Thermodynamic study of manganese tellurides by the electromotive force method

The thermodynamic properties of manganese tellurides were determined using an electromotive force (EMF) method with a liquid electrolyte in a temperature range from 300 to 450 K. EMF measurements were performed using equilibrium samples taken from the two-phase regions, namely MnTe2 + Te and MnTe + MnTe2, of the Mn–Te system. The phase compositions of all samples were controlled with the X-ray diffraction (XRD) method. The partial molar functions of manganese in alloys, as well as the standard thermodynamic functions of the formation and standard entropies of MnTe and MnTe2, were calculated. A comparative analysis of obtained results with literature data is performed.


Introduction
Transition metal chalcogenides are considered promising candidates for spintronics, optoelectronics, and energy storage applications due to their unusual physical and chemical properties [1][2][3][4]. Among them, manganese tellurides are particularly interesting materials that provide a unique connection between semiconductivity and magnetism [5][6][7]. Recent studies show that ternary layered phases based on manganese telluride have the potential to combine two seemingly incompatible properties, topological insulation and magnetism, at the same time [8][9][10][11][12]. The first antiferromagnetic topological insulator [14] -MnBi 2 Te 4 consists of a repetition of septuple blocks where magnetic MnTe bilayers are inserted into the quintuple Bi 2 Te 3 layers periodically [15].
The knowledge of phase equilibria and reliable thermodynamic data of corresponding systems are crucially important for synthesizing novel complex phases and the development of modern sample-preparation techniques [16,17].
Phase equilibria of the Mn-Te binary system have been investigated several times [18][19][20]. There exist two binary compounds of this type, namely MnTe and MnTe 2 . Both compounds are formed by a peritectic reaction at 1424 and 1008 K, respectively. MnTe is a p-type semiconductor and crystallizes the "NiAs" type crystal structure, while MnTe 2 has a pyrite cubic crystal structure at low temperatures. MnTe undergoes several phase transformations from the low-temperature hexagonal phase to the high-temperature cubic phase [20].
An analysis of the literature shows that the first studies on the thermodynamic properties of manganese tellurides began in the late 19th century, and data obtained from both experimentally determined (calorimetry, vapor measurements, EMF) and model-calculated values have been collected in modern handbooks and electronic databases [21][22][23][24][25][26][27][28][29][30][31]. It should be noted that all previous studies, including those conducted by EMF, were performed in high-temperature ranges. An analysis of these works shows that the values of standard integral thermodynamic functions calculated from high-temperature measurements are significantly different from each other. Therefore, in order to obtain a more reliable set of standard thermodynamic functions, it is advisable to use experimental data obtained under conditions as close as possible to the standard.
Considering the above, the purpose of this work is a thermodynamic study of the Mn-Te system by EMF method with a liquid electrolyte in the temperature range from 300 to 450 K.

Experimental
To study the thermodynamic properties of the manganese-tellurium system, several compositions having 52, 60, 70, and 80 at% Te were synthesized from high purity (99.9999 % pure, Alfa Aesar and Sigma-Aldrich) elemental components in evacuated (10 -2 Pa residual pressure) quartz tubes at 1300 K for 5 h. Glassy carbon crucibles were used to synthesize all samples to prevent the manganese reacting with quartz. All samples were subjected to annealing at 600 K for 240 h to reach an equilibrium state. The phase composition of the alloys was identified by means of differential thermal analysis (DTA) and powder X-ray diffraction (PXRD). DTA of the annealed alloys was carried out using the LINSEIS HDSC PT1600 system with a heating rate of 10 K/min. The temperature accuracy was better than 2 K. PXRD data collection was performed at room temperature on a Bruker D2 PHASER diffractometer using CuK a radiation within 2q = 5º-75º.
The concentration cell of type was assembled for EMF measurements in the 300-450 K temperature interval. A glycerol solution of KCl with the addition of 0.1 % MnCl 2 was used as an electrolyte. Glycerol electrolytes are successfully used for the low-temperature thermodynamic analysis of chalcogenide systems [32,33]. In order to avoid having moisture and oxygen in the electrolyte, the glycerol was thoroughly dried and degassed under vacuum at ~450 K and anhydrous chemically pure KCl and MnCl 2 salts were used.
In a cell of type (1), metal manganese was used as a negative electrode, while the positive electrode was an annealed alloy of the Mn-Te system. The phase compositions of all the indicated alloys and correspondence to the phase diagram were confirmed by the PXRD method. As an example, Fig. 1 shows powder diffraction patterns of two selected alloys from these regions. Both electrodes were prepared by pressing the piece of manganese and powdered alloys of the Mn-Te system on a molybdenum wire in the form of pellets weighing 0.5 g.
The electrochemical cell was constructed similar to that in [32,33], which allows measuring the EMF values of several electrodes relative to a reference electrode.
EMF measurements were performed using a Keithley 2100 6 1/2 Digit Multimeter. The first EMF equilibrium values were recorded after keeping the cell at ~360 K for 20-40 h. Values were thereafter obtained every 3-4 h after establishing the desired temperature. The system was considered to achieve an equilibrium state when the EMF values varied by less than 0.5 mV.

Results and discussion
The results of the EMF measurements of the concentration cell of type (1) confirms the existence of two-phase regions, namely MnTe+MnTe 2 and MnTe 2 +Te in the Mn-Te system. The EMF isopleths at 400 K show that the EMF results in each two-phase region remain constant and change dramatically at the border (Fig. 2).
The temperature dependences of the EMF of type (1) cells for two-phase alloys are shown in Fig. 3. As can be seen, the EMF values increase linearly with increasing temperature. The linear relationship between EMF and temperature made it possible to consider the EMF measurement results using the least-squares method via computer software. Experimentally obtained data for temperature (T i ), EMF (E i ) and data associated with the calculation steps for both MnTe + MnTe 2 and MnTe 2 + Te phase regions of the Mn-Te system are listed in Tables 1 and 2. We used the method of processing the results of the EMF measurements described in [34,35]. The obtained linear equation of the type (2) are listed in Table 3 in the literature recommended form:

E a bT t S n S T T
Here n is the number of pairs of E and T values; S E and S b -are dispersions of individual measurements of EMF and constant b; Tthe average absolute temperature; t -the Student's t-test. At the confidence level of 95 %   Table 1. Experimentally obtained data for the temperature (T i ,), EMF (E i ) and data associated with the calculation steps for the MnTe 2 +Te phase region of the Mn-Te system  Table 2. Experimentally obtained data for the temperature (T i ), EMF (E i ) and data associated with the calculation steps for the MnTe+MnTe 2 phase region of the Mn-Te system  and n = 30, the Student's t-test ≤ 2. Using the obtained equations of type (2) and the following thermodynamic expressions: the partial molar functions of manganese in the alloys at 298 K were calculated. The results are given in Table 4. According to the phase diagram of the Mn-Te system, the values of the partial molar functions can be considered thermodynamic functions of the following virtual cell reactions (all substances are solid) [34,35]: According to the (6) and (7)  In the calculations, the values of standard entropies of manganese (32.01±0.13 J/(mol·K)) and tellurium (49.50±0.21 J/(mol·K)) were taken from [25]. The errors were calculated by the error accumulation method. Available literature data and calculated values of the present work are summarized in Tables 5 and 6.
As can be seen from Tables 4 and 5, the values of standard Gibbs free energies of the formation of both MnTe and MnTe 2 compounds obtained by EMF measurements under standard conditions was determined with high accuracy. Our results show a good agreement with the results of hightemperature EMF (580-823 K) [21,22] studies and the combination of EMF with the DSC method [21]. These data are also well matched with the values of Δ f G° of both compounds given in the databases [23][24][25][26].
A comparison of our results for Δ f H° with all available literature data shows that the results calculated for the MnTe compound are in good agreement, except the old calorimetric data of Fabre [29]. For the MnTe 2 compound, our results are very close to the data obtained by a combination of EMF with DSC methods [21] and values recommended in databases [23][24][25][26]. At the same time, the values of the enthalpy of formation calculated by high-temperature EMF  [21,22,27].
In summary, we note that our results on the standard entropies of both compounds are in good agreement with the literature data.

Conclusions
In the present paper, we report the results of a thermodynamic study of the Mn-Te system using the EMF method with a glycerol electrolyte in a temperature range from 300 to 450 K. According to the EMF measurements, the partial molar functions of manganese in two-phase regions, MnTe+MnTe 2 and MnTe 2 +Te at 298 K, as well as the standard thermodynamic functions of the formation and standard entropies of MnTe and MnTe 2 , were calculated. The new mutually consistent values of thermodynamic functions presented by us are the first experimental data obtained from EMF measurements under standard conditions. They supplement and clarify the previously obtained thermodynamic data for manganese tellurides.