Bcc Ti Research Articles

Mechanical properties of pure elements from a comprehensive first-principles study to data-driven insights

Unraveling mechanical properties from fundamental is far from complete despite their vital role in determining applicability and longevity for a given material. Here, we perform a comprehensive study related to mechanical properties of 60 pure elements in bcc, fcc, hcp, and/or diamond structures by means of pure alias shear and pure tensile deformations via density functional theory (DFT) based calculations alongside a broad review of existing literature. The present data compilation enables a detailed correlation analysis of mechanical properties, focusing on DFT-based ideal shear and tensile strengths ( and ), stable and unstable stacking fault energies ( and ), surface energy (), and vacancy activation energy (); and experimental hardness (), ultimate tensile strength (), fracture toughness (), and elongation (). The present work examines models, identifies outliers, and provides insights into mechanical properties, for example, (i) is correlated by , by or , and by ; (ii) data outliers are identified for Cr (related to , , , and ), Be (, , , and ), Hf ( and ), Yb (all properties), and Pt ( vs. ); and (iii) , , , , , , and are highly correlated to elemental attributes, while , , and especially are less correlated due mainly to experimental uncertainty. In particular, the present data compilation provides a solid foundation to model properties such as and of multicomponent alloys and of unstable structures like bcc Ti, Zr, and Hf.

High-throughput determination of interdiffusivity and atomic mobilities in bcc Ti–Cr–Mo alloys

A comprehensive understanding of the diffusion coefficients and atomic mobilities in the Ti–Cr–Mo system is crucial for establishing an atomic mobility database for titanium-based high-strength titanium alloys. In the present work, nine sets of solid/solid diffusion couples were prepared and measured in bcc Ti–Cr–Mo alloys, with the temperatures ranging from 1373 to 1473 K. Scanning electron microscopy (SEM), and Electro Probe Micro-Analysis (EPMA) techniques were used to respectively test its microstructure and composition distance. The diffusion coefficients in bcc Ti–Cr–Mo alloys were determined using the Matano-Kirkaldy method and numerical inverse method respectively. The diffusion coefficients obtained from the above two methods exhibit good consistency. The atomic mobility parameters for the Ti–Cr–Mo systems were provided with the assistance of HitDIC software. A three-dimensional plot of interdiffusivities was generated for chromium and molybdenum contents ranging from 0 to 20 mol % and 0–14 mol %. Moreover, the application of the Arrhenius equation enabled the determination of changes in frequency factors and activation energies concerning temperature and composition.

Machine Learning-Based Prediction of Elastic Properties Using Reduced Datasets of Accurate Calculations Results

In this paper, the applicability of machine learning for predicting the elastic properties of binary and ternary bcc Ti and Zr disordered alloys with 34 different doping elements is explored. The original dataset contained 3 independent elastic constants, bulk moduli, shear moduli, and Young’s moduli of 1642 compositions calculated using the EMTO-CPA method and PAW-SQS calculation results for 62 compositions. The architecture of the system is made as a pipeline of a pair of predicting blocks. The first one took as the input a set of descriptors of the qualitative and quantitative compositions of alloys and approximated the EMTO-CPA data, and the second one took predictions of the first model and trained on the results of the PAW-SQS calculations. The main idea of such architecture is to achieve prediction accuracy at the PAW-SQS level, while reducing the resource intensity for obtaining the training set by a multiple of the ratio of the training subsets sizes corresponding to the two used calculation methods (EMTO-CPA/PAW-SQS). As a result, model building and testing methods accounting for the lack of accurate training data on the mechanical properties of alloys (PAW-SQS), balanced out by using predictions of inaccurate resource-effective first-principle calculations (EMTO-CPA), are demonstrated.

High-throughput determination of the interdiffusion coefficients and atomic mobilities in bcc Ti–Fe–V alloys

A comprehensive understanding of diffusion kinetics of the Ti–Fe–V system is crucial for elucidating the solidification process in high-strength titanium alloys. In this paper, ten sets of diffusion couples within bcc Ti–Fe–V alloys that underwent annealing at temperatures of 1273K, 1323K, and 1373K were prepared. Composition-distance curves were determined using the electron probe microstructure analysis technique. Atomic mobility parameters and interdiffusion coefficients were obtained using the numerical inverse method with the assistance of HitDIC software. It should be noted that the atomic mobility parameters for Ti–Fe and Ti–V were reoptimized using the most up-to-date thermodynamic descriptions. This approach enables the acquisition of comprehensive data regarding the temperature-composition relationship in diffusion. D˜FeFeTi exhibits a markedly greater value compared to D˜VVTi. Both D˜FeFeTi and D˜VVTi demonstrate an increase with the increase of temperature. Furthermore, the Arrhenius equation can be applied to solve for the variation in frequency factors and activation energies concerning temperature and composition.

Corrosion resistance investigation of the Ti–Al–Mo system supported by CALPHAD approach and key experiments

The corrosion resistance of Ti–Al–Mo alloys in seawater were investigated by thermodynamic calculations and electrochemical tests. Four as-cast alloys were designed based on thermodynamic calculations. The calculated results were verified by experimental determination. The Gibbs energy and electrochemical experiment results showed Ti55Al40Mo5 alloy has the most positive Gibbs energy and the best corrosion resistance. The bcc(Ti) phase has best corrosion resistance among AlTi, AlTi3 and bcc(Ti). The present work further proves the important role of phase diagram calculation in alloy design, and thermodynamic database provides important theoretical support for efficient development of new alloys.

Atomic mobilities, diffusion coefficients, and kinetic coefficients in Ti-rich Ti–Mo–Nb system

Diffusion coefficient is an important physical property to control the microstructure, thus the establishment of atomic mobility databank for Ti-based alloy systems is vital to the design of novel Ti alloys. In the present work, ternary Ti–Mo–Nb diffusion couples within the single bcc phase were prepared and measured after annealing at 1273 K for 25 h, and interdiffusion coefficients of bcc Ti–Mo–Nb alloys at 1273 K were determined from the experimental composition profiles by using Matano–Kirkaldy method. Subsequently, the atomic mobility parameters of bcc Ti–Mo–Nb system under the CALculation of PHAse Diagrams (CALPHAD) framework were assessed by using recently proposed diffusion models, which were verified by the comparisons between the experimental interdiffusion coefficients/composition profiles and the model-predicted results. Moreover, diffusion models were carefully discussed for the ternary assessment. Finally, relationships among atomic mobility, kinetic coefficient, and diffusion coefficients were discussed and demonstrated via ternary contour maps. The present work contributes to the development of diffusion databank for computational design of biomedical Ti alloys.

Diffusivities and atomic mobilities in bcc Ti–V–Mo alloys

In pursuit of a comprehensive exploration into the diffusion kinetics of bcc Ti–V–Mo alloys, sixteen sets of diffusion couples were prepared within the bcc phase of Ti–V–Mo alloys. These diffusion couples were subjected to annealing at 1373 K and 1473 K. Composition profiles were obtained by means of the electron probe micro-analysis technique (EPMA). The calculation of diffusivities in bcc Ti–V–Mo alloys was performed using the Whittle-Green and Hall methods. Based on available thermodynamic descriptions, the atomic mobility parameters of the bcc Ti–V–Mo system were assessed by using the DICTRA module of the Thermo-Calc software. A comparison is made between the simulated composition-distance curve and the diffusion path with the experimental values, revealing a significant level of concordance.

Microstructural Control by Cooling Rate in β-type and Sintered Ti-3.6Fe-5Zr-0.2B (Mass%) Alloy Fabricated by Spark Plasma Sintering and Heat Treatment

The β-type and sintered Ti-3.6Fe-5Zr-0.2B (mass%) alloy has been consolidated by spark plasma sintering, followed by a β solution treatment (ST). In order to obtain a high-strength ductile balance, water quenching or air cooling is used after ST. Modification of sintering conditions, which leads to 100% of the relative density, improves the tensile ductility. The Fe addition causes a large local lattice and compressive strain to the bcc Ti lattice; in the water-quenched sample, α” martensite phases appear in the β matrix. When air cooling is applied after the ST, bimodal α lath phases are instead precipitated during the cooling in nanoscale, and the formation of α” martensite phases is suppressed. This results in high strength and better ductility when compared with those in the water-quenched sample, particularly in tensile properties. The air-cooled sample reveals attractive mechanical properties in both tension and compression modes.

Diffusion coefficient measurement and atomic mobility assessment for bcc Ti–V–Fe ternary alloys

Diffusion behaviors in bcc Ti–V–Fe ternary alloys have been investigated at 1273 K and 1473 K by the diffusion couple technique. The composition-distance profiles have been retrieved from Electron Probe MicroAnalysis (EPMA) and analytically represented by the ERror Function EXpansion (ERFEX), and then the ternary inter-diffusion and impurity diffusion coefficients have been extracted by Whittle–Green and generalized Hall methods, respectively. The extracted inter-diffusion coefficients of D˜VVTi and D˜FeFeTi range from 0.89 × 10−13 m2/s to 1.86 × 10−13 m2/s and from 1.33 × 10−12 m2/s to 1.76 × 10−12 m2/s, respectively, at 1273K, and from 6.41 × 10−13 m2/s to 15.98 × 10−13 m2/s and from 82.46 × 10−13 m2/s to 147.08 × 10−13 m2/s at 1473K. D˜VVTi exhibits the similar compositional variation at both temperatures, which decrease with decreasing Fe and minimize at the Ti–V binary. D˜FeFeTi has the maximum value at Ti–corner and eventually decreases with the increasing V and Fe at 1273K, but has the maximum value at Fe-rich Ti–Fe binary and decreases with the increasing V. The atomic mobility parameters of Ti–V, Ti–Fe and V–Fe binary systems have been revised to associate with the lasted ternary interaction parameters in thermodynamics. The ternary atomic mobility parameters for diffusion have been assessed for the first time by reproducing the extracted diffusion coefficients. The composition-distance profiles and the diffusion paths have been successfully reproduced by using the optimized atomic mobility parameters showing a consistency with the experimental data and indicating the accuracy of this work.

Alloying Effect on Elastic and Mechanical Properties of Refractory Medium-Entropy Alloys from First-Principles Calculations

There is still a challenge to rapidly and accurately acquire the composition dependence of mechanical properties of multi-principal element alloys due to their huge composition space and complex electronic structures. Aiming to straightforwardly tune the mechanical properties through alloying, we systematically calculate the elastic and mechanical properties for four selected body-centered-cubic (bcc) Ti–Nb–M (M = Zr, Mo, Sn, Ta) refractory medium-entropy alloys (RMEAs) using a first-principles method. It is shown that the elastic stability of the bcc RMEAs can be significantly (weakly) improved with the increase in Nb, Mo, and Ta (Sn) content, but it is insensitive to Zr. The elastic stability, elastic modulus, hardness, and strength generally enhance, whereas Pugh’s ratio and Zener anisotropy (AZ) decrease with the increase in valence electron concentration. Additionally, there is a correlation between the magnitude of the AZ and the shape of the single-crystal Young’s modulus (E[hkl]). The largest (smallest) E[hkl] appears in the <111> (<100>) direction. Particularly, the most isotropic Ti60Nb20Mo20 has the highest hardness and strength among all the Ti–Nb–M alloys. Moreover, the change of elastic properties induced by alloying is related to the change of density of states. This work sheds deep light on the design of high-performance Ti-based multi-principal element alloys.

Modelling of dislocations, twins and crack-tips in HCP and BCC Ti

Ti exhibits complex plastic deformation controlled by active dislocation and twinning systems. Understandings on dislocation cores and twin interfaces are currently not complete or quantitative, despite extensive experimental and simulation studies. Here, we determine the dislocation core, twin, and crack properties in both HCP and BCC Ti using a Deep Potential (DP), DFT and linear elastic fracture mechanics. We compute the core structures, critical resolved shear stresses and mobilities of the 〈a〉 , 〈c+a〉 , 〈c〉 dislocations in HCP and the 〈111〉/2 dislocations in BCC Ti. The 〈a〉 slip consists of slow core migration on pyramidal-I planes and fast migration on prism-planes, and is kinetically limited by cross-slips among them. This behaviour is consistent with “locking–unlocking” phenomena in TEM and is likely an intrinsic property. Large-scale DFT calculations provide a peek at the screw 〈c+a〉 core and glide behaviour, which is further quantified using DP-Ti. The screw 〈c+a〉 is unstable on pyramidal-II planes. The mixed 〈c+a〉 is nearly sessile on pyramidal-I planes, consistent with observations of long dislocations in this orientation. The edge and mixed 〈c+a〉 are unstable against a pyramidal-to-basal (PB) transition and become sessile at high temperatures, corroborate the difficulties in 〈c〉 -axis compression of Ti. Cracks on basal planes are predicted and shown to be intrinsically brittle, consistent with cleavage facets primarily on this plane in experiments. Twin boundary energies vary considerably but all twin boundary structures possess a mirror reflection symmetry. Finally, in BCC Ti, the 〈111〉/2 screw has a degenerate core with average glide on {112} planes; the 〈111〉/2 edge and mixed dislocations have non-dissociated cores on {110} planes. This work paints a self-consistent, complete picture on all dislocations in Ti, rationalises previous experimental observations on Ti plasticity and fracture, and points to future HRTEM examinations of unusual dislocations such as the mixed and PB transformed 〈c+a〉 cores.

Shape memory effect and aging behavior of Bi-added Ti–Cr alloys for biomedical applications

For the further development of biocompatible metastable β (bcc) Ti alloys, the purpose of this study is to evaluate the potential of bismuth (Bi) addition in terms of shape memory properties and phase stability. It was found that the shape memory effect appeared in Ti–5Cr–1.6Bi (mol%) alloy. However, permanent (unrecoverable) deformation due to dislocations or twinning was also introduced simultaneously from the early stage of deformation. Regarding the formation of isothermal ω phase and the resulting hardness change by aging, it was found that the hardness change was large and that the isothermal ω phase formed in Ti–5Cr–1.6Bi alloy, while age hardening was small and no isothermal ω phase formed in Ti–5Cr–6.1Bi alloy. These results indicate the suppression of not only athermal ω but also isothermal ω phase by Bi addition. However, considering the fact that the alloy becomes brittle when Bi addition is over 3 mol%, it can be concluded that 1–3 mol% Bi addition is worth for the improvement of shape memory effect, suppression of ω phase, X-ray imaging, magnetic resonance imaging, and biocompatibility in metastable β Ti alloys.

Fabrication and mechanical properties of Bi-added Ti–Cr alloys for biomedical applications

The potential of the Bismuth (Bi) addition was evaluated for the development of biocompatible metastable β (bcc) Ti alloys from the viewpoints of mechanical properties and phase stability. The basic alloy was Ti–5 mol% Cr, and 0–9 mol% Bi was added in nominal composition. A Ti–Bi binary alloy was also selected. The alloys were fabricated using a standard laboratory-scale arc melting machine under an Ar atmosphere. The weight loss was significant during melting due to Bi evaporation. The measured Bi content is linearly proportional to the Bi nominal composition with MCBi = 2/3 NCBi, allowing the prediction and control of Bi content of the alloy. Then, the microstructure, workability, and mechanical properties were systematically investigated. The phase constitution of the Ti–5Cr binary alloy was β + α′ (hcp) + ω (hexagonal). The presence of the athermal ω phase resulted in significantly poor cold workability and poor ductility. It was also found that the addition of Bi to the Ti–5Cr alloy stabilized the β phase and suppressed the ω phase formation. The phase stability of Ti–Cr–Bi alloy is discussed using Mo equivalent and electron-to-atom (e/a) ratio. Ti–5Cr–1.6Bi alloy showed improved workability and ductility. However, with further increasing Bi addition, the Ti–5Cr–3.7Bi alloy showed no plastic deformation, and the Ti–5Cr–6.1Bi alloy was broken even during hot-rolling. Thus, it is concluded that ∼2 mol% Bi addition is suitable and that such a small amount of Bi addition is an attractive candidate for the development of β Ti alloys.

High-throughput determination of mechanical and diffusion properties in the Ti–Nb–Fe alloys

Accurate Young's modulus, hardness, and interdiffusion coefficient are the necessary information for the design and production of biomedical multicomponent alloys. In this work, five sets of ternary Ti–Nb–Fe diffusion couples were prepared after annealing at 1273 K for 25 h. The composition-dependent Young's moduli and hardness in the bcc Ti–Nb–Fe system were experimentally determined by means of nanoindentation and electron probe microanalysis (EPMA) techniques. Moreover, the main and cross interdiffusion coefficients of Ti–Nb–Fe alloys at 1273 K were confirmed from the composition gradients of the diffusion couples by using a pragmatic numerical inverse method. A composition-dependent database on the mechanical and diffusion properties of Ti–Nb–Fe alloys was carefully established and utilized for the discussion of the processability during the hot workability. The results indicated that Fe concentration control could be very helpful for the development of Ti–Nb–Fe alloys with low Young's modulus, high hardness, and nice processability during the hot working.

Atomic mobilities and diffusivities in the bcc phase of Ti–Nb–Sn system

Accurate interdiffusion information is essential to control the phase transformation process in metastable β-type titanium alloys. In this work, diffusion behavior in the ternary Ti–Nb–Sn system at 1373 K and 1473 K was experimentally investigated. The ternary interdiffusion coefficients and impurity diffusion coefficients in the bcc Ti–Nb–Sn alloys were determined using the diffusion couple technique, along with the Whittle-Green and Hall methods. Based on the obtained diffusion coefficients, an atomic mobility database for the bcc Ti–Nb–Sn system was established via the CALPHAD (CALculation of PHAse Diagrams) method. In the optimizing procedure, the end members and the binary parameters for the bcc-Ti-Sn system were reassessed. The calculated results using the obtained database agree with the experimental diffusion properties (i.e., interdiffusion, composition-distance profiles and diffusion paths), demonstrating the accuracy of the database developed in this work.

Ab initio systematic description of thermodynamic and mechanical properties of binary bcc Ti-based alloys

The effects of the dissolution of 3d, 4d and 5d metals and Al, Ga, Ge, In and Sn in the bcc Ti lattice (β-phase) were studied within the framework of first-principles calculations. Lattice parameters, mixing enthalpies, single-crystal elastic constants C11, C12, C44 and C′, polycrystalline elastic moduli E, G, and plasticity characteristics of bcc Ti-based solid solutions in a wide concentration range up to 50 at% were investigated using the EMTO-CPA method. The PAW-SQS method was used to study the effects of alloying and local atomic relaxations on the indicated properties of Ti-X bcc alloys, where X is a series of 4d elements Nb, Mo, Tc, Ru, Rh, and 5d elements Ta, W, Re, Os, Ir for the set of concentrations: 6.25, 25 and 50 at%. The effect of concentration and periodic dependences on the properties of alloys and the dependence of elastic properties on the electronic structure were analyzed. It is shown that the calculated elastic constant C′ is a convenient and useful parameter for ranking chemical elements according to the relative strength of the stabilizing effect on the β-phase, in addition, the concentration dependences of C′ demonstrate softening with concentration increasing in the case of late transition metals, thereby reflecting the tendency of these metals to form intermetallic compounds with titanium, while early transition metals show a linear grow in stability with increasing concentration.

Understanding the role of anharmonic phonons in diffusion of bcc metals

Diffusion in the high-temperature bcc phase of IIIB-IVB metals such as Zr, Ti, and their alloys is observed to be orders of magnitude higher than bcc metals of group VB-VIB, including Cr, Mo, and W. The underlying reason for this higher diffusion is still poorly understood. To explain this observation, we compare the first-principles-calculated parameters of monovacancy-mediated diffusion between bcc Ti, Zr, and dilute Zr- Sn alloys and bcc Cr, Mo, and W. Our results indicate that strongly anharmonic vibrations promote both the vacancy concentration and the diffusive jump rate in bcc IVB metals and can explain their markedly faster diffusion compared to bcc VIB metals. Additionally, we provide an efficient approach to calculate diffusive jump rates according to the transition state theory (TST). The use of standard harmonic TST is impractical in bcc IIIB/IVB metals due to the existence of ill-defined harmonic phonons, and most studies use classical or ab initio molecular dynamics for direct simulation of diffusive jumps. Here, instead, we use a stochastically sampled temperature-dependent phonon analysis within the transition state theory to study diffusive jumps without the need of direct molecular dynamics simulations. We validate our first-principles diffusion coefficient predictions with available experimental measurements and explain the underlying reasons for the promotion of diffusion in bcc IVB metals/alloys compared to bcc VIB metals.

Diffusivities and atomic mobilities in BCC Ti-Rich Ti–V–Cr ternary alloys

In this work, we investigate ternary diffusion behaviors in BCC Ti–rich Ti–V–Cr alloys at 1373 K and 1473 K using the diffusion couple technique. We extract the inter-diffusion coefficients by the Whittle-Green method and obtain the impurity diffusion coefficients using the Hall method. Based on a thermodynamic description and validated binary mobility parameters, we evaluate the ternary diffusion coefficients and optimize the atomic mobility parameters of the Ti–V–Cr ternary alloy system in the DICTRA diffusion Module of Thermo-Calc software. Finally, we simulate the composition profiles and diffusion paths using our optimized atomic mobility parameters and find agreement between our simulated and experimentally observed results, providing evidence of the accuracy of our mobility parameters.

Diffusivities and atomic mobilities in bcc Ti–Mo–Ta alloys

Mo and Ta are two important β stable elements that can enhance the fatigue strength and reduce the elastic modulus of titanium alloy, and can significantly improve the biocompatibility of titanium alloy. It is significant to study the diffusion behavior in β Ti–Mo–Ta alloy for understanding the microstructure evolution in production process and developing new alloys. In this study, using several diffusion couples, the interdiffusion coefficients and impurity diffusion coefficients in β Ti–Mo–Ta alloy were extracted via Whittle-Green method and Hall method. The atomic mobilities in bcc phase in Ti–Mo–Ta system were obtained by assessing the experimental data using CALPHAD (CALculation of PHAse Diagrams) method. Simulations of the diffusion process in the diffusion couples were implemented using DICTRA Module in Thermo-Calc software. The calculated data were in good agreement with the experimental data, confirming the accuracy of the database.

Atomistic Modelling of All Dislocations and Twins in HCP and BCC Ti

Atomistic Modelling of All Dislocations and Twins in HCP and BCC Ti