嵌入纳米Fe颗粒的Fe液凝固过程的分子动力学模拟

[Article]

https://www.360docs.net/doc/993976391.html,

物理化学学报(Wuli Huaxue Xuebao )

Acta Phys.?Chim.Sin .2013,29(2),245-249

February Received:December 3,2012;Revised:December 25,2012;Published on Web:December 25,2012.?

Corresponding author.Email:yqwu@https://www.360docs.net/doc/993976391.html,;Tel:+86-21-56332144.

The project was supported by the National Key Basic Research Program of China (973)(2012CB722805),National Natural Science Foundation of China (50504010,50974083,51174131),Joint Funds of National Natural Science Foundation of China-Steel,China (50774112),and “Phosphor"Project of Shanghai Science and Technology Development Funds,China (07QA4021).

国家重点基础研究发展计划(973)(2012CB722805),国家自然科学基金(50504010,50974083,51174131),国家自然科学基金钢铁联合基金(50774112)及上海市青年科技启明星计划(07QA4021)资助项目

?Editorial office of Acta Physico ?Chimica Sinica

doi:10.3866/PKU.WHXB201212251

嵌入纳米Fe 颗粒的Fe 液凝固过程的分子动力学模拟

吴永全*

沈

通

陆秀明

张

宁

赖莉珊

高

帅

(上海大学材料科学与工程学院,上海市现代冶金及材料制备重点实验室,上海200072)

摘要:

采用Sutton-Chen 势函数及分子动力学(MD)方法对嵌入了Fe 纳米团簇(半径从0.4-1.8nm)的Fe 液凝

固过程进行了模拟.模拟结果表明只有当嵌入的纳米团簇半径超过0.82nm 才能降低凝固时所需要的临界过冷度(ΔT *),起到诱导凝固的作用.同时采用原子键型指数法(CTIM-2)对样本在凝固过程中的原子结构进行了标定,通过观察微观结构演变发现当嵌入纳米团簇能够作为凝固核心时,体系按照hcp-fcc 交叉形核的方式长大.同时还发现嵌入纳米团簇对体系凝固过程晶核的生长方向及凝固的最终构型存在“结构遗传效应”.关键词:

Fe 纳米团簇;过冷度;凝固过程;微观结构演化;分子动力学

中图分类号:

O641;O642;TF01

Solidification of Liquid Fe with Embedded Homogeneous Solid Fe

Nanoparticles from Molecular Dynamics Simulations

WU Yong-Quan *

SHEN Tong

LU Xiu-Ming

ZHANG Ning

LAI Li-Shan

GAO Shuai

(Shanghai Key Laboratory of Modern Metallurgy &Materials Processing ,School of Materials Science and Engineering ,

Shanghai University ,Shanghai 200072,P .R.China )Abstract:Solidification processes of liquid Fe with embedded homogeneous solid nanoparticle with radius ranging from 0.4to 1.8nm were studied by molecular dynamics (MD)simulation adopting the Sutton-Chen potential.It was found that the particles whose radii exceed 0.82nm could obviously decrease the critical undercooling (ΔT *)and induce solidification.The microstructural evolution during the solidification process was traced through the atom definition with cluster-type index method (CTIM-2).Results revealed that when the embedded particle induced solidification,the growth process of nucleus would proceed as a cross-nucleation between hcp and fcc structures,a little similar to the eutectic crystallization process.Moreover,the heredity effect attributed by embedded solid nanoparticle was clearly observed during the microstructural evolution.Key Words:Solid Fe nanoparticle;Undercooling;

Solidification process;

Microstructural evolution;

Molecular dynamics simulation

1Introduction

The macro-properties of metallic materials are mainly deter-mined by their microstructures which are mainly affected by the original configurations in liquid state and the solidification

processes.At deep undercooling,solidification process usually takes place by the homogeneous nucleation if impurities are ex-cluded.1-3However,in many cases,the solidification starts from a solid-liquid interface,which is a heterogeneous process.245

Acta Phys.?Chim.Sin.2013V ol.29

To date,some progresses in the investigation of these kinds of

interfaces have been achieved,4-6but there are still limited un-

derstanding of the interfacial microstructures,the mechanisms

of ordering during the solidification,and the kinetics associat-

ed with the interface moving.

Based on our previous works,7-9we performed the study of

this work.Series samples of liquid Fe with solid Fe nanoparti-

cles with different sizes were introduced to produce the homo-

geneous solidification process in detail.Calculations were per-

formed for a wide range of temperatures and different sizes of

solid Fe nanoparticles.Relationships between the nanoparticle

size and the undercooling were examined and the behaviors of

solid nanoparticles in undercooled liquid Fe were investigated

based on the classical nucleation theory(CNT).Then,a tracing

study by the cluster-type index method(CTIM-2)on the micro-

structural evolution during solidification process was carried

out to determine the role of solid nanoparticle on the final so-

lidified structure.

2Computational methods

2.1Potential function

The simulation is based on the classical molecular dynamics

(MD)method.10The Sutton-Chen potential,11which combines

the N-body potential with a van der Waals tail,is implemented

to describe the inter-atomic interactions of Fe.For a system of

N atoms,the total energy of the Sutton-Chen potential is writ-

ten as:

E r=ε[1

2∑∑

i≠j

V(r ij)-c∑iρi](1)

where,c is a dimensionless parameter,εis the energy parame-ter.r ij is the distance between atoms i and j.The pair potential V(r ij)is given by:

V(r ij)=(a

ij

)n(2) where,a is a parameter with dimension of length and is gener-ally referred to the lattice parameter,and the density termρi will be:

ρi=∑j≠i(a r ij)m(3) where,m and n are positive integers with n>m.Parameters of Sutton-Chen potential for Fe-Fe areε=0.0006eV,a=0.36467nm,n=15,m=4,c=1104.7351,which have been proved very successful to simulate the liquid-solid phase transitions from bulkγ-Fe(fcc)toδ-Fe and then to liquid-Fe.7,8

2.2Model construction

The initial configuration is constructed by embedding a sol-id Fe nanoparticle into the bulk liquid Fe.Construction process-es are shown in Fig.1.

Firstly,the liquid bulk Fe in Fig.1(c)is obtained by continu-ously heating the perfect cell of bcc crystal with16000Fe at-oms from0to2800K at the rate of1K?ps-1,and the solid bulk Fe in Fig.1(a)is prepared by cooling the liquid bulk Fe to1400 K at the same rate.

Secondly,the solid Fe nanoparticle in Fig.1(b)with radius R a is dug from the center of solid bulk Fe in Fig.1(a).At the same time,a centered cavity with radius R b is dug out of liquid bulk Fe,as shown in Fig.1(d).

Thirdly,the solid Fe nanoparticle is placed inside the cavity of liquid Fe,and the relative position is adjusted to make sure concentric for the nanoparticle and the cavity(Fig.1(e)).Mean-while,R b is set as0.35nm larger than R a in order to avoid the unexpected proximity of atoms at the solid-liquid interface be-tween the liquid atoms and the solid atoms of nanoparticle. Finally,the liquid Fe atoms are relaxed with frozen solid Fe nanoparticles for20ps at2800K to eliminate the reserved in-terfacial margin between the liquid Fe and nanoparticles, which will inevitably lead to a slight decrease in the size of this initial cubic cell volume.Thus far,the initial configura-tions are completely prepared for the further MD simulations. Using this method,we prepared a series of samples with the solid nanoparticles with different radii.The size(R a)of the sol-id nanoparticle,the number of atoms in the nanoparticle(N1), and the total number of atoms(N2)are listed in Table1.

2.3Simulation process

The MD simulations were executed using the DL_POLY2.0 software12in a NPT ensemble(fixed number of particles,pres-sure,and temperature).Periodic boundary conditions are ap-plied in all three directions.The Hoover-Nose method13,14is used for controlling the temperature,and the Parrinello-Rahman method15,16is applied to control the pressure.The equa-tion of motion is integrated using leap frog algorithm.The time step is set as2.0fs throughout the

entire simulation and a cut-

Fig.1Schematic diagram of the construction of initial configuration

yellow:solid Fe nanoparticle;blue:liquid bulk Fe

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WU Yong-Quan et al .:Homogeneous Solidification of Liquid Fe Induced by Emdedded Solid Nanoparticle

No.2

off radius of 1nm is used.All the simulations are performed for 2000ps,i.e.,106steps.

For each initial condition,the system with solid nanoparticle is directly cooled from 2400to 1600K at 100K interval.Par-ticularly,an interval of 1K is set near the solidification point.The phase transition is determined by the g (r ),i.e.,radius distri-bution function,as well as the n (r ),i.e.,the coordination num-ber within a distance r from a central atom.The microstructur-al details of phase transitions in solidification processes are characterized by CTIM-2,2,17which is based on the HA indi-ces 18and has been confirmed able to well distinguish the cen-tered cluster from body-centered cubic (bcc)cluster,face-cen-tered cubic (fcc)cluster,close-packed hexagonal (hcp)cluster,or amorphous cluster by judging the bond types of the sur-rounding atoms.

3

Results and discussion

3.1

Relationship between the size of solid nanopar-ticle and the undercooling

Fig.2shows the g (r )and the n (r )for typical liquid and solid states.In the g (r )of liquid state,peak intensity is relatively low and peak width is relatively broad compared to the counterpart

of solid state.When liquid phase transits to solid phase,intensi-ty of first peak increases apparently;the original second peak splits into two peaks;new peaks emerge at the first and second original valleys.The most characteristic change is the appear-ance of a small peak at the first valley (r=0.35nm),which is the typical symbol of fcc structure.8,19As we know,the first val-ley in g (r )corresponds to the value position of coordination number (CN)of nearest neighbor in n (r ).It is calculated that CN of liquid is around 10.2,which is 4.1%larger than the ex-periment value (9.8),20and CN of solid is 12.3,which is 2.3%larger than ideal γ-Fe (12).From those obvious differences be-tween liquid and solid states,we can easily determine whether the phase transition occurs.

The calculated phase diagram of liquid or solid state as a function of undercooling (ΔT )and nanoparticle size (R a )is shown in Fig.3(a).It can be observed that for each sample,there is a critical undercooling ΔT *,corresponding to the mini-mum undercooling,to demarcate the liquid and solid states,and when ΔT <ΔT *,no solidification occurs and when ΔT ≥ΔT *,all samples solidify.This ΔT *can only be located in a narrow range due to the thermal fluctuation.19,21Here we define the ΔT *as the minimum degree of undercooling.Obviously,ΔT *in-creases with the decreasing of R a ,and it reaches and maintains the maximum when R a ≤0.8nm,which means when R a >0.8nm,the embedded nanoparticle evidently affects the solidification process thermodynamically while when R a ≤0.8nm,the effect no longer exists.On the other hand,the maximum of ΔT *,when sizes of nanoparticles are smaller than 0.8nm,corre-sponds to the minimum undercooling of bulk liquid Fe.We can also change our perspective.If we regard the embedded nanoparticle with R a as an embryo in the liquid,ΔT *corre-sponds exactly to the critical undercooling of the critical size R a of nucleus.Or on the contrary,we found the critical size of nucleus for each ΔT *.These results lead us to the CNT,22from which a unique critical size of nucleus is determined for any given undercooling through the rivalry between the bulk free

Table 1

Some quantities of constructed samples

a 1size of cubic cell;N 2:total number of atoms in the initial cubic cell;k :N 1/N

2

Fig.2(a)Radial distribution function g (r )and (b)the

coordination number n (r )within a distance r from a central atom

shown for the liquid and solid states

Fig.3Phase diagram showing the liquid/solid state and critical undercooling ΔT *as a function of the nanoparticle radius (a)and

the fitting line of the undercooling ΔT *and the inverse of

nanoparticle radius (b)

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Acta Phys.?Chim.Sin .2013

V ol.29

energy change and the interfacial energy.A key result in CNT is the relationship between the critical radius R *and ΔT *,which is written as:22

ΔT *=2ΓR *

(4)

Here Γis the Gibbs-Thomson coefficient.Hence ΔT *is propor-tional to the inverse of R *.We also reproduced this relationship as shown in Fig.3(b).Actually,we deduced the thermodynamic melting point through extrapolating this linear relation to the 1/R a →0where the temperature is just the thermodynamic melt-ing point.Besides,Fig.3also shows that there exists a mini-mum critical size of nucleus about 0.8nm,under which,no matter how great the undercooling is,the embryo can not be-come nucleus able to spontaneously grow up.Thus,we make the R min precise to be 0.82nm by fitting the data given in Fig.3(b).

3.2Behavior of solid nanoparticle during

solidification

In the following,the evolution of the solid nanoparticle at ΔT *is monitored by the change of the instantaneous energy as well as snapshots for all samples.If the instantaneous energy makes a salutatory drop from a higher value to a lower value,the system will transform from liquid state to solid state.Re-sults in Fig.4indicate that there are two structural evolution processes related to different sizes of the solid nanoparticles.In the case of nanoparticles with radii from 0.4to 0.8nm,instan-taneous energy drops after experiencing a relatively long “incu-bation time ”.And snapshot in Fig.4(b)demonstrates that be-fore solidification occurs,nanoparticle has already been com-pletely melted and diffused in the liquid.It is worth mention-ing that solidification process of these samples is the same as that of bulk Fe,where a critical nucleus is formed by the rare,spontaneous energy fluctuation and the incubation time is ran-dom.On the other hand,the instantaneous energy of nanoparti-cles with radii from 0.9to 1.8nm drops at the very early stage of simulation,and meanwhile,Fig.4(c)shows us that the sys-tem is solidified and the solid nanoparticle still keeps its origi-nal shape.That means,during this solidification process,the

solid nanoparticle acts as an initial nucleus inducing the solidi-fication.These two solidification processes can be reasonably explained again by the CNT,22according to which,there exists a critical radius for a given temperature and the nanoparticle with larger size than the critical radius can grow up spontane-ously,or it will melt.

3.3Microstructure evolution during solidification

process

To analyze the microstructural evolution in solidification af-fected by the solid nanoparticle,CTIM-2is introduced to char-acterize the solidification process of the sample with nanoparti-cles of 0.9to 1.8nm (as described above,nanoparticles rang-ing from 0.4to 0.8nm have dissolved before solidification oc-curs).The sample with nanoparticle of R a =1.5nm is taken as an example to interpret analysis results.

It is concluded from Fig.5that the solidification process has two stages:growth stage (0-100ps)and structural relaxation stage (100-2000ps).The initial nucleus consists of fcc struc-ture with two hcp planes.At first 60ps,fcc and hcp atoms in-crease slowly,and start to grow rapidly from 60ps till reaching a maximum value around 100ps.The percentages of fcc and hcp atoms dramatically increase to 41.24%and 11.34%,respec-tively,while amorphous atoms drop to 47.42%.It is observed from snapshots in Fig.5(b)at t =60,80,100ps that growth of (1,1,1)face proceeds cross-nucleation of the metastable hcp and stable fcc structures,23,24which is essentially governed by kinetics factor.During the structural relaxation stage,the per-centage of fcc atoms is nearly doubled to 73.27%,while hcp at-oms decrease three forths to 2.99%.Decreasing of hcp

atoms

Fig.4Energy curves for all samples with timescale of 2000ps (a);snapshots for samples with nanoparticle size ranging from 0.4to

0.8nm (b)and from 0.9to 1.8nm (c)at ΔT *

yellow:solid Fe nanoparticle;blue:liquid bulk

Fe

Fig.5

CTIM-2analysis on solidification process of sample with

nanoparticle of radius 1.5nm

(a)evolution of the number of fcc,hcp,amorphous atoms with timescale of 2000ps;(b)snapshots of microstructural at 5,60,80,100,and 2000ps.

green:fcc atoms;red:hcp atoms

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WU Yong-Quan et al.:Homogeneous Solidification of Liquid Fe Induced by Emdedded Solid Nanoparticle No.2

during this stage indicates that the metastable hcp structure is gradually converted into the thermodynamically stable fcc structure.In fact,if the simulation time scale is long enough, all metastable structure should finally turn into fcc structure.25 It is also observed that during growth stage,structure such as orientation and shape of solid nanoparticle is imprinted in solidified structure.Besides,the eventually formed structure (snapshot in Fig.5(b)at2000ps)also shows structural match-ing and structural relevance with the original solid nanoparti-cle.Influences of the solid nanoparticle during solidification are reminiscent of the heredity effect.26,27

One last word,our results in this paper give important en-lightenment for understanding the forming mechanisms and mi-croscopic processes during solidification,and are likely to play important role in enhancing the macroscopic properties of Fe-based materials.

4Conclusions

In this paper,we investigated solidification process of liquid Fe with embedded solid Fe nanoparticles with different sizes. Solid and liquid states were well distinguished by g(r)as well as n(r),and the CNs of both liquid and solid states show good agreement with experimental results.

Size of nanoparticle is of great impact on controlling the un-dercooling temperature during solidification:nanoparticle size larger than a minimum radius of0.82nm acts as an initial nu-cleus and decreases the critical undercooling.On the other hand,nanoparticles below0.82nm dissolve in the liquid be-fore solidification occurs and the critical undercooling tempera-ture is the same as that of bulk liquid Fe.

CTIM-2analysis on solidification process revealed that growth mechanism of(1,1,1)plane is cross-nucleation of fcc and hcp structures.Moreover,the solid nanoparticle is attribut-ed to structural and orientation heredity effect.These results give better understanding of the forming mechanisms and mi-croscopic processes during solidification.

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