Structure of Amorphous Materials -2

Oxide glasses

Metallic glasses

Amorphous Polymers

Silicon

Silica - SiO2

Amorphous silica Crystalline SiO2

Si

O

SiO2 - ideal structure characteristics - continuous random network (CRN)

Basic unit - tetrahedron with Si at the center and O at corners Each corner is shared by two tetrahedrons No edges or faces are shared

Two dimensional depiction

SiO2 - radial distribution function and cooling rate effects

Need to define partial g(r)s - gSiSi(r), gSiO(r), gOO(r)

The structure and thus properties depend on the cooling rate

Network modifiers

Replacing cations with cations of lower valency (e.g. +3 into +2) introduces breaks in the network.

This lowers the glass transition temperature and modulus and thus allows to process material at lower temperature

Most commercially used glasses are with network modifiers

Metallic Glasses

TEM image of amorphous zirconium alloy

Metallic glasses are made by rapid cooling of a metallic liquid such that there is not enough time for the ordered, crystalline structure to nucleate and grow. In the original metallic glasses the required cooling rate was as much as a million degrees Celsius per second! Recently, alloys have been developed that form glasses around 1-100 degrees per second cooling rates.

Typically the best glass formers are multicomponent materials such as Zr-Ti-Cu-Ni-Al alloy.

Metallic glasses can be quite strong yet highly elastic, and they can also be quite tough. Furthermore above the the glass transition temperature a metallic glass becomes quite soft and flows easily allowing to form complex shapes.

Schematic of a two component glass

• High yield strength, fracture toughness

• High elastic strain limit (2%)

• Excellent processibility

Mechanical Properties of Bulk Metallic Glasses (BMG)

Mechanical deformation of metallic glasses

Local plastic deformation and shear band formation

Unresolved questions

How does thermo-mechanical history affect the structure of a metallic glass the plastic deformation behavior?

Is there an ideal way to structurally characterize metallic glasses so to get the best structure-property understanding?

Polymer chain structure - Gaussian coilModel: N+1 beads (mers) connected by N links (bonds) of length b0 with random orientation - equivalent of a random walk

Vector representing nth link

End to end distance

Since link orientations are random an average over all conformations (denoted by )

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R ee = RN − R 0 = rnn=1

n=N

∑

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rn = Rn − Rn−1

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rn = 0 and Ree = 0€

...

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Ree

End to end distance The average end to end distance is zero but the average distance square is not - it measures the size of the polymer coil .

The last equality comes for the fact that the average dot product of two randomly oriented vectors is zero

Real chains are typically more rigid that a model one

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Ree

2 = rnn=1

n=N

∑ ⎛

⎝ ⎜

⎞

⎠ ⎟

2

= rm • rnn,m=1

N

∑ = rn2

n=1

N

∑ + 2 rn • rmn>m

N

∑ = Nb02

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Ree

2 = Nb02 1+ cos(θ )

1− cos(θ )

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θ

End to end distance distribution

Probability of having a chain with and to end distance R is a Gaussian distribution

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P(R,N) = (3/2πNb02)3 / 2e−3R2 / 2Nb0

2

Long chains form an entangled network

Chain rigidity

Rigid chain Flexible chain

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Ree

2 = Nb02 1+ cos(θ )

1− cos(θ )

Rigid chains have larger end-to-end distance for the same contour length, but at large scale they are flexible coils anyway

Specific chemical structure, tacticity and ability to crystallize

Chains with a regular attachment (isotactic or syndiotactic) of side groups can crystallize

Chains with irregular side groups (atactic) can not crystallize

Flexible chains are easier to crystallize

Semicrystalline polymers

A mixture of crystalline regions (lamellae) separated by amorphous regions

Amorphous Silicon (aSi)

Largely four-fold coordinated network, with some free-fold coordinated atoms (inducing dangling bonds).

To eliminate dangling bonds that act as electron traps aSi is hydrogenated. Hydrogen saturates dangling bonds

Thin-film amorphous Silicon (a-Si) have good photovoltaic characteristics, are mounted on flexible backings are do not fracture as easily as crystalline Si, which allows them to be formed to fit applications with the bending inherent when used in building materials.

Amorphous solar cells do not convert sunlight quite as efficiently as crystalline Si cells, however, they require considerably less energy to produce, and are superior to crystalline cells in terms of the time required to recover the energy cost of manufacture. 

Amorphous silicon is gradually degraded by exposure to light. This phenomena is called the Staebler-Wronski Effect (SWE). 

Amorphous carbons: property vs. sp2/sp3 content

Bonding and mechanical properties of amorphous networks

Constrain model - each bond and bond angle represent a constrain in the amorphous network

It can be shown that below average coordination, ca, of 2.4

network can be deformed with no energy cost. Based on this modulus is then equal to

E=E0{(ca -2.4)/(4-2.4)}1.5

where 4 corresponds to fully coordinated network

higher coordination larger modulus