Download - Eun Soo Park
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Eun Soo Park
Office: 33-313 Telephone: 880-7221Email: [email protected] hours: by appointment
2019 Fall
10.22.2019
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Glass Formation results when
Liquids are cooled to below Tm (TL) sufficiently fast to avoid crystallization.
Nucleation of crystalline seeds are avoided
Growth of Nuclei into crystallites (crystals) is avoided
Liquid is “frustrated” by internal structure that hinders both events
“Glass Formation”
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A. Homogeneous Nucleation rate, I (by David Turnbull)
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A. Homogeneous Nucleation rate, I (by David Turnbull)
1) η ↑ (dense random packed structure) → I ↓
2) For given T and η, α3β ↑ (σ solid interfacial E & ΔSf ↑/ ΔHf ↓) → I ↓
3) η ~ Trg (=Tg/Tl) & α3β ~ thermal stability of supercooled liquid
* For metallic melt : αβ1/3 ~ 0.5
* if αβ1/3 > 0.9, impossible to crystallization by homogeneous nucleation
under any cooling condition
* if αβ1/3 ≤ 0.25, difficult to prevent crystallization
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B. Growth rate of a crystal from an undercooled liquid, U
1) η ↑ (dense random packed structure) → U ↓
2) For given T , I & U ~ η → Trg or α, β ↑ → GFA ↑3) f ↓ through atomic rearrangement like local ordering or segregation → U ↓
* metallic melt: αβ1/3 ~ 0.5 / Trg > 2/3 ~ high GFA
* Pure metal: Rc ~ 1010-12 K/s, but if Trg = 0.5 , Rc ~ 106 K/s
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C.
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Trg 1/4 1/2 2/3
Rc = 1010 K/s
Rc = 106 K/sRc = 3x103 K/sRc = 3.5x101 K/s
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Critical Cooling Rates for Various Liquids
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TTT Diagram of Pd40Cu30Ni10P20
Appl. Phys. Lett., Vol. 77, No. 5, 31 July 2000
Rc ~ 0.11K/sby calculation
Rc~0.78K/sin ESL
Rc~2.8K/sin DSC
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Thermal Evaporation/ Sputtering/ Vapor Chemical Deposition
2.6 Methods to Synthesize Metallic Glasses
2.6.1 Vapor-state Processes: expensive & slow, electronic & magnetic applications
2.6.2 Liquid-state Processes : Rapid Solidification Process (RSP)most ideal way to obtain metallic glasses, especially the bulk foam
105-6 K/s
Splat Quenching/ Melt-spinning/ Electro Deposition/ Gas Atomization
2.6.3 Solid-state Processes_Solid state diffusional amorphization
Mechanical Alloying & Milling/Hydrogen-induced Amorphization/Multilayer Amorphization/ Pressure-induced Amorphization/ Amorphization by Irradiation/ Severe Plastic Deformation_Intense deformation at low temperatures /Accumulative Roll Bonding (ARB process)
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2.7 Bulk Metallic Glasses (BMGs)
2.7.1 Characteristics of Bulk Metallic Glasses
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2.7.2 The Origins of BMGs
* History of Metallic Glasses
First bulk metallic glass (Pd77.5Cu6Si16.5) produced by droplet quenching at Harvard Univ. by H.S. Chen and D. Turnbull in 1969
First amorphous metal produced by evaporation in 1934.
First amorphous alloy(CoP or NiP alloy)
produced by electro-deposition in 1950.
First metallic glass (Au80Si20) produced by splat quenching at Caltech by Pol Duwez in 1957.
* j. Kramer, Annalen der Phys. 1934; 19: 37.
* A. Brenner, D.E. Couch, E.K. Williams, J. Res. Nat. Bur. Stand. 1950: 44; 109.
* W. Klement, R.H. Willens, P. Duwez, Nature 1960; 187: 869.
* H.S. Chen and D. Turnbull, Acta Metall. 1969; 17: 1021.
produced by water quenching of PdTMSi, Pt-Ni-P and Pd-Ni-P system by H.S. Chen in 1974 ( long glassy roads, 1-3 mm in diameter and several centimeters in length)
* H.S. Chen, Acta Metall. 1974; 22: 1505
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By droplet quenching (CR~800 K/s)
SEM image of a collection of glass spheres
CR~800 K/s* H.S. Chen and D. Turnbull, Acta Metall. 1969; 17: 1021.
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Bulk formation of a metallic glass: Pd40Ni40P20
Alloy Selection: Consideration of Trg
* Pd82Si18 Trg=0.6 - Homogeneous nucleation rate: >105/cm3s- Critical cooling rate: > 800 K/s
* Pd77.5Cu6Si16.5 Trg=0.64
* Pd40Ni40P20 Trg=0.67Tg=590 K, Te = 880 K, Tl = 985 K
Suppression of Heterogeneous nucleation
1. Surface Etching of ingot in a mixture of HCL and H2O2: elimination of surface heterogeneities
2. Thermal cycling –5 cycles: dissolution of nucleating heterogeneities
reduce the temperature at which nucleation occurred
<Schematic diagram of apparatus>
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16A.J. Drehman, A.L. Greer, D. Turnbull, Appl. Phys. Lett. 1982; 41: 716.
recalescence
Bulk formation of a metallic glass: Pd40Ni40P20
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17OM image of the cross section of a crystalline inclusion showing the eutectic structure
Largest ingot
- minimum dimension 0.6 cm and mass of 2.3 g
- Critical cooling rate: ~ 1.4 K/sec.
*Appl. Phys. Lett. 1982; 41: 716.
Bulk formation of a metallic glass: Pd40Ni40P20
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Heterogeneous nucleation
1. Surface oxide layer2. Container walls
3. Motes in the liquid
Suppression1. Ingot = Chemical etching
by dilute aqua regia (HNO3 + HCl)2. Interior of the vessel = Cleaning
by hydrofluoric acid3. Impurities = Successive heating-cooling cycles
in a molten oxide fluxB2O3 melting point 723 K, boiling point <40,000 K
After gravity segregation to the oxide-metal interfacemost heterophase impurities presumably are dissolved or deactivated (e.g., by being wet) by the molten oxide
Formation of bulk metallic glass by fluxing
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Schematic process of fluxing
water
Quartz tube
B2O3
Molten B2O3
Master alloy
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Formation of centimeter-sized BMG by fluxing
Largest ingot
- minimum dimension 1 cm and mass of 4 g
- Critical cooling rate: ~ 1K/sec.
Pd40Ni40P20
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Y.He, et al Appl. Phys. Lett. 1996; 69: 1861.
Pd40Ni40P20 Pd40Ni40P201982 1996
Dmax~5mm Dmax~25mm
Pd40Ni10Cu30P20 1997Appl. Phys. Lett., Vol. 41, No.8, 1982
Dmax~50mm Dmax~72mm
Mat.sci.eng 15 June 1997
1984
Dmax~10mm
After fluxing
treatment
Intermetallics, Vol30, Nov2012, P 19–24
Pd42.5Ni7.5Cu30P20 2012
Dmax 80mm
Formation of centimeter-sized BMG by fluxing
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Figure 2.6X-ray diffraction patterns of La55Al25Ni20glassy samples in the water-quenched rod(0.8 mm dia. → Dmax = 1.2 mm) and melt-spun ribbon (20μm) conditions. Note that in both the cases, the diffraction pattern shows only a broad peak and sharp peaks indicative of any crystalline phase are absent. Furthermore, the position of the broad peak is the same in both the samples, suggesting that the glassy phase produced in same in both the cases.* Inoue A, et al., Mater. Trans. JIM, 30, 722, 1989.
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* Appl. Phys. Lett. 63: 2342-2344.
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Zr47Ti8Cu8Ni10Be27 Johnson (Caltech)
Vitreloy
Pd60Cu30Ni10P20 Inoue (Tohoku Univ.)
Fe48Cr15Mo14Y2C15B6 Poon (Virginia Univ.)
Amorphous steel
Ca65Mg15Zn20 15mm Kim (Yonsei Univ.)
Ca60Mg25Ni20 13mm
Mg65Cu20Ag5Gd10 11mm
Mg65Cu7.5Ni7.5Zn5Ag5Gd5Y5 14mm
Recent BMGs with critical size ≥ 10 mm
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Bulk glass formation in the Pd-/Ni-/Cu-/Zr-element system
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Recent BMGs with critical size ≥ 10 mm
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3. Glass-Forming Ability of AlloysMany glasses were produced more or less by trial and error.→ The ability of a metallic alloy to transform into the glassy state is
defined in this chapter as the glass-forming ability (GFA).
3.2 Critical Cooling Rate
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3.2.1 T-T-T Diagrams: isothermal processes
Liquid
Undercooled
Glass
Tn
tn
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Rc vs Dmax in Ti-Zr-Cu-Ni alloy system
Total cooling time τ ~(R2/κ)
sample dimension (dia. or thickness) : Rinitial temperature: Tmthermal diffusivity : κ
κ=K/C thermal conductivity : Kheat capacity per unit volume: C
Tm-Tg ~400K K~0.1W/cm s-1K-1 C~4J/cm3K-1
For Ti-Zr-Cu-Ni system,
J. Appl. Phys. 78, 1 December 1995
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3.2.2. Effect of Alloying Elements
100
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34Trg 1/4 1/2 2/3
Rc> 1010-12 K/s 104-6 K/s 102 K/s 1.3x10-2 or 0.067 K/s 10-5 to 10-4 K/s
Rc = 1010 K/s
Rc = 106 K/sRc = 3x103 K/sRc = 3.5x101 K/s
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3.2.3 Measurement of Rc
5 10 15 20 25 30 35 40 45
300
400
500
600
700
800
900
1000
Ca65Mg15Zn20
Tem
pera
ture
(K)
(Cu mold casting in air atmosphere)
(a) (b) (c) Tg
Tl
time (sec)
(c) d = 15 mm
45 mm(b) d = 10 mm
(a) d = 6 mm
tTT
R gic ∆
−=
* Cooling curves measured at the center of the three transverse cross sections
bottom position : 149 K/s
middle position : 93 K/s
top position : 20 K/s
* J. Mater. Res. 19, 685 (2004)* Mater. Sci. Forum 475-479, 3415 (2005)
Measurement of Rc in Ca65Mg15Zn20 (Dmax>15 mm)
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3.2.3 Measurement of Rc
tTT
R gic ∆
−=
* Cooling curves measured at the center of the three transverse cross sections
bottom position : 137 K/s
middle position : 64K/s
top position : recalescence
5 10 15 20 25 30 35 40 45
300
400
500
600
700
800
900
1000 Mg65Cu7.5Ni7.5Zn5Ag5Y5Gd5
Tem
pera
ture
(K) (Cu mold casting in air atmosphere)
(a) (b) (c) Tg
Tl
time (sec)
Measurement of Rc in Mg BMG (Dmax=14 mm)
* JAP 104, 023520 (2008)
recalescence(c) d = 15 mm
45 mm(b) d = 10 mm
(a) d = 6 mm
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1) Effect of B2O3 fluxing
2) Effect of # of components
3) Nature of alloying addition
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3.3 Reduced Class Transition Temperature (Kinetic aspect for glass formation)
Trg parameter = Tg/Tl ~ η : the higher Trg, the higher η, the lower Rc
: ability to avoid crystallization during cooling
1.0 0.8 0.6 0.4 0.2 0
30
20
10
0
-10
-20
-30
Trg= 0
Trg= 1/2
Trg= 2/3
Ni
Au4Si
SiO2
Log
I(c
m-3
s-1)
Crys
tal n
ucle
atio
n ra
te
Tr=T/Tliquidus
-6
Turnbull, 1959 ff.
TrgNi < TrgAu4Si < TrgSiO2
RNi > RAu4Si > RSiO2
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Based on the nucleation theory,Turnbull suggested that at Trg≥2/3, homogeneous nucleation of the crystalline phase is completely suppressed. Most typically, a minimum value of Trg~0.4 has been found to be necessary for the glass to form.
One should note the Tl, liquidus temperature as the point at the end of the liquid formation, and not at the beginning of melting.
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High GFA : low free energy
for transformation of liquid to crystalline phase
)(TG∆
ff STHTG ∆−∆=∆ )( G∆ fH∆ fS∆&Enthalpy of fusion Entropy of fusion
fS∆Entropy of fusion
: proportional to the number of microscopic states
Multi-component alloy systems containing more than 3 elements
causes an increase in the degree of dense random packing
* The free energy at a constant temperature also decreases in the cases of low
chemical potential caused by low enthalpy and high reduced glass transition
temperature (=Tl/Tg) and high interface energy between liquid and solid phase.
fH∆Enthalpy of fusion
Large negative enthalpy of mixing among constituent elements
3.4 Deep Eutectics (Thermodynamic aspect for glass formation)
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→ deep eutectic condition: increase stability of stable liquid (= Tg/Tl ↑)
- decreasing melting point less supercooled at Tg
ex) metallic / inorganic system
Compositions near the eutecticGlass forming region:
ΔG = Gliq-Gcryst
fH∆
3.4 Deep Eutectics (Thermodynamic aspect for glass formation)
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Multi-component eutectic alloys with strong negative heat of mixing
P. Haasen, Physical Metallurgy 3rd ed
Tg: also changes depending on
alloy composition
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Trg~ highest value at eutectic composition
Trg~ may not be high at eutectic composition
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Glass region is located between composites with different 2nd phases.
Useful to find the composition with maximum GFA
< Symmetric Eutectic> < Non-symmetric Eutectic>
Appl. Phys. Lett., Vol. 84, No. 20, 17 May 2004Appl. Phys. Lett. 86, 191906 (2005)
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1. A(Zr48Cu38Al14) : eutectic composition but glass and composite X
In Cu-Zr alloy, the composition with high GFA is moved to near
liquidus line with higher slope of Zr-rich composition.
Tie triangle among ZrCu, , → A = “ternary eutectic composition” 3τ 5τ
Composites & Glass forming composition
Acta Materialia 53 (2005) 2969–2979
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2.Three composition forming region (casted into 5 mm-diam copper mold)
Following arrows, +glass (B,C,D), + glass (E,F), ZrCu + glass (I,H) ~
At point G, competing crystalline phase changes
3τ 5τ
G = Formation of fully glass
Composites & Glass forming composition
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3.5 Topological Model (Structural aspect for glass formation)
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* Metallic glass : Randomly dense packed structure
1) Atomic size difference: TM – metalloid (M, ex) Boron)
M is located at interior of the tetrahedron of four metal atoms (TM4M)denser by increasing resistivity of crystallization, GFAEx) Fe-B: tetrahedron with B on the center position
1) interstitial site, B= simple atomic topology2) skeleton structure3) bonding nature: close to covalent bonding
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3.5.2. Egami and Waseda Criterion
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2) min. solute content, CB*: empirical rule By Egami & Waseda: in A-B binary system
ν: atomic volumeA: matrix, B: solute
minimum concentration of B for glass formation Inversely proportional to atomic volume mismatch
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3.5.3. Nagel and Tauc Criterion
a(K) Fourier transform of the pair correlation function g(r)
Kp Nearest neighbor distance of the liquid metal in K-space
Kp = 2 kF3/12
3/12 32)3(22
==
HF eR
nK ππ
: Diameter of Fermi surface
The conduction electrons are suppose to form a degenerate free-electron gas with a spherical Fermi surface.
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3.6 Bulk Metallic Glasses
Additionally, because the number of components is really large, determining the mini-mum solute content will be a formidable problem since the contribution of each compo-nent to the volumetric strain is going to be different depending on their atomic sizes.
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3.7 Inoue Criteria – Empirical Rules
a) Thermodynamic point of view
b) Kinetic point of view
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3.7 Inoue Criteria – Empirical Rules
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< significant difference in atomic size ratios >
Many amorphous alloys are formed by exploiting a phenomeonon calledthe “confusion effect”. Such alloys contain so many different elements(often a dozen or more) that upon cooling at sufficiently fast rates, theconstituent atoms simply cannot coordinate themselves into theequilibrium crystalline state before their mobility is stopped. In this way,the random disordered state of the atoms is “locked in “.
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3.7 Inoue Criteria – Empirical Rules
Significant change in the coordination # of Zr-Al atomic pairs on crystallization→ This suggests that there is necessity for long-range diffusion of Al atoms around Zr atoms during crystallization, which is difficult to achieve due to the presence of dense randomly packed clusters.
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Dense packed structure
Ca19.7 nm
-72-20
-13
Heat of mixing[kJ/mol]
Mg16.0 nm
Zn13.8 nm
Decrease of melting temp.
Deep eutectic conditionTe/ Tm
Ca = 0.560
TmCa = 1112 K
Te = below 623 K
- Large difference in atomic size- Large negative heat of mixing
Ca-Mg-Zn alloy system
Alloy design and new BMG development
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Maximum diameter for glass formation in Ca-rich Ca-Mg-Zn alloy system
Ca
90
80
70
Mg
10 3020 40 Zn
over 10mm over 7mm over 3mm over 1mm below 1mm
* J. Mater. Res. 19, 685 (2004)* Mater. Sci. Forum 475-479, 3415 (2005)
15 mm in diameter sampleusing Cu mold casting method in air atmosphere
(self-fluxing effect by Ca)
Ca65Mg15Zn20
Ca-Mg-Zn alloy system
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3.8 Exceptions to the Above Criteria3.8.1 Less Than Three Components in an Alloy System – Binary BMGs
Two important points: 1) The maximum diameter of the glassy rods obtained in these binary alloys
is relatively small, i.e. a maximum of only about 2 mm.2) The “glassy” rods of the binary BMG alloys often seem to contain some
nanocrystalline phases. (?)
Even though glassy (BMG) alloys of 1 or 2 mm diameter are produced in binary alloy compositions., their GFA improves dramatically with the addition of a third component. This observation again proves that a minimum of three compo-nents is required to produce a BMG alloy with a reasonably large diameter.
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3.8.2 Negative Heat of Mixing
Phase separation is generally expected to occur in alloy systems containing elements that exhibit a positive heat of mixing. This is indicated by the presence of a miscibility gap in the corresponding phase diagram. Therefore, if phase separation has occurred, one immediately concludes that the constituent elements have a positive heat of mixing
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3.9 New Criteria: to develop better and more precise criteria to predict the GFA of alloy systems
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3.10 Transformation Temperatures of Glasses
Tg TxTm
l Tmmix,cal0 Tm
s
Supercooledliquid
Glass Liquid
< V - T diagram >
RcCritical cooling rate
Tx
Supercooledliquid
< TTT diagram >
Mixtures of melting temp.
Tm TmmixTg
Supercooledliquid
Glass
Crystal
Liquid
Temperature
Volu
me
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Based on thermal analysis (Tg, Tx and Tl): thermodynamic and kinetic aspectsTrg = Tg/Tl D. Turnbull et al., Contemp. Phys., 10, 473 (1969)
K = (Tx - Tg) / (Tl - Tx) A. Hruby et al., Czech.J.Phys., B22, 1187 (1972)
ΔT* = (Tmmix-Tl) / Tm
mix I. W. Donald et al., J. Non-Cryst. Solids, 30, 77 (1978)
ΔTx = Tx – Tg A. Inoue et al., J. Non-Cryst. Solids, 156-158, 473 (1993)
γ = Tx / (Tl + Tg) Z.P. Lu and C. T. Liu, Acta Materialia, 50, 3501 (2002)
Based on thermodynamic and atomic configuration aspectsσ = ΔT* × P’ E. S. Park et al., Appl. Phys. Lett. , 86, 061907 (2005)
ΔT* : Relative decrease of melting temperature + P’ : atomic size mismatch
: can be calculated simply using data on melting temp. and atomic size
Representative GFA Parameters
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1) ΔTx parameter = Tx - Tg
- quantitative measure of glass stability toward crystallizationupon reheating the glass above Tg: stability of glass state
- cannot be considered as a direct measure for GFA
2) K parameter = (Tx-Tg)/(Tl-Tx) =ΔTx/(Tl-Tx)- based on thermal stability of glass on subsequent reheating- includes the effect of Tl , but similar tendency to ΔTx
GFA Parameters on the basis of thermodynamic or kinetic aspects :
3) ΔT* parameter = (Tmmix – Tl)/ Tm
mix
-
- evaluation of the stability of the liquid at equilibrium state - alloy system with deep eutectic condition ~ good GFA- for multi-component BMG systems: insufficient correlation with GFA
imT
n
i inmixmT ⋅∑=
Tmmix represents the fractional departure of Tm with variation of compositions
and systems from the simple rule of mixtures melting temperature
( where ni and Tmi are the mole fraction and melting point, respectively,
of the i th component of an n-component alloy.)
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Time Temperature Transformation diagram: 1) ΔTx = Tx - Tg
Tg
Tx1
Tx2
Tem
pera
ture
R1 R2
ΔTx1 < ΔTx2 R1 > R2
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IH = R2 : regression coefficientThe R2 vale can range from 0 to 1 and is an indicator of the reliability of the correlation. The higher R2
value, the more reliable the regression is.
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1) ΔTx parameter = Tx - Tg
- quantitative measure of glass stability toward crystallizationupon reheating the glass above Tg: stability of glass state
- cannot be considered as a direct measure for GFA
2) K parameter = (Tx-Tg)/(Tl-Tx) =ΔTx/(Tl-Tx)- based on thermal stability of glass on subsequent reheating- includes the effect of Tl , but similar tendency to ΔTx
GFA Parameters on the basis of thermodynamic or kinetic aspects :
3) ΔT* parameter = (Tmmix – Tl)/ Tm
mix
-
- evaluation of the stability of the liquid at equilibrium state - alloy system with deep eutectic condition ~ good GFA- for multi-component BMG systems: insufficient correlation with GFA
imT
n
i inmixmT ⋅∑=
Tmmix represents the fractional departure of Tm with variation of compositions
and systems from the simple rule of mixtures melting temperature
( where ni and Tmi are the mole fraction and melting point, respectively,
of the i th component of an n-component alloy.)
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Time Temperature Transformation diagram: 2) K=(Tx-Tg)/(T l-Tx)=ΔTx/(Tl-Tx)
Tg
Tem
pera
ture
R1 R2
K1 < K2 R1 > R2
Tl1
Tl2
Tx
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1) ΔTx parameter = Tx - Tg
- quantitative measure of glass stability toward crystallizationupon reheating the glass above Tg: stability of glass state
- cannot be considered as a direct measure for GFA
2) K parameter = (Tx-Tg)/(Tl-Tx) =ΔTx/(Tl-Tx)- based on thermal stability of glass on subsequent reheating- includes the effect of Tl , but similar tendency to ΔTx
GFA Parameters on the basis of thermodynamic or kinetic aspects :
3) ΔT* parameter = (Tmmix – Tl)/ Tm
mix
-
- evaluation of the stability of the liquid at equilibrium state
- alloy system with deep eutectic condition ~ good GFA
- for multi-component BMG systems: insufficient correlation with GFA
imT
n
i inmixmT ⋅∑=
Tmmix represents the fractional departure of Tm with variation of compositions
and systems from the simple rule of mixtures melting temperature
( where ni and Tmi are the mole fraction and melting point, respectively,
of the i th component of an n-component alloy.)
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2.0*≥∆T in most of glass forming alloys
mixmT
lTmixmT
T−
=∆ *Relative decrease of melting temperature
: ratio of Temperature difference between liquidus temp. Tl and imaginary melting temp. Tm
mix to Tmmix
by I.W. Donald et al. (J. Non-Cryst. Solids, 30, 77 (1978))
TmB
TmA
TmC
AB
C
Te
Tl
mixTm
0.22 0.24 0.26 0.28 0.30 0.32 0.34 0.36 0.38
1
10
R2 = 0.812max
imum
dia
met
er D
max, m
m
∆T *
Ca-Mg-Zn alloy system
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4) Trg parameter = Tg/Tl
- kinetic approach to avoid crystallization before glass formation- Viscosity at Tg being constant, the higher the ratio Tg/Tl,
the higher will be the viscosity at the nose of the CCT curves, and hence the smaller Rc
- Tl ↓and Tg ↑ ► lower nucleation and growth rate ► GFA ↑
▪ significant difference between Tl and Tg in multi-component BMG ▪ insufficient information on temperature-viscosity relationship► insufficient correlation with GFA
GFA Parameters on the basis of thermodynamic or kinetic aspects :
5) γ parameter = Tx / (Tl + Tg)- thermodynamic and kinetic view points - relatively reliable parameter- stability of equilibrium and metastable liquids: Tl and Tg
- resistance to crystallization: Tx
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Trg parameter = Tg/Tl ~ η : the higher Trg, the higher η, the lower Rc
: ability to avoid crystallization during cooling
1.0 0.8 0.6 0.4 0.2 0
30
20
10
0
-10
-20
-30
Trg= 0
Trg= 1/2
Trg= 2/3
Ni
Au4Si
SiO2
Log
I(c
m-3
s-1)
Crys
tal n
ucle
atio
n ra
te
Tr=T/Tliquidus
-6
Turnbull, 1959 ff.
TrgNi < TrgAu4Si < TrgSiO2
RNi > RAu4Si > RSiO2
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R1 R2
Trg1 < Trg2 R1 > R2
Time Temperature Transformation diagram: Trg=Tg/Tl
Tg1
Tg2
Tl
Tem
pera
ture
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R1 R2
Trg1 < Trg2 R1 > R2
Tg
TlTl1Tl2
Time Temperature Transformation diagram: Trg=Tg/Tl
Tem
pera
ture
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4) Trg parameter = Tg/Tl
- kinetic approach to avoid crystallization before glass formation- Viscosity at Tg being constant, the higher the ratio Tg/Tl,
the higher will be the viscosity at the nose of the CCT curves, and hence the smaller Rc
- Tl ↓and Tg ↑ ► lower nucleation and growth rate ► GFA ↑
▪ significant difference between Tl and Tg in multi-component BMG ▪ insufficient information on temperature-viscosity relationship► insufficient correlation with GFA
GFA Parameters on the basis of thermodynamic or kinetic aspects :
5) γ parameter = Tx / (Tl + Tg)- thermodynamic and kinetic view points - relatively reliable parameter- stability of equilibrium and metastable liquids: Tl and Tg
- resistance to crystallization: Tx
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Wide scatter for the tmax correlation
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on the basis of thermodynamic or kinetic aspects
GFA parameters
Trg
K
ΔT*
∆Tx
γ
δ
α
β
φ
γm
β
ξ
Expression
Tg / Tl
(Tx-Tg) / (Tl-Tx)
(Tmmix–Tl) / Tmmix
Tx – Tg
Tx / (Tl+Tg)
Tx / (Tl-Tg)
Tx / Tl
Tx / Tg + Tg / Tl
(Tg / Tl )(Tx-Tg / Tg)a
(2Tx – Tg) / Tl
(Tg / Tl- Tg )(Tg / Tl- Tg )
∆Tx / Tx + Tg / Tl
Year established
1969 D.Turnbull,Contemp.Phys.10(1969) 473
1972 A.Hruby, Czech. J.Phys. B 22 (1972) 1187
1978 I.W.Donald, J.Non-Cryst.Solids 30 (1978) 77
1993 A.Inoue, J.Non-Cryst.Solids 156-158(1993)473
2002 Z.P.Lu, C.T.Liu, Acta Mater. 50 (2002) 3501
2005 Q.J.Chen,Chiness Phys.Lett.22 (2005) 1736
2005 K.Mondal, J.Non-Cryst.Solids 351(2005) 1366
2005 K.Mondal, J.Non-Cryst.Solids 351(2005) 1366
2007 G.J.Fan,J.Non-Cryst. Solids 353 (2007) 102
2007 X.H.Du,J.Appl.phys.101 (2007) 086108
2008 Z.Z.Yuan, J. Alloys Compd.459 (2008)
2008 X.H.Du,Chinese Phys.B 17(2008) 249
GFA Parameters