Zr Sn System Research Articles

Development of machine learning and empirical interatomic potentials for the binary Zr-Sn system

Zirconium alloys are pivotal structural materials in nuclear reactors. Enhancing their properties and performance necessitates a profound understanding of the interactions between alloying elements and lattice defects. However, the atomic-level mechanisms that account for the effects of tin (Sn) on irradiation-induced defect evolution in zirconium (Zr) are not well understood yet. To bridge this gap, we conducted extensive first-principles calculations and utilized the obtained data to develop two interatomic potentials for the Zr-Sn system: a Zr-Sn moment tensor machine learning interatomic potential (MTP) and a modified embedded atom potential (MEAM) built upon existing unary ones. The reliability of the constructed potentials was validated through systematically comparing relevant physical properties of pure Zr, Sn metals, and Zr-Sn solid solutions, calculated using these potentials, to values obtained from density functional theory calculations and/or experiments. The developed potentials exhibit high fidelity and accuracy in capturing the behavior of the Zr-Sn system. Their applicability in terms of both reliability and computational efficiency was also discussed. These potentials provide a solid foundation for further exploration of the atomic-scale behavior of the Zr-Sn alloy systems, thereby facilitating the continuous optimization and application of the zirconium alloys.

CALPHAD assessment of bio-oriented Ti–Zr–Sn system and experimental validation in Ti/Zr-rich alloys

The development of CALPHAD-type thermodynamic database for Ti or Zr based biomedical alloys has been spurred by the increased interest in efficiently tailoring an alloy composition to obtain high stability of β_bcc, low Young's modulus, and free of detrimental phases. However, the thermodynamic prediction is not adequate to be performed without the information of key sub-ternary Ti–Zr–Sn system. In present work, the thermodynamic assessment of Ti–Zr–Sn system is performed via a critical evaluation of phase equilibria and microstructure development in this ternary system. The partial isothermal sections at 1323 K and 1473 K with Sn content below 40 at. % are obtained by analyzing chemical compositions and crystal structures of individual phases in the annealed alloys. The composition homogeneity range of most phases is validated to favor a ternary extension paralleling to the Ti–Zr axis. Particularly, β_bcc and η phases (with the chemical composition (Ti, Zr)5Sn3+x) show complete solubility of Ti and Zr from Ti–Sn edge to Zr–Sn edge. With the database, negligible ternary solubility of Zr4Sn phase, microstructure development in the as-cast samples, and the controversial conclusions in literature are discussed. Most of the experimental findings, including equilibrium phase constitution, solidification sequence, DSC signals, projections of liquidus, are reproduced in a self-consistent way. The work moves towards the completeness of multi-component Ti/Zr thermodynamic database. It can be used for composition design of novel metastable β-type biomedical alloys.

Measurement of Diffusion Coefficients in the bcc Phase of the Ti-Sn and Zr-Sn Binary Systems

Sn and Zr are two important alloying elements in low-modulus biomedical titanium alloys, yet experimental data on Sn diffusion in bcc Ti and bcc Zr are still very limited in the literature, and thus were systematically measured in the present study using solid–solid diffusion couples (SSDCs) and novel liquid–solid diffusion couples (LSDCs). Both interdiffusion and impurity diffusion coefficients in the bcc phase of the Ti-Sn and Zr-Sn systems were extracted with forward-simulation analysis (FSA), and show good agreement with existing literature. The interdiffusion coefficients in the Ti-Sn system at six temperatures, from 950 °C to 1200 °C, extend experimental measurements to a much wider composition range, and the interdiffusion coefficients in the Zr-Sn system at 1200 °C, 1150 °C, and 1100 °C are the first such data experimentally measured. The data obtained from this study, together with our previous data for the Ti-X (X = Cr, Hf, Mo, Nb, V, Zr) systems, provide reliable experimental inputs to improve the mobility databases for advanced Ti alloys development. In addition, the excellent agreement between the LSDCs and SSDCs results validates the reliability of this novel approach by combining LSDC experiments and FSA in evaluating diffusion coefficients at elevated temperatures.

Insight into structural, mechanical, electronic and thermodynamic properties of intermetallic phases in Zr–Sn system from first-principles calculations

The structural, phase stabilities, mechanical, electronic and thermodynamic properties of intermetallic phases in Zr–Sn system are investigated by using first-principles method. The equilibrium lattice constants, enthalpy of formation (ΔHform) and elastic constants are obtained and compared with available experimental and theoretical data. The configuration of Zr4Sn is measured with reasonable precision. The ΔHform of five hypothetical structures are obtained in order to find possible metastable phase for Zr–Sn system. The mechanical properties, including bulk modulus, shear modulus, Young's modulus and Poisson's ratio, are calculated by Voigt–Reuss–Hill approximation and the Zr5Sn4 and Zr5Sn3 show excellent mechanical properties. The electronic density of states for Zr5Sn4, Zr5Sn3 and cP8-Zr3Sn are calculated to further investigate the stability of intermetallic compounds. Through the quasi-harmonic Debye model, the Debye temperature, heat capacity and thermal expansion coefficient under temperature of 0–300K and pressure of 0–50GPa for Zr5Sn3 and Zr5Sn4 are deeply investigated.

The heat capacity in two-phase regions and the heat of phase transformations of some alloys in Zr-Nb and Zr-Sn systems

Analytical expressions are given for the phase boundaries of diagrams of state for Zr-Nb and Zr-Sn systems. Thermodynamically justified temperature dependences of heat capacity of Zr-1% Nb, Zr-2.5% Nb, Zr-1.5% Sn, and Zr-2.5% Sn alloys in two-phase regions are given and recommended for use. The heats of second-order phase transformations α(Zr) ⟺ β(Zr) in alloys of Zr-Nb and Zr-Sn binary systems are obtained, and the heats of monotectoid reaction α(Zr)+β(Nb) ⟺ β(Zr) in the Zr-Nb system and of peritectoid reaction β(Zr)+Zr4Sn ⟺ α(Zr) in the Zr-Sn system are calculated.

Isothermal section of the Ti–Zr–Sn ternary system at 473 K

Ti–Zr–Sn alloys were obtained by melting pure elements in an arc furnace. Mainly by the method of X-ray diffraction (XRD), the character of phase equilibrium at 473 K is studied for the Ti–Zr–Sn system. The isothermal section at 473 K consists of 11 single phase regions, 16 binary phase regions and 6 ternary phase regions. The existence of a binary compound Ti 2Sn 3 was confirmed in the isothermal section. Zr 5Sn 4 was not observed and no ternary compound is found in the ternary system. The solubility of Zr in Ti 3Sn is up to 5 at.% Zr. The solubility of Ti in ZrSn 2 is about 4 at.% Ti. There is continuous solid solubility between Ti 5Sn 3 and Zr 5Sn 3.

Phase stability and elastic modulus of Ti alloys containing Nb, Zr, and/or Sn from first-principles calculations

The alloying effects of Nb, Zr, and/or Sn on the phase stability and elastic properties of Ti are investigated by using a first-principles method. Our calculation results indicate that a carefully designed Ti–Nb–Zr–Sn system can be a good candidate for low modulus biomedical materials. We find that the well-known correlation between the e∕a ratio and both elastic and phase stabilities for Ti alloyed with transition metal elements breaks down for the Ti–Sn alloy.

The melting diagram of the Ti–Zr–Sn system below 40 at.% Sn

By the methods of DTA, X-ray diffraction, metallography and EPMA, phase equilibria in the Ti–Zr–Sn system at <40 at.% Sn were studied. The partial liquidus and solidus projections, and the melting diagram (solidus + liquidus) were constructed. The liquidus surface is characterized by the presence of primary crystallization regions of (βTi) (β), (Ti 3Sn) (α 2) and (Ti,Zr) 5Sn 3 (5/3) phases. The solidus surface is characterized by the presence of two three-phase fields, β + α 2 + 5/3 and α 2 + (Ti 2Sn)(2/1) + 5/3. The first one results from an invariant four-phase equilibrium L U + α 2 ↔ β + 5/3 taking place at 1510 ± 10 °C. The invariant point U is located at the composition ∼53Ti–30Zr–17Sn. The second three-phase region results from an equilibrium at 1515 °C with participation of L + α 2 + 5/3 + 2/1 phases. The character of the equilibrium is not determined. Two invariant three-phase equilibria were found, L e 1 ↔ α 2 + 5 / 3 at 1600–1650 °C and L e 4 ↔ β + 5 / 3 at 1423 °C.

Isothermal section at 1400 °C of the Ti–Zr–Sn system

By the methods of X-ray diffraction, metallography and microprobe examinations the character of phase equilibria at 1400 °C is studied for the Ti–(Ti,Zr) 5Sn 3–Zr region of the Ti–Zr–Sn system. The isothermal section at 1400 °C is constructed. This is similar to the solidus surface and is characterized by two 3-phase regions: 〈βTi,Zr〉 + Ti 3Sn + (Ti,Zr) 5Sn 3 and Ti 3Sn + Ti 2Sn + (Ti,Zr) 5Sn 3. Solubility of Sn in 〈βTi,Zr〉 solid solution is between 10 and 15 at.% Sn. Solubility of zirconium in Ti 3Sn is about 12 at.%.

Structural stability of intermetallic phases in the Zr–Sn system

A thermodynamic description of the intermetallic compounds in the Zr–Sn binary system has been obtained using total energy calculations by means of the Vienna ab initio simulation package. Our calculations show that hexagonal compounds Zr5Sn4 and Zr5Sn3 are the most stable phases in the Zr–Sn binary system. Their high stability is found to be due to hybridization of the Sn 5p with Zr 4d electronic states. Based on the calculated energies, the conclusion is made that Zr substitution on the Sn sites takes place in the Zr4Sn phase, which accounts for the unusual stoichiometry of this Cr3Si structure type compound.

The phase diagram of the Lu–In system

The phase diagram of the Lu–In system has been investigated in the range 25–100 at.% In, using differential thermal analysis, metallographic analysis, X-ray diffraction and electron microscopy. Seven intermediate phases have been found: LuIn 3 (AuCu 3 type), LuIn 2 (ZrGa 2 type), Lu 3In 5 (Tm 3Ga 5 type), LuIn (AuCu type), Lu 5In 4 (Ti 5Ga 4 type), Lu 5In 3 (Mn 5Si 3 type) and Lu 2In (Ni 2In type). Some of them were already known, while the existence of new phases recently discovered has been confirmed. Lu 5In 3 and Lu 5In 4 give rise to a continuous solid solution range as they occur in the Zr–Sn system between Zr 5Sn 3 and Zr 5Sn 4. At least three eutectics occur at about 23 at.% In and 1185°C, 58 at.% In and 960°C, less than 1 at.% In and 156°C.

Diffusion and chemical activity of Zr-Sn and Zr-Ti systems.

A modified evaporation method was used to determine the diffusion coefficients and the emission rates of Sn and Ti in Zr-Sn and Zr-Ti, respectively, at temperatures between 1605 and 1970 K. Results show that both Sn and Ti diffuse in their respective alloys via a vacancy mechanism. Comparison with data in the literature reveals that the activation energy for diffusion of Sn in Zr-Sn, with Sn content between 3 and 5 at.? is relatively constant from 1200 to 1970 K. From the measured emission rates, values of 103 and 98 kcal/mol were obtained for the enthalpies of sublimation for Sn and Ti in their alloys. With a comparison of the solute vapor pressures with those of the pure elements, partial molar free energies, entropies, and enthalpies for the two systems were determined in the temperature range investigated. The Zr-Sn system shows a very large negative heat of formation (-33 kcal/mol) whereas the Zr-Ti system behaves quite ideally, in agreement with phase-diagram predictions.

The solubility of tin in α and β zirconium below 1000°C

The zirconium-rich region of the Zr-Sn system below 1000°C was studied by scanning electron microscopy, electrical resistivity, electron microanalysis and optical microscopy. We used four alloys with the following compositions: 0.5, 2.3, 3.3 and 7.6 at.% Sn, produced from Zr of 99.99% purity. From the experimental observations we obtain the α/(α + β) and α/(α + Zr 4Sn) boundaries, while the (α + β)/β boundary was calculated applying the van't Hoff relation. The influence of iron and oxygen impurities on the (α + β) field was evaluated. A composition slightly different from the stoichiometric value was found for the Zr 4Sn intermediate phase at 950°C.