Heat Flow (W/g)

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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

03.16. 2009

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Contents for previous class Contents for previous class

• Glass transition

• Glass: Solid? or liquid?

• Free volume and the glass transition

- Classification of phase transition

1) Microstructural observation 2) Thermal analysis

- DSC (Differential Scanning Calorimetry)

• Amorphous vs Nanocrystalline

: Characterization of structure by pair distribution function

local clusters with atomic scale are difficult to identify by conventional observation tools of microstructure.

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Free volume and the glass transition Free volume and the glass transition

Free volume = specific volume (volume per unit mass) of glass - specific volume of the corresponding crystal

At the glass transition temperature, T_g, the free volume increases leading to atomic mobility and liquid-like behavior. Below the glass transition temperature atoms (ions) are not mobile and the material behaves like solid

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Silica - SiO

₂

Amorphous silica Crystalline SiO₂

Si

O

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Glass

Glass : undercooled ^: undercooled liquid with high viscosity liquid with high viscosity

A solid is a materials whose viscosity exceeds 10

A solid is a materials whose viscosity exceeds 10^14.6^14.6 poisepoise cf) liquid ~cf) liquid ~1010^-^-2² poisepoise

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Definitions

• A calorimeter measures the heat into or out of a sample.

• A differential calorimeter measures the heat of a sample relative to a reference.

• A differential scanning calorimeter does all of the above and heats the sample with a linear temperature ramp.

• Differential Scanning Calorimetry (DSC) measures the temperatures and heat flows associated with transitions in materials as a function of time and temperature in a

controlled atmosphere.

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Schematic of DSC Instrument Schematic of DSC Instrument

N₂ flow

Pt thermopile

Sample Reference

Pt thermopile

T₁ T₂

heater heater

Low mass 1 gram

ΔW

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79.70°C(I) 75.41°C

81.80°C

144.72°C 137.58°C 20.30J/g

245.24°C

228.80°C 22.48J/g

Cycle 1

-0.5 0.0 0.5 1.0 1.5

Heat Flow (W/g)

0 50 100 150 200 250 300

Temperature (°C)

Sample: PET80PC20_MM1 1min Size: 23.4300 mg

Method: standard dsc heat-cool-heat Comment: 5/4/06

DSC File: C:...\DSC\Melt Mixed 1\PET80PC20_MM1.001 Operator: SAC

Run Date: 05-Apr-2006 15:34

Instrument: DSC Q1000 V9.4 Build 287

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Example DSC

Example DSC – – PET PET

(polyethylene terephthalate(polyethylene terephthalate))

T

_g

T

_c

T

_m

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• Glass transitions

• Melting and boiling points

• Crystallization time and temperature

• Percent crystallinity

• Heats of fusion and reactions

• Specific heat capacity

• Oxidative/thermal stability

• Rate and degree of cure

• Reaction kinetics

• Purity

What Can You Measure with DSC?

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Contents for today

Contents for today ’ ’ s class s class

1) Microstructural observation 2) Thermal analysis

- DSC (Differential Scanning Calorimetry)

• Amorphous vs Nanocrystalline

local clusters with atomic scale are difficult to identify by conventional observation tools of microstructure.

3) Intensive Structural Analysis: radial distribution function

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Amorphous vs Nanocrystalline

1) Microstructural observation XRD, (HR)TEM, EXAFS …

2) Thermal analysis

DSC (Differential Scanning Calorimetry)

cf) - glass nucleation & growth (perfect random)

- local clustering: quenched-in nuclei only growth - Nanocrystalline growth

local clusters with atomic scale are difficult to identify by conventional observation tools of microstructure.

: Measure heat absorbed or liberated during heating or cooling

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Chen & Sapepen (Harvard,1988)

Glass :

glass nucleation & growth (perfect random)

Isothermal annealing

: rapid heating + maintain the temp.

) exp(

1 bt

ⁿ

x = − −

(n: 2~4, nucleation mechanism)

Corresponding heat release

)

1

1 ( − ⋅

⁻

Δ

=

− H x n bt

ⁿ

dt dH

(ΔH: total transformation enthalpy)

crystallized volume fraction after time t

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Fig. 1.4 Isothermal enthalpy release rates for crystallite nucleation and growth (solid line) and crystallite grain-coarsening mechanisms (dashed line)

Glass

: exothermic peak at non-zero time

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r

m

dt M

dr ₌ _⋅ γ

(M: atomic mobility, γ : interficial surface tension) corresponding heat release

/

2

) 0 ( )

0 ( ⋅ ⋅

⁺

=

− H r M r

^m

dt

dH γ

(H(0): zerotime enthalpy of a grain size of r (0))

Nanocrystalline grain growth

Monotonically decreasing curve

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Fig. 1.4 Isothermal enthalpy release rates for crystallite nucleation and growth (solid line) and crystallite grain-coarsening mechanisms (dashed line)

Glass

: exothermic peak at non-zero time

Nanocrystalline

(or quenched-in nuclei)

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cf) - glass nucleation & growth (perfect random)

- local clustering: quenched-in nuclei only growth - Nanocrystalline growth

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Effect of quenched

Effect of quenched - - in in quasicrystal quasicrystal nuclei nuclei

Fully amorphous structure β-Zr particle(~70 nm) in amorphous matrix

50 nm 200 nm

(a)

β-Zr

(b)

(b) Zr₅₇Ti₈Nb_2.5Cu_13.9Ni_11.1Al_7.5 (a) Zr₆₃Ti₅Nb₂Cu_15.8Ni_6.3Al_7.9

2 mm rod

200 nm

I₅ I₃ I₂

I-phase

3 mm rod

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0 20 40 60

3.55 3.60 3.65 3.70

c

Isotherm in DSC

[b]

[a]

Effect of quenched

Effect of quenched - - in in quasicrystal quasicrystal nuclei nuclei

Isothermal annealing

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5 nm

19

HRTEM image in [b] alloy

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1 2 3 4 5 6

0.0 0.5 1.0 1.5 2.0

FT[k

3 ·χ(k)]

r( A )

alloy (2) rib.

alloy (2) 1 mm alloy (2) 2 mm alloy (2) 3 mm

(c)

1 2 3 4 5 6

0.00 0.05 0.10 0.15 0.20

r(A ) FT[k2 ·χ(k)]

alloy (2) rib.

(a)

Zr-K edge

Ni-K edge

1 2 3 4 5 6

0.0 0.5 1.0 1.5 2.0 2.5

r(A ) FT[k3 ·χ(k)]

alloy (2) rib.

(b)

Cu-K edge

EXAFS analysis

Distinctive structural change around Ni atom

Intensity change due to microstructural change

(b) Zr₅₇Ti₈Nb_2.5Cu_13.9Ni_11.1Al_7.5

Effect of quenched

Effect of quenched - - in in quasicrystal quasicrystal nuclei nuclei

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cf) - glass nucleation & growth (perfect random)

- local clustering: quenched-in nuclei only growth - Nanocrystalline growth

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Characterizing the structure

Characterizing the structure - - radial distribution function, radial distribution function

also called pair distribution function

Gas, amorphous/liquid and crystal structures have very different radial distribution function

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Radial distribution function

Radial distribution function - - definition definition

1. Carve a shell of size r and r + dr around a center of an atom. The volume of the shell is dv=4πr²dr 2. Count number of atoms with

centers within the shell (dn) 3. Average over all atoms in the

system

4. Divide by the average atomic density <ρ>

dr

r

g(r) = 1

ρ

dn(r,r + dr)

dv(r,r + dr)

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Properties of the radial distribution function Properties of the radial distribution function

For gases, liquids and amorphous solids g(r) becomes unity for large enough r.

The distance over which g(r) becomes unity is called the correlation distance which is a measure of the extent of so- called short range order (SRO)

The first peak corresponds to an average nearest neighbor distance Features in g(r) for liquids and

amorphous solids are due to packing (exclude volume) and possibly bonding characteristics

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Radial Distribution Function

Radial Distribution Function - - Crystal and Liquid Crystal and Liquid

Q(r) = g(r) −1 ~ 1

r sin(r / d + ϕ )exp(r / λ )

-15 -10 -5 0 5 10 15

0 1 2 3 4 5 6 7

rQ(r)

r [σ]

crystal T=1000K fit numerical data

-6 -4 -2 0 2 4 6

0 1 2 3 4 5 6 7 8

rQ(r)

r [σ]

NaCl melt T=1000K ρ*=0.28 fit simulations

Liquid/amorphous g(r), for large r exhibit oscillatory exponential decay Crystal g(r) does not exhibit an exponential decay (λ → ∞)

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Radial distribution functions and the structure factor Radial distribution functions and the structure factor

• The structure factor, S(k), which can be measured experimentally (e.g. by X-rays such as EXAFS) is given by the Fourier transform of the radial distribution function and vice versa

Radial distribution functions can be obtained from experiment and compared with that from the structural model

S(k) =1+ 4 π ρ

k r[g(r) −1]

0

∞

∫ ^sin(kr)dr

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2 4 6 8 10 12

-4 -2 0 2 4

Cu₆₀Zr₄₀ Cu₅₀Zr₅₀

Cu_47.5Zr₄₀Be_12.5

k3 ·χ(k)

k(Å^-1)

Cu K-edge

1 2 3 4

0 1 2 3 4

Cu₆₀Zr₄₀ Cu₅₀Zr₅₀

Cu_47.5Zr₄₀Be_12.5 1/7 Cu foil

FT[k3 ⋅χ(k)]

r (Å)

Cu K-edge

Radial distribution functions

Radial distribution functions Structure factorStructure factor

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More detailed structural characterization

More detailed structural characterization -- VoronoiVoronoi PolyhedraPolyhedra

• Draw lines between a center of an atom and nearby atoms.

• Construct planes bisecting the lines perpendicularly

• The sets of planes the closest to the central atom forms a convex polyhedron

• Perform the statistical analysis of such constructed polyhedrons, most notably evaluate an average number of faces

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More detailed structural characterization

More detailed structural characterization -- VoronoiVoronoi PolyhedraPolyhedra

• For no-directional bonding promoting packing number of faces is large ~ 13-14 (metallic glasses)

• For directional bonding (covalent glasses) number of faces is small

• Ionic glasses - intermediate

• In all cases the number of faces is closely related to the number of nearest neighbors (the coordination number)

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Medium range order and radial distribution function Medium range order and radial distribution function

Radial distribution functions (and also X-ray) of amorphous silicon and model Si with ~ 2 nm crystalline grains are essentially the same - medium range order difficult to see by standard characterization tools.

Such structure is called a paracrystal.

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Radial Distribution Function

Nanocrystalline material

Nanocrystalline materials shows clear crystalline peaks with some background coming from the grain boundary

0 2 4 6 8 10 12 14

0 0.3 0.6 0.9 1.2

G(r)

r [a0]

nanocrystalline 4nm grain size

Heat Flow (W/g)

Advanced Physical Metallurgy Advanced Physical Metallurgy

“ “ Amorphous Materials Amorphous Materials ” ”

Eun Eun Soo Soo Park Park

2009 spring

03.16. 2009

Contents for previous class Contents for previous class

• Glass transition

• Glass: Solid? or liquid?

• Free volume and the glass transition

• Amorphous vs Nanocrystalline

Free volume and the glass transition Free volume and the glass transition

Silica - SiO

Glass

Glass : undercooled : undercooled liquid with high viscosity liquid with high viscosity

Definitions

• A calorimeter measures the heat into or out of a sample.

• A differential calorimeter measures the heat of a sample relative to a reference.

• A differential scanning calorimeter does all of the above and heats the sample with a linear temperature ramp.

• Differential Scanning Calorimetry (DSC) measures the temperatures and heat flows associated with transitions in materials as a function of time and temperature in a

controlled atmosphere.

Schematic of DSC Instrument Schematic of DSC Instrument

Example DSC

Example DSC – – PET PET

T

T

T

What Can You Measure with DSC?

What Can You Measure with DSC?

Contents for today

Contents for today ’ ’ s class s class

• Amorphous vs Nanocrystalline

Glass :

) exp(

1 bt

x = − −

)

1

( − ⋅

Δ

=

− H x n bt

dt dH

r

dt M

dr = ⋅ γ

/

) 0 ( )

0

( ⋅ ⋅

=

− H r M r

dt

dH γ

Nanocrystalline grain growth

Effect of quenched

Effect of quenched - - in in quasicrystal quasicrystal nuclei nuclei

(a)

(b)

Effect of quenched

Effect of quenched - - in in quasicrystal quasicrystal nuclei nuclei

5 nm

HRTEM image in [b] alloy

Effect of quenched

Effect of quenched - - in in quasicrystal quasicrystal nuclei nuclei

Characterizing the structure

Characterizing the structure - - radial distribution function, radial distribution function

Radial distribution function

Radial distribution function - - definition definition

r

g(r) = 1

ρ

dn(r,r + dr)

dv(r,r + dr)

Properties of the radial distribution function Properties of the radial distribution function

Radial Distribution Function

Radial Distribution Function - - Crystal and Liquid Crystal and Liquid

Q(r) = g(r) −1 ~ 1

r sin(r / d + ϕ )exp(r / λ )

Radial distribution functions and the structure factor Radial distribution functions and the structure factor

Glass : undercooled ^: undercooled liquid with high viscosity liquid with high viscosity

dr ₌ _⋅ γ

∫ ^sin(kr)dr