金基塊狀非晶質合金機械性質與微成形能力之探討 Mechanical Properties and Micro-Forming Ability of Au-Based
Bulk Metallic Glasses
研究生：湯振緯 撰 指導教授：黃志青 博士
中華民國 九十七 年 七 月
五年前的夏天，回憶的片段像口試時撥放的投影片，沒有翻箱倒櫃地搜尋，靜靜地 從五樓材料所的陽台向外望去，蔚藍的海洋逐著波浪，白色的燈塔就輕輕地架起了投影 機，把一切毫無保留地投影在心頭。和西子灣的邂逅，那是一個萬里無雲的好日子，就 像任何一天高雄的夏日，陽光刺著雙眼，讓你不得不謙卑地低頭避開那遠從一百五十百 萬公里來的強力射線，激烈地核融合反應似乎狂妄地想把所有的海水蒸發。凝視著母 親，她似乎還沒有從唯一的犬子要離鄉背井負笈高雄的不捨中釋懷，這樣的相遇可不比 李白詩中對西施的描寫「出自苧蘿山。秀色掩古今，荷花羞玉顏。」那般富有情治詩意，
「阿湯，你快要畢業了」當我把論文初稿交給黃老師志青時，他和緩並帶著他慣有 的微笑對我這麼說道，不知怎麼地突然紅了眼眶，隔著一層鏡片，鏡片上映著的是無數 材料相關的書籍和達文西最後的晚餐，老師充滿慧黠又慈祥的瞳仁在哪瞬間溫柔地把時 間給凝住了。五年間發生了很多事，球場上的汗水，工廠電弧滿目瘡痍的銅坩堝，海堤 旁的空啤酒罐，遺留在沙灘上的腳印，停留在月色的髮香，躺在 E 棟四二零宿舍的友情 碎片，滴在西裝外套上男人間的感情和難過，這一切的一切都默默地存在腦中，直到老 師的話語像晶種般，引發一連串的晶粒成長恣意地蔓延，在西子灣的無限柔情的懷裡慢 慢地沈澱靜置。
生命是由生活的篇章所構成的，這一千八百多個日子，謝謝黃老師志青和材料所的 每一位老師帶領學生認識材料科學之美，在學生的心中灑下神的種子，還有師母在每一 個星期天早晨樂以教和，讓詩歌悠揚的音符縈繞我心。義守大學風趣幽默的鄭老師憲
滿分的敬仁學長。比孤狗大神還神的博士雞排店店長，智多星育誠學長。嚴謹認真扣子 總是扣得很好的志溢學長。個性恬淡，具有客家「硬頸」精神，打死不結婚的的子翔學 長猴爺。一直擔心禿頭立志取小二十歲老婆的優秀 BMG VI 最佳論文得主 MD 模擬達人友 杰學長。人見人愛，開朗熱心一百分，佛羅里達台灣同學會會長宇庭學長。從大專生研 究就給予敝人指導，熱心搞笑有活力的海明學長。好好先生，個性溫和總有削不完 pillar 的炎輝學長。有敬仁學長般研究熱血，不吃青菜的泡麵攝影達人鴻昇學長。專 業籃球 C 級裁判，講話中肯犀利，連續當了敝人兩次學長的浩然學長。內斂實在，韜光 養晦之術值得敝人效法的名哲學長。瘦身之後定能恢復往日排球身手，直升博士班的巧 克力男孩哲男同學。辯才無礙稱霸兩岸，在上海街頭直接跳起街舞，一直很想紅的大豪 同學。台灣第一深情，中秋應景水果愛好者，做事很帶勁的碩陽學弟。捲毛都不捲毛，
英文嚇嚇叫的柏佑學弟。拿書香獎如一塊小蛋糕一般的逸志學弟。材光系所有的同學和 學弟們。還有我親愛的家人們無限的支持，跟思華在線上的支持讓我在寫作論文時可以 當個快樂的陽光宅男，站在巨人的肩榜上，有你們的陪伴持讓我的生命更為豐盈精彩。
朋友對我說道：「要畢業了，應該很高興吧！」我什麼也沒說，回以一個似笑非笑 的表情，記得優子曾經這樣告訴我：「每一次分離，一部份的你也將死去」心中的一股 惆悵，抑鬱在心中吐也吐不掉，只想用快切把胸口切開讓西子灣的水帶走這份感傷，就 像她把貨輪帶走一般，送到世界的其他角落。我沒有像徐志摩那般不帶走一片雲彩的灑 脫，但願敝人無盡的思念能讓緣分感應到我真摯的情感，讓我們得以再次相聚，就像神 又把敬仁和宇庭學長再次送到我們身邊。人生是一連串的選擇，我很驕傲地說我做了一 個美麗的決定，留在黃幫，駐足西子灣。
湯振緯 謹誌 於 國立中山大學材料科學研究所
中 華 民 國 九 十七 年 七 月
Chapter 1 Introduction... 1
1.1 Amorphous metallic alloys ... 1
1.2 The evolution of Au-based amorphous alloys ... 1
1.3 The motivation of this research... 2
Chapter 2 Background and literature review ... 4
2.1 The developments of bulk metallic glasses (BMGs) ... 4
2.2 Thermal stability and glass forming ability of BMGs ... 6
2.3 Mechanical behavior of amorphous metallic alloys ... 9
2.3.1 Deformation mechanisms ... 9
2.3.2 Shear bands ... 13
2.3.3 Size effects in plasticity ... 15
2.4 Comparison between metallic glasses and engineering materials ... 16
2.5 The birth of Au-based BMG (Au49Ag5.5Pd2.3Cu26.9Si16.3)... 18
2.6 The parameters to distinguish plasticity or brittleness... 20
2.7 Applications of bulk metallic glasses ... 21
2.7.1 Golf club heads ... 21
2.7.2 Cases for consumer electronics... 22
2.7.3 Liquidmetal rebounds ... 23
2.7.4 Medical applications ... 23
2.7.5 Defense and aerospace... 24
2.8 Viscous flow behavior ... 24
Chapter 3 Experimental procedures... 26
3.1 Materials ... 26
3.2 Sample preparation ... 26
3.2.1 Arc melting ... 26
3.2.2 Suction casting... 27
3.2.3 Micro-sample fabrication using Focused Ion Beam milling... 27
3.3 Property measurements and analyses... 28
3.3.1 X-ray diffraction ... 28
3.3.2 Qualitative and Quantitative constituent analysis... 28
3.3.3 DSC thermal analysis... 28
3.3.4 Density measurement... 29
3.3.5 TMA analysis... 29
3.3.6 Micro-hardness testing... 30
3.3.7 Macro-compression testing... 30
3.3.8 Micro-compression testing... 30
3.3.9 Microstructure examination... 31
3.3.10 Hot embossing of micro-lens and V-groove... 31
3.3.11 Surface morphologies ... 32
Chapter 4 Results... 33
4.1 Sample preparations... 33
4.2 XRD analyses... 33
4.3 SEM/EDS observations ... 33
4.4 TEM observations... 33
4.5 DSC analyses ... 34
4.6 Density measurement... 34
4.7 Micro-hardness testing... 35
4.8 Macro-compression testing... 35
4.9 Compressive fracture characteristics ... 36
4.10 Micro-compression testing... 37
4.11 TMA Analysis... 38
4.12 Hot embossing of V-groove on Au-based BMG ... 39
4.13 Hot embossing of micro-lens array on Au-based BMG ... 40
Chapter 5 Discussions... 42
5.1 Variation in compositions of Au-based BMG ... 42
5.2 The glass forming ability of Au-based BMG ... 42
5.3 Bulk and micro-scale compressive behavior of Au-based BMG... 43
5.4 Viscous flow behavior for Au-based BMG ... 45
5.5 Hot embossing on Au-based BMG... 47
Chapter 6 Conclusions... 50
Table 2.1 Bulk metallic glasses and their developed year . ... 56 Table 2.2 The composition of representative BMG systems, their glass transition temperature
Tg, onset temperature of crystallization, Tx, and onset melting point, Tm, and glass forming ability represented by reduced glass transition temperature, Trg .. 57 Table 2.3 Properties of the elements in the Au-based BMG alloy. ... 58 Table 2.4 Possible application fields for BMGs . ... 59 Table 4.1 The composition analyses of the Au49Ag5.5Pd2.3Cu26.9Si16.3 rods by SEM/EDS. .. 60 Table 4.2 Summary of the macro-compressive of Au-based BMG at different strain rates. 61 Table 4.3 Summary of the micro-compressive of Au-based BMG at different strain rates.. 62 Table 4.4 Variation in distance and average height under different conditions for V-groove.
... 63 Table 4.5 Variation in height and width under different conditions for micro-lens array... 64 Table 5.1 The negative heat of mixing in unit of kJ/mol of the Au, Ag, Pd, Cu, and Si elements.
... 65 Table 5.2 Thermal properties of the Mg65Cu25Gd10 (Mg-based BMG) and
Au49Ag5.5Pd2.3Cu26.9Si16.3 (Au-based BMG) obtained from DSC at a heating rate of 10 K/min... 66
Figure 2.1 The critical casting thickness versus the year in which alloys were discovered.
Over 40 years, the critical casting thickness has increased by more than three orders of magnitude ... 67 Figure 2.2 The picture of as-cast alloy BMG system . ... 68 Figure 2.3 Relationship between the critical cooling rate for glass formation (Rc), maximum
sample thickness for glass formation (tmax) and reduced glass transition temperature (Tg/Tm) for bulk amorphous alloys. The data of the ordinary amorphous alloys, which require high cooling rates for glass formation, are also shown for comparison . ... 69 Figure 2.4 Relationship between Rc, tmax and the temperature interval of the supercooled liquid region between Tg and Tx for bulk amorphous alloys ... 70 Figure 2.5 A comparison of critical cooling rate between reduced glass transition temperature,
Trg, among BMG, silicate glasses and conventional metallic glasses ... 71 Figure 2.6 The correlation between the critical cooling rate and the parameter γm
glasses ... 72 Figure 2.7 Two-dimensional schematics of the atomistic deformation mechanisms proposed
for amorphous metals, including (a) a shear transformation zone (STZ), after Argon , and (b) a local atomic jump, after Spaepen . ... 73 Figure 2.8 Scanning electron micrographs illustrating the ‘‘slip steps’’ or surface offsets
associated with shear bands in deformed metallic glasses. In (a), a bent strip of Zr57Nb5Al10Cu15.4Ni12.6 illustrates slip steps formed in both tensile and compressive modes of loading, on the top and bottom surfaces, respectively. In (b) the side of a compression specimen of Zr52.5Cu17.9Ni14.6Al10Ti5 is shown, for which the loading axis was vertical; here the slip steps document shear
deformation at an inclined angle to the applied compressive load . ... 74 Figure 2.9 Calculations from the work of (a) Argon and (b) Steif et al. illustrating the process
of strain localization in metallic glasses. In (a), a history of strain rate is shown for both the forming shear band and the surrounding matrix; these quantities are normalized by the applied shear strain rate. In (b), the history of strain in the shear band is shown [51, 64]... 75 Figure 2.10 Examples of mechanical test data that illustrate serrated flow of metallic glasses,
through repeated shear band operation in confined loading. In (a), the compression response of a Pd77.5Cu6Si16.5 specimen of low aspect ratio is shown, while (b) is an instrumented indentation curve for Pd40Cu30Ni10P20 glass.
Because (a) represents a displacement controlled experiment, serrations are represented as load drops, while the load-controlled experiment in (b) exhibits displacement bursts . ... 76 Figure 2.11 Average shear band spacings are plotted as a function of characteristic specimen
dimensions for a variety of metallic glasses (and some derivative composites) deformed in constrained modes of loading, after Conner et al . ... 77 Figure 2.12 Amorphous metallic alloys combine higher strength than crystalline metal
alloys with the elasticity of polymers ... 78 Figure 2.13 Elastic limit σy plotted against modulus E for 1507 metals, alloys, metal matrix
composites and metallic glasses. The contours show the yield strain σy /E and the resilience σy2 =E . ... 79 Figure 2.14 Resilience σy2=E and loss coefficient for the same materials as Figure 2.13 .
... 80 Figure 2.15 Fracture toughness and modulus for metals, alloys, ceramic, glasses, polymers
and metallic glasses. The contours show the toughness Gc in kJ m-2 . ... 81 Figure 2.16 Toughness and elastic limit for the same materials. The contours show the
process-zone size d in mm . ... 82
Figure 2.17 Composition dependence of ΔT and dc for (Au58.5Ag6.6Pd2.8Cu32.1)86-xSi14+x for x = 0-6%. A strong dependence on the Si content of both dc and ΔT is observed. No obvious correlation of dc and ΔT is seen ... 83
Figure 2.18 Position dependence of ΔT and dc for (Au60.1Ag6.8Cu33.1)83.7-yPdySi16.3 for y = 0-5%. A strong dependence on the Pd content of both dc and ΔT is observed. No obvious correlation of dc and ΔT is seen . ... 84
Figure 2.19 The relationship between ν and μ/β... 85
Figure 2.20 The correlation of fracture energy G with elastic modulus ratio μ/B for all the as-cast (unannealed) metallic glasses for which relevant data are available (all compositions in at.%). Elastic constants were used to convert fracture toughness to fracture energy . ... 86
Figure 2.21 The correlation of fracture energy G with Poisson’s ratio for all the data collected on metallic glasses (as-cast and annealed) as well as for oxide glasses ... 87
Figure 3.1 Au-BMG micropillars fabricated by focus ion beam technique: (a) 1 μm in diameter and (b) 3.8 μm in diameter... 88
Figure 3.2 FIB-SEM micrographs of the flat-punch tip: a) top view and (b) side view. ... 89
Figure 3.3 Triangle marks made by flat punch ... 90
Figure 3.4 Hot embossing set-up for oil hydraulic system . ... 91
Figure 3.5 Ni–Co mold with gapless hexagonal micro-lens array. ... 92
Figure 3.6 Profile of V-groove mold. ... 93
Figure 4.1 The appearance of the Au-based BMG rods with 2 and 3 mm. ... 94
Figure 4.2 XRD pattern of the 3 mm and 2 mm Au-based amorphous alloys. ... 95
Figure 4.3 TEM diffraction pattern of the 3 mm diameter Au-based BMG... 96
Figure 4.4 DSC plot of Au-based amorphous alloy with the heating rate of 40 K/ min. ... 97
Figure 4.5 The Au-Cu binary phase diagram... 98
Figure 4.6 DSC plot of Au-based amorphous alloy with the heating rate of 10 K/min. ... 99 Figure 4.7 The compressive stress-strain curves for the Au49Ag5.5Pd2.3Cu26.9Si16.3 BMG.. 100 Figure 4.8 The outer appearance showing fracture plan inclination of the Au-based BMG with a strain rate of 5x10-5 s-1... 101 Figure 4.9 The fracture surface morphology of the Au-based BMG with a strain rate of 5x10-5 s-1... 101 Figure 4.10 The fracture surface morphology of the Au-based BMG with a strain rate of
5x10-5 s-1... 102 Figure 4.11 The outer appearance showing fracture plan inclination of the Au-based BMG
with a strain rate of 1x10-4 s-1... 103 Figure 4.12 The fracture surface morphology of the Au-based BMG with a strain rate of
1x10-4 s-1... 103 Figure 4.13 The fracture surface morphology of the Au-based BMG with a strain rate of
1x10-4 s-1... 104 Figure 4.14 The outer appearance showing fracture plan inclination of the Au-based BMG
with a strain rate of 5x10-4 s-1... 105 Figure 4.15 The fracture surface morphology of the Au-based BMG with a strain rate of
5x10-4 s-1... 105 Figure 4.16 The fracture surface morphology of the Au-based BMG with a strain rate of
5x10-4 s-1... 106 Figure 4.17 The outer appearance showing fracture plan inclination of the Au-based BMG
with a strain rate of 1x10-3 s-1... 107 Figure 4.18 The outer appearance showing fracture plan of the Au-based BMG with strain a
rate of 1x10-3 s-1... 107 Figure 4.19 The outer appearance of the Au-based BMG with a strain rate of 1x10-3 s-1. .. 108 Figure 4.20 The fracture surface morphology of the Au-based BMG with a strain rate of
1x10-3 s-1... 108 Figure 4.21 The fracture surface morphology of the Au-based BMG with a strain rate of
1x10-3 s-1... 109 Figure 4.22 Compression load-displacement curves of the 1 μm Au-BMG at different strain
rates... 110 Figure 4.23 Compression load-displacement curves of the 3.8 μm Au-BMG at different strain
rates... 111 Figure 4.24 Time-and-displacement curves for the 1 μm Au BMG pillars. ... 112 Figure 4.25 Time-and-displacement curves for the 3.8 μm Au BMG pillars. ... 113 Figure 4.26 SEM micrographs showing the appearance of deformed pillars: (a) 3.8 μm,
~1x10-3 s-1, (b) 3.8 μm, ~1x10-2 s-1, (c) 3.8 μm, ~6x10-2 s-1, (d) 1 μm, ~1x10-3 s-1, (e) 1 μm, ~1x10-2 s-1, and (f) 1 μm, ~6x10-2 s-1. ... 114 Figure 4.27 Typical TMA and DTMA curves measured at stress level of 7.1 kPa for the as-cast bulk Au-based BMG. ... 117 Figure 4.28 Measured viscosities of the Au-based and Mg-based BMG in the supercooled
liquid region at a heating rate 10 K/min. ... 118 Figure 4.29 Replicated patterns by OM on the Au-based BMG materials imprinted at 177oC and 137 MPa for 1 min with (a) lower magnification by OM (b) higher magnification. ... 119 Figure 4.30 Replicated patterns by OM on the Au-based BMG materials imprinted at 177oC
and 137 MPa for 5 min with (a) lower magnification by OM (b) higher magnification. ... 120 Figure 4.32 Replicated patterns by OM on the Au-based BMG materials imprinted at 177oC
and 62 MPa for 10 min with (a) lower magnification by OM (b) higher magnification. ... 122 Figure 4.33 Replicated patterns by OM on the Au-based BMG materials imprinted at 177oC
and 156 MPa for 10 min with (a) lower magnification by OM (b) higher magnification. ... 123 Figure 4.34 The morphological curves of V-groove imprinted Au-based BMG at 177oC and
62 MPa, 137 MPa, and 156 MPa, respectively, for 10 min by the α step... 124 Figure 4.35 The morphological curves of V-groove imprinted Au-based BMG at 177oC and
137 MPa for 1, 5, 10 min, respectively, by the α step... 125 Figure 4.36 Replicated patterns by OM on the Au-based BMG materials imprinted at 177oC
and 28 MPa for 10 min. ... 126 Figure 4.37 Replicated patterns by OM on the Au-based BMG materials imprinted at 177oC
and 62 MPa for 10 min with (a) lower magnification (b) higher magnification . ... 127 Figure 4.38 Replicated patterns by OM on the Au-based BMG materials imprinted at 177oC
and 156 MPa for 10 min with (a) lower magnification (b) higher magnification . ... 128 Figure 4.39 The morphological curves of micro-lens array on the Au-based BMG at 177oC
and 28 MPa, 62 MPa, and 156 MPa, respectively, for 10 min by the α step. . 129 Figure 4.40 Replicated patterns by SEM on the Au-based BMG materials imprinted at 177oC
and 156 MPa for 10 min with (a) lower magnification (b) higher magnification.
... 130 Figure 5.1 The strength-sample size relationship for the Au-based BMG with different pillar
diameters from 2 mm down to 1 μm... 131 Figure 5.2 Determination of the STZ size of the Au-based alloys based on the TMA data.132 Figure 5.3 Extraction of the activation energy of the Au-based BMG during shear deformation within the supercooled temperature region... 133 Figure 5.4 XRD pattern of the hot embossing Au-based BMG with different pressures 62 MPa,
137 MPa, and 156 MPa, respectively. ... 134
The mechanical properties and micro-forming of the Au-based bulk metallic glasses are reported in this thesis. The original ingots were prepared by arc melting and induction melting. The Au49Ag5.5Pd2.3Cu26.9Si16.3 bulk metallic glasses with different diameters 2 and 3 mm were successfully fabricated by conventional copper mold casting in an inert atmosphere.
By the observation of transmission electron microscopy diffraction pattern, there are crystalline phases among the amorphous matrix phase.
The Au49Ag5.5Pd2.3Cu26.9Si16.3 bulk metallic glass shows the high glass forming ability and good thermal stability. By the Differential scanning calorimetry (DSC) results, the values of ΔΤx and ΔΤm are 50 and 21 K. And Trg, γ, and γm values for the Au49Ag5.5Pd2.3Cu26.9Si16.3
bulk metallic glass (BMG) at the heating rate of 0.67 K/s are 0.619, 0.430 and 0.774, respectively.
The mechanical properties of Au49Ag5.5Pd2.3Cu26.9Si16.3 in terms of compression testing are examined using an Instron 5582 universal testing machine. Room temperature compression tests are conducted on specimens with various strain rates. To know the size effect, the micro-pillars were made by using a focus ion beam (FIB) technique. The micro-pillars were under the tests of compression at different strain rates, compared with macro-scale 2 mm rod specimens. In contrast to the brittle fracture in a bulk sample, these micro-pillar specimens show significant plasticity. The morphology of compressed pillar samples indicates that the number of shear bands increased with the sample size and strain rates.
本 實 驗 為 金 基 塊 狀 非 晶 質 合 金 之 機 械 性 質 及 微 成 形 能 力 之 研 究 。 Au49Ag5.5Pd2.3Cu26.9Si16.3合金經由傳統的銅模鑄造方式能夠成功的製作出直徑2 和 3 mm 的棒材，藉由穿透式電子顯微鏡的觀察，發現其中絕大部分是非晶質，但有些許結晶相 分佈在其中。
在熱性質方面，Au49Ag5.5Pd2.3Cu26.9Si16.3 非晶質合金顯示出寬的過冷液體區間，顯 示其有良好的熱穩定性，另外，根據非晶質合金玻璃形成能力的參考指標，其結果顯示 Au49Ag5.5Pd2.3Cu26.9Si16.3據有良好的玻璃形成能力。
行壓縮測試。為了瞭解尺寸大小對材料機械性質的影響，直徑3.8 微米和 1 微米的試片
由聚焦離子束製作，試片經由不同形變速率進行測試，和巨觀直徑 2 mm 的棒材做比
藉由熱機械分析儀(TMA)的量測，在熱機性質方面得知在做壓印測試時，攝氏 177 度是其理想的工作溫度，為探討其成行能力，不同的壓力和壓延時間分別進行測試，發 現較高的壓力和壓延時間，可獲得較佳的成形能力。金基塊狀非晶質合金優異的抗氧化 和成形能力，讓其成為理想的微機電材料。
Chapter 1 Introduction
1.1 Amorphous metallic alloys
Amorphous alloys are metallic materials with a disordered atomic-scale structure.
Compared with other metals, which are crystalline and hence have a highly ordered arrangement of atoms, amorphous alloys are non-crystalline. Materials with such a disordered structure formed directly from the liquid state during rapid cooling are called "glasses", and therefore they are commonly referred to as “metallic glasses” or “glassy metals.” Still, there are several other methods to fabricate, including physical vapor deposition, solid-state reaction, ion irradiation, melt spinning, and mechanical alloying.
1.2 The evolution of Au-based amorphous alloys
Ever since human history has taken place, people are obsessed with the charm of gold which has high electrical conductivity, high thermal conductivity, and high corrosion resistance. And that is why gold earn the value as the noblest metal on the earth, and plays an incomparable role in the variety of areas such as jewelry, medical, electronics, and so forth. It becomes more exciting after Turnbull estimated the possibility of formation of metallic glass if heterogeneous nucleation could be restrained , the metallic glass made its first debut in the composition of Au75Si25 in 1960 by Clement et al. at Caltech, USA . They developed the rapid quenching techniques to fabricate the metallic liquids at very high rates of 105-106 K/s; however, the high cooling rate limited the metallic glass geometry to thin sheet, below 50 microns. In order to improve the glass forming ability of this alloy, Si was partially replaced by Ge, but the new composition can only moderately increase the glass forming
ability (GFA) and the width of supercooled liquid region [3,4] which is the parameter for processing large supercooled liquid region gives access to a low forming viscosity.
In an effort to fabricate bulk metallic glasses over the last two decades, several alloys based on Pd , Fe , Pt , and so on were successfully formed. And the researchers found out that the intrinsic GFA and critical casting thickness, dmax, were characterized by the critical coolong rate, Rc . In 2005, by the contribution of Schriers et al. , gold based amorphous, Au49Ag5.5Pd2.3Cu26.9Si16.3, gets on the stage once again showing good glass forming ability; furthermore, the maximum cast thickness can exceed 5 mm in the best glass former and the Vickers hardness of the alloy in this system is approximately 350 Hv, twice of conventional 18-karat crystalline gold alloys which are rather soft and vulnerable to be scratched. With those attractive properties, it becomes the potential material for medical, dental, and jewelry applications.
1.3 The motivation of this research
Size effects in the deformation of sub-micro crystalline Au columns have been reported by Volkert et al. . Unlike in bulk materials, dislocations inside small crystals can travel only small distance before annihilating at the free surface and have little chance for multiplication, leading to dislocation starvation . For the crystalline materials, the dislocation density is expected to be lower in the small pillars due to the loss of dislocations through the sample surface, the applied stress required to nucleate or activate dislocation sources can be argued to increase with decreasing column diameter. However, for the short-range ordered materials, bulk metallic glasses, the model should be another story. To explore this newly invented bulk metallic glass (BMG) material and its size effects, we fabricate a few 2mm Au-based rods with the same composition as reported by Schriers et al.
From the cast glassy rods, the micro-scale pillar specimens are made and subject to compression experiments to research their mechanical response as a function of specimen size and strain rate compared by the macro-scale 2 mm specimens.
Since this new invented Au-based BMG shows high Poisson’s ratio (0.406), the mechanical properties were of interested and it was expected to have plasticity that most BMG materials lack of. With the anti-oxidation and anti-corrosion, the glass forming ability was investigated to see whether the Au-based BMG may be a material with high potential for micro-electro-mechanical systems (MEMS) applications.
Chapter 2 Background and literature review
2.1 The developments of bulk metallic glasses (BMGs)
The first metallic glass of Au75Si25 was produced by California Institute of Technology, Caltech, USA, in 1960 . Duwez et al. discovered that if a molten metal is undercooled uniformly and rapidly enough, e.g. at 1 x 106 K/s, the heterogeneous atoms will not have enough time to rearrange into crystalline state. The liquid then reaches the glass transition temperature, Tg, and solidifies as a metallic glass. This brand new material has application potential for human beings to lead a better life compared with the old fashion way to fabricate which costs more money and fails to meet our expectancy [12–15]. This technique of rapid quenching has been widely used and innovated. In 1969, Chen and Turnbull fabricated amorphous spheres of ternary Pd-M-Si (with M = Ag, Cu, or Au) at critical cooling rates of 100 to 1000 K/s. The Pd77.5Cu6Si16.5 glassy sphere has a diameter of 0.5 mm. With the endless efforts of researches from all over the world, in the early 1970s and 1980s, the continuous casting processes for commercial manufacture of metallic glasses ribbons, lines, and sheets  were developed. However, the size of this material is limited to the form of wires and sheets by the high cooling rate.
The first so called bulk metallic glass, compared the wires and thin sheets, was the ternary Pd–Cu–Si alloy prepared by Chen in 1974 . They used simple suction-casting methods to fabricate millimeter-diameter rods of Pd–Cu–Si metallic glass at a lower cooling rate of 103 K/s . In 1982, Turnbull and coworkers [17,18] successfully produced the famous Pd–Ni–P BMG by using boron oxide fluxing method. Nevertheless, the discovery of Pd-based BMG is an extraordinary milestone for metallic glasses research, due to the high
cost of Pd metal, the possibility of commercial usage seems to be impractical. Yet the passion for new BMG systems still persists. An overview of critical casting thickness and the date of discovery is shown in Figure 2.1 . Progress has been significant and is outlined below.
And in the 1980s, a number of vitrification techniques, such as mechanical alloying, diffusion induced vitrification in multi-layers, ion beam mixing, hydrogen absorption, and inverse melting, had been emerged.
Since the 1980s, Akihisa Inoue, of Institute for Materials Research, Tohoku University, and William L. Johnson of Caltech have discovered a variety of amorphous systems, such as La- , Mg- , Zr- [21,22], Pd- , Fe- [23,24], Cu- , and Ti- [26,27] based alloys with large undercooling and low critical cooling rates of 1-100 K/s. That enables a greater critical casting thickness (>10 mm) by conventional molding. In 1988, Inoue discovered that the La-Al-TM (TM = Ni, Cu) BMGs. By using Cu molds, they cast glassy La55Al25Ni20 up to 5 mm thick in 1988, glassy La55Al25Ni10Cu10 up to 9 mm in 1991 . The Mg-TM-Y system was also shown in 1991 to have high glass-forming ability in the form of Mg65Cu25Y10 . Another promising system is the Zr-Al-Ni-Cu based alloy, for example, Zr65Al7.5Ni10Cu17.5 with a critical casting thickness of 15 mm . Johnson and Peker in Caltech developed Zr41.2Ti13.8Cu12.5Ni10.0Be22.5 in 1991, as part of a US Department of Energy and NASA funded project to develop new aerospace materials. With critical casting thickness of up to 100 mm, the alloy was known as Vitreloy 1 (Vit1), the first commercial BMG.
Figure 2.2 exhibits the as-cast Zr-based BMGs in different shapes prepared by the Institute of Physics, Chinese Academy of Sciences, China . Groups at the Institut National Polytechnique de Grenoble, France, the Leibniz Institute for Solid State and Materials Research Dresden, European Synchrotron Radiation Facility, the Institute of Metallurgy and Materials Science in Krakow, Universidad Complutense Madrid, Universitat Autonoma de Barcelona, and the Universities of Cambridge, Sheffield, Ulm, and Turin collaborated on the
development of Zr-, Mg-, Fe-, Al-, Pd-, Hf-, and Nd-based alloys. Research aimed at increasing the concentrations of light elements such as Ti, Al, and Mg in environmentally safe, as well as Be-free Zr-based alloys. Table 2.1 lists the typical BMG systems and the year in which they were first reported. It is clear that the BMGs were developed in the sequence beginning with the expensive metallic based Pd, Pt and Au, followed by less expensive Zr-, Mg- Ti-, Ni- and Ln-based BMGs .
2.2 Thermal stability and glass forming ability of BMGs
Metallic glasses could be fabricated by rapid quenching from the melt liquid when the quenching rate exceeds its critical cooling rate. Glass forming ability (GFA), which is related to the ease of devitrification, is vital for understanding the origins of glass formation. The GFA of an alloy is evaluated in terms of the critical cooling rate (Rc) for forming metallic glasses, which is the minimum cooling rate necessary to keep the melt amorphous without forming any crystal during the solidification process. The smaller Rc, the higher the GFA.
However, the value of Rc is difficult to evaluate precisely. So many criteria have been proposed to elucidate the relative GFA of bulk metallic glasses by characteristic temperatures measured by differential thermal calorimetry (DSC).
For GFA concern, Figure 2.3 illustrates the relationship between the critical cooling rate (Rc), maximum sample thickness (tmax) and reduced glass transition temperature (Tg/Tm), where Tg glass transition temperature and Tm v.s. solidus temperature for amorphous alloys reported to date [33-36]. And the lowest Rc is as low as 0.10 K/s  for the Pd40Cu30Ni10P20
alloy and the tmax reaches values as high as about 100 mm. It is also noticed that the recent improvement of GFA reaches 6-7 orders lower for the critical cooling rate and 3-4 orders higher for the maximum thickness. What is more, there is a clear trend for GFA to increase
with increasing Tg/Tm. Figure 2.4 elucidates the relationship between Rc, tmax and the temperature interval of a supercooled liquid, Δ Tx, defined by the difference between Tg and crystallization temperature (Tx), (Tx-Tg) [33-36]. One can see a clear tendency for GFA to increase with increasing Δ Tx. The value of Δ Tx exceeds 100 K for several amorphous alloys in Zr-Al-Ni-Cu and Pd-Cu-Ni-P systems and the largest ΔTx reaches 127 K for the Zr-Al-Ni-Cu base system.
The most extensively used criterion is the reduced glass transition temperature, Trg 
(= Tg/Tl, where Tl is the liquidus temperature) and the supercooled liquid region, Δ Tx. Trg
shows a better correlation with GFA than that given by Tg/Tm for bulk metallic glasses.
Usually the Δ Tx and Trg are used as indicators of the GFA for metallic glasses. The tendency for Rc to decrease with increasing Trg is shown in Figure 2.5 . From the view point of Trg
(= Tg/Tl), lqiuidus temperature Tl can be used to indicate the relative stability of stable glass forming liquids; the lower Tl the larger stability of the liquid, so the liquid can remain stable to a lower temperature with no formation of any solid phase. Table 2.2 shows the composition of representative BMG systems, their glass transition temperature, Tg, onset temperature of crystallization, Tx, and onset melting point, Tm, and glass forming ability represented by reduced glass transition temperature, Trg. For another parameter Δ Tx (= Tx-Tg), a largerΔ Tx value may indicate that the undercooled liquid can remain stable in a wider temperature region without crystallization . The onset crystallization temperature Tx
couldbe used to roughly compare the crystallization resistance during glass formation for metallic liquids, although in some compositions the decisive competing solid phase during cooling might be different from that on devitrification . The larger Tx
value suggests a highercrystallization resistance, so the larger GFA. Lu and Liu  proposed that the new parameter γ (= Tx / (Tg + Tl)) was defined for inferring the relative GFA among bulk metallic glasses. Regardless of alloy system, the relationship between γ and the critical cooling rate Rc
(K/s) as well as critical section thickness Zc (mm) has been formulated as follows:
Rc = 5.1x1021exp(-117.19 γ), (1)
Zc = 2.8x10-7exp(41 γ). (2)
Note that these two equations can be utilized to estimate Rc and Zc when γ is measured from DSC. The parameter γ reveals that a stronger correlation with GFA than Trg,and has been successfully applied to glass formation in the bulk metallic glass systems. In 2007, Du et al.
 proposed a new parameter for GFA, γm= (2Tx-Tg)/Tl, which comprised the idea that overall liquid phase stability is positively related to the quantity of (Tx−Tg)/Tl while the crystallization resistance is proportional to Tx.
In order to compare the efficiency of the currently proposed GFA criteria γm with previous parameters such as γ (=Tg /Tx+Tl), Tx /Tl, ΔTx, Trg, and Tx / Tl−Tg, they are all plotted against Rc, the critical cooling rate for glass formation. Figure 2.6 shows the correlation between the critical cooling rate and the parameter γm
for metallic glasses.
Data were taken from the previous reseachers. A linear regression analysis shows that the relation between Rc
can be expressed as:
= 14.99 − 19.441γm. (3)
The fitting parameter R2 value gives the idea of the effectiveness and consistency of different GFA parameters. The higher the R2 value, the better is the correlation between the proposed GFA parameter and Rc. Compared with other parameters invented before, γm exhibits the best correlation with the glass forming ability.
Over the past decade, various empirical BMG formation criteria have been developed.
The first one is the multi-component alloy systems consisting of more than three elements.
And the second criterion is to pick elements with large differences in size, which leads to a complex structure for crystallization unfavorable. The third one is the negative heat of mixing among the major elements. From the thermodynamic point of view, by the generally known relation of ΔG =ΔHmix – ΔSmix, the low ΔG value can be obtained if the value of ΔHmix is small and ΔSmix is large. The large ΔSmix is expected to be obtained in multi-component alloys systems because ΔSmix is proportional to the number of component. The necessity of large negative heat of mixing is a result of the fact such distinct atoms tend to bond together.
Therefore, if there are three different elements mixed together and the difference in atomic size is large, the atomic configuration tends to appear as high dense random packing. The last effective step is to find out alloy compositions with deep eutectics, which form liquids that are stable to relatively low temperatures .
2.3 Mechanical behavior of amorphous metallic alloys
2.3.1 Deformation mechanisms
Due to the fact that the bonding in amorphous alloys is of metallic character, strain can be readily accommodated at the atomic scale through changes in neighborhood; atomic bonds can be broken and deformed at the atomic scale without substantial concern. On the other hand, unlike crystalline metals and alloys, metallic glasses only exhibit short-range order.
Crystal dislocations provide the deformation mechanism at low energies in crystals, the local rearrangement of atoms in metallic glasses is a relatively high-energy or high-stress process.
The mechanism of rearrangement is depicted in the two-dimensional schematic of illustrations Figure 2.7, originally proposed by Argon and Kuo  in 1979 on the basis of an
atomic-analog bubble-raft model. The diagraph depicted in Figure 2.7 has been referred to as a “flow defect” or “s defect” [44,45], a “local inelastic transition” [46–48] and, increasingly commonly, a “shear transformation zone” (STZ) [45,47]. The STZ is essentially a cluster of atoms that undergo an inelastic shear deformation from one relatively low energy configuration to a second such configuration, crossing an activated configuration of higher energy and volume. After the original analog model of Argon and his colleague [41,48], more sophisticated computer models have been employed to study glass deformation in both two and three dimensions [44,45,49,50].
STZs are common for deformation in all amorphous metals, although details of the structure, size and energy scales of STZs may change from one case to another. It needs to be noted that an STZ is not a defect in an amorphous metal, however, lattice dislocation is a crystal defect. An STZ is defined at an instant–it is observed only when a change from one moment in time to the next. In other words, an STZ is an event defined in a local volume, not a feature of the glass structure. For instance, the local distribution of free volume is believed to control deformation of metallic glasses [43,50,51,52], and it is easy to envision that sites of higher free-volume would more readily accommodate local shear. The first quantitative model of STZ behavior was developed by Argon . The STZ operation takes place within the elastic confinement of a surrounding glass matrix, and the shear distortion leads to stress and strain redistribution around the STZ region. Argon calculated the free energy,Δ , for
FSTZ activation in 1979 in terms of the elastic constants of the glass as below :
F ⎥ ⋅ ⋅ ⋅ Ωo
⎡ + + + ⋅
) 2(1 ) - 30(1
μ τ β γ
ν , (4)
where ν is the Poisson’s ratio,
τois the athermal shear stress at which the STZ transforms, and μ(T) is the temperature dependent shear modulus. The second term in the brackets captures the dilatational energy associated with STZ operation, and β is the ratio of the dilatation to the shear strain. Based on analog models of glass plasticity [43,50], the characteristic strain of an STZ, γo, is usually taken to be of order 0.1, although this quantity can certainly be expected to vary across glass compositions and structural states. The characteristic volume of the STZ,Ω , is generally believed to encompass about 100 atoms, as supported by o simulations and many indirect experimental measurements.
An alternative aspect on the mechanism of plastic flow in amorphous alloys is given by the classical free-volume model, proposed by Turnbull and co-workers [54,55] and applied to the case of glass deformation by Spaepen . This model essentially takes deformation as a series of discrete atomic jumps in the glass, as shown schematically in Figure 2.7; these jumps are obviously favored near sites of high free volume which can readily accommodate them. Because of the diffusion-like character of the process, the characteristic energy scale is of the order of the activation energy for diffusion [52,55,56], which is quite similar to the lower end of the range for the expected energy for an STZ operation. However, whereas the STZ activation energy corresponds to a subtle redistribution of many atoms over a diffuse volume, the activation energy in the free volume model corresponds to a more highly localized atomic jump into a vacancy in the glass structure.
The free volume model introduces a simple state variable to the problem of glass deformation, and allows constitutive laws to be developed on the basis of free volume creation and annihilation through a simple mechanism. Although the differences in the STZ-type model and the diffusive-jump-type model, these atomic-scale mechanisms share
many common features that are crucial to understanding the macroscopic deformation response of metallic glasses: Both mechanisms show characteristics of a two-state system;
forward jumps or STZ operations compete with backward ones, and these can occur at the same spatial position in sequence. This behavior has implications for the rheology of flowing glass, as well as anelastic and cyclic deformation. Both of them are thermally activated, and exhibit similar energy scales; strength and flow character are significantly dependent upon temperature, and can be predicted on the basis of transition-state theory activated processes.
And they are dilatational. Such dilatation is vital for flow localization and pressure dependency of mechanical properties.
Some researchers have attempted to explain plasticity in amorphous alloys in terms of dislocation models, for example, the attempt by Gilman in 1975 , although linear structural defects are not easily defined in an amorphous structure. The general definition of a dislocation is the boundary between a region of material which sheared and a region which has not. Under conditions where glass deformation proceeds through shear localization, an ongoing shear band may spread by propagation of a shear front, which therefore represents a kind of dislocation. Professor Li indicated in 1978 that the stress concentration associated with such a shear front (which he viewed as a Somigliana dislocation) can contribute to shear localization ; that is equal to state that the stress concentration activates STZs ahead of the shear front, causing it to advance. Interactions between the so called Somigliana dislocation and microstructure do not determine the mechanical properties of amorphous alloys as crystalline solids. For example, metallic glasses do not show strain harden, even with high shear band densities. The atomic scale mechanisms described above, STZ- and free-volume-type models, form the foundation for more quantitative understanding of metallic glass deformation.
2.3.2 Shear bands
At high stresses and lower temperatures, metallic glasses deform through localization processes. Under most loading, localization usually takes place through the formation of shear bands, which forms very rapidly and can accommodate displacements apparently up to nearly the millimeter scale . The definition of ‘‘shear band’’, a term which is variously used to describe an event, the residual trace of that event seen as a surface offset, a transient structural feature of a deforming body, or a permanently altered region within a metallic glass.
Two experimental of SEM micrographs illustrating shear ‘‘slip steps’’ associated with shear band operations in metallic glasses are shown in Figures 2.8 (a) and 2.8 (b).
Homogeneous flow is well described by using rheological models, but inhomogeneous flow of metallic glasses is not. However, the inhomogeneous formation of shear bands has important practical results for the strength, ductility, and toughness. Shear localization or shear band formation is generally recognized as a direct consequence of strain softening–an increment of strain applied to a local volume element softens that element, enabling continued local deformation. For amorphous alloys, there are many causes for strain softening and localization, including the local formation of free volume due to flow dilatation, local evolution of structural order due to STZ operations, redistribution of internal stresses associated with STZ operation, and local heat generation. Despite all of these have been discussed by researchers, the dominant theory is generally believed to be a local change in the state of the glass.
Argon in 1979  modeled localization as a result of strain softening from free volume accumulation. By the STZ model, he took the origin of a shear band as a local perturbation in strain rate, and examined the growth of this perturbation with applied strain in a
one-dimensional model. He introduced the dynamics of free volume accumulation with strain, and its softening effect. Furthermore, he derived and solved a bifurcation equation describing the divergence of strain rate in the band and in the surrounding matrix. Figure 2.9 (a) elucidates the acceleration of strain development in the shear band as the shear strain γ increases, and meanwhile the decrease of shear strain rate in the surrounding matrix. On the other hand, the free volume model was proposed by Steif et al. . In this case, the perturbation was taken as a fluctuation of free volume, and tracked by numerically solving equations for free volume and strain rate evolution. The works of Steif et al. are illustrated in Figure 2.9 (b), and complement those of Argon from Figure 2.9 (a).
Both of the models imply the same basic notion for events upon loading a metallic glass in the inhomogeneous regime. When stress is increased, strains are first accommodated elastically, until the stress level increases to a threshold where it can activate flow in a locally perturbed region.
Plastic shearing within a shear band ceases when the driving force for shear decreases below some threshold value, i.e, when the applied strain is fully accommodated by the shear accumulated within the band, relaxing the stress. This phenomenon happens usually in constrained modes of loading, for example, indentation , or compression. In these cases, shear bands form exclusively to accommodate the imposed shape change, and strain only to the extent required for this purpose. The result shows a single shear band operates and arrests, the material can be deformed further through sequent shear banding operations.
Load–displacement responses from such experiments exhibit characteristic patterns of flow serration, as shown in Figures 2.10 (a) and 2.10 (b) for constrained compression and indentation loading. Each serration is a relaxation event associated with the formation of a shear band, registered as a load drop when the experiment is displacement controlled (Figure
2.10 (a)), or a displacement burst under load-control (Figure 2.10 (b)). Under constrained loading, the net flow of metallic glasses is manifested through a series of shear banding events, and is typically characterized, as elastic–perfectly plastic [62,63]. The operation of secondary shear bands can be influenced by prior operation of a primary one [64,65].
Actually, secondary shear bands sometimes can operate directly stop primary ones [64,66]; it turns out to be more than one shear banding event on the same shear plane.
2.3.3 Size effects in plasticity
For metallic glasses, the intrinsic structural length scales of the system are generally believed to be of atomic dimensions, 10–100 atom volumes associated with the STZ activity.
For most experiments, the scale of the test (or specimen) is much larger than this intrinsic scale; hence, complications due to size-related constraints on the deformation mechanism can be neglected. But, the process of shear localization introduces additional length scales to the deformation of metallic glasses, including the width of a shear band (cited as 10–1000 nm in the earlier discussion), its shear displacement, and the characteristic spacing between shear bands. Due to these different scales, size effects play an important role in mechanical experiments.
If one performs experiment with a smaller specimen size, then it is obvious that the characteristic shear band spacing on the specimen will decrease if the shear banding events are to individually accommodate the same amount of strain. As a result, shear band spacing and shear displacement of a single shear band are proportional to the characteristic specimen size, an effect proposed by Conner et al., Ravichandran, and Molinari [63-67], as illustrated in Figure 2.11. This effect has significant meaning for the fracture of metallic glasses because fracture is generally believed to take place along a shear band once a critical level of
displacement has been reached. For this phenomenon in a scale dependent fracture, the thinner specimens may be bent to larger plastic strains without fracture and thicker plates are apparently brittle [63-67]. The size effect described above is basically geometrical in nature, and has been discussed without consideration of kinetic effects. What is more, shear band spacing and shear offset are also affected by strain rate and temperature. Although the details of shear band formation are not yet fully resolved, the process of localization is characterized by intrinsic time and length scales larger than those of STZs and, indeed, large enough to measure deformation behavior at small scales. Both the geometric and intrinsic size effects may have practical implications for the toughness and ductility of structural bulk metallic glasses, and are certainly germane for applications involving thin films or micro-devices.
2.4 Comparison between metallic glasses and engineering materials
Due to the fact that metallic glasses lack of periodic arrangement, they show a distinctive localization of the plastic deformation into shear bands instead of dislocations , which results in special properties, for instance, as compared with crystalline steel and Ti alloys in Figure 2.12, glassy alloys have similar densities but high Young’s modulus and elastic strain-to-failure limit. The glasses have high tensile yield strength, i.e. a high strength-to-weight ratio, making them a possible replacement for Al, but with a much greater resistance to permanent plastic deformation.
With enough data of metallic glasses, BMGs, Ashby and Greer  make quantitative comparisons of their properties with conventional engineering materials. Figure 2.12 shows the elastic limit σy and Young’s modulus E for more than 1500 metals, alloys and metal–matrix composites. The ellipses enclose the range of values associated with given materials and material groups. The data on the conventional metallic materials are from a
standard database ; the metallic glasses are identified by their compositions (in at.%). The metallic glasses show at the upper edge of the plot. They have high strength (the highest known exceeds 5 GPa ), which shows a correlation with Young’s modulus. The shading shows the theoretical strength (σy = E/ 20), which the metallic glasses approach more closely than any other bulk metallic crystalline material. The contours on Figure 2.13 imply the material indices σy /E and σy2 /E. And the first one is the yield strain; the second one is called the resilience, a measure of the ability of the material to store elastic energy. By the diagraph, it shows that the metallic glasses is the best among them, having a larger yield strain and storing more elastic energy per unit volume than any of the other 1500 materials on the same plot.
Figure 2.14 shows the resilience, σy2/E and loss coefficient, η, a parameter of the mechanical damping or energy loss in an elastic load cycle. High resilience is associated with low loss coefficient, implying the contribution of local plastic flow to energy loss. Once again the metallic glasses show excellent property. Their combination of high resilience and low energy loss is attractive for vibrating-reed systems such as springs. Figure 2.15 illustrates fracture toughness Kc (a parameter of load bearing capacity before fracture) and modulus E for some 2000 metals, ceramics, glasses and polymers. The metallic glasses (data from Ref.
) are identified by their compositions. For many applications, failure is energy-limited rather than load-limited; the appropriate material parameter is then not Kc, but rather the toughness Gc (=Kc2/E). The toughest metallic glasses lie above the metals. In the view of brittle materials, there is a basic limit: Gc cannot be less than 2γ, where γ is the surface energy.
Figure 2.16 shows the fracture toughness against elastic limitσy. The diagonal contours show the process-zone size, d (=Kc2/σy2). Suppose the ultimate size, d, of the plastic zone at
the tip of a sharp crack is much smaller than the sample size, fracture will take place. On the other hand, if d is greater than the sample size, brittle failure is not expected. Although for some cases of metallic glasses that have very high fracture toughness Kc, they still have small zone sizes (d < 1 mm) in that σy is so large. The high toughness of some metallic glasses appears to exhibit no ductility (in tension experiments), which results from shear localization.
But, their plasticity in compression is measurable and can be impressive in some cases [73,74].
2.5 The birth of Au-based BMG (Au49
The metallic glasses with high Poisson’s ratio are expected to have good plasticity. By the aid of the periodic table, there are only three pure elements that have Poisson’s ratios higher than 0.4 – 0.45 for Tl, 0.44 for Pb, and 0.44 for Au. Due to the shortcomings of toxicity and health problems found in Tl and Pb, Au-based BMG seemed to be the good choice for investigating the relationship between plasticity and Poisson’s ratio and applications. A suitable Au-based BMG for most applications requires a Tg of at least 370 K for the sake of thermal stability, a large gold content (~18 karat or higher), high hardness, good processibility, and a critical casting thickness that permits fabrication of net-shaped articles such as jewelry. In a view of processing, it is desirable to have a large supercooled liquid region, which in turn enables thermoplastic processing.
The binary gold silicon composition was the first alloy found to exhibit metallic glass formation. However, the critical casting thickness, dc, is below 50 microns. By partially substituting Si by Ge, increases in both the glass forming ability and the width of the supercooled liquid region were observed . However, the result properties are not good enough to meet the needs as mentioned above. In 2005, Schroers et al.  invented a
Au-based BMG (Au49Ag5.5Pd2.3Cu26.9Si16.3) by using the Au-Cu-Si ternary system extending to higher alloys by adding one or more alloying elements. Basically, Ag and Pd are used to replace Au. The atomic radius of the five elements in the alloys is listed in Table 2.3. It can be seen that Au, Ag, and Pd belong to the relatively larger atoms, Cu the medium one, and Si the smaller atom.
Schroers et al.  divided the composition into three groups. One is the partial substitution of Au, one group for Cu, and then still another group is for partial substitution of Si. In such an embodiment, Ag is a preferred additional alloying element. Researchers have found that adding Ag to the Au-based alloys of the current invention improve glass forming ability, the supercooled liquid region, and the glass transition temperature. Another additive alloying element is Pd. When Pd is added, it should be added at the expense of Au, where the Pd to Au ratio can be up to 0.3. A preferable range of Pd to Au ratio is in the range of from about 0.05 to about 0.2. Pt has a similar effect on processibility and properties of the Au-based alloy, and it should be added in a similar way as for Pd.
During the development of Au49Ag5.5Pd2.3Cu26.9Si16.3 alloy, the Au content was varied between 40% and 60%, Ag content was varied from 0-20%, Pd from 0-5%, Cu from 0-35%, and Si from 14-20% (all atomic percent). Among the compositions of these alloys, the Si and Pd have the strongest influence on the glass forming ability and ΔT. This is illustrated in Figures 2.17 and 2.18, which illustrate the relationship of the critical casting thickness and ΔT on Si and Pd content. The Si content was varied between 14 and 20%, resulting in a variation of dc from 1 to 5 mm, and a variation of ΔT from 35 to 60 K. By varying the Pd content from 0% to 5%, ΔT increases continuously with some scatter whereas dc reaches a maximum at Pd = 2.3%. In both cases, a strong dependence of ΔT and dc on the composition variations can be observed. And this composition, Au49Ag5.5Pd2.3Cu26.9Si16.3, can be fabricated maximum casting thickness as high as 5 mm .
2.6 The parameters to distinguish plasticity or brittleness
By the inspiration of that the intrinsic plasticity or brittleness of crystalline metals correlates with the ratio of the elastic shear modulus μ to the bulk modulus B; μ/B, Lewandowski et al.  proposed that the amorphous alloys would show the same relationship. For example, when the ratio μ/B exceeds a critical value, the material is brittle.
The resistance to plastic deformation is proportional to the shear modulus, μ. In either case, the resistance to dilatation caused by the hydrostatic stress state present near the crack is proportional to the bulk modulus, B. And the relationship between ν and μ/B can be shown as below:
B B3 / 2 2
3 / 2 1
μ ν μ
= − , (5)
From this equation, it can be seen that ν increases with decreasing μ/B, as shown in Figure 2.19. With the contributions of the researchers, Figure 2.20 shows a clear correlation between fracture energy G and μ/B. With low values of μ/B, the glasses based on palladium, zirconium, copper or platinum, all with fracture energies well in excess of 1 kJ m-2, exhibit extensive shear banding, and have vein-patterns fracture surfaces. With high μ/B the magnesium-based glass approaches the ideal brittle behavior associated with oxide glasses.
The report  of platinum-based glasses with low μ/B and exceptionally high toughness and fit well on the same correlation. This correlation between G and μ/B is similar to crystalline metals. For a metallic glass, the value of μ/B is typically about two-thirds of the value for the polycrystalline pure metal on which it is based. The glasses might therefore be expected to show more plasticity, but this is offset by the shift in value of (μ/B /B)crit which divides plasticity and brittle fracture. For metallic glasses, the value is in the range 0.41–0.43, where
there is a large drop in G with increasing μ/B, and G approaches the toughness of oxide glasses. This is lower than the range of (μ/B)crit values reported earlier for polycrystalline pure metals. Overall, it would appear that glassy alloys are slightly more likely than their crystalline counterparts to show brittle behaviour. The correlation between fracture energy and elastic constants can also be expressed in terms of Poisson’s ratio. Higher values of ν give higher fracture energy, as shown in Figure 2.21. In a word, metallic glasses with μ/B>0.41–0.43 (or with ν<0.31–0.32) are brittle and vice versa.
2.7 Applications of bulk metallic glasses
With the unique and extraordinary characteristics, BMG materials are useful for application in various fields. One of the great advantages of BMGs is the ease of fabrication into complicated shapes. So far, BMGs have already been used as sporting equipment (Zr-Ti-Cu-Ni-Be and Zr-Ti-Ni-Cu BMGs) and electrode materials (Pd-Cu-Si-P BMG). The development of Fe-based BMGs has reached the final stage for application as soft magnetic materials for common mode choke coils. Success in this area will result in the increasing importance of BMGs. Table 2.4 summarizes the present and future application potentials for the BMGs . The company that fabricates BMGs is Liquidmetal Technologies, co-founded in 1987 as Amorphous Technologies International with Caltech’s Johnson as vice chairman and Peker as vice president, was the first company to produce amorphous metal alloys in viable bulk form. With an exclusive worldwide license for the Zr-based alloy Vitreloy (also known as ‘Liquidmetal’), principal areas for products are sports and luxury merchandises, electronics, medical, and defense.
2.7.1 Golf club heads
The first application to be found was as golf club heads. According to the literature of the BMG golf plate manufacturer , steel club heads transfer about 60% of the input energy to the ball and titanium transfers 70%, whereas the metallic glass transfers 99%. With Higher strength-to-weight ratio allows mass to be distributed differently, enabling various shapes and sizes of head. High production costs, however, led to Liquidmetal Technologies to terminate manufacture in favor of licensing the technology to established club makers. Figure 39 shows the outer shapes of commercial golf clubs in wood-, iron- and putter-type forms where the face materials are composed of Zr-Al-Ni-Cu-Be bulk amorphous alloys.
2.7.2 Cases for consumer electronics
The possibility of moulding into components with thin sections allows BMG to challenge magnesium alloys in the electronic appliances market. With the trend of miniaturization of personal electronic devices such as MP3 players and personal digital assistants (PDA), there is a pressing need to make the casing thinner while retaining sufficient mechanical strength. BMGs exhibit obvious advantages over polymeric materials and conventional light alloys. Mobile phones and digital cameras with BMG casing are already developed .
For example, Vitreloy can also yield stronger, lighter, and more easily molded casings for personal electronic products. In September 2002, at a new $45 million factory in Pyongtaek, South Korea, Liquidmetal began making components for liquid crystal display casings on cell phones. But, again, costs became a problem. Manufacturing process limitations, higher-than-expected production costs, unpredictable customer adoption cycles, short product shelf-life, and intense pricing pressures have made it difficult to compete profitably in this commodity-driven market. The company is now focusing on manufacturing
selected, higher-margin cell phones (mainly for Samsung), value-added sports and medical products, as well as research development and prototyping. Liquidmetal Technologies’ is also working with design firm Ideo to create a Vitreloy-encased laptop that rolls up like a piece of paper .
2.7.3 Liquidmetal rebounds
Liquidmetal Technologies also produced leisure equipment that requires good rebound.
It teamed with Rawlings Sporting Goods Company, Inc. to produce baseball and softball bats.
Meanwhile it worked with HEAD on skis and snowboards. Other potential applications in sporting goods include fishing equipment, hunting bows, guns, scuba gear, marine applications, and bicycle frames. Vitreloy can also be used for watch cases to substitute Ni and other metals, which may cause allergic reactions, and. A few years ago, Liquidme tal Technologies teamed up with the watch and jewelry division of LVMH, whose luxury watchmaker TAG Heuer launched a special edition “Microtimer Concept Watch” last April featuring Vitreloy as the scratch- and dent-resistant, and high-gloss casing .
2.7.4 Medical applications
Another area is a biocompatible, non-allergic form of the glassy material that would be suitable for medical components such as prosthetic implants and surgical instruments. The unique properties of BMGs for orthopedic applications include: (1) biocompatible; (2) excellent wear resistance; (3) high strength-to-weight ratio compared to titanium and/or stainless steel; (4) more than twice the strength compared to titanium or stainless steel; (5) possibility of precision net-shape casting with desirable surface texture which results in significant reduction in post-processing.
For example, DePuy Orthopaedics, Inc. is using the material in knee-replacement devices. Other applications include pacemaker casings. In 2002, Surgical Specialties began producing ophthalmic scalpel blades using the Vitreloy alloy. They are higher quality but less expensive than diamond, sharper and longer lasting than steel, and more consisten tly manufacturable, since they are produced from a single mold .
2.7.5 Defense and aerospace
Metallic glasses can also play the role as military materials that are stronger, lighter, and more effective at high temperatures and stresses. These can replace depleted uranium penetrators in antitank armor-piercing projectiles because of their similar density and self-sharpening behavior.
NASA’s Genesis spacecraft, the first mission to collect and return samples of the solar wind—fast moving particles from the Sun—will help scientists to refine the basic definition of the Sun’s characteristics, and understand how the solar nebula, a large cloud of gas and dust, gave rise to our complex solar system. Genesis has received its final piece of science equipment: a solar wind collector made of a new formula of bulk metallic glass .
2.8 Viscous flow behavior
Amorphous alloys are metallic materials with a disordered atomic-scale structure.
Compared with other metals, which are crystalline and hence have a highly ordered arrangement of atoms, amorphous alloys are non-crystalline. Bulk Metallic glasses (BMGs) show some special physical properties such as excellent elasticity and strength as compared
to crystalline alloys. What is more, significant plasticity occurs in the supercooled liquid region, ΔTx (= Tx - Tg, where Tx is the crystallization temperature and Tg the glass transition temperature), due to a tremendous drop in viscosity at temperatures above Tg upon heating . Thus, it is feasible to produce structural parts with complicated shapes in this temperature region [79,80]. Generally, low viscosity and high thermal stability of a supercooled liquid are the two main properties of BMGs for superplastic microforming or imprinting of micro-electro-mechanical (MEMS) devices. The temperature dependence of viscosity in the Zr, Mg, La, and Pd based BMGs has been measured using various thermomechanical techniques to assess the glass fragility before [81-85].
The viscosity, η, is calculated by the Stefan equation  with the geometrical correction of viscous flow,
⎟ • + +−
= ⎛ σ ε d l εn
where σ, ε