Crystal Nucleation in Al-Ni Alloys an Unsupervised Chemical and Topological Learning Approach Sébastien Becker1 2Emilie Devijver3Rémi Molinier4and Noël Jakse1

2025-04-27 0 0 9.76MB 29 页 10玖币

侵权投诉

Crystal Nucleation in Al-Ni Alloys:

an Unsupervised Chemical and Topological Learning Approach

Sébastien Becker,

1, 2

Emilie Devijver,

Rémi Molinier,

and Noël Jakse

Univ. Grenoble Alpes, CNRS, Grenoble INP, SIMaP, F-38000 Grenoble, France

Univ. Grenoble Alpes, CNRS, Grenoble INP, LIG, F-38000 Grenoble, France

CNRS, Univ. Grenoble Alpes, Grenoble INP, LIG, F-38000 Grenoble, France

Univ. Grenoble Alpes, CNRS, IF, F-38000 Grenoble,France

(Dated: October 6, 2022)

Abstract

Crystallization represents a fundamental process engendering solidiﬁcation of a material and

determines its microstructure. Driven by complex phenomena at the atomic scale, its understanding

for alloys still remains elusive. The present work proposes a large scale molecular dynamics simulation

study of the homogeneous crystal nucleation pathways of prototypical undercooled Al-Ni binary

alloys. An unsupervised topological learning analysis shows that the nucleation sets in ﬁrst from

a chemical ordering, followed by a bond-orientational ordering of the underlying crystal phase.

Our results indicate also a diﬀerent polymorph selection that depends on composition. While the

nucleation pathway of Al

displays a single step with the emergence of B2 short-range order, a

step-wise nucleation toward the L1

phase is seen for Al

. The inﬂuence of the nucleation of

pure Al and Ni counterparts is further discussed.

arXiv:2210.01894v1 [cond-mat.mtrl-sci] 4 Oct 2022

I. INTRODUCTION

Understanding homogeneous crystal nucleation during which an undercooled liquid morphs

into its underlying crystalline phase is of importance from a fundamental point of view as well

as on the application side for materials manufacturing in industrial applications [

]. Its

intimate complex mechanisms take their roots at the atomic level and involve local symmetry

breaking that can hardly be observed experimentally until very recently for Fe-Pt binary

metallic nanoparticles by atomic electron tomography [

]. However, especially for metallic

materials, identifying the early stages of nucleation from an experimental point of view is

still merely out of reach, and simulations at the atomic scale remain largely the dedicated

tools, applied to generic models [

–

], pure metals [

–

] and alloys [

–

] to name a few.

In classical nucleation theory, crystal nucleation and its rate can be attributed essentially

to two thermodynamic factors, namely, the enthalpy diﬀerence between the crystal and liquid

at the melting point, and eﬀective crystal-liquid interfacial free energy. They depend also

on atomic transport in the liquid state such as the diﬀusion [

]. The seminal work of

Turnbull [

] on the ability to deeply undercool monatomic liquid metals led to consider

that the local atomic ordering of the undercooled melt might be incompatible with the

crystalline structure, thus impeding crystal nucleation. It was later shown by Frank [

]

that the icosahedral ordering is locally more stable than the crystalline counterpart, which

has triggered many theoretical and experimental works [

] in terms of the variety of

polymorphs [

], competing short-range orders [

], or an interplay between chemical

and ﬁve-fold symmetry orderings in the case of liquid alloys [

]. For the latter

multi-component systems, this raises naturally the question of the nature of the chemical

and topological local orderings, and how they play a role at the onset of nucleation, which

still remains open.

In order to uncover the structural features prior and during homogeneous crystal nucleation

process in large scale molecular dynamics simulations without a priori, an unsupervised

learning approach [

] was proposed very recently [

]. The method is based on topological

data analysis (TDA) through persistent homology (PH) [33, 34], which emerged recently in

the ﬁeld of materials science as a mean to identify local atomic structure as a post-treatment

in atomic scale simulations [

–

], or experimentally in Scanning Electron Microscopy images

of microstructure in aluminium alloys [

]. The originality of our method was to use PH as

a translational and rotational invariant descriptor to encode the local structures. A Gaussian

Mixture Model (GMM) clustering method [

] is then applied, and estimated through an

Expectation Maximization (EM) algorithm [

]. This method called hereafter TDA-GMM,

was shown to be successful to identify and describe the structural and morphological properties

of the nuclei for various monatomic metals, namely Al, Zr, Ta and Mg, revealing their speciﬁc

nucleation pathways [

]. The application of the PH to multi-component alloys as a post-

treatment was the subject of very recent works on ice [

] imposing speciﬁc constraints on

O-H and O-O bonds, or on Pd-Si alloy [

] by removing the central atom of a given type

to discriminate local structures around Pd or Si. However, in the latter case, while the

topological ordering was successfully captured, the chemical short-range order (CSRO) seems

to be more diﬃcult to describe that way.

In the present work, large-scale molecular dynamics simulations (MD) are carried out

to investigate the homogeneous nucleation and nucleation pathways of deep undercooling

of Al-Ni alloys for two speciﬁc compositions, namely Al

and Al

, that possess

diﬀerent underlying stable crystalline phase, namely B2 and L1

, respectively. Interestingly,

Al-Ni alloys are known to be poor glass forming alloys [

] with small crystallization

times that are reachable by brute force MD. From a methodological point of view, the PH

descriptor in our TDA-GMM scheme is extended here with the objective of describing both

the chemical ordering, focusing on the central atom and its distance to the ﬁrst neighborhood

shell, and the topological local ordering using edge-weighted persistent homology (EWPH),

in a similar way as it was used in biomolecular data analysis [

–

] to capture information

between diﬀerent elements and/or molecules. Then a GMM is built speciﬁcally for each alloy

by including in the training set samples of all possible crystalline structures [

], liquid

conﬁgurations in the stable and undercooled states, and out-of-equilibrium conﬁgurations at

various stages of the homogeneous nucleation process. Our results show that the nucleation is

initiated ﬁrst from the chemical ordering, followed by progressive bond-orientational ordering

of the underlying crystal phase. Our ﬁndings further indicate that the nucleation pathway

depends on composition, with Al

displaying a single step nucleation with the emergence

of B2 short-range order, and for Al

a step-wise nucleation toward the L1

phase with

the emergence of fcc-, hcp-, and bcc-type polymorphs in a ﬁrst stage.

II. UNSUPERVISED LEARNING APPROACH FOR ALLOYS

A. Molecular dynamics simulations

In order to track homogeneous nucleation in Al-Ni alloys, large-scale MD simulations were

performed using the lammps code [

]. A number of atoms

=1 024 000 atoms were

considered, of which 512 000 of each specy for Al

, and 256 000 Al and 768 000 Ni

for Al

. They were placed randomly in a cubic simulation box subject to the standard

periodic boundary conditions (PBC) in the three directions of space. Interactions were taken

into account through the semi-empirical potentials of Purja and Mishin [

] based on the

embedded atom model. Equations of motion are solved numerically with Verlet’s algorithm in

its velocity form with a time step of 1fs [

]. Control of the thermodynamic parameters

was done with the Nosé-Hoover thermostat and barostat [

] and all the simulations

were conduced at constant pressure. Nucleation events were produced in undercooled states

at constant temperature. Properties of each alloy are summarized in Table I, and Fig. 1

shows a comparison between the classical MD simulation with the EAM potential [

] and

our previous ab initio MD simulations [

] for the two compositions considered here at

= 1795 K taking the same densities. A reasonably good agreement can be seen for both

alloys, and more importantly, an excellent match of the ﬁrst peaks position for the three

partials is found, indicating that the Al-Al, Al-Ni and Ni-Ni bond lengths are well reproduced.

Especially, the ﬁrst peak of Al-Ni partials are well reproduced indicating that the strong

chemical aﬃnity between the two species is well predicted and that the EAM potential is

reliable.

For the study of the crystal nucleation, the alloys were equilibrated in the liquid state, at

= 2500 K and

= 2000 K respectively for Al

and Al

, far above their liquidus

temperatures

(see Table I). They were subsequently brought in the undercooled states,

using a ramp of temperature with a cooling rate

= 5

K.s

-1

and

= 1

Alloy NAl NNi TL(K) Tg(K) Tiso (K) Trg ∆T Q (K.s-1)Qc(K.s-1)

Al50Ni50 5.12 ×1055.12 ×1051780 915 1150 0.51 0.35 5.0×1012 1.4×1012

Al25Ni75 2.5×1057.5×1051678 815 1050 0.49 0.37 1.0×1011 9.0×1010

TABLE I. Characteristic parameters of MD simulations.

NAl

and

NNi

are the number of Al and

Ni in the simulation boxes. Liquidus temperatures

are taken from Ref. [

represents the

glass transition temperature,

Tiso

the chosen isotherm for the analysis of the nucleation events,

Trg

Tg/Tm

,∆

= (

Tm−Tiso

)

/Tm

the cooling rate, and

the critical cooling rate, inferred

from the nose of the TTT curves.

FIG. 1. Partial pair-correlation functions for Al

(a) and Al

(b) at

= 1750 K. Classical

MD simulation with the EAM potential of Ref. [

] (solid lines) are compared with AIMD simulations

of Ref. [55, 56] (dashed lines).

K.s

-1

respectively, to below the glass transition

to avoid crystallization during the quench.

The resulting observed values of

are given in Table I. Conﬁgurations are recorded during

the quench by temperature steps of 50 K. They were used to determine the time-temperature-

transformation (TTT) curve in the vicinity of the nose region, as shown in Fig. 2 for both

alloys. For each temperature, nucleation time was determined from a sharp drop of the

energy as was done in our preceding work [

], and is averaged over ﬁve independent runs

where initial velocity distribution were randomized.

文档加载中……请稍候！
如果长时间未打开，您也可以点击刷新试试。

下载文档到电脑，查找使用更方便

10 玖币 0人已下载

立即下载

摘要：

CrystalNucleationinAl-NiAlloys:anUnsupervisedChemicalandTopologicalLearningApproachSébastienBecker,1,2EmilieDevijver,3RémiMolinier,4andNoëlJakse11Univ.GrenobleAlpes,CNRS,GrenobleINP,SIMaP,F-38000Grenoble,France2Univ.GrenobleAlpes,CNRS,GrenobleINP,LIG,F-38000Grenoble,France3CNRS,Univ.GrenobleAlpes,Gr...

展开>> 收起<<

Crystal Nucleation in Al-Ni Alloys an Unsupervised Chemical and Topological Learning Approach Sébastien Becker1 2Emilie Devijver3Rémi Molinier4and Noël Jakse1.pdf

共29页,预览5页

还剩页未读，继续阅读

声明：本站为文档C2C交易模式，即用户上传的文档直接被用户下载，本站只是中间服务平台，本站所有文档下载所得的收益归上传人(含作者)所有。玖贝云文库仅提供信息存储空间，仅对用户上传内容的表现方式做保护处理，对上载内容本身不做任何修改或编辑。若文档所含内容侵犯了您的版权或隐私，请立即通知玖贝云文库，我们立即给予删除！

Crystal Nucleation in Al-Ni Alloys an Unsupervised Chemical and Topological Learning Approach Sébastien Becker1 2Emilie Devijver3Rémi Molinier4and Noël Jakse1

相关推荐

开通VIP享超值会员特权

作者详情

相关内容

热门标签

举报选择: