**1. Introduction**

Titanium-based alloys have been widely accepted for biomedical applications due to comparatively superior biocompatibility and anti-corrosion properties [1–5]. Efforts are being made to explore new alloys that contain elements that are not toxic, as well as develop alloys with Young's modulus comparable to human bone to avoid stress shielding [2]. Young's modulus (YM) of common implant materials varies between 100–230 GPa, which is significantly higher when compared with that of bone, which is between 10 and 40 GPa [1]. This difference in YM results in non-uniform distribution of stress in the implant materials and the surrounding bone structure. This can result in the failure of an implant [1]. Titanium alloys containing β-phase as the predominant phase are known to have lower values of Young's modulus [2–9]. Thermodynamically, α and β are stable phases, while α" and ω-phase are metastable phases [2]. Composition and processing of alloys play an important role in determining the concentrations of various phases, which directly affect mechanical properties of these alloys [6–9].

During processing or heat-treatment of Ti-based alloys, they are subjected to cooling from an elevated temperature at various cooling rates [10–14]. The cooling rate can affect the stability of β-phase and it can transform into α, α˝ or ω-phase, while ω-phase can also form isothermally during ageing [12]. Among these phases, ω-phase possesses the

**Citation:** Jha, R.; Dulikravich, G.S. Discovery of New Ti-Based Alloys Aimed at Avoiding/Minimizing Formation of α" and ω-Phase Using CALPHAD and Artificial Intelligence. *Metals* **2021**, *11*, 15. https://dx.doi.org/ 10.3390/met11010015

Received: 28 November 2020 Accepted: 19 December 2020 Published: 24 December 2020

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highest modulus value. Precipitation of α and ω-phase can result in an increase in the Young's modulus of the alloy [12,13]. Regarding α"-phase, it is a desired phase in shape memory alloys [12]. In Ti-based biomaterials, precipitation of α, α˝ or ω-phase can lead to degradation of mechanical properties, specifically Young's modulus [2,10–14]. In titanium alloys, experiments show that ω-phase can be stabilized and has been observed at cryogenic temperatures [15]. From first-principle calculations, researchers have demonstrated the scope of development of ω-phase free Ti-Ta-X shape memory alloys [16].

In this work, we chose the Ti-Nb-Zr-Sn system, which is free of toxic chemical elements [17] such as aluminum [18] and vanadium [19]. Niobium is a strong β-phase stabilizer [9]. In the presence of Nb, Zr also becomes a strong β-phase stabilizer [1]. Additionally, Nb and Zr are biocompatible and demonstrate excellent resistance to corrosion [20]. Sn is also biocompatible and has been used as an alloying element in small amounts [21]. The addition of Sn leads to a decrease in elastic modulus of Ti-based biomaterials [22]. Sn addition can help in suppressing precipitation of α˝ and ω-phase for lower and higher cooling rates, respectively [22]. One of the aims is to optimize the alloy composition so that an optimum amount of Sn addition can prove to be beneficial in the lowering of the elastic modulus and in the suppression of precipitation of α˝ and ω-phase [22].

The Ti-Nb-Zr-Sn system was studied under the framework of CALculation of PHAse Diagram (CALPHAD) approach through Thermo-Calc software [23]. It was used for determining concentrations of various stable and metastable phases for a large set of compositions and temperatures, and thus generating a dataset suitable enough for applying artificial intelligence (AI) algorithms, including deep learning [24] and self-organizing maps (SOM) [25]. These data were then used for developing deep learning artificial neural network (DLANN) models for various phases as a function of alloy composition and temperature. Software for developing the DLANN model was written in Python programming language using TensorFlow [26] and Keras [27] libraries. DLANN models were used as a predictive tool for predicting the concentrations of metastable phases for new compositions and temperatures. This resulting dataset was then analyzed by the concept of self-organizing maps (SOM) [25] for determining various patterns and correlations within the dataset among alloying elements, temperatures, and stable and metastable phases.

Through this work, we were able to identify the composition and temperature regimes that will provide ω-phase free Ti-based alloys with a minimal amount of α" phase. We have reported chemical compositions of several candidate alloys along with temperatures that will be helpful in achieving ω-phase free Ti-based alloys (Ti-Nb-Zr-Sn system). Our research team has significant experience in designing alloys by application of artificial intelligence (AI) algorithms on data generated from experiments and data generated under the framework of the CALPHAD approach. We have successfully designed titanium alloys [28], aluminum alloys [29,30], hard magnets (AlNiCo) [31,32], soft magnets (FINEMET type) [33,34], and Ni-based superalloys [35]. Thus, we propose this computational design approach, which can be easily adopted in other alloy systems and can help in developing ω-phase free Ti-based biomaterials with improved mechanical properties.

#### **2. Materials and Methods**

As mentioned, we chose the Ti-Nb-Zr-Sn system for this work. Bounds for concentrations for each of the four alloying elements were defined on the basis of available literature [1–21]. Bounds for temperature include cryogenic temperature [15] for determining the amount of ω-phase in the presence and absence of thermodynamically stable phases. Variable bounds for the chemical composition of the Ti-Nb-Zr-Sn system are presented in Table 1. Chemical compositions are in atomic %, while the temperature is in degrees Kelvin. Phase stability calculations for approximately 3000 candidate alloys were performed for random values of concentrations and temperatures within theranges reported in Table 1. There is no correlation between the minimum and maximum values of composition with the minimum and maximum values of temperature reported in Table 1. Combinations of alloy composition and temperature are randomly generated in five-dimensional (5-D)

space for achieving a uniform distribution of support points in 5-D space shown in Table 1. Uniform distribution of support points is helpful in improving the accuracy of prediction for models developed through AI algorithms.

**Table 1.** Concentration bounds for alloying elements (atomic %) for the Ti-Nb-Zr-Sn system and temperature range (K) chosen for study.


#### *2.1. Identification of Stable and Metastable Phases*

We used commercial software Thermo-Calc [23,36] along with thermodynamic database TCTI2 [37] for titanium alloys for performing phase stability calculations. In the Ti-Nb-Zr-Sn system, α and β are stable phases, while α" and ω-phase are metastable phases. Regarding the crystal structure, α phase has a hexagonal close packed (HCP) structure, while β phase is body centered cubic (BCC). In the TCTI2 database [37], HCP\_A3 is the notation for α phase. Regarding β phase, it exists in two forms: BCC\_B2 and BCC\_B2#2. Metastable phase α" is denoted by ALTI3\_D019, while metastable phase ω is denoted by OMEGA in TCTI2 database [37]. These notations were also mentioned in our previous publication on titanium-based alloys [28], which is featured on Thermo-Calc's website [38]. We have provided our previous publication on titanium alloys as a reference since the titanium database was recently launched by Thermo-Calc in 2018. There are only a few references on thorough studies of various stable and metastable phases in titanium alloys using Thermo-Calc. While performing phase stability calculations, metastable phases are unstable in the presence of stable phases and thus are absent from phase stability data. However, these metastable phases have been observed in the microstructure obtained after performing experiments [39]. Among α, β, α˝ and ω-phase, α and β are thermodynamically stable, while α˝ and ω phases are metastable [2].

For multi-component systems, several equilibria exist for a given composition and temperature. The CALPHAD approach works on the principles of Gibbs energy minimization. Phases that have the lowest Gibbs energy of formation values are thermodynamically stable, and other phases are deemed unstable or metastable. Through the CALPHAD approach, only the thermodynamically stable phases will be shown on the phase diagram. Metastable phases cannot be shown on the phase diagram, nor is there any estimate of the amount (mole) of these phases. Metastable phases can be preferentially stabilized by suppressing/removing a set of stable phases while performing phase stability calculations [29,33,34,40]. Once a set of thermodynamically stable phases are suppressed/removed, we are left with the remaining phases of that system. In the absence of thermodynamically stable phases, few metastable phases become stable as now these phases possess the lowest Gibbs energy of formation values among the remaining phases. Through this preferential stabilization, one can obtain an estimate of the concentrations of metastable phases that can exist under equilibrium conditions for a given composition and temperature. A brief understanding of the formation of metastable phases for a given system can be helpful while designing experiments including heat treatment protocols. We have published articles on stabilizing metastable phases in aluminum alloys [29] and soft magnetic FINEMET-type alloys [33,34]. In soft magnetic alloys, we even performed heat treatment simulations for studying the nucleation and growth of metastable phases and some of the results were experimentally verified using advanced diagnostic tools such as atom probe tomography [34]. Thus, in this work, we were able to generate a large dataset comprised of about 3000 randomly selected candidate alloy compositions and temperatures along with various stable and metastable phases.

#### *2.2. Deep Learning Artificial Neural Network (DLANN) Model*

We developed DLANN models within the framework of deep learning [24]. These models were coded in Python programming language and used TensorFlow [26] and Keras [27] libraries for developing this code. For visualization, we used Tensorboard [41]. DLANN models were developed separately for each of the phases. A separate dataset was prepared for each phase and the data were scaled between 0 and 1. These scaled data were randomly divided into training and testing sets where 33% data were assigned to the testing set while the remaining 67% were included in the training set. DLANN architecture includes 4 hidden layers. The number of neurons in the initial hidden layer was fixed at 50, 60, 70, 80, 90, and 100, while the number of neurons in the other three hidden layers was fixed at 100, 120, 140, 160, 180 and 200 neurons. In short, the number of neurons in the initial layer was half of the number of neurons in each of the other three layers. Activation function was Rectified Linear Unit (ReLU) and optimizer was "Adam" which stands for Adaptive Moment Estimation, while number of epochs was fixed at 100. Tensorboard was used for visualizing the DLANN performance [41]. One of the criteria for the selection of a model was its performance on validation set, which was determined through error metrics such as mean squared error (MSE) and mean absolute error (MAE). One has to be careful while relying on error metrics such as MAE and MSE alone as we are dealing with ANN models that are susceptible to "overfitting". Although we are dealing with a large dataset, there are still many "missing" points. Therefore, we used statistical terms for guidance, while we gave priority to physical metallurgy of titanium alloys for DLANN model selection. These DLANN models can be used on a personal computer and even on an Android mobile phone to predict various metastable and stable phases, and thus provide us with a dataset with additional support points for determining various patterns and correlations within this dataset.

#### *2.3. Self Organizing Maps (SOM)*

Data obtained from CALPHAD-based calculations and predicted through DLANN models were further studied by the concept of self-organizing maps (SOM) [25,28,31,42]. SOM maps are known for preserving topology of the data, which is helpful in determining various correlations in the dataset among concentrations of alloying element, temperature, and stability of various stable and metastable phases. Regarding prediction via SOM, one must be careful while drawing conclusions as SOM values over a hexagonally-shaped cell are the average value of candidates positioned at the vertices of the hexagonally-shaped cells. Thus, for prediction we used DLANN models, while for determining correlations over a large dataset of about 3000 candidate alloys, we considered SOM. Through this study, we identified several candidate alloys that are free of ω-phase. For SOM analysis, we used a commercial software ESTECO-modeFRONTIER, version 4.5, Trieste, Italy [42].

#### *2.4. Computational Infrastructure*

#### 2.4.1. CALPHAD-Based Work

Thermo-Calc version 2019b [23,37] was installed on a desktop computer in a computer lab. The operating system was Windows 10, Core i7 processor (CPU) with 16 GB RAM. Phase transformation calculation time varied between 20 and 30 min.

#### 2.4.2. Artificial Intelligence-Based Work

AI-based work was performed on a laptop. The operating system was Windows 10, Core i7 processor (CPU) with 32 GB RAM. DLANN model development took about 20 to 30 min. Once the model was developed, prediction was completed in a few seconds. DLANN models were also used on an Android phone with 6 GB RAM and octa-core processor (CPU). Prediction time is a few seconds on the Android phone. SOM model development took about 20–30 min for each case.
