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The solubility values of eight common alloying elements Al, Ca, Ce, Gd, Nd, Sn, Y and Zn in hcp Mg are experimentally measured from diffusion profiles obtained from diffusion multiples and liquid-solid diffusion couples (LSDCs) using electron probe microanalysis. These solubility values are used to establish solidus and solvus lines and compared with the experimental results reported in the literature as well as the computed phase boundaries using two CALPHAD (CALculation of PHAse Diagrams) databases. Our experimental values for Mg-Ca (530, 580, 600, 630 °C), Mg-Ce (605, 630 °C), Mg-Gd (570, 600, 630 °C) and Mg-Nd (615, 630 °C) are the first ever measurements of the hcp solidus for these four binary systems. Additional solubility data obtained from our experiments are reported for Mg-Al (375, 420, 450, 500, 550, 600 °C), Mg-Sn (375, 420, 500, 550, 600 °C), Mg-Y (590, 610, 630 °C), and Mg-Zn (275, 450, 500, 550 °C). Our experimental data are valuable input to future thermodynamic reassessments of the eight binary systems. This study also clearly shows the effectiveness of measuring solidus data using the elegant LSDCs. 

The Fe-Nb and Fe-Nb-Ni systems are remodeled using updated sublattice models for the topologically close packed (TCP) phases of Laves_C14, δ and μ with new experimental data and first-principles and phonon calculations based on density functional theory (DFT). Experimental techniques are used to determine phase compositions and tie-lines in the Fe-Nb-Ni system. The three-, three-, and five- sublattice models are used for Laves_C14, δ, and μ phases, respectively. DFT calculations are employed to predict thermochemical data as a function of temperature for Laves_C14, δ, and μ phases. The new thermodynamic description of the Fe-Nb-Ni system includes a new hexagonal phase named - hP24 - and the updates for the Fe-Nb system and reproduces better the experimental and computational thermochemical and phase equilibrium data from the present study and the literature. The new results will improve thermodynamic predictions of TCP and other phases in both Fe-based and Ni-based alloy systems. 

Both CALPHAD (CALculation of PHAse Diagrams) and machine-learning (ML) approaches were employed to analyze the phase formation in 2,436 experimentally measured high entropy alloy (HEA) compositions consisting of various quinary mixtures of Al, Co, Cr, Cu, Fe, Mn, and Ni. CALPHAD was found to have good capabilities in predicting the BCC/B2 and FCC phase formation for the 1,761 solid-solution-only compositions, excluding HEAs containing an amorphous phase (AM) or/and intermetallic compound (IM). Phase selection rules were examined systematically using several parameters and it revealed that valency electron concentration (VEC) < 6.87 and VEC > 9.16 are the conditions for the formation of single-phase BCC/B2 and FCC, respectively; and CALPHAD could predict this with essentially 100% accuracy. Both CALPHAD predictions and experimental observations show that more BCC/B2 alloys are formed over FCC alloys as the atomic size difference between the elements increases. Four machine learning (ML) algorithms, decision tree (DT), k-nearest neighbor (KNN), support vector machine (SVM), and artificial neural network (ANN), were employed to study the phase selection rules for two different datasets, one consisting of 1,761 solid-solution (SS) HEAs without AM and/or IM phases, and the other set consisting of all the 2,436 HEA compositions. Cross validation (CV) was performed to optimize the ML models and the CV accuracies are found to be 91.4%, 93.1%, 90.2%, 89.1% for DT, KNN, SVM, and ANN respectively in predicting the formation of BCC/B2, BCC/B2 + FCC, and FCC; and 93.6%, 93.3%, 95.5%, 92.7% for DT, KNN, SVM, and ANN respectively in predicting SS, AM, SS + AM, and IM phases. Sixty-six experimental bulk alloys with SS structures are predicted with trained ANN model, and the accuracy reaches 81.8%. VEC is found to be most important parameter in phase prediction for BCC/B2, BCC/B2 + FCC, and FCC phases. Electronegativity difference and FCC-BCC-index (FBI) are the two additional dominating features in determining the formation of SS, AM, SS + AM, and IM. A separation line ΔH_mix=28.97×VEC-246.77 was found in the VEC-vs-ΔH_mix plot to predict the formation of single-phase BCC/B2 or FCC with a 96.2% accuracy (ΔH_mix = mixing enthalpy). These insights will be very valuable for designing HEAs with targeted crystal structures. 

Liquid–solid diffusion couples (LSDCs) are employed to generate a composition gradient in the single‐phase hexagonal closed‐packed (hcp) solid solution with compositions up to the solubility limit of various solutes in Mg. Nanoindentation scanning across the composition gradient in LSDCs allows effective evaluation of composition‐dependent hardness of eight alloying elements (Al, Ca, Ce, Gd, Li, Sn, Y, and Zn) in the hcp Mg phase. The hardening coefficients, an indicator of the potency of solid‐solution hardening, are evaluated from the measured composition‐hardness data and correlated with various materials properties such as atomic radius, shear modulus, and elastic modulus of the solutes. The rank of hardening potency of Al, Gd, Sn, Y, and Zn measured by nanoindentation is in good agreement with that measured by microindentation reported in the literature. The hardening coefficient (potency) from the strongest to the weakest is Ce > Ca > Y ≈ Gd > Zn > Al ≈ Sn > Li in Mg‐based hcp binary solid solutions. The hardening coefficient is found to be closely correlated with the strengthening potency.