On the orientation dependence of ion-induced phase transformations in austenitic stainless steel

TL;DR

This paper shows how the crystal orientation of stainless steel affects how it transforms when exposed to ion beams.

Contribution

The study reveals orientation-dependent phase transformation behaviors in austenitic stainless steel under ion beam exposure.

Findings

Grains with beam orientations close to ⟨100⟩γ and ⟨110⟩γ axes remained untransformed or amorphized.

Grains near ⟨111⟩γ axis partially transformed into non-contiguous products.

Grains not aligned with the three principal axes fully transformed into a single contiguous product.

Abstract

This study characterises the effects of crystal orientation on the evolution of austenite decomposition to ferrite/martensite in AISI-304 stainless steel, induced by exposure to gallium ions with a focused ion beam. Samples were exposed to the beam multiple times and imaged by electron backscatter diffraction before and after successive exposures, with the data aggregated by orientation clustering to derive insights into the effects of orientation on phase change processes. Propensity to decomposition and produced surface morphologies were observed to have a strong dependence on orientation. Three distinct orientation-based transformation behaviours were observed: grains with beam orientations close to the \documentclass[12pt]{minimal}
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\begin{document}$$\langle 1 1 1\rangle \gamma$$\end{document}⟨111⟩γ axis were partially transformed to non-contiguous products at various absolute orientations with beam orientations close to the \documentclass[12pt]{minimal}
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\begin{document}$$\langle 1 1 0\rangle \alpha$$\end{document}⟨110⟩α axis; and grains with beam orientations not close to any of the three principal axes were fully transformed to a single contiguous product with beam orientations close to the \documentclass[12pt]{minimal}
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Figures

Pattern quality map of sample surface, showing pairs of parallel guide trenches used to divide surface into cells for EBSD scan alignment. Scans of Cells A and B are showcased in Figs. [3](#Fig3), [4](#Fig4) and [5](#Fig5). Image dimensions: 1.90 × 1.42 mm

Implantation concentration and nuclear energy deposition profiles for gallium dosing of AISI-304 stainless steel by FIB, generated by SUSPRE software [[13](#CR13)].

Cells A (left) and B (right) on the sample surface, as shown in Fig. [1](#Fig1), imaged by EBSD prior to ion dosing. The upper pair of maps show phase, the middle pair show orientation in the z-direction (normal to the surface), and the lower pair show orientation in the y-direction (the vertical axis of the maps). Selected grains are labelled 1–7 for discussion.Figure 4Cells A (left) and B (right) on the sample surface, as shown in Fig. [1](#Fig1), imaged by EBSD after a total ion dose of 3,000 µC cm^−2^. The upper pair of maps show phase, the middle pair show orientation in the z-direction (

IPF diagrams for the beam direction, with bubbles marked for each orientation cluster in the collected data across the five cells. The beam vector used for each cluster’s projection depends on the ion beam incidence angle used for that cluster’s cell. Bubbles are centred on the beam direction projection coordinates, have areas proportional to the number of constituent map pixels, and have colours denoting their transformation morphology. Figure 6a (left) shows bubbles for γ-Fe orientation clusters prior to ion dosing. Figure 6b (right) shows bubbles for α-Fe orientation clusters at a total ion

IPF diagrams showing channelling fraction at each orientation, with γ-Fe on the left and α-Fe on the right, determined from a channelling model calibrated with a Monte Carlo simulation [[18](#CR18)]. For each diagram, the upper unit triangle shows channelling fraction as a heatmap, while the lower triangle shows regions of zero and nonzero channelling fraction in white and black respectively.

Full text

Introduction

It is well known that a focused ion beam (FIB) can cause damage to the microstructure of crystalline materials. This includes the triggering of phase transformations, the introduction of lattice defects, and, in extremis, amorphisation [1–4]. These changes result from the localised thermal and strain energies imparted to the material by the impact of energetic ions, in addition to the changes in phase stabilities induced by the chemistry of implanted beam species. One such effect is the ion-induced decomposition of austenite (γ-Fe) in austenitic stainless steels, which transforms to ferrite or martensite (α-Fe), or to amorphous material [5–12]. Austenite decomposition can drastically alter the mechanical properties and corrosion resistance of samples. Specifically, gallium, the most widely utilised FIB species, is known to have embrittling effects [10], leading to several comparative studies into the efficacy of alternatives, notably xenon [2, 3, 7]. Gallium has also been demonstrated to have a ferrite-stabilising effect [10].

Such FIB-induced austenite decomposition has been found to depend on beam energy, incidence angle, material properties, and crystal orientation [5–12]. However, studies investigating the effects of crystal orientation are few in number, generally tightly scoped, and lacking in consensus. Specifically in the literature on AISI-304 stainless steel, several studies have examined the degree of transformation with respect to ion dose [6–8]. The highest reported dose for which the microstructure was observed to remain untransformed was 2,080 µC cm^−2^ [6] and the lowest for which it was observed to be fully transformed was 4,640 µC cm^−2^ [6], suggesting a critical dose required to trigger the transformation in this interval.

Some studies have reported that the transformed products of each parent grain adopt a single dominant orientation [7, 8], while others found that a large range of product orientations were produced [7]. Grains with particular orientations parallel to the beam were found by some studies to transform more readily than others, particularly those with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\langle 1 1 1\rangle \gamma$$\end{document} poles normal to the surface versus those with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\langle 1 0 0\rangle \gamma$$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\langle 1 1 0\rangle \gamma$$\end{document} surface normals, respectively [6, 7]. This dependence on orientation is currently understood to be a result of ion channelling [5, 6, 12]. In direct contradiction, another study found no orientation dependence [8]. Several studies have observed transformation products to adopt certain well-known FCC/BCC orientation relationships with parent grains, namely the Kurdjumov–Sachs and Nishiyama–Wasserman orientation relationships [6–8]. Others report similar austenite decomposition dependent on beam orientation in experiments involving in AISI-316 stainless steel [8] and super-duplex steels [5].

While there has been some limited commentary on the evolution of the phase change for specific orientations with low-order zone axes parallel to the beam, there remains a distinct gap in published literature for studies over the full range of austenite orientations. Informed by these findings, this study seeks to begin addressing this gap by conducting a systematic study of the effects of crystal orientation on this phase transformation over a carefully chosen range of ion doses.

Materials and methods

The samples discussed in this study are sections of a commercial AISI-304 stainless steel bar. The composition of the bar was measured by laser-induced breakdown spectroscopy performed using a SciAps Z-902 Carbon Analyser and is given in Table 1. The samples were heat treated to ensure relatively large grains and low dislocation densities, by holding at 1100 °C for 4 h and furnace cooling. They were then first polished on an ATM Saphir 520 rotary polisher using standard metallographic methods and finished on an ATM Saphir Vibro polisher using a 40-nm colloidal silica polishing agent.Table 1. Composition of AISI-304 stainless steel samples as measured by laser-induced breakdown spectroscopyElementContent (wt.%)FebalanceCr18.4Ni7.7Mn1.9Si0.21Mo0.04C0.016S0.007P0.006Nnone

In order to ensure that the same areas of the sample surfaces could be consistently reimaged before and after ion exposures, a grid was used to divide the surface into regions of interest. The grid cells were created by milling two parallel guide trenches into the surface using a TESCAN FERA3 dual beam SEM/Xe-FIB, at a distance apart equal to the desired EBSD map width (230 µm), as shown in Fig. 1. When performing EBSD, the vertical edges of the map were aligned with the trenches and the upper corners of the map with the top of each trench. This approach meant the deep trenches were easily visible by secondary electron imaging and difficult to inadvertently remove. However, there was associated damage to the surface around the trenches due to the ion beam tails.Figure 1. Pattern quality map of sample surface, showing pairs of parallel guide trenches used to divide surface into cells for EBSD scan alignment. Scans of Cells A and B are showcased in Figs. 3, 4 and 5. Image dimensions: 1.90 × 1.42 mm

To eliminate this surface damage, the samples were repolished following milling, leaving only the deeper trenches. Based on polishing depth tests, this was expected to remove roughly 1.3 µm of material from the sample surface. EBSD maps were taken of the region around preliminary test trenches before and after repolishing, and it was found that, prior to repolishing, an appreciable difference in pattern quality extended further than 100 µm from each trench, whereas after repolishing there was no apparent damage more than 10 µm from each trench. The pattern quality map in Fig. 1 was taken after repolishing.

Pairs of horizontally adjacent grid cells were selected for the gallium ion exposures in which either a single large grain or two grains with a mutual twin interposed overlapped both cells. This allowed investigation of the effects of exposing each of the two paired cells at different beam tilts, in order to compare the resulting phase transformation using the same crystal orientations. Each cell of interest was imaged by EBSD prior to performing any exposures, using a Jeol JSM-7100F SEM equipped with a Thermo Lumis EBSD detector and Thermo Pathfinder acquisition software. All EBSD scans were taken with an accelerating voltage of 20 keV, a sample tilt of 70°, a scan area of 230 × 173 µm^2^, and a pattern resolution of 640 × 400 pixels.

Based on dosing tests, an ion dose of 3,000 µC cm^−2^, a beam energy of 30 keV, and a beam current of 20 nA were selected as the initial gallium ion exposure conditions. Beam tilts of either 0° (normal to the surface) and 5° were used for each cell of interest, which were individually exposed to gallium ions at their respective beam tilts with an FEI Nova 600 NovaLab dual beam SEM/Ga-FIB, using a beam spot size of 300 nm and a step size of 150 nm. The cells were then reimaged by EBSD. Finally, the cells of interest were individually exposed under the same conditions as previously with an additional ion dose of 1,000 µC cm^−2^ (for a total of 4,000 µC cm^−2^), before being reimaged a final time.

SUSPRE software [13] was used to determine some implantation statistics. For the composition given in Table 1, a mass density of 7.800 g cm^−3^, a beam energy of 30 keV, and a beam current of 20 nA, SUSPRE produced the implantation concentration and nuclear energy deposition profiles shown in.

Figure 2 for the doses used. SUSPRE also reported a mean implantation depth of 10.3 nm and an average sputter yield of 5.61 atoms per ion.Figure 2. Implantation concentration and nuclear energy deposition profiles for gallium dosing of AISI-304 stainless steel by FIB, generated by SUSPRE software [13].

Observations

Figures 3, 4 and 5 show a selected pair of adjacent cells, henceforth Cells A (left) and B (right), at each of three ion doses: 0, 3,000, and 4,000 µC cm^−2^, respectively. Six maps are shown in each figure: a phase map (top), a z-direction orientation map (middle), and a y-direction orientation map (bottom) for each of the two cells. Throughout this paper, the z-direction refers to the normal to the sample surface, and the y-direction refers to the vertical axis of the maps. Grains of interest for discussion are marked with numeric labels. These two cells were chosen for presentation to highlight a critical case, that of Grains 4A and 4B, which have the same orientation via an interposed mutual twin. Cell A was exposed to ions at a tilt of 5° to the surface normal, while Cell B was exposed at normal incidence, with no other differences in exposure conditions.Figure 3. Cells A (left) and B (right) on the sample surface, as shown in Fig. 1, imaged by EBSD prior to ion dosing. The upper pair of maps show phase, the middle pair show orientation in the z-direction (normal to the surface), and the lower pair show orientation in the y-direction (the vertical axis of the maps). Selected grains are labelled 1–7 for discussion.Figure 4. Cells A (left) and B (right) on the sample surface, as shown in Fig. 1, imaged by EBSD after a total ion dose of 3,000 µC cm^−2^. The upper pair of maps show phase, the middle pair show orientation in the z-direction (normal to the surface), and the lower pair show orientation in the y-direction (the vertical axis of the maps). Selected grains are labelled 1–7 for discussion.Figure 5. Cells A (left) and B (right) on the sample surface, as shown in Fig. 1, imaged by EBSD after a total ion dose of 4,000 µC cm^−2^. The upper pair of maps show phase, the middle pair show orientation in the z-direction (normal to the surface), and the lower show maps orientation in the y-direction (the vertical axis of the maps). Selected grains are labelled 1–7 for discussion.

For all the cells exposed during the experimental programme, four distinct microstructural changes were observed in different grains in response to ion dosing:

• Remaining predominantly untransformed up to 4,000 µC cm^−2^. Exemplified by Grains 7 and 4A.
• Remaining predominantly untransformed up to 3,000 µC cm^−2^, and then becoming predominantly amorphised by 4,000 µC cm^−2^. Exemplified by Grains 2 and 4B.
• Remaining predominantly untransformed up to 3,000 µC cm^−2^, and then becoming predominantly transformed by 4,000 µC cm^−2^, to produce a contiguous product of a single orientation. Exemplified by Grains 3 and 6.
• Undergoing a partial transformation by 3,000 µC cm^−2^, which continues to proceed up to 4,000 µC cm^−2^, to produce non-contiguous products at various orientations. Exemplified by Grains 1 and 5.

Other than grains directly bordering the milled trenches, and very small grains that could not be easily resolved, all grains were observed to conform to one of these transformation morphologies over all experiments performed. The critical case of Grains 4A and 4B, which differed only in orientation relative to the beam, illustrates the orientation dependence in the development of the morphologies. These morphologies are henceforth referred to as “untransformed”, “amorphised”, “fully transformed”, and “partially transformed”, respectively. The term “amorphised” is here used to refer to previously ordered surface areas that appeared amorphous following dosing. This is expected to comprise material formed partially by disordering of existing material and partially by newly deposited material following sputtering.

Of further note, grains that were partially transformed often had products with various orientations, but which all had similar projections in the z-direction. This can be seen in Fig. 5, in which the products of Grains 1 and 5 appear green in the z-direction orientation map, but have different colours in the y-direction orientation map. Analysis of such transformation products showed that particularly dominant orientations in partial transformations always had qualities that favoured their formation, either an orientation relationship with the parent (Kurdjumov–Sachs or Nishiyama-Wassermann) or a high channelling fraction for the ion exposure conditions used.

Analysis

To further investigate the orientation dependence of the transformation morphologies, data across five cells was aggregated by clustering, including Cells A and B. Though other cells had been subject to ion doses as part of the overall experimental programme, their dosing conditions were different, and so their data were not directly comparable in this analysis. Similar effects were however observed in those cells and, vitally, no cases contradicting the conclusions drawn in this paper were observed [14].

The EBSD data were exported from the acquisition software in comma-separated value format with columns for the indexed phase ID, Bunge-Euler angles, pattern quality, and index quality of each pixel. These were then read into bespoke Python programmes for processing, made available under open licence [15]. The pixels comprising each map were aggregated into discrete orientation clusters using an implementation of the popular DBSCAN clustering algorithm [16]. Terms specific to this algorithm are highlighted when appearing for the first time in this text.

Clustering was based only on orientation with no consideration of spatial position, so that pixels in two separate grains with similar enough orientations within the same cell would be aggregated into the same cluster. Clusters did not combine pixels from different cells. The implementation takes two parameters: the maximum misorientation \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Theta$$\end{document} between two pixels (the neighbourhood radius) in order for them to be considered directly reachable, and the minimum number \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n$$\end{document} of directly reachable neighbours for a pixel to be considered a core point and seed cluster formation. Two pixels \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p$$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q$$\end{document} with orientation matrices \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\boldsymbol{R}}}_{p}$$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\boldsymbol{R}}}_{q}$$\end{document} , respectively, are directly reachable if their misorientation \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta \theta$$\end{document} (the distance function) is less than \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Theta$$\end{document} :

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Delta }\theta \left( {p,q} \right) \le {\Theta }$$\end{document}

where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta \theta$$\end{document} is given by:

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Delta }\theta \left( {p,q} \right) = {\mathrm{acos}}\left( {\frac{{{{\boldsymbol{\Delta}}}{\boldsymbol{R}}_{ii} \left( {p,q} \right) - 1}}{2}} \right)$$\end{document} \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\boldsymbol{\Delta}}}{\boldsymbol{R}}\left( {p,q} \right) = {\boldsymbol{R}}_{q} {\boldsymbol{R}}_{p}^{ - 1}$$\end{document}

The selection of clusters for border points has the potential to be non-deterministic, depending on the implementation, as a border point can be connected to core points in more than one cluster. In this implementation, each border point is assigned to the same cluster as its closest directly reachable core point, which makes the method fully deterministic. As a result, for a given pair of clustering parameters \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n$$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Theta$$\end{document} , the same orientation clusters were always produced for the same EBSD data.

Having performed orientation clustering, average cluster metrics were computed over the pixels in each cluster. For scalar metrics, such as pattern quality, a simple arithmetic mean was used. The average Bunge–Euler angles for each cluster were determined from the average rotation matrix \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\overline{{\boldsymbol{R}} }$$\end{document} over the cluster’s pixels. For the set of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N$$\end{document} rotation matrices \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\boldsymbol{R}}}_{n}$$\end{document} belonging to a cluster, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\overline{{\boldsymbol{R}} }$$\end{document} is obtained by first determining the entrywise arithmetic mean \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\widetilde{{\boldsymbol{R}}}$$\end{document} and then taking a singular value decomposition:

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tilde{\user2{R}} = \frac{1}{N}\mathop \sum \limits_{n}^{N} {\boldsymbol{R}}_{n}$$\end{document} \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tilde{\user2{R}} = {\boldsymbol{USV}}$$\end{document} \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\overline{\user2{R}} = {\boldsymbol{UV}}$$\end{document}

where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\boldsymbol{U}}$$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\boldsymbol{V}}$$\end{document} are orthogonal rotation matrices and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\boldsymbol{S}}$$\end{document} is a diagonal scaling matrix. The projection of each cluster’s orientation in the beam direction was determined from the average Bunge–Euler angles. The beam vector used for a cluster’s projection depended on the dosing conditions for that cluster’s cell, either normal to the surface (e.g. for Cell B) or 5° from the normal (e.g. for Cell A). In addition to computed metrics, each cluster in the 0 µC cm^−2^ maps was examined to classify its transformation morphology following dosing, evaluated according to the following criteria in order of precedence:

1. A cluster observed to remain largely untransformed at 4,000 µC cm^−2^ was labelled “untransformed”.
2. A cluster observed to be partially transformed to non-contiguous products at 3,000 µC cm^−2^ was labelled “partially transformed”.
3. A cluster observed to be mostly amorphised at 4,000 µC cm^−2^ was labelled “amorphised”, regardless of the phase of the minority non‐amorphous pixels.
4. A cluster observed to be untransformed at 3,000 µC cm^−2^ and fully transformed to a single contiguous product at 4,000 µC cm^−2^ was labelled “fully transformed”.

Clusters that met any of the following criteria were not classified and excluded from this analysis:

• Those that did not occur in the maps for both subsequent doses due to misalignment.
• Those that shared large fractions of their perimeters with a cell-marking trench with respect to their area.
• Those that were too small to confidently determine their states of transformation at both subsequent doses.

All clusters in the 0 µC cm^−2^ maps were classified or excluded according to these criteria, with little scope for ambiguity.

Results

Figure 6a shows an IPF diagram for the beam direction, with each orientation cluster across the five cells at 0 µC cm^−2^ marked as a bubble centred on the coordinates given by its beam direction projection, with an area proportional to the number of its constituent pixels, and a colour given by its classification. Some trends are immediately visible:

• Grains with orientations close to the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\langle 1 0 0\rangle \gamma$$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\langle 1 1 0\rangle \gamma$$\end{document} axes tend to remain untransformed or become amorphised.
• Grains with orientations close to the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\langle 1 1 1\rangle \gamma$$\end{document} axis tend to be partially transformed.
• Grains with orientations not close to any of the three principal axes tend to be fully transformed. Figure 6IPF diagrams for the beam direction, with bubbles marked for each orientation cluster in the collected data across the five cells. The beam vector used for each cluster’s projection depends on the ion beam incidence angle used for that cluster’s cell. Bubbles are centred on the beam direction projection coordinates, have areas proportional to the number of constituent map pixels, and have colours denoting their transformation morphology. Figure 6a (left) shows bubbles for γ-Fe orientation clusters prior to ion dosing. Figure 6b (right) shows bubbles for α-Fe orientation clusters at a total ion dose of 4,000 µC cm^−2^. A diagram showing γ-Fe orientation clusters after dosing is not included, as it simply shows the untransformed bubbles unmoved from their pre-dosing positions. Grains 1–7 featured in Figs. 3, 4 and 5 are outlined and labelled.

Further, Fig. 6b shows another IPF diagram in the same style, with bubbles marked for the orientation clusters across the five cells at 4,000 µC cm^−2^ that showed either the partial or full transformation morphologies, according to the classification of their transformation parents. Again, some trends are visible:

• Grains produced by partial transformations had orientations closer to the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\langle 1 1 0\rangle \alpha$$\end{document} axis.
• Grains produced by full transformations had orientations closer to the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\langle 1 0 0\rangle \alpha$$\end{document} axis.
• Grains were not produced close to the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\langle 1 1 1\rangle \alpha$$\end{document} axis in either morphology.

Discussion

Before discussing the physical mechanisms behind the trends observed, it is necessary to take into account the quality of the data. Based on control measurements taken with the EBSD system, a total uncertainty of 5° was found on orientations due to various misalignments, while the FIB system showed no significant deviation. Additionally, the descriptive nature of the morphology classification process has the potential to result in mis-classifications. Despite these factors, the trends apparent in the bubble charts are distinct enough to give broad confidence as to their veracity and significance. Close agreement was also observed with some of the key findings of previous studies [5–7].

The trends observed firmly establish the dependence of the transformation morphology on the orientation of parent grains and of the orientation of product grains on the transformation morphology. Barring a few small anomalies, there is a sharp division between the range of orientations that transformed partially and fully. Combined with the lack of observations of grains producing both morphologies at once, this suggests that competing physical transformation mechanisms lead to the two morphologies. The physics involved in the transformations are understood to comprise a number of phenomena, including channelling effects, surface and interfacial energies, strain, and chemical potential, though some correlations with predications made by current channelling theory are apparent.

Figure 7 shows channelling fraction maps generated by a model calibrated using a Monte Carlo simulation [17], using code provided by one of the authors, fully explained in Ref. [18] and included in the codebase for this paper [15]. The strongest channelling direction, the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\langle 1 1 0\rangle \gamma$$\end{document} axis, is close to the orientations of most untransformed grains seen in Fig. 6a, confirming the notion that channelled ions interact less strongly with the target than those moving in other directions. Similarly, the maximum at the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\langle 1 1 1\rangle \gamma$$\end{document} axis, near which no untransformed grains were observed, is significantly weaker than those at the other principal axes. The presence of the channelling fraction maximum along the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left(1 1 1\right)\gamma$$\end{document} plane is also reasonably well-aligned with the division between the fully and partially transformed areas. These correlations demonstrate a possible direct dependency between channelling and the observed transformation morphologies. It is worth considering that the underlying Monte Carlo model used does not consider second-order effects of ions not moving in the beam direction, particularly post-scattering motion of beam ions, and motion of target ions due to recoil, which has preferentially larger components perpendicular to the beam direction.Figure 7IPF diagrams showing channelling fraction at each orientation, with γ-Fe on the left and α-Fe on the right, determined from a channelling model calibrated with a Monte Carlo simulation [18]. For each diagram, the upper unit triangle shows channelling fraction as a heatmap, while the lower triangle shows regions of zero and nonzero channelling fraction in white and black respectively.

There is no similarly clear division between the range of orientations producing untransformed and amorphised morphologies. Initial dosing tests showed that all γ-Fe grains were eventually either transformed or amorphised at sufficiently high doses, and these two morphologies can be attributed to the same mechanism, whereby the untransformed grains are simply those that have not received a sufficient volumetric dose to trigger amorphisation. Grains with orientations closer to channelling fraction maxima would receive lower volumetric doses for the same planar dose, due to higher mean free paths resulting in sparser deposition within the crystal matrix. It is speculated that, with improved data quality, this trend would be directly apparent in the results.

The three competing morphologies raise the question of how they might map onto the possible mechanisms of phase transformation. The operation of two quite distinct mechanisms of phase transformation, diffusive/diffusional and displacive/martensitic/shear has been a consensus for several decades, even if the terminology is used inconsistently and some uncertainties remain concerning the atomic-scale mechanisms of interface migration. One possible explanation for the two forms of transformation of γ-Fe to α-Fe might be that one is diffusive and the other displacive. Substantiating such a proposal raises a number of challenging issues, not least (1) whether there is sufficient local volume diffusion for a diffusive transformation and (2) the creation of strain and stress arising from a displacive transformation.

The existence of the unambiguous third option, amorphisation, is instructive. Amorphisation is the result solely of mechanical displacement of atoms as a result of ion incidence and the resulting cascade of atomic displacement. Where this occurs, there is evidently no possibility for sufficient diffusion to enable the formation of α-Fe iron, or for possible shearing mechanics. Given that even small doses of gallium will thermodynamically favour α-Fe over γ-Fe, the occurrence of amorphisation points to diffusion being very limited. It is suggested that this limited diffusion, enabled by the ion beam in this study, indicates that both phase transformations observed are displacive and that the resulting differences in their ease of completion, albeit in a thin surface layer, and crystallography are the result of the limitations placed on transformation by the stress that accompanies the lattice shearing. Work is ongoing to understand how the invariant plane relates to both of the observed transformations in terms of the grain orientation and the adoption of distinct variants of the Kurdjumov–Sachs and Nishiyama-Wasserman orientation relationships.

Conclusions

Surface morphologies of α-Fe grains produced by FIB-induced γ-Fe decomposition in AISI-304 stainless steel were found to have a strong dependence on crystal orientation relative to the incident ion beam. Three distinct behaviours were observed: grains with beam orientations close to the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\langle 1 0 0\rangle \gamma$$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\langle 1 1 0\rangle \gamma$$\end{document} axes remained untransformed or become amorphised; grains with beam orientations close to the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\langle 1 1 1\rangle \gamma$$\end{document} axis were partially transformed to non-contiguous products at various absolute orientations with beam orientations close to the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\langle 1 1 0\rangle \alpha$$\end{document} axis; and grains with beam orientations not close to any of the three principal axes were fully transformed to a single contiguous product with beam orientations close to the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\langle 1 0 0\rangle \alpha$$\end{document} axis. Grains were not produced close to the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\langle 1 1 1\rangle \alpha$$\end{document} axis in any case. The physical transformation mechanisms behind these behaviours remains an open question, with further development of current theories of channelling and phase changes likely necessary to fully explain the observed trends.

Data Availability

The data used to generate the bubble charts, in addition to the code used to conduct the analysis, are available on GitHub under open licence: https://github.com/james-whiteside/ebsd-utils.