Phase transitions in copper tellurides

This paper presents the results of model calculations of the structure of the Cu-Te system at low temperatures, as well as the results of a study of the structure and phase transitions of synthesized non-stoichiometric compounds of copper tellurides. For the ﬁrst time, using the USPEX evolutionary algorithm, model computer calculations of the search for stable phases of copper tellurides Cu n Te m ( n , m = 1 ÷ 10 ) were carried out. At temperature T = 0 K and pressure p = 1 atm. As stable structures, the compositions Cu 5 Te 4 , Cu 3 Te 2 , and Cu 7 Te 4 were identiﬁed, which are indicated in the triclinic and monoclinic syngonies. Based on the study of the phase diagram, calorimetric measurements and X-ray diffraction studies of experimentally synthesized samples of copper telluride, it was found that the non-stoichiometric compositions Cu 1.96 Te , Cu 1.85 Te , Cu 1.80 Te and Cu 1.75 Te at room temperature are single-phase. The Cu 1.85 Te , Cu 1.80 Te , and Cu 1.75 Te compounds are described by hexagonal crystalline superstructures obtained on the basis of the Novotny phase for Cu 2 Te with different degrees of unit cell parameter multiplicity. Cu 1.96 Te at room temperature is indicated in an orthorhombic phase with lattice parameters that are also multiples of the unit cell parameters of the Novotny phase. At high temperatures, all compositions of Cu 2 − x Te ( x =0.04, 0.15, 0.20, 0.25) transform into high-temperature disordered FCC structures that exist up to their melting point. It is shown that in these compounds the transition of a low-temperature hexagonal and orthorhombic structure to a high-temperature FCC phase occurs through a series of polymorphic phase transformations.


Introduction
Copper tellurides belong to the family of copper chalcogenides and have a wide variety of electrical properties due to the presence of mixed ionic-electronic conductivity and the existence of compounds of variable composition.Copper chalcogenides have been addressed to be functional materials for thermoelectric [1], batteries [2], photovoltaic [3] and bioapplications [4].The Cu-Te system has a complex phase diagram of states.This is due to the existence of different phases of copper tellurides of non-stoichiometric composition, the structures and properties of which have been little studied.Studies of phase transitions depending on the stoichiometric composition are necessary, since the operation of devices based on copper tellurides occurs in different temperature ranges.In this regard, this paper presents the results of a study of phase transitions in copper tellurides of non-stoichiometric composition Cu 2−x Te (0 ≤ x ≤ 0.25) .

Materials and Methods
Using the USPEX algorithm [5] based on the density functional theory (DFT), model computer calculations of stable Cu n Te m (n, m = 1 ÷ 10) phases in the Cu-Te system at ultralow temperatures were carried out.The USPEX algorithm is based on an approach in which a small number of structures are randomly generated and their energy is calculated.The calculation continues until a stable model of the structure with the lowest total energy is determined.Compounds of copper tellurides of non-stoichiometric composition Cu 2−x Te (0 ≤ x ≤ 0, 25) were chosen as objects of experimental study.The starting materials for the production of copper tellurides were tellurium (chemically pure grade) and copper with a purity of 99.999%.
Synthesis was carried out by direct sintering of the corresponding amounts of elements at a temperature of 873-923 K in quartz ampoules evacuated to a residual pressure of p = 1 atm.The thermal process of synthesis was carried out at a temperature rise rate of 1 K per minute with an intermediate exposure in the temperature range of 473-523 K for 48 hours.The total time of heating and holding the mixture was 150-200 hours.Then the mixture obtained was ground in an agate mortar and annealed for homogenization at a temperature of 773 K in a vacuum at a pressure of 10 −3 Pa for 100-150 hours.The single-phase nature of the obtained samples was controlled by X-ray phase analysis, their composition was determined by chemical analysis and coulometric titration.
X-ray diffraction studies of the studied powder samples were carried out using Cu Kα radiation on a Bruker D 8 Advance X-ray diffractometer with a step of 20-25 K up to a temperature of about 660 K (up to 773 K for some samples).Refinement of the crystal structure of the synthesized compounds was carried out using the Fullprof Suite software package.Calorimetric measurements were carried out on an automated instrument NETZSCH STA 449 F 1 Jupiter.Argon was used as an inert medium.

Results and discussion
Model computer calculations [6] of the search for stable phases Cu n Te m (n, m = 1 ÷ 10) based on the USPEX evolutionary algorithm at a temperature T = 0 K and pressure p = 1 atm.revealed the following model compounds of copper tellurides: Cu 5 Te 4 , Cu 3 Te 2 and Cu 7 Te 4 (in calculated per 1 tellurium atom, the chemical formula is Cu 1.25 Te , Cu 1.5 Te , and Cu 1.75 Te , respectively).On Figure 1 shows the model crystal structures of these compounds.According to the calculations, the Cu 1.5 Te and Cu 1.75 Te compounds are indexed in the triclinic phase, except for the composition Cu 1.25 Te , which is a special case of the triclinic syngony -a monoclinic structure.temperature range of 303-875 K.According to the TG dependences, one can see that there is practically no mass loss of the samples upon heating and cooling.This result allows us to state that the samples under study are stable and the phase transitions are reversible in this temperature range.From the DSC curves of the studied compounds, the temperatures of the onset of phase transitions and the specific heats of phase transitions ∆H were determined.It should be noted that the phase transitions in copper telluride Cu 1.96 Te in the temperature range 298-658 K represent polymorphic transformations of one structural modification into another, accompanied by the formation of a number of single-phase and two-phase regions.
Copper telluride Cu 1.85 Te at room temperature [9] is single-phase and crystallizes in the hexagonal syngony with space group P3m1 and lattice parameters a = 8.38 Å, c = 21.73Å, α = β = 90 • , γ = 120 • .The unit cell parameters of copper telluride Cu 1.85 Te monotonically increase with increasing temperature, showing a linear dependence up to a temperature of ∼ 613 K.At a temperature of 613 K, the low-temperature hexagonal phase (sp. group P3m1 ) transforms into a high-temperature hexagonal phase (sp. group P6/mmm , a ≈ a 0 , c ≈ 3c 0 ).In the temperature range 615-658 K, the Cu 1.85 Te compound is also single-phase.At a temperature of 707 K, the high-temperature hexagonal phase transforms into the FCC phase.These results are in good agreement with the literature data [8].
The hexagonal structure of copper telluride of non-stoichiometric composition Cu 1.80 Te with the space group P3m1 is similar to the compound Cu 1.85 Te .The low-temperature hexagonal modification Cu 1.80 Te exists up to a temperature of ∼ 533 K, above which, according to the results of DSC measurements and X-ray diffraction analysis, a phase transition to the second hexagonal phase begins with cell parameters a  Copper telluride of non-stoichiometric composition Cu 1.75 Te at room temperature is also single-phase and is indexed in the hexagonal syngony [10] with space group P3m 1 and lattice parameters a = 8.31 Å, c = 7.21 Å, α = β = 90 • , γ = 120 • , which is a layered superstructure of the Novotny phase with parameters a ≈ 2a 0 and c ≈ c 0 .In the temperature range of 298-538 K, the parameters of the hexagonal (I) phase grow monotonically, and Cu 1.75 Te is single-phase in the indicated temperature range (Figure 6).
In the temperature range of 540-658 K, this compound is two-phase, consisting of a set of two-phase regions in rather narrow temperature ranges: 540-618 According to the DSC curves (Figure 7), copper telluride Cu 1.75 Te undergoes phase transitions at temperatures of 504 , 543 , 621 and 630 K, which are clearly manifested in the temperature dependence of the unit cell parameters, confirming the results of calorimetric measurements.The specific heats of phase transitions ∆H for the Cu 1.75 Te compound at temperatures of 504 and 543 K are (0.13 ± 0.02) kJ/mol and (1.45 ± 0.15) kJ/mol, respectively (for Cu 1.75 Te -1 J/g ≈ 0, 2388 kJ/mol).Due to the strong superposition of the peak areas for the phase transitions at 621 and 630 K, the total heat of the phase transition was determined to be (6.62 ± 0.67) kJ/mol.

Conclusions
The model computer calculations performed at a temperature T = 0 K and a pressure p = 1 atm.using the USPEX evolutionary algorithm revealed the Cu 5 Te 4 , Cu 3 Te 2 and Cu 7 Te 4 compositions, which are indicated in the triclinic and monoclinic syngonies.In the Cu 1.75 Te compound, the transition of the low-temperature hexagonal modification to the high-temperature FCC phase, similarly to copper tellurides Cu 1.96 Te , Cu 1.85 Te , Cu 1.80 Te , occurs through a series of polymorphic phase transformations associated with the redistribution of lattice atoms to energetically favorable positions.At 698 K, copper telluride of non-stoichiometric composition Cu 1.75 Te completely transforms into the FCC phase and becomes single-phase [11,12].

Figure 1 .
Figure 1.Models of the crystal structure of copper tellurides with the composition Cu 1.25 Te , Cu 1.5 Te , and Cu 1.75 Te .

Figure 3 .
Figure 3. Experimental X-ray diffraction patterns of the composition Cu 1.75 Te in the temperature range 298-658 K.

Figure 4 .
Figure 4. TG (dashed lines) and DSC (solid lines) curves obtained with heating (red) and cooling (blue) for Cu 1.96 Te .

Figure 5 .
Figure 5. TG (dashed lines) and DSC (solid lines) curves obtained with heating (red) and cooling (blue) for Cu 1.80 Te .

Figure 6 .
Figure 6.Dependence of unit cell parameters and volume of copper telluride of composition Cu 1.75 Te in the temperature range 298-658 K: 1, 2, 3 -parameters a , c and V of hexagonal (I) and hexagonal (II), 4, 5, 6, 7parameters a , c , b and V of the orthorhombic phase, 8, 9 -parameters a and V of the FCC phase, respectively.

Figure 7 .
Figure 7. TG (dashed lines) and DSC (solid lines) curves obtained with heating (red) and cooling (blue) for Cu 1.75 Te .