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Intermetallics 66 (2015) 48e55

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Intermetallics

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Viscosity and fragility of the supercooled liquids and melts from theFeeCoeBeSieNb and FeeMoePeCeBeSi glass-forming alloy systems

R. Parthiban a, b, *, M. Stoica a, c, I. Kaban a, d, Ravi Kumar b, J. Eckert a, d

a IFW Dresden, Institute for Complex Materials, Helmholtzstr. 20, D-01069 Dresden, Germanyb Department of Metallurgical and Materials Engineering, Indian Institute of Technology Madras, 600036 Chennai, Indiac POLITEHNICA University of Timisoara, P-ta Victoriei 2, RO-300006 Timisoara, Romaniad University of Technology Dresden, Institute of Materials Science, D-01062 Dresden, Germany

a r t i c l e i n f o

Article history:Received 6 February 2015Received in revised form23 March 2015Accepted 13 June 2015Available online xxx

Keywords:Metallic glassGlass forming abilityViscosityPhysical propertiesDifferential scanning calorimetryDifferential thermal analysis

* Corresponding author. IFW Dresden, Institute foholtzstr. 20, D-01069 Dresden, Germany.

E-mail address: p.ramasamy@ifw-dresden.de (R. P

http://dx.doi.org/10.1016/j.intermet.2015.06.0160966-9795/© 2015 Elsevier Ltd. All rights reserved.

a b s t r a c t

The dynamic viscosity of four Fe-based bulk metallic glass-forming alloys, [(Fe0.5Co0.5)0.75B0.2Si0.05]96Nb4(alloy A), {[(Fe0.5Co0.5)0.75B0.2Si0.05]0.96Nb0.04}99.5Cu0.5 (alloy B), Fe74Mo4P10C7.5B2.5Si2 (alloy C) and(Fe0.9Ni0.1)77Mo5P9C7.5B1.5 (alloy D), was investigated as a function of temperature in the supercooledliquid region, as well as above the melting point. The alloy B is Cu-added alloy A, while the alloy D wasobtained upon fine-tuning the alloy C composition. All these alloys may form bulk metallic glasses uponcopper mold casting. The viscosities in the supercooled liquid region were calculated using the dataobtained upon parallel plate rheometry measurements, as well as upon differential scanning calorimetry(DSC). The values of the supercooled fragility parameter m, 61, 66, 52 and 60 for the alloys A, B, C and Drespectively, indicate that these alloys are intermediate glass formers. The behavior of the same alloys, inthe molten state, was studied using a high temperature torsional oscillation cup viscometer. The values ofthe corresponding fragility parameter M was calculated as 5.03, 5.91, 4.25, 4.93 for the alloys A, B, C andD, respectively. They confirm the supercooled liquid behavior and predict that the alloys A and C mayform glasses easier than the fine-tuned compositions B and D. Angell plot is constructed for the entirerange of viscosities and the values from both regions, i.e. above melting point and supercooled liquidregion, fit well with the model.

© 2015 Elsevier Ltd. All rights reserved.

1. Introduction

The dynamic viscosity of the liquid metals is considered as a keyparameter in the prediction of fluid flow in many metallurgicalresearches and industrial manufacturing processes [1]. The vis-cosity plays an important role as well in determining the glass-forming ability (GFA) of liquid alloys [2]. High temperature vis-cosity governs the transformation kinetics close to the solidificationpoint and hence the critical cooling rate for the vitrification [3]. Thehigh temperature viscosity of metallic materials is rarely studiedmainly because of the experimental problems, especially the re-action between the melt and crucible material. The viscosities ofglass-forming alloy systems increase over many orders of magni-tude upon cooling from a stable, equilibrium liquid into the glassy

r Complex Materials, Helm-

arthiban).

state [2]. Such increase in viscosity in respect with the change intemperature indicates the resistance to atomic movement [4]. Theconcept of fragility was for the first time introduced by Angell in1985 [5]. The term “fragility” has been chosen in order to indicatethe sensitivity of the liquid structure to the change of temperature.In 1992 B€ohmer et al. [6,7] introduced a new fragility parameter,m,to quantify the fragility of the supercooled liquids. The supercooledfragility is measured from solid amorphous state (metallic glasses),it reflects the stability and structural change in glasses. Smaller them lesser the liquid structural variationwith increase in temperatureand higher themmore the liquid structural variation with increasein temperature. However, the fragility parameter m in undercooledmelts can be calculated only after producing the glassy samples. Toovercome this, Bain et al. [8] measured the viscosity of alloy meltsin Al-based systems and defined a new fragility parameter, M,calculated for temperatures above the respective melting point.They established a good correlation between the GFA and thefragility of the alloy. The glass forming ability of a liquid mainlydepends on two competing processes, liquid phase stability and

Fig. 1. Schematic illustration of oscillation cup viscometer.

R. Parthiban et al. / Intermetallics 66 (2015) 48e55 49

precipitation of the crystallization phase [9].M is considered as thetheoretical parameter which reflects the relative stability of theliquid phase. The smaller the M, the stronger the liquid is, andlarger the GFA. The liquid with high values of M experiences rapidstructure rearrangement towards the melting point.

In recent years the Fe-based metallic glasses are gaining moreinterest because of their high strength and soft magnetic proper-ties, but there are very limited viscosity data available on the lit-eratures [10,11]. However, their GFA is relatively poor whencompared with the typical Zr- or (Cu, Zr)- based alloys [12].Therefore, the analysis of the viscosities above melting may give aproper image on their GFA. In the present work, we concentratedon FeeCoeBeSieNb and FeeCoeBeSieNbeCu alloys because theyhave a good combination of structural and functional properties(sf: ~4000 MPa, Ms: ~1T, m:~12,000, Hc: ~2 A/m) [13e16]. Similarlythe FeeMoePeCeBeSi and FeeNieMoePeCeB alloyswere chosenbecause of their enhanced glass forming ability, good ductility andhigh magnetic saturation [17,18]. Viscosity measurements wereperformed on the aforementioned metallic glasses, in both super-cooled liquid regions and above liquidus temperature, using par-allel plate rheometry, differential scanning calorimetry (DSC) andhigh temperature torsional oscillation cup viscometer respectively.The fragility parameters m and M were calculated and it will beshown that their trend is in good agreement with g-parameter, aswell as with the reduced glass transition temperature Trg, the well-known parameters that are usually associated with the GFA [19].Moreover, they correlate as well with the maximum achievablegeometrical dimensions under which the respective alloys can becast as fully amorphous samples.

2. Experimental details

2.1. Sample preparations

The master alloys [(Fe0.5Co0.5)0.75B0.2Si0.05]96Nb4 (alloy A) and{[(Fe0.5Co0.5)0.75B0.2Si0.05]0.96Nb0.04}99.5Cu0.5 (alloy B) were pre-pared in several steps. First, the eutectic Fe25Nb75 (wt.%) prealloywas produced by arc melting pure Fe (99.9 mass%) and pure Nb(99.9 mass%) lumps. The FeNb prealloy, together with Fe and Columps (99.9 mass%), crystalline B (99.5 mass%) and crystalline Si(99.99 mass%) were melted together by induction melting underprotective Ar atmosphere. Similarly, the master alloysFe74Mo4P10C7.5B2.5Si2 (alloy C) and (Fe0.9Ni0.1)77Mo5P9C7.5B1.5 (alloyD)were prepared by inductionmelting using Fe, Ni, Mo lumps (99.9mass%), as well as crystalline B (99.5 mass%) and crystalline Si(99.99 mass%). As C it was used pure graphite and as P it was usedan industrial FeP pre-alloy, with P content of 14 at.%. In this process,induction melting was preferred in order to assure good homoge-neity of the entire master alloy. Pieces of master alloy wereremelted in quartz tubes and then the melt was injected into awater-cooled copper mold under a high purity Ar atmosphere toproduce rod shaped specimens of 2 mm in diameter and 60 mm inlength. The thermal stability and the melting behavior of glassysamples were evaluated using a NETZSCH DSC 404C differentialscanning calorimeter (DSC) at a heating rate of 20 K/min. Cylin-drical samples of 2 mm diameter and 0.5 mm thickness were usedin parallel plate rheometry (PerkineElmer dynamic mechanicalanalyzer).

2.2. Viscosity measurements

The parallel plate rheometry as described by Stefan [20] andDiennes et al. [21] was used to measure the viscosity of the glassesin supercooled liquid region (SLR). In this method quartz penetra-tion probes of 3 mm diameter were used as parallel plates, and the

sample was placed between the plates. The measurements wereperformed under Ar atmosphere at a constant heating rate of 20 K/min, with the penetration probes compressed by a force of 2.6 N. Bymeasuring the change in height of the sample as a function of time,the viscosity at any temperature is given by the Stefan equation[20,21]:

h ¼ � 2Fh3

3pa4�dhdt

� (1)

where F is the applied load, a is the radius of the samples, and h isthe height of the sample.

The temperature dependent viscosities of the samples above themelting point were measured using an oscillation cup viscometerduring cooling. Fig. 1 illustrates schematically the oscillation cupviscometer. Boron nitride crucibles were used to avoid the frictionbetween the liquid metal and container wall, as well as for mini-mizing the chemical reactions that may give rise to experimentalartifacts. The wire suspension system is constructed in such a waythat it gives low moment of inertia and in the same time is used toposition the sample container exactly in the middle of the heatingzone. The heating zone is well insulated from the outer water-cooled body. The detailed measuring process is described in Ref.[22]. The dynamic viscosity of the liquid was calculated directlywithout the use of any reference liquid, i.e. upon the absolutemethod.

The suitable equation for the calculation of dynamic viscositywas proposed in 1958 by Roscoe and Bainbridge [23]. Brooks et al.[1] subsequently modified the equation and it is given by

h ¼�

JLpR3 HZ

�2 1prT

; (2)

where

Z ¼�1þ R

4H

�a0 �

�32þ 4RpH

�1Pþ�38þ 9R4H

�a1

P2(3)

Table 1Glass transition temperature (Tg), crystallization temperature (Tx), liquidus tem-perature (TL), g parameter and reduced glass transition temperature Trg for[(Fe0.5Co0.5)0.75B0.2Si0.05]96Nb4 (alloy A), {[(Fe0.5Co0.5)0.75B0.2Si0.05]0.96Nb0.04}99.5Cu0.5

(alloy B), Fe74Mo4P10C7.5B2.5Si2 (alloy C) and (Fe0.9Ni0.1)77Mo5P9C7.5B1.5 (alloy D)metallic glasses.

Alloys Tg (K) Tx (K) TL (K) g Trg

Alloy-A 825 858 1475 0.372 0.559Alloy-B 793 818 1475 0.361 0.537Alloy-C 733 768 1283 0.380 0.571Alloy-D 698 732 1260 0.374 0.554

R. Parthiban et al. / Intermetallics 66 (2015) 48e5550

P ¼�pr

hT

�1=2

R

a0 ¼ 1� 32

L

2p� 3

8L2

4p2 (4)

a1 ¼ 1þ 12

L

2pþ 1

8L2

4p2 (5)

In these equations R denotes the inner radius of the crucible,which can be directlymeasured.H, the height of the samples withinthe cup, was calculated from the sample's mass taking the tem-perature dependency of the mass density r into account. Themethod is described elsewhere [24]. The Eq. (3) was then solvednumerically using the experimentally determined oscillation pa-rameters time period T and logarithmic decrement L. The loga-rithmic decrement a0 of the empty pendulumwas subtracted priorto the determination of the viscosity [22].

3. Results

The DSC traces for the as cast 2 mm diameter rods of alloys A, B,C and Dweremeasured at a constant heating rate of 20 K/min Fig. 2,which clearly shows the glass transition event followed by the SLRand crystallization. Further, all alloys melted completely in a rangeof temperatures, indicating that none of them is eutectic. The glasstransition temperature Tg, crystallization temperature Tx, and themelting temperature TL were considered as the onsets of therespective events upon heating, and their values are given inTable 1. From the DSC curve (Fig. 2) of the alloy B, it is clear that Tgand Tx decrease with addition of 0.5 at.% Cu. This can be easilyattributed to the early growth of nano-crystals [25]. The GFAparameter g¼ Tx/(Tgþ TL) [19] and reduced glass transition tem-perature Trg¼ Tg/Tm, (were Tm is usually considered to be the liq-uidus temperature TL) are listed in Table 1.

3.1. Viscosity measurement in supercooled liquid region

The viscosity variation with respect to temperature in the SLR

Fig. 2. DSC traces of the [(Fe0.5Co0.5)0.75B0.2Si0.05]96Nb4 (alloy A), {[(Fe0.5Co0.5)0.75B0.2-

Si0.05]0.96Nb0.04}99.5Cu0.5 (alloy B), Fe74Mo4P10C7.5B2.5Si2 (alloy C) and (Fe0.9Ni0.1)77-Mo5P9C7.5B1.5 (alloy D) glassy alloys, measured at a constant heating rate of 20 K/min.

for the alloys A, B and C, D are shown in Fig. 3(a) and (b) respec-tively. From the graphs it is clearly evident that the glassy alloysundergo large variation in viscosity, more than one order ofmagnitude. In the case of alloy A, the viscosity decreases from2.0 � 109 to 7.0 � 107 (±35 � 106) Pa s. The alloy B shows aparticular behavior, with two distinct viscosity drops: from 2 � 109

to 6 � 107 (±35 � 106) Pa s during the first one and from 2 � 109 to5 � 107 (±35 � 106) Pa s during the second. This indicates that thealloy B possesses two glass-transition-like events, results which arein agreement with our previous findings (manuscript submittedelsewhere). There we have shown that above the first crystalliza-tion the structure of the sample consists of only bcc-(Fe, Co) solid

Fig. 3. Viscosity as a function of temperature of the amorphous (a)[(Fe0.5Co0.5)0.75B0.2Si0.05]96Nb4 (alloy A) and {[(Fe0.5Co0.5)0.75B0.2-

Si0.05]0.96Nb0.04}99.5Cu0.5 (alloy B), (b) Fe74Mo4P10C7.5B2.5Si2 (alloy C) and (Fe0.9Ni0.1)77-Mo5P9C7.5B1.5 (alloy D) alloys. The connecting lines are just guide for the eyes.

R. Parthiban et al. / Intermetallics 66 (2015) 48e55 51

solution along with the residual amorphous matrix, which laterundergoes glass-transition like event. The alloy D has a similarvariation (like alloy-A), from 2� 109 Pa s to 7� 107 (±35� 106) Pa s.A somehow smaller variation is observed in the case of alloy C, forwhich the viscosity decreases from 1.5 � 109 to 3 � 108 (±35� 106)Pa s. The re-increase in the viscosity takes place at the peak tem-peratures (Tp) as observed upon DSC measurement.

In order to calculate the fragility of the supercooled liquids thevariation of the viscosity in SLR as a function temperaturewas fittedwith both Arrhenius type relation (Eq. (6)) andVogeleFulchereTamman (VFT) type relation (Eq. (7)).

h ¼ h0exp�EaRT

�(6)

where, h0 is a constant, Ea the activation energy for viscous flowandR the molar gas constant.

h ¼ haexp�

BT � T0

�(7)

where ha is a pre-exposed factor, B and T0 are fit parameters and T istemperature in K.

The value ha was calculated according to the relation [15].

ha ¼ NA$hV

(8)

where NA is Avogadro's constant, h is Planck's constant and V is themolar volume [23]. The parameter T0 is “ideal” glass transitiontemperature [26,27], where the barriers with respect to flowwouldgo to infinity [28]. Fig. 4(a)e(d) show the measured viscosity as afunction of temperature fitted with Arrhenius type relation (redline) as well as with VFT type relation (blue line) for the wholesupercooled region for the alloys A, B, C and D respectively. Thefitting parameters h0, ha, B, T0 and activation energy for viscous flowEa are given in Table 2. The values obtained from the above equa-tions were used to calculate the fragility parameter of the alloys.

The fragility parameter m (steepness index) is given by the Eq.(9) [6,7].

m ¼������dlog10tðTÞd�TgT

�������T¼Tg

¼������dlog10hðTÞd�TgT

�������T¼Tg

(9)

If the experimental measured viscosity values are in goodagreement with the Arrhenius type relation (Eq. (6)), thenm can beexpressed as:

m ¼ EaRTgln10

(10)

On the other side, if the VFT type relation (Eq. (7)) is used tomodel the experimental values, then m can be expressed as:

m ¼ BTg�Tg � T0

�2ln10 (11)

For the present case, both Arrhenius and VFT fitting give similarvalues. The fragility parameter m calculated at different heatingrate for all the alloys A, B, C and D are almost the same. Therefore,since 20 K/min is considered as a standard heating rate for all themeasurement, the fragility parameterm calculated at a heating rate20 K/min for all the alloys A, B, C and D are summarized in Table 3.

Sokolov et al. introduced in 1993 a new equation to calculate thefragility parameter m from non-equilibrium state [29]. In this

model they used the activation energy for viscous flow E(h) andglass transition temperature Tg to calculate the fragility. Later, Huet al. [30] modified the equation introduced by Sokolov. Themodified equation can be written as

m ¼ DH*

RTg(12)

whereDH* is the activation enthalpy for the glass transition and thevalue of DH* can be calculated from the equation [31,32]:

ln ðФÞ ¼ � DH*

RTg Фþ constant (13)

where f is the scanning heating rate, R is the gas constant, Tgf is theglass transition temperature at different heating rate. Fig. 5 showsthe plot ln(f) vs 1000/Tgf and the slope m values are given inTable 3, under the name “DSC fit”.

3.2. Viscosity measurement above the melting temperature

The high temperature viscosities of the alloys were measuredabove their liquidus temperature and, in order to minimize theerrors, the experimental data were recorded during the cooling,which was performed at a constant rate of 1 K/min. Due to thetechnical limitations the alloys were overheated only up to 1530 K.The alloys A and B reach the viscosity of 10.8 (±0.5) and 9.9 (±0.5)mPa s respectively at their liquidus temperature TL ¼ 1475 K,whereas alloys C and D reach the viscosity of 16.5 (±0.5) and 15.9(±0.5) mPa s at their respective liquidus temperatures of 1283 Kand 1260 K. In case of alloy D the viscosity of the melt drops downsteeper after 1425 K, this may be due to further breakdown of liquidstructure. Fig. 6 shows the viscosity data for the alloys at temper-atures above liquidus. The full curves represent the fitting of theexperimental data according to the Eq. (6). The results (i.e. theplots) confirm that the measured data for alloys melts obeyArrhenius equationwithin the experimental error. The values of thefitting parameters h0 and E/R for the alloys are given in Table 5. Thefragility of the melt can be defined as the viscosity variation rate ofoverheated liquid towards the liquidus temperature. Mathematicalconcept given by Bain et al. [8] about fragility of the melts can bewritten as

M ¼������v½hðTÞ=hðTLÞ

v

�TTL

�������T¼TL

¼��������dhrdTr

����Tr¼1

����; (14)

where, hr¼ h/hL, Tr¼ T/TL, TL is the liquidus temperature and hL isthe viscosity at the liquidus temperature. If the viscosity variationh(T) can be expressed by Arrhenius-type relation (Eq. (6)) then thefragility M becomes [33]:

M ¼���� hoEahLRTL

exp�EaRTL

����� (15)

The calculated M values are summarized in Table 5.

4. Discussion

Recently Takeuchi et al. proposed a newmethod to calculate theGFA of the alloys from VFT plot [34], but in general the mostcommonly accepted means to evaluate the GFA of the alloys are thereduced glass transition temperature Trg and g parameter [19].Higher Trg and g values usually mean a better GFA. The existence ofcorrelation between the Trg and g for all studied alloys indicates

Fig. 4. Viscosity in the supercooled liquid region as a function of inverse temperature, calculated from parallel plate rheometry, measurement performed at a constant heating rateof 20 K/min, for (a) [(Fe0.5Co0.5)0.75B0.2Si0.05]96Nb4 (b) {[(Fe0.5Co0.5)0.75B0.2Si0.05]0.96Nb0.04}99.5Cu0.5, (c) Fe74Mo0P10C7.5B2.5Si2 and (d) (Fe0.9Ni0.1)77Mo5P9C7.5B1.5 glasses. The experi-mental data (open symbols) are fitted with both Arrhenius-type relation (continuous line) and VFT-type relation (discontinuous red line). (For interpretation of the references tocolour in this figure legend, the reader is referred to the web version of this article.)

Table 2Fit parameters h0, ha, B, T0, and activation energy for viscous flow Ea for [(Fe0.5Co0.5)0.75B0.2Si0.05]96Nb4 (alloy A), {[(Fe0.5Co0.5)0.75B0.2Si0.05]0.96Nb0.04}99.5Cu0.5 (alloy B),Fe74Mo4P10C7.5B2.5Si2 (alloy C) and (Fe0.9Ni0.1)77Mo5P9C7.5B1.5 (alloy D) metallic glasses.

Alloys Fitting type h0, ha (Pa s) Ea (kJ/mole) B (K) T0 (K)

Alloy-A Arrhenius h0 ¼ 6.39 � 10�6 406 ± 8 e e

VFT ha ¼ 6.34 � 10�7 e 20,455 ± 250 273 ± 3Alloy-B Arrhenius h0 ¼ 4.29 � 10�6 315 ± 6 e e

VFT ha ¼ 6.36 � 10�7 e 19,083 ± 250 260 ± 3Alloy-C Arrhenius h0 ¼ 1.30 � 10�6 282 ± 4 e e

VFT ha ¼ 5.93 � 10�7 e 21,062 ± 250 173 ± 3Alloy-D Arrhenius h0 ¼ 1.24 � 10�7 350 ± 5 e e

VFT ha ¼ 5.85 � 10�7 e 14,945 ± 250 320 ± 3

Table 3Calculated supercooled fragility parameter m for [(Fe0.5Co0.5)0.75B0.2Si0.05]96Nb4(alloy A), {[(Fe0.5Co0.5)0.75B0.2Si0.05]0.96Nb0.04}99.5Cu0.5 (alloy B), Fe74Mo4P10C7.5B2.5Si2(alloy C) and (Fe0.9Ni0.1)77Mo5P9C7.5B1.5 (alloy D) metallic glasses.

Alloys Supercooled fragility m

Arrhenius fit VFT fit DSC fit

Alloy-A 26 ± 0.5 24 ± 0.6 62 ± 0.5Alloy-B 21 ± 0.5 23 ± 0.6 66 ± 0.5Alloy-C 19 ± 0.5 21 ± 0.6 52 ± 0.5Alloy-D 26 ± 0.5 31 ± 0.6 60 ± 0.5

R. Parthiban et al. / Intermetallics 66 (2015) 48e5552

that these alloys have a good GFA [19]. Among the four alloysinvestigated, the alloy C has the highest and the alloy B has thesmallest Trg and g values: 0.571, 0.380 and 0.537, 0.361 respectively.All values (see Table 1) are very close to those measured for otherknown BMGs [19,35] and are in good agreement with themaximum achievable diameter for which the samples are stillamorphous: 3 mm for alloy A [36], 2 mm for alloy B (present work),5 mm for alloy C [37] and 2.5 mm for alloy D [18]. Compared toother alloys, alloy C encounters a relatively lesser drop in viscositymagnitude in supercooled liquid region, which indicates the exis-tence of a stronger relationship between better GFA and dynamicbehavior of supercooled liquids. In order to estimate the real GFA of

Fig. 5. The variation of ln(f) vs. 1000/Tg for [(Fe0.5Co0.5)0.75B0.2Si0.05]96Nb4 (alloy A),{[(Fe0.5Co0.5)0.75B0.2Si0.05]0.96Nb0.04}99.5Cu0.5 (alloy B), Fe74Mo4P10C7.5B2.5Si2 (alloy C)and (Fe0.9Ni0.1)77Mo5P9C7.5B1.5 (alloy D) glasses.

Fig. 6. Viscosity as a function of inverse temperature of the liquid alloys[(Fe0.5Co0.5)0.75B0.2Si0.05]96Nb4 (alloy A), {[(Fe0.5Co0.5)0.75B0.2Si0.05]0.96Nb0.04}99.5Cu0.5(alloy B), Fe74Mo4P10C7.5B2.5Si2 (alloy C) and (Fe0.9Ni0.1)77Mo5P9C7.5B1.5 (alloy D). Theexperimental data (open symbols) are fitted with Arrhenius-type relation (continuousred line). (For interpretation of the references to colour in this figure legend, the readeris referred to the web version of this article.)

Table 4Variation of the crystallization Tx and glass transition Tg temperatures with the in-crease of the heating rate for the [(Fe0.5Co0.5)0.75B0.2Si0.05]96Nb4 (alloy A),{[(Fe0.5Co0.5)0.75B0.2Si0.05]0.96Nb0.04}99.5Cu0.5 (alloy B), Fe74Mo4P10C7.5B2.5Si2 (alloy C)and (Fe0.9Ni0.1)77Mo5P9C7.5B1.5 (alloy D) metallic glasses.

Alloys Temperature (K) Heating rate (K/min)

5 10 15 20

Alloy-A Tx 837 843 849 858Tg 812 817 821 825

Alloy-B Tx 797 804 811 818Tg 780 786 790 793

Alloy-C Tx 751 759 764 768Tg 720 725 729 733

Alloy-D Tx 718 727 730 732Tg 688 693 695 698

Table 5Fitting parameters h0 and E/R of the Arrhenius equation (Eq. (7)), liquidus temper-ature TL, viscosity at liquidus temperature hL and the calculated fragility parameterM for [(Fe0.5Co0.5)0.75B0.2Si0.05]96Nb4 (alloy A), {[(Fe0.5Co0.5)0.75B0.2-

Si0.05]0.96Nb0.04}99.5Cu0.5 (alloy B), Fe74Mo4P10C7.5B2.5Si2 (alloy C) and (Fe0.9Ni0.1)77-Mo5P9C7.5B1.5 (alloy D) glass-forming alloys.

Alloys ho(m Pa s) E/R (K) TL ± 3 (K) hL ± 0.5 (mPa s) M ± 0.2

Alloy-A 0.0673 7485.3 1475 10.8 5.03Alloy-B 0.0281 8661.7 1475 9.9 5.92Alloy-C 0.2443 5418.3 1283 16.5 4.25Alloy-D 0.0948 6426.4 1260 15.9 4.94

R. Parthiban et al. / Intermetallics 66 (2015) 48e55 53

these alloys it is vital to know how strong or fragile the liquid is. Theconcept of fragility in liquids, polymers and plastic crystals was firstapplied by Angell and co-workers [38,39]. The temperaturedependence of the viscosity in open network glasses such as SiO2can be described very well by Arrhenius law (i.e. Eq. (6)). Theseglass formers are called strong liquids and exhibit high equilibriummelt viscosities of the order of 104 Pa s. On the contrary, materialssuch as polymers show strong deviation from Arrhenius law andthey are termed as fragile liquids which can be described by a VFTtype relation [41]. In 1995, Komatsu [40] applied the concept offragility to metallic glass formers and found that the alloys havingfragility parameter in the rage of 30e40 are strong liquids with alower limit z16, and the fragile liquids exhibit values greater than80. The alloys with values between 40 and 80 were referred to asthe intermediate category [41]. For the alloys presented here, theviscosities in SLR were fitted with both Arrhenius type relation andVFT-type relation (see Fig. 4). As it can be observed, Arrhenius-typerelation gives relatively better fit than the VFT-type relation.Moreover, the T0 (temperature at which the barriers to flow wouldgo to infinity) values for the alloys A, B, C and D are 273, 260, 173and 320 K, respectively; these T0 values are very small, and hencesupercooled viscosities of these alloys cannot be fitted with VFTtype relation. The calculated supercooled fragility m values(Table 3) for these alloys A, B and D are 26, 21 and 26 respectivelywhich are smaller than those of other glasses [40,41] and close tosilica [6,7]. In the case of alloy C, the m value is 19 being almostcloser to the lower limit of the fragility parameter. This is mainlybecause fragility is a dynamic parameter [6] and it is more signif-icant in the non-equilibrium state. The viscosity value obtained inthe supercooled region is not an equilibrium value (the viscositywas measured at a heating rate of 20 K/min). The glass transitionand crystallization events shift to higher temperatures with in-crease in heating rate. Tx and Tg for different heating rates of 5,10,15and 20 K/min are given in Table 4. Fig. 7 shows the plot of ln(f) vs.1/Tgf. Them value calculated by this method for the alloys A, B, C andD are 61, 66, 52 and 60, respectively. These fragility parameter mvalues predict that these alloys belong to the category of interme-diate glass formers, which is in between strong glass formers likeSiO2 and GeO2 (m~20) and weak glass formers like polystyrene andpolypropylene (m ¼ 139 and 137, respectively) [41,7]. These valuesare in agreement with the experimental findings [13e18].

In 1972 Uhlmann [42] suggested that the GFA of materialsmainly depends on the magnitude of the viscosity at the meltingpoint and on the rate of increase in viscosity with decrease intemperature below the melting point. Among the four alloys cho-sen for this study, the alloy C has the highest viscosity at its liquidustemperature and also highest Trg and g (data summarized inTables 5 and 1, respectively) indicating the best GFA, whereas alloyB has the lowest viscosity at its liquidus temperature and also it hasthe lowest Trg and g. This proves the positive correlation betweenmelt viscosity and GFA for the glass forming systems. Ultimately,the Fe-based alloy system obeys the Uhlmann theory. The viscosity

Fig. 7. Angell plot over the entire range of measured viscosities for[(Fe0.5Co0.5)0.75B0.2Si0.05]96Nb4 (alloy A), {[(Fe0.5Co0.5)0.75B0.2Si0.05]0.96Nb0.04}99.5Cu0.5(alloy B), Fe74Mo4P10C7.5B2.5Si2 (alloy C) and (Fe0.9Ni0.1)77Mo5P9C7.5B1.5 (alloy D) glasses.

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reflects the bonding nature of atoms in liquid, which in turn de-termines the stability of the liquid structure. Recently A.L. Bel'-tyukov et al. [10] studied the variation of the melt viscosity in FeeSiand FeeSieB systems above their liquidus temperature with in-crease in Si and B contents respectively. In their work they studiedhow the addition of Si and B atoms influences the bonding nature ofother atoms, which in turn affects the liquid viscosity of the alloys.It was found that in the range from 15 to 30% Si the melt viscosity ismaximal, presumably due to the implementation of the Fe3Si-typeshort-range ordering in this range of concentration. Bain et al. [8]studied the fragility of Al-based alloys above liquidus tempera-ture and they correlated the fragility parameter M with the GFAdirectly. In certain alloy systems such as Al-based, it is very difficultto describe m, since the alloy melts are easier to obtain than thesupercooled state, and M allows the evaluation of the dynamicbehavior of the alloy systems. This method has been successfullytested in AleCoeCe [8] and in PreFeeCueAl [43] systems. Thecalculated fragility M value for all the four alloys A, B, C and D aregiven in Table 3. The calculated fragility values of the alloymelts arein good agreement with Bain's theory and our experimental find-ings, i.e. alloy C with smaller M can be easily cast as metallic glassrods with diameter up to 5 mm, whereas alloy B with larger Mcould have been cast as glassy rods with maximum 2mm diameter.

Both the supercooled and alloy melts fragilities exhibit thechange of viscosity with respect to temperature, which in turn re-flects the stability and change of liquid structure with increase intemperature. The supercooled fragility is measured from solidamorphous state (metallic glasses), hence the supercooled fragilityis more important since it reflects the stability and structuralchange in glasses. On the contrary, the fragility of the alloy melts isobtained from completely molten alloy liquids, which reflects thechanging of the viscosity at higher temperature. While the fragilityof the melts is obtained at the beginning of the process, thesupercooled fragility rather is obtained at the end of the process.Hence, the ability of an alloy to produce glass could be predicted bystudying the fragility of the corresponding melt.

Angell plot or fragility plot introduced by Angell et al. in 1988[38] is constructed by plotting logarithm of relaxation time t(T) orviscosity h(T) as a function of the temperature ratio Tg/T. This plotreflects the stability of the structure in the liquids with increase intemperature. There they have shown that strong and fragile liquids

refer to the stability of the structure in the liquids against increasein temperature. Fig. 7 shows the Angell plot constructed for thealloys A, B, C and D for the entire range of measured viscosities, i.e.abovemelting point and supercooled liquid region. From the Angellplot it is clear that alloy C has relatively stronger glass formingtendency. These observations are in good agreement with experi-mental findings.

5. Conclusion

The viscosity of [(Fe0.5Co0.5)0.75B0.2Si0.05]96Nb4,{[(Fe0.5Co0.5)0.75B0.2Si0.05]0.96Nb0.04}99.5Cu0.5, Fe74Mo4P10C7.5B2.5Si2and (Fe0.9Ni0.1)77Mo5P9C7.5B1.5 bulkmetallic glass forming liquids insupercooled liquid state was studied using parallel plate rheometryand also calculated using the values obtained from differentialscanning calorimetry. The viscosities measured from the abovemethods were used to calculate the fragilities in supercooled liquidstate. The fragility values calculated for the alloys A, B, C and D usingTg and DH*are 61, 66, 52, 60 respectively, this method gives morereasonable fragility parameter values than parallel plate rheometry(non-equilibrium state). These values clearly show that these alloysbelongs to intermediate category in glass forming alloys group.

The high temperature viscosities of these alloys were studiedusing torsional oscillation cup viscometer, and the calculatedfragility parameter M of the alloys A, B, C, D are 5.03 (±0.2), 5.92(±0.2), 4.25 (±0.2), and 4.94 (±0.2) respectively. The values are ingood agreement with the experimental findings, i.e. the maximumachievable diameter upon copper mold casting for which thesamples were still amorphous. Thus, the alloys having relativelystable structure, i.e. M less than 5, can be easily frozen in to glass,whereas the alloys having higher M values needs higher coolingrate.

Acknowledgments

The authors are very grateful for the financial support providedby the “DAAD-IIT Masters Sandwich Program”. The authors wouldlike to thank B. Bartusch, S. Donath and M. Frey for technicalassistance and K.G. Prashanth for the interesting discussions. Thesupport of the EU through VitriMetTech ITN network FP7-PEOPLE-2013-ITN-607080, as well as of the German Science Foundation(DFG) through the Grant STO 873/2 is fully acknowledged.

References

[1] R.F. Brooks, A.T. Dinsdale, P.N. Quested, The measurement of viscosity ofalloys-a review of methods, data and models, Meas. Sci. Technol. 16 (2005)354e362.

[2] D. Turnbull, Under what conditions can a glass be formed, Contemp. Phys. 10(1969) 473e488.

[3] A. Masuhr, T.A. Waniuk, R. Busch, W.L. Johnson, Time scales for viscous flow,atomic transport, and crystallization in the liquid and supercooled liquidstates of Zr41.2Ti13.8Cu12.5Ni10.0Be22.5, Phys. Rev. Lett. 82 (1999) 2290e2293.

[4] T. Iwashita, D.M. Nicholson, T. Egami, Elementary excitations and crossoverphenomenon in liquids, Phys. Rev. Lett. 110 (2013) 2055041e2055045.

[5] C.A. Angell, Spectroscopy simulation and scattering, and the medium rangeorder problems in glass, J. Non Cryst. Solids 73 (1985) 1e17.

[6] R. Bohmer, C.A. Angell, Correlations of the nonexponentiality and statedependence of mechanical relaxations with bond connectivity in Ge-As-Sesupercooled liquids, Phys. Rev. B 45 (1992) 10091e10094.

[7] R. Bohmer, K. Nagi, C.A. Angell, D.J. Plazek, Nonexponential relaxations instrong and fragile glass formers, J. Chem. Phys. 99 (1993) 4201e4209.

[8] X.F. Bian, B.A. Sun, L.N. Hu, Y.B. Jia, Fragility of superheated melts and glass-formability in Al-based alloys, Phys. Lett. A 335 (2005) 61e67.

[9] D.N. Perera, Compilation of the fragility parameters for several glass-formingmetallic alloys, J. Phys. Condens. Matter 11 (1999) 3807e3812.

[10] A.L. Bel'tyukov, V.I. Lad'yanov, A.I. Shishmarin, S.G. Menshikova, Viscosity ofliquid amorphizing alloys of iron with boron and silicon, J. Non Cryst. Solids401 (2014) 245e249.

[11] T. Yamasaki, N. Yufune, H. Ushio, D. Okai, T. Fukami, H.M. Kimura, A. Inoue,Viscosity measurements for Fe-Ni-B and Fe-Ni-Al-B liquid alloys by an

R. Parthiban et al. / Intermetallics 66 (2015) 48e55 55

oscillating crucible method, Mater. Sci. Eng. A 375e377 (2004) 705e708.[12] A. Inoue, Stabilization of metallic supercooled liquid and bulk amorphous

alloys, Acta Mater. 48 (2000) 279e306.[13] A. Inoue, B.L. Shen, Formation and soft magnetic properties of Co-Fe-Si-B-Nb

bulk glassy alloys, Mater. Trans. 43 (2002) 1230e1234.[14] A. Inoue, B.L. Shen, C.T. Chang, Super-high strength of over 4000 MPa for Fe-

based bulk glassy alloys in [(Fe1-xCox)0.75B0.2Si0.05]96Nb4 system, Acta Mater.52 (2004) 4093e4099.

[15] M. Aykol, M.V. Akdeniz, A.O. Mekhrabov, Solidification behavior, glass formingability and thermal characteristics of soft magnetic FeCoBSiNbCu bulk amor-phous alloys, Intermetallics 19 (2011) 1330e1337.

[16] X. Li, H. Kato, K. Yubuta, A. Makino, A. Inoue, Effect of Cu on nano-crystallization and plastic properties of FeSiBPCu bulk metallic glasses, Mater.Sci. Eng. A 527 (2010) 2598e2602.

[17] F. Li, S. Pang, R. Li, T. Zhang, Ductile FeeMoePeCeBeSi bulk metallic glasseswith high saturation magnetization, J. Alloys Compd. 483 (2009) 613e615.

[18] A. Seifoddini, M. Stoica, M.N. Ahmadabadi, S.H. Manesh, U. Kühn, J. Eckert,New (Fe0.9Ni0.1)77Mo5P9C7.5B1.5 glassy alloys with enhanced glass-formingability and large compressive strain, Mater. Sci. Eng. A 560 (2013) 575e582.

[19] Z.P. Lu, C.T. Liu, A new glass-forming ability criterion for bulk metallic glasses,Acta Mater. 50 (2002) 3503e3512.

[20] M.J. Stefan, Akad. Wiss. Wein. Math. Natur. Kl. 69 (1874) 713. Abt 2.[21] G.J. Diennes, H.F. Klemm, Theory and application of the parallel plate plas-

tometer, J. Appl. Phys. 17 (1946) 458e471.[22] S. Gruner, W. Hoyer, A statistical approach to estimate the experimental un-

certainty of viscosity data obtained by the oscillation cup technique, J. AlloysCompd. 480 (2009) 629e633.

[23] R. Roscoe, W. Bainbridge, Viscosity determination by the oscillating vesselmethod I: theoretical considerations, Proc. Phys. Soc. 72 (1958) 576e584.

[24] S. Gruner, M. K€ohler, W. Hoyer, Surface tension and mass density of liquid Cu-Ge alloys, J. Alloys Compd. 482 (2009) 335e338.

[25] M. Stoica, R. Li, S. Roth, J. Eckert, G. Vaughan, A.R. Yavari, (Fe 0.5 Co 0.5 ) 0.75 B0.20 Si 0.05 ] 96 Nb 4 metallic glasses with small Cu additions, Metall. Mater.Trans. A 42 (2011) 1476e1480.

[26] H.G. Jiang, J. Baram, Estimation of the glass transition temperature in metallicglasses, Mater. Sci. Eng. A 208 (1996) 232e238.

[27] S.V. Nemilov, Genesis of the vitreous state: effect of pressure on the ther-modynamic properties of the glasses, Glass Phys. Chem. 21 (1995) 379e391.

[28] R. Busch, E. Bakke, W.L. Johnson, Viscosity of the supercooled liquid and

relaxation at the glass transition of the Zr46.75Ti8.25Cu7.5Ni10Be27.5 bulkmetallic glass forming alloy, Acta Mater. 46 (1998) 4725e4732.

[29] A.P. Sololov, E. Rossler, A. Kisliuk, D. Quitmann, Dynamics of strong and fragileglass formers: differences and correlation with low temperature properties,Phys. Rev. Lett. 71 (1993) 2062e2065.

[30] L. Hu, X. Bian, W. Wang, J. Zhang, Y. Jia, Liquid fragility and characteristic ofstructure corresponding to the prepeak of AlNiCe amorphous alloys, ActaMater. 52 (2004) 4773e4781.

[31] C.T. Moynihan, Correlation between the width of the glass transition regionand the temperature dependence of the viscosity of high-Tg glasses, J. Am.Ceram. Soc. 76 (1993) 1081e1087.

[32] Y.C. Guo, Z.X. Wang, Physics of the Amorphous Materials, Science Press, Bei-jing, 1984, p. 1409.

[33] Y. Zhao, X. Bain, X. Hou, Viscosity and fragility of the supercooled and su-perheated liquids of the Ni60Zr30Al10 metallic glass-forming alloy, Phys. A 367(2006) 42e54.

[34] A. Takeuchi, H. Kato, A. Inoue, VogeleFulchereTammann plot for viscosityscaled with temperature interval between actual and ideal glass transitionsfor metallic glasses in liquid and supercooled liquid states, Intermetallics 18(2010) 406e411.

[35] Zhang, C. Fang, Y. Li, Ferromagnetic Fe-based bulk metallic glasses with highthermoplastic formability, Scripta Mater. 69 (2013) 77e80.

[36] M. Stoica, R. Li, A.R. Yavari, G. Vaughan, J. Eckert, N.V. Steenberge, D.R. Romera,Thermal stability and magnetic properties of FeCoBSiNb bulk metallic glasses,J. Alloys Compd. 504S1 (2010) 123e128.

[37] T. Zhang, F.J. Liu, S.J. Pang, R. Li, Ductile Fe-based bulk metallic glass with goodsoft-magnetic properties, Mater. Trans. 48 (2007) 1157e1160.

[38] C.A. Angell, Structural instability and relaxation in liquid and glass phasesnear the fragile liquid limit, J. Non Cryst. Solids 102 (1988) 205e221.

[39] C.A. Angell, Relaxation in liquids, polymers and plastic crystals-strong/fragilepatterns and problems, J. Non Cryst. Solids 131e133 (1991) 13e31.

[40] T. Komatsu, Application of fragility concept to metallic glass formers, J. NonCryst. Solids 185 (1995) 199e202.

[41] D.R. Uhlmann, A kinetic treatment of glass formation, J. Non Cryst. Solids 7(1972) 337e348.

[42] Z.P. Lu, C.T. Liu, Glass formation criterion for various glass-forming systems,Phys. Rev. Lett. 91 (2003) 155051e155054.

[43] Q.G. Meng, J.K. Zhou, H.X. Zheng, J.G. Li, Fragility of superheated melts andglass-forming ability in Pr-based alloys, Scr. Mater. 54 (2006) 777e781.