Data-mining of In-Situ TEM Experiments on the Dynamics of Dislocations in CoCrFeMnNi Alloys_2

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Data-mining of In-Situ TEM Experiments: on the

Dynamics of Dislocations in CoCrFeMnNi Alloys

Chen Zhanga, Hengxu Songa, Daniela Oliverosb, Anna Fraczkiewiczc, Marc

Legrosb, Stefan Sandfelda,d,∗

aInstitute for Advanced Simulations: Materials Data Science and Informatics (IAS-9),

Forschungszentrum J¨ulich GmbH, 52425, J¨ulich, Germany

bCEMES-CNRS, 29 Rue J. Marvig, 31055, Toulouse, France

c´

Ecole des Mines de Saint ´

Etienne, 42100 , Saint- ´

Etienne, France

dFaculty of Georesources and Materials Engineering, RWTH Aachen University, 52068,

Aachen, Germany

Abstract

High entropy alloys are a class of materials with many signiﬁcant improve-

ments in terms of mechanical properties as compared to “classical” alloys. The

corresponding structure-property relations are not yet entirely clear, but it is

commonly believed that the good mechanical performance is strongly related to

dislocation interactions with the complex energy landscape formed due to al-

loying. Although in-situ Transmission Electron Microscopy (TEM) allows high-

resolution studies of the structure and dynamics of moving dislocations and

makes the local obstacle/energy “landscape” directly visible in the geometry

of dislocations; such observation, however, are merely qualitative, and detailed

three-dimensional analyses of the interaction between dislocations and the en-

ergy landscape is still missing. In this work, we utilized dislocations as “probes”

for the local energy maxima which play the role of pinning points for the disloca-

tion movement. To this end, we developed a unique data-mining approach that

can perform coarse-grained spatio-temporal analysis, making ensemble averag-

ing of a considerable number of snapshots possible. We investigate the eﬀect of

pinning points on the dislocation gliding behavior of CoCrFeMnNi alloy during

in-situ TEM straining and ﬁnd that (i) the pinning point strength changes when

∗Corresponding author.

Email address: s.sandfeld@fz-juelich.de (Stefan Sandfeld)

Preprint submitted to Elsevier October 4, 2022

arXiv:2210.00478v1 [cond-mat.mtrl-sci] 2 Oct 2022

dislocations glide through and (ii) the pinning point moves along the direction

close to the Burgers vector direction. Our data-mining method can be applied

to dislocation motion in general, making it a useful tool for dislocation research.

Keywords: In-situ transmission electron microscopy (TEM), High entropy

alloy, Data mining, Coarse graining, Pinning point

1. Introduction

Multi-component complex alloys (MCCA) comprising near-equiatomic four

or more elements have gained increasing attention due to their promising me-

chanical properties when compared to traditional single-phase alloys [1–5]. Hy-

potheses brought forward to explain these enhanced properties include severe

lattice distortion, high entropy eﬀect (from which the initial acronym HEA-

High Entropy Alloy derives), and sluggish diﬀusion. These factors, speciﬁc to

this new class of alloys may reinforce the regular strengthening mechanisms

found in classical alloys and help achieve superior mechanical properties. The

single-phase face-centered-cubic (fcc) CoCrFeMnNi alloy (also known as “Can-

tor” alloy [2]) is one of the most studied [6, 7] and it exhibits high strength and

toughness, even at cryogenic temperature [8, 9].

The lattice friction, or Peierls barrier, is considered to be one of the key

aspects involved in strengthening mechanisms. The magnitude of the lattice

friction depends on the crystal lattice and atomic bonds and ultimately on the

dislocation core structure. However, the dislocation core is usually planar in fcc

material, consisting of two partial Shockley dislocations separated by a stacking

fault. Therefore, lattice friction is often neglected when considering strengthen-

ing mechanisms in fcc metals and alloys. However, due to large lattice distortion

and ubiquitous interactions among multiple principal atomic species, disloca-

tions face a rugged atomic and energy landscape, possibly resulting in a new

type of friction [10]. Through investigating thermal activation processes from

stress-strain measurements with varying temperatures and strain rates for a fam-

ily of equiatomic fcc single phase solid-solution alloys, Wu et al. [11] concluded

that the Labusch-type solution strengthening mechanism, rather than lattice

friction, governs the deformation behavior in equiatomic alloys. The solute

strengthening in HEAs is likely to be associated with either short-range clus-

tering or short-range ordering of solute atoms [12–15]. However, Lee et al. [16]

did not observe any chemical heterogeneity or ordered structures in the CoCr-

FeMnNi alloy of sizes down to the resolution limits of 1 nm at cryogenic temper-

atures using experimental techniques based on electron diﬀraction, STEM-EDS

(Scanning Transmission Electron Microscopy-Energy Dispersing Spectroscopy)

and APT (Atom Probe Tomography).

Some researchers believe that strengthening is caused by phase transforma-

tion, since ﬁrst-principle models anticipated a stable hcp phase at low tempera-

tures [17, 18]. Yu et al.[17] observed that the fraction of the stronger hcp phase

progressively increases during plastic deformation in the fcc phase in a Cantor-

like Cr20Mn6Fe34Co34Ni6alloy serving as the major source of strain hardening.

However, the hcp phase has not been found in the equiatomic cantor alloy for

the time being [16].

More people have recently recognized that local chemical ﬂuctuation (LCF)

is a common feature in HEAs and is considered to inﬂuence dislocation mo-

tion [19–22]. Curtin et al. [19] proposed a theory to explain the plastic yield

strength for fcc HEAs that has been validated by molecular simulations on model

Fe-Ni-Cr alloys. They consider each elemental component as a solute embedded

in the eﬀective matrix of the surrounding alloy, and deduced that the strength-

ening is mainly achieved due to dislocation interactions with the random local

concentration ﬂuctuations around the average composition. Ma et al. [20] con-

structed an atomic interaction potential for CrCoNi medium-entropy alloy and

demonstrated that the local chemical ordering changed during processing and

increased the ruggedness of the local energy landscape and raised the activation

barriers that govern dislocation activities.

These studies, mainly theoretical, therefore consider that strong pinning

points are impeding the dislocation movement on their gliding planes in HEA,

that these pinning points result from chemical and physical distortions of the

lattice and are potentially dense enough to generate a general friction force on

all dislocation movements. However, there are currently very few quantitative

reports on pinning eﬀects, because the interplay between energy and the very

local chemical ordering is diﬃcult to characterize and measure. Besides, small-

scale simulations are spatially and temporally constrained, which does not allow

them to grab a realistic and statistical view of such obstacles and their potential

strength. As moving dislocations carry a shear that has an interatomic length

scale, the landscape seen by one dislocation may diﬀer substantially from the

one seen by the following dislocations. This is especially true in alloys where

local order may be built up or inversely deconstructed by successive shears of

dislocations gliding on the same plane. As so, a moving dislocation, if one can

follow its individual or collective motion, is the ultimate probe to explore such

distorted landscapes as well as the vector of the on-going plastic deformation.

We aim to characterize and quantify the essence of the pinning points encoun-

tered by moving dislocations at a larger time span and nanometer scale, based

on experimental data from in-situ TEM straining.

For that purpose, we observed representative pile-up of dislocations gliding

on compact planes of a Cantor (CoCrFeMnNi equiatomic) alloy, then recon-

structed the three-dimensional dislocation microstructures, which allowed us to

detect the dislocation movement directly on a given glide plane. Next, based

on the bent angle of dislocation when passing by the pinning point, we built a

simple model to quantify the force of the pinning point and its evolution. In

the last section, we carried out the spatio-temporal analysis of the local pinning

points through coarse-graining of dislocation microstructure, in a way like the

conventional scanning technique [23]. We show that dislocation lines face an

evolving landscape as the deformation proceeds and that these local obstacles

are probably at the root of hardening mechanisms in the Cantor alloy. The

presented method may be generalized to other MCCA to assess the average

“friction stress” that would result from these multiple local interactions.

2. Methods

Below, we explain all the methods utilized in the analysis in detail. Sec-

tion 2.1 describes how the experiments were performed. Section 2.2 is con-

cerned with the three-dimensional reconstruction of dislocation lines from the

projected, two-dimensional TEM images. Section 2.3 introduces how the pin-

ning point strength can be estimated, and Section 2.4 derives and explains the

spatio-temporal coarse graining of dislocation microstructures.

2.1. In-situ TEM straining experiment

In-situ TEM straining experiments were carried out on a Cantor alloy pro-

cessed at Mines Saint-Etienne, France, and prepared as electron-transparent

stretchable samples following the method described in the previous work [24].

Additional videos can be found here. Videos are generally acquired after strain

increments are imposed to the sample on a Gatan straining holder model 671,

operated at 96K. They are captured on a Megaview III SIS CCD camera, di-

rectly connected to a hard drive where they are stocked in mpeg4 format.

2.2. 3D reconstruction of dislocation microstructure from TEM images

Dislocations as observed in the TEM images are essentially the projection of

the real dislocation lines in 3D space onto the experimental screen plane. There

are three orthogonal coordinate systems involved:

1. The World Coordinate System (WCS): is deﬁned as the coordinate

system of the TEM experiment bench. Usually, the sample is tilted by

an angle θalong a certain axis (in our experiments, the tilt is along the

y-axis) in WCS, as shown in Fig. 1.

2. The Sample Coordinate System (SCS), is typically aligned with some

of the axes of the sample geometry. For example, in Fig. 1, the sample

coordinate system xs, ys, zsis deﬁned along the sample edges.

3. The Crystal Coordinate System (CCS) is deﬁned along with the

lattice basis.

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Data-miningofIn-SituTEMExperiments:ontheDynamicsofDislocationsinCoCrFeMnNiAlloysChenZhanga,HengxuSonga,DanielaOliverosb,AnnaFraczkiewiczc,MarcLegrosb,StefanSandfelda,d,aInstituteforAdvancedSimulations:MaterialsDataScienceandInformatics(IAS-9),ForschungszentrumJulichGmbH,52425,Julich,GermanybCEMES...

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