Thermodynamic modeling of the Co–Hf system supported by key experiments and first-principles calculations
Graphical abstract
Introduction
Cobalt-based alloys are known for the unique combinations of properties, such as high temperature creep and fatigue strength as well as good resistance to aggressive corrosion and various forms of wear [1]. Recent studies have shown that small additions of Hf into Co–Al–W ternary system can stabilize the γ′-Co3(Al,W) phase, making it possible to develop a new class of cobalt-based alloys with a greater high-temperature strength than that of the conventional nickel-based superalloys [2], [3], [4]. Meanwhile, the Co–Hf binary alloys were also reported to be able to form metallic glass over a wide range of composition, and have been investigated as a promising bulk metallic glass (BMG) system by several authors [5], [6], [7], [8], [9], [10]. Therefore, in order to control the microstructures in multi-component cobalt-based superalloys and to develop new classes of bulk amorphous materials, knowledge of accurate thermodynamic description of the Co–Hf binary system is necessary.
The Co–Hf phase diagram was critically assessed by Ishida and Nishizawa [11] based on the previous experimental investigations [12], [13], [14], and their work was accepted by Okamoto [15] during his review on the system. With limited experimental information, Bratberg and Jansson [16] performed a simplified thermodynamic assessment for the Co–Hf system. However, the calculated phase diagram deviates greatly from the assessed work by Ishida and Nishizawa [11], as shown in Fig. 1. Recently, the Co–Hf binary phase diagram was systematically investigated by the present authors [17], and the phase equilibria were revised based on the reliable experimental observations. On the other hand, thermodynamic information for the Co–Hf binary compounds is relatively limited, making it difficult to perform accurate thermodynamic modeling for the system.
Therefore, the objective of the present work is to develop a set of self-consistent thermodynamic parameters for the Co–Hf system via a hybrid approach of calorimetric experiments, first-principles calculations and CALPHAD (CALculation of PHAse Diagram) modeling. Then the glass forming behavior of Co–Hf amorphous alloys will be discussed based on the obtained thermodynamic description of the system.
Section snippets
Evaluation of literature information
Both the experimental data published in the literature [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [18], [19], [20], [21], [22], [23] and those from our previous work [17] are evaluated in this section. All of the data are summarized in Table 1 and concisely categorized as follows.
Experimental procedure
Co–Hf binary alloys were prepared at the stoichiometries of Co2Hf and CoHf2 with 99.999 wt.% Co (Jinchuan Group Co., Ltd., China) and 99.99 wt.% Hf (China New Metal Materials Technology Co., Ltd., China) in an arc melting furnace (WKDHL-I, Opto-electronics Co., Ltd., Beijing, China) under high purity argon atmosphere (1 bar) using a non-consumable W electrode. The ingots were re-melted four times to improve their homogeneities. No chemical analysis for the alloys was conducted since the weight
First-principles calculations for enthalpy of formation
First-principles calculations based on density functional theory (DFT) [27] within generalized gradient approximation (GGA) along with projector augmented-wave (PAW) [28] method were employed to obtain the enthalpy of formation for Co23Hf6, as implemented in the Vienna ab initio simulation package (VASP) [29], [30]. The GGA proposed by Perdew et al. [31] was used in the calculation. The atoms were relaxed toward equilibria until the Hartree forces were less than 0.02 eV/Å. A plane-wave cut off
Unary phases
The thermodynamic properties of pure elements Co and Hf are taken from the SGTE-compilation by Dinsdale [33] described in the form of:where, is the molar enthalpy of the element i at 298.15 K and 1 bar in its standard element reference (SER) state, and T is the absolute temperature. The last two terms in Eq. (2) are used only outside the ranges of the melting point, I × T7 for a liquid below the melting point and J × T−9 for solid phases above
Glass forming behavior
The glass forming behavior of Co–Hf alloys has been investigated by several authors [5], [6], [7], [8], [9], [10]. By means of melt spinning technique and DSC, Buschow and Beekmans [10] prepared three Co–Hf amorphous alloys, Co91Hf9, Co40Hf60 and Co22Hf78 (at.%) and measured the crystallization temperatures (Tx) to be 555, 550 and 485 °C, respectively. Using the same methods, Jansson and Nygren [8] reported the Tx of a Co33Hf67 (at.%) alloy to be 503 °C with a crystallization heat of 9.0
Summary
All the experimental phase diagram and thermodynamic data available for the Co–Hf system have been critically evaluated. Heat content values of Co2Hf and CoHf2 were obtained through drop calorimetry measurements. The enthalpy of formation for Co23Hf6 at 0 K was calculated via first-principles calculations.
A set of self-consistent thermodynamic parameters for the Co–Hf system was obtained by considering the present results and critically assessed literature data. The comprehensive comparison
Acknowledgements
The financial support from the National Science Foundation for Youth of China (Grant No. 51101172), the National Basic Research Program of China (Grant No. 2011CB610401) and the Sino-German Cooperation Group “Microstructure in Al alloys” (Grant No. GZ755) are greatly acknowledged. One of the authors Xingxu Lu is also grateful to Prof. M. Turchanin for sharing their experimental data on the enthalpies of mixing of the liquid phase.
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