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1D paracrystal

In this example we simulate the scattering from a grating with cumulative spacing disorder. This is done by using Paracrystal1D together with very long boxes.

Paracrystal1D describes a chain of particles along one in-plane direction, with distances between neighbors drawn from a probability distribution. Position uncertainties accumulate with the distance along the chain, as in the ideal one-dimensional paracrystal model. The structure factor depends on the projection of the scattering vector onto the chain direction.

  • For the perfectly ordered counterpart of this structure, see the 1D lattice.
  • For the isotropic, angular-averaged paracrystal, see the radial paracrystal.

Scattering intensity

Open the complete example.

Paracrystal1D constructor

The structure is created with

structure = ba.Paracrystal1D(particle, length, xi, linear_density,
                             damping_length)

Arguments:

particle        # particle or Mixture placed at lattice sites
length          # mean nearest-neighbor distance, in nanometers
xi              # rotation of the lattice with respect to x-axis, in radians
linear_density  # number of lattice lines per nanometer in the transverse axis
damping_length  # damping/coherence length, in nanometers

The parameter damping_length introduces finite size effects by applying a multiplicative coefficient equal to $exp \left(-\frac{length}{damping\_length}\right)$ to the Fourier transform of the probability density of a nearest neighbor. A value of 0 means no damping-length correction.

Probability distribution

The distribution of nearest-neighbor distances must be assigned with setProbabilityDistribution(pdf) before the structure can be used in a simulation:

structure = ba.Paracrystal1D(particle, 30*nm, 0, 1/box_length, 1000*nm)
structure.setProbabilityDistribution(ba.Profile1DGauss(4*nm))

The available distributions are listed under correlation profiles. A zero-width profile represents the ordered limit: together with a finite damping_length, the structure factor then equals that of a Crystal1D with decay function ba.Profile1DCauchy(damping_length).

Domain size

The scattering from a finite portion of the chain can be calculated using the setDomainSize(nm) method. The resulting behaviour is similar to the case when damping_length is used.

Independent position disorder

Unlike Crystal1D, Paracrystal1D has no separate Debye-Waller position disorder. Its cumulative positional disorder is defined by the nearest-neighbor probability distribution described above.