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Acta Materialia 54 (2006) 2975–2982

Computational thermodynamics to identify Zr–Ti–Ni–Cu–Alalloys with high glass-forming ability

Hongbo Cao a, Dong Ma a, Ker-Chang Hsieh b, Ling Ding a, William G. Stratton a,Paul M. Voyles a, Ye Pan c, Mingdong Cai d, J. Thomas Dickinson d, Y. Austin Chang a,*

a Department of Materials Science and Engineering, University of Wisconsin–Madison, 1509 University Avenue, Madison, WI 53706, USAb Institute of Materials Science and Engineering, Sun Yat Sen University, Kaohsiung 80424, Taiwan

c Department of Materials Science and Engineering, Southeast University, Nanjing 210096, Chinad Department of Physics and Astronomy, Washington State University, Pullman, WA 99164-2814, USA

Received 26 December 2005; received in revised form 17 February 2006; accepted 22 February 2006Available online 16 May 2006

Abstract

We have used a thermodynamic computational approach to identify the compositions of Zr–Ti–Ni–Cu–Al alloys exhibiting low-lyingliquidus surfaces, which tend to favor the formation of bulk metallic glasses. Guided by these calculations, we have identified severalseries of new Zr-based alloys with excellent glass formability, some of which can be cast into glassy rods up to 14 mm in diameter. Thesealloys exhibit wide undercooled liquid regions (Tx � Tg) up to 85 K and high Vickers hardness from 550 to 700 kg/mm2. The best glass-forming alloy is Zr51Ti5Ni10Cu25Al9. The computational thermodynamic approach coupled with the reduced glass transition temperaturecriterion of Turnbull can rapidly identify regions of alloy composition suitable for experimental tests for glass formation. The glass-forming ability of the alloys we studied can be understood in terms of the relative liquidus temperature in a thermodynamically calculatedtemperature vs. composition section through a multicomponent phase diagram. It does not follow several other proposed thermody-namic or topological criteria. Our general approach may be extended into a universal tool to identify alloys with good potential to formbulk glasses.� 2006 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Keywords: Bulk metallic glass; Thermodynamics; Multicomponent phase diagram calculation

1. Introduction

The ability to make novel non-crystalline metallicmaterials such as bulk metallic glasses at cooling ratesapproaching those of conventional casting conditionsaffords opportunities for investigating the fundamentalbehavior of deeply undercooled metallic melts and manu-facturing structural and functional materials for practicalapplications. However, there is an urgent need to use ascientific approach to identify potential compositions ofmulticomponent alloys for glass formation instead ofempirical rules such as large differences in the atomic

1359-6454/$30.00 � 2006 Acta Materialia Inc. Published by Elsevier Ltd. All

doi:10.1016/j.actamat.2006.02.051

* Corresponding author. Tel.: +1 608 262 0389; fax: 1 608 262 8353.E-mail address: chang@engr.wisc.edu (Y.A. Chang).

sizes of the component elements and exothermicity ofthe liquid alloys [1]. In his 2003 review paper, Loffer [2]said ‘‘the search for new bulk metallic glass compositionsis somewhat a ‘trial-and-error’ method, involving in manycases the production of hundreds to thousands of differ-ent alloy compositions.’’ Yan et al. [3] used a computa-tional thermodynamic approach to identify potentialcompositions of alloys exhibiting low-lying liquidus sur-faces that favor glass formation. They applied thisapproach to the quaternary Zr–Ti–Ni–Cu alloys andshowed that the thermodynamically calculated composi-tions of the liquid alloys at the five-phase invariant equi-libria are in reasonable accord with those determinedexperimentally for bulk metallic glass formation by Linand Johnson [4].

rights reserved.

0.00 0.25 0.50 0.75 1.00

0.00

0.25

0.50

0.75

1.000.00

0.25

0.50

0.75

1.00

G5

G3G1

G4G2

Calculated Published Bulk Glasses

G1-5 Representative Alloys

800750700640 oC

Cu+Ni

Zr+T

i

Al

Fig. 1. Comparison of thermodynamically calculated compositionalregion of the quinary Zr–Ti–Ni–Cu–Al system for bulk metallic glassformation with data reported in the literature and representative alloysfound in the present study.

2976 H. Cao et al. / Acta Materialia 54 (2006) 2975–2982

The objective of the present study is to apply the sameapproach to find new alloy compositions with high glass-forming ability (GFA) in the quinary Zr–Ti–Ni–Cu–Alsystem. We employ a thermodynamic description of thissystem that we have recently developed [5] and verify thecomputational predictions experimentally. A salient fea-ture of this approach is that the thermodynamic modelsof the phases implicitly incorporate the multiple chemicaland topological interactions among component elementsthrough the enthalpy and entropy terms. In the following,we present the computational thermodynamic approach,the experimental method used, the experimental verifica-tion of the alloy compositions identified for glass forma-tion, a discussion, and finally conclusions.

2. Computational thermodynamic approach

Even though this paper is not concerned with the devel-opment of a thermodynamic description of the quinary Zr–Ti–Ni–Cu–Al system, we will give a brief summary of theCalphad approach for obtaining such a description of amulticomponent system [6–8]. The term ‘‘thermodynamicdescription’’ means that the parameters of the thermody-namic models for all the phases in a system in questionare available. The basic premise of the modeling is thatthe thermodynamic description of a higher order system,i.e. more than three components, can be obtained viaextrapolation from those of the lower order systems, nor-mally binaries and ternaries. Experience has shown thatthis indeed is the case when there are no new quaternaryphases formed and the homogeneities of the lower orderintermetallic phases do not extend to the higher order com-positional space [6,9]. On the basis of the thermodynamicdescription obtained, it becomes possible to calculate avariety of phase diagrams for materials research in an alliedfield and for practical applications. For the quinary Zr–Ti–Ni–Cu–Al system, there are 10 constituent binaries and 10constituent ternaries. No quaternary and quinary interme-tallic phases were found in the literature. Thus, the descrip-tion of this quinary system was obtained by extrapolationbased on descriptions of the lower order systems developedin terms of experimental data. Using the quinary thermo-dynamic description obtained and the commercial softwarePandat [10], we calculated the invariant temperatures forall the six-phase equilibria in the Zr–Ti–Ni–Cu–Al alloyssystem and the compositions of the liquid, one of the sixcoexisting phases. Several of these invariants are of theeutectic type, i.e. L = S1 + S2 + S3 + S4 + S5 and denotedas type I according to Rhine [11], where L denotes theliquid and Si the various solid phases. Other invariantsare of the type II: L + S1 = S2 + S3 + S4 + S5; type III:L + S1 + S2 = S3 + S4 + S5; etc. to type V: L + S1 +S2 + S3 + S4 = S5. Normally the eutectic alloy composi-tions, particularly those considered deep eutectics, shouldfavor the formation of bulk glasses. However, since thethermodynamic descriptions obtained for this quinarymay not be perfect, due to the fact that experimental phase

diagram data for several of the constituent ternaries arescarce [6], we considered the compositions of the liquidphase at the invariant equilibria as the compositionalregions with potential alloys for glass formation.

Thermodynamics provides a necessary but not sufficientcondition for bulk glass formation, so we also consideredthe reduced glass transition temperature, Trg = Tg/Tl,where Tg and Tl are the glass transition and liquidus tem-peratures, respectively. Turnbull suggested that Trg shouldbe equal to or larger than 2/3 for good GFA, based primar-ily on experimental data for Au–Si, Pd–Si, and Pd–Cu–Sialloys [12]. As Trg increases from �1/2 to �2/3, the rateof homogeneous nucleation of the undercooled liquid isanticipated to be very sluggish (less than 10�6/(cm3 s)),favoring bulk glass formation [12]. Since values of Tg forZr alloys vary from 640 to 715 K [4], so this criteriarequires Tl 6 1073 K (800 �C). Applying this Trg criterioneliminated many of the calculated liquid compositionswhose invariant equilibrium temperatures are higher than800 �C, leaving a total of 83 alloy compositions focusingon Zr-rich ones for us to study. These are shown inFig. 1, in which one axis is the mole fraction of Al, oneis that of (Cu + Ni), and the third is that of (Zr + Ti).The different colors show three groups of alloys with thecalculated temperatures at the invariant equilibria between800 and 750, 750 and 700, and 700 and 640 �C, respectively.The compositions of previously published Zr-rich bulkglasses [13–18] are denoted by green dots, which all fallin the compositional region calculated thermodynamicallyfor high GFA. Table 1 summarizes the results of the ther-mal analysis, the detailed alloy compositions, and the crit-ical casting diameter for the previously reported bulkmetallic glass-forming alloys in this quinary system.

Table 1GFA and the thermal properties of the experimentally determined bulkmetallic glass-forming compositions for the Zr–Ti–Ni–Cu–Al alloy system

Alloy composition (at.%) dmax (mm) Tg (K) Tx (K) Refs.

Zr52.5Ti5Ni14.6Cu17.9Al10 10.0 682–713 [13]Zr60Ti5Ni8Cu17.5Al7.5 2.0 [14]Zr57Ti5Ni8Cu20Al10 10.0Zr54.5Ti7.5Ni8Cu20Al10 8.0Zr53Ti5Ni12Cu20Al10 8.0Zr62.5Ti0Ni10Cu20Al7.5 2.5 640 730 [15]Zr60Ti0Ni10Cu20Al10 2.5 670 774Zr57.5Ti0Ni10Cu20Al12.5 2.5 653 757Zr55Ti0Ni10Cu20Al15 2.5 709 805Zr60Ti2.5Ni10Cu20Al7.5 2.5 641 749Zr57.5Ti2.5Ni10Cu20Al10 2.5 655 757Zr55Ti2.5Ni10Cu20Al12.5 2.5 690 775Zr52.5Ti2.5Ni10Cu20Al15 2.5 638 708Zr57.5Ti5Ni10Cu20Al7.5 2.5 684 799Zr55Ti5Ni10Cu20Al10 2.5 669 752Zr52.5Ti5Ni10Cu20Al12.5 2.5 708 780Zr55Ti7.5Ni10Cu20Al7.5 2.5 700 744Zr52.5Ti7.5Ni10Cu20Al10 2.5 711 756Zr50Ti7.5Ni10Cu20Al12.5 2.5 715 769Zr57Ti5Ni8Cu20Al10 5.0 [16]Zr62Ti0Ni8Cu20Al10 3.0 654 758 [17]Zr59Ti3Ni8Cu20Al10 3.0 655 719Zr57Ti5Ni8Cu20Al10 3.0 662 714Zr54.5Ti7.5Ni8Cu20Al10 3.0 679 709Zr53.1Ti5.4Ni11.7Cu19.8Al10 5.0 657 751Zr51.92Ti5.28Ni11.44Cu19.36Al12 5.0 681 770 [18]Zr50.56Ti5.14Ni11.14Cu18.85Al14.3 5.0 689 786Zr49.56Ti5.04Ni10..92Cu18.48Al16 5.0 697 793

dmax is the maximum diameter of a fully amorphous rod obtained bycasting, Tg is the measured glass transition temperature, and Tx is themeasured onset crystallization temperature.

H. Cao et al. / Acta Materialia 54 (2006) 2975–2982 2977

3. Experimental

Each of the alloys studied was prepared by arc-melting amixture of the component elements of 99.7 at.% purity orhigher. Alloys were arc-melted in a Ti-gettered, high-purityargon atmosphere. Each ingot was flipped and remelted atleast three times in order to ensure thorough mixing. Theingots were then drop-cast or suction-cast into coppermolds. These molds have internal cylinder-shaped cavities40 mm in length, with diameters of 1–14 mm. Transversecross-sections of the cast ingots (cut along a plane normalto the length of the ingots) were examined by X-ray diffrac-tion (XRD) using a STOE X-ray diffractometer with a col-limated Cu Ka X-ray source. The glass transition andcrystallization temperatures of the samples were measuredusing differential scanning calorimetry (DSC; Perkin–Elmer DSC7) at a heating rate of 0.33 K/s under a flowof purified argon. The DSC samples were taken fromcross-sections of these ingots. The amorphous structuresof selected samples were further confirmed by transmissionelectron microscopy (TEM) and scanning electron micros-copy (SEM) in backscattered electron imaging mode. Vick-ers hardness of a selected group of samples was measuredon fully amorphous disks using a Buehler Micrometmicrohardness tester at a load of 500 g. Nanoindentation

was carried out on a selected amorphous alloy using a Hys-itron program (Minneapolis, MN). The diamond indenterused was a cube corner with an inclined angle of 90�.The indentations were performed in a load control modeto a maximum load of 5 mN at loading rates of 0.005,0.04, 0.16, and 0.5 mN/s. A dynamic stiffness test was alsoperformed using the software package DSM 3.0 from Hys-itron. The hardness and the Young’s modulus were derivedfrom all the load–displacement curves using the Oliver–Pharr method [19]. The nanoindentations were furtherexamined using SEM and atomic force microscopy (AFM).

4. Results and discussion

Although we have carried out experimental measure-ments on many samples based on the calculations, we willpresent only the results obtained for five representativesamples designated G1–G5. Table 2 summarizes the com-positions and properties of these alloys. We will use themaximum glassy cast rod diameter as a measure of GFA.As shown in Fig. 2, rod-shape glassy alloys with diametersfrom 2 up to 14 mm were obtained. The samples withdiameter smaller than 5 mm were obtained using the cop-per mold suction-casting method (by evacuation) whilethose with larger diameters were prepared using the con-ventional copper mold drop-casting method. Sample G5exhibits the lowest GFA while G1 has the highest with adiameter of at least 14 mm. We do not have the experimen-tal capability to cast rods with diameter greater than14 mm, so the true limit may in fact be even larger. Thismakes G1 (Zr51Ti5Ni10Cu25Al9) among the best bulkglass-forming alloys in this quinary system ever reported.All the glassy rods exhibit shiny metallic luster, also shownin Fig. 2, typical for this class of zirconium alloy glasses.Their smooth surface appearance indicates a lack of anycrystalline phases.

Fig. 3 shows the XRD patterns obtained from differentdiameters of G1, G2, and G3, including the G1 14 mmdiameter sample. (Similar XRD results were obtained forall other alloy compositions with various casting diame-ters.) The XRD pattern of alloy G3 exhibits two typicalamorphous halos in the 9 mm diameter rod sample, buttwo sharp crystalline peaks superimposed on a broad dif-fraction background in the 10 mm diameter rod sample.These results indicate that the critical casting diameter dmax

for alloy G3 is about 9 mm. The XRD results for alloy G2also indicate that the critical casting diameter is about9 mm. However, the XRD diffraction pattern obtainedfrom alloy G1 with the 14 mm casting rod is smooth inboth the first and second diffuse diffraction bands, indicat-ing the absence of any crystallinity in this cast rod! Theamorphous nature of the 14 mm G1 sample was confirmedby TEM, as shown by the electron diffraction pattern inFig. 4. There is no discernible evidence of crystallinity inimaging or diffraction anywhere from this specimen.

Fig. 5 shows the DSC traces of amorphous samples ofG1–G5. Each of these traces depicts a clear endothermic

Tab

le2

GF

Ava

lues

,th

erm

alan

dm

ech

anic

alp

rop

erti

es,

and

the

mic

roh

ard

nes

sd

ata

of

the

rep

rese

nta

tive

allo

ys

All

oy

com

po

siti

on

(at.

%)

dm

ax

(mm

)C

alcu

late

din

vari

ant

reac

tio

nT

l(K

)T

g(K

)T

x(K

)T

x�

Tg

(K)

Tg/T

lT

x/(

Tg

+T

l)V

ick

ers

har

dn

ess

(kg/

mm

2)

G1

(Zr 5

1T

i 5N

i 10C

u25A

l 9)

>14

Liq

+N

iTiZ

r=

s 3_A

lCu

Zr

+C

u2T

iZr

+C

uZ

r 2+

NiZ

r 210

0268

072

444

0.67

90.

430

550

±20

G2

(Zr 4

7.9

Ti 0

.3N

i 3.1

Cu

39.3

Al 9

.4)

�9

Liq

=C

uZ

r 2+

s 3_A

lCu

Zr

+C

u2T

iZr

+N

iZr 2

+C

u10Z

r 792

770

178

685

0.75

60.

483

565

±25

G3

(Zr 5

1.1

Ti 6

.4N

i 3.5

Cu

30.7

Al 8

.3)

�9

Liq

+B

CC

_A2

=s 3

_AlC

uZ

r+

NiT

iZr+

Cu

2T

iZr

+C

uZ

r 210

0766

971

142

0.66

40.

424

551

±30

G4

(Zr 4

4.8

Ti 0

.2N

i 4.7

Cu

40A

l 10.3

)�

9L

iq=

s 3_A

lCu

Zr

+C

u2T

iZr

+C

u10Z

r 7+

NiZ

r+

AlC

u2Z

r91

571

879

375

0.78

50.

486

586

±53

G5

(Zr 5

9.3

Ti 2

.4N

i 2.6

Cu

26.3

Al 9

.5)

�7

Liq

+s 2

_AlC

uZ

r=

s 3_A

lCu

Zr

+C

uZ

r 2+

NiZ

r 2+

BC

C_A

210

4666

172

867

0.63

20.

426

519

±33

GF

Ais

exp

ress

edin

term

so

fth

em

axim

um

dia

met

ero

ffu

lly

amo

rph

ou

sro

ds

dm

ax

ob

tain

edb

yca

stin

g.T

lis

the

ther

mo

dyn

amic

ally

calc

ula

ted

liq

uid

us

tem

per

atu

rean

dT

gan

dT

xar

eth

eD

SC

mea

sure

dgl

ass

tran

siti

on

and

on

set

crys

tall

izat

ion

tem

per

atu

res.

Fig. 2. Surface appearance of the selected glassy alloys rods obtained inthe present study. The rod on the left side is G1 (14 mm diameter), thenG3 (6 mm diameter), G4 (4 mm diameter) and G5 (2 mm diameter).

20 30 40 50 60 70 80

G3, 9mm rod

G3, 10mm rod

G2, 9mm rod

G2, 10mm rod

G1, 14mm rod

Inte

nsity

(a.u

.)

Two Theta (degree)

Fig. 3. X-ray diffraction patterns (Cu Ka radiation) taken from the as-castsamples of three representative glass-forming alloys: G1 (Zr51Ti5Ni10-Cu25Al9) obtained in a 14 mm diameter rod; and G2 (Zr47.9Ti0.3Ni3.1-Cu39.3Al9.4) and G3 (Zr51.1Ti6.4Ni3.5Cu30.7Al8.3) in both 9 and 10 mmdiameter rods.

2978 H. Cao et al. / Acta Materialia 54 (2006) 2975–2982

event, characteristic of a glass transition, followed by acharacteristic exothermic event, associated with the succes-sive stepwise transformations from the undercooled liquidstate to the equilibrium crystalline states at different tem-peratures. The arrows, pointing up, indicate the glass tran-sition temperatures Tg (endothermic) and the arrows,pointing down, indicate the crystallization temperature Tx

(exothermic).Based on these thermal data as given in Table 2, we can

compare the GFA of G1–G5 in terms of the three criteriaproposed in the literature [2,12,19]. Turnbull [12] has sug-gested that alloys with the highest Trg will have the bestGFA. This criterion predicts that G2 and G4 will have

550 600 650 700 750 800 850

No

rmal

ized

Hea

t F

low

(a.u

.)E

nd

oth

erm

ic U

p

G4 (Zr44.8

Ti0.2

Ni4.7

Cu40.0

Al10.3

)

G2 (Zr47.9

Ti0.3

Ni3.1

Cu39.3

Al9.4

)

G1 (Zr51.0

Ti5.0

Ni10.0

Cu25.0

Al9.0

)

G5 (Zr59.3

Ti2.4

Ni2.6

Cu26.3

Al9.5

)

G3 (Zr51.1

Ti6.4

Ni3.5

Cu30.7

Al8.3

)

Temperature (K)

0.5J/g

Tx

Tg

Fig. 5. DSC traces of representative glass-forming alloys at a heating rateof 0.33 K/s, showing the temperatures where glass transition andcrystallization occur.

Fig. 4. Electron diffraction pattern taken from an electropolished sampleof alloy G1 (Zr51Ti5Ni10Cu25Al9) of 14 mm in diameter.

H. Cao et al. / Acta Materialia 54 (2006) 2975–2982 2979

the best GFA since their liquidus temperatures are the low-est, and G5 will have the worst GFA. These predictions areinconsistent with the experimental findings. Inoue [1] hassuggested that the best GFA alloys exhibit the largestdegree of undercooling, Tx � Tg. This criterion predictsthat G2 has the best GFA and G1 or G3 the worst, whichis again inconsistent with the experimental results. Lu andLiu [22] have proposed the c criterion, which predicts thatG2 or G4 will have the best GFA and G1 and G5 theworst, once again inconsistent with the experimentalfindings.

Let us now examine the criterion that a eutectic, or adeep eutectic, favors the formation of bulk glass without

defining what we mean by deep eutectic or bulk glass.A review of the results given in Table 2 shows that thecompositions of the liquid alloys at G2 and G4 corre-spond to a type I invariant reaction, i.e. a eutectic withthe liquid phase transforming to five other solids isother-mally, with the temperatures being 1002 and 915 K,respectively. G1, G3, and G5 correspond to a type IIinvariant reaction, i.e. the liquid phase reacting with onesolid phase to from four other solids, with the tempera-tures being 927, 1007, and 1046 K, respectively. Accord-ing to the eutectic criterion, either the alloy G2 or thealloy G4 will exhibit the best GFA since the compositionsof both alloys correspond to those of the eutectic liquids.Yet experimentally we found that the alloy G1 exhibitsthe best GFA. However, as noted above, the thermody-namic description obtained could be improved in viewof the fact limited phase diagram data exist for more thanone of the constituent ternary systems. In contrast, on thebasis of the experiments carried out in the present study,we have not found that glass formation occurs at any ofthe types III, IV, or V invariants. Glasses form only at aeutectic, type I, or a type II invariant. We can thus ratio-nalize that while it is plausible to calculate a type I invari-ant (or type II) for a type II (or type I) due to theuncertainties in the model-calculated thermodynamic val-ues of the phases involved, it is difficult to calculate a typeI invariant for a types III, IV, or V invariant. It is clearthat we do not yet have a clear understanding of the fac-tors governing the multicomponent alloys for bulk glassformation. We do need to have improved thermodynamicdescriptions for this quinary system when additional ter-nary phase diagram data are available. Nevertheless, thecomputational thermodynamic approach presented herecoupled with the Turnbull Trg criterion can rapidly iden-tify regions of alloy compositions for glass formation.

Ma et al. [23] have recently reported that the GFA of aseries of Zr56.2�cTicCu31.3Ni4.0Al8.5 alloys with c varyingfrom 0 to 10 at.% follows the liquidus temperature. Thisis consistent with the Turnbull criterion since the glasstransition temperatures of alloys are known to remain con-stant over a range of composition. An isopleth in terms oftemperature vs. Ti composition was calculated thermody-namically at constant pressure with fixed compositions ofCu, Ni, and Al at 31.3, 4.0, and 8.5 at.%, respectively.According to this isopleth, the liquidus temperaturedecreases with increasing Ti concentration, reaching a min-imum at 4.9 at.% Ti and increases again. The experimen-tally measured GFA of this series of alloys followsexactly the same trend, increasing from the quaternaryalloy, without Ti, to the maximum at 4.9 at.% Ti and thendecreasing again. This striking result raises the question: isthis a general result or only true for this particular isopleth?Ma et al. also studied alloys along other temperature–composition sections by replacing Ti for Cu, Ni, Al, or(Zr56.2Cu31.3Ni4.0Al8.5), respectively. The results theyobtained are also in accord with the calculated liquidustemperature for each of the isopleths.

Fig. 6. Thermodynamically calculated isopleth of quinary Zr–Ti–Ni–Cu–Al system, expressed in terms of temperature as a function of thecomposition of Ti. The compositions of Cu, Ni, and Al are maintained at32.8, 8.7, and 10.7 at.%, respectively. The shaded area denotes theexperimentally observed bulk glass-forming range (GFR).

20 30 40 50 60 70 80

2.6%Ti, 9mm

0.0%Ti, 9mm

1.0%Ti, 9mm

5.0%Ti, 5mm

Inte

nsi

ty (

a.u

.)

Two Theta (degree)

Fig. 7. XRD patterns from three 9 mm diameter rods of Zr47.8�c-TicNi8.7Cu32.8Al10.7 (c = 0, 1.0, 2.6) and one 5 mm diameter rod of thealloy with an addition of 5 at.% Ti. The 5 mm diameter rod is included forcomparison.

2980 H. Cao et al. / Acta Materialia 54 (2006) 2975–2982

Following Ma et al. [23], we studied another series ofalloys by replacing Zr with Ti from a quaternaryZr47.8Cu32.8Ni8.7Al10.7 alloy. The maximum GFA for thisquaternary alloy is 6 mm, expressed in terms of the diameterof the amorphous rod obtained by casting. We obtained thesame conclusion by Ma et al. and summarized the resultsbelow. Fig. 6 shows the calculated isopleth from c = 0 to45 at.% using the same thermodynamic description [6] andthe Pandat software [10]. The parameter c is the composi-tion of Ti in terms of at.%. Starting at c = 0, the liquidustemperature decreases with additions of Ti, reaches the min-imum at 2.6% Ti, and increases again with further additionsof Ti. Experiments were performed for alloys with c = 0,1.0, 2.6, 5.0, and 6.0 at.%. Fig. 7 shows the XRD patternsof the 9 mm diameter as-cast rods of alloys with c = 0,1.0, 2.6. The quaternary alloy, with c = 0, Zr47.8Cu32.8-Ni8.7Al10.7, exhibits two crystalline peaks superimposed ona broad diffraction hump in its XRD pattern, indicativeof a partially amorphous structure in the as-cast state.The alloy with 1% Ti shows a similar pattern except forthe four crystalline peaks visible on the main halo peak.However, the XRD pattern of the alloy with 2.6% Ti con-

Table 3Thermal and mechanical properties of the bulk metallic glass-forming alloys Z

Ti content (at.%) dmax (mm) Tl (K) Tg (K) Tx (K)

0.0 6 1077 712 7821.0 6 1048 716 7852.6 9 1001 702 7655.0 3 1039 703 7516.0 2 1046 699 748

Values of Tl are thermodynamically calculated and those of the other quantit

sists of only a broad maximum (halo) without any discern-ible Bragg peaks, characteristic of a monolithic amorphousphase. For the alloys containing more than 2.6% Ti, theXRD patterns possess even more and sharper peaks. Oneexample is given in Fig. 7 for an alloy with 5.0% Ti castin a 5 mm diameter rod. Once the Ti concentration reaches7%, it is no longer possible to cast bulk amorphous alloy.These observations are confirmed by SEM, which showscrystalline dendrites in an amorphous matrix for the sam-ples showing sharp XRD peaks or no structure in theimages from samples without sharp XRD peaks. The max-imum diameter dmax obtained for the five alloys along theisopleth are given in Table 3, along with other measuredand calculated thermal and physical properties. Traces ofthe DSC curves obtained from amorphous rods cast in2 mm diameter are shown in Fig. 8. We found that DTx

decreases monotonically with increasing Ti content, andthe largest value of Tx � Tg � 70 K does not correspondto the best glass-forming alloy, at c = 2.6%. Unlike our pre-vious results (G1–G5), these experimental results are consis-tent with the Trg and c criteria, as well as the criterion of thebest GFA at the minimum liquidus temperature.

r47.8�cTicNi8.7Cu32.8Al10.7 (c = 0–6.0)

Tx � Tg (K) Tg/Tl Tx/(Tg + Tl) Vickers hardness(kg/mm2)

70 0.661 0.437 520 ± 3069 0.683 0.445 560 ± 5363 0.701 0.449 560 ± 3448 0.677 0.431 590 ± 4349 0.668 0.429 700 ± 33

ies are measured using DSC.

650 700 900

Tx

Tg

0.0%

1.0%

2.6%

5.0%

6.0%

750 800 850

Temperature (K)

Nor

mal

ized

Hea

t F

low

(a.

u.)

End

othe

rmic

up

0.5J/g

Fig. 8. DSC traces of the bulk glass-forming alloys Zr47.8�cTicNi8.7-Cu32.8Al10.7 (c = 0, 1.0, 2.6, 5.0, 6.0), from 2 mm diameter cast rods. Theupward arrows refer to the glass transition temperatures and thedownward ones denote the onset crystallization temperatures.

0

1

2

3

4

5

100 nm

Lo

ad (

mN

)

Displacement (nm)

Loading rate=0.005mN/s Loading rate=0.04 mN/s Loading rate=0.16 mN/s Loading rate=0.5 mN/s

Fig. 9. Load–displacement curves of the G1 alloy measured duringnanoindentation tests under load control mode with different rates: (a)0.005 mN/s; (b) 0.04 mN/s; (c) 0.16 mN/s; (d) 0.5 mN/s.

H. Cao et al. / Acta Materialia 54 (2006) 2975–2982 2981

Our results and those of Ma et al. lead us to concludethat the minimum liquidus temperature is a robust criterionfor maximizing GFA along an isopleth (i.e. by addition ofa single element to a base composition), at least in Zr-basedalloys. We emphasize that in both cases, this is the calcu-

lated liquidus; extensive experiments are not required toimplement this criterion for any isopleth in a system witha reliable thermodynamic description. Perhaps this resultis only true for the Zr–Ti–Ni–Cu–Al alloys, but if this turnsout to be true for most alloys, then calculated phase dia-grams of multicomponent systems provide an extremelyuseful guide to identify alloys with high GFA. However,this criterion applies only to isopleths (T vs. compositionsections of a phase diagram), not to the full multidimen-sional T-composition space, likely due to the complex nat-

Fig. 10. SEM and AFM images for nanoindentation

ure of the thermodynamic functions in multidimensionalcompositional space.

Vickers hardness of five representative samples desig-nated G1–G5 are shown in Table 2. The Vickers hardnessvaries from 520 to 585 kg/mm2. Although the accuracy ofthis type of measurement is nominally ±3%, analysis ofthese data suggests that a more realistic uncertainty isabout twice as much. This means that, within the uncer-tainty of the measurements, the hardness of these glassesis nearly compositional independent with an average valueof 555 ± 35 kg/mm2. The yield strength of these amor-phous alloys is estimated to be 1.67 GPa from the approx-imate scaling relationship ry = 3HV, in agreement withthose other Zr-based glasses [4]. Nanoindentation wascarried out for the selected amorphous alloy G1. Fig. 9

at a loading rate of 0.5 mN/s for the G1 alloy.

2982 H. Cao et al. / Acta Materialia 54 (2006) 2975–2982

shows the load–displacement nanoindentation curvesobtained under load control mode for various loadingrates. It can be seen that the curve tends to become smoothwith increasing loading rate; however, no distinctive serra-tion was observed even at a small loading rate of 0.005. Thecalculated hardness for this bulk metallic glass is 6.2 ±0.6 GPa and an elastic modulus is estimated to be102 ± 10 GPa from these curves, which are in accord withthe reported values [20]. Mechanical properties measuredby nanoindentation do not exhibit loading rate dependencewithin the range 0.005–0.16 mN/s in the current study.Fig. 10 shows a typical SEM image for the nanoindenta-tion and the corresponding AFM image. The SEM imageclearly resolves the pile-up of the materials during thenanoindentation depth-profiling process and the pile-upspreads out by about 450 nm from the edge of the indenta-tion. AFM measurement shows that the height of the pile-up in the middle is about 110 nm, which is similar to whatTang and Zeng reported though no quantitative data wereprovided [21]. Both SEM and AFM examinations show lit-tle difference of the nanoindentations at various loadingrates in terms of both the morphology and pile-up heightof the materials at the edge of the nanoindentations.Dynamic stiffness testing using nanoindentation demon-strates little change in Young’s modulus with thicknessup to 400 nm, which demonstrates a uniform structureobtained in this bulk metallic glass. In addition, Vickershardness of the bulk metallic glass series Zr47.8�cTicNi8.7-Cu32.8Al10.7 (c = 0–6.0) was also measured and is listed inTable 3. As the Ti content is increased, the hardness ofthese bulk metallic glasses increases from 520 to 700 HV,slightly higher than those of Zr-based bulk metallic glassesreported earlier [24].

5. Conclusions

We have shown that a thermodynamic computationalapproach can identify the compositions of Zr–Ti–Ni–Cu–Al alloys exhibiting low-lying liquidus surfaces, which inturn exhibit exceptionally high bulk GFA. We have synthe-sized a series of novel bulk metallic glasses with exception-ally high GFA following this approach, includingZr51Ti5Ni10Cu25Al9, which can be drop-cast into ingotsat least 14 mm in diameter. These new glass alloys exhibithigh thermal stability with an undercooled liquid regionup to 85 K and excellent mechanical properties, includinga Vickers hardness of �500–700 kg/mm2. The computa-tional thermodynamic approach coupled with Turnbull’sreduced glass transition temperature criterion can rapidlyidentify regions of alloy compositions for glass formationpre-experiment. In addition, the liquidus temperaturesof a thermodynamically calculated isopleth of a series of

multicomponent alloys can be used to predict, certainlyestimate, the trend of GFA of these alloys.

Acknowledgements

The authors are grateful for the financial supportfrom the Defense Advanced Research Projects Agency(DARPA), under ARO Contract No. DAAD 19-01-1-525and the Wisconsin Distinguished Professorship. P.M.V.and W.G.S. acknowledge support from the NSF (DMR-0347746). This work was partly supported by the Departmentof Energy under Grant Number DE-FG03-02ER45988.We thank Professor D.S. Stone at Materials Science andEngineering Department of UW-Madison, and J.A. Reid,C.M. McCarter, and Dr. D.F. Bahr at the School of Mate-rials and Mechanical Engineering of Washington StateUniversity for valuable discussions on the nanoindentationstudy.

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