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Scripta Materialia 63 (2010) 1045–1048

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An experimental and modeling study on the role of damage cascadeformation in nanocrystalization of ion-irradiated

Ni52.5Nb10Zr15Ti15Pt7.5 metallic glass

Michael Myers,a E.G. Fu,b Michelle Myers,c Haiyan Wang,c Guoqiang Xie,d X. Wang,e

W-K Chue and Lin Shaoa,⇑aDepartment of Nuclear Engineering, Texas A&M University, College Station, TX 77843, USA

bLos Alamos National Laboratory, Los Alamos, NM 87545, USAcDepartment of Electrical and Computer Engineering, Texas A&M University, College Station, TX 77843, USA

dInstitute for Materials Research, Tohoku University, Sendai 980-8577, JapaneTexas Center for Superconductivity and Department of Physics, University of Houston, Houston, TX 77204, USA

Received 30 June 2010; revised 21 July 2010; accepted 22 July 2010Available online 30 July 2010

We have shown that 1 MeV Ni+ ion irradiation can cause nanocrystal formation in Ni52.5Nb10Zr15Ti15Pt7.5 metallic glass (MG).The process requires precipitate formation and subsequent crystal growth within the precipitates. Temperature evolution modelingof damage cascades suggests a locally melted region within the damage cascade with substantial temperature gradients and rapidenergy dissipation, with a quenching rate much larger than MG’s critical cooling rate. Thus, the damage cascade regions do notdirectly develop nanocrystals.� 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Keywords: Finite element analysis; Metallic glass; Ion irradiation; Crystallization

Metallic glasses (MGs) have high yield strengths[1], superior resistance to corrosion [2,3] and wear [4],but their applications have been limited by poor ductil-ity [5]. Under high stress, MGs develop shear bandswhich quickly propagate through the material, leadingto failure in a brittle fashion after only a few percentstrain [6]. Previous studies have shown that introducingnanometer size structures such as new phases or crystalsin MGs can enhance ductility [7]. Such partial crystalli-zation can be realized by bending [8], annealing [9] andindentation [10].

Bending and indentation are destructive and cannotbe used in practical applications. Recently, electronand ion irradiation have been explored as means tointroduce nanocrystals [11–15], but the fundamentalmechanisms are not clear. Ion irradiation can lead tothe formation of a damage cascade – a localized regionwith high density displacements [16]. During thermalequilibration and subsequent energy dissipation of dam-

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⇑Corresponding author. Tel.: +1 330 984 7996; fax: +1 979 8456443; e-mail: lshao@mailaps.org

age cascades, structural relaxation is expected. It is notclear whether nanocrystal formation is a direct resultof localized heating induced by damage cascade forma-tion. To reveal the role of damage cascade in nanocrys-tal formation in ion-irradiated MGs, both atomic scalecharacterization and multiscale modeling are performedin the present study. Two key questions to be answeredin the present study are: (i) whether the nanocrystals aredeveloped along the ion track and within the damagecascades and (ii) whether the thermal spike inducedannealing has a thermal budget high enough to inducelocalized crystallization.

MG ribbons, 20 lm thick and 1.5 mm wide, wereproduced by rapid solidification of the liquid metal solu-tion of Ni52.5Nb10Zr15Ti15Pt7.5 on a single copper rollerat a surface velocity of 42 m s�1 [17]. This particularmetallic glass was chosen because it exhibits a largesuper cooled liquid region [18], which makes it stable un-der ion milling for transmission electron microscopy(TEM) specimen preparation [19]. It belongs to onegroup of recently developed MGs which can be pro-duced in larger critical diameters for practical applica-tion [19]. The sample was irradiated at room

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1046 M. Myers et al. / Scripta Materialia 63 (2010) 1045–1048

temperature with 1 MeV Ni+ ions to a fluence of1 � 1016 cm�2 and a beam current of 160 nA cm�2.The irradiated samples were prepared by 2 keV Ar ionmilling and characterized with TEM using a JEOL2010 microscope operated at 200 kV.

Figure 1a shows a typical bright-field TEM micro-graph obtained from the as-spun sample. The inset isthe corresponding selected area electron diffraction pat-tern. The featureless micrograph suggests the sample’samorphous state, which is further corroborated by thebright diffuse rings. It can be concluded that the sampledoes not undergo structural transformation during2 keV Ar ion milling. Our previous studies have shownthat MGs can form nanocrystals under ion milling atan energy larger than 2 keV [20]. The resistance for suchstructural changes is determined by the width of theMG’s supercooled liquid region along with the temper-ature and energy of ion milling [20]. The selected ionmilling conditions in the present study do not introducenoticeable artifacts.

Figure 1b shows a typical bright-field TEM micro-graph obtained from the sample after ion irradiation.

Figure 1. TEM micrographs with SAD of (a) as-spun Ni52.5Nb10Zr15-Ti15Pt7.5, (b) 1 MeV Ni+ ion-irradiated and (c) the correspondingdark-field.

The structure is featured by three distinctive regions, la-beled as 1, 2 and 3 in the figure. Region 1 refers to amor-phous matrix which shows bright contrast. Region 2refers to precipitated regions which have relatively dar-ker contrast and irregular shapes. The difference in con-trast between these two regions suggests they havedifferent compositions. Within region 2, some structures(labeled as 3) with regular shapes are clearly visible. Theinset selected area electron diffraction (SAD) pattern inFigure 2b shows sharp rings and sharp diffraction spots,which suggests the existence of irradiation induced crys-talline phases.

Figure 1c shows the corresponding dark-field TEMmicrograph. The triangular structure, labeled as 3 inFigure 1b, shows bright contrast under dark-field mode,which suggests its crystalline phase. In both Figure 1band c, the nanocrystals show band-like features, whichare frequently observed within nanocrystals when stack-ing faults are formed [21]. Other evidence of the crystallinephase formation comes from the structure’s well-definededge and regular boundaries, which are often caused bythe energy minimization of nanocrystals [22].

The energy deposition in the displacement core ishigh enough to induce local melting. Therefore it is pos-sible that nanocrystal formation is a consequence ofsuch localized heating, given that heated region has en-ough time to structurally reorder. Metallic glass is

Figure 2. Temperature profile of Ni52.5Nb10Zr15Ti15Pt7.5 experiencing1 MeV Ni+ ion bombardment after (a) 1 ps, (b) 6 ps and (c) 12 ps.

M. Myers et al. / Scripta Materialia 63 (2010) 1045–1048 1047

created by quenching a molten alloying solution above acritical cooling rate to ensure an amorphous structure atroom temperature [23,18]. Therefore, direct nanocrystal-lization is not expected if the quenching rate of the en-ergy transfer is greater than the critical cooling rate. Itis necessary to model temperature evolution of the dam-age cascade during the quenching stage to determinewhether such non-equilibrium heating can lead to local-ized phase transitions in MG.

The modeling in the present study consists of twosteps. First, SRIM (stopping and range of ions in mat-ter) code is used to obtain the coordinates of displace-ments resulting from a single ion bombardment [24].The second step is to convert the displacements intopoint source of heating and to model the temperatureevolution of the damage cascades. Finally, the finite ele-ment method (FEM) is used to predict the quenchingprocess by solving a three-dimensional (3-D) time-dependent heat transfer equation described by

qcp@

@tT ð~r; tÞ ¼ jr2T ð~r; tÞ þ

XN

i¼1

Qið~r; tÞ ð1Þ

where q is the material density, cp is the specific heat, j isthe thermal conductivity, T is the temperature and Qi

are point sources. Two approximations are made inthe modeling. First, each displacement shares the energyequally and the total energy sums to 1 MeV, the incidentenergy of one Ni ion. Second, the specific heat of thesample, which is supposed to increase with increasingtemperature, is assumed to be constant and takes a typ-ical value measured at room temperature for MG,(420 J kg�1 K�1) [25]. Thus, the predicted temperatureevolution is slower than the actual value due to anunderestimated specific heat value.

Eq. (1) was first discretized in time using the Crank–Nicolson method, after which a series of coupled ordin-ary differential equations were solved in space using thedeal.II FEM libraries [26]. The resulting system of equa-tions was preconditioned and solved using linear ele-ments and the conjugate gradient method [27]. Thegradient recovery estimator first proposed by Kellyet al. [28] is employed as a basis to perform grid refine-ment and coarsening. In this way, a 3-D solution is firstconstructed on a coarse mesh after which the solution isobtained on successively refined grids. The finest meshobtained is then carried forth for all subsequentcalculations.

Figure 2a shows the initial temperature profile rightafter ion bombardment. The ion is incident along theZ direction. Over the ion’s track a large number of col-lisions take place (�15,000) which deposit the largestportion of their energy near the end of projected range,which is �420 nm beneath the sample surface. A local-ized “hot spot” of 950 K, which is the melting point(Tm) of the metallic glass [17], forms with a diameterof 20 nm. At a distance of 30 nm away from the hotspot, temperature quickly drops to �50 K (blue coloredregion1). Two other regions near this largest hot spot

1 For interpretation of the references to colour in this text, the reader isreferred to the web version of this article.

were also found to have temperatures above Tm, butthe spot sizes are much smaller, measuring �1 nm.

Figure 2b shows the temperature profile after anelapsed time of 6 ps. The maximum temperature every-where decreases below Tm. Only a small region stillhas temperatures slightly above the glass transition tem-perature (Tg), which is 860 K [17]. The most notable fea-ture is a complete collapse of the leftmost region, wheretemperatures have undergone a dramatic decrease of225 K. Figure 2c shows that the sole remaining featureafter 12 ps is a small region which initially containedthe highest energy density. Temperatures throughoutthe sample are well below both Tm and Tg.

By analyzing the temperature evolution over 12 ps, the

average cooling rate is determined to be�1013 K s�1. Thesignificance of the finding here is that the cooling rate ismany orders of magnitude larger than the critical coolingrate (102 K s�1) to form Ni52.5Nb10Zr15Ti15Pt7.5 metallicglasses. In other words, although the damage cascadescreate hot spots at temperatures above Tm, the subse-quent quenching is too fast to allow materials to developordered structures. If ion bombardment does not alterthe composition significantly and the MG still keeps theoriginal properties, this melting and solidification processwill not lead to crystallization.

The observed large cooling rate is typical for damagecascade quenching in solids [16]. Such quenching is real-ized by phonon and electron transport through phonon–phonon and electron–phonon scattering. Generally, thethermal conductivity of MGs is lower than that of crys-talline materials, since disorder is everywhere and servesas scattering centers for phonons. Nevertheless, a highcooling rate is expected due to the large temperaturegradients.

Figure 3 plots the temperature evolution as a func-tion of time in the hottest region within the damage cas-cade. The dashed line refers to the melting temperatureof the MG (�950 K) [17]. Upon bombardment, the hot-test region reaches a temperature of �5000 K, thenquickly drops to the melting temperature at �4.5 ps.This time period suggests melting indeed occurs in theMG since heating above the melting temperature islonger than the time required for one atomic vibration,which is the minimum requirement for structural relax-ation. Estimated from a typical Debye frequency of

Figure 3. Temperature evolution as a function of time in the hottestregion within the damage cascade.

1048 M. Myers et al. / Scripta Materialia 63 (2010) 1045–1048

1013 s�1, a typical atomic vibration period is around0.1 ps.

The conclusion obtained from the FEM simulationagrees with the TEM results. If nanocrystals are formeddue to localized structural changes within damage cas-cades, it is expected that crystals should have nanometersizes; furthermore, their densities should be comparableto ion fluencies. However, TEM images suggest thatMG experiences multistage transitions. Precipitates witha composition different from original MG matrix prob-ably form first, then nanocrystals form as a result ofcrystal growth within the precipitates. This happenswhen the activation energy for crystal growth is higherthan the activation energy of nucleation.

Previous studies have pointed out that the activationenergy for crystal nucleation could be larger than thatfor crystal growth [29]. Thus, crystal growth can occurwith a smaller thermal budget than crystal nucleation.In other words, damage cascades might cause strikingeffects on crystal growth if crystal nucleation is intro-duced prior to the irradiation. It is of interest to furtherexplore this effect, e.g. by ion bombarding a deformedMG near the crack plane, which is found to cause nucle-ation without growth [30].

The study suggests that nanocrystallization is a resultof structural changes caused by enhanced system energy,due to displacement creation. The displacements causedensity fluctuations, which lead to enhanced atomicmobilities. This is equivalent to heating at elevated tem-perature with increased atomic diffusivities. Althoughnanocrystals form non-uniformly, they do so as a resultof homogeneous phase transition. Direct and localizedstructural changes might occur if MGs are heated dur-ing ion irradiation at elevated temperature, which mightreduce the quenching rate if the temperature gradientbetween the matrix and the damage cascade regions islow enough that the damage cascade heating can be sus-tained for a time period long enough to allow crystalnucleation and growth.

In summary, we have studied the radiation responseof Ni52.5Nb10Zr15Ti15Pt7.5 after 1 MeV Ni+ ion irradia-tion at room temperature. Nanocrystals form within pre-cipitates with a composition deviating from that of theoriginal matrix. However, no evidence is found to sup-port the mechanism that nanocrystals are locally devel-oped along the ion tracks and within the damagecascade regions. Multiscale modeling combining MonteCarlo damage simulation and 3-D finite element analysiswas performed to simulate the quenching of damage cas-cades. Although MG is melted locally within the damagecascades, the subsequent solidification has a quenchingrate many orders of magnitude larger the critical coolingrate to form the MG. Thus, melting and solidification donot lead to localized crystallization. Nanocrystals formas a result of a homogeneous phase transition.

L.S. acknowledge the support from NRCEarly Career Development Program and National Sci-ence Foundation under Career Award CMMI-0846835.

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