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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
€
Ree
2 = rnn=1
n=N
∑ ⎛
⎝ ⎜
⎞
⎠ ⎟
2
= rm • rnn,m=1
N
∑ = rn2
n=1
N
∑ + 2 rn • rmn>m
N
∑ = Nb02
€
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
€
P(R,N) = (3/2πNb02)3 / 2e−3R2 / 2Nb0
2
Long chains form an entangled network
Chain rigidity
Rigid chain Flexible chain
€
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
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