Evaluation of liquid fragility and thermal stability of Al-based metallic glasses by equivalent structure parameter

Physics Letters A 374 (2010) 3784–3788

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Physics Letters A www.elsevier.com/locate/pla

Evaluation of liquid fragility and thermal stability of Al-based metallic glasses by equivalent structure parameter Xuelian Li, Xiufang Bian ∗ , Lina Hu Key Laboratory for Liquid-Solid Structural Evolution and Processing of Materials, Ministry of Education, Shandong University, Jinan 250061, China

a r t i c l e

i n f o

Article history: Received 7 January 2010 Received in revised form 29 May 2010 Accepted 14 July 2010 Available online 17 July 2010 Communicated by R. Wu

a b s t r a c t Based on extended Ideal-Atomic-Packing model, we propose an equivalent structure parameter “6x + 11 y” to evaluate fragility and thermal stability of Al–TM–RE metallic glasses, where x and y are composition concentrations of transition metal (TM) and rare earth (RE), respectively. Experimental results show that glass forming compositions with “6x + 11 y” near 100 have the smallest fragility parameter and best structure stability. In addition, “6x + 11 y” parameter has a positive relationship with onset-crystallization temperature, T x . Al–TM–RE glassy alloys with (6x + 11 y )  100 undergo primary crystallization of fcc-Al nanocrystals, while alloys with (6x + 11 y ) > 100 exhibit nanoglassy or glassy crystallization behavior. © 2010 Elsevier B.V. All rights reserved.

1. Introduction Al-based metallic glasses (MGs) have attracted more and more attention especially after Al–TM–RE bulk glassy alloys have been reported recently [1–3]. They exhibit unusual high specific strength which can be over twice as high as that of conventional aluminum alloys, and further increase of fracture strength of Al-based MGs can be achieved when nanoscale fcc-Al particles are dispersed in amorphous matrix [1,4]. To promote application of Al-based MGs, we prefer that Al-based MGs can persist for a very long period and can be stable at temperature even higher than the primary crystallization temperature of fcc-Al, which physically refers to fragility and thermal stability of glassy alloys, respectively. We know that liquid fragility can be indicated by relaxation time, which is the time that glasses need to approach more stable supercooled liquid state [5]. Bian et al. believe that in Al-based glassy alloys, the smaller fragility parameter comes from higher stability of mediumrange order structure [6]. Therefore, the structure of Al-based metallic glasses is crucial on exploring the origin of liquid fragility. As for the local structure in Al–TM–RE glassy systems, the current knowledge is that RE element is surrounded by Al atoms according to the local coordination number (CN), and TM element has covalent-like bonding with Al, in addition there are no TM– RE direct bonds [7–13]. No definite pictures of Al–TM–RE amorphous structure have yet been figured out. How to construct an equivalent structure is urgent to evaluate fragility. Recently, an Idealized-Atomic-Packing (IAP) model was proposed to evaluate quasi-equivalent structure of binary glass forming alloys [14]. According to this model, a stable MG is considered to have maximal

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solute-centered chemical short-range-order (SRO) clusters, which tends to have 12 neighboring clusters with icosahedral-like fivefold arrangement. IAP model has been successfully used to predict glass formation of a large number of binary glassy alloys, including explaining why Al–RE glasses are located away from their eutectic points [14]. In this Letter we propose an equivalent structure for ternary Al–TM–RE glass-forming alloys by using the extended IAP model for evaluating liquid fragility and thermal stability. We also explore the possibility of predicting T x for a given Al–TM–RE system. 2. Methods According to IAP model, certain compositions are structurally favorable for glass formation when the key packing requirements are satisfied [14]. In the hypothesis of the ideal local structure for Al–RE glasses, each RE-centered SRO cluster should have one RE atom and CN Al atoms. The CN of RE can be easily calculated using following Eq. (1a), where the atomic size ratio R = rRE /rAl [14]. Metallic radii used in this Letter are taken from Ref. [15].







CNAl-RE = 4π / 10 arccos sin(π /5) 1 − 1/( R + 1)2

− 3π



(1a)

1/2    − 2π CNAl-TM = 4π / 8 arccos sin(π /4) 1 − 1/( R + 1)2 



1/2 

(1b) Since each Al solvent in this particular cluster is shared by this cluster itself and 12/CN times by the neighboring clusters, only 1/(1 + 12/CN) of this solvent Al atom belongs solely to this cluster. Then the total number of solvent Al per solute RE, S, can be CN derived from S = 1+(12 /CN) [14].

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Fig. 1. The | H chem |–(6x + 11 y ) function for six kinds of Al-based MGs [20–25].

Table 1 The calculated atomic size ratio (R) and the number (S) of Al atoms per TM or RE-centered clusters. Systems

R

S

Al–La Al–Ce Al–Y Al–Nd Al–Gd Al–Pr Al–Fe Al–Ni Al–Co

1.31243 1.2745 1.25874 1.14685 1.2587 1.18881 0.86694 0.87022 0.87413

10.8155 10.3107 10.1033 8.69903 10.1033 9.21182 5.11321 5.14142 5.17466

According to IAP model, glass formers will tend to crystallize with small enthalpy release and volume change. Then amorphous structure may be preferentially stabilized at compositions close to that of equilibrium compounds [14]. Previous investigations on crystallization of Al–TM–RE MGs have shown that the crystalline phases are Al3 TM, Al–RE and/or fcc-Al after totally annealing [16– 18]. In order to approach the structure of equilibrium compounds, the solute-centered clusters in Al–TM–RE glasses can be considered as RE and TM-centered SROs, and the rest Al atoms. We calculate the SROs in Al–TM systems using Eq. (1b), and the atomic size ratio R between Al–TM and Al–RE together with the number of Al atoms per TM or RE centered clusters, S, are tabulated in Table 1. As we can see in Table 1, the numbers of Al atoms for different RE or TM-centered SROs are very close. Thereby we decide to consider the equivalent structure of Al–TM–RE MGs as (Al5 TM)x(Al10 RE) y, where x and y are compositions for TM and RE, respectively. Then the structure of Al100−x− y TMx RE y can be described by equivalent structure Al5 TM and Al10 RE for three cases: When Al atoms needed for equivalent structure (5x + 10 y ) is equal to Al atoms provided (100 − x − y ), which is (6x + 11 y ) parameter equals to 100, the equivalent structure of Al–TM–RE MGs can be considered to contain only (Al5 TM) and (Al10 RE) SROs. And equivalent structure with insufficient or residual Al atoms relative to (Al5 TM) and (Al10 RE) SROs will be reflected by (6x + 11 y ) values above or below 100, respectively.

3. Results and discussion As is well known, RE elements have weak metallic bond and large atomic size difference compared with Al element and will turn to destroy Al crystallinity, and TM elements which have been proved to have strong interactions with Al will further restrict the movement of Al atoms [13]. Hence the values of (6x + 11 y ) can reflect the restriction strength of diffusion of Al atoms during thermal excitation. Considering that the negative chemical enthalpy  H chem also reflects the interaction strength of solid solutions and general chemical interactions between atoms, we assume that (6x + 11 y ) parameter will have a positive relationship with | H chem |. The  H chem values for binary and ternary amorphous alloys on the basis of the extended regular soluting model can be calculated by Eq. (2) [19],

 H chem =

n 

Ωi j c i c j

(2)

i =1 i = j

where Ωi j (= 4 H imix j ) is the regular solution interaction parameter between the ith and jth elements, and  H mix is the mixing enthalpy resulting from Miedema’s macroscopic model; c i is the composition of the i element; n is the total number of the elements. Fig. 1 shows the absolute values of  H chem against (6x + 11 y ) parameter for six kinds of Al–TM–RE glassy systems. And there indeed is a positive relationship between | H chem | and (6x + 11 y ), and in the range studied, the variation is good linear. Based on cluster kinetics for metallic glasses, the negative chemical enthalpy, | H chem | reflects activation energy of cluster kinetics during relaxation process, h [6,19]. Here h can be displaced by parameter (hm − hc ), where hc is the energy needed for cluster association and hm is the energy needed for a separating from cluster [26]. Because the agglomeration processes of glass forming systems are always less than the breakage processes in glass transition, the h values for glass formers are usually positive [6,19,26]. Then a larger h value suggests that particles will be easier separating from clusters. And the stability of clusters during reheating can be reflected by the competition be-

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Table 2 Values of the negative chemical enthalpy, | H chem |, onset-crystallization temperature, T x , the equivalent structure parameter, (6x + 11 y ) and the calculated | H chem |/ T x for Al–Ni–Nd, Al–Ni–Pr and Al–Yb [24] metallic glasses. Alloys

| H chem |, kJ/mol

Tx, K

| H chem |/ T x × 103 , kJ/(mol K)

6x + 11 y

Al88 Ni10 Nd2 Al87 Ni9 Nd4 Al87 Ni8 Nd5 Al84 Ni10 Nd6 Al86 Ni4 Nd10 Al84 Ni8 Nd8 Al87 Ni10 Pr3 Al85 Ni10 Pr5 Al84 Ni10 Pr6 Al91 Yb9 Al90 Yb10 Al89 Yb11

10.66 12.61 13.22 15.77 16.58 16.90 11.98 14.54 15.77 6 .5 7 .2 7 .8

378 460 477 544 561 571 452 550 554 433 435 446

28.20 27.41 27.71 28.99 29.55 29.60 26.4 26.5 28.5 15.0 16.5 17.5

82 98 103 126 134 136 93 115 126 99 110 121

Fig. 2. The equivalent structure indicator (6x + 11 y ) versus T x for Al–Ni–(Pr, La, Y, Ce, Nd, Gd) and Al–Co–(Y, Ce) MGs [20–25]. The solid line denotes the compositions with “6x + 11 y = 100”.

tween breakage process against devitrification process, which can be described by h/ T x , kJ/(mol K)). Hu and Bian have proved that | T  H chem |/ T x has a close correlation with liquid fragility [19]. Therefore, if | H chem |/ T x is small, clusters will be stable and liquid fragility will be small. And MGs with bigger | H chem |/ T x will mean that clusters are easier to breakage, which will behave as more fragile liquids. For the purpose of checking the validity of equivalent structure parameter (6x + 11 y ) in evaluating liquid fragility, we tabulate (6x + 11 y ) and the fragility index, | H chem |/ T x for Al–Ni–Nd, Al– Ni–Pr and Al–Yb MGs in Table 2. We can see that Al87 Ni9 Nd4 , Al87 Ni10 Pr3 and Al91 Yb9 MGs with (6x + 11 y ) values closer to 100 show smaller | H chem |/ T x values. And | H chem |/ T x and (6x + 11 y ) values can be influenced by both RE and TM elements. It’s worthwhile pointing out that liquid fragility is not simple influenced by RE or TM alloying, but reaches its minimum at compositions fulfilling “6x + 11 y = 100” criterion. In other words, “6x + 11 y = 100” is an important criterion controlling liquid fragility. The alloying effect on liquid fragility appears in correspondence with disturbing equivalent SRO clusters. The relationship between liquid fragility and “6x + 11 y = 100” criterion can also be comprehended from Adam–Gibbs entropy model [27]:

η = η0 exp(μ/ T S c )

where S c is the configurational entropy, and is in contrast to the size of rearrangeable region. μ is the activation energy of rearrangeable region and is related to the degree of short-range order [28]. Based on Adam–Gibbs equation, the higher the short-range order and the smaller the size of SRO clusters, the viscosity near the glass transition temperature will change more slowly and then liquid fragility will be smaller. According to the equivalent structure of Al–TM–RE metallic glasses we proposed, when (6x + 11 y ) is equal to 100, the equivalent structure of Al–TM–RE metallic glasses will show higher short-range order. And the equivalent structure with (6x + 11 y ) less than 100 can be considered to have smaller size of clusters because of the existence of residual Al atoms. So Al–TM–RE MGs with (6x + 11 y ) close to 100 can be regarded as strong liquids with smaller liquid fragility parameter. As for thermal stability, which is the stability of amorphous alloys against crystallization, is controlled by the kinetic feature under thermal excitation and can be reflected by the onsetcrystallization temperature, T x [29]. According to thermally induced crystallization process, Al-based MGs can be classified into three categories-nanocrystalline, glassy, and nanoglassy alloys [29]. Nanocrystalline and nanoglassy alloys undergo primary crystallization of fcc-Al nanocrystals without and with clearly resolved T g preceding T x , respectively. Glassy alloys usually devitrify after a clearly resolved T g and undergo either eutectic-like or polymorphic reactions at T x [29]. It is believed that the competition among

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Fig. 3. Compositional triangles for (a) Al–Ni–Y and (b) Al–Ni–Gd systems divided by “λ0.1 ” line (black line), and “6x + 11 y = 100” line (red line), describing the composition dependence of crystallization behaviors; () glassy, () nanoglassy, and () nanocrystalline alloys [27].

different clusters in the amorphous structure are responsible for primary crystallization [30]. Then the competition between stability of Al clusters and intermetallic compound forming clusters will play an important role on determining thermal stability of Al-based MGs. We have pointed out that both RE and TM atoms can prevent movement of Al atoms. During thermal relaxation, the more RE and/or TM atoms, the higher resistance against agglomeration of Al clusters. Thereby, larger (6x + 11 y ) values may imply higher primary crystallization temperature. In Fig. 2, we plot T x versus values of (6x + 11 y ) for eight kinds of Al–TM–RE metallic glasses. It is found that T x has a positive relationship with (6x + 11 y ). And since the equivalent structure Al5 TM or Al10 RE is Al supersaturation clusters compared to equilibrium crystalline phases, e.g. Al5 TM versus Al3 TM phase, Al–TM–RE MGs with “6x + 11 y = 100” will undergo primary crystallization of fcc-Al. Thus, (6x + 11 y ) less than 100 will corresponds to nanocrystalline alloys, and Al–TM– RE MGs with (6x + 11 y ) higher than 100 will have eutectic-like or polymorphic crystallization and show glassy crystallization behaviors. These findings reflect that whether there are quenched-in nuclei (fcc-Al clusters) in Al–TM–RE glassy alloys can be easily judged by the “6x + 11 y = 100” criterion. Previous proposed extended topological instability parameter, λ0.1 , obtained from the critical solute concentration for topological instability of fcc-Al solid solution, has quantitatively correlated chemical compositions with crystallization behavior of Al-based glass formers [29]. Fig. 3 displays the composition dependence of “λ0.1 ” as well as the newly proposed “6x + 11 y = 100” criterion on the crystallization behavior in Al–Ni–Y and Al–Ni–Gd glassy alloys. We can see that the “6x + 11 y = 100” line divides the composition triangle into the above part — nanoglassy and glassy alloys and the below part — nanocrystalline alloys, which agrees well with “λ0.1 ” criterion, except for a little deviation on compositions corresponding to the “line”. These deviations may be due to the structure model used in this work is icosahedral-like while the fcc lattice of Al crystals is discussed in the topological instability model. Another important phenomenon in Fig. 3 should be mentioned that Al–Ni–Y and Al–Ni–Gd MGs with “6x + 11 y = 110” undergo nanoglass crystallization behavior. To ensure that this phenomenon is not occasional, we prepare three kinds of Al–Ni–Ce metallic glasses, Al87 Ni7 Ce6 , Al85 Ni9 Ce6 and Al84 Ni10 Ce6 with (6x + 11 y ) values of 108, 120 and 126, respectively. The DSC curves are shown in Fig. 4. We can see that the onset-crystallization temperature increases with (6x + 11 y ), and Al87 Ni7 Ce6 with (6x + 11 y ) near 110 does show nanoglass crystallization behavior. The icosahedral-like idealized configuration is not, of course, the accurate description of the exact structural features in Al– TM–RE MGs. However, it intends to represent a quasi-equivalent

Fig. 4. DSC curves of the Al84 Nix Ce6 (x = 7, 9, 10) samples prepared at scanning heating rate of 20 K/min.

configuration. In this work, we can see that the (Al5 TM)x(Al10 RE) y structure model can not only correlate compositions with their thermal stability, but also evaluate the liquid fragility conveniently. Thus this quasi-equivalent structure model can be used as a prediction method in detecting new Al–TM–RE metallic glasses. The significance of such an equivalent model is that it allows prediction of macroscopically equivalent properties from chemical compositions by catching the main atomic packing principles. 4. Conclusions An equivalent structure parameter (6x + 11 y ), considered from the extended IAP model is a good indicator for evaluating liquid fragility and thermal stability of Al–TM–RE MGs. Al–TM–RE metallic glasses with “6x + 11 y = 100” will have the most stable structure. And (6x + 11 y ) parameter has a positive relationship with T x . Al–TM–RE glasses with parameter (6x + 11 y ) less than 100 correspond with nanocrystalline glasses. In contrary, when (6x + 11 y ) values are bigger than 100, Al–TM–RE glasses will undergo nanoglassy or glassy crystallization behavior. Acknowledgements We would like to acknowledge financial support from the National Basic Research Program of China (973 Program 2007CB613901), the National Natural Science Foundation of China

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