Non-isothermal crystallization kinetics and fragility of

Journal of Thermal Analysis and Calorimetry https://doi.org/10.1007/s10973-018-7367-8 (0123456789().,-volV)(0123456789().,-volV)

Non-isothermal crystallization kinetics and fragility of Zr56Co28Al16 and Zr56Co22Cu6Al16 bulk metallic glasses Masoud Mohammadi Rahvard1 • Morteza Tamizifar1 • Seyed Mohammad Ali Boutorabi1 Received: 5 July 2017 / Accepted: 11 May 2018 Akade´miai Kiado´, Budapest, Hungary 2018

Abstract The role of substitution of Cu for Co on the non-isothermal crystallization kinetics and fragility of Zr56Co28Al16 and Zr56Co22Cu6Al16 bulk metallic glasses (BMGs) were evaluated by differential scanning calorimetry (DSC). The X-ray diffraction, transmission electron microscopy and microhardness test were used to investigate the glassy alloys structure. DSC results exhibited two crystallization processes for both BMGs. All the characteristic temperatures except glass transition temperature of parent alloy were more sensitive to heating rate than those of Cu containing alloy. The activation energies of characteristic temperatures were obtained by Kissinger and Ozawa methods. The results showed that the activation energy of glass transition decreased and the other activation energies increased with Cu addition. Also, the local Avrami exponents at various heating rates were calculated by the Johnson–Mehl–Avrami equation. The n value variations for each crystallization process were in almost similar trends for both BMGs. The results demonstrated that the transformation kinetics is dominated by diffusion-controlled three-dimensional growth with increasing nucleation rate for the first crystallization process and also for initially stage of the second crystallization process. However, the crystallization is dominated by interface-controlled three-dimensional growth with increasing nucleation rate at final stage of the second crystallization processes. In addition, both BMGs were classified into ‘‘strong glasses’’, depending on the calculated values of fragility index. Keywords Bulk metallic glasses Non- isothermal crystallization kinetics Effective activation energy Local Avrami exponent Fragility

Introduction Zr Bulk metallic glasses (BMGs) have attracted unprecedented interest in research communities due to their unique properties such as high glass-forming ability (GFA), superior mechanical properties, good corrosion resistance, good biocompatibility and high wear resistance [1–3]. However, the deformation of BMGs under mechanical loading is highly localized in the shallow shear bands

Electronic supplementary material The online version of this article (https://doi.org/10.1007/s10973-018-7367-8) contains supplementary material, which is available to authorized users. & Masoud Mohammadi Rahvard [email protected] 1

School of Materials Science and Engineering, Center of Excellence for High Strength Alloys Technology, CEHSAT, Iran University of Science and Technology, IUST, Tehran, Iran

region as a result of shear softening, leading to catastrophic failure with limited plastic strain. Therefore, their applications and processing methods are limited severely by their poor room-temperature plasticity [4, 5]. Zr-based BMGs have been developed in various alloy systems so far, but the ternary Zr–Co–Al alloy system as compared to other Zr base glassy alloys possesses the unique properties such as high fracture strength exceeding 2000 Mpa, displaying extensively potential applications in practices such as biomedical applications [6, 7]. Inoue et al. [8, 9] systematically studied on this glassy alloy system and finally succeed in synthesizing Zr56Co28Al16 BMG with the highest GFA among the ternary Zr–Co–Al glassy alloys. Many researches have been done to tune the composition and properties, especially plasticity and GFA which are important features for the applications, e.g., it was found that the appropriate micro-alloying of Fe or Cu in Zr–Co–Al-based BMGs could improve the plasticity and GFA simultaneously [10, 11]. As to the processing of

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M. Mohammadi Rahvard et al.

Experimental The master alloy ingots with composition of Zr56Co28Al16 and Zr56Co22Cu6Al16, denoted as Z and C6, respectively, were prepared via arc melting the high purity constituent elements, Zr(99.9%), Co(99.99%), Al(99.999%), Cu(99.999%), under a Ti-gettered high-purity argon atmosphere. The ingots were remelted four times to ensure compositional homogeneity. Then, rods with diameter of 2 mm and 5 cm in length were fabricated via water cooled copper mold suction casting method. The as-cast rods structure was examined by X-ray diffraction (XRD, PANalytical X’Pert PRO Diffraction, Cu-Ka radiation) and transmission electron microscopy (TEM, FEI Tecnai G2 F20 200 kV Cryo-STEM). TEM samples were prepared using the Dual Beam FIB system. The thermal behaviors of samples were characterized using differential scanning calorimetric (TG-DSC, Setaram, France) at the continuous heating rates of 10, 20, 30 and 40 K min-1 under a continuous helium flow. The specimens were cut from the ascast rods with the thickness of 1 mm and Al2O3 pans were utilized for continuous heating. To negate the influence of the sample mass, the samples’ mass was maintained to be approximately 10 mg. The microhardness test was performed on the as-cast and as annealed samples by (Leitz) machine with a load of 100 g and holding time of 10 s. The structural relaxation heat treatment was performed in the resistance furnace under high purity argon atmosphere at

123

70 C below Tg and holding time of 2 h for the samples placed in the vacuumed sealed quartz tube. The density of samples was measured using Archimedean principles by (Sartorius) electrical balance with an accuracy of 0.0001 g.

Results and discussion Structural analysis The XRD patterns of the as-cast Z and C6 BMGs with diameter of 2 mm are shown in Fig. 1. As can be seen, a broad halo peak in the range of 2h = 35–40 and no other diffraction peaks of crystalline phases are observed for both samples, indicating the fully amorphous phase within the resolution limit of the XRD instrument. Figure 2 shows the HRTEM images and selected area electron diffraction (SAED) patterns of the as-cast Z and C6 glassy rod with a diameter of 2 mm. The uniform featureless contrast in the images and a broad halo in the SAED patterns confirm the samples amorphous nature. The atomic size and mixing enthalpy of the constituents of ZrCoCuAl glassy alloy are shown in Fig. 3. The Cu size is similar to that of Co which does not cause a more sequential change in atomic size, such that Zr Al Co = Cu. Therefore, it seems that this marginal mismatch of the atomic size of Co and Cu would not be affected the packing state of the glassy alloy. In addition, the mixing enthalpy of the alloy has been decreased as a result of positive mixing enthalpy of the mix mix DHmix Cu–Co as well as the lower DHCu–Zr and DHCu–Al commix mix pared to the DHCo-Zr and DHCo–Al.

Intensity/a.u.

BMGs, hot temperature formation is usually used for these materials because of better plasticity in super cooled liquid region. But it is worth nothing that the metallic glasses are metastable materials and also would transform into crystalline phase under hot forming process which affects the properties [12, 13]. Thus, great attention was paid to the crystallization kinetics of metallic glasses to understand the thermal stability and crystallization process of metallic glasses. Hence, non-isothermal and isothermal crystallization kinetics have been widely used to provide theoretical basis for optimizing the process parameters and investigating the effects of crystallization on the performance of metallic glasses [14–18]. In the present work, non-isothermal crystallization and fragility kinetics of Zr56Co28Al16 and Zr56Co22Cu6Al16 were extensively analyzed by DSC at various heating rates. The crystallization kinetics parameters including the effective and local activation energies corresponding to the characteristic temperatures, sensitivity of the characteristic temperatures to heating rate, crystallized volume fraction and the local Avrami exponent were calculated to explain the transformation kinetics. Also structural dependence of crystallization kinetics parameters was discussed.

Zr56Co22Cu6Al16

Zr56Co28AI16

20

30

40

50

60

70

80

2θ/° Fig. 1 XRD patterns of the as-cast Z and C6 BMGs with diameter of 2 mm

Non-isothermal crystallization kinetics and fragility of Zr56Co28Al16 and Zr56Co22Cu6Al16… Fig. 2 HRTEM images and selected area electron diffraction (SAED) patterns of the a as-cast Z glassy rod, b ascast C6 glassy rod

AI

ΔH

–1

r = 0.143 nm

=

19

ΔH

=–

ΔH = –44

=

=–

ΔH 3

ΔH

–2

Cu

41

Zr r = 0.160 nm

r = 0.128 nm

Co r = 0.125 nm

ΔH = +9

Fig. 3 The mixing enthalpy and atomic radius of the constituent elements of the ZrCoCuAl glassy alloy

The mixing enthalpy variations show the decrement trend with addition of Cu content, respectively. Mixing enthalpy of BMGs could be calculated by the (Eq. 1) [19]: X DH mix ¼ 4DHijmix xi xj ð1Þ i6¼j

The alloys mixing enthalpy has been summarized in Table 1. It can be suggested that the decrease of mixing enthalpy for the monolithic BMGs would be resulted to the open structure with the less dense packing state due to decreasing the negative interaction between constituents. To confirm the above discussion, the microhardness test was performed as well and the related results have been

Table 1 The microhardness and density of the Z and C6 samples at as-cast and as-structural relaxation state

State Samples

As-cast q/g cm-3

summarized in Table 1. The microhardness decrease along with decrease of mixing enthalpy can prove the structure with less dense randomly packing state or without polytetrahedral packed cluster such as icosahedral short range ordering (ISRO). Aiming at precisely investigating the structure, the microhardness and density of the Z and C6 samples have been measured at as-cast and as-structural relaxation state, which are summarized in Table 1. The increase in the microhardness difference from 10% for the Z sample to 15% for the C6 sample indicates the presence of excess free volume in the structure of C6 sample annihilated through structural relaxation. In addition, the density difference variations also show the same as mentioned above result as well. One can found that the Cu addition changes the atomic configuration of base alloy, hence, leading to less dense packing structure.

Non-isothermal crystallization behavior Figure 4 a, b shows the DSC curves for the both samples at different heating rate. The DSC curves exhibit the endothermic peak, characteristic of glass transition to supercooled liquid temperature Tg, followed by double stage exothermic peak corresponding to the crystallization processes. All the characteristic temperatures, the glass transition Tg, onset crystallization peaks Tx1 and Tx2, crystallization peak temperatures TP1 and TP2 are marked by arrow in the figures and also are summarized in Table 2. The

Relaxed q/g cm-3

Dq/q %

As-cast HV

Relaxed HV

DHV/HV %

DHmix kJ mol-1

Z

6.6837 ± 0.056

6.7648 ± 0.023

1.2

630.8

698.66

* 10

44.9

C6

6.7480 ± 0.052

6.8437 ± 0.026

1.4

596.8

702.66

* 15

41.3

123


(a)

(b)

Tp2

Tp2

Zr56Co28Al16

Zr56Co22Cu6Al16

Tx2

Tg

40 K min–1

Heat flow/mW Exo.

Heat flow/mW Exo.

Tp1

Tx1

30 K min–1

Tp1

Tg

40 K min–1

Tx1

Tx2

30 K min–1

20 K min–1

20 K min–1 10 K min–1

600

650

10 K min–1

700

750

800

850

900

600

650

700

Temperature/K

750

800

850

900

Temperature/K

Fig. 4 DSC curves of a Z and b C6 BMGs at different heating rates Table 2 The characteristic temperatures of Z and C6 BMGs at different heating rates

Heating rate/K min-1

Zr56Co28Al16 Tg/K

Tx1/K

Tp1/K

Tx2/K

Tp2/K

Tg/K

Tx1/K

Tp1/K

Tx2/K

Tp2/K

10

745

790

806

848

865

736

780

797

844

857

20

753

802

818

859

878

745

789

808

853

867

30

758

808

824

865

885

751

796

816

860

874

40

763

812

831

872

892

755

802

820

864

880

results show that the characteristic temperatures have been decreased with Cu addition. The supercooled region which is defined as DTx = Tx - Tg is almost same for both the samples at any heating rate. But, the interval between onset crystallization peaks of first and second crystallization processes Tx2 - Tx1, has been slightly increased for C6 sample. As can also be seen, all the characteristic temperatures are shifted to higher temperatures as heating rate increases, indicating that both glass transition and crystallization temperatures depend on the heating rate during the continuous heating. The value of Tg increases little and that of other characteristic temperatures increases rapidly as heating rate increases. This phenomenon is attributed to the fact that the nucleation and growth are a thermally activated process, whereas the rate dependence of the glass transition kinetic relates to the relaxation processes in glass transition region [20]. The relationship between the characteristic temperatures and ln b for Z and C6 BMGs is shown in Fig. 5a, b. This relationship can be described using Lasocka’s empirical relation [21] as follows: T ¼ A þ B ln b

ð2Þ

where A and B are constants. The values of A and B obtained from the linear fittings of the data are listed in

123

Zr56Co22Cu6Al16

Table 3. The more value of B means the more sensitivity to heating rate of the characteristic temperature. As can be seen, glass transition Tg process has the least sensitivity to heating rate. Moreover, the B values of all the characteristic temperatures for the C6 sample except Tg are smaller than those of Z sample, suggesting that the crystallization processes of C6 sample have less sensitivity to heating rate and also glass transition process of C6 sample has more sensitivity to heating rate than those of Z sample. The volume fraction of the crystalline phases during the crystallization process can be calculated from DSC. The x at any temperature T is given as x = A/A0, Where A0 is the area under the DSC curve between the onset and the end of crystallization temperature, and A is the area between the onset temperature and a given temperature. The relationship between the crystallized volume fraction and temperature of first crystallization stage for Z and C6 BMGs is shown in Fig. 6a, b, and the curves for the second crystallization process are shown in Fig. S1 in supplementary materials, respectively. The curves represent a sigmoid dependence with temperature. Generally, crystallization transformation with the sigmoid curve can be divided into three stages. At first, nuclei precipitates from the amorphous matrix slowly and bulk crystallization

Non-isothermal crystallization kinetics and fragility of Zr56Co28Al16 and Zr56Co22Cu6Al16…

(a)

(b) 900

880

Zr56Co28Al16

860

Tp2

840

Tx2

Temperature/K

Temperature/K

880

820 Tp1

800 780

Tx1

Zr56Co22Cu6Al16

860

Tp2

840

Tx2

820 800

Tp1

780

Tx1

760 760 Tg

740

740

2.2

2.4

2.6

2.8

3.0

3.2

3.4

3.6

3.8

Tg

2.2

2.4

2.6

2.8

3.0

Inβ

3.2

3.4

3.6

3.8

Inβ

Fig. 5 Relationship between characteristic temperatures and ln b a Z and b C6 BMGs Table 3 Values of A and B for Z and C6 BMGs

Zr56Co28Al16

Zr56Co22Cu6Al16

Tg/K

Tx1/ K

Tp1/ K

Tx2/ K

Tp2/ K

Tg/K

Tx1/ K

Tp1/ K

Tx2/ K

Tp2/ K

A

715

752

765

808

820

704

743

758

810

818

B

12.72

16.20

17.57

17.07

19.13

13.73

15.65

16.85

14.7

16.38

(a) 1.0

(b) 1.0

0.8

Zr56Co22Cu6Al16

1th peak

Crystallized volume fraction x


Zr56Co28Al16

0.6

0.4 min–1

10 K 20 K min–1

0.2

0.0 780

30 K min–1 40 K min–1

790

800

810

820

830 840

850

860

870

0.8

1th peak

0.6

0.4 10 K min–1 20 K min–1

0.2

30 K min–1 40 K min–1

0.0 770

780

790

Temperature/K

800

810

820

830

840

850

Temperature/K

Fig. 6 Crystallized volume fraction x of Z and C6 BMGs versus temperature at different heating rates for the first crystallization process

plays a dominant role; then, the nuclei grows with a rapid reaction rate owe to increases of the surface area of nucleation; at last the surface between crystalline phase and amorphous matrix decreases as a result of grain coalescence [22].

Activation energy The effective activation energy E for crystallization under continues heating conditions can be determined by the Kissinger equation [23]: b E ln 2 ¼ þC ð3Þ T RT

123


where b is the heating rate, R is the gas constant and T is a characteristic temperature. The Ozawa method is also used to calculate E, which can be expressed as follows [24]: lnðbÞ ¼

E þC RT

ð4Þ

The Kissinger plots of ln(b/T2) versus 103/RT and Ozawa plots of ln(b) versus 103/RT are shown in Fig. 7, in which Tg, Tx1, Tp1, Tx2, and Tp2 at various heating rates are adopted. The effective activation energies could be deduced from the slopes of the linear fittings of the data summarized in Table 4. The results show that both methods yield almost the same effective activation energies and only the results obtained from Ozawa method are slightly higher than that of Kissinger method. It is well known that the values of Eg, Ex and EP represent the activation energy for atomic rearrangement, nucleation and grain growth, respectively [25]. One can

(a)

(b)

–9.2

–9.2

–9.4

Zr56Co28Al16

Tg

–9.4

Zr56Co22Cu6Al16

Tg

–9.6

Kissinger plots

Tx1

–9.6

Kissinger plots

Tx1

Tp1

–9.8

In(β /T2)

–10.4 –10.6

–10.4 –10.6 –10.8

–11.0

–11.0

–11.2

–11.2 0.140

0.145

0.150 0.155

0.160

0.165

–11.4 0.135

0.170

Tp2

–10.2

–10.8

0.135

Tx2

–10.0

Tp2

–10.2

–11.4

Tp1

–9.8

Tx2

–10.0

In(β /T2)

found that the Eg is larger than Ex1 activation energies, indicating that the atomic rearrangement in the glass transition process is much difficult as compared to the nucleation and growth processes. Also, it is found that the Eg for C6 sample is slightly lower than that of Z sample, implying that this alloy needs to overcome lower barrier for atomic rearrangement in the glass transition process. This phenomenon is attributed to the less dense packing structure of C6 sample which was discussed in the structural analysis section. Also, a decrease of Tg for C6 sample as compared to that of the Z sample proves the lower barrier for atomic rearrangement in the glass transition process. The Ex1 and Ep1 corresponding to nucleation and growth process of first crystallization process are also almost same for both samples. As mentioned above, the thermal stability which is determined by DTx = Tx - Tg is similar for both the samples at any heating rate, hence, leading to the similar effective activation energies.

0.140

0.145

0.150

(c)

(d)

4.2 4.0 3.8

Zr56Co28Al16

Tg

4.0

Tx1

3.8

Tp1

Zr56Co22Cu6Al16 Ozawa plots

0.165

0.170

Tg Tx1 Tp1

3.6

Tx2

3.4

Tx2

3.4

Tp2

3.2

Tp2

3.2

Inβ

Inβ

0.160

4.2

Ozawa plots

3.6

3.0

3.0

2.8

2.8

2.6

2.6

2.4

2.4

2.2

2.2 0.135

0.140

0.145

0.150 0.155

0.160

0.165

0.170

0.135

0.140

0.145

1000/RT/K–1

Fig. 7 Kissinger and Ozawa plots for calculation effective activation energies in Z and C6 BMGs

123

0.155

1000/RT/K–1

1000/RT/K–1

0.150

0.155

1000/RT/K–1

0.160

0.165

0.170

Non-isothermal crystallization kinetics and fragility of Zr56Co28Al16 and Zr56Co22Cu6Al16… Table 4 Effective activation energies derived by Kissinger and Ozawa methods for the Z and C6 BMGs Activation energy Kissinger Ozawa

Samples

Eg/kJ mol-1

Ex1/kJ mol-1

EP1/kJ mol-1

Ex2/kJ mol-1

Ep2/kJ mol-1

Zr56Co28Al16

356 ± 20

313 ± 15

301 ± 15

342 ± 19

319 ± 11

Zr56Co22Cu6 Al16

323 ± 11

315 ± 22

307 ± 10

397 ± 49

365 ± 19

Zr56Co28Al16

368 ± 20

327 ± 15

314 ± 15

357 ± 19

334 ± 11

Zr56Co22Cu6Al16

371 ± 11

328 ± 22

321 ± 10

411 ± 49

380 ± 19

The main reason for improving the thermal stability of the C6 sample despite the less dense packing structure can be attributed to Egami’s model [26]. According to this model, introducing repulsive interactions between small atoms and increasing the interaction between the small and large atoms would favor bulk metallic glass formation. In this glassy alloy, Cu and Co atoms with the smaller atomic size as compared to that of the Zr and Al atoms have the -1 positive heat of mixing (DHmix Cu–Co= ? 9 kJ mol ). The addition of Cu causes Co atom to be attracted to big atoms such as Zr and Al through negative heat of mixing. Thus, this phenomenon leads to decreasing the mobility of Co atom for rearrangement. A similar phenomenon has been reported by Liu [27, 28] for (Zr0.62Cu0.23Fe0.05Al0.10)97Ag3 and Zr53Co18.5Al23.5Ag5 with positive heat of mixing between constituents. The great difference in activation energies of second crystallization process between Z and C6 samples as compared to that of first crystallization process shows the more thermal stability of C6 samples at second crystallization process. It is worth nothing that the Cu alloying in Zr–Al–Co alloy most likely causes to be occurred the complex crystallization products at second crystallization peaks. At this regard, a number of crystalline phases are attended to compete with each other for the nucleation and growth, requiring the extensive atomic fluctuation and rearrangement to form the crystalline phases and, thus, contribute to the enhancement of thermal stability. The larger interval between onset peak of first and second crystallization processes of C6 sample is in agreement with thermal stability of second crystallization process.

than E(x)1 for both samples. This is consistent with the results of the effective activation energy. The average local E(x) values are lower than those of the effective activation energy. This decrease is related to the fact that this local activation energy is the sum of nucleation and growth activation energies processes. Noticeably, the energy required for nucleation can disappear as crystallization progresses, hence, resulting in a decrease of local values of activation energy at final stage [29]. One can found that the required activation energy for nucleation at initial stages is higher than the growth activation energy at final stages in the present glassy alloy. Moreover, the less decreasing trend of local values of activation energy for C6 sample as compared to that of Z sample implies the higher barrier for growth process, corresponding to the aforementioned results.

Local Avrami exponent The local Avrami exponent is usually used to define the mechanisms of nucleation and growth behavior during crystallization. For isothermal transformation, the crystallization kinetics can be deduced from the Johnson–Mehl– Avrami (JMA) equation [30]: x ¼ 1 exp½kðt sÞn

ð5Þ

where x is the crystallized volume fraction, t is the time concerning the crystallized volume fraction, s is the incubation time, which is a fitting parameter, k is a kinetic coefficient depending on the annealing temperature and n is the Avrami exponent. Thus, JMA equation is often transformed to

Local activation energy

ln½ lnð1 xÞ ¼ n lnðt sÞ þ constant

The local values of activation energy E(x) for the first crystallization process of Z and C6 samples at different crystallized volume fraction are calculated from Fig. 8 via Kissinger equation and those values are summarized in Table 5; the curves for the second crystallization process are shown in Fig. S2 in supplementary materials. The average E(x)1 and E(x)2 value of C6 sample are larger than E(x)1 and E(x)2 of Z sample. Also the average E(x)2 is larger

For isothermal process, based on JMA equation, the local Avrami exponent can be calculated by the following equation: nðxÞ ¼

d ln½ lnð1 xÞ d lnðt sÞ

ð6Þ

ð7Þ

But JMA equation is only suitable for isothermal process. Nakamura et al. [31] extend the JMA equation to nonisothermal process, which gives the relation:

123


(a)

(b)

–9.6 Zr56Co28Al16

–9.8

Zr56Co22Cu6Al16

–9.8

1th peak

–10.0

1th peak

–10.0

–10.2

–10.2 x = 0.1 x = 0.2 x = 0.3 x = 0.4 x = 0.5 x = 0.6 x = 0.7 x = 0.8 x = 0.9

–10.4 –10.6 –10.8 –11.0

In(β /Tx2)

In(β /Tx2)

–9.6

–10.4 –10.6 –10.8 –11.0

x = 0.1 x = 0.2 x = 0.3 x = 0.4 x = 0.5 x = 0.6 x = 0.7 x = 0.8 x = 0.9

–11.2 0.142

0.144

0.146

1000/RTx

0.148

–11.2 0.144

0.150

0.146

0.148

0.150

0.152

1000/RTx/K–1

/K–1

Fig. 8 Kissinger plots for different crystallized volume fractions (x), ranging from 0.1 to 0.9 in a Z and b C6 BMGs for the first crystallization process Table 5 Local activation energies derived by Kissinger method for different crystallization volume fractions (x), in Z and C6 BMGs for the first and second crystallization processes

nðxÞ ¼

x

Zr56Co28Al16 E(x)1/kJ mol

E(x)2/kJ mol

-1

E(x)1/kJ mol-1

E(x)2/kJ mol-1

0.1

311 ± 12

337 ± 16

313 ± 16

381 ± 9

0.2

308 ± 13

333 ± 15

311 ± 13

375 ± 8

0.3

307 ± 14

327 ± 15

311 ± 14

372 ± 8

0.4

301 ± 14

324 ± 14

310 ± 15

373 ± 8

0.5

298 ± 14

321 ± 13

309 ± 15

373 ± 8

0.6

293 ± 14

317 ± 13

307 ± 15

372 ± 8

0.7

289 ± 15

314 ± 12

303 ± 16

368 ± 10

0.8

282 ± 15

310 ± 12

299 ± 18

361 ± 11

0.9

273 ± 15

300 ± 13

294 ± 21

345 ± 14

Average value

296 ± 14

320 ± 14

306 ± 16

369 ± 9

1 d ln½ lnð1 xÞ ð1 þ E=RTð1 T=T0 Þ d lnðT T0 =bÞ

ð8Þ

where T0 can be considered as the onset temperature of crystallization for each exothermic peak and E is the activation energy. By plotting ln[-ln(1 - x)] versus ln[(T - T0)/b], the n values from the slope of the curves and Eq. (8) can be obtained. The curves for the first crystallization process of the samples are shown in Fig. 9; also, the curves for the second crystallization process are shown in Fig. S3 in supplementary materials. The varied n values corresponding to varied slope of the curves imply that the nucleation and growth behaviors differ during the whole crystallization process. The mechanism of nucleation and growth at each heating rate can be determined by Ranganathan–Heimendahl equation [32]:

123

Zr56Co22Cu6Al16

-1

n ¼ a þ bc where a is the nucleation index which includes four types as follows: (1) a = 0 for zero nucleation rate; (2) 0 \ a \ 1 for decreasing nucleation rate; (3) a = 1 for constant nucleation rate; (4) a [ 1 for increasing nucleation rate. b is the dimensionality of the growth with values of 1, 2 or 3 corresponding to one, two and three-dimensional growth, respectively. c is the growth index which includes two types, c = 1 for interface-controlled growth and c = 0.5 for diffusion-controlled growth. The local Avrami exponents n for the first and second crystallization processes of samples at different heating rate were calculated by Eq. 8. The local Avrami exponents n as a function of crystallized volume fraction are considered in the range (0.1 \ x \ 0.9), because the error is too serious at low and high crystallized volume fraction. It can be seen that the results for the first crystallization step


(a)

(b) 2

2

Zr56Co28Al16

Zr56Co22Cu6Al16

1th peak

1th peak 0

In[–In(1–x)]

In[–In(1–x)]

0

–2

–4

10 K min–1 20 K min–1

–6

–2

–4

10 K min–1 20 K min–1

–6

30 K min–1 40 K min–1 –8 –3

–2

–1

0

1

30 K min–1 40 K min–1 –8

–3

–2

–1

0

1

In[(T–T0)/β ]

In[(T-T0)/β ]

Fig. 9 ln[-ln(1 - x)] versus ln[(T - T0)/b] in a) Z and b) C6 BMGs at various heating rates and first crystallization process

for Z sample are in the same tendency with that of C6 sample with increasing n value first and then decreasing. But, the results for the second crystallization step are different, i.e., n value increases during the whole crystallization process for the Z sample and increases first and then decreases for the C6 sample (Fig. 10). The average n value of the first crystallization step for both samples increases gradually first and then decreases. However, n values are larger than 2.5 during the whole crystallization process, indicating that the crystallization in this range is dominated by diffusion-controlled three-dimensional growth and increasing nucleation rate. But, the increasing trend of nucleation rate rises at initially stage of crystallization process and then slows down. One can found that the average n values for both samples are almost same due to the fact that the effective activation energies of crystallization did not have significant different. The average n value of the second crystallization step increases rapidly from 3 to n [ 4 during the whole crystallization process for Z samples, indicating that the crystallization is governed by diffusion-controlled three-dimensional growth and increasing nucleation rate when 3 \ n \ 4, and then by the interface-controlled three-dimensional growth and increasing nucleation rate when n [ 4. It is well known that the value of Avrami exponent should be smaller than 4 for three-dimensional bulk nucleation. It was suggested that the relatively high value of Avarami exponent is possibly attributed to surface-induced abnormal grain growth with fractal dimensionality [33, 34]. As to the second crystallization step of the C6 sample, average n values increase rapidly from 2.5 to above 4 when (0.1 \ x \ 0.5) and then decrease to 4 (0.5 \ x \ 0.9). Thus, the crystallization mechanism in second crystallization step is similar to that of Z sample, but the increasing

trend of nucleation rate slows down at finally stage of crystallization process.

Fragility index The fragility provides a measure of the sensitivity of the structure of a liquid to temperature changes and is also used to estimate the glass-forming ability and thermal stability of glassy alloys. A convenient method to measure the fragility of glass-forming liquids is through the fragility index m on the basis of Angell’s theory [35, 36]: mAngell ¼

Eg RTg ln 10

ð9Þ

where the Eg is the activation energy on the glass transition temperature Tg. In the classification of Angell [35, 37], liquids are classified into three groups as strong, intermediate and fragile. For strong materials, m is less than 30 with a lower limit of 16, while fragile materials which have thermally sensitive structures that can be easily disrupted by slight variation of temperature display large value of m C 100. For an intermediate material, the value of m is approximately in the range of 30 \ m \ 70. For amorphous material with a deviation from the Arrhenius law, the fragility index can be obtained as follows [33, 35]: D Ta b ¼ A exp ð10Þ Ta Tg where b is the heating rate, Ta is the glass transition temperature at infinitely slow heating, A is the constant and D is the fragility parameter which describes the deviation the system from Arrhenius relationship. D can be obtained from the slope of ln b versus Tg as follows:

123


(a) 5.0

(b) Zr56Co28Al16

1th peak 4.0 3.5 3.0 2.5 2.0

10 K min–1 20 K min–1

1.5

30 K min–1 40 K min–1

1.0 0.0

0.2

0.4

Zr56Co22Cu6Al16

4.5

Local activation exponent n(x)


4.5

5.0

0.6

0.8

3.5 3.0 2.5 2.0

10 K min–1 20 K min–1

1.5

30 K min–1 40 K min–1

1.0 0.0

1.0

1th peak

4.0

0.2


(d)

6.0

Zr56Co28Al16

5.5

Zr56Co22Cu6Al16

5.0

1th peak

5.0

1th peak

4.5 4.0 3.5 3.0 10 K min–1 20 K min–1

2.0

30 K min–1 40 K min–1

1.5

1.0

6.0

5.5

2.5

0.8




(c)

0.6

0.4

4.5 4.0 3.5 3.0 2.5

10 K min–1 20 K min–1

2.0

30 K min–1 40 K min–1

1.5 1.0

1.0

0.4

0.2

0.8

0.6

0.9

0.6

0.4

0.2


0.8


Fig. 10 Local Avrami exponent n(x) versus crystallized volume fraction x at different heating rates for the a 1st peak of Z, b 1st peak of C6, c 2nd peak of Z, d 2nd peak of C6 Table 6 Data of Tg/K, Ta/K, D , mDA and mAngell

Heating rate

30 K min-1

D Ta ln b ¼ ln A Ta Tg

Zr56Co28Al16 Tg/K

Ta/K

D

mDA

mAngell

Tg/K

Ta/K

D

mDA

mAngell

758

576

4.27

24.49

24.53

751

450

14.08

22.80

22.46

ð11Þ

Subsequently, (mDA) can be expressed as follows [38]: mDA ¼

D Tg Ta ðTg Ta Þ2 ln 10

ð12Þ

Two fragility indexes for both the samples were calculated at heating rate of 30 K min-1. The data obtained from Eqs. 9 and 12 are summarized in Table 6.

123

Zr56Co22Cu6Al16

The results show that the two fragility indexes for each sample are consistent with each other, and also fragility indexes for both samples are close to the value of m \ 30, implying that the Z and C6 BMGs can be classified into strong glasses.

Conclusions 1.

DSC results exhibited two crystallization processes for both BMGs. Heating rate dependence of glass


2.

3.

4.

5.

6.

transition temperature is lower than that of other characteristic temperatures. Also, all the temperatures corresponding to nucleation and growth process of Z sample except glass transition temperature are more sensitive to heating rate than those of C6 sample. The effective activation energy of glass transition process of C6 BMG is lower than that of the Z BMG, indicating that structural relaxation is easier for C6 BMG. This is related to the less dense packing structure. The effective activation energies of characteristic temperatures corresponding to crystallization process for the C6 BMG are higher than that of the Z BMG, indicating that the nucleation and growth processes are more difficult for C6 BMG. It was suggested that the difficult rearrangement depending on Egami’s model and complex crystallization products are reasons for thermal stability enhancement. The local Avrami exponents is in similar trend between Z and C6 BMGs with n [ 2.5 for the first crystallization process, indicating that the transformation kinetics is dominated by diffusion-controlled three-dimensional growth and increasing nucleation rate. But, the increasing trend of nucleation rate is changed during the whole crystallization process for both samples. As to the second crystallization processes of both BMGs, the crystallization is dominated by diffusioncontrolled three-dimensional growth with increasing nucleation rate at initial stage, and then by interfacecontrolled three-dimensional growth with increasing nucleation rate at final stage. Z and C6 BMGs can be classified into ‘‘strong glasses’’, depending on the calculated values of fragility index.

Acknowledgements The authors want to express their gratitude to Iran University of Science and Technology for the financial support. Also, the authors would like to thank Dr. Reza Gholamipour for his assistance and giving his laboratory equipment.

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