Quantifying short-range order using atom probe tomography

Medium- and high-entropy alloys are an emerging class of materials that can exhibit outstanding combinations of strength and ductility for engineering applications. Computational simulations have suggested the presence of short-range order (SRO) in these alloys, and recent experimental evidence is also beginning to emerge. Unfortunately, the difficulty in quantifying the SRO under different heat treatment conditions has generated much debate on the atomic preferencing and implications of SRO on mechanical properties. Here we develop an approach to measure SRO using atom probe tomography. This method balances the limitations of atom probe tomography with the threshold values of SRO to map the regimes where the required atomistic neighbourhood information is preserved and where it is not. We demonstrate the method with a case study of the CoCrNi alloy and use this to monitor SRO changes induced by heat treatments. These species-specific SRO measurements enable the generation of computational simulations of atomic neighbourhood models that are equivalent to the experiment and can contribute to the further understanding and design of medium- and high-entropy alloys and other materials systems where SRO may occur.

Since the reconstitution procedure introduced here was based on estimating the detection loss and spatial resolution, some variance in the predicted SRO values is to be expected between instruments.Moreover, the relationship between SRO values and detector loss is alloy dependent.In equi-atomic ternary alloys, SRO diminishes with decreasing detector efficiency while it was previously shown to remain similar in a dilute binary system 7 .Additionally, the SRO parameters calculated from the experimental datasets were taken from the results for the first 7NN, which represents the atoms present in the first atomic shell distance from each reference atom in an FCC lattice.In the MEAs studied here, the 1 st and 2 nd shell distances were ~0.25 nm and ~0.36 nm, respectively.However, the spatial noise in the x-y direction was estimated to be  !,#$ = ~0.25 nm (also supported by Supplementary Fig. 8).The influence of inter-shell crossover due to spatial noise was simplified and the following 2 nd and 3 rd shells were assumed to be near random in the subsequent reconstitution process presented in Figure 5. Notwithstanding these assumptions, the approach appears to work.
Understanding the relatively simple FCC ternary alloy system studied here can set out a pathway for the development of more general reconstitution procedures 8 .We suggest that the simulation procedure introduced here can be applied to generate correction factors and a reconstitution procedure for any alloy composition, enabling ranging of the go/no-go regimes for the quantification of SRO, depending on instrumental performance.The present work allows an instrument-specific assessment of the capacity for SRO measurements based on spatial resolution and detection efficiency characteristics of the particular atom probe microscope.This is akin to electron microscopy where different electron optical configurations enable certain imaging over other modes.Here for example, one might expect that atom probes containing a reflectron have merit for high mass resolution but the degraded spatial resolution expected with the additional lensing and the degraded detection efficiency from additional mesh inserts will be to the detriment of SRO measurements.

Discussion of current advances in SRO measurements
This method was used to demonstrate that heat treatments can indeed generate changes in the degree of SRO in this system.Given the discussion and debate on these topics in the M/HEAs literature, the notion of using APT to measure SRO is a significant advance.Two classes of issues were considered to achieve this measurement.The primary or first order issues relate to the instrument-specifically finite detection efficiency and ion trajectory uncertainties.The secondary issues relate to the accuracy of the tomographic reconstruction and could be addressed by acquiring high quality data and applying crystallography-informed calibrations.The primary issues were addressed using a data science approach involving multiple atomistic simulations of both random and embedded SRO values to devise corrections to the SRO values for the detection efficiency and trajectory uncertainty.The SRO values measured from experimental APT data could then be used to as inputs to initialise a reconstitution process to determine the true SRO embedded in the sample.Our simulation framework enables the determination of when SRO can and cannot be measured using an atom probe microscope of given instrumental performance, and for a given alloy composition.The simulations provided here enable detection efficiency, lateral and in-depth spatial noise and alloy composition to serve as inputs to determine the threshold values of SRO that are measurable in APT.
We suggest that the quantification of the SRO in multicomponent equiatomic systems such as the M/HEAs studied here offers a new way to characterise and ultimately control atomicscale microstructure of these materials.For example, navigation of the thermomechanical processing of these alloys can be grounded in SRO assessments.
Supplementary Table 1 The specific values of the imposed SRO parameters for Figure 2b and the related maximum 95% confidence levels (CL) of different SRO values.