Ideal Mechanical Strength

Lindsay O’Brien, Course 229/27/12

Clarification of VariablesVariable Units Description

eV/atom Binding energy per atom

-- Shear elastic strain

-- Hydrostatic invariant

GPa Shear modulus

GPa Bulk modulus

m2 Slip plane area

-- Bravais translational vector

energy/area Generalized stacking fault

energy/area Unstable stacking energy

Potential Learning Landscape

Metallic Bonding• Explanation of Metal

Properties• Metastable State of

Matter• Binding Energy

Ideal Strength• Potential Energy

Landscape• Thought Experiment

Versus Frenkel Sinusoidal

• Shear Modulus G, Bulk Modulus B

Dislocations• Types of Dislocations• Explanation of

Strength Discrepancies

Potential Energy Landscape

Activation Energy

Turning Point

Things to Remember:• First derivative of potential is force

• Force = 0 corresponds to minimum or saddle point

• When the second derivative of potential is zero, you’re at a turning point

Convex

Concave

http://www.engr.ucsb.edu/~shell/che210d/Exploring_the_energy_landscape.pdf

Shear and Bulk Moduli

Hydrostatic!

Measurement of Ideal Stress• Assumptions• Perfect lattice with no defects• Temperature = 0 K

ɛ hydro

ɛ shear

Oh no!

Prove it!• Electron glue is local

(only care about atomic planes directly below and above)

Further Simplification

Small Deformation (Small x) Large Deformation (Large x)

Thanks!