Design of High Entropy Alloys of Single Phase Random Solid Solutions

關於單相無序固溶體高熵合金的設計

Student thesis: Doctoral Thesis

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Award date19 Apr 2017

Abstract

High-entropy alloys (HEAs) are presently of great research interest in materials science and engineering. Unlike conventional alloys, which contain one and rarely two base elements, HEAs comprise multiple principal elements, with the possible number of HEA compositions extending considerably more than conventional alloys. Due to the complex interplay between multi-principal elements, different phases, such as single- and multi-phased solid-solution, intermetallic compounds and even metallic glasses, can be formed upon solidification of the corresponding metallic melts.

Assuming ideal mixing of atoms, design of HEAs was used to follow a simple route by maximizing their configurational entropy of mixing. In theory, this concept originates from an implicit assumption that the constituent elements of an alloy have the identical size and are very loosely packed. However, this is certainly not true for real alloys, in which the atomic sizes can be very different and the atomic packing is generally dense, forming typical lattice structures like face centered cubic (fcc) lattice or body centered cubic (bcc) lattice. To formulate the problem, we adapt the Manssori’s theory, according to which the total configurational entropy of mixing ST for an alloy can be expressed as ST = SC+SE, where SC denotes the configurational entropy of mixing for an ideal gas while SE the excessive entropy of mixing that is a function of atomic packing and atom size. By taking into account of the formation enthalpy and the excessive entropy of mixing, a generalized thermodynamic rule is proposed to govern the complex phenomena of phase selection in HEAs. The proposed paradigm is verified using the experimental data hitherto reported and proven to be a physically accepted thermodynamic parameter for the design of HEAs.

In general, the X-ray diffraction results are widely used to judge whether an HEA can form single-phase solid solution or not, however, recent experiments showed that elemental segregation occurs in some HEAs though their XRD patterns exhibit a nominal single-phase solid solution structure. Based on the 3-D atom probe tomography (APT) results obtained from the FeNiCoCrCu HEA, we further proposed a simple thermodynamics model based on the notion that elemental segregation facilitates stabilizing the solid solution phase with a minimized Gibbs free energy. Our model enables distinguishing nominal single-phased solid solution HEAs with and without elemental segregation. The predictions of our model are found in good agreement with the experimental data reported hitherto in the literature.

Complementary to the thermodynamic criterion, a geometric model was also developed to calculate the intrinsic residual strain in HEAs. For conventional alloys, such an intrinsic residual strain can be derived with the continuum theory of elasticity; however, the lack of distinction between solvent and solute atoms in recently developed HEAs simply defies such an approach. To solve this problem, we developed a general self-contained geometrical model that enables the calculation of the intrinsic residual strains around different sized elements in a multi-component alloy, which links the average lattice constant of the alloy to a few critical geometric variables related to the close atomic packing in that lattice, such as atomic size, atomic fraction and packing density. When applied to HEAs, our model unravels that the transition from a single- to multi-phase solid solution takes place when the RMS residual strain approaches ~5%. Furthermore, with this simple geometric model, we are able to show that glass formation in over two hundred glass forming alloys, including conventional and HEAs, can be correlated with the excessive fluctuation in the intrinsic residual. Generally, amorphization occurs when the RMS residual strain rises above ~10%, in good agreement with the Lindemann’s lattice instability criterion.