Evaluation of glass forming ability of alloys
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1 Vol. 2 No. 1, Feb CHINA FOUNDRY Evaluation of glass forming ability of alloys *Anhui CAI, Ye PAN, Guoxiong SUN ( Department of Materials Science and Engineering, Southeast University, Nanjing , Jiangsu, P. R. China) Abstract: Key step of exploiting a new type BMG (Bulk Metallic Glass) is quickly judging GFA (Glass Forming Ability) of the alloys. The mole melting heats of BMGs are calculated using the weighted averages principle. The reliability and limitation of T rg criterion for GFA are discussed. The reason why T rg of BMGs is larger than 0.5 is discussed. Two new criteria for GFA,, are proposed. GFA sequence of BMGs is calculated using the criterion, the result agrees with that of A. Inoue and the R c Furthermore, as an example, the R c of the alloys developed by Chuang DONG et al is calculated using the. The ascending sequence of these alloys calculated with the criterion agrees with that of Chuang DONG et al. On the contrary, the result by the criterion is in contrary with Chuang DONG et al, indicating that the criterion is better and more convenient than the Calculation showed that the optimum is kj/mol. Keywords: bulk metallic glasses; glass forming ability; weighted averages principle; GFA criterion CLC number: TG146 Document: A Article ID: (2005) Introduction Bulk metallic glasses (BMG) have been one of the hotspots in material fields because of their excellent properties in physics, chemistry, optics, magnetism and mechanics. The glass forming ability (GFA) parameters were extensively researched at the point of thermodynamics, kinetics and physical structure [1-4]. Two initial GFA parameters were the super-cooled liquidus region ΔT x = T x - T g (T x and T g are the onset crystallization temperature and the glass transition temperature) and the reduced glass transition temperature T rg = T g /T m (T m is the onset-melted temperature). Subsequently, on the base of T rg, Z. P. LU et al [5] proposed a new parameter, the reduced glass transition temperature, i.e. T rg =T g /T L (T L is the final-melted temperature). Recently, Takeuchi Akira et al [6-7] reported a function for multi-component alloys combining ΔH and S σ /k B, and successfully obtained two critical values of typical multi-component metallic glasses, i.e. 15 kj/mol and 0.1 respectively, and found that more negative the ΔH was and the bigger the S σ / k B (S σ and k B are the misfit-term and the Boltzmann constant) was, the stronger the GFA of the alloys was. In addition, A. Inoue [8] proposed of three empirical rules for BMG. However, those GFA parameters needed to determine many parameters. Among those, some can be obtained only after BMGs have been obtained, even cannot be obtained. and some Therefore, to research criteria *Anhui CAI: Ph.D., research direction: preparation of advanced materials and structure of alloy. caianhuil970@21cn.com [Received date] ; [Accepted date] quickly and exactly evaluating GFA of the alloys has been a concerned problem. In this paper, total 35 alloys of 7 groups are used in this study. The reliability and limitation of T rg criterion for GFA are discussed. Two new criteria the for the evaluation of the GFA of the alloys are proposed and discussed. And the GFA sequence of BMGs is calculated by using the criterion, agrees with that of A. Inoue's and the result [8]. In addition, as an example, the R c of the alloys (Zr-Al-Cu-Ni) developed by Chuang DONG et al criteria. [3] is calculated by use of the new The ascending sequence of GFA of these alloys calculated by the criterion agrees with that of Chuang DONG et al. On the contrary, the result by the criterion doesn't accord with that of Chuang DONG et al, indicating that the criterion is better and more convenient than the 2. Physic background and calculation methods The Gibbs free energy (G) of the super-cooled melt is higher than that of the crystal, so there is a tendency of crystallization in super-cooled melt. The difference in the free energy (ΔG) between solid and liquid is a force of crystallization. The larger the ΔG is, the bigger the force is. The force is a critical factor influencing formation of crystal nucleus and nucleation rate, crystal nucleus, the critical radius of crystal nucleus growth and growth rates from solidification theory point of view. Therefore, the ΔG directly influences the formation of BMG. According to thermodynamic theory, the Gibbs free
2 CHINA FOUNDRY Feb energy of system is expressed as, the first approximation, proposed. the following equation is When one mole melt crystallizes, which leads to the change of, i.e., the change of chemical potential of system is as follows: Where,, ΔH g and ΔS g are the differences for G, H and S between solid and liquid when one mole melt crystallizes respectively. Since the melt and crystal are in equilibrium at melting point (T m ), therefore, there is the following expression. When the melt transforms to the metallic glass, let T= T g, the expression (5) is rewritten as the following expression, According to Ziman liquid theory and supposing that the melt is an ideal solution, the can be calculated by using the following expression: Where, ΔG mg and ΔS mg are the difference of G, H and 5 between solid and liquid phases when one mole melt crystallizes at the melting point respectively. When the melt is cooled slightly down under T m the crystallization can happen immediately. Because of the small super-cooling, the adequate approximation. Hence, the difference in the mole free energy of solid and liquid is: However, at large super-cooling, supposing that the ΔG and the ΔH change linearly with temperature [13,14], as Where, x i is the mole percent of i-th component, n is component number, ΔH m is the mole melting heats of i-th component. 3. Results and discussion Total 35 alloys of 7 groups are used in this study. Their critical cooling rates (R c ) [9-11], and calculated and using above equation [6] are all listed in Table 1. Their average values of the critical cooling rates (R c ) [9-11], are also calculated and shown in Table 2. Table 1 Parameters of Mg-based, Nd-based, Pd-based, La-based and Zr-based
3 Vol. 2 No. 1 Evaluation of glass forming ability of alloys Table 2 The average values of five parameters (T rg,, and R c ) of seven sub-groups Using the data in Table 1 a three-dimensional graph for, T rg and is shown in Fig.1. It is seen from Fig.1 that when T rg is fixed, increases with the increase of. When is invariable, there exits a minimum position or critical point, T rg =0.5. When absolute value of the, decreases with the increase of T rg, which is the forming region of BMG. In addition, it could be the reason why T rg of BMG is larger than 0.5 presently. In addition, the larger the is, the bigger the driving force is for the melt to crystallize. Normally for forming BMG, should be as small as possible, and value reflects the GFA of BMG. Fig.2 shows the curves between and T rg for two : -1 kj mol -1 and -2 kj mol -1 respectively. It is seen from Fig.2, for an alloy with large T rg, a larger can be found for large, its GFA is weaker. This shows that although T rg of the alloy is high, its GFA may not be always strong. T rg has a certain limitation for the GFA Fig.1 Three-dimensional sketch for equation (6) Fig.2 The relationships between and T rg for two : -1 kj mol -1 and -2 kj mol -1 respectively
4 CHINA FOUNDRY Feb For the six groups (except for Nd-based) of MGF alloys the fitted coefficients for the equations between R c and or (using regression equation R c = A+B 1 X + B 2 X 2, X represents or ) and their minimal values are calculated and shown in Table 3. The relationships between R c and the three parameters (T rg, ) are shown in Fig.3. It is seen that the relationships between R c and are simple parabolic, but the relationships between T rg and R c is quite complicated, indicating T rg is not a very good GFA Table 3 The parameters and fitted coefficients for equations between R c and /, their Minima for the six sub-groups and those of Zr-AI-Ni-Cu alloys (in bracket) the cluster [16] is big but less, and if excessive heats exhausting in the solidification of melt cannot be carried about, obviously it will influence the formation of BMG. On the contrary, less heats leads to small and more clusters even though the exhaustion of heats is easy. The comprehensive effects above-mentioned result in the decrease of GFA of BMG. And thus, only when Fig.3 The relationships between four parameters (T rg, ) and R c As shown in Table 3, the two correlation coefficients, R, are both larger than 0.74, indicating the regressed equations have relatively good reliability. And the relationships between R c and the two parameters ( or ) are similar to one another in Fig.3, which indicates the T rg influences not the tendency but the magnitude of the. It is also shown that the T rg is not a good Furthermore, since the relationships all present the parabola, and then there is other BMGs whose GFA are better than the BMGs presented. Fortunately, it is testified, recently, by C. DONG et al [15] developed other Zr-Al-Ni-Cu BMGs with better GFA. And the optimal values are calculated in terms of the fitted equations in Table 3, that of are kj/mol, kj/mol respectively. It is shown that when is excessive large, it is unfavorable to the formation of BMG. Large reflects the stronger bonding force and is moderate, it is favorable to the formation of BMG. Furthermore, GFA sequences are performed on seven subgroups. According to the R c, the GFA ascending sequence is Pd-Cu-Si, Mg-based, La-based, Zr-Al-TM, Zr-Ti-TM and Pd-P-TM. According to, that is Pd-Cu-Si, Mg-based, Zr-Al-TM, Pd-P-TM, Zr-Ti-TM and La-based. And according to ) it will be Pd-Cu-Si, Mg-based, Zr-Al-TM, Zr-Ti-TM, Pd-P-TM and La-based. It is shown that the GFA ascending sequences in three cases agree with that of A. Inoue's [12] except for La-based. If the above-mentioned rules are correct, one can develop more BMGs with better GFA in La-based alloy system. In addition, the GFA of Nd-based was predicted by the use of two above-mentioned criteria, and the results of the predictions are that the GFA of Nd-based is in the vicinity of that of Mg-based. And furthermore, J. XU et al [l7], recently, reported Mg 65 Cu 20 Zn 5 Y 10 BMGs with thickness up to 6 mm and its R c may reduce to 25 K/s. Particularly, the fitted equations between R c and the parameters ( or ) for Zr-Al-Ni-Cu alloys are tabulated in Table 3 (in bracket) and the corresponding relationships are shown in Fig.4 respectively. The minimum, i.e., optimum value, is kj/mol for the and kj/mol for the ΔC g. And then, five Zr-Al-Ni-Cu BMGs [15] (shown in Table 4) developed recently are examined by means of criteria
5 Vol. 2 No. 1 Evaluation of glass forming ability of alloys respectively. As in Table 4 and Fig.4, the values are in the vicinity of kj/mol and kj/mol, which indicates that the GFA of these alloys is strong. Furthermore, as shown in Table 3, the correlation coefficients of the equation for Zr-Al-Ni-Cu base system between R c and the parameters ( or ) are both larger than 0.99, indicating that these relationships are fairly reliable. And thus, the R c of the alloys developed by C. DONG et al [l5], is calculated (shown in Table 4). From criterio n, the GFA ascending sequence is Zr 65.5 Al5 5.6 Cu 22.4 Ni 6.5, Zr 65.3 Al 6.5 Cu 20 Ni 8.2, Zr 6.5 Al 7.5 Cu 17.5 Ni 10, Zr 64.8 Al 8.3 Cu 1.55 Ni 11.4, Zr 64.5 Al 9.2 Cu 13.1 Ni 13.2 Zr 63.8 Al 11.4 Cu 17.2 Ni 7.6 Obviously, Inoue alloy, i.e. Zr 65 Al 7.5 Cu 17.5 Ni 10, don't own highest GFA in these alloys. This is in agreement with C. DONG et al [1]. However, from the criterion, the ascending Fig.4 The relationships between two parameters( ) and R c for Zr-Al-Ni-Cu alloy system Table 4 The calculated parameters ( ) and predicted R c for the alloys developed by Dong Chuang et al. Note: R ch and R cg are the critical cooling rates calculated by the parameters of the respectively. sequence is contrary with the result of the criterion, indicating the criterion is better and more convenient than the Furthermore, it could be predicted that there will be another Zr-Al-Cu-Ni base alloys characterized by higher GFA. 4. Conclusions (l)the reliability and limitation of T rg criterion for GFA are discussed. And the reason that T rg of the BMGs is larger than 0.5 is also stated. (2)Two new criteria the for the evaluation of the GFA of the alloys are proposed. And the GFA sequence of BMGs is calculated by using the criterion, and the result agrees with that of A. Inoue's [8]. In addition, as an example, the R c of the alloys (Zr-Al-Cu-Ni) developed by Chang DONG et al calculated by use of the new criteria. The ascending sequence of GFA of these alloys calculated by the criterion agrees with that of Chang DONG et al. On the contrary, the result by the criterion doesn't accord with that of Chang DONG et al, indicating that the criterion is better and more convenient than the [3] is References [1] Shouguo ZHANG and Yang YU. The rhomb unit structural model of amorphous alloys [J]. Materials Science and Engineering, 1991, A134: (in Chinese) [2] A. Inoue and Tsutomu Shibata. Thermal properties of Zr-TM-B and Zr-TM-Ga (TM=Co, Ni, Cu) amorphous alloys with wide range of supercooling [J]. Mater. Trans. JIM, 1995, 36(12): [3] Xiaodong WANG, Min Ql and Chuang DONG. Electronic structure models for the effect of Al addition on the glass forming ability of Zr-base amorphous alloys [J]. Acta Metal Sin, 2002, 38 (12): [4] Dawei XING, Feijian SUN, Wang GANG, et al. Influence of Sn addition on the glass forming ability of Zr 52.5 Ti 5 Ni 14.6 Cu 17.9 AI 10 bulk metallic glass alloy [J]. Special Casting and Nonferrous Alloys, 2002, (6): 12-14(in Chinese) [5] Z. P. LU, Y. LI and S. C. NG. Reduced glass transition temperature and glass forming ability of bulk glass forming alloys [J]. J Non-Cryst Solids, 2000, 270 (1-3): [6] Huanrong WANG, Zhiqiang SHI and Xinying TENG, et al. Progress in amorphous forming ability of alloys [J]. Functional Materials, 2002, 33(4): (in Chinese) [7] A. Takeuchi and A. Inoue Calculation of mixing enthalpy and mismatch entropy for ternary amorphous alloys [J]. Mater Trans JIM,2000,41(11): [8] A. Inoue. High strength bulk amorphous alloys with low critical cooling rates [J]. Mater Trans JIM, 1995, 36 (7): [9] Z. P. LU, H. TAN, Y. LI, et al. The correlation between reduced glass transition temperature and glass forming ability of bulk metallic glasses [J]. Scripta Materialia, 2000, 42 (7):
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