways,the valence sum calculations may provide a guide-line forestimating migration barrier energies for the elementary

hopping processes in terms of valence mismatch barriersDV. The direct comparison betweenDV and the migrationenthalpy values assessed in the previous sections seems tobe not straightforward, however, especially for configura-tions with significant cation–cation interactions [18].

In the following sections, transport mechanisms for thedifferent defect species in the two distinct directionsk cand ' c will be treated employing diagrams, in which theb-AgI structure is sketched schematically as layers of tetra-hedra occupied by silver ions (ABAB…) as shown inFig. 7. Fig. 7(a) indicates the defect species underconsideration while Fig. 7(b) illustrates the principaltransport pathways.

4.3. Vacancy mechanisms vk and v' at low temperatures

Since AgI is typically contaminated by higher-valencecations, vacancies (V0Ag VT), as designated by an emptytetrahedral site pair in Fig. 7(a) can be assumed to be thedominating mobile defects with an extrinsically fixedconcentration at low temperatures. Moreover, chargeneutrality demands that they remain the mobile chargecarriers with the highest concentration in the intrinsic


Fig. 6. Valence sum pseudopotential isosurfaces with different valence mismatch barriers: (a) the tetrahedral sites are silver position atequilibrium �DV � 0:01�; (b) octahedral sites are connected atDV � 0:082; (c) tetrahedral sites are connected via octahedral sites atDV �0:114; (d) tetrahedral site pairs are directly connected atDV � 0:125: Different conduction pathways are schematically illustrated: path (I)consisting of alternating tetrahedra and octahedra essentially in theab-plane; path (II) consisting of face-sharing octahedra along thec-axis; path(III) including the short-distance migration within tetrahedral site pairs along thec-direction combined with theab-direction migration viaoctahedral sites resulting in migration in both crystallographic directions.

regime since the neutral associate pairs (V0Ag AgT

z ) do notcontribute to the conduction.

Fig. 8(a) shows how the migration of a vacancy' c isassumed to be accomplished (v'): vacancies can migratealong path (I), i.e. the infinite pathways of alternating octa-hedral and tetrahedral sites in theab-plane. An Ag1 ionjumps to the right from a regular site (Ag) via an octahedralinterstitial site (O) into an adjacent vacant regular site with

the T site of the pair being unoccupied (V0Ag VT). As a resultsuch a vacancy configuration (V0Ag VT) is transported to theleft. The transport steps shown in Fig. 8(a) can be equallyexpressed using Kro¨ger–Vink notation as

�V 0AgVT�1 VO 1 �AgAgVT�O ��V 0AgVT�1 AgzO 1 �V 0AgVT��

O �AgAgVT�1 VO 1 �V 0AgVT�: (7)


Fig. 8. Schematic diagram of vacancy mechanisms. (a)v': migration of a vacancy�V 0Ag VT� ' calong path (I) of Fig. 7(b). An Ag1 ion (designatedby large X) jumps to the right from a regular site via an octahedral site into an adjacent vacant regular site resulting in a vacancy�V 0Ag VT� transportto the left. (b)vk: migration of a vacancyk c along path (III) of Fig. 7(b). An Ag1 ion jumps to the right from a regular Ag site via an octahedral siteinto the T site of a vacancy�V 0Ag VT� (transport essentially' c), forming a defect associate occupancy�V 0Ag Agz

T� and then from the T site into theregular site in the upper layer, breaking a defect associate (transportk c). A vacancy migration in opposite direction results.

Fig. 7. (a) Schematic structure ofb-AgI represented by layers of coloured tetrahedra occupied by silver ions (ABAB…): X stands for silver ionsin regularly occupied tetrahedra, T for silver ions in regularly unoccupied tetrahedra and O for silver ions in octahedral sites (not shown). Thedefect species such as vacancies�V 0Ag VT� with both tetrahedral sites of the pair unoccupied, tetrahedral interstitials�AgAgAgz

T� with bothtetrahedral sites of the pair occupied, neutral associates with inverted silver occupancy�V 0Ag Agz

T� as well as octahedral interstitials AgzO can be

unambiguously represented. (b) Transport pathways of Fig. 6(d) are schematically illustrated using the layer diagram.

No vacancy conduction pathways exist exactly along thec-axis. Vacancies can effectively migrate in thec-axis direc-tion along path (III) or analogous pathways. They all consistof short distance migrations within tetrahedral site pairsalong the c-direction and ab-migrations via octahedralsites resulting in a translation with non-zero projections inboth crystallographic directions (k c and ' c). Since this isthe mechanism which has to be involved in any netk cvacancy transport, we term itvk. It is depicted in Fig. 8(b):an Ag1 ion jumps from a regular Ag site, via an octahedralinterstitial site, into the T site of a vacancy configuration(V 0Ag VT), forming intermediately a defect associate (V0Ag

AgTz ) (transport essentially' c). A subsequent jump from

the T site to the regular Ag site in the upper layer convertsthe defect associate into the regular configuration (AgAg VT)(transportk c). Conversely, the vacancy configuration (V0Ag

VT) migrates in the opposite direction. The transport steps ofthisvk mechanism in Fig. 8(b) can be expressed by Kro¨ger–Vink notation similarly as in Eq. (7) viz.

�AgAgVT�1 VO 1 �V 0AgVT�O ��V 0AgVT�1 Agz

O 1 �V 0AgVT�O �V 0AgVT�1 VO 1 �V 0AgAgz

T��O �V 0AgVT�1 VO 1 �AgAgVT�: (8)

Here, the regular Ag sites of the two tetrahedra pairsinvolved belong to differentab-planes (see Fig. 8(b))while in Eq. (7) they are on the sameab-plane as representedin Fig. 8(a). The intermediate steps in brackets in Eq. (8)can be reversed, i.e. Ag! [T ! O]! Ag instead ofAg! [O! T] ! Ag.

We assume that in both directions an extrinsic vacancymechanism prevails at low temperatures. As shown in Fig.4, thec-axis conductivity exhibits an activation energy ofDkH

‡�V� � 0:45 eV at low temperatures. The width of thisextrinsic regime varies depending on the purity of the speci-men as can be seen in Fig. 2. Perpendicular to thec-axis theconductivity exhibits an only slightly lower activationenergy ofD'H‡�V� � 0:38 eV at low temperature. Thissimilarity can be explained by the common major migrationbarrier for both transport modes, namely, the transient stateof the silver ions on the common triangular face betweentetrahedral and octahedral sites as shown in the l.h.s. of Fig.5. In the bond valence representation, this corresponds to theneck between tetrahedra and octahedra in Fig. 6, whichoccurs at a valence mismatch barrier ofDV $ 0:082:Since the regular silver ions involved inv' transport alwaysneighbor a vacancy in the sameab-plane, their energyshould be somewhat higher and their migration enthalpycorrespondingly lower than that of silver ions involved invk transport which jump from theab-plane with all the adja-cent Ag1 ions at regular sites (see Fig. 8). Moreover, thereorientation of the associate (V0Ag AgT

z ) which is necessaryin vkmechanism in Eq. (8), but not in thev' mechanism (see

Eq. (7)), may contribute to the slightly higher activationenergy.

In spite of the similar activation energy values the abso-lute values of the low-temperature conductivity differ by anorder of magnitude between both directions as shown inFigs. 1–3. Even if one accounts for the contribution of theessentially isotropicvk mechanism to the ion transport' c,largely different pre-exponential factors for the two modesof transport should exist. Partly this may be traced back tothe difference in jump distances: a rough estimate of the pathlengths assuming linear connections between the centers ofthe involved regular and interstitial sites yields a displace-ment ofa < 4:6 �A ' c after a total jump length of 5.6 A˚ forthe v' mechanism, while thevk mechanism producesmean displacements ofc=2 < 3:75 �A k c and nearly thesame displacement' c after a total jump length of 7.5 A˚ .However, more subtle considerations for the pathways canbe given by the bond valence isosurfaces. Bond valenceisosurfaces in Figs. 5 and 6 showed that Ag1 ions preferablymove along the rim of the octahedral sites rather thanthrough the very center of octahedral voids due to theirlarge negative valence mismatches. As schematically repre-sented in Fig. 6(d) the migration of silver ions for the' ctransport via path (I) would be the shortest distance near theconnecting necks of octahedral channels in the isosurface(corresponding to the common plane between neighbouringoctahedra in the real structure). This favorable arrangementof the necks indicates the high probability for this hoppingprocess. On the other hand, a transportk c requires that anAg1 ion enters the octahedral site from a regular Ag site,moves along the rim of the octahedral void and jumps to theT site from the opposite corner of the octahedral void (cf.path (III) in Fig. 6(d)). In addition to longer jump distances,the low-probability configuration involved in thek c migra-tion process might thus provide an explanation for thesmaller pre-exponential factor for this mechanism.

4.4. Interstitial mechanisms ik and i' at intermediatetemperatures

An octahedral interstitial mechanism for thec-axis direc-tion (ik) is obviously the migration through the face-sharingoctahedral channels of path (II) shown in Fig. 6. Thetransport steps are schematically represented in Fig. 9(a),which can be written as

AgzO 1 VO 1 VO O VO 1 Agz

O 1 VO O VO 1 VO 1 AgzO:

�9�We attribute the regime of activation energy of 0.73 eV,which is unique for k c transport, to this process. MDcalculations [9,10] show that apart from the neutralassociates, octahedral defects AgO

z and vacancies (V0Ag VT)are the prevailing intrinsic defects throughout the coveredtemperature range. Thus the concentrations of the defectsresponsible for the transport can be approximated as�Agz

O� � �V 0Ag� ��KOp

: Since we are in the intrinsic


regime, the activation energy of thec-axis conductivitycurve can be expressed as

Ek � DOH8

21 DkH

‡�O� � 0:73 eV: �10�

The insertion of the value ofDOH8 � 0:55 eV from the MDcalculations in Refs. [9,10] leads to a migration enthalpyDkH

‡(O) of 0:73 eV2 0:55 eV=2� 0:46 eV: The migrationbarrier is expected to be the transient state of the silver ions onthe common triangular plane between two octahedral sites.

It is to be noted thatDkH‡(O) is almost the same as the

activation enthalpyDkH‡�V� � 0:45 eV to reach the transi-

ent state between tetrahedral and octahedral sites as derivedfrom the extrinsic vacancy mechanism in the low-tempera-ture regime. Hence, in view of the estimated migrationenthalpy value a vacancy migration in the intrinsic regimemight explain the temperature dependence as well. Thesupposition of a predominantly octahedral interstitialmechanism is grounded on the anisotropy in the conductiv-ity in this regime. If a vacancy mechanism persisted throughthe intrinsic regime, a corresponding rise in activationenergy for the' c transport according toE' � DOH8=2 1D'H‡�V� � 0:55 eV=2 1 0:4 eV < 0:7 eV should havebeen observed in the same temperature range. However,the ' c conductivity exhibits essentially the same activa-tion energy of 0.38 eV continuously from the lowertemperature range.

The i' mechanism of an octahedral interstitial migrationin the ab-plane as shown in Fig. 9(b) is more precisely ofinterstitialcy type: an Ag1 ion on the octahedral site�Agz

O�pushes the regular AgAg into a neighboring octahedralsite and occupies the regular site instead. This can berepresented by

AgzO 1 �AgAgVT�1 VO O VO 1 �AgAgVT�1 Agz

O: �11�

The activation energy of this' c conductivity can beexpressed as

E' � DOH8

21 D'H‡�O� � 0:38 eV; �12�

resulting in the migration enthalpyD'H‡(O) of 0:38 eV20:55 eV=2� 0:11 eV: Such a small value ofD'H‡(O) israther typical for the interstitial migration in silver halides.

The extrinsic vacancy mechanism and the intrinsic inter-stitial mechanism are not distinguishable from the' cconductivity alone. For both mechanisms silver ions migratealong the basically same transport pathway of alternatingtetrahedral and octahedral sites as shown in Figs. 8(a) and9(b).

A change from extrinsic vacancy mechanism to intrinsicinterstitial implies a higher mobility of the interstitials andthus the appearance of a knee in the logs vs. 1=T (Wagner–Koch-effect [20]) corresponding to a maximum in theE vs.1=T curve. There seems to be a slight indication for thisin k c mode as can be seen in Figs. 2 and 4(a). A directinterstitial migration along the octahedral channels (ik)would indeed imply a higher mobility of interstitials (ui)than that of vacancies (uv) in k c mode (vk), resulting in aWagner–Koch-effect. Since such a knee effect is hardlysignificant even in k c mode, a Wagner–Koch-effectfor ' c mode, which in principle should also occur, willbe too small to be detected considering the smallerui =uv

ratio in ' c transport mode. The observation that thevalence sum mismatchDV�O! O� � 0:082 required forhops between octahedral sites is smaller thanDV�Ag!O� � 0:114 for jumps between octahedral and tetrahedralsites might serve as an additional evidence supporting thepresented model of a dominating interstitial mechanism forthe intrinsic k c transport.

The transition from the extrinsic vacancy to intrinsicinterstitial regime is in agreement with literature data. InRef. [6], the thermoelectric power (u ) of polycrystallineb-AgI indicated a change from vacancy to interstitialmechanism. The higher switch-over temperature giventhere (,808C) compared to that of the present work(,08C) may be due to the approximations in the evaluationsand/or a different impurity content.

4.5. Interstitial mechanism ip at high temperatures

For the low-temperature vacancy mechanisms describedin Section 4.3, we assumed that the vacant T site is onlyaccessible to an Ag1 ion if the adjacent regular site is unoc-cupied, i.e. in case of an effective vacancy configuration�V 0AgVT�; leading to the formation of a defect associate�V 0AgAg z

T�: Note that this configuration exists abundantly[9,10]. MD calculations suggest that at higher temperaturesa small but increasingly significant number of energeticallyunfavorable doubly occupied configurations�AgAg Agz

T� areformed according to the Frenkel equilibrium in Eq. (5) witha formation enthalpy ofDTH8 � 1:2 eV [9,10]. Their high


Fig. 9. Schematic diagram of interstitial mechanisms. (a)ik: migra-tion of an octahedral interstitial Agz

O k c along the face-sharingoctahedral channels of path (II) of Fig. 7(b). (b)i': migration ofan octahedral interstitial' c along the same path (I) of Fig. 7(b) asin the vacancy mechanism in Fig. 8(a). An octahedral interstitialAgz

O pushes the regular Ag1 ion into the neighboring octahedralsite, occupying the regular site instead.

energy is caused by the small distance of only 1.9 A˚ betweenthe centers of the two face-sharing tetrahedral sites so that adouble occupancy of the site pair requires a considerabledistortion of the local structure. Nevertheless, this opensthe way for the following highly activated but quite effectivehigh temperature transport mechanismi p shown schemati-cally in Fig. 10: a jump of an Ag1 ion from an O site to a Tsite in the vicinity of an occupied regular Ag site producesan energetically unfavorable double occupancy of the tetra-hedral site pair��AgAgAgz

T��p: This transient state may leadto a ' c transport if the entrant AgzT subsequently hops toanother O site (upper mechanism in Fig. 10 following thepath (I)) or approximatelyk c if the regular AgAg is pushedinto an O site, probably followed by an immediate reorien-tation of the tetrahedral site pair (lower mechanism follow-ing the path (III)). Even though not completely identical,both mechanisms can be formally written as

AgzO 1 �AgAgVT�1 VO O �VO 1 �AgAgAgz

T�1 VO�p

O VO 1 �AgAgVT�1 AgzO: �13�

The upper mechanism in Fig. 10 can be regarded as adirect interstitial mechanism' c compared to the indirectinterstitial or interstitialcy mechanism (i') at intermediatetemperature (Fig. 9(b)). The lower mechanism is an (indir-ect) interstitialcy mechanismk c. The same transient state��AgAgAgz

T��p: may also be attained if the AgzO jumps to an

occupied regular site pushing the regular Ag onto the T site.Both of the upper and lower mechanisms should be more orless equally probable since the double occupancy of thetetrahedral site pair may be conceived as a symmetricaltransient state.

This i p mechanism is highly activated since it requires theenergetically unfavorable double occupation of tetrahedral

site pairs. The migration enthalpy for the mechanismDi pH‡(O) may be estimated considering the energy cycleillustrated in the inset of Fig. 10. Assuming the transientstate ��AgAgAgz

T��p to be energetically approximatelyequal to the thermodynamically stable tetrahedral interstitialsite �AgAgAgz

T�; the migration enthalpyDi pH‡(O) can berelated to the formation enthalpy values of two Frenkelequilibria as Dip H

‡�O� < DTH8 2 DOH8 < 0:65 eV:Adding to this, the contribution of the formation enthalpyof interstitials (0.55 eV/2) would lead to an activationenergy of about 1 eV or somewhat higher in agreement toour conductivity measurements shown in Figs. 1 and 4.Furthermore, the presenti p mechanism provides a plausibleexplanation for the isotropization of the conductivity.

4.6. Cube-root-law at high T

In the temperature range close to thea/b transition, thedefect concentration is further increased by defect–defectinteractions according to the cube-root-model [9,10,21].There the excess defect formation enthalpy is taken to beproportional to the cube root of the defect concentration as2Jc1/3 (quasi-Madelung defect superlattice approach [21])with an interaction parameterJ of ,0.5 eV. Eventually, thedefect–defect interaction leads to the phase transition tothe a-phase [21]. It has been shown that such a transitioninto a highly disordered phase occurs even if structuralchanges are suppressed [9,10]. This conductivity anomalysuperimposes thei p mechanism in the high-temperatureregime.

4.7. Surface- and interface-enhanced transport' S

Fig. 4(b) exhibits a further type ofE vs. T relationship


Fig. 10. Schematic diagram ofi p mechanism: an octahedral interstitial AgzO jumps into a T site producing a double occupancy of the tetrahedral

site pair��AgAg AgzT��p: Transport' c is followed by subsequent hopping of the entrant AgT

z into another O site (upper mechanism followingpath (I)) or approximatelyk c if the regular Ag is pushed into an O site (lower mechanism following path (III)). The migration enthalpy fori p

mechanism may be estimated from the energy cycle in the inset asDip H‡ < DTH8 2 DOH8 assuming the activated transient state to be equal to

the thermodynamically stable tetrahedral interstitial�AgAg AgzT�:

designated by' S. It refers to conductivity values perpen-dicular to the c-axis obtained with the cleaved singlecrystalline AgI (Type II, Single). Data obtained from themicroelectrode measurements on the cleavedab-plane inthis study and the data set by Cava and Rietman [7] forthe specimen without sealing exhibit essentially the sametemperature dependence. The activation energy is,0.3 eVin the low-temperature region and increases above 408Capproaching the isotropic values at high temperature.

Type II single crystalline specimens prepared for theconductivity measurements' c designate the parallelepi-peds with two large opposite lateral sides incleaved(0001)ab-planes. Fig. 1 indicates pronouncedly higher conductiv-ity values for the Type II specimen (curve (d)) compared toType I (curve (b)) and even higher values obtained bymicroelectrode measurements on the cleavedab-plane.This supports the existence of a highly conducting surfacelayer on the cleavedab-planes. One might expect a spacecharge layer of high defect concentration generated at thecleavedab-plane. The presence of a surface space-charge

layer inab-plane was already suggested from the gas-sensi-tivity in Ref. [5]. According to Cava and Rietman [7] sealingthe specimen prevents the surface conduction even thoughthis could not be reproduced in this work. It is to be notedthat not only the magnitude of conductivity is enhanced butalso the observed activation energy of 0.3 eV is somewhatlower than for the' c conductivity in the extrinsic regime�D'H‡�V� � 0:38 eV�: Ideal space charge layers wouldrather assume a slightly higher value [22].

Type II polycrystalline samples, produced from themelting process show the same activation energy of0.3 eV as the Type II single crystalline specimens andexhibit high conductivities comparable to the valuesestimated from microelectrode measurements as shownby curve (e) in Fig. 1. On the other hand, curve (b) fora Type I polycrystalline specimen represents the typicalconductivity curve of polycrystallineb-AgI. The conduc-tivity of Type I polycrystalline AgI may be regarded as adirection average of single crystal data ink c and ' cmode. It is worth noting that the average diffusion coef-ficients of silver ions calculated by molecular dynamicssimulation showed an activation energy of 0.46 eV atlow temperature [9,10], comparable to 0.47 eV observedexperimentally.

The SEM micrographs of a fractured surface in Fig. 11show small plate-like grains for the specimen of Type IIpolycrystalline AgI (a) whereas large and randomly orientedgrains are observed for Type I polycrystalline specimen (b).The X-ray powder diffraction pattern in Fig. 12 also indi-cates the preferred orientation of Type II AgI by a strong(002) reflection compared to the as-receivedb-AgI powder.b-AgI crystals grow or cleave preferentially as platesperpendicular to thec-axis. So the behavior of Type II poly-crystalline AgI specimen is considered to be qualitativelythe same as the enhanced surface conduction for the cleavedsingle crystalline specimen of Type II. It is to be noted thatthe conductivity values determined by microelectrodes onthe cleaved single crystalline specimen lie on the conduc-tivity curve of Type II polycrystalline AgI. Considering thecomparable sizes of the microprobe on the surface of singlecrystalline AgI and of the grains of the Type II polycrystal-line specimen (of the order of a fewmm), it can be assumedthat the microprobe detects the enhanced conductivity of‘one’ microcrystalline grain with highly conducting inter-faces (see Eq. (1)). Ida and Kimura [23] recently showedthat the activation energy of conductivity of small-grainedpolycrystals of AgI changes from 0.38 to 0.28 eV withdecreasing mean crystallite size below ambient temperature,which is consistent with our observation on Types I and IIpolycrystalline specimens. The smaller conductivity valueof Type II polycrystalline specimen above thea/b transitiontemperature (curve (b) in Fig. 1) compared to that of thenormal Type I specimen (curve (e) in Fig. 1) may beexplained by the blocking effect of the internal boundarieswith respect to the superionic conducting bulk. Resistancevalues derived from the impedance spectra may include the


Fig. 11. SEM micrographs of polycrystalline AgI Type II (a) andType I (b). Thin plate-like grains for Type II polycrystalline speci-men can be compared to large grains for Type I polycrystalline AgI.

grain boundary resistance in which the small bulk resistancecannot be experimentally distinguished.

Besides the preferential orientation of the crystallites, thepowder diffraction pattern in Fig. 12 shows a substantialamount ofg-AgI and also indicates a high density of stack-ing faults by the broadening of the (h0l) reflexes ofb-AgI.The enhanced defect concentration can thus be explained interms of the stacking disorder of the regular wurtzite struc-ture. The cleaved surface ofab-plane of single crystallinespecimen may also be extensively disordered by stacking

faults. AgI:Al2O3 composites exhibit the same activationenergy of 0.29 eV and a 7-layer polytype of an orderedstacking fault phase has been recently identified in thesecomposites [11,12]. Surfaces of single crystalline samples,grain boundaries of polycrystalline samples and interfacesof AgI:Al 2O3 composites qualitatively point toward thesame boundary-phenomenon. Note that in other silver halidesystem as AgCl and AgBr in which ideal space chargeeffects dominate, boundary effects are also similar for poly-crystalline material and for Al2O3 composites. Even the


Fig. 12. X-ray power diffraction patterns for Type II AgI from the melting process compared to that for Type I AgI (the reagentb-AgI powderfrom Alfa). Preferred orientation of the crystallites is indicated by strong (002) reflection and the strong intensity of reflection in common withg-AgI reflections can be observed. The (h0l) peaks ofb-AgI (X) are significantly broadened in Type II AgI.

Fig. 13. A valence sum pseudopotential isosurface forg-AgI with valence mismatch barrierDV � 0:11: 3D networks of alternating tetrahedraand octahedra are constructed.

defect inducing mechanism in AgI system may be the sameas in AgCl and AgBr (excess vacancy formation as a conse-quence of Ag1 segregation to the boundaries) [22]. Inconsequence of the liability to form stacking faults in AgIsystem, however, a much more extended and completelydisordered boundary structure can result. Uvarov et al.reported the formation of stacking faults and thus a randomb–g polytype after an intense mechanical treatment on AgI,to which they ascribed the abnormal electrical properties[24–26].

4.8. Conduction in stacking faults

The enhanced conductivity along with the modified

migration enthalpy in the interface-dominated conductionin AgI system can be attributed to the structural modificationin the form of stacking faults. Stacking faults in hexagonalb-AgI (ABABAB…) locally lead to the cubic stackingsequence ofg-AgI stacking (ABCABC…) or vice versa.Stacking faults in the hexagonalb-AgI structure break theoctahedral channels and the isolated tetrahedra pairs in Fig.5 and generate a 3D network of alternating tetrahedra andoctahedra, which bears some similarity to the 2D network inthe ab-plane ofb-AgI. In g-AgI with the sphalerite struc-ture, this network of alternating tetrahedra and octahedra isthe only possible transport pathway as illustrated by thebond valence model in Fig. 13. The valence sum mismatchbarrier in g-AgI for the connection of tetrahedral and


Fig. 14. Impedance spectra for Type II polycrystalline AgI. Impedance arcs become more and more broadened with decreasing temperaturebelow,608C corresponding to the regime with 0.29 eV activation energy (see Fig. 1).

octahedral sites isDV � 0:11; which is essentially the sameas inb-AgI shown in Fig. 6(c). No data for single crystallineg-AgI exist and one may assume that the reported conduc-tivity behavior of the polycrystallineg-AgI specimens isprobably dominated by boundary effects. The reported acti-vation energy data ofg-AgI ranging from 0.23 to 0.30 eV[1] is consistent with the surface- and boundary-enhancedab-plane conductivity ofb-AgI.

Stacking faulted regions in AgI samples may beconceived as heterolayers consisting ofb-AgI and g-AgI.The high absolute conductivity values may then beexplained by the increased number of mobile defects atthe interface of the two polymorphs quite similar to theconductivity anomalies observed in two-phase mixture ofionic conductors AgCl:AgI and AgBr:AgI [22]. In fact,mixed phase effects at the interface ofb-AgI and g-AgIhave been recently confirmed in deliberately producedb/gphase mixtures as detailed elsewhere [11,12]. If the stackingfaults exist abundantly e.g. the spacing of the two phasesbecomes smaller than the Debye-length and a mesoscopicmultiphase effect is expected [22] as suggested for the peri-odicb-AgI/g-AgI heterolayers in the 7-layer polytype (7H)AgI (with a period of <26 A) identified in AgI:Al2O3

composites [11,12]. Surface and grain boundary effects in

Type II single and polycrystalline AgI may be similarlyunderstood whereby the effects are confined to the boundaryregion while in AgI:Al2O3 composites the stacking faultphase is formed extensively.

The conducting pathways in the stacking faulted structureare essentially the same as theab-plane transport ofb-AgIor in g-AgI, i.e. consisting of networks of alternating tetra-hedra and octahedra in close-packed layers. The migrationenthalpy for the extrinsic vacancy mechanism for' c trans-port in b-AgI is 0.38 eV while all the interface-dominatedAgI systems exhibit an activation energy of 0.29 eV. Thedifference of ,0.1 eV is comparable to the formationenthalpy of neutral Frenkel associates�D 0

TH8� in the orderedsilver sublattice inb-AgI structure (see Eq. (4)). Please notethat this reaction expresses the tendency to disorder of thesilver sublattice (see Fig. 7(a)). We assume that silver ionsin the stacking faulted structure are randomly distributedamong all the available sites and thus they should be in ahigher energy state than in the orderedb-AgI structure. Thisalready activated state of the silver ions might provide asatisfactory explanation for the corresponding decrease inthe migration barrier.

4.9. Highly depressed impedance spectra in interface-dominated regime

Fig. 14 shows impedance spectra for the interface-dominated Type II polycrystalline specimens. The impe-dance arcs become more and more broadened in thetemperature range below,608C corresponding to theregime with 0.29 eV activation energy as shown incurve (e) in Fig. 1. A similar behavior is observed forthe surface-enhanced' c conductivity of the Type II singlecrystalline AgI. On the other hand, all the other specimensas the normal polycrystalline AgI of Type I, Type I singlecrystalline specimen for' c conductivity and the singlecrystalline AgI for the k c conductivity exhibited moder-ately depressed bulk arcs for the whole temperature rangeinvestigated.

Fig. 15 shows the log conductivity vs. log frequencyrepresentation of the spectra shown in Fig. 14. A power-law frequency dispersion ofs , v n with n values changingfrom 0.6 to 0.4 was observed with decreasing temperature,which is related to the stronger broadening of the impedancespectra. Then values for the other types of specimens wereconstant as,0.6 in the same temperature range. The valueof 0.6 around room temperature is in accordance with thosereported by Funke et al. [27] in their extensive study usingfrequencies up to 1013 Hz above the room temperature.According to the jump relaxation model, the onset ofthe frequency dispersion is shifted to lower frequencies asthe temperature decreases [28]. Therefore, even within thelimited frequency range of this work (,107 Hz), thefrequency dispersion was monitored at temperatures belowroom temperature.


Fig. 15. Conductivity spectra for the impedance spectra of Type IIpolycrystalline AgI as shown in Fig. 14. The open circles are thepeak frequencies in the impedance spectra as shown in Fig. 14. Apower-law frequency dispersion ofs , v n is observed withnvalues changing from 0.6 to 0.4 as temperature decreases.

5. Concluding remarks

In Fig. 16, we summarize schematic conductivity curvesof the AgI system which are deduced from this analysis. Thepronounced curvature in the conductivity curves over thewide temperature range reflects the temperature dependentcontribution of different defects and different transportpathways. Regime A stands for the isotropic conductionmechanism involving the double occupancy of the tetra-hedral site pairs and defect–defect interactions describableby a cube-root-law. In regime B, an intrinsic interstitialmechanism is proposed to be dominant with different trans-port mechanisms for the different crystallographic direc-tions: along thec-axis the interstitials are expected tomigrate through the octahedral channels while inab-planetransport interstitials should migrate via alternating tetra-hedra and octahedra. Regime C represents an extrinsicregime dominated by vacancy mechanisms in both direc-tions: a slightly higher activation energy and much lowerabsolute conductivity values for thec-axis conductivity canbe explained by a detouring transport involving shortdistance jumps within isolated tetrahedral site pairs.

Cleaved surfaces inab-plane, grain boundaries or inter-faces of the composites are liable to form a stacking-faultdisordered AgI structure with an extremely high conductiv-ity. The reduced vacancy migration enthalpy of 0.29 eV inthe surface- and interface-enhanced systems compared tovalue 0.38 eV observed for orderedb-AgI bulk is explained

by the extensive disorder of Ag ions in the stacking faultedstructure. Strongly depressed impedance spectra and a pecu-liar frequency dispersion were observed for the interface-dominated conduction.

Acknowledgements

We would like to thank the service group of crystalpreparation in MPI FKF headed by E. Scho¨nherr for provid-ing AgI crystals for this study. Helpful discussions with F.Zimmer are greatly acknowledged. The microelectrodemeasurement was gratefully performed by S. Rodewald.One of the authors (J.-S. Lee) is grateful to the Alexandervon Humboldt foundation in Bonn for financial support.

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Fig. 16. Schematic overview of the conductivity behavior in different types of AgI samples below the transition to thea-phase.

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Defect chemistry and transport characteristics of β-AgI