Correlation between thermodynamics and glass forming ability in the Al–Ce–Ni system

Intermetallics 18 (2010) 900–906

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Correlation between thermodynamics and glass forming ability in the Al–Ce–Ni system Chengying Tang a, b, *, Yong Du b, *, Jiong Wang b, Huaiying Zhou a, Lijun Zhang b, Feng Zheng c, Joonho Lee d, Qingrong Yao a a

Department of Materials Science and Engineering, Guilin University of Electronic Technology, 1 Jinji, Guilin, Guangxi 541004, China State Key Laboratory of Powder Metallurgy, Central South University, Changsha, Hunan 410083, China Key Laboratory of Non-ferrous Materials of Ministry of Education and School of Materials Science and Engineering, Central South University, Changsha, Hunan 410083, China d Department of Materials Science and Engineering, Korea University, 5-1 Anam-dong, Seongbuk-gu, Seoul 136-713, Republic of Korea b c

a r t i c l e i n f o

a b s t r a c t

Article history: Received 13 September 2009 Accepted 19 December 2009 Available online 25 January 2010

The Al–rich corner of ternary Al–Ce–Ni metallic glass forming system was investigated by a hybrid approach of thermodynamic modeling and first–principles calculations. A consistent thermodynamic data set for the Al–Ce–Ni system was obtained. Based on the correlation between glass forming ability and thermodynamics, we found that there are no deep eutectics in the Al–rich corner. Alloys with high GFA appear in off–eutectic area with heat of mixing ranging from 15 to 49 kJ/mol of atom, and the alloy with a local minimum driving forces show highest GFA according to the melt spinning and copper mold casting experiments and the calculation of driving force for the formation of crystalline phases in the supercooled liquid state. The nucleation driving force is the dominant factor determining the formation of amorphous phases, among several other factors such as heat of mixing, viscosity, and glass transition temperature. Ó 2009 Elsevier Ltd. All rights reserved.

Keywords: A. Ternary alloy systems B. Thermodynamic and thermochemical properties B. Metallic glasses E. Phase diagram, prediction (including CALPHAD) E. Ab initio calculations

1. Introduction Bulk metallic glasses (BMG) have received a great deal of attention due to scientific and technological interest ever since the first successful synthesis of an amorphous phase in the Au–Si system in 1960 [1,2]. A large number of novel amorphous alloy systems based on various elements have been developed recently [3–7]. Meanwhile, many criteria for evaluating the glass forming ability (GFA) of an amorphous alloy have been proposed [8–12]. The supercooled liquid region DTx(¼ Tx–Tg, where Tg and Tx are the glass transition temperature and the crystallization temperature, respectively), the reduced glass transition temperature Trg(¼ Tg/Tl, where Tl is the liquidus temperature) [9] and the recently defined parameters g½ ¼ Tx =ðTg þ Tl Þ[10], d½ ¼ Tx =ðTl  Tg Þ[11] are useful parameters to evaluate the GFA of an amorphous alloy. In order to guide the design of alloy compositions with high GFA, Inoue and Johnson have proposed the following empirical rules [3,13]: (I) multicomponent systems, (II) significant atomic size ratios above

* Corresponding authors. Department of Materials Science and Engineering, Guilin University of Electronic Technology, 1 Jinji, Guilin, Guangxi 541004, China. E-mail addresses: [email protected] (C. Tang), [email protected] (Y. Du). 0966-9795/$ – see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.intermet.2009.12.027

12%, (III) negative heat of mixing and (IV) deep eutectic rule based on the Trg criterion. Al–based amorphous, which was discovered in 1988 [14,15], is of particular interest because of its low density, good bending ductility and high tensile strength. It was found that, however, most of above mentioned parameters and rules capable of searching metallic glasses with high GFA are not applicable to Al–based amorphous [16–20]. The glass forming range (GFR) of the Al–based alloys tends to lie on the solute–rich side of the eutectic point, where the liquidus temperature rises rapidly [16–18], resulting in a low Trg. An investigation of the relationship between GFA and some GFA related parameters in Al–Ni–Gd ternary alloys indicates that the better GFA is not observed experimentally in those alloys exhibiting positive changes in the GFA related parameters [19]. The addition of as many as seven alloying elements does not improve the GFA of the Al–based alloys [20]. Among the various Al–based Al–Ce–M (M ¼ Fe, Co, Ni or Cu) alloys, the Al–Ce–Ni system is unique, which can be synthesized into a strong, flexible metallic glass with the widest GFR covering 2–15 at% Ce and 1–30 at% Ni [21–25]. It was found that the GFA and the thermal stability in the Al–rich corner were enhanced by increasing the solute content and specifically the Ce content [22–24]. Experimental results of the Al–Ce–Ni bulk amorphous

C. Tang et al. / Intermetallics 18 (2010) 900–906

alloys prepared with copper mold casting indicate that the amorphous sheets with 5 mm width and 0.2 mm thickness are obtained in Al86Ce4Ni10 and Al88Ce6Ni6 alloys without appreciable glass transition. On contrary, alloys Al82Ce8Ni10 and Al80Ce6Ni14 with DTx values of 20 and 21 K consist mainly of crystalline phases [24]. So far, several attempts [26–31] have been made successfully to investigate the GFA and predict GFR in several binary [26–28] and ternary [26,28–31] amorphous alloy systems, using a pure thermodynamic approach or a hybrid approach of thermodynamics and kinetics. However, the investigation on the GFA of the Al–based alloys is still limited. It is thus of interest to find fundamental factors contributing to the formation of the Al–Ce–Ni amorphous. The constituent binary systems Al–Ce [32], Al–Ni [33] and Ce–Ni [34] in the Al–Ce–Ni [35–37] ternary system have been assessed thermodynamically. The isothermal sections at 500 and 800  C in the range of 0–33 at% Ce [35,36] have been determined by the present authors. Three ternary compounds, s5(Al4CeNi), s6(Al5CeNi2) and s8(Al23Ce4Ni8), are observed in the Al–rich corner (>60 at%). The orthorhombic structure of s5 and s6 was well established [38], and the monoclinic structure for s8 was determined by Gout et al. [39]. One invariant reaction Liquid / (Al) þ (Al3Ni) þ Al11Ce3 [40] and the enthalpy of formation for s5 [41] have been experimentally determined. The objective of the present study is to establish the correlation between the thermodynamics and the GFA in the Al–Ce–Ni system by developing a self–consistent thermodynamic database through combinative effects of experiments, CALPHAD approach and first– principles calculation.

901

To verify the established correlation between the negative heats of mixing and the GFA of the Al–Ce–Ni system, ribbons (about 30 mm thickness and 3 mm width) of four Al–Ce–Ni alloys with different heats of mixing for liquid were prepared by a single–roller melt spinning technique under an Ar atmosphere. The structure of the ribbons was characterized by XRD with Cu Ka radiation. 3. Thermodynamic assessment and first–principles calculations 3.1. CALPHAD approach In the present modeling, the Gibbs energy of the individual phases is described by the sublattice model [42] and defined relative to the standard element reference (SER) state at 298.15 K and 1 atm. The liquid, fcc and bcc phases were modeled with a single sublattice and expressed as: f

f

f

Gf ¼ xAl 0 GAl þ xCe 0 GCe þ xNi 0 GNi þ RTðxAl lnxAl þxCe lnxCe þ xNi lnxNi Þ þ E Gf þ mg Gf

(1)

0 Gf i

where is the molar Gibbs energy of the pure element i in the structure of phase f in the nonmagnetic state [43]. The excess Gibbs energy is expressed by the Redlich–Kister polynomial [44]: E

Gf ¼ xAl xCe

X f i LAl;Ce ðxAl  xCe Þi þxAl xNi i

X f i  LAl;Ni ðxAl  xNi Þi þxCe xNi i

X f f i  LCe;Ni ðxCe  xNi Þi þxAl xCe xNi LAl;Ce;Ni

2. Experimental procedure

(2)

i

f

The phase transition temperatures for four alloys along the vertical sections at 10 at% Ni and 10 at% Ce and for three ternary compounds (s5, s6 and s8) were measured in the present work. The compositions of the prepared alloys are listed in Table 1. Seven button alloys, each with a mass about 1.5 g, were prepared by arc– melting weighed ingots of Al (99.999%), Ce (99.9%) and Ni (99.9%) in an arc furnace under a 99.999% purity argon atmosphere using a non–consumable tungsten electrode. Each button was re–melted four times to improve its homogeneity with a total mass loss of less than 0.5%. The samples encapsulated in an evacuated silica capsule under vacuum were annealed at 500  2  C in a high precision diffusion furnace for 40 days and then quenched in water. Phase identification was performed by X–ray diffraction (XRD) using monochromatic Cu Ka radiation (l ¼ 1.5405 Å, Rigaku D/max2550VB, Japan). Differential thermal analysis (DTA) was performed using a Netzsch DSC 404C system in an Al2O3 crucible under a flow of pure argon. The DTA measurements were performed from room temperature to 1300  C with a heating rate of 5  C/min. The invariant reaction temperatures were determined from the onset of the thermal effect, and the peak value of the last thermal effect was taken as the liquidus temperature.

The ternary interaction parameters LAl;Ce;Ni were set to zero for these phases, except for liquid. The magnetic contribution to Gibbs energy of fcc is described as: mg

Gf ¼ RTlnðb þ 1Þf ðsÞ

(3)

where b is the Bohr magnetic moment per mole of atoms and s ¼ T=TC ; TC is defined as the critical temperature for magnetic ordering (i.e., the Curie or Neel temperature). f(s) is a polynomial function obtained by Hillert–Jarl–Inden [45] TC andb are described, respectively, as: f

TC ¼

X

f

xi 0 T Ci þ

X

i

bf ¼

f

f

xi xj TCi;j þ xAl xCe xNi TCAl;Ce;Ni

(4)

i;j

X

f

xi b i þ

X

i

f

f

xi xj bi;j þ xAl xCe xNi bAl;Ce;Ni

(5)

i;j

f

f

where0 T Ci and bi correspond to the critical temperature for magnetic ordering and Bohr magnetic moment of pure element i, fcc fcc andbAl;Ni , all the binary respectively. With the exception of TCAl;Ni and ternary parameters were set to zero.

Table 1 Summary of XRD and DTA measurements for the Al–Ce–Ni alloys annealed at 500  C for 40 days. No.

1 2 3 4 5 6 7

Composition (at%) Thermal effect temperature ( C)

Phase identified by XRD

Al

Ce

Ni

1st

2nd

80 75 68 70 66.6 62.5 69.7

10 15 22 10 16.6 12.5 12.1

10 10 10 20 16.6 25 18.2

627.8 705.1 931.3 844.2 1213.4 1236.6 1000.5

740.5 900.2 1234.6 984.2

1172.9

3rd 901.5 999.6 1153.4

4th 1083.8 1230.0

(Al) þ Al11Ce3 þ Al3Ni Al11Ce3 þ Al3Ni þ s8 aAl3Ce þ Al2Ce þ s5 Al3Ni2 þ Al3Ni þ s8

s5 s6 s8

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C. Tang et al. / Intermetallics 18 (2010) 900–906

In view of the negligible solubility of the third element in Al11Ce3, Al3Ce, Al3Ni and Al3Ni2, and the fact that other phases have no noticeable effect on the phase equilibria in the amorphous forming range, these compounds are assumed to have no solubility for the third element. The three ternary phases, s5, s6 and s8, in the Al–rich corner are modeled as stoichiometric compounds based on their crystal structures. For example, the Gibbs energy of s5 relative to the pure elements is expressed as: 0 fcc 0 fcc Gs5  0:6670 Gfcc Al  0:167 GCe  0:167 GNi ¼ a1 þ b1 T

(6)

where the coefficients a1 and b1 are assessed from the experimental 0 fcc , 0 Gfcc phase diagram data. The parameters, 0 Gfcc Ce and GNi are the Al energies of fcc_Al, fcc_Ce and fcc_Ni, respectively. The enthalpies of formation for s5, s6 and s8 obtained by means of the direct calorimetric technique [41] and first–principles calculation were used to optimize their thermodynamic parameters. The optimization was carried out by means of the optimization module PARROT of the Thermo–CalcÒ software package [46]. The presently calculated Al–Ce–Ni phase diagrams are verified to be really stable with the PandatÒ program [47]. 3.2. First–principles calculation In order to provide the initial values in the thermodynamic assessment and to verify if the presently calculated thermodynamic properties are reliable for ternary compounds, the density functional theory (DFT) calculation within the generalized gradient approximation (GGA) [48], as implemented in the highly efficient Vienna ab initio simulation package (VASP) [49,50], was utilized to calculate the enthalpy of formation for the ternary phases. The Perdew–Burke– Ernzerhof [48] GGA for the exchange correlation potential was used for the calculation, and the valence electrons were explicitly treated by projector augmented plane–wave (PAW) potentials. The ions were relaxed toward equilibrium until the Hellmann–Feynman forces were less than 102 eV Å1. A plane–wave cutoff energy of 400 eV and an energy convergence criterion of 104 eV for electronic structure self–consistency were used in the calculation. Brillouin zone integrations were performed using the Monkhorst–Pack [51] k– point meshes scheme, and the total energy differences were converged to within 0.1 kJ mol–atoms1. Both the unit cell sizes and the ionic coordinates were fully relaxed to find the stable state. The equilibrium enthalpies of formation are given according to the composition–weighted averages of the energies of the pure constituents in their equilibrium crystal structures. Thus, the enthalpy of formation at 0 K for s5 is given by an equation of the form:



DH eq ðs5 Þ ¼ Eðs5 Þ  0:667Eeq ðAlÞ þ 0:167Eeq ðCeÞ þ 0:167Eeq ðNiÞ



(7) where E(s5), Eeq(Al), Eeq(Ce) and Eeq(Ni) are the energies (per mole– atoms) of s5, Al, Ce and Ni, respectively. Each of them is relaxed to its equilibrium geometry at zero pressure. The reference states are fcc_Al (nonmagnetic), fcc_Ce (nonmagnetic) and fcc_Ni(ferromagnetic), respectively. 4. Results 4.1. DTA experimental results Table 1 lists the phases identified by XRD and the phase transition temperatures for the Al–Ce–Ni alloys annealed at 500  C for 40 days. The DTA measurements show that compounds s5 and s6 melt congruently at 1213.4 and 1236.6  C, respectively, while s8 melts incongruently at 1000.5  C with a tail extending to 1172.9  C.

These experimental data were used to check the reliability of the thermodynamic modeling, as described below. 4.2. Results of the thermodynamic assessment In the evaluation of the model parameters, the observed isothermal section at 500  C [35] and 800  C [36], the measured and calculated enthalpies of formation for three ternary compounds as well as the invariant reaction Liquid / (Al) þ (Al3Ni) þ Al11Ce3 [40] at 625  C and 2.6 at% Ce and 2.6 at% Ni, were employed for the thermodynamic assessment. As shown in Table 2, a good agreement is obtained for the enthalpies of formation for three ternary compounds between the CALPHAD–type values and first–principles calculations. For s5, the calculated results agree reasonably with the measured one obtained by Borzone et al. [41] using the calorimetric technique. It is notable that s6 with the assessed largest enthalpy of formation agrees with the measured highest melting temperature among three ternary compounds. Table 3 lists the optimized thermodynamic parameters in the Al–Ce–Ni system. Based on the obtained thermodynamic parameters and the published binary parameters [32–34], the calculated isothermal sections at 500 and 800  C in the Al–rich corner are shown in Fig. 1, which agree with the measured ones [35,36], respectively. The calculated vertical sections at 10 at% Ce and 10 at% Ni shown in Fig. 2 agree well with the XRD and DTA data, respectively. On the basis of the obtained thermodynamic parameters, ten invariant reactions in the Al–rich corner are computed and listed in Table 4. For the eutectic reaction (E1): Liquid / (Al) þ Al3Ni þ Al11Ce3, the calculated eutectic point agrees well with the experimental results [41]. The thermodynamic calculation yields a peritectic reaction (P1) of Liquid þ s5 þ s6 / s8 at 998.2  C. This temperature agrees well with the DTA event associated with the peritectic reaction for the alloy with s8 composition. For s8, the DTA signals exhibit one strong thermal effect at 1000.5  C, which is attributed to the peritectic melting of s8. The other thermal effect at 1172.9  C corresponds to the liquidus temperature. 5. Discussion 5.1. GFR in the Al–Ce–Ni system It is experimentally by melt spinning indicated that the Al–Ce–Ni alloys have the widest GFR among the Al–Ce–M systems [24]. Fig. 3 shows the calculated projection of the Al–Ce–Ni liquidus surface along with the GFR based on the reported amorphous compositions [23–25]. The areas enclosed by the lines in this figure are the primary crystallization of the phases indicated. It is noted that the primary crystallization region for fcc_Al is narrow, in comparison with wide fields for other phases (Al11Ce3, Al4Ce, s5, s6 and s8), which encompass the GFR. As can be seen in the figure, the alloys with high GFA are situated away from the eutectic point, which is consistent with the previous observations on the Al–based amorphous [17–20]. Additionally, thermodynamic calculation results indicate about half of the alloys with high GFA are located in Table 2 Calculated and measured enthalpies of formation for the ternary compounds in the Al–Ce–Ni systema. No.

Ternary phase

Measured (DC, [41])

Calculated (CALPHAD, TW)

Calculated (FP, TW)

1 2 3

Al4CeNi (s5) Al5CeNi2 (s6) Al23Ce4Ni6 (s8)

53.3  2.5 N/A N/A

47.08 51.29 46.14

49.30 55.10 48.50

a In kJ/mol of atom; DC¼direct calorimetry; CALPHAD¼CALculation of PHase Diagram; FP¼first–principles calculation; TW¼this work; N/A¼No data available.

C. Tang et al. / Intermetallics 18 (2010) 900–906

903

Table 3 Optimized thermodynamic parameters of the Al–Ce–Ni system at Al–rich cornera. Liquid: (Al, Ce, Ni)

0 LL Al;Ce;Ni

¼ 39573:65  58:0$T

s5(Al4CeNi): Al4CeNi

0 fcc Gs5  0:6660 Gfcc  0:1660 Gfcc Ce  0:166 GNi Al

s6(Al5CeNi2): Al5CeNi2

0 fcc Gs6  0:6250 Gfcc  0:1250 Gfcc Ce  0:25 GNi Al

s8(Al23Ce4Ni6): Al23Ce4Ni6

0 fcc Gs8  0:6970 Gfcc  0:1210 Gfcc Ce  0:182 GNi Al

¼ 47079:2 þ 0:81669$T

¼ 51290:7 þ 0:37633$T

¼ 46143:6 þ 2:73423$T

a The binary parameters for the Al–Ce, Al–Ni and Ce–Ni systems are taken from Refs. [32–34], respectively.

solid–liquid two–phase regions even at 1000  C, which is much higher than the eutectic temperature at about 628  C, resulting in a low Trg. These results indicate that there must have no deep eutectic in the region of high GFA for the Al–Ce–Ni alloys. This conclusion is consistent with the GFA for the Al–RE binary [16] and Al–Fe(Ni)–Gd ternary alloys [17,18]. 5.2. GFA and the heat of mixing for liquid During a melt–quenching process for metallic glass formation, the glass formation is exposed to crystallization competition of

Fig. 2. Calculated vertical sections at (a) 10 at% Ce (a) and (b) 10 at% Ni(b) with the experimental data from the present work.

Table 4 Measured and calculated invariant reactions in the Al–Ce–Ni system. Symbol Temperatures Liquid composition Reaction (at%)a ( C) Cal.

Fig. 1. Calculated isothermal sections at (a) 500  C and (b) 800  C for Al–Ce–Ni system at Al–rich corner.

E1 U1 U2 U3 U4 P1 U5 U6 U7 P2 a

Exp.

Ce

628.2 627.8 1.6 735.7 2.7 843.0 844.2 1.5 896.5 901.5 6.2 901.1 2.0 998.2 1000.5 4.7 1019.4 10.3 1104.7 13.2 1167.6 16.5 1191.9 17.06

Ni 2.1 7.4 16.4 7.2 18.2 14.8 5.1 5.1 5.4 2.7

Liquid / (Al) þ Al11Ce3 þ Al3Ni Liquid þ s8 / Al11Ce3 þ Al3Ni Liquid þ Al3Ni2 / s8 þ Al3Ni Liquid þ s5 / s8 þ Al11Ce3 Liquid þ s6 / s8 þ Al3Ni2 Liquid þ s5 þ s6 / s8 Al4Ce þ s5 / Liquid þ Al11Ce3 Liquid þ bAl3Ce / s5 þ Al4Ce Liquid þ Al2Ce / bAl3Ce þ s5 Liquid þ Al4Ce þ Al2Ce / bAl3Ce

The compositions are according to the thermodynamic calculation.

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C. Tang et al. / Intermetallics 18 (2010) 900–906 Table 5 Calculated heats of mixing for liquid with specified Al–Ce–Ni compositions.

Fig. 3. Calculated projection of the Al–Ce–Ni liquidus surface and the GFR based on the observed amorphous compositions [23–25]. The amorphous sheet with 5 mm width and 0.2 mm thickness are obtained by copper mold casting, respectively [24]. The amorphous wires with diameters about 40–80 um and lengths of several meters are obtained by melt–extracted [24].

other crystalline phases from the undercooled melt between liquidus temperature Tl and glass transition Tg. The GFA of a melt is virtually determined by the stability of the undercooled melt and the competing crystalline phases. A negative heat of mixing can maintain macrostructural homogeneity without phase separation in an undercooled melt, resulting in the stability thermodynamically of the melt to improve the GFA of an alloy [16]. Table 5 lists the calculated heat of mixing of the liquid phase for the reported Al–Ce–Ni amorphous compositions [23–25], based on the obtained parameters. As can be seen from this table, the heat of mixing for the alloys in the GFR are from 15 to 49 kJ/mol of atom, while the heat of mixing for the alloy with the eutectic composition is only about 6 kJ/mol of atom. These results indicate that the negative heat of mixing enhances the tendency to form chemically short– range ordering (CSRO) and improves the metastability of the undercooled liquid and the GFA of the Al–Ce–Ni alloys. The alloys with the eutectic composition or those close to the eutectic point show poor GFA due to their smaller heat of mixing in spite of their lower melting temperature. This conclusion coincides with the empirical rules proposed by Inoue [3], as demonstrated for the Al–RE [16] and other Fe–B, Ni–Nb and Zr–Al–Ni systems [52]. To establish the correlation between the negative heat of mixing and the GFA of the Al–Ce–Ni alloys in the GFR, the melt spinning experiments were carried out. Fig. 4 shows the XRD patterns of four Al–Ce–Ni melt–spun ribbons with different heat of mixing for liquid. Two broad diffraction halos for alloy 1 (Al80Ce10Ni10) indicate an amorphous phase was formed, while the dominant crystalline phases appeared in the other three alloys. The X–ray diffraction pattern for alloy 4 (Al64Ce6Ni30) is identified directly as Al3Ni2, s6 and s8, indicating poor GFA. Consequently, the GFA of alloy 1 with heat of mixing of 28 kJ/mol of atom is better than that of the other three alloys with more negative heat of mixing. This finding agrees well with the experimental results obtained by copper mold casting. Table 6 summarizes the experimental results obtained by the present melt spinning and copper mold casting [24]. It is found that alloys 5–8 with heat of mixing for liquid about 18 to 23 kJ/mol of atom show highest GFA with a width of 5 mm

No.

Al

Ce

Nir

DHmix(kJ/mol)

Comment

Ref.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

94.7 96.3 65 70 60 61 70 75 80 85 89 89 82 85 80 84 85 86 87 88 65 75 80 85 87 90 80 85 86 78 88

2.6 1.6 15 15 10 10 10 10 10 10 10 8.6 8 7 6 6 6 6 6 6 5 5 5 5 5 5 4.4 4 4 3.5 2

2.6 2.1 20 15 30 29 20 15 10 5 1 2.4 10 8 14 10 9 8 7 6 30 25 15 10 8 5 15.6 11 10 18.5 10

8.303 5.901 43.481 38.356 49.221 48.484 40.103 34.359 28.106 21.553 16.217 16.382 28.590 22.076 29.002 23.601 22.221 20.832 19.435 18.033 46.060 41.253 29.181 22.350 19.537 15.269 29.278 22.463 21.048 32.039 18.286

Experimental Eutectic Calculated Eutectic Amorphous Amorphous Amorphous Amorphous Amorphous Amorphous Amorphous Amorphous Amorphous Amorphous Amorphous Amorphous Amorphous Amorphous Amorphous Amorphous Amorphous Amorphous Amorphous Amorphous Amorphous Amorphous Amorphous Amorphous Amorphous Amorphous Amorphous Amorphous Amorphous

[40] This work [25] [25] [25] [25] [25] [25] [25] [23, 25] [25] [23] [24] [23] [24] [24] [23,25] [24] [25] [24] [25] [25] [25] [23,25] [25] [23,25] [23] [23] [24] [23] [25]

and thickness of 0.2 mm amorphous sheet [24]. On contrary, alloys 9 and 10 with heat of mixing for liquid about 26 and 29 kJ/mol of atom, respectively, show relatively lower GFA with mainly crystalline phases of a sheet [24]. In general, thermal stability of the amorphous solid and/or supercooled liquid, a higher viscosity of the melt, and a higher Trg result in sluggish transformation kinetic for crystallization, and therefore give favorable conditions for forming an amorphous phase. A higher glass transition temperature, which reflects atomic transport and viscosity properties, and the structural relaxation and the thermal stability of amorphous alloys, is expected to indicate a good GFA [7]. A higher crystallization temperature means

Fig. 4. XRD patterns of the four as melt–spun Al–Ce–Ni ribbons.

C. Tang et al. / Intermetallics 18 (2010) 900–906 Table 6 Summary of the experimental results obtained by the present melt spinning and copper mold casting. No. Composition

1 2 3 4 5 6 7 8 9 10 a

Al

Ce

Ni

80 72 75 64 86 88 86 84 82 80

10 10 15 6 4 6 6 6 8 6

10 18 10 30 10 6 8 10 10 14

DHmix (kJ/mol) DTx ( C) XRD Results 28.106 37.880 32.671 46.786 21.048 18.033 20.832 23.601 25.951 29.002

31

Noa Noa 19 17 20 21

Amorphous ribbon Crystalline ribbon Crystalline ribbon Crystalline ribbon Amorphous sheet Amorphous sheet Amorphous sheet Amorphous sheet Crystalline sheet Crystalline sheet

Ref.

This This This This [24] [24] [24] [24] [24] [24]

work work work work

No means no supercooled liquid region.

a higher thermal stability of the amorphous phase. A larger DTx means a more stable supercooled liquid against crystallization and improved GFA. It has been observed that the Al–10Ce–Ni alloys show the higher thermal stability (Tx: 500–730 K) than the Al–Ce–

905

10Ni alloys (402–620 K) [22,24]. This generally agrees with the better GFA and wider GFR (1–30 at% Ni) in the Al–10Ce–Ni alloys than that of the Al–Ce–10Ni alloys (2–10 at% Ce) [22,24]. On the other hand, it is experimentally found that glass transition phenomenon prior to crystallization was only observed in the vicinity of 6 at% Ce for the Al–Ce–Ni system. Tg and Tx increase significantly with increasing solute concentration, indicating enhanced thermal stability [22–24]. Additionally, it is observed in the melt spinning process that the alloy with lower Al content exhibited a high viscosity [19]. However, it is experimentally by copper mold casting indicated that the GFA of alloys 9 and 10 with the enhanced thermal stability (Table 6) and higher viscosity is lower than that of alloys 5 and 6 with no appreciable glass transition and lower viscosity. It is noteworthy that the correlation between GFA and the thermal stability for liquid indicated by heat of mixing is consistent with that indicated by DTx. Consequently, these findings indicate that thermal stability as well as the atomic transport and viscosity properties of melt has little effect on the GFA in the Al–Ce–Ni alloys.

Fig. 5. Calculated normalized nucleation driving force (per mole of atoms) for crystalline phases from undercooled (a) Al–10Ce–Ni, (b) Al–Ce–10 Ni and (c) Al–6Ce–Ni metastable liquid at 800  C.

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C. Tang et al. / Intermetallics 18 (2010) 900–906

was revealed that the nucleation driving force is the dominant factor determining the formation of amorphous phases, as compared with the negative heat of mixing for the Al–Ce–Ni alloys in the glass forming range. This is confirmed by the melt spinning and copper cold casting experimental results.

5.3. GFA and the driving force for the crystallization Actually, it is well known that crystallization is the only event that prevents the formation of an amorphous phase. Crystallization is usually through the nucleation and growth process. There are three dominating factors for the kinetics, (i) chemical driving force, (ii) interfacial energy, as an energy barrier, between the amorphous phase and the crystalline phases, (iii) the atomic mobility for rearrangement or transport of the partitioning atoms. According to the classical nucleation theory, the driving force for the formation of the crystalline phases is the major factor affecting the nucleation kinetics of crystalline phases from amorphous alloy melts, as compared to the interfacial energy between liquid and crystalline phases. It is believed that alloys with lower driving force for the formation of crystalline phases under the supercooled liquid state suggest higher GFA in the glass forming range. Based on the application of this idea in the Cu–Ti–Zr system, Kim and coworkers proposed the minimum driving force criterion as a new thermodynamic calculation scheme to evaluate the composition dependence of the GFA [30]. Fig. 5 shows the calculated nucleation driving forces of the (a) Al–10Ce–Ni, (b) Al–Ce–10Ni and (c) Al–6Ce–Ni alloys precipitating from the supercooled liquid phase at 800  C in order to demonstrate the effect of the addition of Ni/Ce on the GFA of these Al–based alloys. As shown in the figure, the relatively smaller nucleation driving forces for the formation of crystalline phases for the Al–10Ce based alloys (Fig. 5a) are generally indicative of their higher GFA with a reportedly wider GFR (1–30 at% Ni) [25]. In contrast, the relatively larger driving forces in the Al–10Ni based alloys (Fig. 5b) are associated with their poorer GFA and narrower GFR (2–10 at% Ce) [25]. This finding is further confirmed by the present melt spinning and the copper mold casting experimental results [24]. The GFA of alloys 1–10, indicated in Table 6, are in good agreement with the corresponding driving forces for crystalline phases. The small driving forces for the formation of crystalline phases for amorphous sheet alloys 5 to 8 (Fig. 5b and c) are in good agreement with their reported highest GFA in the Al–Ce–Ni system [24]. As discussed above, only those Al–Ce–Ni alloys with heat of mixing ranging from 15 to 49 kJ/mol of atom show high GFA. The alloy with the eutectic composition demonstrated poor GFA, due to its smaller heat of mixing. For the alloys in the GFR, however, the nucleation driving force is a dominant factor that affects the formation of an amorphous phase, as compared with the negative heat of mixing for the Al–Ce–Ni alloys. This conclusion is in good agreement with the present melting spinning and the reported copper mold casting experimental results [24]. 6. Conclusions C

C

C

To better understand the GFA of the Al–based glass forming system, a self–consistent thermodynamic database at the Al–rich corner of the Al–Ce–Ni system was developed via thermodynamic modeling, supplemented with first–principles calculations and key experiments. The calculated thermodynamic properties and phase relationship show good agreement with the present experimental data and the literature data. The calculated thermodynamic properties for all of reported amorphous compositions indicated that the alloys with high GFA in the Al–Ce–Ni system are far from the eutectic point, and the heat of mixing are from 15 to 49 kJ/mol of atom for the observed amorphous alloys. There are no deep eutectics in the Al–rich corner. To establish the correlation between the GFA and negative heat of mixing, a melt spinning experimental investigation and nucleation driving force calculation were performed. It

Acknowledgements The financial support from the National Natural Science Foundation of China (NSFC) (Grants No. 50861006, 50831007, 50571114), the Creative Research Group of NSFC (Grant No. 50721003), the Natural Science Foundation of Guangxi (Grant No. 0991002Z) and the Open Project Program of State Key Laboratory of Powder Metallurgy (2008112039) are greatly acknowledged. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25]

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