1
“Advanced Physical Metallurgy”
‐ Bulk Metallic Glasses ‐
Eun Soo Park
Office: 33‐313
Telephone: 880‐7221 Email: [email protected]
Office hours: by appointment
2014 Spring
04.17.2014
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.
3.7 Inoue Criteria – Empirical Rules
a) Thermodynamic point of view
b) Kinetic point of view
3.7 Inoue Criteria – Empirical Rules
< significant difference in atomic size ratios >
Many amorphous alloys are formed by exploiting a phenomeonon called
the “confusion effect”. Such alloys contain so many different elements
(often a dozen or more) that upon cooling at sufficiently fast rates, the
constituent atoms simply cannot coordinate themselves into the
equilibrium crystalline state before their mobility is stopped. In this way,
the random disordered state of the atoms is “locked in “.
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.
Dense packed structure
Ca
19.7 nm
-20 -72
-13
Heat of mixing [kJ/mol]
Mg
16.0 nm
Zn
13.8 nm
Decrease of melting temp.
Deep eutectic condition T
e/ T
mCa= 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
Maximum diameter for glass formation in Ca-rich Ca-Mg-Zn alloy system
Ca
90 80
70
Mg
10 20 30 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 sample using Cu mold casting method in airatmosphere
(self-fluxing effect by Ca)
Ca
65Mg
15Zn
20Ca-Mg-Zn alloy system
3.8 Exceptions to the Above Criteria
3.8.1 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 diamet er.
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
3.9 New Criteria: to develop better and more precise criteria to predict the GFA of alloy systems
3.10 Transformation Temperatures of Glasses
T
gT
xT
mlT
mmix,cal0 T
msSupercooled liquid
Glass Liquid
< V - T diagram >
Rc
Critical cooling rate
T
xSupercooled liquid
< TTT diagram >
Mixtures of melting temp.
T
mT
mmixT
gSupercooled liquid
Glass
Crystal
Liquid
Temperature
Volume
Based on thermal analysis (T
g, T
xand T
l): thermodynamic and kinetic aspects T
rg= T
g/T
l D. Turnbull et al., Contemp. Phys., 10, 473 (1969)K = (T
x- T
g) / (T
l- T
x)
A. Hruby et al., Czech.J.Phys., B22, 1187 (1972)∆T* = (T
mmix-T
l) / T
mmix I. W. Donald et al., J. Non-Cryst. Solids, 30, 77 (1978)∆T
x= T
x– T
g A. Inoue et al., J. Non-Cryst. Solids, 156-158, 473 (1993)γ = T
x/ (T
l+ T
g)
Z.P. Lu and C. T. Liu, Acta Materialia, 50, 3501 (2002)Based on thermodynamic and atomic configuration aspects σ = ∆T* × P’
E. S. Park et al.,Appl. Phys. Lett. , 86, 061907 (2005)∆T* : Relative decrease of melting temperature + P’ : atomic size mismatch : can be calculated simply using data on melting temp. and atomic size
Representative GFA Parameters
1) ∆T
xparameter = T
x- T
g- quantitative measure of glass stability toward crystallization upon reheating the glass above Tg: stability of glass state - cannot be considered as a direct measure for GFA
2) K parameter = (T
x-T
g)/(T
l-T
x) =∆T
x/(T
l-T
x)
- based on thermal stability of glass on subsequent reheating - includes the effect of Tl , but similar tendency to ∆Tx
GFA Parameters on the basis of thermodynamic or kinetic aspects :
3) ∆T* parameter = (T
mmix– T
l)/ T
mmix-
- 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
i T m n
i n i mix
T m
Tmmixrepresents the fractional departure of Tmwith variation of compositions and systems from the simple rule of mixtures melting temperature
( where niand Tmiare the mole fraction and melting point, respectively, of the i th component of an n-component alloy.)
Time Temperature Transformation diagram:
1) ΔT x = T x - T g
T
gT
x1T
x2Te mperature
R
1R
2ΔT x1 < ΔT x2 R 1 > R 2
IH2 = R
2: regression coefficient The R
2vale can range from 0 to 1 and is an indicator of the reliability of the
correlation. The higher R
2value, the more reliable the
regression is.
1) ∆T
xparameter = T
x- T
g- quantitative measure of glass stability toward crystallization upon reheating the glass above Tg: stability of glass state - cannot be considered as a direct measure for GFA
2) K parameter = (T
x-T
g)/(T
l-T
x) =∆T
x/(T
l-T
x)
- based on thermal stability of glass on subsequent reheating - includes the effect of Tl , but similar tendency to ∆Tx
GFA Parameters on the basis of thermodynamic or kinetic aspects :
3) ∆T* parameter = (T
mmix– T
l)/ T
mmix-
- 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
i T m n
i n i mix
T m
Tmmixrepresents the fractional departure of Tmwith variation of compositions and systems from the simple rule of mixtures melting temperature
( where niand Tmiare the mole fraction and melting point, respectively, of the i th component of an n-component alloy.)
Time Temperature Transformation diagram:
2) K=( T x - T g )/( T l - T x )= ΔT x /(T l -T x )
T
gTe mperature
R
1R
2K 1 < K 2 R 1 > R 2
T
l1 T
l2
T
x1) ∆T
xparameter = T
x- T
g- quantitative measure of glass stability toward crystallization upon reheating the glass above Tg: stability of glass state - cannot be considered as a direct measure for GFA
2) K parameter = (T
x-T
g)/(T
l-T
x) =∆T
x/(T
l-T
x)
- based on thermal stability of glass on subsequent reheating - includes the effect of Tl , but similar tendency to ∆Tx
GFA Parameters on the basis of thermodynamic or kinetic aspects :
3) ∆T* parameter = (T
mmix– T
l)/ T
mmix-
- 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
i T m n
i n i mix
T m
Tmmixrepresents the fractional departure of Tmwith variation of compositions and systems from the simple rule of mixtures melting temperature
( where niand Tmiare the mole fraction and melting point, respectively, of the i th component of an n-component alloy.)
2 . 0
*
T in most of glass forming alloys
m mix T
T l m mix
T T
*
Relative decrease of melting temperature
: ratio of Temperature difference between liquidus temp. Tland imaginary melting temp. Tmmix to Tmmix
by I.W. Donald et al. (J. Non-Cryst. Solids, 30, 77 (1978))
T
mBT
mAT
mCA
B C
T
eT
lT
mmix0.22 0.24 0.26 0.28 0.30 0.32 0.34 0.36 0.38
1 10
R
2= 0.812
maximum diameter D max, mm
T *
Ca-Mg-Zn alloy system
4) T
rgparameter = T
g/T
l- kinetic approach to avoid crystallization before glass formation - Viscosity at T
gbeing constant, the higher the ratio T
g/T
l,
the higher will be the viscosity at the nose of the CCT curves, and hence the smaller R
c- T
l↓and T
g↑ ► lower nucleation and growth rate ► GFA ↑
▪ significant difference between T
land T
gin 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 = T
x/ (T
l+ T
g)
- thermodynamic and kinetic view points
- relatively reliable parameter- stability of equilibrium and metastable liquids: T
land T
g- resistance to crystallization: T
xT rg parameter = T g /T l ~ η : the higher T
rg, the higher η, the lower R
c: ability to avoid crystallization during cooling
1.0 0.8 0.6 0.4 0.2 0 30
20 10 0
‐10
‐20
‐30
T
rg= 0
T
rg= 1/2
T
rg= 2/3
Ni
Au
4Si
SiO
2Log I (cm
‐3s
‐1) Cry stal nucleation ra te
T
r=T/T
liquidus‐6
Turnbull, 1959 ff.
T rgNi < T rgAu4Si < T rgSiO2
R Ni > R Au4Si > R SiO2
R
1R
2T rg1 < T rg2 R 1 > R 2
Time Temperature Transformation diagram:
T rg =T g /T l
T g1 T g2 T l
Te mperature
R
1R
2T rg1 < T rg2 R 1 > R 2 T g
T l T l 1 T l 2
Time Temperature Transformation diagram:
T rg =T g /T l
Te mperature
4) T
rgparameter = T
g/T
l- kinetic approach to avoid crystallization before glass formation - Viscosity at T
gbeing constant, the higher the ratio T
g/T
l,
the higher will be the viscosity at the nose of the CCT curves, and hence the smaller R
c- T
l↓and T
g↑ ► lower nucleation and growth rate ► GFA ↑
▪ significant difference between T
land T
gin 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 = T
x/ (T
l+ T
g)
- thermodynamic and kinetic view points -
relatively reliable parameter- stability of equilibrium and metastable liquids: T
land T
g- resistance to crystallization: T
xWide scatter for the t
maxcorrelation
on the basis of thermodynamic or kinetic aspects
GFA parameters T
rgK
∆T*
∆T
xγ δ α β φ γ
mβ ξ
Expression T
g/ T
l(T
x-T
g) / (T
l-T
x) (T
mmix–T
l) / T
mmixT
x– T
gT
x/ (T
l+T
g) T
x/ (T
l-T
g) T
x/ T
lT
x/ T
g+ T
g/ T
l(T
g/ T
l)(T
x-T
g/ T
g)
a(2T
x– T
g) / T
l(T
g/ T
l- T
g)(T
g/ T
l- T
g)
∆T
x/ T
x+ T
g/ T
lYear established
1969
D.Turnbull,Contemp.Phys.10(1969) 4731972
A.Hruby, Czech. J.Phys. B 22 (1972) 11871978
I.W.Donald, J.Non-Cryst.Solids 30 (1978) 771993
A.Inoue, J.Non-Cryst.Solids 156-158(1993)4732002
Z.P.Lu, C.T.Liu, Acta Mater. 50 (2002) 35012005
Q.J.Chen,Chiness Phys.Lett.22 (2005) 17362005
K.Mondal, J.Non-Cryst.Solids 351(2005) 13662005
K.Mondal, J.Non-Cryst.Solids 351(2005) 13662007
G.J.Fan,J.Non-Cryst. Solids 353 (2007) 1022007
X.H.Du,J.Appl.phys.101 (2007) 0861082008
Z.Z.Yuan, J. Alloys Compd.459 (2008)2008
X.H.Du,Chinese Phys.B 17(2008) 249GFA Parameters
No universal model to predict and evaluate what families of alloy compositions are likely to form BMGs
Combination of categories
that are viewed as decisive in the formation of amorphous alloys
New criterion
for predicting and evaluating Glass Forming Ability
• useful guideline for BMG alloy system design - save time and experimental cost
new alloy system with enhanced GFA
Approach 1. combine thermodynamic and structural points
'
* P
T
*
T
: Relative decrease of melting temp.P’
:Effective atomic mismatch per solute atomm mix T
T l m mix T
T
*
vA vA vC CC CB
CC vA
vA vB CC CB
CB P
'
( where, Ci(i=A,B,C) = solute content, νi= atomic volume )
Approach 2. combine thermodynamic and kinetic points
mix T m
T x T x
T m
Tx Tm
: Liquid phase stability+ Tx
:Resistance to cristallization( where, Tx = crystallization onset temperature ) ( where, ΔTm = Tmmix – Tl , ΔTx = Tx – Tg )
Maximum diameter for glass formation in Ca-rich Ca-Mg-Zn alloy system
Ca
90 80
70
Mg
10 20 30 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 sample using Cu mold casting method in airatmosphere
(self-fluxing effect by Ca)
Ca
65Mg
15Zn
20Ca-Mg-Zn alloy system
2 . 0
*
T in most of glass forming alloys
m mix T
T l m mix
T T
* Relative decrease of melting temperature
: ratio of Temperature difference between liquidus temp. Tland imaginary melting temp. Tmmix to Tmmix
by I.W. Donald et al. (J. Non-Cryst. Solids, 30, 77 (1978))
T
mBT
mAT
mCA
B C
T
eT
lT
mmix0.22 0.24 0.26 0.28 0.30 0.32 0.34 0.36 0.38
1 10
R
2= 0.812
maximum diameter D max, mm
T *
Ca-Mg-Zn alloy system
Thermodynamic aspect for glass formation
v A v A v C
C C v A
v A v B
C B P
v A v A v C C C C B
C C v A
v A v B
C C C B
C B P
'
Effect of atomic size difference can be represented as follows;
by dividing by the total amount of solute contents
Maximum dia.(D
max) at P’=0.625 Similar trend of D
maxwith P
Where, Ci(i=A,B,C) = solute, νi= content atomic volume
20 25 30 35 40 45
0.10 0.15 0.20 0.25 0.30
0 5 10 15
Dmax/mm
P
0.50 0.55 0.60 0.65 0.70
0 5 10 15
Dmax/mm
Zn-rich Mg-rich
P'
Ca-Mg-Zn alloy system
; effective atomic mismatch of solute atom
Structural aspect for glass formation
* Metall.& Mater. Trans. A 32, 200 (2001)
T
mBT
mAT
mCT
mliqA
B C
T
eA B
C
P’ P’(x
c)
P’(A-B) P’(A-C)
T
eA B
C
σ
max~D
maxP’
(A-B)≤P’(Xc)≤P’
(A-C)Deep eutectic condition Large difference
in atomic size
'
* P
T
New criterion for GFA, σ parameter
*
T
: Relative decrease of melting temp. : Effective atomic mismatch per solute atomP’
liquid phase stability solid phase stability
* Appl. Phys. Lett., 86, 061907 (2005)
σ parameter (thermodynamic and atomic configuration aspects)
0.14 0.16 0.18 0.20 0.22 0.24
R 2 = 0.857
maxi mum di ameter D
max, mm 0.5 20 10
1
sigma
* Sigma, σ parameter has a stronger correlation with GFA than other parameters suggested so far (∆T
x: R
2=0.358, T
rg: R
2=0.787, K : R
2=0.607) in Ca-Mg-Zn alloy system.
* J. Metastable and Nanocrystalline Materials, 24-25, 697 (2005)
1) Calculation of GFA parameters in Ca-Mg-Zn alloy system
T
gT
xT
lT
l-T
g∆T
xT
rgK γ ∆T* σ D
maxCa
65Mg
15Zn
20 379 412 624 245 33 0.607 0.156 0.411 0.376 0.234 15Ca
60Mg
25Ni
15 431 453 683 252 22 0.631 0.095 0.406 0.409 0.256 13Ca
65Mg
20Ag
20 422 440 677 255 18 0.624 0.075 0.400 0.384 0.228 4Ca
60Al
30Mg
10 449 474 709 260 24 0.634 0.103 0.409 0.318 0.201 2Ca
60Al
30Ag
10 483 534 805 322 51 0.600 0.187 0.415 0.248 0.165 2Ca
63Al
32Cu
5 512 523 831 320 11 0.615 0.037 0.389 0.221 0.150 2Ca
60Al
30Zn
10 517 540 775 258 24 0.667 0.100 0.418 0.238 0.160 1.5Ca
66.4Al
33.6 527 534 841 315 8 0.626 0.025 0.391 0.200 0.133 1Thermal analysis, GFA parameters and maximum diameter (D
max)
for glass formation in the Ca-based ternary BMG systems
2) Application of σ parameter for BMG-forming Ca-based ternary systems
300 350 400 450 500 550 600 650 700 750 800 Ca60Al30Zn10
Ca63Al32Cu5 Ca60Al30Ag10 Ca66.4Al33.6
Ca60Al30Mg10
Ca60Mg25Ni15 Ca60Mg20Ag20
Ca65Mg15Zn20
Exot her m ic ( 1 w /g per di v. )
Temperature (K)
DSC traces for BMG-forming Ca-based ternary systems
T
gT
m0.10 0.15 0.20 0.25 0.30
R2 = 0.809
20
1 10
maximum diameter D max, mm
Sigma, σ parameter has a stronger correlation with GFA than other parameters suggested so far (∆T
x: R
2=0.056, T
rg: R
2=0.080, K : R
2=0.148) in Ca-based BMG alloy systems.
2) Calculation of GFA parameters in Ca-based BMG alloy systems
* Appl. Phys. Lett. 86, 201912 (2005)
0.385 0.390 0.395 0.400 0.405 0.410 0.415 0.420
R2 = 0.057
20
1 10
maximum diameter D max, mm
Thermal analysis, GFA parameters and maximum diameter (D
max) for glass formation in the ternary BMG systems
T
gT
xT
lT
mmix∆T
xT
rgK γ ∆T* P' σ D
maxCa
65Mg
15Zn
20 379 412 624 1032 33 0.607 0.156 0.411 0.395 0.624 0.234 15Nd
60Fe
30Al
10 750 784 958 1385 34 0.783 0.195 0.459 0.308 0.620 0.199 15Pd
40Ni
40P
20 590 671 991 1519 81 0.595 0.253 0.424 0.348 0.476 0.158 6Mg
65Cu
25Y
10 425 486 720 1062 61 0.590 0.261 0.424 0.322 0.470 0.167 4Mg
65Ni
20Nd
15 459 501 805 1076 42 0.571 0.139 0.397 0.252 0.504 0.148 3.5La
55Al
25Ni
20 491 555 941 1226 64 0.521 0.166 0.388 0.232 0.623 0.148 3La
55Al
25Cu
20 456 495 896 1166 39 0.509 0.097 0.366 0.231 0.613 0.139 3Pd
73.5Cu
10Si
16.5 642 686 1128 1785 44 0.569 0.100 0.388 0.368 0.300 0.107 23) Application of σ parameter for BMG-forming ternary systems
Calculation of G.F.A parameters
Ternary BMG system
30 35 40 45 50 55 60 65 70 75 80 85
0.5 20
1 10
T
xmaximum diameter Dmax, mm
0.50 0.55 0.60 0.65 0.70 0.75 0.80
0.5 R2 = 0.567
20
1 10
T
rgmaximum diameter Dmax, mm
0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22 0.24 0.26 0.28
0.5 20
1 10
K
maximum diameter Dmax, mm
0.36 0.38 0.40 0.42 0.44 0.46
0.5 R2 = 0.547
20
1 10
maximum diameter Dmax, mm
3) Calculation of GFA parameters in ternary BMG alloy systems
0.10 0.15 0.20 0.25
R2 = 0.881
20
1 10
maximum diameter D max, mm
* Sigma, σ parameter has a stronger correlation with GFA than other parameters suggested so far (∆T
x: R
2=0.085, T
rg: R
2=0.567, K : R
2=0.136) in ternary BMG alloy systems.
* Appl. Phys. Lett., 86, 061907 (2005)
D
max= 2.0х10
-1exp (20.01 σ )
0.36 0.38 0.40 0.42 0.44 0.46
0.5 R2 = 0.547
20
1 10
maximum diameter D max, mm
T
gT
xT
lT
mmixUndercooled liquid
Glass
Liquid
∆T
*∆T
xK T
rg, γ
*
0
Elapsed Time, log t
Te mperature, K ↓
T
gT
LT
xUndercooled liquid
Glass
Crystalline phase Liquid
R
c(~ t
xA)
Heating
Cooling
T
mmixMotivation for new criterion (1) : temperature range related with GFA parameters
With T
x↑and T
l↓, GFA parameter ↑. But, the role of T
gis not consistent.
Motivation for new criterion (2) : Role of characteristic temp. for GFA
- from thermodynamic consideration
γ : stability of metastable liquid for glass formation
T
g↓ GFA ↑
- from kinetic consideration
- T
rg: crystallization kinetics on GFA
T
g↓ nucleation and growth rate ↑ -> GFA ↓
- Stability of the liquid during undercooling (i.e. metastable state, Tg)
: Liquid with lower Tg has the potential to be undercooled to lower temp., inducing its higher stability.
Role of T
gwith respect to GFA : Two different viewpoints
- constant cooling to temp. below Tg
X(T) : time dependent volume fraction of crystalline phase
I & U = the steady-state nucleation frequency and the crystal growth rate
If glass formation : X<10-6
1/R
c increasingglass transition temp. Tg viscosity of the supercooled liq.,activation E for viscous flow, fusion entropy decreasing liquidus temp. Tl
1. Combination of categories for glass formation - γ parameter: thermodynamic/ kinetic aspects
New parameter combining thermodynamic/ kinetic aspects
2. Temperature scale for GFA parameter
∆T
xparameter : T
x- T
gK parameter : T
g- T
x- T
lT
rgparameter : T
g- T
lγ parameter : T
g- T
x- T
l∆T* parameter : T
l- T
mmixNew parameter covering temperature range T
g- T
x- T
l- T
mmixwith considering about two different role of T
gPoints of issue for new GFA parameter
T
gT
xT
lT
mmixUndercooled liquid
Glass
Liquid
ΔT
*ΔT
xK T
rg, γ
*
0
a. Liquid phase stability :
- Relative stability of stable liquid : distance from the T
mmixto liquidus melting temp.,
∆T
m= T
mmix– T
l(γ parameter: T
l)
- Stability of metastable liquid : range of supercooled liquid,
∆T
x= T
x- T
g(γ parameter: T
g) b. Resistance to crystallization : T
x(γ parameter: T
x)
- relative difficulties for the formation (nucleation and crystal growth) of the competing crystalline phases in various BMG forming alloy system
- Retarding incubation time for crystallization : relative position of the CCT curves along the time axis
c. nomalizing : T
mmix- Exclusion of systematic and compositional effects in various BMG alloy systems
A New criterion for GFA of BMGs
mix T m
T x T x
T m
E. S. Park et al., submitted to Acta Mater.(2005)
ε parameter
A new criterion for GFA :
* CCT curve showing temperature range for ε parameter
ε parameter (thermodynamic and kinetic aspects)
Stable Liquid stability
Metastable liquid stability
Resistance to crystallization
normalization
Elapsed Time, log t
Te mperature, K ↓
T
gT
LUndercooled liquid
Glass
Crystalline phase Liquid
T
mmixB **
A **
A B A** > B **
ε
A< ε
BR
BR
AR
A> R
BIf Tg, Tl, Tmmix= const in A, B
A New criterion for GFA of BMGs
mix T m
T x T x
T m
ε parameter (thermodynamic and kinetic aspects)
Cu-Zr
Cu-based
Cu-Zr-Ti
Cu-Zr-Ti-Ni-(Si,Sn) Cu-Zr-Al
Cu-Zr-Al-Al Cu-Zr-Al-Y
Fe-B
Fe-based
Fe-Ni-B Fe-Si-B Fe-P-C Fe-Nb-Y-B
Fe-Cr-Mo-C-B-(Y)
La-Al-Ni La-based
La-Al-Cu La-Al-Ni-Cu
La-Al-Ni-Co-Cu Cu-Zr-Ti-Be
Mg-Ni-Nd Mg-based
Mg-Cu-Y-(Ag) Mg-Cu-Gd-(Ag) Mg-Cu-Ag-Pd-Gd
Ni-Nb
Ni-based
Ni-Zr-Ti-(Sn-Si) Ni-Nb-Ta
Ni-Nb-Ti-Hf Ni-Si-B
Pd-Si
Pd-based
Pd-Cu-Si Pd-Ni-P
Pd-Cu-Ni-P Mg-Cu-Ni-Zn-Ag
-Y-(Gd) Ni-Zr-Ti-Si-Sn-Nb
Pt-Ni-P Pt-based
Pt-Cu-Ni-P Pt-Cu-Co-P Y-Al-Co Y-based
Y-Al-Co-Sc Y-Al-Co-Ni-Sc
Zr-based Zr-Al-Ni
Zr-Be-Cu-Ni-Ti Zr-Al-Cu-Ni Zr-Al-Cu-Ni-Ti
Ca-Al
Ca-based
Ca-Al-Cu Ca-Mg-Ni Ca-Mg-Zn
Co-Si-B Co-based
Co-Fe-Ta-B Co-Fe-Nb-Zr-B
Nd-Al-Fe
Nd-based
Nd-Al-Ni-Cu-Co
Nd-Al-Ni-Cu-Fe
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 104
108 1012
100
R
2= 0.848
10-2
ε
critical cooling rate, Rc(K/s) BMGs
Conventional Metallic glasses
0 20 40 60 80 100 120
critical cooling rate, Rc(K/s) 106
104 102
100
R
2= 0.282
10-2
∆ T
x0.0 0.1 0.2 0.3 0.4 0.5
102 104 106
100
R
2= 0.473
10-2
K
critical cooling rate, Rc(K/s)
0.2 0.3 0.4 0.5 0.6 0.7 0.8 104
108 1012
100
R
2= 0.491
10-2
T
rgcritical cooling rate, Rc(K/s)
0.2 0.3 0.4 0.5
104 108 1012
100
R
2= 0.824
10-2
γ
critical cooling rate, Rc(K/s)
0.0 0.1 0.2 0.3 0.4 0.5
1012
104 108
100
R
2= 0.594
10-2
∆ T
*critical cooling rate, Rc(K/s)
Critical cooling rate (R
c) vs. GFA parameters
* Epsilon has a stronger correlation with R
cthan other parameters suggested so far
(∆T
x: R
2=0.282, T
rg: R
2=0.491, ∆T*: R
2=0.594, γ : R
2=0.824) in various BMG alloy systems.
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
10
410
810
1210
0R 2 = 0.848
10
-2
critical cooling rate , R
c(K/s)
Correlation between R c and ε parameter
0 20 40 60 80 100 120 maximum thickness Zmax, mm 102
101
100
R
2= 0.172
10-1
∆ T
x0.0 0.1 0.2 0.3 0.4 0.5
maximum thickness Zmax, mm 102 101
100
R
2= 0.425
10-1
K
0.4 0.5 0.6 0.7 0.8
maximum thickness Zmax, mm 102
101
100
R
2= 0.281
10-1
T
rg 0.0 0.1 0.2∆ T
*0.3 0.4 0.5maximum thickness Zmax, mm 102 101
100
R
2= 0.536
10-1
Maximum section thickness of BMGs (Z
max) vs. GFA parameters
0.5 0.6 0.7 0.8 0.9 1.0
ε
maximum thickness Z max, mm 102 101
100
R
2= 0.716
10-1
0.30 0.35 0.40 0.45 0.50
maximum thickness Z max, mm 102 101
100
R
2= 0.575
10-1
γ
Conventional BMGs Metallic glasses
Maximum section thickness of BMGs (Z
max) vs. GFA parameters
• Epsilon parameter has a stronger correlation with Dmax
than other parameters suggested so far (∆T
x: R
2=0.172, T
rg: R
2=0.281, ∆T*: R
2=0.536, γ: R
2=0.536) in various BMG alloys.
Correlation between D max and ε parameter
0.5 0.6 0.7 0.8 0.9 1.0
maximum thickness D
max, mm 10
210
110
0R 2 = 0.716
10
-1Estimation of the attainable maximum thickness for newly developed BMGs
* Relationship between ε and maximum section thickness D
max:
D
max(mm) = 1.71 х 10
-5exp(15.81ε)
∆Tx Trg ∆T * K γ ε Zmax, exp
(mm)
Zmax, cal (mm) Ca66.4Al33.6 7 0.627 0.201 0.023 0.390 0.715 1 1.4 Ni60Nb30Ta10 13 0.599 0.287 0.021 0.380 0.726 2 1.7 Fe74Nb6Y3B17 48 0.597 0.290 0.094 0.396 0.763 3 2.9 Ni59Zr16Nb7Ti13Si3Sn2 40 0.650 0.302 0.096 0.412 0.798 5 5.1 Ti45Zr5Ni15Cu25Be7Sn3 61 0.595 0.328 0.152 0.407 0.800 5 5.3 Cu54Zr27Ti9Be10 42 0.637 0.310 0.114 0.412 0.801 5 5.3 Mg65Cu25Gd10 61 0.572 0.325 0.238 0.416 0.822 8 7.5 Cu46Zr42Al7Y5 100 0.604 0.335 0.293 0.432 0.856 10 12.8 Y36Al24Co20Sc20 115 0.600 0.322 0.365 0.442 0.874 20 17.0
Application of ε parameter
Thermodynamical aspect
Small change in free E. (liq. cryst.)
Kinetic aspect
Low nucleation and growth rates
Structural aspect
Highly packed random structure
Glass formation
Formation of crystalline phases Retention of liquid phase
High glass-forming ability (GFA ) 1 / R
cor Z
maxImprovement of GFA
In estimating the GFA, the combinational effects of thermodynamic, kinetic and structural aspects for glass formation should be considered.
'
* P
T
( T
m T
x T
x) / T
mmixIH2: Explain the detail how to get R
2(regression coefficient) during fitting.
IH1: What is the glass with lowest T
gwhich is close to T
K? &
Please make a table for T
gand T
Kof BMGs.
IH3: Please make a summary of other GFA parameters based on termo- dynamic modeling, structural and topological parameters, physical properties of alloys, computational approches, etc. You can read and summarize our text from 93 page to 135 page or find other references.
Midterm: 29
thApril (Tuesday) 7 PM – 9 PM
Scope: text ~ 144 pages/ teaching note ~ #14/ and references
