Quantitative chemical-structure evaluation using atom probe tomography: Short-range order analysis of Fe–Al

Highlights

• Short-range-order (SRO) is quantitatively evaluated using atom probe tomography data.

• Chemical species-specific SRO parameters have been calculated.

• The accuracy of this method is tested against simulated D0₃ ordered data.

• Imperfect spatial resolution combined with finite detector efficiency causes a randomising effect.

• Lattice rectification of the data prior to GM-SRO analysis is demonstrated to improve information sensitivity.

Abstract

Short-range-order (SRO) has been quantitatively evaluated in an Fe–18Al (at%) alloy using atom probe tomography (APT) data and by calculation of the generalised multicomponent short-range order (GM-SRO) parameters, which have been determined by shell-based analysis of the three-dimensional atomic positions. The accuracy of this method with respect to limited detector efficiency and spatial resolution is tested against simulated D0₃ ordered data. Whilst there is minimal adverse effect from limited atom probe instrument detector efficiency, the combination of this with imperfect spatial resolution has the effect of making the data appear more randomised. The value of lattice rectification of the experimental APT data prior to GM-SRO analysis is demonstrated through improved information sensitivity.

Introduction

Short-range order (SRO) is typically characterised in terms of well-established SRO parameter formalism [1], [2], where the apparent structure is commonly determined by Fourier analysis of the diffuse scattering intensity measured experimentally using bulk, volume-averaged techniques such as X-ray scattering, neutron scattering and Mössbauer spectroscopy. Atom probe tomography (APT), on the other hand, is a direct microscopy technique that provides a unique combination of highly resolved atomistic information, both chemically and spatially in three dimensions (3D), which can be data-mined for quantitative nanostructural information [3], [4]. Developing and applying methods for reliably revealing the SRO in alloys is essential for interpreting phase transformation phenomena and stress–strain response.

In this work, an Fe–18Al (at%) alloy has been investigated after thermal treatment to produce a state of SRO (further details contained elsewhere [5]), where analysis of the experimental APT data has been carried out using the recently developed generalised multicomponent short-range order (GM-SRO) parameters [6], [7]. Details are given in Section 2.3. This new definition is an extension of the pairwise multicomponent SRO (PM-SRO) parameter developed by de Fontaine [2], which itself has roots in the pairwise Warren–Cowley SRO (WC-SRO) parameter for binary systems [1]. GM-SRO analysis can handle not only correlations of pairs of atoms in multicomponent systems (i.e. the PM-SRO), but due to its generalised nature it can also consider multicomponent correlations in multicomponent systems [6], [7] and is, therefore, highly amenable to the highly spatially and chemically resolved tomographic data provided directly by atom probe microscopy [3], containing many millions of atoms.

GM-SRO analysis is carried out on APT data by shell-based counting of the atoms at discrete 3D radial distances, making this atom-by-atom analysis very similar to the calculation of radial distribution functions (RDFs) [8], [9], [10], [11]. While the latter refers to both chemical species-specific ‘partial RDFs’ and pair correlation functions, the former provides a complete set of GM-SRO parameters that statistically describe the atomic architecture. In a ternary A–B–C alloy for example, GM-SRO analysis results in the following set of parameters: $\alpha ={({\alpha }_{\left\{A\right\}\left\{A\right\}}^m,{\alpha }_{\left\{A\right\}\left\{B\right\}}^m,{\alpha }_{\left\{B\right\}\left\{A\right\}}^m,{\alpha }_{\left\{A\right\}\left\{C\right\}}^m,\dots ,{\alpha }_{\left\{A\right\}\left\{AB\right\}}^m,\dots ,{\alpha }_{\left\{AB\right\}\left\{BC\right\}}^m,\dots ,{\alpha }_{\left\{A\right\}\left\{ABC\right\}}^m)}^{m=1,2,3,\dots }$, for each shell number m at discrete radii. The parameter α_{AB}{BC}, for example, represents the distribution of B- and C-type atoms around A- and B-type atoms. Similarly, the parameter α_{A}{ABC} represents the distribution of A-, B- and C-type atoms around A-type atoms. By standard convention, a positive value of a GM-SRO parameter defines co-segregation (clustering) for a particular set of elements in a certain crystallographic shell, whereas a negative value indicates anti-segregation (ordering) of the two sets of elements [6], [7]. Accordingly, this parameter is equal to zero for a random configuration.

A standard definition of SRO with respect to the exact length scale of ordering does not exist, but clearly differs from long-range order (LRO), which refers to periodic repetition of the crystal lattice over larger distances. There also exists a definition for medium-range order (MRO), used within the amorphous materials community, which refers to order that extends over intermediate distances, beyond the second or third atomic shell, e.g. 1–2 nm [12], [13]. SRO, therefore, exists somewhere below these approximate values with the number of coordination (nearest-neighbour) shells depending on the material's lattice parameter.

In addition to RDFs, GM-SRO analysis extends the application of 3D atom probe data from statistical analysis using one-dimensional (1D) Markov chains and the Johnson and Klotz ordering parameter [14], [15], [16], [17], [18] to a more detailed description of SRO that compliments existing capability for LRO and site occupancy investigation [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29]. Whilst GM-SRO analysis has previously been carried out on systems containing clustering of solute atoms [7], [30], this work demonstrates its first application towards quantitative assessment of SRO.