國立中山大學材料與光電科學學系 博士論文
多種二元金屬玻璃之結構相變與週期變形機制之原子模擬研究 Atomic Simulations on Phase Transformation and Cyclic Deformation
Mechanisms in Various Binary Metallic Glasses
研究生：羅友杰 撰 指導教授：黃志青 博士
中華民國 九十八 年 七 月
致謝
十年寒窗無人問，是古今讀書人共有的心路歷程，這六年來從碩士到博士研究結 束，真是相當漫長的路。首先感謝這四年來擔任我研究指導者角色的黃志青教授，老師 是一位專業學術涵養豐富、知識廣博，待人處事的手腕與身段都相當令人推崇也讓人折 服的傑出學者。我要深深感謝您在我研究遇到瓶頸，有時脾氣暴躁甚至在想法上跟您有 所衝突時，您的耐心跟愛始終看照著我，四年來真是辛苦您了。同時感謝本所謝克昌教 授、高伯威教授、化學系陳正隆教授、成大土木王雲哲教授，當任學生口試委員時，仔 細聆聽並用心給予學生許多寶貴建議，讓學生的論文得以充實完整，成就一本有參考價 值的學術論文，因此在此對老師們致上最高謝意。
接著感謝碩士班的指導者朱訓鵬教授，朱老師是中山機械系令人讚賞，學術期刊量 史無前例的豐盛，人際關係廣闊，拼勁充滿的年輕老師，是常人所不能及的。感謝您在 我念博士班期間，不吝借我使用那些貴重的計算電腦叢集，讓需要沈重計算負擔的工作 能順利完成。同時要感謝朱老師研究室一直以來的同學及歷任學弟妹，你們對我的關懷 與體貼是很大的幫助。這些人有王中鼎博士、李文頡博士、張鈞奕博士、猛雄、勝輝、
阿禾、阿耀、阿娟、文賢、暐霖、泓翔、小欽、幸蓉、家紘、鼎威、根凰。我真的很開 心與你們一起渡過這些日子。
黃老師的研究團隊是相當優秀的，這些人有洪子祥博士、張志溢博士、賴炎暉博士 與陳海明博士、周鴻昇以及名哲跟浩然，相當感謝你們四年來不斷的參與討論跟合作。
研究室未來棟梁的碩陽、柚子、哲男、大豪、阿官、顗任、逸志、捲捲跟婷婷，你們都 是我親愛的學弟妹，你們是研究室的未來。感謝鄭宇庭博士，跟你一起合作相處的日子，
一起參加英文辯論比賽，真是開心。張育誠博士，我要特別感謝你，沒有你一路的幫忙 跟支持，我恐怕早就被迫出局了！李敬仁博士，在最後一年，你回到實驗室來，使整個
研究團隊越發完整。2009 世運期間，因為有你，所以我們可以一起去看開幕去看球賽，
共享高雄人的光榮與驕傲。
另外，這四年來有不少老師陸陸續續在適當的時候給我幫忙。我要感謝遠在美國的 廖凱輝教授、聶台岡教授、Morris 教授、李莫教授以及李巨教授，感謝老師們不吝指 導我研究上的知識與觀念，我很感謝！陳維仁博士、黃爾文博士、莊志彬博士都曾參與 過討論，並給予相當寶貴的建議！開物老師一家人，小杰、馨慧、小玲也給我許多美好 的回憶與照顧，感謝你們。最後是 D.Frenkel 和 B.Smit 教授，若是沒有你們合著的那 本書，我肯定半途放棄，屍沈無涯學海了。
最後要感謝身邊一直關心我的好友跟親人。台南成大的楊安政學長，我對你的感 激，你知道的。吳清吉學長和煜聰、伯父、伯母，你們是我在南部的家人，我愛你們！
施依姿，我感謝人生有你這樣的朋友。行政大樓第一美女史麗伶大姐，感謝您這六年來 的關懷與照顧。渚晴暉老師、楊天祥老師、陳國聲老師、陳碧燕老師、楊建民老師，感 謝你們在大學時期教授我治學及人生觀念、是我生命的燈塔與警鐘，我愛你們！李若彤
（靜怡），人生中能有妳為良師益友是一種幸福。李大哥、邱婉筑（瑞柳）夫婦、李典
蓉、李尚儒，是我在高雄的家人，我愛你們！深深感謝我的奶奶 羅江碧雲女士、父親 羅 嘉仁先生、母親 蔡月鳳女士、以及所有親人，你們是我最大的依靠！最後，有許多許 多好朋友來不及提了，也謝不完。所以我要感謝主！也感謝有你們一路相伴。在博士班 最後一年，我親愛的叔叔 羅嘉賢先生，同時也是我乾爹，他在今年四月因病早逝，回 想過去他對我的關愛，我沒有報答的機會，僅以這本論文紀念他對我的支持，一位奉公 守法的台中市政府公務員。
羅友杰 謹誌 於中山大學材料與光電科學學系 中華民國九十八年七月
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Content
Content ... i
List of Tables ... v
List of Figures ... vi
Abstract ...xviii
中文摘要 ... xx
Chapter 1 Introduction and motivation ... 1
1-1 Introduction ... 1
1-2 Motivation ... 4
Chapter 2 Background and Literature Review of metallic glasses ... 7
2-1 The development of metallic glasses ... 7
2-2 Microstructures in metallic glasses ... 10
2-3 Mechanical properties ... 13
2-4 Deformation mechanisms ... 15
2-5 Fatigue properties in BMGs ... 20
Chapter 3 Background of Molecular Dynamics Simulation ... 23
3-1 Equations of motion and potential function ... 23
3-2 Ensembles ... 27
3-3 Integration of the Newtonian equation ... 29
3-4 Periodic boundary conditions ... 30
3-5 List method and cut-off radius ... 30
Chapter 4 Model and Theory ... 32
4-1 Cyclic transformation between nanocrystalline and amorphous phases in Zr based intermetallic alloys during ARB ... 32
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4-1-1 Tight-binding potential ... 32
4-1-2 Simulation model and conditions ... 33
4-1-3 Analysis methods for structural properties ... 35
4-2 Atomic simulation of vitrification transformation in Mg-Cu thin film ... 37
4-2-1 Effective-medium theory potential ... 37
4-2-2 Derivation of force for EMT potential ... 40
4-2-3 Simulation model and conditions ... 43
4-3 Cyclic loading fatigue in a binary Zr-Cu metallic glass ... 43
4-3-1 Interatomic potential used in Zr-Cu ... 43
4-3-2 Isothermal-isobaric ensemble and Nosé-Hoover Chain ... 44
4-3-3 Simulation model and conditions ... 46
4-3-4 Observation of local shear strains ... 48
Chapter 5 Simulation results ... 50
5-1 The results of phase transformation in Zr based intermetallic alloys during ARB 50 5-1-1 Morphologies of Zr-Ni and Zr-Ti during ARB cycles ... 50
5-1-2 Morphologies of pure Zr during ARB cycles ... 51
5-1-3 The results of radial distribution function (RDF) calculations for Zr-Ni, Zr-Ti, and pure Zr ... 52
5-1-4 The average coordination number and potential energy for Zr-Ni, Zr-Ti, and pure Zr ... 54
5-1-5 The results of HA analysis for Zr-Ni, Zr-Ti, and pure Zr ... 55
5-2 The simulation results of vitrification transformation in Mg-Cu Thin Film ... 58
5-2-1 Morphologies of Mg-Cu during different temperatures ... 58
5-2-2 The results of density distribution profiles for the Mg-Cu ... 59
5-3 The simulation results of cyclic loading fatigue in Zr-Cu binary amorphous alloy ... 59
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5-3-1 The simulation results for Zr50Cu50 under different cooling rates ... 59
5-3-2 The mechanical properties of monotonic tension tests at different strain rates ... 60
5-3-3 The results of structural analysis for different cyclic loading conditions ... 62
5-3-4 Potential energies for different cyclic loading conditions ... 64
5-3-5 Variations of density (dilatation) analysis for different cyclic loading conditions ... 65
5-3-6 The results of local atomic strain for different cyclic loading conditions ... 68
5-3-7 The stress-strain curves for different cyclic loading conditions... 70
Chapter 6 Discussion ... 72
6-1 The phase transformation in Zr based intermetallic alloys during ARB ... 72
6-1-1 The transformation of Zr-Ni from nanocrystalline to amorphous phase during ARB ... 72
6-1-2 The transformation of Zr-Ti from nanocrystalline to amorphous phase during ARB ... 75
6-1-3 The transformation of pure Zr from nanocrystalline to amorphous phase during ARB ... 76
6-2 Vitrification transformation in Mg-Cu thin film ... 78
6-3 Cyclic loading fatigue in Zr-Cu binary amorphous alloy ... 80
6-3-1 The crystallization in cyclic loading fatigue ... 80
6-3-2 The structural relaxation in cyclic loading fatigue ... 81
6-3-3 Microscopic deformation in cyclic loading ... 82
6-3-4 The phenomenon of dynamic recovery ... 84
6-3-5 Fatigue softening or hardening in current model ... 87
6-4 Short discussion on the comparison of MD simulation and experimental results .. 88
Chapter 7 Conclusions ... 90
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Reference ... 94 Tables ... 106 Figures ... 110
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List of Tables
Table 2-1 Bulk metallic glasses and their developed years ... 106
Table 2-2 Summary of yield and ultimate tensile strengths, fatigue-endurance limits at 107 cycles, and fatigue ratios based on the stress amplitudes of Zr-based BMGs and various crystalline alloys from the current study and literature reports. Test configuration refers to the fatigue-test geometry and R is the stress ratio of σmin to σmax ... 107
Table 3-1 Parameters for Lennard-Jones potential for inert molecules ... 107
Table 4-1 Parameters used in the tight-binding potential ... 108
Table 4-2 Effective medium potential parameters ... 109
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List of Figures
Fig. 2-1. (a) The fivefold symmetry and an icosahedral arrangement are shown with the brighter spheres (b) A face-centered-cubic arrangement. The same pair will become the hcp arrangement if the top close-packed plane is shifted to take the same type of position as the bottom plane ... 110 Fig. 2-2. (a) HREM image taken from an annealed specimen (773 K), together with
nanobeam electron-diffraction patterns in (b), (c), and (d). Simulated HREM image is also shown in the inset of (a). (e) HREM image of minor regions in the specimen annealed up to 773 K ... 111 Fig. 2-3. The portions of a single cluster unit cell for the dense cluster packing model. (a) A two-dimensional representation of a dense cluster-packing structure in a (100) plane of clusters illustrating the features of interpenetrating clusters and efficient atomic packing around each solute. (b) A portion of a cluster unit cell of model in [12109 ] system representing a Zr-(Al,Ti)-(Cu,Ni)-Be alloy. The α sites are occupied by blue spheres, the β sites are occupied by purple spheres and the γ sites are occupied by orange spheres. Pink Zr solvent spheres form relaxed icosahedra around each α solute ... 112 Fig. 2-4. The coordination number distribution of the solute atoms in several representative metallic glasses obtained from ab initio calculations ... 113 Fig. 2-5. The packing of the solute-centred quasi-equivalent clusters, showing their medium range order. (a) The cluster common-neighbour analysis showing that the local clusters in the metallic glasses exhibit icosahedral type ordering. The typical cluster connections, exhibiting the fivefold symmetry, are detailed for Ni81B19, Ni80P20 and Zr84Pt16 in (b), (c) and (d), respectively ... 114
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Fig. 2-6. (a) The structure of the as-cast bulk metallic glasses after reverse Monte Carlo refinement, (b) clusters of imperfect icosahedral and cubic forms extracted from……… ... 115 Fig. 2-7. Relationship between tensile strength, Young’s modulus, and Vickers hardness for
bulk glassy alloys. The data of crystalline metallic alloys are also shown for comparison ... 116 Fig. 2-8. (a) Failure surface from a tensile sample which exhibited cup and cone morphology.
The droplets are indicative of localized melting reprinted from. (b) Typical vein pattern on the fracture surface of a ductile Pd30Ni50P20 bulk metallic glass subjected to compression testing ... 117 Fig. 2-9. (a) SEM backscattered electron image of in situ composite microstructure. (Inset:
X-ray diffraction pattern for Zr-Ti-Nb in situ composite). (b) Compressive stress strain curve for cylindrical in situ composite specimen ... 118 Fig. 2-10. (a) Stress-strain curve of amorphous monolithic Pt-Cu-Ni-P. The curve was
determined under quasistatic compression of a bar shaped sample. The material undergoes about 20% plastic deformation before failure. (b) Optical micrograph of the Pt-Cu-Ni-P BMG which was bent over a mandrel of radius 6.35 mm, which corresponds to a strain of about 14 %. ... 119 Fig. 2-11. SEM micrograph showing shear bands near a notch in a bend-test specimen coated with tin ... 120 Fig. 2-12. Illustration of free-volume for an atom to move into a open space ... 120 Fig. 2-13. A two dimensional schematic of a shear transformation zone deformation process in an amorphous metal. (a) A two-dimensional schematic of a shear transformation zone in an amorphous metal. A shear displacement occurs to accommodate an applied shear stress τ, with the darker upper atoms moving with respect to the lower atoms. (b) The applied shear stress t necessary to maintain a given atomic
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shear displacement, normalized by the maximum value of τ at σn = 0, τ0 ... 121 Fig. 2-14. Plot of effective temperature χ as a function of time for (a) an STZ solution for δχ0
= 0.01 that localizes and (b) an STZ solution for δχ0 = 0.001 that does not localize.
Dashed vertical lines correspond to calculated values for the time the material first reaches the yield stress, τy, and the time the material reaches its maximum stress τmax ... 122 Fig. 2-15. The local shear strain distribution at different mean sample strains, (a) 4.10%, (b)
12.28%, (c) 20.44%, and (d) 40.81%. The color scheme reflects the change in the rotation angle of the nearest atomic bonds. Only a small section containing the shear band and its immediate vicinity is shown in the sample containing 288000 atoms arranged in a 49.73×4.07×97.60 nm3 rectangular box ... 123 Fig. 2-16. The Voronoi volume distributions for (a) Cu and (b) Zr atoms at different mean
sample shear strains (%). The lower dotted lines are the Voronoi volumes of the undeformed samples at 300 K and the upper dotted lines are the volumes of the undercooled liquid at Tg. The changes due to the finite size at the sample boundaries can be seen ... 123 Fig. 2-17. Aged-rejuvenation-glue-liquid (ARGL) model of shear band in BMGs. The
shading represents temperature ... 124 Fig. 2-18. GSF γ(δ) of a glass as a function of a sharp displacement discontinuity δ. The solid curve illustrates the behavior without any recovery process. The dashed curve shows that, as time increases, recovery occurs and the energy traps get deeper . 124 Fig. 2-19. Comparison between glass-transition temperature and calculated shear-band
temperature at fracture strength for different bulk metallic glasses ... 125 Fig. 2-20. A proposed fatigue-crack-initiation mechanism: (a) formation of shear band, (b)
formation of shear-off step, and (c) microcrack initiation ... 126 Fig. 2-21. The fatigue fracture surface of the Zr50Al10Cu40 specimen was tested at σmax = 1. 2
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GPa in vacuum. The whole fatigue fracture surface consisted of four main regions:
the fatigue-crack-initiation, crackpropagation, final-fast-fracture, and apparent-melting areas ... 126 Fig. 2-22. Schematic illustrating how overall alteration of the fatigue and fracture properties in BMGs can be obtained by concurrently controlling: (a) residual stresses to improve both the fatigue threshold, KTH, and the fracture toughness, KIC, and (b) the free volume to improve the fatigue limit but degrade the fracture toughness, KIC ... 127 Fig. 3-1. Form of the Lennard-Jones (12-6) potential which describes the interaction of two
inert gas atoms ... 128 Fig. 3-2. The energy of the atom i is determined by the local electron density at the position of i atom and the ρi describes the contribution to the electronic density at the site of the atom i from all atoms j ... 129 Fig. 3-3. Periodic boundary conditions. As a particle moves out of the simulation box, an
image particle moves in to replace it. In calculating particle interactions within the cutoff range, both real and image neighbors are included ... 130 Fig. 3-4. The Verlet list on its construction, later, and too late. The potential cutoff range
within rc (solid circle), and the list range within rv (dashed circle), are indicated. The list must be reconstructed before particles originally outside the list range (black) have penetrated the potential cutoff sphere... 131 Fig. 3-5. The cell structure. The potential cutoff range is indicated. In searching for
neighbours of an atom, it is only necessary to examine the atom's own cell, and its nearest-neighbour cells (shaded) ... 131 Fig. 3-6. Flow chart of molecular dynamics simulation ... 132 Fig. 4-1. A schematic representation of the simulated strain-and-stack process: (a) two of
polycrystalline elemental bilayer structures (b) are elongated to twice its original
x
length and half its original thickness and (c) subsequently halved along the solid line and stacked atop itself. The inset (d) shows a typical atomic structure at their interfaces ... 133 Fig. 4-2. Two decomposition methods for parallel MD: (a) is particle decomposition method, and (b) is spatial decomposition method; each forty particles are allotted to 4 processors ... 134 Fig. 4-3. The schematic drawing of the related HA pairs ... 135 Fig. 4-4. Different type of clusters formed in crystals and glasses ... 135 Fig. 4-5. The scheme of the initial Mg-Cu simulation model. The blue particles represent Mg atoms and red particles represent Cu atoms ... 136 Fig. 4-6 (a) Density map V, position P(x) and velocity P(V) distribution functions obtained from Nosé-Hoover dynamics of a harmonic oscillator (dotted line). The solid line is the exact result. (b) Those three properties of a harmonic oscillator obtained from the Nosé-Hoover chain dynamics (dotted line). The solid line is the exact result . 137 Fig. 4-7. Fatigue-loading conditions during MD simulations of Zr-Cu metallic glass: (a) the
stress-control mode for a tension fatigue experiment at σmax = 2 GPa, and (b) the strain-control mode for a tension-compression fatigue experiment at εmax = 10%
(showing the induced stress amplitude ... 138 Fig. 4-8. Illustration of simulation model in cyclic loading fatigue ... 138 Fig. 5-1. The 2-D sliced plots parallel to the xz plane of the Zr-Ni metallic layers for (a) Ni layer and (b) Zr layer, rrespectively. (c) Schematic illustration of the transformation mechanism via interdiffusion, and (d) the interface between Ni grain (blue particles) and Zr grain (red particles) ... 139 Fig. 5-2. The microstructural evolution and the associated two-dimensional Fourier transform of bi-layered Zr32Ni68 model subjected to various ARB cycles: (a) initial state, (b) 1, (c) 2, (d) 3, (e) 4, (f) 5 and (g) 6 ARB cycles ... 140
xi
Fig. 5-3. The microstructural evolution and the associated two-dimensional Fourier transform of the bi-layered Zr50Ni50 model subjected to (a) 8 and (b) 9 F&R cycles ... 141 Fig. 5-4. The microstructural evolution and the associated two-dimensional Fourier transform of the bi-layered Zr50Ti50 model subjected to various ARB cycles: (a) initial state, (b) 1, (c) 4, and (d) 6 F&R cycles ... 142 Fig. 5-5. Microstructures of pure Zr upon the end of second cycle at the condition of strain rate at 8.35×108 s-1, (a) composed of 1421 HA pairs, (b) composed of 1422 HA pairs, (c) composed of 1321 HA pairs, and (d) composed of 1431, 1541, and 1551 HA pairs ... 143 Fig. 5-6. Microstructures of pure Zr upon the end of 7th cycle at the condition of strain rate at 8.35×108 s-1, (a) composed of 1421 HA pairs, (b) composed of 1422 HA pairs, (c) composed of 1321 HA pairs, and (d) composed of 1431, 1541, and 1551 HA pairs ... 144 Fig. 5-7. Microstructures of pure Zr upon the end of 7th cycle at the condition of strain rate at
8.35×108 s-1, (a) composed of 1421 HA pairs, (b) composed of 1422 HA pairs, (c) composed of 1321 HA pairs, and (d) composed of 1431, 1541, and 1551 HA pairs.
Inset in the corner at (c) show an amplification of twin plan in the Zr matrix ... 145 Fig. 5-8. microstructures of pure Zr upon the end of first cycle at the condition of strain rate at 9.25×109 s-1, (a) composed of 1421 HA pairs, (b) composed of 1422 HA pairs, (c) composed of 1321 and 1551 HA pairs (dominated in the icosahedrons), and (d) composed of 1431, 1541, and 1551 HA pairs ... 146 Fig. 5-9. microstructures of pure Zr upon the end of 13th cycle at the condition of strain rate at 9.25×109 s-1, (a) composed of 1421 HA pairs, (b) composed of 1422 HA pairs, (c) composed of 1321 and 1551 HA pairs (dominated in the icosahedrons), and (d) composed of 1431, 1541, and 1551 HA pairs ... 147 Fig. 5-10. An uncertain re-crystallized-like Zr phase whose size approach to 2 nm is
xii
identified in the matrix at the end of 14th cycle ... 148 Fig. 5-11. PRDF of the Zr-Ni alloys during different ARB cycles: (a) Ni-Ni pair, (b) Zr-Zr
pair, and (c) Zr-Ni pair. R is referred to the real-space atomic distance. The numbers in the figures are referred to the ARB cycle passes ... 149 Fig. 5-12. The variation of (a) RDF and (b) volume-based number density distribution of the Zr32Ni68 alloy subjected to various F&R cycles ... 150 Fig. 5-13. The variations of the HA indices of the Zr-Ti alloys during different ARB cycles: (a)
1421 and 1422, (b) 1431, 1541, and 1551, and (c) 1441, 1661, and 1321 ... 151 Fig. 5-14. The simulated RDF curves for the pure Zr bi-layers subjected to ARB with (a) a higher rolling speed of 0.025 nm/fs, and (b) a lower rolling speed of 0.001 nm/fs.
The two layers of the front case become amorphous after 6 ARB cycles ... 152 Fig. 5-15. The variation of potential energy of (a) Zr32Ni68 and (b) Zr50Ti50 alloys subjected to different F&R cycles ... 153 Fig. 5-16. The variation of potential energy of pure Zr alloys subjected to different F&R
cycles... 153 Fig. 5-17. The variation of average coordination number of the Zr-Ni alloy subjected to
different ARB cycles ... 154 Fig. 5-18. The variation of average coordination number of the Zr-Ti alloys subjected to
different ARB cycles ... 154 Fig. 5-19. The variation of average coordination number of the pure Zr alloys for the different rolling speed subjected to different ARB cycles ... 155 Fig. 5-20. Variations of the HA indices of the Zr-Ni alloys during different ARB cycles: (a) 1421 and 1422, (b) 1431, 1541, and 1551, and (c) 1441, 1661, and 1321 ... 156 Fig. 5-21. The variations of the HA indices of the Zr-Ti alloys during different ARB cycles: (a)
1421 and 1422, (b) 1431, 1541, and 1551, and (c) 1441, 1661, and 1321 ... 157 Fig. 5-22. The variations of the HA indices of the pure Zr during different ARB cycles at a
xiii
higher speed of 0.025 nm/fs (strain rate of 9.25×109 s-1): (a) 1421 and 1422, (b) 1431, 1541, and 1551, and (c) 1441, 1661, and 1321 ... 158 Fig. 5-23. The variations of the HA indices of the pure Zr during different ARB cycles at a lower speed of 0.001 nm/fs (strain rate of 8.35×108 s-1): (a) 1421 and 1422, (b) 1431, 1541, and 1551, and (c) 1441, 1661, and 1321 ... 159 Fig. 5-24. The schemes of the projections of atomic positions annealed at (a) 300 K, (b) 413 K, and (c) 500 K. The red circle represents Cu and blue circle represents Mg ... 160 Fig. 5-25. The density profiles ρMg(z) of Mg species (green line) and ρCu(z) of Cu (red line) along the z axis at three temperature conditions corresponding to Fig. 5-24 (a), (b), and (c), respectively ... 161 Fig. 5-26. Volume versus temperature curves for Zr50Cu50 obtained by quenching the sample model at four cooling rates from 2,000 down to 300 K ... 162 Fig. 5-27. The curves of different bond pairs of PRDF for the Zr50Cu50 amorphous alloy as quenched before fatigue loading at 300 K ... 162 Fig. 5-28. Potential energy versus strain curves for the three different strain conditions during the monotonic deformation tests ... 163 Fig. 5-29. Density versus strain curves for the three different strain conditions during the
monotonic deformation tests ... 163 Fig. 5-30. The stress-strain curves for three strain control conditions during the
monotonic test ... 164 Fig. 5-31. 2D sliced plots extracting from the 3D simulated results for the local strain
distribution of the monotonic strain-control at different strains (strain rate of 5 × 109 s-1): (a) 5 %, (b) 10 %, and (c) 30 %. The color scheme represents the degree of the atomic-bond rotation, or shear strain. The numbers of the horizontal and vertical axes are in the unit of angstrom ... 164 Fig. 5-32. 2D sliced plots extracting from the 3D simulated results for the local strain
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distribution of the monotonic strain-control at different strains (strain rate of 2.5 × 109 s-1): (a) 5 %, (b) 10 %, and (c) 20 %. The color scheme represents the degree of the atomic-bond rotation, or shear strain. The numbers of the horizontal and vertical axes are in the unit of angstrom ... 165 Fig. 5-33. The curves of different bond pairs of PRDF for the Zr50Cu50 amorphous alloy at 300 K after 100 cycles at σmax = 2 GPa under the stress-control mode ... 165 Fig. 5-34. Variations of the HA indices of the Zr-Cu amorphous alloy during different loading cycles: (a) 1421 and 1422, (b) 1431, 1541, and 1551, and (c) 1441, 1661, and 1321 under compression-compression stress-control at σmax = 1 GPa ... 166 Fig. 5-35. Variations of the HA indices of the Zr-Cu amorphous alloy during different loading cycles: (a) 1421 and 1422, (b) 1431, 1541, and 1551, and (c) 1441, 1661, and 1321 under tension-tension stress-control at σmax = 1 GPa ... 167 Fig. 5-36. Variations of the HA indices of the Zr-Cu amorphous alloy as a function of loading cycles: (a) 1421 and 1422, (b) 1321, 1441, and 1661, and (c) 1431, 1541, and 1551 under the cyclic strain-control mode at εmax = 10% ... 168 Fig. 5-37. The scheme of the superimposed projections of close-packed atoms at (a)
compression-compression, (b) tension-tension at σmax = 1 GPa, respectively. The blue circle represents FCC atoms and green circle represents HCP atoms. The superimposed projections of the B2 atoms during the stress-control tensile mode at σmax = 2 GPa are shown in (c). The blue circles represent the central atoms, and red circles represent the surrounding atoms of a B2 structure. Note that this scheme represents the superimposition of all occurrences of the those atoms that have occurred over the whole 50 cycles ... 169 Fig. 5-38. The Comparison of potential energies between tension and compression of cyclic loading under stress-control at σmax = 1 GPa ... 170 Fig. 5-39. The Comparison of potential energies between tension and compression of cyclic
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loading under stress-control at σmax = 2 GPa ... 170 Fig. 5-40. The Comparison of potential energies between long and short periods for the cyclic stress-control at σmax = 2 GPa. The equilibrium time for long period is twice as much as short one... 170 Fig. 5-40. The Comparison of potential energies between tension and compression of cyclic loading under strain-control at strain rate of 2.5 × 1010 s-1 ... 171 Fig. 5-41. The comparison of potential energies of cyclic loading under strain-control among
three different strain ranges ... 171 Fig. 5-42. Variations of the density as a function of the fatigue-time step at different loading modes for stress-control loading at σmax = 1 GPa. The blue dotted line presents the density variation under tension and the red solid line presents the variation of density variation under compression ... 172 Fig. 5-43. Variations of the density as a function of the fatigue-time step at different loading modes for stress-control loading at σmax = 2 GPa. The blue dotted line presents the density variation under tension and the red solid line presents the variation of density variation under compression ... 172 Fig. 5-44. Variations of the density as a function of the fatigue-time step at different loading periods for stress-control loading at σmax = 2 GPa. The blue dotted line presents the density variation for long period and the red solid line presents the variation of density variation for short period ... 173 Fig. 5-45. Variations of the density as a function of the fatigue-time step at different loading modes for strain-control loading at εmax = 10 % and strain rate at 2.5×1010 s-1. The blue dotted line presents the density variation under tension and the red solid line presents the variation of density variation under compression ... 173 Fig. 5-46. Variations of the density as a function of the fatigue-time step at different three
loading conditions under strain-control loading ... 174
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Fig. 5-47. Density profile of the strain-control fatigue at different cycles: (a) cycle twelve, loading, (b) cycle twelve, unloading, (c) cycle twenty-five, loading, and (d) cycle twenty-five, unloading. The blue color represents the lower density (as the regions with the free volume). The numbers of the horizontal and vertical axes are in the unit of angstrom ... 175 Fig. 5-48. 2D sliced plots extracting from the 3D simulated results for the local strain
distribution of tension mode of the stress-control fatigue at different cycles at σmax
= 1 GPa: (a) Cycle ten, (b) Cycle thirty, and (c) Cycle fifty. The color scheme represents the degree of atomic bond rotation, or shear strain ... 176 Fig. 5-50. 2D sliced plots extracting from the 3D simulated results for the local strain
distribution of compression mode of the stress-control fatigue at different cycles at σmax = 1 GPa: (a) Cycle ten, (b) Cycle thirty, and (c) Cycle fifty. The color scheme represents the degree of atomic bond rotation, or shear strain ... 176 Fig. 5-51. 2D sliced plots extracting from the 3D simulated results for the local strain
distribution of the stress-control fatigue at different cycles at σmax = 2 GPa: (a) cycle ten, (b) cycle fifty, and (c) cycle one hundred. The color scheme represents the degree of the atomic-bond rotation, or shear strain. The numbers of the horizontal and vertical axes are in the unit of angstrom ... 177 Fig. 5-49. 2D sliced plots extracting from the 3D simulated results for the local strain
distribution of the strain-control fatigue at different cycles: (a) cycle five, (b) cycle ten, and (c) cycle twenty-five. The color scheme represents the degree of atomic-bond rotation, or shear strain. The numbers of the horizontal and vertical axes are in the unit of angstrom ... 177 Fig. 5-50. The accumulation numbers of deformation atoms as a function of loading cycles:
(a) the stress-control mode in the Fig. 5-50 and (b) the strain-control mode in the Fig. 5-51, respectively. The change of growth rate of plastic flows implies a
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resistance against the sustained development of STZ groups occurs when accumulation deformations reach a specific amount during the cyclic loading .... 178 Fig. 5-51. The stress-strain curves for (a) 2.5%, (b) 4% (both nearly in elastic regime) and (c) 10% strain (highly plastic regime), respectively ... 179 Fig. 6-1. Equilibrium phase diagram of Zr-Ni ... 180 Fig. 6-2. Equilibrium phase diagram of Zr-Ti... 180 Fig. 6-3. XRD patterns of pure Zr specimen after different roll bonding cycles at room
temperature ... 181 Fig. 6-4. Equilibrium phase diagram of Mg-Cu ... 181 Fig. 6-5. (a) TEM image and (b) XRD pattern showing the structural transformation of the Mg-Cu multilayer system annealed at 413 K ... 182 Fig. 6-6. Equilibrium phase diagram of Zr-Cu ... 182 Fig. 6-7. The schematic drawings of metallic glass showing the models of dynamics recovery during cyclic loading: (a) the dynamic recovery model of reversible relaxation centers (RRCs) with a symmetry potential barrier which causes the local elastic events during the cyclic loading process, (b) the dynamic recovery model of irreversible relaxation centers (IRRCs) with an asymmetry potential barrier which causes the local plastic events during the cyclic loading processFig. 6- 8. Variation of (a) the induced strain as a function of the fatigue cycle for the stress-control mode at max = 2 GPa, and (b) the induced stress as a function of fatigue cycle for the strain-control mode at max = 10% ... 183 Fig. 6-8. Variation of (a) the induced strain as a function of the fatigue cycle for the
stress-control mode at σmax = 2 GPa, and (b) the induced stress as a function of fatigue cycle for the strain-control mode at εmax = 10% ... 183
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Abstract
The bulk metallic glasses (BMGs) are potential metallic materials due to their interesting properties, such as the high strength, high elastic strain limit, and high wear/corrosion resistance. Over the past four decades, a variety of studies have been done on the characteristics of the mechanical, thermodynamic properties of such category of metallic materials, but there still remain many questions about basic deformation mechanisms and their microstructures so far. Molecular dynamics (MD) simulation can provide significant insight into material properties under the atomic level and see a detailed picture of the model under available investigation in explaining the connection of macroscopic properties to atomic scale. MD simulation is applied to study the material properties and the deformation mechanisms in various binary metallic glasses and intended to examine the feasibility of MD simulation to compare the experimental results obtained in our laboratory over the past few years.
The gradual vitrification evolution of atom mixing and local atomic pairing structure of the binary Zr-Ni, Zr-Ti alloys and pure Zr element during severe deformation at room temperature is traced numerically by molecular dynamic simulation. It is found that the icosahedra clusters will gradually develop with the increasing of disorder environment of alloys in the Zr-Ni, Zr-Ti systems, forming amorphous atomic packing. Other compound-like transition structures were also observed in transient in the Zr-Ni couple during the solid-state amorphization process under severe plastic deformation. The crystalline pure Zr can be vitrified in the simulation provided that the rolling speed is high enough and the rolling temperature is maintained at around 300 K.
On the other hand, the effective medium theory (EMT) inter-atomic potential is
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employed in the molecular dynamics (MD) simulation to challenge the study of the diffusion properties in the Mg-Cu thin films. The transition of local structures of Mg-Cu thin films is traced at annealing temperatures of 300, 413, and 500 K. Furthermore, the simulation results are compared with the experimental results obtained from the transmission electron microscopy and X-ray diffraction. The gradual evolution of the local atomic pairing and cluster structure is discussed in light of the Mg and Cu atomic characteristics.
Lately, the progress of the cyclic-fatigue damage in a binary Zr-Cu metallic glass in small size scale is investigated using classical molecular-dynamics (MD) simulations. The three-dimensional Zr-Cu fully amorphous structure is produced by quenching at a cooling rate 5 K/ps (ps = 10-12 s) from a high liquid temperature. The Nose-Hoover chain method is used to control the temperature and pressure to maintain a reasonable thermodynamic state during the MD-simulation process, as well as to bring the imposed cyclic stress on the subsequent simulation process. Both the stress- and strain-control cyclic loadings are applied to investigate the structural response and free-volume evolution. The overall structure would consistently maintain the amorphous state during cyclic loading. The plastic deformation in simulated samples proceeds via the network-like development of individual shear transition zones (STZs) by the reversible and irreversible structure-relaxations during cyclic loading, dislike the contribution of shear band in large-scale specimens. Dynamic recovery and reversible/irreversible structure rearrangements occur in the current model, along with annihilation of excessive free volumes. This behavior might be able to retard the damage growth of metallic glass and enhance their fatigue life.
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中文摘要
金屬玻璃具有高強度、高彈性應變極限、甚好的抗腐蝕能力等特殊性質，因此被視 為是具有應用潛力的金屬材料。過去四十年來，已經有許多的學習專注在這一類金屬玻 璃的機械性質、熱力學性質上面，但仍然有許多關於基本的變形機制與微結構的問題尚 未釐清。分子動力學可以為原子尺度的材料性質提供一個明顯的洞悉力，亦即提供我們 一個原子結構細節的圖像去瞭解材料的微觀性質。分子動力學在此論文被用來學習多種 二元金屬玻璃合金的材料性質與變形機制，並且試圖去探討將它與本研究室的實驗結果 相互印證的可能性。
本研究的第一部份是用分子動力學來模擬鋯鎳、鋯鈦等二元合金、以及純鋯元素在 室溫下以應力誘導方式使其逐漸玻璃化過程中，其原子混和與局部結構的轉變機制。研 究發現二十面體的原子團簇會伴隨著鋯鎳、鋯鈦合金系統內的無序環境增加而逐漸發 展，形成非晶型的原子堆積。同時也觀察到當施予劇烈塑性變形而發生固態非晶化過程 時，在鋯鎳系統中出現疑似介金屬化合物的過渡結構。模擬結果亦顯示，當滾壓速度夠 快同時環境溫度被控制在 300 K 左右時，結晶的純鋯元素理論上可以被非晶化。
研究的第二部份，採用等效介質理論所發展的鎂銅勢能函數去學習鎂銅薄膜介面間 的擴散性質。在 300、413 以及 500 K 等不同溫度探討鎂銅薄膜介面的局部結構轉變，
並將模擬結果與電子顯微鏡、X-Ray 繞射的實驗結果作比對。依照鎂銅原子特性來討論 局部原子配對與團簇結構的演變行為。
最後一個部分是以分子動力學研究二元鋯銅金屬玻璃在小空間尺度下的週期性疲 勞損壞的過程，藉由適當的冷凝速率 5K/ps 由高溫急速冷卻至室溫以產生一個三維空間 的鋯銅金屬玻璃模型。並採用 Nose-Hoover chain 方法來控制模擬時系統的溫度、壓力，
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使其維持在合理的熱力學狀態，並用來控制週期變形時系統應力狀態。同時使用應力控 制、應變控制兩種模式來學習結構反應行為與自由體積的演變。研究結果顯示，在週期 變形的過程中，結構始終被維持在非晶態。塑性變形的發展乃是藉由可逆與不可逆結構 鬆弛行為，由個別的剪變形區帶（shear transition zone）開始逐漸形成網狀連結發 展所貢獻，與在大空間尺度下是由剪帶（shear band）所貢獻而成的機制有所不同。動 態回復與可逆/不可逆的結構重組行為不斷發生在本模型中，同時伴隨著多餘自由體積 的消除。這個行為也許能夠阻止金屬玻璃的疲勞損害並增加他們的疲勞週期。
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Chapter 1 Introduction and motivation
1-1 Introduction
The development of metallic industry always plays a very important role in the history of human beings. Most of the metallic elements exiting in the nature are present with crystalline structures which are the most stable structures with the lowest energy state, but sometimes they can be made by various ways into metastable amorphous solid forms, such as rapid quenching techniques [1-5], mechanical alloying [6-10], accumulative roll bonding [11-16], and vapor condensation [17]. The characteristics of the mechanical, thermodynamic properties of such category of metallic materials are very similar to ceramic glasses, and thus they are also called as metallic glasses.
Over the past four decades, a considerable number of studies have been done on the BMGs due to their high yield strength, relatively high fracture toughness, low internal friction, as well as better wear and corrosion resistance [18-20]. Although bulk metallic glasses (BMGs) are one of such species of materials which are considered to be high potential for the industrial applications, the insufficient plastic deformation at room temperature is still the Achilles’ hell for the industrial applications regardless of its highly scientific worth.
In general, metallic glasses (MGs) are disordered materials which lack the periodicity of long range ordering in the atom packing, but the atomic arrangement in amorphous alloys is not completely random as liquid. In fact, many scholars believe that amorphous structures are composed of short range ordering, such as icosahedra clusters or other packing forms related
2
to the intermetallic compounds that would form in the corresponding equilibrium phase diagram [21, 22]. The short range order is identified as a structure consists of an atom and its nearest neighbors perhaps two or three atom distance. Recently, it has also been focused more attention on the study of medium range order, which is viewed as a new ordering range between short range order and long range order in the amorphous structure [23]. When an amorphous structure is achieved by quenching, it may be composed of icosahedral local short-range ordering, network-forming clusters medium-range ordering, and other unidentified-random local structures [23, 24], that is, a complex association in their topology.
How to build the atomic structural model in BMGs and how to fill three dimension spaces with these local structural units are still important problems although only limited research has been reported so far.
Due to the difference in the structural systems between metallic glasses and crystalline alloys, it has an unusual performance on the mechanical properties [25-28]. For example, most metallic glasses exhibit evident brittle behavior under a uniaxial tensile test, but sometimes give very limited plastic behavior before failure by means of shear-band propagation. Also, BMGs can perform a large global plasticity through the generation of multiple shear bands during unconfined or confined compression test. Activities of shear band are viewed as the main factor on the plastic deformation of BMGs.
Despite a wealth of investigations, many questions about shear bands and their microstructures are still unclear so far. For instance, how does a shear band initiate in the MG and develop mature shear band from its embryo, how do shear bands interact with each other, and how would the shear band develop in a composite surroundings such as interactions with embedding crystals? These issues not only depend on the effect of temperature but are also related to the strain rate and other else. The width of a typical shear band is around 101-102
3
nm, and the size scale used to define the structures of metallic glasses is within 1-3 nm.
The studies in the microstructures of metallic glasses in this shortest length scale by electron-microscopy such as X-Ray, scanning electron microscope (SEM) or Transmission electron microscopy (TEM) are usually excellent and interesting, but they are relatively less in the theoretic models either in the statistic or continuum simulation computing than those in experiments. Through the studies of simulation methods to compare with experimental data, such as electron scattering data and pair distribution functions, it is expected to be able to investigate the shear-band mechanisms and the microstructures of BMGs in depth. Also, a completely theoretic model could be built up due to the combination of computing model and experiments, not only to explain the current experimental phenomena but also to predict the probative behavior in the future.
Molecular dynamics (MD) simulation is one of important simulation methods provided significant insight into material properties under the atomic level. The major advantage of MD simulations is to see a detailed picture of the model under available investigation, and so they have been very instrumental in explaining the connection of macroscopic properties to atomic scale [29]. For instances, MD simulation has been carried out successfully in the studies of various metallic systems such as point defect movement [30], dislocation mechanisms [31, 32], and grain-boundary structures in polycrystalline materials [33-36] in recent years. However, a number of limitations in the simulations will also be confronted, while simulations are treated as key insights in the study.
Generally, there are three limitations in the current MD simulation, namely the availability of MD potential, time-scale limitations, and the limit on the system size. Two of the later can be alleviated in the promotion of computer efficiency and by adding the
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parallelization techniques in program, but the former is still challenged on the accuracy of material specificity and on the development for the multicomponent system, especially for the BMGs. In this thesis, the MD simulation is applied to study the material properties and the deformation mechanisms in various binary metallic glasses. It is intended to examine the feasibility of MD simulation and to compare the experimental results obtained in our laboratory over the past few years. The work is divided into three parts.
1-2 Motivation
In the first part, the MD simulation is adopted to model the phase transition from nanocrystalline to amorphous in the Zr based intermetallic alloys during accumulative roll bonding (ARB) process. The ARB method is one of solid-state vitrification methods which could force the atoms of adopted elements to diffuse in a solid state under low temperatures in order to produce the amorphous materials in bulk form without the limitation of cooling rates.
According to our previous ARB experimental studies at ambient temperature [37-39] of binary Zr based alloys made by ARB, the grain size of the ARB specimen was gradually refined down to ~2 nm, such nanocrystals would disappear in the matrix and form the complete amorphous phase upon subsequent ARB passes. The role played by the short range ordering, such as icosahedra, or other packing forms related to the intermetallic compounds during solid-state vitrification is still not well understood. The motivation of this part is to study the atomic structure evolution of the Zr based binary alloys (Zr-Ni, Zr-Ti), even extending to the pure Zr metal finally, during the repeated ARB strain-and-stack procedure.
The gradual evolutions of atom mixing and local atomic crystal structure of the binary alloys are traced numerically by the radial distribution function (RDF) and the Honeycutt-Anderson
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(HA) pair analysis technique.
In the second part, the MD simulation is used to challenge the study of the diffusion properties between incoherent interfaces of the binary metallic glasses. In this part of MD study, there is no stress involved, thus excluding the dynamic deformation of materials; only the thermal effect is considered. The multi-layer sputtered Mg-Cu thin film, which is meaningful and interesting to explore the structure transition from the pure Mg and pure Cu crystalline thin layers to the mixed amorphous phase during post-sputtering annealing. A composite multi-layer consisting of hexagonal closed-packed (HCP) structure (Mg atoms), face-centered cubic (FCC) structure (Cu atoms), and amorphous structure (mixed with Mg and Cu) is examined during thermal annealing at a suitable temperature [40, 41].
Finally, in order to explore the feasibility of MD simulation in dynamic deformation of MGs, the progress of the cyclic-fatigue damage in a binary Zr-Cu metallic glass in small size scale is investigated. Compared with the literatures on the study of deformation mechanisms of BMGs under compression or even tension monotonic testing, there remain much fewer reports on the fatigue behavior, especially at the atomic scale. As well known, the concepts of free volume and shear transition zones (STZs) are viewed as the main defects and basic deformation units in the metallic glasses. Free volumes and STZs are also relevant to the fatigue damage mechanism of BMGs. The shear band formation and propagation usually go along with the local increase of free volumes and crack sites within BMGs due to the weakness in the shear bands or shear-off steps [42, 43], subsequently leading a fracture and fatigue damage. It follows that, if we can reduce the free volumes in BMGs, the plastic deformation and fatigue damage might be retarded and the fatigue life might be extended.
However, the theoretical model and basic fatigue-damage mechanism in fatigue behavior of BMGs still need further exploration. The aim of the final part on this dissertation is to
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examine the relationship between the variation of free volume and the basic development of shear deformation events under cyclic loading in small size scale, and to further understand the mechanism of deformation retardation under cyclic-loading process.
The following Chapter 2 discusses some aspects of the background and theory of BMGs such as the development, mechanical properties, plastic deformation mechanisms, fatigue behavior, and structural topology of BMGs. Chapter 3 introduces the fundamental background of MD simulation methods, including the fitting of the interatomic potential and basic concept of ensembles in MD. Chapter 4 describes the theory and simulation model applied in this work. The results of simulation models are presented in Ch. 5 and are further discussed in Chapter 6. Chapter 7 is for the final conclusions.
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Chapter 2 Background and Literature Review of metallic glasses
2-1 The development of metallic glasses
In 1960, Klement et al. [44] developed the first metallic glasses of Au75Si25 by the rapid quenching techniques for cooling the metallic liquids at very fast rates of 105-106 K/s.
Their works initiate broad interest quickly among the scientists and engineers because they showed the process of nucleation and growth of crystalline phase could be skipped to produce a frozen liquid configuration. A few years later, the ternary amorphous alloys of Pd-Si-X (X = Ag, Cu or Au) were prepared successfully by Chen and Turnbull [45], and the Pd-T-Si (T = Ni, Co or Fe) ternary amorphous alloys which included the magnetic atoms were also presented soon after [46]. The maximum diameter of these metallic glasses was reached to 1 mm by using the die casting and roller-quenching method. The effects of the alloy systems, compositions and the existence of a glass transition was demonstrated, it leaded to the first detailed studies in the formation, structure and property investigations of amorphous alloys.
Because of their fundamental sciences and engineering application potential, metallic glasses have attracted great attention.
The geometry of metallic glasses, however, is limited to thin foils or lines as a result of high cooling rate, which are not easy to find the wide application. How to determine the glass forming ability (GFA) of amorphous alloys and increase the diameter of specimens becomes the important topic in that period. Turnbull and Fisher [47]advanced a criterion to predict the glass forming ability of an alloy. According to his criterion, the reduced glass transition temperature Trg, equal to the glass transition temperature Tg over liquids temperature Tl, or Trg = Tg/Tl is the primary factor. If Tg is larger and Tl smaller, the value of Trg will be higher so that such a liquid can be easily undercooled into a glassy state at a lower
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cooling rate. Although there are several new criteria proposed following them [48, 49], the Trg
has been proved to be useful in reflecting the GFA of metallic glasses including BMGs.
In 1974, the rods of Pd-Cu-Si alloy measuring 1-3 mm in diameter, the first bulk metallic glasses were prepared by Chen [46] using simple suction-casting methods. In 1982, Turnbull’s group [50, 51] pushed the diameter of critical casting thickness of the Pd-Ni-P alloys up to 10 mm by processing the Pd–Ni–P melt in a boron oxide flux, and eliminate heterogeneous nucleation. A series of solid state amophization techniques that are completely different from the mechanism of rapid quenching had been developed during this time. For example, mechanical alloying, diffusion induced amorphization in multilayers, ion beam mixing, hydrogen absorption, and inverse melting [52]. The thin films or powders of metallic glasses can be acquired as well by interdiffusion and interfacial reaction when the temperature is just below the glass transition temperature.
In the late 1980s, Inoue’s group [53, 54]in Tohoku University of Japan developed many new multicomponent metallic glass systems with lower cooling rates in Mg-, Ln-, Zr-, Fe-, Pd-, Cu-, Ti- and Ni- based systems. They found exceptional glass forming ability in La-Al-Ni and La-Al-Cu ternary alloys system [53]. By casting the alloy melt in water-cooling Cu molds, the cylindrical samples with diameters up to 5 mm or sheets with similar thicknesses were made fully glassy in the La55Al25Ni20 alloy, and the La55Al25Ni10Cu10 alloy was fabricated later with a diameter up to 9 mm by the same method.
In 1990s, the Inoue group further developed a series of multicomponent Zr-based bulk metallic glasses, such as Zr-Cu-Ni, Zr-Cu-Ni-Al, etc., along with Mg-based, e.g. Mg–Cu–Y and Mg–Ni–Y alloys, all exhibiting a high GFA and thermal stability [55-58]. For one of the Zr-based BMGs, Zr65Al7.5Ni10Cu17.5,the critical casting thickness was raised up to 15 mm,
9
and the largest critical casting thickness could reach to 72 mm in the Pd–Cu–Ni–P family[59].
The evolution of such category alloys demonstrated that bulk metallic glass composition were not a laboratory curiosity and could be quite interesting and for promising engineering applications. In fact, the Zr-based bulk metallic glasses found application in the industries just three years after it was invented. The typical bulk metallic glasses systems and the reported years are listed in Table 2-1[20]. Subsequently, a set of empirical rules in order to direct the selection of alloying elements and composition of glass forming alloys have been proposed by Inoue and Johnson as follows[19, 60]:
(1) Multicomponent alloys with three or more elements.
(2) More than 12% atomic radius difference among them.
(3) Negative heat of mixing between constituent elements.
(4) The deep eutectic rule based on the Trg criterion.
These rules provide an important role for the synthesizing of BMGs in the last decade.
However, in the subsequent experiments finding some binary alloys such as Ni-Nb[61], Ca-Al [62] Zr-Ni[63, 64], and Cu-Zr [65-67] etc., BMGs can also be obtained with several millimeters and the best glass formers are not fixed on the eutectics of them, indicating that the above mentioned rules are not the necessary concern in all cases for designing BMGs.
Formation mechanism and criteria for the binary BMGs may be distinct from the multicomponent systems. These results suggest that there are many potential forming systems of the metallic glasses to be discovered. On the other hand, these kinds of simple binary systems of BMGs are the very ideal model for studying their characteristics of the deformation mechanism and structure by computer simulation and theorizing.
Recently, many scholars attempt to detect the regulations on the glass forming ability from thermodynamic modeling or statistical mechanics that can help to design the larger size
10
of amorphous alloys in general [49, 53]; others focus on the studies of their mechanical properties and structural topology that can build the structural modeling of BMGs as well as improve their strength and ductility. In future, the trends of investigations of BMGs are not only kept on the experimental competition but also extended into complete modeling of fundamental theory.
2-2 Microstructures in metallic glasses
In 1959, a structural model of dense random packing of hard spheres is first suggested by Bernal [68] to be a simple model for metal liquids, and subsequently indicated by Cohen and Turnbull [69] that this simple model can be also applied to describe the metallic glasses.
In 1979, Wang [70] supposed that the amorphous metal alloys may be a special class of the glassy state whose short-range structure is random Kasper polyhedral close packing of soft atoms similar to those in the crystalline counterparts. This short-range structure is described based on a new type of glassy structure with a high degree of dense randomly packed atomic configurations. The density measurements show that the density difference is in the range 0.3~1.0% between bulk metallic glasses and fully crystallized state [71, 72]. There is neither splitting of the second peak nor pre-peak at the lower wave vector as seen in the reduced density function curve of the BMGs [71, 73, 74]. These results confirm that the multicomponent BMGs has a homogeneously mixed atomic configuration corresponding to a high dense randomly packing.
One of the most important topological short range structures developed among glasses and supercooled liquids is the local icosahedral clusters, which are revealed by many simulation studies [75-79]. Figure 2-1 (a) shows a typical fragment of an icosahedron, the central atom forms a fivefold symmetry arrangements with each of its 12 neighbors. In
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contrast as shown in Fig. 2-1 (b) is a regular fragment of an FCC order, and the same pair will become an HCP order if the bottom close-packed plane is shifted as the same as the top plane.
This fivefold symmetry and icosahedral clusters is also detected from the experiments of liquids and metallic glasses [80, 81], even though in an immiscible binary system with positive heat of mixing [77-79]. The binding energy of an icosahedral cluster of 13 Lennard-Jones (LJ) atoms is 8.4% lower than an FCC or HCP arrangement [82]. The critical size for a transition from icosahedral cluster to icosahedral phase is about 8 nm [54].
Icosahedral packing is a basic structural unit in extended amorphous systems, and the existence of icosahedral clusters offer seeds for the precipitation of the icosahedral phase.
The icosahedral quasicrystalline phase will precipitate in the primary crystallization process and then transforms to stable crystalline phases when the amorphous alloys is annealing at higher temperatures [83-85].
In recent years, an order effect, called the medium range order, existing over length scale larger than the short range order but not extends to the long range order as crystalline state, has been detected in the some amorphous alloys [86-88]. Figure 2-2 shows a typical high-resolution electron microscopy image of the BCC-Fe medium range order with the sizes around 1-3 nm existing in the Fe-Nb-B amorphous matrix [89]. Although the icosahedral type model gives a sound description on the structure in the short range order of metallic glasses but fails beyond the nearest-neighbor shell. For instance, how can the medium range order be defined with the local structural unit, and how would the local structural units be connected to full three-dimensional space?
Miracle [90] suggested a compelling structural model for metallic glasses based on the dense packing of atomic clusters. An FCC packing of overlapping clusters is taken as the building scheme for medium range order in metallic glasses. Figure 2-3 illustrate his
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promoted model of medium range order. A reality check for these previous structural concepts was proposed by Sheng et al. [23] with experiments and simulations. They indicate the icosahedral ordering of single-solute-centered quasi-equivalent clusters is an efficient packing scheme, but is not the only type of medium range order. The atomic packing configurations of different binary amorphous alloys are shown in Fig. 2-4. For each one of the metallic glasses, the several types of local coordination polyhedra units are geometrically different, and not identical in their topology and coordination number. They can be considered quasi-equivalent, or cluster-like units for a given glass, supporting the framework of cluster packing. The cluster connection diagrams for the several metallic glasses are shown in Fig. 2-5 to illustrate the specific packing and connection schemes of the quasi-equivalent clusters, through the sharing of edges, faces and vertices. This maybe represents the important question of how the clusters are connected and packed to fill the three-dimensional space, giving rise to the medium range order. It is short range for the packing of clusters, but already medium range from the standpoint of atomic correlation beyond one cluster.
A new insight, imperfect ordered packing, which is closely related to the cooling rate, is exposed on the medium range order embedded in the disordered atomic matrix by selected simulation of high-resolution electron microscopy image [91]. It points out that the packing character of medium range ordering structures can be of two types, i.e. icosahedron-like and lattice-like, and indicates that the solidification from melts or crystallization of metallic glasses is controlled by preferential growth of the most stable imperfect ordered packing. On the other hand, Fan et al. [92-94] proposed a structural model for bulk amorphous alloys based on the pair distribution functions measured using neutron scattering and reverse Monte Carlo simulations. Figure 2-6 shows a refined model of bulk amorphous alloys due to the reverse Monte Carlo method that has a good agreement with the experimental measurement.
There are many clusters of imperfect icosahedral and cubic forms extracted from Fig. 2-6.
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These clusters are randomly distributed, strongly connected, and result in the space between the clusters. The space between the clusters forms free volume, which provides a degree of freedom for the rotation of the clusters under applied load. This cooperative rotation of clusters forms a layer motion (i.e. shear bands), and plastically deforms the amorphous alloys.
This model implies that the mechanical properties, e.g. strength and ductility, are dominated by the combination of the bonding characteristics inside and between these clusters.
2-3 Mechanical properties
Unlike the dislocation mechanisms for plastic deformation in crystalline alloys, the amorphous alloys only allow limited atomic displacements to resist deformation as a result of the glassy structure with a high degree of dense randomly packed atomic configurations, when the applied stress is on the amorphous alloys. Figure 2-7 summarizes the relationship between tensile strength, Vickers hardness and Young’s modulus for bulk glassy alloys, and the data on crystalline metallic alloys are also included for comparison [54, 95]. As the figure indicates, the BMGs have higher tensile fracture strength σf of 0.8-2.5 GPa, Vickers hardness Hv of 200-600, and lower Young’s modulus E of 47-102 GPa, than ordinary metallic crystals [54]. It is considered that the significant difference in the mechanical properties is due to the discrepancy in the deformation and fracture mechanisms between bulk metallic glasses and crystalline alloys.
It has been widely accepted that shear-band propagation is the major cause affecting the ductility and toughness of the amorphous alloys. Plastic deformation in metallic glasses is generally associated with inhomogeneous flow in highly localized shear bands. When the shear band went through in the metallic glasses, it is often accompanied with locally rising high temperature to influence the shear flow. Figure 2-8 (a) is good evidence from tensile
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experiments to show that local melting occurs under high strain rate situations through unstable fracture [96]. Even under slower loading rates, a veined fracture surface indicates a decrease in the glass viscosity, as shown in Fig. 2-8 (b). Due to the highly localized nature of flow and the lack of microstructural features in the metallic glass to distract the flow, shear band formation typically leads to catastrophic failure. The strain softening and thermal softening mechanisms are tightly associated with the localization of shear band [97].
Generally speaking, the metallic glasses have high fracture toughness but brittle as well as negligible plasticity. For instance, the Zr-based bulk metallic glasses present high Charpy impact fracture energies ranging from 110-140 kJ/m2 and high fracture toughness limit [98].
Their fatigue limit is close to those of the crystalline alloys. However, standard stress–strain fatigue tests show that the Vitreloy alloy (commercial Zr-based BMG) has an extremely low resistance to crack initiation and a crack propagates rapidly once it has formed. If this alloy does start to yield or fracture, it fails quickly. Geometrical confinement of shear bands can dramatically enhance overall plasticity.
Furthermore, the plastic yield point of most bulk metallic glasses is located within a small range around εy = 2% at room temperature [99]. Composite approach is used to enhance the ductility and toughness of metallic glasses in recent fabricating efforts[100].
Figure 2-9 (a) shows the scanning electron microscopy (SEM) backscattered electon image of in situ Zr-Ti-Nb-Cu-Ni-Be composite microstructure, and Fig. 2-9 (b) is the compressive stress strain curve for a cylindrical in situ composite specimen. From Fig. 2-9 (a), a variety of reinforcing crystalline phase consisting of a ductile crystalline Ti-Zr-Nb β-phase, with body-centered cubic (BCC) structure, has been formed in the bulk metallic glass matrix. This bulk metallic glass matrix composite successfully increases the plastic strain to over 8% prior to failure, as shown in Fig. 2-9 (b). Later, a plastic strain of 20% is measured in the
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Pt-Cu-Ni-P bulk metallic glasses before failure, as seen in Fig. 2-10 (a). Its behavior is like a typical bulk metallic glasses initially but performs as a perfectly plastic deformation after passing the yielding point of 2%. This Pt-Cu-Ni-P bulk metallic glass has a high Poisson ratio of 0.42, which causes the tip of a shear band to extend rather than to initiate a crack. This results in the formation of multiple shear bands in Fig. 2-10 (b), and is the origin of the large ductility [101].
2-4 Deformation mechanisms
Due to the absence of dislocation and grain boundary structures, the plastic deformation mechanism of metallic glasses is well known as shear-band evolution that deeply associates with the mechanical properties and failure behavior in bulk metallic glasses. A SEM observation showing the shear bands is given in Fig. 2-11. Nevertheless, the shear band is not the basic defect unit in the deformation mechanisms in the metallic glasses under microscopic scale. In the 1960s, Cohen and Turnbull [102] as well as Spaepen [103] suggested a concept of free volume which is considered as vacancy-like defect (Fig. 2-12) in the metallic glasses, and Argon [104] proposed a theoretical model of plastic flow in metallic glasses, termed shear transformation zone (STZ), which is the fundamental shear unit consisting of a free volume site and its close adjacent atoms in amorphous metals.
The concept of free volume
In the conceptual framework of free volume, the mechanical coupling is weak to the surrounding of free volumes, and hence the inelastic relaxation becomes possible by local atom rearrangement, without affecting the surroundings significantly [105]. Thus, free volume regions could be the preferred sites where easy caused the glass structure
