Ag2Se to KAg3Se2: Suppressing OrderâDisorder Transitions via

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AgSe to KAgSe: Suppressing order-disorder transitions via reduced dimensionality Alexander J. E. Rettie, Christos D. Malliakas, antia sanchez botana, James M. Hodges, Fei Han, Ruiyun Huang, Duck Young Chung, and Mercouri G. Kanatzidis J. Am. Chem. Soc., Just Accepted Manuscript • DOI: 10.1021/jacs.8b04888 • Publication Date (Web): 27 Jun 2018 Downloaded from http://pubs.acs.org on June 30, 2018

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Ag2Se to KAg3Se2: Suppressing order-disorder transitions via reduced dimensionality Alexander J. E. Rettie1, Christos D. Malliakas,2 Antia S. Botana1, James M. Hodges,2 Fei Han,3,4 Ruiyun Huang,5 Duck Young Chung1, Mercouri G. Kanatzidis1,3 1. Materials Science Division, Argonne National Laboratory, Argonne, IL, 60439, USA 2. Department of Chemistry, Northwestern University, Evanston, IL, 60208, USA 3. Center for High Pressure Science and Technology Advanced Research, Shanghai 201203, China 4. HPSynC, Geophysical Laboratory, Carnegie Institution of Washington, Argonne, Illinois 60439, United States 5. Department of Materials Science, Northwestern University, Evanston, IL, 60208, USA Order-disorder transition, dimensional reduction, ultralow thermal conductivity, high electron mobility ABSTRACT: We report an order-disorder phase transition in the 2D semiconductor KAg3Se2, which is a dimensionally-reduced derivative of 3D Ag2Se. At ~695 K the room temperature β-phase (CsAg3S2 structure-type, monoclinic space group C2/m) transforms to the high temperature α-phase (new structure-type, hexagonal space group R-3m, a = 4.5638(5) Å, c = 25.4109(6) Å), as revealed by in situ temperature-dependent X-ray diffraction. Significant Ag+ ion disorder accompanies the phase transition, which resembles the low temperature (~400 K) superionic transition in the 3D parent compound. Ultralow thermal conductivity of ~0.4 W m-1 K-1 was measured in the “ordered” β-phase, suggesting anharmonic Ag motion efficiently impedes phonon transport even without extensive disordering. The optical and electronic properties of β-KAg3Se2 are modified as expected in the context of the dimensional reduction framework. UV-Vis spectroscopy shows an optical band gap of ~1 eV that is indirect in nature as confirmed by electronic structure calculations. Electronic transport measurements on β-KAg3Se2 yielded n-type behavior with a high electron mobility of ~400 cm2 V-1 s-1 at 300 K due to a highly disperse conduction band. Our results thus imply that dimensional reduction may be used as a design strategy to frustrate order-disorder phenomena while retaining desirable electronic and thermal properties.

INTRODUCTION Order-disorder phase transitions underlie an enormous range of physical phenomena,1 from bulk melting to shear thickening in colloidal suspensions.2 In the solid-state, order-disorder phase transitions may be subtle, i.e., vacancy ordering,3 or striking as in the case of superionic conductors, where the ionconducting phase possesses “liquid-like” ionic conductivity.4 The high ionic conductivity of these materials has traditionally found application in solid-state electrolytes5 and recently as a proposed route to low thermal conductivity.6-7 In both cases, strategies to control order-disorder phenomena are desirable, especially in thermoelectric energy conversion where operation in the superionic state eventually results in device failure.8-10 It is convenient to classify superionic transitions by their abruptness after Boyce and Huberman.11 Type I compounds are exemplified by AgI, where a sharp, first-order structural phase transition coincides with a dramatic increase in the ionic conductivity. In Type II, a continuous phase transition is observed (e.g., PbF2) and in Type III, no obvious phase transition is present and superionic conductivity is gradually approached with increasing temperature as in Na+:β-alumina. The Type I superionic conductors are dominated by copper and silver chalcogenides, M2Q (M = Cu, Ag; Q = S, Se, Te), which transform to their ion-conducting phases abruptly just above room

temperature, between 400 and 450 K. Strategies to tune these solid-solid transitions are limited to nanoscale confinement which depresses the superionic state to lower temperature,12-14 and the non-trivial effects of applied pressure, which decreases the transition temperature in some Type I materials (AgI and Cu2Se)15-16 and increases it in others (Ag2Se).17 With respect to our interest in layered materials with emergent structural and electronic properties we recently reported KCu3xSe2, which was shown to be a p-type semiconductor with a low hole mobility arising from a relatively flat valence band.18 Electronic structure calculations revealed a disperse conduction band and thus light, mobile electrons. By analogy with the binary Ag2Se, which is commonly electron-doped,19-21 we hypothesized that n-type material with high electron mobility could be produced by replacing the Cu+ ions with Ag+ in this 2D structure type. In evaluating KAg3Se2 (β-phase),22 we discovered an order-disorder phase transition that produces a new form α-KAg3Se2 at high temperature, behavior that is absent in KCu3-xSe2. KAg3Se2 can be viewed as a dimensionally-reduced 2D form of 3D Ag2Se, represented by the formula, (K2Se)m(Ag2Se)n, where K2Se is the dimensional reduction agent, m = 1 and n = 3. Within the [Ag3Se2]- layers, the Ag-Se coordination geometries (bent trigonal planar and distorted tetrahedral) and connectivity are preserved. Dimensional reduction has been ap-

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plied to dismantle the covalent networks of binary compounds, progressively widening band gaps and flattening bands as network connectivity is decreased from 3D to 0D.23-25 This raises the interesting question whether the 3D Ag sublattice which is prone to an order-disorder phase transition in Ag2Se will still be susceptible to such behavior confined in 2D, and if so how? Although the crystal structures of several AAg3Q2 (A = K, Rb, Cs, Q = S, Se, Te)22, 26-30 isostructural analogues are known, no physical or chemical properties have been reported in detail. We report here the synthesis and physical properties of βKAg3Se2, showing that it is an n-type semiconductor with a ~1 eV band gap and high electron mobility measured by the Hall effect. Electronic structure calculations indicate a highly disperse conduction band and low effective mass electrons in agreement with this observation. The blue-shifted band gap and lower carrier mobility relative to β-Ag2Se are consistent with the dimensional reduction framework. We also report a high temperature Ag+ ion order-disorder phase transition to a very different 2D structure, α-KAg3Se2 that bears the hallmarks of a Type I superionic phase transition based on structural and thermal analyses. This occurs at ~700 K, about 300 K higher than the relevant transition in the parent compound. Finally, we measured an ultralow thermal conductivity in the “ordered” phase and preliminarily attribute this to anharmonic thermal motion of Ag ions. Thus, we highlight dimensional reduction as a potential route to suppress Type I order-disorder phase transitions, while retaining desirable electronic and thermal properties. By analogy with the binary copper and silver chalcogenides, the room temperature phase will be designated β-KAg3Se2 and the high temperature phase α-KAg3Se2 (cf., Table 2 in ref 4).

EXPERIMENTAL SECTION Reagents. The following reagents were used as received: potassium metal (99%, Sigma-Aldrich) and selenium beads (99.999%, Plasmaterials Inc.). Silver shot (99.99%, Alfa Aesar) was reacted with nitric acid to form AgNO3 (aq) which was subsequently reduced using NaBH4 (98%, Strem Chemicals) to produce silver powder for the preparation of KAg3Se2. Before use, the Ag powder was loaded into fused-silica tube and heated with a flame under dynamic vacuum to remove surface oxidation (evidenced by a color change from dark grey to light grey). Synthesis. All chemical manipulations were conducted inside an argon-filled glovebox (M-Braun) with oxygen and moisture levels < 0.1 ppm. Phase-pure KAg3Se2 was synthesized from a stoichiometric mixture of K2Se3, Ag and Se in a 1:6:1 molar ratio. The precursor K2Se3 was synthesized using a tube-intube vapor transport method,31 where a stoichiometric amount of Se (2.631 g, 33.3 mmol) was suspended in an alumina crucible above K metal pieces (0.869 g, 22.2 mmol) and flame sealed in an 18 mm o.d. × 16 mm i.d. fused-silica tube under < 10-4 mbar. This assembly was placed upright in a muffle furnace and heated to 500 °C in 12 hrs and held at that temperature for 12 hrs before natural cooling to room temperature. A

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black K2Se3 ingot could be removed from the bottom of tube and its phase purity was verified by powder X-ray diffraction (PXRD). In a typical experiment, K2Se3 (0.303 g, 0.96 mmol), Ag (0.622 g, 5.76 mmol) and Se (0.076 g, 0.96 mmol) were homogenized in a mortar and pestle, loaded into a graphite crucible and capped with a graphite plug before being flamesealed in a 15 mm o.d. × 13 mm i.d. fused-silica tube under < 10-4 mbar. The mixture was heated to 500 °C in 12 hrs and soaked for 12 hrs before the furnace was turned off. A black, homogeneous KAg3Se2 powder compact was produced. Vertical Bridgman crystal growth was conducted using a carboncoated fused-silica tube (9 mm o.d. × 7 mm i.d.) with a sharp tip, flame sealed under < 10-4 mbar in a vertical three-zone furnace and pre-melted at 700 °C prior to growth. The top and middle zones were set at 725 and 400 °C respectively, with these temperatures being informed by thermal analysis. A growth rate of ~5 mm hr-1 was used. Phase-pure Ag2Se for heat capacity measurements was synthesized from Ag and Se powders, which were homogenized in a mortar and pestle before being sealed under vacuum in a fused-silica ampule. This mixture was heated to 400 °C in 3 hrs and soaked for 12 hrs before natural cooling to room temperature in a muffle furnace. Subsequently, this powder was re-sealed in an evacuated fused-silica ampule and held at 950 °C for 10 mins before natural cooling to form a polycrystalline ingot. Powder X-ray Diffraction. Phase purity was routinely determined by powder X-ray diffraction (PXRD). Data were collected using a Panalytical X’Pert Pro diffractometer with a Ni filtered Cu Kα source operating at 45 mA and 40 kV. Continuous scanning was utilized with a step size of 0.0167°. Materials were finely ground and uniformly coated on a flat plate sample holder. KAg3Se2 powder was mildly sensitive to ambient air (evidenced by a loss of intensity of known peaks after several hrs), so it was sealed under a dry Ar atmosphere with vacuum grease Kapton film for PXRD. Scanning Electron Microscopy. A Hitachi S-4700-II scanning electron microscope with an energy-dispersive X-ray spectrometer (EDX) was used to inspect crystal morphology and composition. The spectrometer utilizes a Li-drifted Si detector with an ultra-thin window, and a beam current of 20 µA at 15 kV accelerating potential were used for data collection. Optical Properties. The optical band gap was determined using UV-Vis diffuse reflectance spectroscopy on KAg3Se2 powder. Data were collected under flowing N2 at room temperature using a Shimadzu model UV-3600 UV-Vis-NIR spectrophotometer. BaSO4 was used as a 100% reflectance standard. The data were transformed using the Kubelka−Munk equation (Equation 1), f(R) = (1-R)2/2R = α/S,

(1)

where, R is absolute reflectance, α is the absorption coefficient and S is the scattering coefficient.32

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Charge Transport Properties. Temperature-variable conductivity and Hall effect measurements on polycrystals (approximate dimensions: 1.5 × 1 × 0.3 mm3) were conducted on a Quantum Design Dynacool Physical Property Measurement System (PPMS) between 1.8 and 300 K. Conductivity was measured in a 4-point collinear geometry and the Hall effect measured using two Hall voltage contacts placed perpendicular to the axis of current flow. The magnetic field was applied perpendicular to the axis of current flow from -9 to +9 T. Temperature and field were cycled multiple times to confirm data reproducibility. Electronic conductivity and Hall effect measurements were performed simultaneously on the same sample in all cases. Silver paste contacts were found to result in unstable contact resistances. Stable, Ohmic contact was achieved using colloidal graphite paste (Ted Pella). Melted hydrocarbon grease (Apiezon N) was used to encapsulate the sample for transport to the PPMS. All sample preparation and contact fabrication was done in an Ar-filled glovebox. Electronic Structure Calculations. The electronic structure calculations were performed within DFT using the allelectron, full potential code WIEN2k33 based on the augmented plane wave plus local orbitals (APW+lo) basis set.34 We have studied the electronic structure of KAg3Se2 by using the modified Becke Johnson exchange potential which does not contain any system-dependent parameter. This is a local approximation to an atomic exact-exchange potential and a screening term) + LDA-correlation (from hereon mBJ) that allows the calculation of band gaps with an accuracy similar to the much more expensive GW or hybrid methods.35-37 Spin orbit coupling (SOC) was introduced in a second variational procedure.38 RmtKmax= 7.0, was chosen for all the calculations. A k-mesh of 19 × 19 × 10 was used for β-KAg3Se2 and 26 × 26 × 4 for α-KAg3Se2. Muffin-tin radii of 2.49, 2.37 and 2.5 a.u. were used for Ag, Se, and K, respectively. From the calculated band structure, carrier effective masses (m*) at the band edges were calculated using Equation 2, 1/mij* = (1/ℏ2) ∂2ε(k)/∂ki∂kj,

(2)

where, ε(k) is the energy as a function of k, the wavevector. High Temperature Powder X-ray Diffraction. A Stoe STADI-MP high-resolution diffractometer with oven attachment was used to obtain data for Rietveld structure refinements at room temperature and 823 K. KAg3Se2 powder was finely ground and sieved to < 40 µm particle size before being diluted in a ~5:1 volume ratio with carbon powder (99.9%, Aldrich) and sealed under vacuum in a 0.5 mm o.d. fusedsilica capillary. The capillary was spun during collection. Rietveld refinements were carried out using GSAS-II software (version 0.2.0). The β-phase was refined from the single crystal structure of Bensch and Duriche.22 The crystal structure of the high temperature α-phase was solved by analogy with a related compound discovered in our laboratory, NaCu3S2. The single crystal structure of NaCu3S2 was used to refine the crystal structure of α-KAg3Se2.

Synchrotron X-ray Diffraction. Temperature-dependent synchrotron X-ray diffraction (SXRD) data from room temperature to 600 °C were collected on beamline 11-ID-C at the Advanced Photon Source (APS) at Argonne National Laboratory. Undiluted KAg3Se2 powder was loaded into a fusedsilica capillary (0.3 mm o.d.) and flame-sealed in under < 10-4 mbar. Integration of the 2D images was performed using Dioptas software (version 0.2.4) using CeO2 as a standard. Le Bail refinements were carried out using GSAS-II software (version 0.2.0). The linear coefficients of thermal expansion, αL, were calculated from the unit cell parameters using Equation 3, αL = 1/L × dL/dT,

(3)

where L is length. Thermal Analysis and Heat Capacity. Differential thermal analyses (DTA) were carried out with a Shimadzu DTA-50 thermal analyzer. The sample (∼20 mg total mass) was sealed in a fused-silica ampule under vacuum. A fused-silica ampule containing alumina powder was used as a reference. The sample was heated to 923 K at 5 K min-1, followed by cooling at the same rate to 343 K. Residues of the DTA experiments were examined with PXRD. High temperature heat capacity (Cp) data were collected according to the standard procedure ASTM E1269 on a Netzsch 404 Differential Scanning Calorimetry (DSC) cell under flowing He gas with Proteus software (version 6.0.0). The sample (∼20 mg total mass) was loaded in an alumina crucible with a lid and heated to 973 K at a rate of 20 K min-1. Thermogravimetric analysis indicated a negligible (< 0.1%) weight change under these experimental conditions. Prior to sample measurement, several baseline runs and calibration with a sapphire standard of comparable mass (Netzsch) were performed using the experimental heating profile. Transition temperatures were measured from the peak onset. The entropy change of transition, ∆St, was determined using Equation 4, ∆St = ∆Ht/Tp = (1/Tp) ∫Cp(T)dT

(4)

where. ∆Ht is the enthalpy change of the transition and Tp is the peak temperature of the relevant thermal feature. Low temperature Cp was measured on a Quantum Design Dynacool Physical Property Measurement (PPMS) System between 1.8 and 300 K. Apiezon N grease was used to fix samples to the heat capacity stage. Data were collected on warming. Thermal Diffusivity. KAg3Se2 powder was densified by spark plasma sintering (SPS, Dr. Sinter) at 623 K in a graphite die and samples were shaped by hand polishing in a nitrogenfilled glovebox. Samples were fabricated such that κ was measured both parallel (∥) and perpendicular (⊥) to the SPS pressing direction as preferred orientation may occur during SPS processing of anisotropic materials. Thermal diffusivity (D) was measured using a Netzsch LFA457 laser flash diffusivity instrument. Samples were spray coated with a thin layer of graphite to minimize radiative heat loss from the material. The total thermal conductivity was calculated from κ = D × Cp × ρ where the specific heat capacity (Cp) was measured as a



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function of temperature in a DSC and the density (ρ) was determined using the dimensions and mass of the sample to be ~5.39 g cm-3 or ~90% of the theoretical density. The uncertainty of the thermal conductivity is estimated to be ~10%.

The x-intercept yielded the band-gap energy. This is analogous to Tauc plot analyses for direct allowed transitions,39 justification for this assignment comes from electronic band structure calculations to be presented below.

RESULTS AND DISCUSSION

Electronic Charge Transport. The electronic conductivity and Hall effect of a polycrystalline plate isolated from a Bridgman-grown boule was measured from 2 to 300 K, with current flow approximately parallel to the layers. The temperature-dependent electronic conductivity, σ, is shown in Figure 2a. The modest room temperature σ of ~0.1 S cm-1 is reasonable for a semiconductor. A weak, negative temperaturedependence of σ was observed – decreasing by a factor of about 2 over this temperature range – indicating degenerate semiconducting behavior.

Synthesis. Phase pure KAg3Se2 powder was synthesized from a stoichiometric mixture of K2Se3, Ag and Se. Polyselenide precursors were used to avoid the exothermic reaction between K and Se. Room temperature unit cell parameters from Rietveld refinements (wR = 3.44%, χ2 = 2.16) on the PXRD data (Figure S1a in the Supporting Information (SI)) were in good agreement with those from the layered single crystal structure solution of

Figure 1. Tauc plot (allowed direct) showing a band gap transition at ~1.0 eV. Inset: photograph of black KAg3Se2 powder in a glass vial (27.5 mm diameter).

Hall effect data showed a linear dependence with field (Figure S3 in the SI) and were negative at all temperatures implying that electrons are the majority carriers (n-type). Calculation of electron concentration (nHall) yielded a value of 1015 cm-3 that was effectively constant with temperature (Figure 2b). Degenerate behavior can result from defects that have a negligible ionization energy or the formation of impurity bands. Due to the low concentration of carriers in our samples we prefer the former explanation, which was also suggested to explain the electronic transport of Ag2Se and Ag2Te at low temperatures.40 Defect energy calculations for KAg3Se2 would be very interesting as doping in the binary silver chalcogenides is notoriously difficult to control, usually being self-doped n-type at levels > 1018 cm-3 during synthesis.41-42 By analogy with Ag2Se we attribute n-type doping in our samples to a small Ag excess.43-44 The Hall mobility for electrons was estimated at ~400 cm2 V-1 s-1 at room temperature and rose to ~700 cm2 V-1 s-1 at 5 K (Figure 2b). These results were reproducible on additional samples (Figure S4 in the SI). Band Structure Calculations. Electronic structure calculations showed semiconducting behavior, which was expected

Bensch and Duriche:22 a = 16.613(1) Å, b = 4.39149(7) Å, c = 8.7768(4) Å, β = 115.546(2)°, Z = 4 and V =577.71(1) Å3. Scanning electron microscopy (SEM) showed a layered crystal morphology (Figure S1b in the SI) and elemental analysis by EDX yielded K1.00(2)Ag2.90(4)Se2.05(6), close to the expected 1:3:2 atomic ratios. Vertical Bridgman crystal growth was utilized to produce crystal samples for property measurements. The crystal boule produced was easily cleaved into visually polycrystalline samples (see Figure S2 in the SI). This is likely due to the formation of multiple domains while cooling through the phase transition. Optical Properties. (K+)(Ag+)3(Se2-)2 is a valence-precise compound and therefore expected to be a semiconductor. Indeed the sample exhibits a sharp optical transition at ~1 eV, consistent with the black color of KAg3Se2 powder (Figure 1). To extract the band gap energy, we squared the product of f(R) and hν (where f(R) is directly proportional to the absorption coefficient as in eq 1) and plotted it against photon energy.


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Order-disorder Phase Transition. DTA indicates that KAg3Se2 melts congruently at ~890 K and crystallizes at ~885 K (see Figure S6 in the SI). An additional set of reproducible exothermic and endothermic features, however, appear below bulk melting/crystallization transitions at ~700 and 670 K respectively. These thermal events raised the possibility of a phase transition and this was investigated by high temperature XRD. At 823 K a clear change in the diffraction pattern was observed (Figure 4a). The high temperature structure was solved by analogy with a related compound previously discovered by our group: NaCu3S2 (hexagonal space group R-3m, a = 3.9346(6) Å, c = 21.971(4) Å, Z = 3, Robs = 0.0573, wRall = 0.1359). This structure was used as a starting point for subsequent refinements. Rietveld refinements yielded a structural model (Figure 4b) with very good agreement with the data (wR = 2.63%, χ2 = 2.05). Details of the structure refinement and comparison with

Figure 2. Electronic transport from 2-300 K on a polycrystalline ingot of KAg3Se2. a) conductivity b) Hall effect data. Open triangles (blue) denote Hall mobility, open circles (green) denote the Hall carrier concentration.

Figure 3. a) Electronic band structure and b) orbital-projected density of states plots for the low temperature, monoclinic phase of KAg3Se2.

from the valence-precise nature of the compound (Figure 3a). It can be seen that our calculations reproduce the experimental band gap well, giving a value of 0.9 eV. Although the band gap is formally indirect at Γ-L, the direct transition at Γ is extremely close in energy (< 0.05 eV), hence we justify the use of Tauc analysis for direct transitions in the analysis above. Monoclinic KAg3Se2 has a highly disperse conduction band around Γ, mainly comprised of Ag s and Se p orbitals (Figure 3b). The calculated effective masses of ~0.4me and 0.5me for Γ-N and Γ-Z respectively are consistent with the high electron mobility measured by the Hall effect. It is noteworthy to point out the almost linear dispersion of the conduction band along Γ-N. Conversely, a relatively flat valence band, consisting of Ag 3d and Se 2p orbitals in equal contribution, suggests holes should have high effective masses and low intrinsic mobility. Indeed, this has been recently observed in the p-type copper analogue, KCu3-xSe2, which is isostructural and shares a similar band structure.18 The corresponding Brillouin zone is given in the SI (Figure S5 in the SI). Decreased carrier mobility due to flatter bands and the larger optical band gap of β-KAg3Se2 relative to β-Ag2Se (Table 1) agree with the expected trends for dimensional reduction.



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Figure 4. a) Rietveld refinement of α-KAg3Se2 (R-3m) at T = 823 K. Vertical ticks represent the simulated reflection positions. The broad feature at seen ~22° is due to the fused-silica capillary and carbon powder used for dilution. b) Crystal structure of αKAg3Se2 viewed in the ab-plane. Layers of Ag (grey) are sandwiched in between Se (red) sheets which are separated by K ions (light blue). Thermal ellipsoids are shown at 50%.

β-KAg3Se2 are located in Table 2. Atomic coordinates, anisotropic displacement parameters, selected bond lengths and angles for α-KAg3Se2 are presented in Tables 3-6 with full refinement details given in the SI. Crystallographic information for β-KAg3Se2 (Beta_KAg3Se2.cif) is provided in the SI. It is instructive to first summarize the main structural details of the room temperature structure. β-KAg3Se2 crystallizes in the CsAg3S2 structure type (monoclinic space group C2/m),28, 45 with corrugated infinite [Ag3Se2]- layers separated by K+ ions (Figure 5a). Briefly, these layers can be visualized as Ag4Se4 columns that run along the b-axis, bridged by Ag atoms in a distorted tetrahedral environment. Three unique Ag atoms stabilize this network. Ag(1) and Ag(3) form the periodic “throwing star” columns (shaded in Figures 5a and b) and are 3-fold


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Figure 5. a) Comparison of β and α crystal structures shown parallel to the [Ag3Se2]- layers. Unit cells are indicated with black lines. Enlarged unique K and Ag atoms and their bonding environments are shown next to each phase. b) Single [Ag3Se2]- layers viewed perpendicular to the c-axis. c) Se-Se sheets that cap each [Ag3Se2]- layer shown perpendicular to the c-axis with an intermediate cartoon illustrating a geometric relationship between the low and high temperature Se atom arrangements. The “throwing star”-shaped columns that run along the b-axis in β-KAg3Se2 are shaded in grey.

coordinated with Se in a bent planar geometry. Joining each column are two Ag(2) atoms in a 2+2 distorted tetrahedral environment with Se. It is worth noting that in the original room temperature single crystal refinement22 the anisotropic displacement parameters (ADPs) for the Ag ions are significant – the largest being U22 of Ag(2): the bridging Ag ion between columns – which can be indicative of static or dynamic disorder. Bent trigonal planar and distorted tetrahedral (2+2) Ag-Se arrangements also describe the two unique Ag atoms in β-Ag2Se,46-47 evidencing the structural relationship between these phases (Figure S7 in the SI).

KAg3Se2 have flattened into 2D hexagonal sheets in αKAg3Se2. Based on the small ADPs and analogy with other Ag ionic conductors,48-49 the Se ions comprise the immobile sublattice. Transformation from the initial combination of trigonal and near-square motifs to the purely trigonal can be accomplished by each trigonal Se chain translating by ~1 Å in the y-direction relative to each other (Figure 5c). Sandwiched between the Se sheets are two unique Ag sites. Ag1 is 3-fold coordinated with

As illustrated in Figure 5a, the high temperature structure also consists of infinite [Ag3Se2]- layers, ~4.1 Å thick, spaced ~4 Å apart by K+ ions. The uneven Se atoms that cap the layers in β-



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~109.5°). Ag1 and Ag2 both have 0.75 occupancy and large anisotropic thermal displacement parameters (ADPs), suggesting a heavily disordered Ag layer. The ADPs of the Ag2 atom in particular have a striking disk shape in the ab-plane (Figure 4b). The K ions are 6-fold coordinated with Se in a distorted octahedral arrangement. The APDs are larger than those for Se, but significantly smaller than the Ag ions, implying that the K sublattice is likely immobile. Electronic band structure calculations were also performed for this hexagonal phase, which predicted a larger direct band gap of ~1.3 eV and a less disperse conduction band (see Figure S8 in the SI). Temperature-dependent synchrotron XRD (SXRD) studies revealed several other key features of the β and α phases. A smooth variation in the patterns with temperature up to the phase transition was observed and the β-phase returned on cooling back to room temperature (Figure 6a and Figures S9 and S10 in the SI). Figure 6b shows an abrupt increase in the normalized cell volume at the transition. The change in lattice parameters with temperature was positive and approximately linear over the temperature range studied. The linear coefficients of thermal expansion (calculated using eq 3) varied from 2.3-3.3×10-5 K-1 and 2.7×10-5 K-1 for the principal axes in the β- and α-phases respectively (see Figure S11 in the SI). These values for αL are about one order of magnitude larger than covalently bonded, “stiff” semiconductors like Si50 (34×10-6 K-1) and comparable to the mechanically soft Ag2Se51 (β-phase ~1.8×10-5 K-1, α-phase = ~3.5×10-5 K-1) and metallic lead52 (~3×10-5 K-1). We note that poor sample-heater coupling in the in situ synchrotron XRD experiment resulted in a transition temperature that was greater than those from thermal analyses (~770 K vs. ~700 K), thus the reported temperatures for the SXRD should be considered nominal. Accordingly, the coefficients of thermal expansion should be considered underestimates, especially at high temperatures.

Figure 6. a) Integrated synchrotron XRD patterns (normalized) showing evolution of low temperature phase to high temperature phase on heating. b) Evolution of normalized unit cell volume as a function of temperature. The discrepancy in transition temperature is attributed to poor sample-heater coupling at high temperatures, thus all temperatures given should be considered nominal. c) 2D synchrotron X-ray diffraction patterns showing both diffuse background scattering in the high temperature phase (T = 803 K) and grain growth relative to the pristine material at 303 K. The Xray wavelength for all synchrotron experiments was 0.11742 Å.

Se in a near-planar triangular arrangement – reminiscent of Ag1 in β-KAg3Se2. Ag2, which sits in the middle of the [Ag3Se2]- layer, is in a distorted tetrahedral environment with a 3+1 coordination and bond angle of 119.32(10)° (ideal

At temperatures above the phase transition, prominent diffuse scattering was observed (Figure 6c). The onset of diffuse scattering and large ADPs of Ag ions has also been observed in high temperature XRD studies of superionic Ag2S.48 A large amount of grain growth occurred during the experiment (Figure 6c and S10 in the SI), again consistent with highly mobile ions. The structural cues for fast Ag+ ion conduction in αKAg3Se2 and the occasional growth of actual Ag metal whiskers in high temperature annealing experiments of the KAg3Se2 samples or even during slow cooling from the melt (Figure S12 in the SI) strongly suggested that the Ag+ ions in the structure are highly mobile. Fast ion or “superionic” conductors are defined by ionic conductivities or ionic diffusivities that approach those observed in liquids,11 i.e., ~0.1-1 S cm-1 or 10-5 cm2 s-1 respectively. Experiments aimed at determining the Ag+ ion contribution to the conductivity by AC or DC techniques were inconclusive due to the lack of suitable electon-blocking electrodes (see Section S4 in the SI). Spectroscopic techniques such as solid-state NMR53 or quasielastic neutron scattering54 may be of use to determine the mobility of Ag+ ions but these are out of the scope of the current study.


Page 9 of 14 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Heat Capacity. The thermal events revealed by DTA were quantified with heat capacity (Cp) measurements in a DSC. A sharp, symmetrical peak (onset at ~ 695 K) in the heat capacity and hysteresis between heating and cooling (Figure 7) were observed. Taken together with the discontinuous change in unit cell volume (Figure 6a), these are strong evidence for the order-disorder transition being first-order. Thus, the orderdisorder transition in KAg3Se2 at ~695 K most closely resembles a Type I superionic phase transition.4, 11 Comparable changes in entropy at the solid transition and the melting point have been suggested previously to indicate “melting” of a sublattice in superionic conductors.55 The thermodynamic properties of the solid and melting transitions of KAg3Se2 (calculated using eq 4) and known Type I superionic conductors are given in Table 7. KAg3Se2 is unique amongst these compounds as the transition temperature is high and the 2D character is retained in the new structure of the high temperature phase. Comparison shows that the entropy change of the transi

ured from the onsets. The heating and cooling rates were 20 K min-1.

tion (∆St) is comparable to that of AgI and Ag2Se, but that the entropy of fusion was markedly greater. Taking ∆St as a fraction of the total entropy change implies that ~1/2 of the Ag+ ions are highly mobile at the β → α transition. As shown in Figure 7a, the heat capacity is in good agreement with the Dulong-Petit limit (~150 J mol-1 K-1) below 675 K. Between 750 K and the bulk melting point there is a significant increase of Cp up to ~350 mol-1 K-1 at 850 K. This is not typically observed in related disordered phases – in superionic AgI and Ag2Se Cp only slightly increased (< 10%) with increasing temperature.56-57 We speculate that the elevated Cp post-transition may be a broad peak associated with a subsequent, subtler order-disorder transition in the α-phase, e.g., gradual changes in Ag site occupancy with increasing temperature as seen in AgCrQ2 (Q = S, Se)58-59 compounds, convoluted with the melting peak. Low temperature Cp data were measured for both β-KAg3Se2 and β-Ag2Se between 1.8 and 300 K in a Dynacool PPMS (Figure S13 in the SI). Qualitative analysis indicated the presence of low energy phonon modes in both materials, with those in β-KAg3Se2 being even lower in energy than β-Ag2Se (Section S5 in the SI). As low energy phonon modes and large thermal expansion coefficients are often correlated with efficient scattering of phonons, we measured the thermal conductivity of this material. Thermal Conductivity. The thermal conductivity measured on the SPS processed pellet sample of β-KAg3Se2 is ~0.4 W m-1 K-1 at room temperature and reaches a minimum of ~0.3 W m-1 K-1 between 325 and 700 K (Figure 8). This compares well with the estimated range of lattice thermal conductivity for β-Ag2Se (~0.3-0.5 W m-1 K-1 at room temperature)60 indicating that ultralow thermal conductivity is retained after dimensional reduction. In β-KAg3Se2 the difference in thermal conductivity perpendicular and parallel to the pressing direction was < 20%, indicating that anisotropy does not play a strong role in the low thermal conductivity. A steep increase in κ occurred above the phase transition, roughly doubling from 725 to 825 K. This increase was driven by the larger heat capacity in this phase (Figure 7a) as the density decreases a little (Table 1) and the diffusivity, D, is approximately constant (Figure S14 in the SI). The weak temperature dependence of D is consistent with high levels of disorder and has been observed in a number of Ag+-ion superionic phases.41, 61-62 For the SPS processed sample of the α-phase the values of κ for different pressing directions converge. This is likely due to microstructural evolution (Figure 6c) eliminating the small difference in crystallite orientation with pressing direction.

Figure 7. a) Heat capacity of KAg3Se2. The Dulong-Petit baseline is given by a dashed red line. b) DSC signal on heating and cooling through the solid transition. Transition temperatures are meas-

We attribute the ultralow thermal conductivity to efficient scattering of phonons by Ag+ ions even in the “ordered” βKAg3Se2, similar to the rattling mechanism proposed in CsAg5Te3 which shares the structural motif of columns bridged by distorted Ag-Q tetrahedra.63 Our results highlight



that an order-disorder transition is not necessary for ultralow κ. Indeed, a recent study attributes the low thermal conductivity of Cu2Se to Cu+ ion anharmonicity and not the quasi-molten Cu+ sublattice.64 Therefore, structures that facilitate anharmonic thermal motion (i.e., those with all the ingredients for superionic conduction but are inhibited in some way) may yield desirable functional properties without superionic conductivity that leads to eventual material failure under dc operating conditions. Related Materials. A comparison to KCu3-xSe2 is apt due to the similarities between the parent and derivative compounds; KCu3-xSe2 is also layered and isostructural with β-KAg3Se2. The parent binary phase is Cu2-xSe, another Type-I superionic conductor with an order-disorder transition at 395 K,65 where the unique Cu-Se environments are distorted tetrahedral and trigonal planar. The relevant physical properties of Cu2-xSe are: band gap66-67 = ~1.2 eV and hole mobility68 of ~15 cm2 V-1 s-1 at a carrier concentration of 1020 cm-3). We showed recently18 that KCu3-xSe2 is a p-type semiconductor with a wider band gap (~1.35 eV) and lower hole mobility (on the order of ~1 cm2 V-1 s-1 for a carrier concentration of 1019 cm-3) relative to the parent. These trends in physical properties are in agreement with the dimensional reduction framework. In that report, DTA indicated no phase transition prior to the melting point of the material (~1030 K), consistent with the orderdisorder transition at 395 K in Cu2-xSe also being suppressed. Additional known members of the homologous series (K2Se)m(Ag2Se)n are: K2Ag12Se7 (m = 6, n = 1), a 3D-openframework structure with K+ filling the channels,69 K2Ag4Se3 (m = 2, n = 1) and KAgSe (m = 1, n = 1), which are 2D like βKAg3Se2, but with Ag in either in only distorted tetrahedral or trigonal planar coordination respectively.70-71 Relevant physical properties, e.g., thermal analysis, optical and transport properties, are currently unknown. Thus, thorough characterization studies of these compounds will be necessary to include them in this framework, in addition to the discovery of 1D and 0D members.

Page 10 of 14

Figure 8. Total thermal conductivity of KAg3Se2 from 325 to 825 K. The symbols “⊥” and “//” represent measurements perpendicular and parallel to the SPS pressing direction respectively.

CONCLUSIONS The monoclinic 2D semiconductor β-KAg3Se2 exhibits a firstorder phase transition to a higher symmetry phase (αKAg3Se2) at high temperature. The β-phase is a dimensionallyreduced derivative of β-Ag2Se, with a band gap of ~1 eV and features a high room temperature electron mobility of ~400 cm2 V-1 s-1 at a carrier concentration of ~1015 cm-3 which is attributed to a highly disperse conduction band. Above ~695 K, the system transforms to a new hexagonal layered structure (R-3m), and this is accompanied by extensive Ag ion disorder confined in infinite layers ~4 Å thick. This order-disorder transition is found to strongly resemble a Type I superionic phase transition based on our structural and thermal analyses. Interestingly, the solid transition temperature is significantly higher than its 3D parent compound, a known Type I superionic conductor. Finally, ultralow thermal conductivity in the “ordered” β-phase was ascribed to anharmonic thermal motion of the Ag ions. Our results hint that the concept of dimensional reduction may include order-disorder transitions and thermal conductivity, while also revealing a family of layered chalcogenide compounds where functional properties can be chemically tuned in this context.

ASSOCIATED CONTENT Supporting Information The Supporting Information is available free of charge on the ACS Publications website. Details of Rietveld refinements, additional transport and structural data, electronic structure calculations and thermal diffusivity data.

AUTHOR INFORMATION Corresponding Author * [email protected]

ACKNOWLEDGMENTS This work was supported by the U.S. Department of Energy, Office of Science, Materials Sciences and Engineering Division. We gratefully acknowledge the computing resources provided on Blues, the high-performance computing clusters operated by the Laboratory Computing Resource Center at Argonne National Laboratory. We are indebted to S.M. Haile for the generous use of electrochemical apparatus and thank K. Selkregg of Monofrax LLC for the donation of Na:β-alumina material for preliminary experiments. A.J.E.R. acknowledges fruitful discussions with M. Agne, M. Murphy and J. Bao. This work made use of the IMSERC at Northwestern University, which has received support from the Soft and Hybrid Nanotechnology Experimental (SHyNE) Resource (NSF


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ECCS-1542205); the State of Illinois and International Institute for Nanotechnology (IIN). The electron microscopy was accomplished at the Electron Microscopy Center for Materials Research at Argonne National Laboratory, a U.S. Department of Energy Office of Science Laboratory operated under Contract No. DE-AC02-06CH11357 by UChicago Argonne, LLC.

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Table 1. Comparison of room temperature optical and electronic properties of polycrystalline β-Ag2Se and βKAg3Se2. Compound β-Ag2Se β-KAg3Se2

Eg (eV)

µHall (cm2 V-1 s-1)

nHall (cm-3)

References

0.07-0.15

~1700

5-8 × 1018

40 (Eg), 41 (µHall, nHall)

1.0

~400

1015

This work

Table 2. Crystal data and Rietveld refinement for β- and α-KAg3Se2. β-KAg3Se2 Empirical formula

α-KAg3Se2 KAg3Se2

Formula weight

520.62

Wavelength

1.54059 Å

Temperature

300 K

823 K

Crystal system

monoclinic

trigonal


Page 13 of 14 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Space group

Volume

C 2/m a = 16.613(1) Å, α = 90° b = 4.39149(7) Å, β = 115.546(2)° c = 8.7768(4) Å, γ = 90° 577.71(1) Å3

R -3 m a = 4.5638(5) Å, α = 90° b = 4.5638(5) Å, β = 90° c = 25.4109(6) Å, γ = 120° 458.36(6) Å3

Z

4

3

Density (calculated)

5.986 g/cm3

5.658 g/cm3

Goodness-of-fit

1.47

1.43

Profile R indices

wR = 0.03442

wR = 0.02633

Unit cell dimensions

Table 3. Atomic coordinates (×104) and equivalent isotropic displacement parameters (Å2×103) for α-KAg3Se2 at 823 K with estimated standard deviations in parentheses.

*

Label

x

y

z

Occupancy

Ueq*

K

0

0

0

1.000

82(9)

Ag(1)

0

0

4390(2)

0.750

131(4)

Ag(2)

0

0

1444(2)

0.750

275(2)

Se

0

0

2472(2)

1.000

59(4)

Ueq is defined as one third of the trace of the orthogonalized Uij tensor.

Table 4. Anisotropic displacement parameters (Å2×103) for α-KAg3Se2 at 823 K with estimated standard deviations in parentheses. Label

U11

U22

U33

U12

U13

U23

K

103(9)

103(9)

39(9)

51(4)

0

0

Ag(1)

124(4)

124(4)

148(3)

62(2)

0

0

Ag(2)

386(2)

386(2)

55(3)

193(1)

0

0

Se

68(4)

68(4)

39(3)

0

0

34(2) 2

2 *2

* *

The anisotropic displacement factor exponent takes the form: -2π [h a U11 + ... + 2hka b U12].

Table 5. Bond lengths [Å] for α-KAg3Se2 at 823 K with estimated standard deviations in parentheses. Label

Distances

K-Se ×6

3.4250(23)

Ag(1)-Se ×3

2.6813(12)

Ag(2)-Se

2.614(5)

Ag(2)-Se ×3

3.022(3)

Se-Se

4.5638(4)

Table 6. Bond angles [°] for α-KAg3Se2 at 823 K with estimated standard deviations in parentheses. Label

Angles


13


Page 14 of 14

Se-K-Se ×3

83.56(7)

Se-K-Se ×3

96.44(7)

Se-Ag(1)-Se ×3

116.65(9)

Se-Ag(2)-Se ×3

119.32(10)

Se-Ag(2)-Se ×3

98.06(13)

Table 7. Comparison of thermodynamic data with Type-I superionic conductors. Solid Transition

Melting

Compound

Tf/Tt (-) -1

-1

-1

Reference

-1

Tt (K)

∆St (J mol K )

Tf (K)

∆Sf (J mol K )

AgI

420

15.0

830

11.3

2.0

56

Ag2Se

406

16.8

1170

7.0

2.9

57

KAg3Se2

704

12.5

890

39.6

1.3

This work


14

Ag2Se to KAg3Se2: Suppressing OrderâDisorder Transitions via

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