Ti₂N MXene · Construction details
Notch geometry and crack-length relations
The nominal crack length is defined from the removed titanium and nitrogen sites. The armchair and zigzag construction families follow different geometric relations.
The symbols NTi and NN denote removed titanium and nitrogen sites. The lattice spacings are δx and δy. The zigzag relation applies to the constructed nonzero-notch family; a pristine sheet is assigned zero crack length.
The inset expresses the nominal crack length and total removed-atom count relative to their maxima in each family. It illustrates the construction geometry.
Nominal length calculation
This geometry routine evaluates the nominal full crack length from removed-atom counts. It is the length bookkeeping step; selecting and deleting atoms from a LAMMPS configuration requires the construction workflow.
def nominal_full_length(family, n_ti, n_n, delta_x, delta_y):
if min(n_ti, n_n) < 0:
raise ValueError("Atom counts must be nonnegative")
if n_ti + n_n == 0:
return 0.0
if family == "AC":
return 2 * delta_y * (n_ti + n_n)
if family == "ZZ":
return delta_x / 2 * (n_ti + 2 * n_n + 2)
raise ValueError("Use AC or ZZ")Use consistent length units for the lattice spacings and the returned full crack length.