Several synthesis techniques are available for the preparation of Sn_1−xEr_xTe crystals, each offering specific advantages depending on the desired crystal quality, size, and compositional uniformity. Commonly used approaches include melt-based single-crystal growth methods, solid-state reactions, and vapor-phase techniques. A comparative overview of these methods is presented in Table 1.

Considering the objectives of obtaining large, compositionally uniform single crystals suitable for phase and thermal analysis, the vertical Bridgman technique was selected as the primary growth method. This approach has been demonstrated to be particularly effective for IV–VI semiconductors and their doped derivatives.

Single crystals of Sn_1−xEr_xTe (x = 0.00–0.10) were grown using the vertical Bridgman method under controlled conditions. High-purity elemental tin (Sn, 99.999%), tellurium (Te, 99.999%), and erbium (Er, 99.99%) were weighed according to the desired stoichiometric ratios and sealed in evacuated quartz ampoules (≈10⁻⁴ Pa).

The ampoules were heated to approximately 1150°C, exceeding the melting temperatures of all constituents, and held at this temperature for 12–24 h to ensure complete melting and homogenization of the melt. During homogenization, periodic rocking of the ampoule was applied to promote compositional uniformity.

Crystal growth was achieved by slowly moving the ampoule through the crystallization zone at a cooling rate of 1–3°C h⁻¹, which is critical for suppressing multi-nucleation and obtaining large, defect-minimized single crystals. After crystallization, the samples were cooled to room temperature at a rate of approximately 10°C h⁻¹ to reduce thermal stress and prevent cracking.

A combination of structural, microstructural, and thermal analysis techniques was employed to characterize the synthesized Sn_1−xEr_xTe crystals.

The synthesized Sn_1−xEr_xTe crystals were characterized using a combination of structural, microstructural, and thermal analysis techniques. These analytical methods allowed the identification of phase composition, crystal structure, morphology, and elemental distribution in the samples. The instruments used and their corresponding measurement conditions are summarized in Table 2.

XRD measurements were performed to identify crystalline phases and determine lattice parameters. SEM was used to examine surface morphology and crystal quality, while EDS provided qualitative and quantitative information on erbium incorporation and distribution. DTA measurements were carried out to identify phase transitions and thermal stability regions. For selected samples, ICP–MS and Raman spectroscopy were employed to confirm erbium concentration and probe local lattice distortions.

The experimental methodology was designed to establish reliable correlations between growth conditions, erbium concentration, and phase stability in Sn_1−xEr_xTe single crystals. Particular emphasis was placed on identifying solubility limits, detecting secondary phase formation, and understanding the thermal behavior of Er-doped SnTe systems. Detailed results and discussion of structural evolution, phase composition, and thermophysical properties are presented in subsequent sections.

The experimental results obtained for Sn_1−xEr_xTe single crystals show good agreement with previously reported studies on lanthanide-doped SnTe systems. A comparative overview of key structural and thermoelectric parameters is presented in Table 3.

The close similarity in lattice contraction and transport behavior confirms that erbium acts analogously to other lanthanide dopants. In particular, the enhancement of the Seebeck coefficient and the reduction of thermal conductivity observed in the present study fall within the same range as Ce- and Yb-doped SnTe, indicating that Er is an effective dopant for tuning thermoelectric performance without fundamentally altering the host lattice.

The influence of erbium doping on the properties of SnTe can be attributed to partial substitution of Sn atoms by Er ions within the NaCl-type lattice. Despite the valence mismatch (Er³⁺ vs. Sn²⁺), charge compensation occurs through defect formation, which significantly modifies phonon and charge-carrier transport [17].

Two dominant mechanisms govern the observed behavior: 1.

Enhanced phonon scattering. The large mass difference and local strain fields introduced by Er substitution increase phonon scattering, leading to a pronounced reduction in lattice thermal conductivity.

A summary of these effects is given in Table 4.

These mechanisms are consistent with models reported for lanthanide-doped chalcogenide thermoelectrics and confirm that Er doping modifies both electronic and phononic transport pathways.

The emergence of secondary phases such as Er₂Te₃ and ErTe at erbium concentrations of x ≥ 0.05 indicates that the solubility limit of Er in the SnTe lattice is relatively low. This observation is consistent with predictions from Sn–Ln–Te phase diagrams and earlier experimental reports.

Beyond the solubility threshold, several adverse effects become evident:

Degradation of crystallinity due to lattice distortion,

To mitigate these effects, erbium concentration should be maintained below approximately x = 0.03. In addition, post-growth annealing and careful control of cooling rates may improve dopant distribution and suppress secondary phase formation.

The analysis of experimental results indicates that several technological and materials-related challenges arise during the synthesis of Sn_1−xEr_xTe crystals. These challenges mainly include the formation of secondary phases due to exceeding the Er solubility limit, an increase in defect density caused by lattice mismatch and phase boundary strain, a reduction in electrical conductivity associated with enhanced carrier scattering, and mechanical fragility resulting from thermal stress accumulation. To mitigate these issues, it is recommended to optimize Er concentration, apply post-growth annealing, optimize the cooling rate, use co-doping strategies, and implement controlled stress management approaches (Table 5).

The combined structural and transport analyses demonstrate that erbium doping provides an effective route for reducing thermal conductivity and enhancing the Seebeck coefficient in SnTe. However, excessive doping introduces phase instability and electrical conductivity degradation, highlighting the need for precise compositional control.

Future optimization strategies should focus on:

Identifying the exact solubility limit through fine-step doping studies,

Overall, the present results confirm that carefully controlled erbium doping can significantly improve the thermoelectric performance potential of SnTe while preserving structural stability within an optimal doping window.

SnTe and its structural analogues GeTe and PbTe, as well as solid solutions based on these compounds, play a significant role in the development of thermoelectric generators. Although the thermoelectric efficiency of pristine SnTe is relatively low, its good chemical and structural compatibility with other thermoelectric materials enables its practical use as a functional component in thermoelectric systems. Consequently, enhancing the thermoelectric performance of SnTe remains a relevant and important research challenge. Various approaches have been proposed to address this issue, including controlled modification of stoichiometry and the introduction of suitable dopants or additives.

Differential thermal analysis (DTA) is one of the most widely used physicochemical methods for investigating phase transformations and constructing phase diagrams. This technique allows detailed examination of thermal effects associated with chemical reactions, dissociation processes, solid–solid and solid–liquid phase transitions, as well as qualitative and quantitative determination of phase composition and transition enthalpies.

Lanthanide-containing compounds and solid solutions are distinguished by their high melting temperatures, enhanced mechanical strength, preservation of semiconducting properties at elevated temperatures, and improved thermoelectric performance. By modifying the chemical composition of such materials, it is possible to obtain new substances with tailored structural and functional properties. In this context, studying the influence of lanthanide elements on the structure and properties of SnTe, a promising thermoelectric compound, represents an urgent and scientifically relevant task.

In the present work, the differential thermal analysis method was applied to investigate the SnTe–ErTe system. To construct the phase (state) diagram, a series of alloys with a mass of 2 × 10⁻³ kg each were prepared using different component ratios, with composition steps of 1 mol%. The samples were synthesized in evacuated quartz ampoules; the air was pumped down to a residual pressure of 0.0133 Pa, after which the ampoules were sealed. Following synthesis, the alloys were crushed and loaded into glass containers designed for thermographic measurements.

Al₂O₃ was used as the reference material for DTA measurements. The reference substance was placed in identical thermography ampoules, evacuated, and sealed under the same conditions as the samples. Differential thermal analysis was carried out using an NTR-74 pyrometer, with both heating and cooling rates set to 9°C/min.

Based on the combined results of DTA and X-ray phase analysis (XRPA), the phase diagram of the SnTe–ErTe system was constructed. The resulting state diagrams are presented in Fig. 1a,b, illustrating the phase equilibria and transformation temperatures within the investigated composition range.

Fig. 1a presents the equilibrium phase diagram of the Er–Te binary system as a function of temperature and atomic percent tellurium. The diagram reveals a complex phase behavior characterized by the formation of several intermediate erbium telluride compounds and well-defined phase transformation boundaries.

On the erbium-rich side, solid erbium (Er) coexists with intermetallic phases at relatively low tellurium concentrations. As the Te content increases, the formation of stoichiometric intermediate compounds such as ErTe, Er₂Te₃, and ErTe₂ is observed. These compounds are separated by narrow homogeneity ranges, indicating limited solid solubility and strong chemical affinity between erbium and tellurium.

The compound ErTe appears as a stable intermediate phase with a congruent melting behavior, as evidenced by the sharp phase boundary near its stoichiometric composition. At higher tellurium concentrations, Er₂Te₃ and ErTe₂ phases form sequentially, each exhibiting distinct phase transition temperatures. The presence of these phases confirms that the Er–Te system is dominated by ordered intermetallic compounds rather than extensive solid solutions.

On the tellurium-rich side of the diagram, the liquid phase (L) is stable over a wide temperature range, followed by crystallization into solid tellurium (Te) at lower temperatures. The eutectic and peritectic reactions identified in the diagram reflect the thermodynamic complexity of the system and are consistent with strong bonding interactions between Er and Te atoms.

The dashed liquidus line indicates metastable or experimentally determined boundaries, suggesting sensitivity of the phase equilibria to synthesis conditions and cooling rates. This aspect is particularly important for crystal growth processes, as deviations from equilibrium cooling may promote the formation of secondary phases.

Overall, the Er–Te phase diagram demonstrates that erbium has limited solubility in tellurium-rich matrices, and excess erbium tends to form secondary erbium telluride phases. This behavior has direct implications for Er-doped SnTe systems, where exceeding the solubility limit leads to the precipitation of ErTe- and Er₂Te₃-type phases, as confirmed by XRD and DTA results in the present study. Understanding the Er–Te phase equilibria therefore provides a crucial thermodynamic basis for interpreting phase stability, solubility limits, and microstructural evolution in Sn_1−xEr_xTe solid solutions. Fig. 1b illustrates the state diagram of the SnTe–ErTe quasi-binary system, constructed on the basis of differential thermal analysis (DTA) and X-ray phase analysis results. The diagram reflects the phase equilibria between tin telluride and erbium telluride components and provides important insight into the solubility limits, phase stability, and interaction mechanisms within the system.

The diagram is characterized by a limited mutual solubility of the components, indicating that SnTe and ErTe do not form an extended continuous solid solution. Instead, the system is dominated by distinct phase fields separated by narrow compositional regions. In the SnTe-rich region, the stability field of cubic SnTe is clearly defined, with only a small tolerance for erbium incorporation. This confirms that erbium acts as a low-solubility dopant in the SnTe lattice.

As the ErTe content increases, the system transitions from the SnTe solid solution region into multiphase domains containing intermediate erbium telluride compounds. The presence of Er₂Te₃ and ErTe phases indicates that excess erbium beyond the solubility limit preferentially forms secondary phases rather than substituting into the SnTe lattice. These phase boundaries are sharp, suggesting strong chemical interactions and thermodynamic stability of erbium tellurides.

The central region of the diagram reveals invariant reactions involving SnTe, ErTe, and Er₂Te₃ phases, which are associated with eutectic or peritectic transformations. These reactions are consistent with the thermal effects observed in DTA thermograms and confirm the non-ideal behavior of the system. The formation of such invariant points plays a critical role in determining the microstructural evolution during crystal growth and cooling.

On the erbium-rich side, the diagram is dominated by ErTe-based compounds with negligible solubility of SnTe. This asymmetry in solubility behavior reflects the significant differences in ionic radius, valence state, and bonding characteristics between Sn and Er atoms. Consequently, substitutional incorporation of Er into Sn sites is energetically unfavorable beyond low concentrations.

From a practical standpoint, the SnTe–ErTe state diagram demonstrates that single-phase Sn_1−xEr_xTe crystals can only be obtained at low erbium concentrations (x ≲ 0.02–0.03). At higher erbium contents, the system inevitably undergoes phase separation, leading to the precipitation of ErTe- and Er₂Te₃-type secondary phases. These findings are in full agreement with the structural and microstructural observations obtained by XRD and SEM analyses in the present study.

Overall, the constructed SnTe–ErTe state diagram provides a thermodynamic framework for understanding the phase behavior of erbium-doped SnTe systems. It confirms that precise control of erbium concentration is essential for maintaining phase purity and optimizing the structural and thermoelectric properties of Sn_1−xEr_xTe materials.

To date, the phase diagrams of the binary Er–Sn, Er–Te, and Sn–Te systems have been reported separately in the literature. At room temperature, the Er–Sn system is known to contain several intermetallic compounds. According to Massalski, five stable phases—Er₂Sn, Er₅Sn₃, Er₁₁Sn₁₀, ErSn₂, and ErSn₃—were identified. Subsequent reinvestigation of the Sn-rich region by Palenzona and Manfrinetti revealed the additional existence of Er₂Sn₅. Later studies of ternary systems such as Co–Er–Sn and Cu–(Sm,Er)–Sn confirmed the stability of Er₅Sn₃, Er₁₁Sn₁₀, ErSn₂, Er₂Sn₅, and ErSn₃ at 670 K, while investigations of the Ag–Er–Sn system further verified the presence of Er₅Sn₃, Er₁₁Sn₁₀, ErSn₂, Er₂Sn₅, and Er₃Sn₇ under similar thermal conditions.

In contrast, the Er–Te binary system is structurally simpler and consists of three well-established compounds—ErTe, Er₂Te₃, and ErTe₃—whereas the Sn–Te system forms only a single stable intermetallic phase, SnTe. Despite the availability of binary phase diagram data, systematic experimental information on the Er–Sn–Te ternary system, particularly at room temperature, remains limited.

The primary objective of the present study is therefore to experimentally investigate the Er–Sn–Te phase diagram using the equilibrated alloy method and to construct a detailed isothermal section at room temperature. To achieve this, 15 binary and 54 ternary alloys, each with a mass of approximately 2 g, were synthesized and annealed under controlled conditions. These data provide essential phase-equilibrium information relevant to the development of Sn–Te-based diluted magnetic semiconductors (DMS). The crystallographic parameters of the identified binary compounds are summarized in Table 1.

In addition, a series of Sn_1−xEr_xTe solid solutions was synthesized to evaluate the solubility of erbium in the SnTe lattice. X-ray diffraction (XRD) analysis revealed that the maximum solubility of Er in SnTe is approximately 7.5 at.%. Single-phase SnTe with a cubic NaCl-type structure was obtained for compositions in the range x = 0–0.07. When the erbium content exceeded this limit (x ≥ 0.08), a secondary ErTe phase appeared, indicating the onset of phase separation.

Representative XRD patterns for Sn_1−xEr_xTe (x = 0.04, 0.07, and 0.08) are presented in Fig. 2, clearly demonstrating the transition from a single-phase solid solution to a multiphase state. Furthermore, the dependence of the lattice parameter a on erbium concentration x, shown in Fig. 3, exhibits a systematic contraction of the unit cell with increasing Er content, confirming partial substitution of Sn by Er within the solubility range.

Overall, these results establish the solubility limit of erbium in SnTe and provide a reliable experimental basis for understanding phase formation and structural stability in the Er–Sn–Te system.

The lattice parameter a exhibits a gradual decrease from 0.6346 nm to 0.6326 nm with increasing erbium concentration, indicating effective incorporation of Er atoms into the SnTe crystal lattice. This systematic lattice contraction reflects the substitution of Sn by the smaller Er ions and confirms the formation of a substitutional solid solution. Based on these observations, the solubility range of erbium in SnTe is estimated to extend from x = 0.0 to x ≈ 0.075. Accordingly, the maximum solid solubility of Er in SnTe at room temperature is approximately 7.5 at.%.

No significant homogeneity ranges were detected for other phases in the Er–Sn–Te system at room temperature, suggesting that these compounds exist as line compounds with limited compositional flexibility.