Why are some materials much stronger than others?
What happens when materials deform permanently?
Navigate through the menu on the left to learn more about the mechanical behavior of crystalline materials:
Do the quizes to see how much you have learned already.
Take a look at the different crystal structures and their unit cells (blue atoms). You can also change the camera perspective and the size of the crystals with the buttons on the right.
Crystal structures are categorized into Bravais lattices.
Most common crystal structures of metals:
See where those elements are located in periodic table of elements.
Read more about Lattice Structures in Crystalline Solids.
FCC Structure
Atomic packing factor:
0.74, close packed structure,
Coordination number: 12
Typical for noble metals
Bond type is predominantly metallic, i.e. noble-gas-like electron configuration of metal ion and overlapping valence and conductance bands for delocalized electrons.
Metallic bonds are easy to shear → low mechanical strength
Belongs to the family of cubic lattices
HCP Structure
Atomic packing factor:
0.74, close packed structure for c/a=1.633 (ratio of prism height to radius of basal plane)
Coordination number: 12
Similar to FCC, but different stacking sequence
Anisotropic plastic slip behavior for basal, prismatic and pyramidal slip planes
Belongs to the family of hexagonal lattices
BCC Structure
Atomic packing factor:
0.68, i.e. less than FCC or HCP,
coordination number: 8, only small difference between nearest and second nearest neighbors
Typical for refractory metals
Bond type is mixture of metallic and covalent bonds.
High bond energy → high mechanical strength
Belongs to the family of cubic lattices
SC Structure
Atomic packing factor:
0.52, i.e. less than FCC or HCP
coordination number: 6
Very rare crystal structure, Po is the only metal with SC structure
Related to orthorombic and tetragonal crystal structures.
Belongs to the family of cubic lattices
Rigid shearing of crystals
Periodic energy profile
Shear strain = displacement / lattice parameter
Reversible (elastic) deformation up to shear strain γ=25% in highly idealized
situation of rigid shearing. Corresponds to inflection point in energy curve and
to first maximum in force.
Linear elastic behavior according to Hooke's law
τ = G γ for small strains (shear stress τ,
shear modulus G).
Ideal shear strength τ0 ≈ G / (2π)
Press button "Equations" to see mathematical derivation.
Crystal can shear indefinitely under applied stress equal to ideal strength.
Rigid tearing of crystals
Tensile strain = displacement / lattice parameter
Bond energy can be
split up:
Repulsion: caused by Pauli exclusion principle, preventing electron orbitals to
overlap
Attraction: classified into ionic, covalent, metallic,
and van der Waals bond types
Reversible (elastic) deformation up to
to maximum in force (inflection point in energy curve) for ideal case.
Linear elastic behavior following Hooke's law
σ = Y ε for small strains (tensile stress σ,
Young's modulus Y).
Ideal tensile strength σ0 ≈ Y / 10
Press button "Equations" to see mathematical derivation.
Crystal will loose strength and fracture under decreasing stresses when the critical strain is exceeded.
Test your knowledge about crystal structures and their ideal strength.
Score: 0/100
Find out more about crystals under mechanical stress here.
Something more to think about:
Construction of edge and screw dislocations with out-of-plane line direction.
Dynamics of dislocation motion and the resulting shear deformation of the crystal can be visualized.
An elastic shear deformation causes a homogeneous distortion of the crystal lattice, which
changes the bond angles of the atoms.
This elastic deformation is completely reversible because the atoms can return
back to their original positions in the minimum energy configuration.
The stored elastic energy density corresponds to
the change in potential energy of the atoms, defined by the equation
Wel = 1/2 τ2 / G = 1/2 G γel2
(shear modulus G, shear stress τ,
elastic shear strain γel).
Plastic shear is created by moving a dislocation through the distorted lattice with
fixed atom positions on the top and bottom planes. This
relieves the elastic strain
γel = γtot - γpl
and also the shear stress
τ = G γel = G (γtot - γpl)
(plastic shear strain γpl,
total shear strain γtot).
The stored elastic energy, which is a function of the stress,
decreases during plastic deformation, a process called energy dissipation.
The plastic shear strain depends on the distance Δx that the dislocation has moved through the crystal, as γpl = b Δx / A (Burgers vector b, cross sectional area of the crystal A).
The motion of the dislocation causes a permanent deformation of the lattice because the neighborhood of the atoms below and above the slip plane has changed. This change is permanent since the atoms have moved into a minimum energy configuration in their new neighborhood, such that there is an energy barrier that prevents the atoms from changing back into their original configuration.
Scientific concept and design:
Alexander Hartmaier
Code development:
Alexander Hartmaier
Mostafa Joulaian
Waseem Amin
ICAMS / Ruhr-Universität Bochum, Germany
