A predictable glass forming ability expression by statistical learning and evolutionary intelligence

Highlights

• A new predictable GFA expression in terms of generic elemental attribute has been developed.

• Five ternary alloy systems have been validated.

• The GFA expression has shown good correspondence with energy of formation of stable compounds of the alloy systems.

Abstract

This paper demonstrates how principal component analysis of multivariate BMG alloy data and the genetic programming of the extracted features in the form of principal components can be used to develop a meta-modeling scheme for GFA expression. The proposed GFA model can estimate the glass forming potential of an alloy from its composition data, unlike the characteristic temperature based glass forming ability expressions, consisting of T_g, T_xand T_l. The BMG alloys have been described by means of generic attributes of the constituent elements and corresponding composition of the alloy yielding a multi-dimensional descriptor space for a 594 BMGs compiled from literature. The PCA model of the data base plausibly reduced the dimensionality into a two dimension in terms of two extracted features by first two principle components capturing the 82% of the data knowledge. Successively, these principle components are used to develop a constitutive model for glass forming ability using genetic programming. The combinatorial analysis of the meta-model for GFA expression is applied to the prediction of potential compositional zone in five different experimentally explored ternary systems. The predicted composition zones are discussed in the context of available experimental data in literature and the energy of formation of the stable phases in respective alloy systems.

Introduction

The bulk metallic glasses (BMGs) offer attractive properties to consider them as potential material for many advanced technological applications [1]. However, the limited section thickness, which can be produced as glass, without significant crystallization, limits such possibilities. Many compositional design methodologies have been proposed and used to design the composition of the bulk metallic glasses, with marginal success. For instance, the compositions explored and established for high glass forming ability generally bear costly elements like Pd and rare earths [1]. Therefore, it is essential to search for low cost BMGs with high glass forming ability (GFA) to utilize the technological advantages offered by these glassy materials. The experimental exploration for the compositions with high glass forming ability is an expensive and tedious method. Therefore, as an alternative, it is proposed to predict the glass forming ability of an alloy composition, before its actual physical preparation.

The glass forming ability indicator expressions may be instrumental to formulate a better compositional design strategy. Nevertheless, different glass forming ability indicator expressions have been reported in terms of characteristic temperatures(T_g, T_x and T_l,whereT_g stands for glass transition temperature, T_x-onset temperature of crystallization and T_l is offset temperature of melting)of the metallic glass [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21]. These characteristic temperatures based GFA indicator expressions are useful to estimate the glass forming ability once the metallic glass is physically prepared. These GFA expressions lack the predictive capability from the generic data of the alloy, i.e. they cannot be used to estimate the glass forming ability of a composition before actual preparation of alloy [12]. Despite of the intensive efforts from the metallic glass workers, quantifying as well as predicting the glass forming ability still remains an open question [12].

Also few alternative approaches have been reported in the literature. The Inoue's empirical rule [3], deep eutectic based compositional design [22], [23], structure and topologybased approach [24], [25], [26], data training of artificial neural network [27], [28] are to name a few effort made to develop a strategy for compositional design.Also the thermodynamics based approach [29], [30], [31], [32], [33], cluster line based approach [34], [35], [36], molecular dynamics simulation based approach [37], [38] and a golden mean analysis based approach [39] has been attempted to design the BMG compositions.However, these attempts have led to limited success due to one or other constraints.

Nevertheless, over the past few years the data driven approachesare gaining reasonable attention of the metallic glass workers to derive more plausible solution of the problem [40], [41], [42], [43], [44], [45].Therefore, development of data driven model-capable to predict glass forming ability of a composition may providebetter opportunity for combinatorial analysis to audit a wide range of species of BMG composition.In this work, a meta-modeling approach using principle component analysis to statistically model the new features,i.e. principal components, subsequently used as model input, to model the GFA expression using evolutionary intelligence of genetic programming has been presented.The prediction results of the proposed meta-model of GFA expression has been discussed as case study in few ternary alloy systems.