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Effect of Cu-substitution on the conductivity of Ag-rich AgI–CuI solid solutions
Journal of Physics and Chemistry of Solids 64 (2003) 961–966 www.elsevier.com/locate/jpcs
Effect of Cu-substitution on the conductivity of Ag-rich AgI –CuI solid solutions P.S. Kumara, P. Balayab, P.S. Goyalb, C.S. Sunandanaa,* a
School of Physics, Central University P.O., University of Hyderabad, Hyderabad 500 046, India b IUC-DAEF, Mumbai Centre, B.A.R.C., Mumbai 400 085, India Received 17 May 2002; accepted 15 November 2002
Abstract The ionic conductivity of the silver rich solid solutions Ag12xCuxI (0 , x , 0.25) was measured using complex impedance spectroscopy over the frequency range 100 Hz –15 MHz and in the temperature range 25 – 250 8C. As observed in undoped AgI, two conducting regions (above and below Tc) are found in these solid solutions also. Despite the large size difference in the ionic radii of Agþ and Cuþ ions, the bigger sized Agþ ion dominates the overall conductivity of the system. Arrhenius plots of the dc conductivity demonstrates clearly the enhanced defect concentration and grain boundary effects in the low temperature phase as well as the smallness of the observed activation energy along with the softening of the AgI lattice in the high temperature phase. The pertinent effect of Cu doping in AgI is discussed in terms of the recent experimental and theoretical facts. A plausible conduction mechanism is being worked out. q 2003 Elsevier Science Ltd. All rights reserved. Keywords: D. Ionic conductivity; C. Impedance spectroscopy; A. Nano-crystallization
1. Introduction AgI and CuI are well known materials for their interesting physics of phase transitions as well as their applications as fast ionic conductors and also as chemical sensors. While AgI is already an ionic (Agþ) conductor at ambient, CuI is a mixed ionic– electronic conductor at room temperature with predominant electron-hole conduction up to 200 8C [1]. AgI undergoes a first order structural phase transition (wurtzite (b)/zincblende (g) ! body centered cubic (a) phase) at 147 8C to a highly dynamic ‘superionic’ state. Study of the effects of chemical substitution (both cationic and anionic) on the superionic conductivity of AgI provides further insight into the complexities of this phase transition thus helps arriving at a mechanism governing the ion transport/mobility within the crystal lattice [2]. * Corresponding author. Tel.: þ 91-40-3010500x4324; fax: þ 9140-3010227. E-mail address: [email protected] (C.S. Sunandana).
Heterovalent cation (like Cdþ þ , Pbþ þ etc.) substitution must necessarily be accompanied by an accumulation of cationic vacancy defects. However, in interpreting these experimental results, it is not straightforward to distinguish between the effects of cation substitution and vacancy formation. In order to isolate the effect of cation substitution in AgI, we have chosen the homovalent Cuþ cation for study in the present investigation. Solid solutions of AgI and CuI were prepared so as to change the property of the material in a single component [3]. This is possible because of the extended mutual solid solubility range of AgI and CuI despite their unequal ionic ˚ ; rCu ¼ 0.96 A ˚ ; rAg/rCu ¼ 1.31). This radii (rAg ¼ 1.26 A large size mismatch in mobile cation size points to the possibility of a mixed mobile ion effect controlled ionic conductivity in the AgI– CuI system. Furthermore, the fact that CuI is an electronic conductor in the temperature range of investigation brings into play factors such as p – d hybridization to the conduction process—essentially including subtle changes in ion mobility and concentration.
0022-3697/03/$ - see front matter q 2003 Elsevier Science Ltd. All rights reserved. PII: S 0 0 2 2 - 3 6 9 7 ( 0 2 ) 0 0 4 5 5 - 9
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Nontrivial modification of the cation sublattice in the zincblende/bcc phases and the possibility of realizing interfacial polytypes are expected to decrease the defect concentration ‘n’ and hence the conductivity ‘s’ [2] of the high temperature a-phase thereby increasing the ‘Tc’ of AgI. In the present paper, we investigate experimentally the conductivity and phase transition behavior in Ag12xCuxI (0 # x # 0.25), the Ag-rich solid solution of the AgI – CuI binary phase diagram. The changes in the conductivity profiles on either side of the phase transition anomaly in AgI as well as the transition temperature itself, induced by the addition of Cu are discussed in terms of changes in structure, electronic structure and bonding in context with the recently reported works.
2. Experimental methods The solubility difference between CuI and AgI has been utilized in the synthesis of solid solutions using the simple conversion process in an aqueous suspension [3]. All the basic investigations described in this paper are concerned with Ag12xCuxI (x ¼ 0.05, 0.1, 0.15, 0.2 and 0.25) compositions. These samples were prepared by the gradual addition of the required molar aqueous solutions of the nitrates of silver and copper (Analar grade, LOBA, INDIA) under continuous stirring and precipitating them with a 2 to 5% excess solution of potassium iodide (LOBA, INDIA) just below the normal boiling temperature [4]. After several decantations with double distilled water to remove the excess nitrates present if any, the samples were dehydrated in an oven at 60 8C for several hours. Structural characterization on these powder samples was performed using a PHILIPS X-ray diffractometer. Sample pellets of 5 mm thickness and 8 mm diameter were used for the impedance measurements. To avoid electrode diffusion problems, chemically inert, commercial grade graphite paste was applied on opposite parallel surfaces of the sample pellet followed by baking at 200 8C for 30 min to ensure a good electrical contact. Impedance measurements in the frequency and temperature range, 100 Hz– 15 MHz and 25 – 250 8C, respectively, were carried out using an Impedance/Gain Phase Analyzer (HP 4194A) at IUC-DAEF, Mumbai. All measurements were carried out under rotary vacuum (, 1022 mbar) in order to avoid any oxidation problem. The reproducibility of the impedance data of these polycrystalline specimens was confirmed by repeated temperature cycles above the b/g ! a transition temperature.
3. Results and discussion Fig. 1 shows the powder XRD patterns of the as-prepared samples. These patterns consist of three
Fig. 1. X-ray powder diffraction patterns for the Ag12xCuxI solid solutions of various compositions. The presence of considerable amount of sphalerite g-AgI structure is evidenced by the dominant (111), (220) and (311) Bragg peaks. The ‘circle’ marked weak intensity peaks corresponds to the random distribution of b-AgI arising from the stacking disorder in the sample.
prominent Bragg peaks, characteristic of a substantial amount of g-AgI (JCPDS, card no. 9-399) and the presence of additional weak reflections, which are attributed to the co-existence of other polymorphs (e.g. 2, 4, 8, 16 H) of AgI [5]. As g-AgI cannot be stabilized easily at ambient [6], a more subtle but important role of Cuþ ions (higher polarizability and smaller ionic size than Agþ) is probably to impede the crystal growth to a significant extent, thereby lowering the average crystallite size and thus reinforces the cation sublattice to stabilize the zincblende phase g-AgI, which has a smaller unit cell than that of the wurtzite or b-AgI. This is evident from the estimates of the particle size (,40 – 60 nm) from the broadened (111), (220) and (311) XRD lines using the Debye – Scherrer formula. Moreover, the smaller Cuþ-ions are expected to be present mostly in the subsurface region of the crystals rather than on the crystal bulk, facilitating further reduction in the interfacial energies between the randomly distributed polytypes of AgI, leading to the stabilization of the metastable cubic zincblende g-AgI with smaller crystallites [7]. The ease of nano-crystallization of the silver halides and the essential but marginal
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change in lattice size with Cu-addition, as determined by the rigid I2 sublattice, effectively plays down the effect of strain in nanoparticle formation. As seen in our work on Cu-stabilized g-AgI films, Cu assists nanoparticle formation in a more natural way without introducing any CuI or related phases [8]. Fig. 2 shows the impedance spectra of Ag12xCuxI solid solutions at two selected temperatures. In the low temperature (LT) phase (T , 150 8C), the impedance profile is a neat semicircle (arising from the Debye type relaxation of ions) along with a protruding straight line, caused by the effect due to electrode polarization. The intercept of the xaxis gives the total ‘average’ resistance of the sample grains including the grain boundaries [9,10]. The resistance values of 10 and 38 kV derived from the impedance spectra for the compositions, x ¼ 0.05 and 0.15, respectively, provides the quantitative evidence for the effect of Cu-doping. At temperatures above 150 8C (HT phase), the impedance spectra (inset in Fig. 2) mainly show the electrode contributions, because the absolute values of the sample resistance are very small at these temperatures. Similar impedance spectra were also observed for all the other samples both at LT and HT. Since there are a number of conducting pathways for Agþ ions to move from site to site, the true resistance of the sample is not significantly affected by substituent cations in the a-phase, interfacial effects are negligible and percolating paths of AgI particles determine the overall ionic conductivity. In reality, the solid solutions at high temperature are in a state of highly dynamic configuration, with an appreciable degree of correlation between the mobile ions [11].
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Arrhenius plots of the dc conductivity (sdc) were extracted from the analysis of above impedance spectra are shown in Fig. 3. An abrupt increase in the conductivity indicates the g ! a phase transition. As in pure AgI, two regions with different activation energies (above and below Tc) are found in these solid solutions also, but the conductivity jump at Tc is less steep as found in the case of AgI12xBrx [12]. Also, the small but clearly visible hump around 100 8C (2.75 K21) is reasonably attributed to the interfacial phase transition that occurs due to strong surface interactions aided by the small free energy difference between the competing b- and g-phases of AgI, randomly distributed in our samples. More significantly, the transition temperature increases with increasing Cu-content—a trend quite opposite to that observed in the case of Br-substituted AgI. However, unlike in the case of AgI12xBrx, the anion sublattice is intact in the present case. This implies that the increase in the transition temperature upon Cu substitution is essentially due to the reinforcement of the cation sublattice; at the most fundamental level, the average Ag– I bond becomes more covalent and the ionicity becomes less critical than that deduced by Phillips for AgI [13]. This ensures that the high temperature conductivity of Cu-doped AgI is less than that of undoped AgI. The significant increase in the conductivity behavior of the LT phase upon Cu addition (Fig. 3) can be directly attributed to the existence of different structural modifications (as shown by XRD in Fig. 1) with randomly distributed stacking faults. The enhanced defect concentration and the grain boundary effects [2] dominate the LT ionic conductivity because of an increase in the number of
Fig. 2. Impedance spectra for the LT and HT (inset) phases of Ag12xCuxI solid solutions. The intercept on the x-axis (in both the LT and HT phases) represents the average resistance of the sample grains. The broadening of the impedance semicircle with Cu content in the LT phase is presently being studied in detail. The solid lines are only guide to the eye.
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Fig. 3. Arrhenius plot of the temperature dependence of the dc conductivity for the Ag12xCuxI solid solutions along with pure AgI. The presence of large amount of g-AgI along with small amount of other polymorphs (as seen from XRD in Fig. 1) drastically increases the s of the LT phase as compared with pure AgI. The visible hump around 100 8C is attributed to the interfacial phase transition as explained in the text. Increasing Tc with Cu content corresponds to the progressive strengthening of the Ag–I bond. The decrease in s of the HT phase could be attributed to the expected increase in the lattice parameter of the a-phase. The solid lines are only guide to the eye.
mobile cations through the interstitial positions accompanying chemical replacement [14]. Moreover, the presence of b-AgI/g-AgI polytypes in the same sample facilitates the formation of anti-phase domain boundaries within the crystal structure, which are the most probable sources of cationic Frenkel defects governing both high ionic conductivity and anomalous dielectric property [15 – 17]. The high absolute conductivity may then be explained by the increased number of mobile defects at the interface of the two polymorphs. The conductivity anomalies observed in two-phase mixtures of the ionic conductors AgCl/AgI [11] and AgBr/AgI [18] are quite similar to the one observed in the present case. Also, mesoscopic multiphase effects are expected when the spacing between different existing polymorphs becomes smaller than the Debye length [19]. Therefore, in the LT phase of Ag12xCuxI (0 # x # 0.25) solid solutions, due to the increasing gradient of Cuþ-ion distribution with ‘x’ in the crystal subsurface, the nano-sized silver ions are randomly distributed among all the available sites on the crystal bulk and thus in a state of higher energy than that of the ordered b-AgI structure [20]. This already activated state of the silver ions would then provide a satisfactory explanation for the corresponding decrease in the LT activation energy barrier (Es) for ion migration obtained by fitting the conductivity data to an Arrhenius type equation, as given in Table 1. From the reported activation energy values for various polymorphs of AgI [5,19], it can be inferred that the LT (,100 8C) activation energy values of our ambient solution processed polycrystalline samples (Table 1) lies intermediate between that for the two crystallographic directions ( ’ a and ’ c) of the wurtzite b-AgI single crystal. The variation of Tc with Cu-content as
derived from the conductivity plot is also in accordance with that predicted by Shahi [2]. But, the composition dependence of activation energy for the solid solutions Ag12xCuxI (0 , x , 0.25) in the HT phase is rather small (Table 1). This is attributed to the fact that even though both Ag and Cu ions have the same conduction paths, the amplitudes of their anharmonic thermal vibrations are different. Moreover, the Arrhenius plot in the high temperature region is almost parallel to the T 21 axis, implying smaller activation energy, ,kBT. This would be possible only when the Agþ ion has a higher coordination in the HT phase as compared to Cuþ ion, which is supported by the Monte Carlo simulation studies on AgI [21]. Also in this HT phase, the presence of Cuþ-ions clearly underlines the fact that defect – defect interactions are minimal [22]. In addition, the interaction energy of mobile Agþ-ions among themselves as well as with Cuþ-ions in the lattice Table 1 Variation of Tc with Cu-content and their activation energies at LT and HT phases Sample
AgI Ag0.95Cu0.05I Ag0.85Cu0.15I Ag0.75Cu0.25I
Transition temperature (Tc) in 8C
147 162 174 179
Activation energy (Ea) in eV LT phase (,100 8C)
HT phase (.150 8C)
0.41 0.38 0.47 0.41
0.11 0.09 0.1 0.06
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is smaller than that in the low temperature phase, suggesting the softening of the AgI lattice by Cuþ substitution [23]. This fact is attributed to the possible reduction in the lattice contraction at the transition region for the Ag12xCuxI mixed systems relative to that of undoped AgI [24], leading to the observed decrease in magnitude of the conductivity jump and thus makes it quite difficult to determine the small activation energy differences reliably. Theoretically, the transport characteristics of the a-phase Ag12xCuxI (0 , x , 0.25) solid solutions were simulated using the molecular dynamics technique [25] and found that activation energy of all the Cu-substituted phases should be higher than that of pure AgI in contrast with our present experimental observation. Furthermore, it has also been clearly established that the diffusion constant of the cations decreases with increasing copper concentration and their concentration curves of the activation energy of diffusion also show a maximum at x . 0.15. Then, the most important effect of Cu-substitution seems to be in the overall ion dynamics rather than any systematic changes in the defect concentration unlike that observed in the case of divalent ion doped AgI [26,27]. Thus, the systematics of the HT phase in Cu-doped AgI with respect to undoped AgI needs to be explained in terms of the basic parameters of ion transport. The decrease in s with respect to AgI would probably arise from a progressively reduced transport number for Agþ ion transport. The experimentally measured values of the transport number ‘tAg’ in the high temperature a-phase of Ag-rich AgxCu12xI (0.6 # x # 1.0) decreases from 0.915 for x ¼ 0.9 to ,0.7 for x ¼ 0.6 [28]. Thus, by reasonable interpolation, even the most probable reduction in transport number for Agþ ion transport in our samples with x ¼ 0.05, 0.15 and 0.25, lying in between 0.915 and 0.71, thereby makes only small contribution to the experimentally observed decrease in s with increasing Cu content. (Note that tCu , 1026 < 0 for Cuþ conduction in CuI up to 200 8C) [1]. Recently, the linear combination of atomic orbitals (LCAO) calculations of Kobayashi and co-workers have established that the d-bands of Ag are much more weakly coupled to the p-bands of I than those of Cu ions. The lower value of the strength of p – d hybridization in AgI loosens freely the coupling of Agþ and I2 bonds, leading to the experimentally observed low activation energy and thus results in about ten times higher ionic conductivity than that of CuI [29,30]. Also, the important empirical criteria for a material to behave as a superionic conductor, i.e. an open structure in which each mobile ion has a low coordination number [31] thereby ensuring easy movement of mobile ions from one place to another, is being reflected indirectly in these band structure calculations on the strength of p – d hybridization. Then, the superionic conductivity in AgI should primarily stem from a combination of the effects of
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deformability of the d-shell and the weakness of the p – d hybridization. The imparted covalency and thus the change in ionicity of the Ag– I bond due to Cu-doping drastically increases the strength of p – d hybridization and considerably restricts the mobility of the Agþ-ions by reducing its bond-breaking with the p-electrons of the I2 ions, as shown by the decrease in conductivity of the high temperature a-phase (Fig. 3). While the above discussions qualitatively account for a reduction in conductivity of the Ag12xCuxI solid solutions, the identification of specific mechanisms of conduction must await (a) diffusion measurements and (b) molecular dynamics calculations. Investigation of the local structure of Ag12xCuxI solid solutions would also strengthen our interpretation and provide a better understanding of the ion conduction process. The changes in the crystal structure upon Cu-substitution should be clarified to discuss the thermally induced change of electrical conductivity and the mechanism of the phase transition in the Ag12xCuxI solid solutions.
4. Conclusions Metastable g-AgI has been stabilized along with small amount of other polymorphic modifications in Ag-rich solid solutions Ag12xCuxI (0 # x # 0.25). Debye type relaxation of the mobile ions in the low temperature phase and the dominant electrode contribution to conductivity in the high temperature a-phase are clearly demonstrated in the impedance spectra. Arrhenius plots of the dc conductivity extracted from the analysis of the impedance spectra shows the dominant grain boundary effects (due to stacking disorder) and enhanced defect concentration in the low temperature phase, while softening of the AgI lattice in the high temperature phase possibly contributes to the smallness of the composition dependence of observed activation energy. Microscopically, the fundamental change in ionicity of the Ag – I bond and increase in strength of p – d hybridization upon Cu-substitution are the two factors, which strongly determine the ionic conductivity of these solid solutions.
Acknowledgements One of the authors PSK gratefully acknowledges the Council of Scientific and Industrial Research (CSIR, INDIA) for the award of a Research Fellowship. The authors are thankful to the Referees for their critical reading and constructive comments on the manuscript.
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References [1] S. Chandra, Superionic Solids: Principles and Applications, North Holland, Amsterdam, 1981. [2] K. Shahi, Phys. Status Solidi A 41 (1977) 11. [3] K. Endo, T. Fujito, Bull. Chem. Soc. Jpn 63 (1990) 1860. [4] J.W. Brightwell, C.N. Buckley, B. Ray, Phys. Status Solidi A 69 (1982) K11. [5] J.S. Lee, S. Adams, J. Maier, J. Phys. Chem. Solids 61 (2000) 1607. [6] A. Yohiasa, K. Koto, F. Kanamaru, S. Emura, H. Horiuchi, Acta Crystallogr. B 43 (1987) 434. [7] J. Rogez, O. Schaf, P. Knauth, Solid State Ionics 136–137 (2000) 955. [8] P.S. Kumar, C.S. Sunandana, Nano Lett. 2 (2002) 431. [9] J. Fleig, J. Maier, Solid State Ionics 85 (1996) 9. [10] S. Rodewald, J. Fleig, J. Maier, J. Euro. Ceram. Soc. 19 (1999) 797. [11] U. Lauer, J. Maier, Ber. Bunsen-Ges. Phys. Chem. 96 (1992) 111. [12] K. Shahi, J.B. Wagner Jr., Phys. Rev. B 23 (1981) 6417. [13] J.C. Phillips, Bonds and Bands in Semiconductors, Academic Press, New York, 1973. [14] A. Murakami, T. Sakuma, H. Takahashi, Y. Onoda, R.B. Beeken, Solid State Ionics 120 (1999) 61. [15] I.D. Brown, Acta Crystallogr. B 48 (1992) 553. [16] S. Adams, J. Maier, Solid State Ionics 105 (1998) 67.
[17] J. Maier, Prog. Solid State Chem. 23 (1995) 171. [18] N.F. Uvarov, E.F. Hairetdinov, A.I. Rykov, Yu.T. Pavlyukhin, Solid State Ionics 96 (1997) 233. [19] J.S. Lee, S. Adams, J. Maier, J. Electrochem. Soc. 147 (2000) 2407. [20] T. Takahashi, K. Kuwabara, O. Yamamoto, J. Electrochem. Soc. 116 (1969) 357. [21] R.A. Montani, J. Phys. Chem. Solids 53 (1992) 1211. [22] R.B. Beeken, E.M. Beeken, Solid State Ionics 136 –137 (2000) 463. [23] T. Ishii, O. Kamishima, J. Phys. Soc. Jpn 70 (2001) 159. [24] P.S. Kumar, N.S. Kini, A.M. Umarji, C.S. Sunandana, in: B.V.R. Chowdhari, W.J. Wang (Eds.), Solid State Ionics: Materials and Devices, World Scientific, Singapore, 2000, p. 121. [25] A.K. Ivanov-Shitz, B.Y. Mazniker, E.S. Povolotskaya, Crystallogr. Rep. 46 (2001) 292. [26] S.M. Nair, A. Ahmad, J. Phys. Chem. Solids 58 (1997) 331. [27] T.K. Mallick, S. Ganguli, N. Chatterjee, J. Phys. Chem. Solids 45 (1984) 661. [28] M. Kusakabe, Y. Ito, M. Arai, Y. Shirakawa, S. Tamaki, Solid State Ionics 86–88 (1996) 231. [29] M. Kobayashi, H. Iyetomi, S. Ono, T. Tomoyose, Int. J. Mod. Phys. B 15 (2001) 678. [30] S. Ono, M. Kobayashi, H. Iyetomi, T. Tomoyose, Solid State Ionics 139 (2001) 249. [31] M. Aniya, Solid State Ionics 50 (1992) 125.
Effect of Cu-substitution on the conductivity of Ag-rich AgI –CuI solid solutions P.S. Kumara, P. Balayab, P.S. Goyalb, C.S. Sunandanaa,* a
School of Physics, Central University P.O., University of Hyderabad, Hyderabad 500 046, India b IUC-DAEF, Mumbai Centre, B.A.R.C., Mumbai 400 085, India Received 17 May 2002; accepted 15 November 2002
Abstract The ionic conductivity of the silver rich solid solutions Ag12xCuxI (0 , x , 0.25) was measured using complex impedance spectroscopy over the frequency range 100 Hz –15 MHz and in the temperature range 25 – 250 8C. As observed in undoped AgI, two conducting regions (above and below Tc) are found in these solid solutions also. Despite the large size difference in the ionic radii of Agþ and Cuþ ions, the bigger sized Agþ ion dominates the overall conductivity of the system. Arrhenius plots of the dc conductivity demonstrates clearly the enhanced defect concentration and grain boundary effects in the low temperature phase as well as the smallness of the observed activation energy along with the softening of the AgI lattice in the high temperature phase. The pertinent effect of Cu doping in AgI is discussed in terms of the recent experimental and theoretical facts. A plausible conduction mechanism is being worked out. q 2003 Elsevier Science Ltd. All rights reserved. Keywords: D. Ionic conductivity; C. Impedance spectroscopy; A. Nano-crystallization
1. Introduction AgI and CuI are well known materials for their interesting physics of phase transitions as well as their applications as fast ionic conductors and also as chemical sensors. While AgI is already an ionic (Agþ) conductor at ambient, CuI is a mixed ionic– electronic conductor at room temperature with predominant electron-hole conduction up to 200 8C [1]. AgI undergoes a first order structural phase transition (wurtzite (b)/zincblende (g) ! body centered cubic (a) phase) at 147 8C to a highly dynamic ‘superionic’ state. Study of the effects of chemical substitution (both cationic and anionic) on the superionic conductivity of AgI provides further insight into the complexities of this phase transition thus helps arriving at a mechanism governing the ion transport/mobility within the crystal lattice [2]. * Corresponding author. Tel.: þ 91-40-3010500x4324; fax: þ 9140-3010227. E-mail address: [email protected] (C.S. Sunandana).
Heterovalent cation (like Cdþ þ , Pbþ þ etc.) substitution must necessarily be accompanied by an accumulation of cationic vacancy defects. However, in interpreting these experimental results, it is not straightforward to distinguish between the effects of cation substitution and vacancy formation. In order to isolate the effect of cation substitution in AgI, we have chosen the homovalent Cuþ cation for study in the present investigation. Solid solutions of AgI and CuI were prepared so as to change the property of the material in a single component [3]. This is possible because of the extended mutual solid solubility range of AgI and CuI despite their unequal ionic ˚ ; rCu ¼ 0.96 A ˚ ; rAg/rCu ¼ 1.31). This radii (rAg ¼ 1.26 A large size mismatch in mobile cation size points to the possibility of a mixed mobile ion effect controlled ionic conductivity in the AgI– CuI system. Furthermore, the fact that CuI is an electronic conductor in the temperature range of investigation brings into play factors such as p – d hybridization to the conduction process—essentially including subtle changes in ion mobility and concentration.
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Nontrivial modification of the cation sublattice in the zincblende/bcc phases and the possibility of realizing interfacial polytypes are expected to decrease the defect concentration ‘n’ and hence the conductivity ‘s’ [2] of the high temperature a-phase thereby increasing the ‘Tc’ of AgI. In the present paper, we investigate experimentally the conductivity and phase transition behavior in Ag12xCuxI (0 # x # 0.25), the Ag-rich solid solution of the AgI – CuI binary phase diagram. The changes in the conductivity profiles on either side of the phase transition anomaly in AgI as well as the transition temperature itself, induced by the addition of Cu are discussed in terms of changes in structure, electronic structure and bonding in context with the recently reported works.
2. Experimental methods The solubility difference between CuI and AgI has been utilized in the synthesis of solid solutions using the simple conversion process in an aqueous suspension [3]. All the basic investigations described in this paper are concerned with Ag12xCuxI (x ¼ 0.05, 0.1, 0.15, 0.2 and 0.25) compositions. These samples were prepared by the gradual addition of the required molar aqueous solutions of the nitrates of silver and copper (Analar grade, LOBA, INDIA) under continuous stirring and precipitating them with a 2 to 5% excess solution of potassium iodide (LOBA, INDIA) just below the normal boiling temperature [4]. After several decantations with double distilled water to remove the excess nitrates present if any, the samples were dehydrated in an oven at 60 8C for several hours. Structural characterization on these powder samples was performed using a PHILIPS X-ray diffractometer. Sample pellets of 5 mm thickness and 8 mm diameter were used for the impedance measurements. To avoid electrode diffusion problems, chemically inert, commercial grade graphite paste was applied on opposite parallel surfaces of the sample pellet followed by baking at 200 8C for 30 min to ensure a good electrical contact. Impedance measurements in the frequency and temperature range, 100 Hz– 15 MHz and 25 – 250 8C, respectively, were carried out using an Impedance/Gain Phase Analyzer (HP 4194A) at IUC-DAEF, Mumbai. All measurements were carried out under rotary vacuum (, 1022 mbar) in order to avoid any oxidation problem. The reproducibility of the impedance data of these polycrystalline specimens was confirmed by repeated temperature cycles above the b/g ! a transition temperature.
3. Results and discussion Fig. 1 shows the powder XRD patterns of the as-prepared samples. These patterns consist of three
Fig. 1. X-ray powder diffraction patterns for the Ag12xCuxI solid solutions of various compositions. The presence of considerable amount of sphalerite g-AgI structure is evidenced by the dominant (111), (220) and (311) Bragg peaks. The ‘circle’ marked weak intensity peaks corresponds to the random distribution of b-AgI arising from the stacking disorder in the sample.
prominent Bragg peaks, characteristic of a substantial amount of g-AgI (JCPDS, card no. 9-399) and the presence of additional weak reflections, which are attributed to the co-existence of other polymorphs (e.g. 2, 4, 8, 16 H) of AgI [5]. As g-AgI cannot be stabilized easily at ambient [6], a more subtle but important role of Cuþ ions (higher polarizability and smaller ionic size than Agþ) is probably to impede the crystal growth to a significant extent, thereby lowering the average crystallite size and thus reinforces the cation sublattice to stabilize the zincblende phase g-AgI, which has a smaller unit cell than that of the wurtzite or b-AgI. This is evident from the estimates of the particle size (,40 – 60 nm) from the broadened (111), (220) and (311) XRD lines using the Debye – Scherrer formula. Moreover, the smaller Cuþ-ions are expected to be present mostly in the subsurface region of the crystals rather than on the crystal bulk, facilitating further reduction in the interfacial energies between the randomly distributed polytypes of AgI, leading to the stabilization of the metastable cubic zincblende g-AgI with smaller crystallites [7]. The ease of nano-crystallization of the silver halides and the essential but marginal
P.S. Kumar et al. / Journal of Physics and Chemistry of Solids 64 (2003) 961–966
change in lattice size with Cu-addition, as determined by the rigid I2 sublattice, effectively plays down the effect of strain in nanoparticle formation. As seen in our work on Cu-stabilized g-AgI films, Cu assists nanoparticle formation in a more natural way without introducing any CuI or related phases [8]. Fig. 2 shows the impedance spectra of Ag12xCuxI solid solutions at two selected temperatures. In the low temperature (LT) phase (T , 150 8C), the impedance profile is a neat semicircle (arising from the Debye type relaxation of ions) along with a protruding straight line, caused by the effect due to electrode polarization. The intercept of the xaxis gives the total ‘average’ resistance of the sample grains including the grain boundaries [9,10]. The resistance values of 10 and 38 kV derived from the impedance spectra for the compositions, x ¼ 0.05 and 0.15, respectively, provides the quantitative evidence for the effect of Cu-doping. At temperatures above 150 8C (HT phase), the impedance spectra (inset in Fig. 2) mainly show the electrode contributions, because the absolute values of the sample resistance are very small at these temperatures. Similar impedance spectra were also observed for all the other samples both at LT and HT. Since there are a number of conducting pathways for Agþ ions to move from site to site, the true resistance of the sample is not significantly affected by substituent cations in the a-phase, interfacial effects are negligible and percolating paths of AgI particles determine the overall ionic conductivity. In reality, the solid solutions at high temperature are in a state of highly dynamic configuration, with an appreciable degree of correlation between the mobile ions [11].
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Arrhenius plots of the dc conductivity (sdc) were extracted from the analysis of above impedance spectra are shown in Fig. 3. An abrupt increase in the conductivity indicates the g ! a phase transition. As in pure AgI, two regions with different activation energies (above and below Tc) are found in these solid solutions also, but the conductivity jump at Tc is less steep as found in the case of AgI12xBrx [12]. Also, the small but clearly visible hump around 100 8C (2.75 K21) is reasonably attributed to the interfacial phase transition that occurs due to strong surface interactions aided by the small free energy difference between the competing b- and g-phases of AgI, randomly distributed in our samples. More significantly, the transition temperature increases with increasing Cu-content—a trend quite opposite to that observed in the case of Br-substituted AgI. However, unlike in the case of AgI12xBrx, the anion sublattice is intact in the present case. This implies that the increase in the transition temperature upon Cu substitution is essentially due to the reinforcement of the cation sublattice; at the most fundamental level, the average Ag– I bond becomes more covalent and the ionicity becomes less critical than that deduced by Phillips for AgI [13]. This ensures that the high temperature conductivity of Cu-doped AgI is less than that of undoped AgI. The significant increase in the conductivity behavior of the LT phase upon Cu addition (Fig. 3) can be directly attributed to the existence of different structural modifications (as shown by XRD in Fig. 1) with randomly distributed stacking faults. The enhanced defect concentration and the grain boundary effects [2] dominate the LT ionic conductivity because of an increase in the number of
Fig. 2. Impedance spectra for the LT and HT (inset) phases of Ag12xCuxI solid solutions. The intercept on the x-axis (in both the LT and HT phases) represents the average resistance of the sample grains. The broadening of the impedance semicircle with Cu content in the LT phase is presently being studied in detail. The solid lines are only guide to the eye.
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Fig. 3. Arrhenius plot of the temperature dependence of the dc conductivity for the Ag12xCuxI solid solutions along with pure AgI. The presence of large amount of g-AgI along with small amount of other polymorphs (as seen from XRD in Fig. 1) drastically increases the s of the LT phase as compared with pure AgI. The visible hump around 100 8C is attributed to the interfacial phase transition as explained in the text. Increasing Tc with Cu content corresponds to the progressive strengthening of the Ag–I bond. The decrease in s of the HT phase could be attributed to the expected increase in the lattice parameter of the a-phase. The solid lines are only guide to the eye.
mobile cations through the interstitial positions accompanying chemical replacement [14]. Moreover, the presence of b-AgI/g-AgI polytypes in the same sample facilitates the formation of anti-phase domain boundaries within the crystal structure, which are the most probable sources of cationic Frenkel defects governing both high ionic conductivity and anomalous dielectric property [15 – 17]. The high absolute conductivity may then be explained by the increased number of mobile defects at the interface of the two polymorphs. The conductivity anomalies observed in two-phase mixtures of the ionic conductors AgCl/AgI [11] and AgBr/AgI [18] are quite similar to the one observed in the present case. Also, mesoscopic multiphase effects are expected when the spacing between different existing polymorphs becomes smaller than the Debye length [19]. Therefore, in the LT phase of Ag12xCuxI (0 # x # 0.25) solid solutions, due to the increasing gradient of Cuþ-ion distribution with ‘x’ in the crystal subsurface, the nano-sized silver ions are randomly distributed among all the available sites on the crystal bulk and thus in a state of higher energy than that of the ordered b-AgI structure [20]. This already activated state of the silver ions would then provide a satisfactory explanation for the corresponding decrease in the LT activation energy barrier (Es) for ion migration obtained by fitting the conductivity data to an Arrhenius type equation, as given in Table 1. From the reported activation energy values for various polymorphs of AgI [5,19], it can be inferred that the LT (,100 8C) activation energy values of our ambient solution processed polycrystalline samples (Table 1) lies intermediate between that for the two crystallographic directions ( ’ a and ’ c) of the wurtzite b-AgI single crystal. The variation of Tc with Cu-content as
derived from the conductivity plot is also in accordance with that predicted by Shahi [2]. But, the composition dependence of activation energy for the solid solutions Ag12xCuxI (0 , x , 0.25) in the HT phase is rather small (Table 1). This is attributed to the fact that even though both Ag and Cu ions have the same conduction paths, the amplitudes of their anharmonic thermal vibrations are different. Moreover, the Arrhenius plot in the high temperature region is almost parallel to the T 21 axis, implying smaller activation energy, ,kBT. This would be possible only when the Agþ ion has a higher coordination in the HT phase as compared to Cuþ ion, which is supported by the Monte Carlo simulation studies on AgI [21]. Also in this HT phase, the presence of Cuþ-ions clearly underlines the fact that defect – defect interactions are minimal [22]. In addition, the interaction energy of mobile Agþ-ions among themselves as well as with Cuþ-ions in the lattice Table 1 Variation of Tc with Cu-content and their activation energies at LT and HT phases Sample
AgI Ag0.95Cu0.05I Ag0.85Cu0.15I Ag0.75Cu0.25I
Transition temperature (Tc) in 8C
147 162 174 179
Activation energy (Ea) in eV LT phase (,100 8C)
HT phase (.150 8C)
0.41 0.38 0.47 0.41
0.11 0.09 0.1 0.06
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is smaller than that in the low temperature phase, suggesting the softening of the AgI lattice by Cuþ substitution [23]. This fact is attributed to the possible reduction in the lattice contraction at the transition region for the Ag12xCuxI mixed systems relative to that of undoped AgI [24], leading to the observed decrease in magnitude of the conductivity jump and thus makes it quite difficult to determine the small activation energy differences reliably. Theoretically, the transport characteristics of the a-phase Ag12xCuxI (0 , x , 0.25) solid solutions were simulated using the molecular dynamics technique [25] and found that activation energy of all the Cu-substituted phases should be higher than that of pure AgI in contrast with our present experimental observation. Furthermore, it has also been clearly established that the diffusion constant of the cations decreases with increasing copper concentration and their concentration curves of the activation energy of diffusion also show a maximum at x . 0.15. Then, the most important effect of Cu-substitution seems to be in the overall ion dynamics rather than any systematic changes in the defect concentration unlike that observed in the case of divalent ion doped AgI [26,27]. Thus, the systematics of the HT phase in Cu-doped AgI with respect to undoped AgI needs to be explained in terms of the basic parameters of ion transport. The decrease in s with respect to AgI would probably arise from a progressively reduced transport number for Agþ ion transport. The experimentally measured values of the transport number ‘tAg’ in the high temperature a-phase of Ag-rich AgxCu12xI (0.6 # x # 1.0) decreases from 0.915 for x ¼ 0.9 to ,0.7 for x ¼ 0.6 [28]. Thus, by reasonable interpolation, even the most probable reduction in transport number for Agþ ion transport in our samples with x ¼ 0.05, 0.15 and 0.25, lying in between 0.915 and 0.71, thereby makes only small contribution to the experimentally observed decrease in s with increasing Cu content. (Note that tCu , 1026 < 0 for Cuþ conduction in CuI up to 200 8C) [1]. Recently, the linear combination of atomic orbitals (LCAO) calculations of Kobayashi and co-workers have established that the d-bands of Ag are much more weakly coupled to the p-bands of I than those of Cu ions. The lower value of the strength of p – d hybridization in AgI loosens freely the coupling of Agþ and I2 bonds, leading to the experimentally observed low activation energy and thus results in about ten times higher ionic conductivity than that of CuI [29,30]. Also, the important empirical criteria for a material to behave as a superionic conductor, i.e. an open structure in which each mobile ion has a low coordination number [31] thereby ensuring easy movement of mobile ions from one place to another, is being reflected indirectly in these band structure calculations on the strength of p – d hybridization. Then, the superionic conductivity in AgI should primarily stem from a combination of the effects of
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deformability of the d-shell and the weakness of the p – d hybridization. The imparted covalency and thus the change in ionicity of the Ag– I bond due to Cu-doping drastically increases the strength of p – d hybridization and considerably restricts the mobility of the Agþ-ions by reducing its bond-breaking with the p-electrons of the I2 ions, as shown by the decrease in conductivity of the high temperature a-phase (Fig. 3). While the above discussions qualitatively account for a reduction in conductivity of the Ag12xCuxI solid solutions, the identification of specific mechanisms of conduction must await (a) diffusion measurements and (b) molecular dynamics calculations. Investigation of the local structure of Ag12xCuxI solid solutions would also strengthen our interpretation and provide a better understanding of the ion conduction process. The changes in the crystal structure upon Cu-substitution should be clarified to discuss the thermally induced change of electrical conductivity and the mechanism of the phase transition in the Ag12xCuxI solid solutions.
4. Conclusions Metastable g-AgI has been stabilized along with small amount of other polymorphic modifications in Ag-rich solid solutions Ag12xCuxI (0 # x # 0.25). Debye type relaxation of the mobile ions in the low temperature phase and the dominant electrode contribution to conductivity in the high temperature a-phase are clearly demonstrated in the impedance spectra. Arrhenius plots of the dc conductivity extracted from the analysis of the impedance spectra shows the dominant grain boundary effects (due to stacking disorder) and enhanced defect concentration in the low temperature phase, while softening of the AgI lattice in the high temperature phase possibly contributes to the smallness of the composition dependence of observed activation energy. Microscopically, the fundamental change in ionicity of the Ag – I bond and increase in strength of p – d hybridization upon Cu-substitution are the two factors, which strongly determine the ionic conductivity of these solid solutions.
Acknowledgements One of the authors PSK gratefully acknowledges the Council of Scientific and Industrial Research (CSIR, INDIA) for the award of a Research Fellowship. The authors are thankful to the Referees for their critical reading and constructive comments on the manuscript.
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