Relative effects of enthalpy and entropy on the phase stability of equiatomic high-entropy alloys

Abstract

High configurational entropies have been hypothesized to stabilize solid solutions in equiatomic, multi-element alloys which have attracted much attention recently as “high-entropy” alloys with potentially interesting properties. To evaluate the usefulness of configurational entropy as a predictor of single-phase (solid solution) stability, we prepared five new equiatomic, quinary alloys by replacing individual elements one at a time in a CoCrFeMnNi alloy that was previously shown to be single-phase [1]. An implicit assumption here is that, if any one element is replaced by another, while keeping the total number of elements constant, the configurational entropy of the alloy is unchanged; therefore, the new alloys should also be single-phase. Additionally, the substitute elements that we chose, Ti for Co, Mo or V for Cr, V for Fe, and Cu for Ni, had the same room temperature crystal structure and comparable size/electronegativity as the elements being replaced to maximize solid solubility consistent with the Hume–Rothery rules. For comparison, the base CoCrFeMnNi alloy was also prepared. After three-day anneals at elevated temperatures, multiple phases were observed in all but the base CoCrFeMnNi alloy, suggesting that, by itself, configurational entropy is generally not able to override the competing driving forces that also govern phase stability. Thermodynamic analyses were carried out for each of the constituent binaries in the investigated alloys (Co–Cr, Fe–Ni, Mo–Mn, etc.). Our experimental results combined with the thermodynamic analyses suggest that, in general, enthalpy and non-configurational entropy have greater influences on phase stability in equiatomic, multi-component alloys. Only when the alloy microstructure is a single-phase, approximately ideal solid solution does the contribution of configurational entropy to the total Gibbs free energy become dominant. Thus, high configurational entropy provides a way to rationalize, after the fact, why a solid solution forms (if it forms), but it is not a useful a priori predictor of which of the so-called high-entropy alloys will form thermodynamically stable single-phase solid solutions.

Introduction

Metallic multi-component alloys containing four or more elements in equiatomic concentrations and referred to as high-entropy alloys, are currently receiving significant attention from the scientific community. Most such alloys are multi-phase alloys [2], [3], [4], [5], but occasionally there have been reports of single-phase (i.e. solid solution) high-entropy alloys [1], [6], [7]. Cantor et al. [1] were the first to report that an equiatomic alloy consisting of the five transition metals Co, Cr, Fe, Mn and Ni crystallized as a single solid solution phase (although these authors referred to their alloy as a multi-component alloy, not as a high-entropy alloy). From a metallurgical standpoint, the suppression of intermetallic phases in such an alloy, which consists of several disparate elements, is intriguing. In their pure form, these five elements have four different crystal structures at room temperature: Co is hexagonal close-packed (hcp), Cr and Fe are body-centered cubic (bcc), Mn has the A12 structure (Pearson symbol cI58) and Ni is face-centered cubic (fcc). Nevertheless, Cantor et al. [1] showed that a simple dendritic microstructure, containing no precipitates, formed after induction melting. Although some variations in the chemical compositions between dendritic and interdendritic regions were observed, an almost identical fcc crystal structure was found in both regions. These results contradict the usual observation that the highest mutual solubilities are found among atomic species that have the same crystal structure [8].

Yeh et al. [9] reasoned that the high configurational entropy of alloys containing multiple elements would be sufficient to thermodynamically stabilize a single-phase solid solution via a reduction of the Gibbs free energy. This led them to propose a new class of materials with potentially beneficial properties, the so-called high-entropy alloys, consisting of at least five elements, with atomic concentrations between 5 and 35%, that are solid solutions. Clearly, the equiatomic CoCrFeMnNi alloy of Cantor et al. [1] fits this definition. However, Cantor et al. had also demonstrated that simply increasing the system complexity (i.e. increasing the number of alloying elements) did not significantly extend single-phase stability in multi-component alloys. As an extreme case, they produced an alloy containing 20 elements (including non-transition and semi-metals) in equiatomic proportions, among them Co, Cr, Fe, Mn and Ni. Assuming ideal mixing, such an alloy has a significantly greater configurational entropy than the five-element CoCrFeMnNi alloy, but it nevertheless resulted in a brittle multi-phase microstructure [1]. Interestingly, Cantor et al. found that the primary fcc solid solution phase in the 20-element alloy was “particularly rich in transition metals, notably Cr, Mn, Fe, Co and Ni”. That is, despite the presence of multiple other alloying elements, the solid solution phase nevertheless consisted principally of their original five elements. This suggests that other factors, such as good chemical compatibility among the elements Co, Cr, Fe, Mn and Ni, are more important in determining the microstructural state than configurational entropy.

In spite of the above results of Cantor et al. [1] results, phase formation in multi-component alloys is often discussed in the literature on the basis of a high configurational entropy and the concomitant relaxation of the Hume–Rothery rules. As most of the investigated alloys contain at least three or four of the elements that were also present in Cantor’s CoCrFeMnNi alloy, it is not surprising that microstructures consisting predominantly of fcc solid solution phases of these elements were frequently obtained [2], [10], [11]. However, they also exhibited spinodal decomposition [2], [10] and/or the presence of ordered phases/particles [2], [11], and were not true single-phase microstructures.

To obtain a better understanding of the various factors that affect phase stability in high-entropy alloys, we undertook the present investigation to determine what happens when different elements are substituted one by one in the quinary CoCrFeMnNi alloy of Cantor et al. [1]. Our approach was predicated on the following premise: if any one element in Cantor’s alloy is replaced by another element while keeping the total number of elements constant, the configurational entropy of the alloy is, to first approximation, unchanged. Therefore, if the magnitude of the configurational entropy is what determines single-phase stability in equiatomic multi-component alloys, as implied by Yeh et al. [9], each of our modified Cantor alloys should also exhibit single-phase solid solution microstructures, especially if the substitutional elements are similar to those that they replace in the sense of the Hume–Rothery rules.

To test this hypothesis, we started with the base CoCrFeMnNi alloy of Cantor et al. [1] and produced a series of equiatomic, quinary alloys by replacing the elements Co, Cr, Fe and Ni one at a time by 3d and 4d transition metals having the same room temperature crystal structure. In addition, the substitutional elements were chosen so as to match the replaced elements as closely as possible in terms of atomic radius and electronegativity. Our procedure resulted in the following five new equiatomic alloys, in which the substitutional element is italicized for ease of identification: CoCrFeMnCu, TiCrFeMnNi, CoMoFeMnNi, CoVFeMnNi and CoCrVMnNi. In addition, we also produced the original CoCrFeMnNi alloy of Cantor et al. for comparison (this alloy is referred to as the “base alloy” in this paper).

As will be discussed in the body of the paper, each alloy underwent a three-day annealing treatment to ensure a near-equilibrium microstructural state. The resulting microstructures were investigated by means of scanning electron microscopy (SEM), energy-dispersive X-ray spectroscopy (EDX), and X-ray diffraction (XRD). Thermodynamic calculations were performed to interpret the experimental observations and to determine the magnitudes of the driving forces responsible for phase stability in our equiatomic multi-component alloys.

For the readers’ convenience, the numerical values of the Pauling electronegativities EN [12] and atomic radii r_atom [13] for all elements considered in the present study are compiled in Table 1. In keeping with the Hume–Rothery rules, except for the element pair Ni–Ti, the differences in the atomic radii of the constituent elements in each alloy were kept below 15% (as obtained using the relationship |r_atom,i − r_atom,j|/0.5(r_atom,i + r_atom,j) and based on the metallic atomic radii for a coordination number of 12, as given in Ref. [13]). The bottom line of Table 1 lists the average differences in electronegativities and atomic radii, which were obtained by simply averaging the absolute differences of all possible binary combinations in each alloy. It can be seen that both of these averaged quantities are lowest for the CoCrFeMnCu alloy while the highest values are obtained for CoMoFeMnNi and TiCrFeMnNi. Thus, on the basis of the Hume–Rothery rules, the Cu-containing alloy is expected to be the most likely to form a single-phase solid solution compared to the other five alloys in Table 1.