Phase Transition in TlS, TlSe and TlInS2 Crystals Caused by Nanoscale Defects

In this paper, we report the results of our studies on temperature and electric field dependences of conductivity in TlS, TlSe and TlInS2 crystals. At a certain temperature (typical for all three crystals) a switching effect has been observed for the conductivities of all crystals. The switching effect is explained by the phase transition to superionic conductivity. It is suggested that in TlS and TlSe crystals the ion conductivity is caused by the diffusion of Tl+ ions over vacancies in the thallium sub-lattice between (TlS2) and (TlSe2) chains. In TlInS2 crystals, this effect is due the diffusion of Tl+ ions towards vacancies in the Tl sub-lattice. In all crystals the S-type switching effect is revealed. It is suggested that the switching effect is related to the transition of crystals to the superionic state, which is accompanied by diffusion of Tl+ ions.


Introduction
Materials with quasi low-dimensional crystalline structure, have been objects of intensive studies due their promising physical properties caused by nanoscale effects.These materials have been largely used in fabricating of miniature accumulators, ionistors, gas sensors, solid-state fuel elements and other devices.The superionic conductivity is one of the unique phenomenon observed in quasi low-dimensional crystals.In particular, the superionic conductivity exists under the following conditions: the network of channels in crystal's structure must be though for moving ions; the energy of ion disordering over lattice positions and the energy lost during motion should be small; the number of potentially mobile ions per unit cell should exceed the number of immobile ions.These conditions are satisfied for only few crystals, the structure of which excludes long-range ordering in the spatial arrangement of one or several types of atoms but retain long-range order for other particles.These compounds are considered crystals with intrinsic structural disordering.Crystals with structural disordering, which have mainly ion conductivity, can be in two qualitatively different states.At temperatures below the critical, they behave like conventional ionic crystals (dielectric phase), while at temperatures above the critical they pass to a peculiar superionic state (electrolytic phase).
TlS, TlSe and TlInS2 belong to this class of materials, in which the features of low dimensional system manifest themselves under certain conditions [1].These crystals are attracting attention in association with features of their crystal structure, more specifically, the pronounced chain (TlS and TlSe) and layered (TlInS2) structures.Weak links between chains (in TlS and TlSe) and layers (in TlInS2) result in fact that such structures are inclined to nanoscale defects.For example, even in single crystals of this class of compounds, the density of uncontrolled defects can reach 10 20 cm -3 .In this case, crystals exhibit hopping conductivity similar to that observed in amorphous or highly disordered crystals, which is well described within the Mott approximation.
TlS and TlSe crystals belong to compounds of A 3 B 6 group, which crystallize into tetragonal system with the space group D 18 4h.A characteristic feature of these crystals is that their structure is formed by (Tl 3+ S 2-

2)
-and (Tl 3+ Se 2-) -chains, elongated along tetragonal axis c of the crystal (Fig. 1.2, [1]).The tetragonal axis is an optical axis.Monovalent Tl + atoms 116-2 are in the octahedral environment of S and Se atoms in the TlS and TlSe crystals, respectively.Based on the crystalchemical considerations, it can be suggested that this crystal structure is most favourable for mobile Tl + ions.In this case, the favourable factor is the presence of extensive cavities, which are linked by shared faces (conductivity windows), as well as the fundamental possibility of deficit of monovalent thallium ions, as a result of which the ionic conductivity may significantly rise.TlInS2 is a p-type semiconductor with a layers structure made of In4S10 (which in turn consist of four tetrahedrons InS4) groups that form layers extending perpendicular to the c-axis of the material (Fig. 1).These layers of negatively charged are bonded together by Tl + ions.The resulting monoclinic lattice is characterized by a group symmetry.Much attention has been paid to such crystallographic systems, which behave as if they have less than three spatial dimensions.Such materials are often called quasi-two-dimensional (2D) layers.
In this paper, we report the results of experimental study of conductivity and switching effects in TlS, TlSe and TlInS2 crystals in wide temperature range.

Growth of Materials and Experimental Setup
The compounds were synthesized by alloying primary components (purity no less than 99.99) in evacuated quartz cells; the single crystals were grown by the modified Bridgman method.The tetragonal axis c of the freshly cleaved rectangular crystal samples prepared for study was oriented in the cleavage plane.The conductivity was measured by the four contact method in two directions: parallel and perpendicular to tetragonal axis c of the crystal.The experimental samples were prepared in the form of rectangular plates 0.4-0.6 mm thick.Contacts with the samples were formed by a silver conducting paste on the plate surface.The permittivity and conductivity were measured by Е7-25, digital immittance meters at frequencies of 20-10 6 Hz in a temperature range of 100-450 K.The measuring field amplitude did not exceed 1 V cm -1 .

116-3
The temperature dependences of conductivity σ(T), in TlS, TlSe and TlInS2 are shown in Figs. 2, 3 and 4 respectively.The measurements were performed in an electric field oriented perpendicular to the tetragonal crystal axis σ(T) and parallel to it σII(T).

Discussions
As follows from the insets to Figs. 2, 3 and 4, for all crystals, the experimental points of the temperature dependence ln(σ•T) in the range of the sharp jump of conductivity are described well by a straight line, which is given by the following equation: where  is the conductivity of sample, 0 is the constant within the experimental interval of temperature, ΔE is the conductivity activation energy, T is the temperature in Kelvins and k is the Boltzmann constant.It is known that this temperature dependence of conductivity indicates the dominant character of ionic conductivity above the critical temperature [2][3][4][5].The values of critical temperatures and activation energies for TlS, TlSe and TlInS2 crystals are shown in the Table 1.The observed jumps in the conductivity at critical temperatures can be explained by the sharp change in the number of ions in the states characterized by high ion mobility, i.e., by the phase transition to the superionic state.The linear character of the dependence ln(σ•T) on 1/T above indicates dominance of ionic conductivity.It is suggested that in TlS and TlSe crystals the ion conductivity is caused by the diffusion of Tl + ions over vacancies in the thallium sub-lattice between (Tl 3+ S 2- 2) and (Tl 3+ Se 2- 2) chains.In TlInS2 crystals, this effect is due the diffusion of the Tl + ions towards vacancies in the Tl sub-lattice.In all crystals S-type switching effect are revealed.It is suggested that the switching effect is related to the transition of crystals to the superionic state, which is accompanied by diffusion of Tl + ions.This conduction mechanism is typical of superionic conductors [6][7][8][9].The transition to the high-conductivity state in superionic conductors occurs generally as a result of the first order phase transition and is explained by the stepwise disordering of one of the crystal sub-lattices (generally cationic) with the other sub-lattice either remaining invariable or transforming but retaining the crystal hardness.This effect was found experimentally in α-AgSbS2, where application of an external electric field caused gradual increase in conductivity with a subsequent sharp increase when the field reached the critical value [10].
As one can see from the field dependences of the conductivity (Fig. 5), in relatively weak fields, conductivity σ is almost independent of the applied field E because of the dominance of the electronic component in σ in this range of field strengths.A further increase in E led to a linear increase in σ, which is explained by the increase in the ionic component of conductivity as a result of gradual is ordering of the cationic Tl sub-lattice in the electric field; in this range, the ionic conductivity begins to dominate over the electronic component and, when reaching the critical temperature, the conductivity sharply rises.
The values of the critical transition field and the jump of conductivity during the phase transition increase with a decrease in temperature (Fig. 5).Voltage oscillations were observed in the range of negative differential resistance in both compounds; these were also revealed in.
In our opinion, the discovered effect of S type switching in the TlS, TlSe and TlInS2 crystals, as well as the voltage oscillations in the range of negative differential resistance, are related to the transition of these crystals to the superionic state, which is accompanied by melting of the Tl sub-lattice.
The measured dependences of the TlS and TlSe conductivities on the electric field strength E indicate that, at a certain value of critical field (at a temperature T = 300 K, Ecr =800, and 41 and 40 V/cm for TlS, TlSe and TlInS2, respectively), the Tl + ion sub-lattice may undergo step wise disordering, which is accompanied by a step wise change in conductivity.We find possible that the applied field causes disordering (melting) of the cationic sub-lattice, which leads to a stepwise increase in the occupancy of interstitial sites throughout the crystal volume. 116-6

Conclusion
Our studies shows that the temperature dependences of the conductivity of TlS, TlSe and TlInS2 crystals indicate the dominant character of ionic conductivity above the critical temperatures.We explain this effect by the sharp change in the number of ions in the states characterized by high ion mobility, i.e., by the phase transition to the superionic state.It is remarkable that for all three crystals this phase transition occurs approximately at 380 K.We have evaluated the values of activation energy for ionic conductivity in TlS, TlSe and TlInS2 crystals.
The electric field dependences of the conductivity reveal the effect of S type switching in these crystals.This effect can be explained by the stepwise increase in the occupancy of interstitial sites throughout the crystal volume under the applied electric field.
In our opinion, due this effect, TlS, TlSe and TlInS2 crystals could be considered as promising materials for fabricating nano-size switches.

Fig. 2 :
Fig. 2: Temperature dependence of conductivity of TlS parallel (on the left) and perpendicular (on the right) to axis c.

Fig. 3 : 4 Fig. 4 :
Fig. 3: Temperature dependence of conductivity of TlSe parallel (on the left) and perpendicular (on the right) to axis c.

Table 1 :
Critical temperatures and activation energies for TlS, TlSe and TlInS2.