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Page 2 of 15 Hansen et al. Microstructures 2023;3:2023029 https://dx.doi.org/10.20517/microstructures.2023.17

INTRODUCTION
The martensitic transformation is an important phenomenon, which is widely observed in many metals
[6-8]
[1-5]
[e.g., steels, shape memory alloys (SMAs), etc.] and ceramics (e.g., ZrO , VO , etc.) . During a
2
2
martensitic transformation, the martensite grains exhibit a well-defined crystallographic orientation
relationship with the parent austenite grains. For example, in Ni Ti Hf SMAs, the orientation
48.5
15
36.5
relationship between the B2 austenite and B19′ martensite is described as [100]B2//[100]B19′ and
(001)B2//(011)B19′ . Moreover, although the number of martensite grains in the same prior austenite grain
[9]
can be numerous, the martensite variant number is limited. Theoretical predictions based on the lattice
correspondences of B2 and B19 showed that 12 martensite variants are permitted . Note that not all 12
[10]
[10]
martensite variants will show up due to self-accommodation constraints . For example, only four
martensite variants were observed in a solution-treated Ni Ti Hf SMA, and there are well-defined
50.3
29.7
20
[11]
orientation relationships between the martensite variants .
The transformation behavior and properties of solid-state phase change materials are dictated by their
structure and substructure (e.g., martensite size, variant numbers, orientation relationship, the presence/
absence of internal twins, etc.). However, martensite characterization, in particular identifying the
martensite variant number and orientation relationship, has posed a challenge using conventional
microscopy techniques. Traditional transmission electron microscopy (TEM) imaging can reveal the size of
martensite grains but provides no information on the number of martensite variants and their
distribution [12,13] . Electron backscatter diffraction (EBSD) can be used to map martensite variants, but the
orientation maps are generally very noisy, with low indexing rates . Because of its limited resolution, EBSD
[14]
also fails to capture the crystallographic information if the martensite grains are small (e.g., plates or laths
[14]
< 150 nm in width) . Hence, there is a demand for techniques that can efficiently reveal martensite variant
information with high spatial resolution.

Precession electron diffraction (PED) is a powerful characterization technique to reveal the crystal structure
and orientation information at the nanoscale [15-22] . The electron beam in TEM is converged to a small probe
(~ 1-3 nm) and rastered on the specimen. Precession (typically 0.3-0.8 ) is applied to excite higher-order
o
reflections and to reduce the dynamical effect [15,23] . The experimentally acquired diffraction patterns from
each pixel are compared to the simulated diffraction patterns in a database to determine the crystal structure
and orientation. The information is then used to create phase (crystal structure) and orientation maps.
Naturally, the PED should be the ideal technique to obtain the martensite variant information in various
materials. Unfortunately, there are several associated challenges. First, many martensite grains contain high-
density twins, which leads to additional spots (and streaking) in diffraction patterns . The simulated
[11]
diffraction patterns in the database assume single crystals. Thus, the experimentally acquired diffraction
patterns that contain both diffraction spots from the matrix and the twin cannot find a good match in the
database and are considered bad indexing. Second, orientation indexing is generally poor for low-symmetry
crystals (monoclinic, triclinic, etc.) in PED because the small differences between different sets of lattice
planes cannot be easily distinguished by the orientation indexing software. The confusion leads to noisy
orientation maps (an example, see Figure 1).

In this work, by taking advantage of the superior spatial resolution and the diffraction information from
each pixel in PED, we developed three methods to create “crystallographic variant maps”. All methods
identify the crystallographic variants by comparing the diffraction patterns in the PED data, with the first
approach more manual and the second and third more automatic. The advantages and disadvantages of
each approach are described. Different methods to quantify the similarity between diffraction patterns, as
well as their influence on the final crystallographic variant maps, are also discussed. These new semi-