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Advanced Physical Metallurgy Advanced Physical Metallurgy
“ “ Amorphous Materials Amorphous Materials ” ”
Eun Eun Soo Soo Park Park
Office: 33-316
Telephone: 880-7221
Email: espark@snu.ac.kr
Office hours: by an appointment
2009 spring
03. 25. 2009
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Bonding type: covalent, ionic, metallic, van der waals, hydrogen bond Glass has one of those bonding
Glass has one of those bonding. .
Some examples which do not fit into any one category.
Some examples which do not fit into any one category.
Ex) Silica : some ionic + predominant covalent Ex) Silica : some ionic + predominant covalent
Contents for previous class
Contents for previous class
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T
f= T
gT
g= fictive temperature, T
fthermodynamic property
thermodynamic property ?
Glass transition
: region over which change of slope occurs
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Normalizing as T9 g
1) 1) Difference of C Difference of C
ppat T at T
ggdepending on materials depending on materials
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400 500 600 700 800 900
(a) Ni
61Zr
22Nb
7Al
4Ta
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(b) Cu
46Zr
42Al
7Y
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(c) Zr
36Ti
24Be
40 (a)
(b)
(c)
(d)
(d) Mg65Cu
15Ag
10Gd
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Temperature (K)
Exothermic (0.5 w/g per div.)
2) change of T
gs depending on alloy compositions
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3) T 3) T
ggdepends on thermal history. depends on thermal history.
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• • Formation of glass during cooling Formation of glass during cooling
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Variation of (a) Cp and (b) excess entropy, S depending on temp. for glass, crystal and liquid. Ideal glass transition temp, Toc. is the temperature when excess entropy is disappeared.
• Ideal glass transition temperature (T
oc)
.lower temperature limit to occur glass transition thermodynamically
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The Clapeyron equation
i.e. the chemical potential coincides with the specific Gibbs function for a unary system.
During a phase change, neither pressure nor temperature vary, hence
= 0 +
− vdP sdT dg
specific Gibbs function
For stable equilibrium states it holds:
&
d μ − vdP + sdT = 0
Gibbs-Duhem relation
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0 g
1g
dg = ⇔ =
&d μ = 0 ⇔ μ
1= μ
2We will demonstrate that the Clausius-Clapeyron Eq. represents the inclination of the locus of points in the PT plane for which it holds μ1 = μ2.
Nota Bene: the specific volume and entropy, defined as and may be discontinuous at the interface.
The situations described here are the so called first-order phase change, because discontinuity occurs not in the specific Gibbs function but in its first derivative.
P T
v g ⎟
⎠
⎜ ⎞
⎝
⎛
∂
= ∂
Tg ⎟P
⎠
⎜ ⎞
⎝
⎛
∂
− ∂
= s
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The Clapeyron equation
' ' & B B
A
A μ μ μ
μ = = phase equilibrium
dP v dT s
vdP sdT
A B
A B
´
' ´
' − = − +
+
−
=
− μ μ
μ μ
P
T state A
state A´
state B
state B´
assuming
0 0
' '
' '
≈
=
≈
=
B A AB
B A AB
dT dT
dP
dP we have:
Gibbs-Duhem for each phase
v v
s s dT dP
−
= −
´
´
v s dT
dP
Δ
= Δ
where Δv, Δs represent the discontinuity in specific entropy and volume. Since the latent heat is equal to L = T Δs, it yields
)
´ (v v T
L dT
dP
= −
for thermally perfect gases v << v´, hence
´ RT2
PL Tv
L dT
dP
v
=
=
.
ln , const
T R P L
v
S ∞ =− +
Clausius-Clayperon
good approximation of sublimation &
evaporation curves, although the Eq. of perfect gases is much more accurate near the triple point than at the critical point.
