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Strengthening mechanisms of Zr-based devitrified amorphous alloy nanocomposites
Scripta Materialia 48 (2003) 43–49 www.actamat-journals.com
Strengthening mechanisms of Zr-based devitrified amorphous alloy nanocomposites Hyoung Seop Kim
*
Department of Metallurgical Engineering, Chungnam National University, Taejon 305-764, South Korea Received 5 March 2002; received in revised form 30 April 2002; accepted 2 August 2002
Abstract Devitrified amorphous alloy nanocomposites with nanoscale precipitates are regarded as new prospective structural materials with superior mechanical properties such as high strength and shear resistance. However, the strengthening mechanism of the devitrified amorphous nanocomposites has not been clearly elucidated. In order to analyse the strengthening behaviour of the partially devitrified amorphous alloys, the change in solute concentration of Zr-based alloys during the devitrification process by heat treatment was investigated. It was found that the solute concentration of the remaining amorphous matrix increases during the devitrification when the solute concentration of the initial amorphous alloy is higher than that of the precipitate, such as Zr2 Cu precipitate from Zr60 Cu20 Ni10 Pd10 alloy. On the other hand, the solute is diluted in the remaining amorphous matrix during the devitrification when the solute concentration of the initial amorphous alloy is lower than that of the precipitate, such as Zr2 Cu precipitate from Zr70 Cu10 Ni10 Pd10 alloy. Investigating this solute concentration change and the associated mechanical properties shows that it is the phase mixtures model, and not the solute concentration model, that provides an adequate description of the devitrified amorphous nanocomposites. Ó 2003 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved. Keywords: Metallic glasses; Composite; Strengthening mechanism; Mechanical properties
1. Introduction Partially devitrified amorphous alloys, referred to as amorphous nanocomposites, are of great interest for their superior mechanical properties such as high strength and shear deformation resistance due to their very fine microstructure [1]. For example, it has been reported that Al-based amorphous alloys exhibit high tensile strength
*
Tel.: +82-42821-6596; fax: +82-42-822-5850. E-mail address: [email protected] (H.S. Kim).
above 1000 MPa [2] and a nanocomposite composed of a homogeneous dispersion of nanoscale Al particles within the remaining amorphous matrix can significantly increase the tensile strength up to about 1.5 times as high as that of the corresponding amorphous single phase alloy [3]. The increase in the strength has been reported in most of devitrified amorphous alloy systems, e.g. Zrbased alloys [4,5]. Several contradictory explanations for the strengthening mechanism in these nanocomposite amorphous materials have been proposed. InoueÕs group [3,4] suggested that the increase of strength
1359-6462/03/$ - see front matter Ó 2003 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved. PII: S 1 3 5 9 - 6 4 6 2 ( 0 2 ) 0 0 3 4 4 - 5
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H.S. Kim / Scripta Materialia 48 (2003) 43–49
is due to an enhancement of the resistance to shear deformation caused by the nanoscale precipitate particles. Greer [1] attributed the strengthening of devitrified amorphous alloys to the solute enrichment of the remaining amorphous phase. He also concluded that the hardness would be simply that of the glassy matrix, referring to the Scanlon and CammarataÕs experimental results [6] that the hardness values of magnetron cosputtered nanocomposite Ag–Al2 O3 granular metal films did not follow the rule of mixtures type behaviour. However, a discontinuity in the rate of change of hardness in the Ag–Al2 O3 nanocomposite with metal volume fraction near the percolation threshold could be an artefact of the measurement technique, as Scanlon and Cammarata discussed the elastic modulii of the nanocomposites. In addition, there were several considerable factors affecting the overall mechanical properties of composites, such as a crystal size effect and an interface debonding effect due to oxide phases, in Scanlon and CammarataÕs experiments. Meanwhile, from the mechanics point of view, the effective hardness of particulate composites could be described better by iso-stress type than iso-strain type behaviour [7]. However, whether the rule of mixtures of isostress or iso-strain type holds does not overturn the fact that the overall mechanical properties of nanocomposites are determined by the properties of every component; the more the fraction of the harder component is, the higher is the overall strength. It should also be noted that there is much experimental and theoretical evidence reporting that the mechanical properties of the nanocomposites do follow the rule of mixtures type behaviour [8–10]. Recently, the present author [11–13] has proposed a phase mixtures model in order to describe quantitatively the strengthening behaviour and the ductile–brittle transition behaviour of the partially devitrified amorphous Al–Ni–Y alloys. In the phase mixtures model, the partially devitrified amorphous alloy is regarded as a mixture of a precipitate particle phase and a remaining amorphous matrix phase with varying solute concentration; the overall mechanical properties of the mixtures are described by the rule of mixtures based on the volume fractions of each phase.
Understanding the strengthening mechanism of the partially devitrified amorphous alloys is very important not only for better development of amorphous alloys but also for developing optimum devitrification processes for the amorphous nanocomposites. However, the validity of the solute concentration model and the phase mixtures model is not clear. This is because the calculated results by both the solute enrichment model and the phase mixtures model have accidentally been in reasonably good accord with the experimental data of Al–Ni–Y alloys [1,13]. This accord is because the hardness increments due to the nanoparticle precipitation and due to the solute enrichment were similar in Al–Ni–Y alloys. Hence, it is necessary to elucidate the valid mechanism for the strengthening behaviour of the partially devitrified amorphous composites by means of other experimental and/or theoretical approaches. In the present study, the author devised an experimental scheme using Zr-based alloys of solute enrichment and solute dilution systems during devitrification in order to gain a basis for assessing the validity of the strengthening mechanism of the partially devitrified amorphous alloy nanocomposites.
2. Hardening models As heat treatment proceeds, solute elements rejected from the precipitates during heat treatment are distributed in the remaining amorphous matrix leading to a change in the solute concentration there (i.e. solute enrichment or dilution), depending on the relative composition of the particles and the matrix. Fig. 1 shows a schematic of the composition changes of the partially devitrified amorphous alloy after heat treatment of the fully amorphous alloy. The nanoscale precipitates can be pure metal [3], alloys [4,5] and quasi-crystalline icosahedral phase (I-phase) [14–17]. The devitrification process can be classified into (i) solute enriching system, (ii) constant solute concentration system and (iii) solute diluting system according to the variations in the solute concentration during heat treatment. In other words, the solute composition of the amorphous matrix increases,
H.S. Kim / Scripta Materialia 48 (2003) 43–49
45
Fig. 1. Schematic model of partially devitrified amorphous alloys having precipitated particles embedded in remaining amorphous matrix and schematic concentration profile of solute; (a) solute enriching alloy, (b) constant solute alloy and (c) solute diluting alloy systems.
remains constant or decreases when the concentration of the precipitate is higher than, equal to or lower than the concentration of the initial amorphous alloys, respectively. Examples of the solute enriching systems are Al–Ni–Y alloys with pure Al precipitates, Zr–Cu–Al–Ni and Zr–Cu–Al with Zr2 Cu precipitates [4,5] and Zr–Al–Cu–Pd [4] with Zr2 (Cu,Pd). Examples of the constant solute concentration systems are Zr–Pd [16] with quasicrystalline icosahedral (I) phase precipitates and Zr–Al–Ni–Cu–Ag and Zr–Al–Ni–Cu–Pd [17] with I-phase precipitates. Finally, examples of solute diluting systems are Zr–Al–Ni–Cu–Ag [14,15] with Zr3 (Al,Ag)2 precipitates and Zr–Cu–Al–Ni and Zr–Cu–Al with Zr2 Cu precipitates [4,5]. The composition of the amorphous matrix will change as the volume fraction of the particles increases during microstructural evolution. The composition changes of the amorphous alloy matrix in Zr0:65 Al0:075 Ni0:1 Cu0:125 Ag0:05 and Zr–Al–Cu–Pd alloy systems can be obtained using the following reaction equations (Eqs. (1) and (2)) respectively.
Zr65 Al7:5 Ni10 Cu12:5 Ag5 ! fI-phase ðI-phaseÞ þ ð1 fI-phase ÞZr65 Al7:5 Ni10 Cu12:5 Ag5 ; Zr1CAl CCu CPd AlCAl CuCCu PdCPd !
ð1Þ
fZr2 Cu Zr2 Cu 3
þ ð1 fZr2 Cu ÞZr123fZr Cu CAl CCu CPd 2
1fZr Cu 2
Al
CAl 1fZr Cu 2
CuCCu 13fZr
2 Cu 1fZr Cu 2
Pd
CPd 1fZr Cu 2
;
ð2Þ
where C and f represent initial concentrations of elements and volume fraction of particles, respectively. Fig. 2 shows the composition changes with volume fractions of particles in (a) Zr0:65 Al0:075 Ni0:1 Cu0:125 Ag0:05 and (b) Zr–Al–Cu–Pd systems. In Zr0:65 Al0:075 Ni0:1 Cu0:125 Ag0:05 alloy (Fig. 2(a)) the icosahedral phase (I-phase) particles precipitate. The analytical compositions of the I-phase of 20–30 nm and in the amorphous phase of the Zr65 Al7:5 Ni10 Cu7:5 Ag10 amorphous alloy obtained
Fig. 2. Variation of solute concentration during devitrification; (a) constant concentration alloy and (b) solute enriching alloy and solute diluting alloy systems.
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H.S. Kim / Scripta Materialia 48 (2003) 43–49
by the nanobeam energy dispersive X-ray spectroscopy technique were the same, indicating that the precipitation of the I-phase takes place by the polymorphous mode without redistribution of alloy components [17]. Hence, the compositions of the initial alloy, I-phase precipitate and the remaining amorphous matrix are all the same. In Zr–Al–Cu–Pd alloys (Fig. 2(b)) Zr2 Cu particles are precipitates. In this case, the solute concentration of the remaining amorphous matrix increases or decreases according to Eq. (2), when the initial solute concentration is higher or lower than 33.3% (@Cu concentration in Zr2 Cu particle), respectively. In the phase mixtures model the overall strength of the mixture reff can be described by the rule of mixtures based on the volume fractions of each phase (Eq. (3)) while the solute concentration model, in which the overall strength would be simply that of the remaining amorphous matrix, is given by Eq. (4): reff ¼ fp rp þ fam ram ðCÞ;
ð3Þ
reff ¼ ram ðCÞ;
ð4Þ
where r and f refer to strength and volume fraction of each phase. The subscripts am and p refer to amorphous matrix phase and precipitate particle phase, respectively. C is the solute concentration of the amorphous phase, which depends on the initial composition, the volume fraction and the composition of the precipitate. The rule of mixtures based on the volume fraction of each phase in the phase mixtures model agrees well with the results of finite element analysis of the unit cell model [18] since there is no special interaction between the particles and the matrix, except for the force and energy balances. The necessary parameters for the phase mixtures model are the mechanical properties and the volume fraction of each phase.
3. Comparison with experimental data and discussion Hardness variations of the partially devitrified amorphous alloys can be analyzed by using the solute concentration model (Eq. (4)) or the phase
mixtures model (Eq. (3)) associated with the variation of the solute concentration of the remaining amorphous phase with particle volume fraction. Since the goal of this paper is to identify the valid model for the strengthening mechanism of the partially devitrified amorphous nanocomposites, one should find the suitable alloy systems which can make apparent difference in strength between the two models. The possible issues for obtaining different strengthening (or softening) responses during devitrification are (i) the strength of precipitate particles as compared to the amorphous matrix; whether the particle is harder or softer than the matrix, (ii) the strength variation of the amorphous matrix with solute concentration; whether the amorphous alloy is Ôsolution hardeningÕ or Ôsolution softeningÕ material, and (iii) variation of solute concentration in the remaining amorphous matrix with devitrification; whether the concentration is ÔenrichingÕ or ÔdilutingÕ during devitrification. In other words, (i) if the precipitate is softer than the amorphous matrix in the solution hardening and solute enriching alloy system, (ii) if the amorphous alloy is a solution softening system in the hard particle precipitating and solute enriching system, and (iii) if the amorphous matrix is diluted during devitrification in hard particle precipitating and solution hardening system, the hardness of the devitrified nanocomposite increasing or decreasing according to the solute concentration model or the phase mixtures model, respectively. Therefore, by investigating one of the above three cases, the valid strengthening mechanism can be clearly proven, as the predicted strength of the devitrified nanocomposite should exhibit opposite trends for the two strengthening models under discussion. With respect to the strength of particles in light of the above three categories, the hardness of nanoscale precipitate particles is usually higher than that of the amorphous matrix. This is because the size of the crystalline particles in nanocomposites is so small that dislocations or any defects cannot be active within a particle so that it can be regarded as a perfectly elastic material. For example, the hardness of nanocrystalline Al particle taken from the theoretical strength of a perfect crystal is about 8 GPa [7], which is higher than
H.S. Kim / Scripta Materialia 48 (2003) 43–49
that of amorphous Al–Ni–Y alloys (1–5 GPa). Of course, the strength of the nanoscale particle could decrease by its growth. Concerning the second factor (i.e. solution hardening or weakening of amorphous alloys), in general, the strength of the amorphous alloys increases with solute composition––Ôsolution hardeningÕ alloys. In the fully amorphous alloys of Al–Ni–Y [2,3,19,20] and Zr– Ti–Al–Ni–Cu from reference [10], the hardness increases almost linearly as the solute concentration of the amorphous matrix increases. Therefore, the main factor controlling the trend between the strengthening and the softening of the devitrified amorphous alloys during devitrification should be the variation of the solute concentration in this process. Fig. 3 shows the trends of hardness of the partially devitrified amorphous alloy nanocomposites with volume fraction of hard nanoscale particles in various solution hardening amorphous alloys; Fig. 3(a) and (b) correspond to the solute concentration model and the phase mixtures model, respectively. For the solute concentration model (Fig. 3(a)) the predicted hardness of the nanocomposite increases, remains constant or decreases with the volume fraction of nanoparticles regardless of the relative strength of the particles compared to the amorphous matrix, when the solute concentration of amorphous matrix increases, remains constant or decreases during devitrification, respectively. On the other hand, the hardness predicted by the phase mixtures model of the partially devitrified nanocomposite depends both on the hardness of particles relative to the matrix
47
and on the solute concentration of amorphous matrix. Since the nanoscale precipitate particle is harder than the amorphous phase and usually the strengthening effect by the nanoscale particle is higher than the matrix strengthening or weakening effect, the hardness of the devitrified amorphous nanocomposite increases in all amorphous alloy systems. Comparing Fig. 3(a) to (b), it can be found that the most evident difference between the solute concentration model and the phase mixtures model occurs in the solute diluting alloy system. In order to assess the validity of the two strengthening models, experimental hardness data against volume fraction of precipitate were compiled from literature on Zr-based amorphous alloys (see Fig. 4). The Zr-based amorphous alloys
Fig. 4. Experimental hardness values from reference as a function of the volume fraction of precipitate particles for various Zr-based alloy compositions.
Fig. 3. The theoretical hardness of amorphous alloy with the volume fraction of precipitate particles; (a) solute concentration model and (b) phase mixtures model.
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H.S. Kim / Scripta Materialia 48 (2003) 43–49
represented in Fig. 4 show dramatic results, in that all of the solute concentration enriching (ZrAlCuPd þ Zr2 (Cu,Pd)), the constant solute concentration (ZrAlNiCuAg þ I-phase) and the solute diluting (ZrAlCuAg þ Zr3 Al2 ) alloy systems exhibit strengthening behaviour during devitrification. It should be stressed again that the solute concentration model predicts the strengthening, constant hardness and weakening behaviour during the devitrification processes of (ZrAlCuPd þ Zr2 (Cu,Pd)), (ZrAlNiCuAg þ I-phase) and (ZrAlCuAg þ Zr3 Al2 ) alloy systems, respectively, while the phase mixtures model predicts hardening behaviour for all alloys. From the above strong piece of experimental evidence for Zr-based amorphous alloys, the validity of the phase mixtures model of strengthening of devitrified amorphous nanocomposites seems to be confirmed. From the point of view of the verification of the model developed, more experimental evidence is needed. Indeed, the phase identification of the particle Zr3 Al2 in ZrAlNiCuAg is in controversy, whereas the I-phase in ZrAlNiCuAg looks reliable. Therefore, the experimental data of the same alloy components with different composition, e.g. ZrAlCuPd and ZrAlCuPd, could be useful for assessing the validity of the two competing strengthening models. Experimental research on these amorphous alloys is underway.
meters, i.e. (i) the strength of precipitate particles as compared to the amorphous matrix, (ii) the variation of strength of amorphous matrix with solute concentration and (iii) the variation of solute concentration of the remaining amorphous matrix with devitrification. A comparison of the hardness variation during the devitrification with the two competing models of strengthening leads to the conclusion that the phase mixtures model, rather than the solute concentration model, can explain the increase in hardness of the devitrified nanocomposite of the constant and diluting solute concentration systems of Zr-based amorphous alloy.
Acknowledgements This work was supported by grant number: 2001-6-301-05-2 from Joint Research Project under the Korea–Japan Basic Scientific Promotion Program of the Korea Science and Engineering Foundation and the Japan Society for the Promotion of Science. The author would like to acknowledge the possibility of spending his study leave at University of Oxford made possible through the Korean– Britain Government Scholarship Programme.
References 4. Conclusions In conclusion, the strengthening mechanisms, viz. the phase mixtures model and the solute concentration model, for the partially devitrified amorphous nanocomposites with fine nanoscale precipitate particles embedded in the amorphous matrix have been investigated. The phase mixtures model uses the rule of mixtures based on the volume fractions of the phases and considers the variation of solute concentration in the remaining amorphous matrix, while the solute concentration model considers the effect of solute concentration on the strength of amorphous matrix only. By investigating the devitrification phenomenon, three factors were addressed as the controlling para-
[1] Greer AL. Mater Sci Eng A 2001;304–306:68. [2] Inoue A, Ohtera K, Tsai AP, Matsumoto T. Jpn J Appl Phys 1988;27:L479. [3] Kim YH, Inoue A, Matsumoto T. Mater Trans JIM 1990;31:747. [4] Inoue A. Acta Mater 2000;48:279. [5] Eckert J, Kuhn U, Mattern N, Reger-Leonhard A, Heilmaier M. Scripta Mater 2001;44:1587. [6] Scanlon MR, Cammarata RC. J Appl Phys 1994;76: 3387. [7] Kim HS. Mater Sci Eng 2000;289A:30. [8] Kim HS, Bush MB, Estrin Y. Mater Sci Eng A 2000;276: 175. [9] Kim HS, Estrin Y, Bush MB. Z Metallkd 1999;90: 863. [10] Oh S-T, Sekino T, Niihara K. Processing and mechanical properties of alumina matrix copper nanocomposites. In: Niihara K, Hirano S, Kanzaki S, Komeya K, Morinaga K,
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[11] [12] [13] [14]
editors. 6th International Symposium on Ceramic Materials and Components for Engines, Arita, Japan, 1997. p. 887–91. Kim HS, Warren PJ, Cantor B, Lee HR. Nanostruct Mater 1999;11:241. Kim HS, Hong SI. Acta Mater 1999;47:327. Kim HS. Mater Sci Eng A 2001;304–306:327. Inoue A, Zhang T, Kim YH. Mater Trans JIM 1997;38: 749.
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[15] Han TK, Kim SJ, Yang YS, Inoue A, Kim YH, Kim IB. Met Mater Int 2001;7:91. [16] Murty BS, Hono K. Mater Sci Eng A 2001;312:253. [17] Inoue A, Zhang T, Saida J, Matsushita M. Mater Trans JIM 2000;41:1511. [18] Kim HS, Suryanarayana C, Kim S-J, Chun BS. Powder Metall 1998;41:217. [19] Zhong ZC, Jiang XY, Greer AL. Phil Mag 1997;76:505. [20] Chio YT. Machine Mater 1995;7:81.
Strengthening mechanisms of Zr-based devitrified amorphous alloy nanocomposites Hyoung Seop Kim
*
Department of Metallurgical Engineering, Chungnam National University, Taejon 305-764, South Korea Received 5 March 2002; received in revised form 30 April 2002; accepted 2 August 2002
Abstract Devitrified amorphous alloy nanocomposites with nanoscale precipitates are regarded as new prospective structural materials with superior mechanical properties such as high strength and shear resistance. However, the strengthening mechanism of the devitrified amorphous nanocomposites has not been clearly elucidated. In order to analyse the strengthening behaviour of the partially devitrified amorphous alloys, the change in solute concentration of Zr-based alloys during the devitrification process by heat treatment was investigated. It was found that the solute concentration of the remaining amorphous matrix increases during the devitrification when the solute concentration of the initial amorphous alloy is higher than that of the precipitate, such as Zr2 Cu precipitate from Zr60 Cu20 Ni10 Pd10 alloy. On the other hand, the solute is diluted in the remaining amorphous matrix during the devitrification when the solute concentration of the initial amorphous alloy is lower than that of the precipitate, such as Zr2 Cu precipitate from Zr70 Cu10 Ni10 Pd10 alloy. Investigating this solute concentration change and the associated mechanical properties shows that it is the phase mixtures model, and not the solute concentration model, that provides an adequate description of the devitrified amorphous nanocomposites. Ó 2003 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved. Keywords: Metallic glasses; Composite; Strengthening mechanism; Mechanical properties
1. Introduction Partially devitrified amorphous alloys, referred to as amorphous nanocomposites, are of great interest for their superior mechanical properties such as high strength and shear deformation resistance due to their very fine microstructure [1]. For example, it has been reported that Al-based amorphous alloys exhibit high tensile strength
*
Tel.: +82-42821-6596; fax: +82-42-822-5850. E-mail address: [email protected] (H.S. Kim).
above 1000 MPa [2] and a nanocomposite composed of a homogeneous dispersion of nanoscale Al particles within the remaining amorphous matrix can significantly increase the tensile strength up to about 1.5 times as high as that of the corresponding amorphous single phase alloy [3]. The increase in the strength has been reported in most of devitrified amorphous alloy systems, e.g. Zrbased alloys [4,5]. Several contradictory explanations for the strengthening mechanism in these nanocomposite amorphous materials have been proposed. InoueÕs group [3,4] suggested that the increase of strength
1359-6462/03/$ - see front matter Ó 2003 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved. PII: S 1 3 5 9 - 6 4 6 2 ( 0 2 ) 0 0 3 4 4 - 5
44
H.S. Kim / Scripta Materialia 48 (2003) 43–49
is due to an enhancement of the resistance to shear deformation caused by the nanoscale precipitate particles. Greer [1] attributed the strengthening of devitrified amorphous alloys to the solute enrichment of the remaining amorphous phase. He also concluded that the hardness would be simply that of the glassy matrix, referring to the Scanlon and CammarataÕs experimental results [6] that the hardness values of magnetron cosputtered nanocomposite Ag–Al2 O3 granular metal films did not follow the rule of mixtures type behaviour. However, a discontinuity in the rate of change of hardness in the Ag–Al2 O3 nanocomposite with metal volume fraction near the percolation threshold could be an artefact of the measurement technique, as Scanlon and Cammarata discussed the elastic modulii of the nanocomposites. In addition, there were several considerable factors affecting the overall mechanical properties of composites, such as a crystal size effect and an interface debonding effect due to oxide phases, in Scanlon and CammarataÕs experiments. Meanwhile, from the mechanics point of view, the effective hardness of particulate composites could be described better by iso-stress type than iso-strain type behaviour [7]. However, whether the rule of mixtures of isostress or iso-strain type holds does not overturn the fact that the overall mechanical properties of nanocomposites are determined by the properties of every component; the more the fraction of the harder component is, the higher is the overall strength. It should also be noted that there is much experimental and theoretical evidence reporting that the mechanical properties of the nanocomposites do follow the rule of mixtures type behaviour [8–10]. Recently, the present author [11–13] has proposed a phase mixtures model in order to describe quantitatively the strengthening behaviour and the ductile–brittle transition behaviour of the partially devitrified amorphous Al–Ni–Y alloys. In the phase mixtures model, the partially devitrified amorphous alloy is regarded as a mixture of a precipitate particle phase and a remaining amorphous matrix phase with varying solute concentration; the overall mechanical properties of the mixtures are described by the rule of mixtures based on the volume fractions of each phase.
Understanding the strengthening mechanism of the partially devitrified amorphous alloys is very important not only for better development of amorphous alloys but also for developing optimum devitrification processes for the amorphous nanocomposites. However, the validity of the solute concentration model and the phase mixtures model is not clear. This is because the calculated results by both the solute enrichment model and the phase mixtures model have accidentally been in reasonably good accord with the experimental data of Al–Ni–Y alloys [1,13]. This accord is because the hardness increments due to the nanoparticle precipitation and due to the solute enrichment were similar in Al–Ni–Y alloys. Hence, it is necessary to elucidate the valid mechanism for the strengthening behaviour of the partially devitrified amorphous composites by means of other experimental and/or theoretical approaches. In the present study, the author devised an experimental scheme using Zr-based alloys of solute enrichment and solute dilution systems during devitrification in order to gain a basis for assessing the validity of the strengthening mechanism of the partially devitrified amorphous alloy nanocomposites.
2. Hardening models As heat treatment proceeds, solute elements rejected from the precipitates during heat treatment are distributed in the remaining amorphous matrix leading to a change in the solute concentration there (i.e. solute enrichment or dilution), depending on the relative composition of the particles and the matrix. Fig. 1 shows a schematic of the composition changes of the partially devitrified amorphous alloy after heat treatment of the fully amorphous alloy. The nanoscale precipitates can be pure metal [3], alloys [4,5] and quasi-crystalline icosahedral phase (I-phase) [14–17]. The devitrification process can be classified into (i) solute enriching system, (ii) constant solute concentration system and (iii) solute diluting system according to the variations in the solute concentration during heat treatment. In other words, the solute composition of the amorphous matrix increases,
H.S. Kim / Scripta Materialia 48 (2003) 43–49
45
Fig. 1. Schematic model of partially devitrified amorphous alloys having precipitated particles embedded in remaining amorphous matrix and schematic concentration profile of solute; (a) solute enriching alloy, (b) constant solute alloy and (c) solute diluting alloy systems.
remains constant or decreases when the concentration of the precipitate is higher than, equal to or lower than the concentration of the initial amorphous alloys, respectively. Examples of the solute enriching systems are Al–Ni–Y alloys with pure Al precipitates, Zr–Cu–Al–Ni and Zr–Cu–Al with Zr2 Cu precipitates [4,5] and Zr–Al–Cu–Pd [4] with Zr2 (Cu,Pd). Examples of the constant solute concentration systems are Zr–Pd [16] with quasicrystalline icosahedral (I) phase precipitates and Zr–Al–Ni–Cu–Ag and Zr–Al–Ni–Cu–Pd [17] with I-phase precipitates. Finally, examples of solute diluting systems are Zr–Al–Ni–Cu–Ag [14,15] with Zr3 (Al,Ag)2 precipitates and Zr–Cu–Al–Ni and Zr–Cu–Al with Zr2 Cu precipitates [4,5]. The composition of the amorphous matrix will change as the volume fraction of the particles increases during microstructural evolution. The composition changes of the amorphous alloy matrix in Zr0:65 Al0:075 Ni0:1 Cu0:125 Ag0:05 and Zr–Al–Cu–Pd alloy systems can be obtained using the following reaction equations (Eqs. (1) and (2)) respectively.
Zr65 Al7:5 Ni10 Cu12:5 Ag5 ! fI-phase ðI-phaseÞ þ ð1 fI-phase ÞZr65 Al7:5 Ni10 Cu12:5 Ag5 ; Zr1CAl CCu CPd AlCAl CuCCu PdCPd !
ð1Þ
fZr2 Cu Zr2 Cu 3
þ ð1 fZr2 Cu ÞZr123fZr Cu CAl CCu CPd 2
1fZr Cu 2
Al
CAl 1fZr Cu 2
CuCCu 13fZr
2 Cu 1fZr Cu 2
Pd
CPd 1fZr Cu 2
;
ð2Þ
where C and f represent initial concentrations of elements and volume fraction of particles, respectively. Fig. 2 shows the composition changes with volume fractions of particles in (a) Zr0:65 Al0:075 Ni0:1 Cu0:125 Ag0:05 and (b) Zr–Al–Cu–Pd systems. In Zr0:65 Al0:075 Ni0:1 Cu0:125 Ag0:05 alloy (Fig. 2(a)) the icosahedral phase (I-phase) particles precipitate. The analytical compositions of the I-phase of 20–30 nm and in the amorphous phase of the Zr65 Al7:5 Ni10 Cu7:5 Ag10 amorphous alloy obtained
Fig. 2. Variation of solute concentration during devitrification; (a) constant concentration alloy and (b) solute enriching alloy and solute diluting alloy systems.
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H.S. Kim / Scripta Materialia 48 (2003) 43–49
by the nanobeam energy dispersive X-ray spectroscopy technique were the same, indicating that the precipitation of the I-phase takes place by the polymorphous mode without redistribution of alloy components [17]. Hence, the compositions of the initial alloy, I-phase precipitate and the remaining amorphous matrix are all the same. In Zr–Al–Cu–Pd alloys (Fig. 2(b)) Zr2 Cu particles are precipitates. In this case, the solute concentration of the remaining amorphous matrix increases or decreases according to Eq. (2), when the initial solute concentration is higher or lower than 33.3% (@Cu concentration in Zr2 Cu particle), respectively. In the phase mixtures model the overall strength of the mixture reff can be described by the rule of mixtures based on the volume fractions of each phase (Eq. (3)) while the solute concentration model, in which the overall strength would be simply that of the remaining amorphous matrix, is given by Eq. (4): reff ¼ fp rp þ fam ram ðCÞ;
ð3Þ
reff ¼ ram ðCÞ;
ð4Þ
where r and f refer to strength and volume fraction of each phase. The subscripts am and p refer to amorphous matrix phase and precipitate particle phase, respectively. C is the solute concentration of the amorphous phase, which depends on the initial composition, the volume fraction and the composition of the precipitate. The rule of mixtures based on the volume fraction of each phase in the phase mixtures model agrees well with the results of finite element analysis of the unit cell model [18] since there is no special interaction between the particles and the matrix, except for the force and energy balances. The necessary parameters for the phase mixtures model are the mechanical properties and the volume fraction of each phase.
3. Comparison with experimental data and discussion Hardness variations of the partially devitrified amorphous alloys can be analyzed by using the solute concentration model (Eq. (4)) or the phase
mixtures model (Eq. (3)) associated with the variation of the solute concentration of the remaining amorphous phase with particle volume fraction. Since the goal of this paper is to identify the valid model for the strengthening mechanism of the partially devitrified amorphous nanocomposites, one should find the suitable alloy systems which can make apparent difference in strength between the two models. The possible issues for obtaining different strengthening (or softening) responses during devitrification are (i) the strength of precipitate particles as compared to the amorphous matrix; whether the particle is harder or softer than the matrix, (ii) the strength variation of the amorphous matrix with solute concentration; whether the amorphous alloy is Ôsolution hardeningÕ or Ôsolution softeningÕ material, and (iii) variation of solute concentration in the remaining amorphous matrix with devitrification; whether the concentration is ÔenrichingÕ or ÔdilutingÕ during devitrification. In other words, (i) if the precipitate is softer than the amorphous matrix in the solution hardening and solute enriching alloy system, (ii) if the amorphous alloy is a solution softening system in the hard particle precipitating and solute enriching system, and (iii) if the amorphous matrix is diluted during devitrification in hard particle precipitating and solution hardening system, the hardness of the devitrified nanocomposite increasing or decreasing according to the solute concentration model or the phase mixtures model, respectively. Therefore, by investigating one of the above three cases, the valid strengthening mechanism can be clearly proven, as the predicted strength of the devitrified nanocomposite should exhibit opposite trends for the two strengthening models under discussion. With respect to the strength of particles in light of the above three categories, the hardness of nanoscale precipitate particles is usually higher than that of the amorphous matrix. This is because the size of the crystalline particles in nanocomposites is so small that dislocations or any defects cannot be active within a particle so that it can be regarded as a perfectly elastic material. For example, the hardness of nanocrystalline Al particle taken from the theoretical strength of a perfect crystal is about 8 GPa [7], which is higher than
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that of amorphous Al–Ni–Y alloys (1–5 GPa). Of course, the strength of the nanoscale particle could decrease by its growth. Concerning the second factor (i.e. solution hardening or weakening of amorphous alloys), in general, the strength of the amorphous alloys increases with solute composition––Ôsolution hardeningÕ alloys. In the fully amorphous alloys of Al–Ni–Y [2,3,19,20] and Zr– Ti–Al–Ni–Cu from reference [10], the hardness increases almost linearly as the solute concentration of the amorphous matrix increases. Therefore, the main factor controlling the trend between the strengthening and the softening of the devitrified amorphous alloys during devitrification should be the variation of the solute concentration in this process. Fig. 3 shows the trends of hardness of the partially devitrified amorphous alloy nanocomposites with volume fraction of hard nanoscale particles in various solution hardening amorphous alloys; Fig. 3(a) and (b) correspond to the solute concentration model and the phase mixtures model, respectively. For the solute concentration model (Fig. 3(a)) the predicted hardness of the nanocomposite increases, remains constant or decreases with the volume fraction of nanoparticles regardless of the relative strength of the particles compared to the amorphous matrix, when the solute concentration of amorphous matrix increases, remains constant or decreases during devitrification, respectively. On the other hand, the hardness predicted by the phase mixtures model of the partially devitrified nanocomposite depends both on the hardness of particles relative to the matrix
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and on the solute concentration of amorphous matrix. Since the nanoscale precipitate particle is harder than the amorphous phase and usually the strengthening effect by the nanoscale particle is higher than the matrix strengthening or weakening effect, the hardness of the devitrified amorphous nanocomposite increases in all amorphous alloy systems. Comparing Fig. 3(a) to (b), it can be found that the most evident difference between the solute concentration model and the phase mixtures model occurs in the solute diluting alloy system. In order to assess the validity of the two strengthening models, experimental hardness data against volume fraction of precipitate were compiled from literature on Zr-based amorphous alloys (see Fig. 4). The Zr-based amorphous alloys
Fig. 4. Experimental hardness values from reference as a function of the volume fraction of precipitate particles for various Zr-based alloy compositions.
Fig. 3. The theoretical hardness of amorphous alloy with the volume fraction of precipitate particles; (a) solute concentration model and (b) phase mixtures model.
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represented in Fig. 4 show dramatic results, in that all of the solute concentration enriching (ZrAlCuPd þ Zr2 (Cu,Pd)), the constant solute concentration (ZrAlNiCuAg þ I-phase) and the solute diluting (ZrAlCuAg þ Zr3 Al2 ) alloy systems exhibit strengthening behaviour during devitrification. It should be stressed again that the solute concentration model predicts the strengthening, constant hardness and weakening behaviour during the devitrification processes of (ZrAlCuPd þ Zr2 (Cu,Pd)), (ZrAlNiCuAg þ I-phase) and (ZrAlCuAg þ Zr3 Al2 ) alloy systems, respectively, while the phase mixtures model predicts hardening behaviour for all alloys. From the above strong piece of experimental evidence for Zr-based amorphous alloys, the validity of the phase mixtures model of strengthening of devitrified amorphous nanocomposites seems to be confirmed. From the point of view of the verification of the model developed, more experimental evidence is needed. Indeed, the phase identification of the particle Zr3 Al2 in ZrAlNiCuAg is in controversy, whereas the I-phase in ZrAlNiCuAg looks reliable. Therefore, the experimental data of the same alloy components with different composition, e.g. ZrAlCuPd and ZrAlCuPd, could be useful for assessing the validity of the two competing strengthening models. Experimental research on these amorphous alloys is underway.
meters, i.e. (i) the strength of precipitate particles as compared to the amorphous matrix, (ii) the variation of strength of amorphous matrix with solute concentration and (iii) the variation of solute concentration of the remaining amorphous matrix with devitrification. A comparison of the hardness variation during the devitrification with the two competing models of strengthening leads to the conclusion that the phase mixtures model, rather than the solute concentration model, can explain the increase in hardness of the devitrified nanocomposite of the constant and diluting solute concentration systems of Zr-based amorphous alloy.
Acknowledgements This work was supported by grant number: 2001-6-301-05-2 from Joint Research Project under the Korea–Japan Basic Scientific Promotion Program of the Korea Science and Engineering Foundation and the Japan Society for the Promotion of Science. The author would like to acknowledge the possibility of spending his study leave at University of Oxford made possible through the Korean– Britain Government Scholarship Programme.
References 4. Conclusions In conclusion, the strengthening mechanisms, viz. the phase mixtures model and the solute concentration model, for the partially devitrified amorphous nanocomposites with fine nanoscale precipitate particles embedded in the amorphous matrix have been investigated. The phase mixtures model uses the rule of mixtures based on the volume fractions of the phases and considers the variation of solute concentration in the remaining amorphous matrix, while the solute concentration model considers the effect of solute concentration on the strength of amorphous matrix only. By investigating the devitrification phenomenon, three factors were addressed as the controlling para-
[1] Greer AL. Mater Sci Eng A 2001;304–306:68. [2] Inoue A, Ohtera K, Tsai AP, Matsumoto T. Jpn J Appl Phys 1988;27:L479. [3] Kim YH, Inoue A, Matsumoto T. Mater Trans JIM 1990;31:747. [4] Inoue A. Acta Mater 2000;48:279. [5] Eckert J, Kuhn U, Mattern N, Reger-Leonhard A, Heilmaier M. Scripta Mater 2001;44:1587. [6] Scanlon MR, Cammarata RC. J Appl Phys 1994;76: 3387. [7] Kim HS. Mater Sci Eng 2000;289A:30. [8] Kim HS, Bush MB, Estrin Y. Mater Sci Eng A 2000;276: 175. [9] Kim HS, Estrin Y, Bush MB. Z Metallkd 1999;90: 863. [10] Oh S-T, Sekino T, Niihara K. Processing and mechanical properties of alumina matrix copper nanocomposites. In: Niihara K, Hirano S, Kanzaki S, Komeya K, Morinaga K,
H.S. Kim / Scripta Materialia 48 (2003) 43–49
[11] [12] [13] [14]
editors. 6th International Symposium on Ceramic Materials and Components for Engines, Arita, Japan, 1997. p. 887–91. Kim HS, Warren PJ, Cantor B, Lee HR. Nanostruct Mater 1999;11:241. Kim HS, Hong SI. Acta Mater 1999;47:327. Kim HS. Mater Sci Eng A 2001;304–306:327. Inoue A, Zhang T, Kim YH. Mater Trans JIM 1997;38: 749.
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[15] Han TK, Kim SJ, Yang YS, Inoue A, Kim YH, Kim IB. Met Mater Int 2001;7:91. [16] Murty BS, Hono K. Mater Sci Eng A 2001;312:253. [17] Inoue A, Zhang T, Saida J, Matsushita M. Mater Trans JIM 2000;41:1511. [18] Kim HS, Suryanarayana C, Kim S-J, Chun BS. Powder Metall 1998;41:217. [19] Zhong ZC, Jiang XY, Greer AL. Phil Mag 1997;76:505. [20] Chio YT. Machine Mater 1995;7:81.