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Evaluation and thermodynamic optimization of phase diagram of lithium niobate tantalate solid solutions

This study experimentally determined the heats of fusion for lithium niobate and lithium tantalate end members via DTA and XRF analysis, then utilized these data within a thermodynamic solution model and Calphad optimization to construct and refine the phase diagram of their solid solutions, ultimately deriving the segregation coefficient as a function of tantalum concentration.

Original authors: Umar Bashir, Detlef Klimm, Michael Rusing, Matthias Bickermann, Steffen Ganschow

Published 2026-10-14

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CC BY 4.0

Original authors: Umar Bashir, Detlef Klimm, Michael Rusing, Matthias Bickermann, Steffen Ganschow

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the world of advanced materials, some crystals are more than just beautiful stones; they are the silent engines behind modern technology. Among these, two specific compounds, lithium niobate and lithium tantalate, stand out for their ability to manipulate light and electricity. Scientists have long known that these two materials can be mixed together, much like blending two types of clay, to create a new material with properties that can be tuned for specific tasks. By adjusting the ratio of one ingredient to the other, researchers can change how the material bends light or responds to electric fields, opening doors for better sensors, lasers, and electronic devices. However, there is a catch. When you melt these two materials together to grow a crystal, they do not always mix perfectly. One ingredient often prefers to stay in the liquid while the other solidifies first, leading to a final product that is uneven inside. This unevenness, known as segregation, can ruin the performance of the crystal, making it difficult to use for high-precision applications.

To solve this puzzle, a team of researchers from Germany set out to map the exact behavior of these mixed materials as they transition from liquid to solid. They focused on the lithium niobate–lithium tantalate system, aiming to create a precise guide, or phase diagram, that shows exactly what happens at every temperature and mixture ratio. Previous studies had offered a rough sketch, but the details were blurry, particularly regarding how much the two materials separated during the cooling process. The team began by growing large, high-quality crystals using a method that slowly pulls a seed crystal out of a molten bath. They carefully measured the chemical makeup of these crystals to ensure they were uniform, using a technique that maps the distribution of elements with high precision. They found that while some crystals had significant clumps of one element or the other, others were remarkably homogeneous, providing a clean slate for their experiments.

With these well-characterized crystals in hand, the researchers turned to a thermal analyzer to watch how the materials behaved when heated and cooled. They observed the exact temperatures at which the solid crystals began to melt and when the liquid fully solidified. By repeating this process, they could see how the internal structure of the material changed after it had been melted and re-frozen. The data revealed that the separation between the melting and freezing points was not uniform across all mixtures; it was widest for certain combinations and narrowed as the mixture approached the pure forms of either material. This information was crucial, as it allowed them to calculate the energy changes involved in mixing the two substances. They used a computer model to simulate the thermodynamics of the system, feeding in the experimental data along with known properties of the pure ingredients. This model helped them construct a detailed phase diagram that accurately predicts the behavior of the mixture under any condition.

The results painted a clearer picture than ever before. The new map confirmed that the two materials mix completely in all proportions, but it also quantified exactly how much they tend to separate during growth. The researchers calculated a value called the segregation coefficient, which tells us how much of one ingredient ends up in the solid crystal compared to the liquid melt. They found that for every mixture, the crystal tends to pull in more of the tantalum-rich component than the liquid has, leaving the remaining liquid poorer in that ingredient as the crystal grows. This means that if you start with a mixture that is half-and-half, the beginning of the crystal will be much richer in one component, and the end will be much poorer, unless the growth process is carefully controlled. The study also revealed that the energy required to mix these materials is lower than if they were an ideal, perfect mixture, indicating a strong natural tendency for the atoms to interact in a specific way.

By combining precise measurements with sophisticated modeling, the team has provided a reliable roadmap for growing these crystals. This work does not just fill a gap in scientific knowledge; it offers a practical tool for engineers and scientists who need to grow large, uniform crystals for real-world devices. The new phase diagram allows them to predict exactly how the composition will change from the top to the bottom of a crystal, enabling them to adjust their growth parameters to minimize unevenness. While the materials themselves are complex, the path forward is now clearer: by understanding the exact thermal and chemical dance of these atoms, researchers can finally grow the high-quality, homogeneous crystals needed to power the next generation of optical and electronic technologies.

Technical Summary: Evaluation and Thermodynamic Optimization of the Phase Diagram of Lithium Niobate Tantalate Solid Solutions

Problem Statement
Lithium niobate (LiNbO₃, LN) and lithium tantalate (LiTaO₃, LT) are critical oxide compounds for functional electronics, yet their solid solutions (LiNb₁₋ₓTaₓO₃, LNT) present significant challenges in crystal growth. While LNT solid solutions offer tunable physical properties, such as birefringence and piezoelectric coefficients, across the entire composition range, the growth of homogeneous single crystals is hindered by a large separation between the solidus and liquidus lines in the phase diagram. This separation causes compositional inhomogeneity (segregation) during growth, particularly in the Czochralski (CZ) method. Previous studies on the LN-LT phase diagram have yielded conflicting results, often relying on congruent melting compositions or failing to account for the distinction between stoichiometric and congruent melting points. Consequently, a detailed, thermodynamically optimized phase diagram covering the full composition range between congruent compositions is required to understand and mitigate segregation effects.

Methodology
The study employed a combined experimental and thermodynamic modeling approach:

Crystal Growth: Large volume LNT single crystals (5 cm length, 1.5 cm diameter) were grown using the Czochralski method with induction heating. Starting materials were congruent melting compositions of LN and LT (averaged at 48.4 mol% Li₂O).
Characterization:
- Elemental Analysis: Energy dispersive micro X-ray fluorescence (μ-XRF) was used to map the distribution of Nb and Ta, assessing crystal homogeneity and identifying segregation gradients.
- Thermal Analysis: Differential Thermal Analysis (DTA) was performed on as-grown and recrystallized samples to determine solidus and liquidus temperatures. The onset of melting peaks defined the solidus, while the return to the baseline defined the liquidus.
Thermodynamic Modeling:
- End Member Data: Thermodynamic parameters for pure LN and LT were generated using the Neumann-Kopp rule based on constituent oxides (Li₂O, Nb₂O₅, Ta₂O₅) and corrected using experimental heat capacity data.
- Optimization: The CALPHAD method was applied using the FactSage software. A Redlich-Kister polynomial expansion was used to model the excess Gibbs free energy ( $G_{excess}$ ) of the solid solution, assuming the liquid phase behaves ideally. Experimental DTA data and heats of fusion served as input constraints for the optimization.

Key Results

Phase Diagram Optimization: A pseudo-binary phase diagram was successfully constructed for the LN-LT system. The diagram confirms complete miscibility across the entire composition range ( $x=0$ to $x=1$ ).
Solidus-Liquidus Separation: The optimized diagram reveals a separation between solidus and liquidus lines that is narrower than previously reported by Peterson et al., though still significant enough to cause segregation. The separation is widest for intermediate compositions and decreases as the system approaches the end members.
Homogeneity Analysis: μ-XRF mapping demonstrated that crystals grown at the Institute of Crystal Growth (IKZ) exhibit high homogeneity (composition gradients $\Delta x < 1\%$ in many samples), contrasting with the severe segregation ( $\Delta x = 40\%$ ) observed in some previous studies. DTA results indicated that inhomogeneous samples exhibit prolonged melting ranges, particularly in second heating cycles due to segregation-induced inhomogeneity.
Thermodynamic Parameters: The excess Gibbs energy ( $G_{excess}$ ) of the solid solution was found to be negative (exothermic), with a minimum at $x=0.5$ ($-2703$ J/mol), indicating a deviation from ideal mixing behavior. The interaction coefficients ( $L_0, L_1, L_2$ ) were derived, with $L_0$ showing the dominant effect.
Segregation Coefficient: The segregation coefficient ( $K = C_s/C_l$ ) for Tantalum was calculated from the phase diagram. $K$ is consistently greater than unity for all compositions, approaching unity only as the composition nears pure LT. This implies that during solidification, the melt becomes progressively depleted in Ta, leading to a Ta-rich initial crystal section and a Ta-depleted final section.
Scheil Simulation: Simulations of the solidification process for a starting composition of $x=0.5$ predicted a significant initial Ta concentration in the crystal ( $x \approx 0.85$ ) that decreases along the growth axis, eventually reaching pure LN characteristics as the melt is depleted.

Significance and Claims
The paper claims to provide the first detailed thermodynamic optimization of the LN-LT phase diagram based on a solution model that accounts for excess enthalpies of mixing. By utilizing high-quality, homogeneous crystals and precise DTA measurements, the authors establish a reliable reference for the solidus and liquidus boundaries. The study emphasizes that understanding the specific segregation behavior (where $K > 1$ ) is essential for growing crystals with uniform composition for applications in ferroelectrics and nonlinear optics. The work validates the use of the CALPHAD method for this system and provides the necessary thermodynamic parameters (including $G_{excess}$ ) to predict phase behavior and guide the growth of optimized LNT single crystals.

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