Crate vegas_lattice

Intro

This is a library for generating and manipulating 3D lattices.

Examples

Lattice creation

vegas_lattice provides simple ways to create cubic and body centered cubic lattices. But you can create any number of custom lattices by creating the sites and vertices manually.

Here is an example of how to create a simple cubic lattice:

use vegas_lattice::Lattice;

let lattice = Lattice::sc(1.0);

assert_eq!(lattice.size(), (1.0, 1.0, 1.0));
assert_eq!(lattice.sites().len(), 1);
assert_eq!(lattice.vertices().len(), 3);

Here is an example of how to create a body centered cubic lattice:

use vegas_lattice::Lattice;

let lattice = Lattice::bcc(1.0);

assert_eq!(lattice.size(), (1.0, 1.0, 1.0));
assert_eq!(lattice.sites().len(), 2);
assert_eq!(lattice.vertices().len(), 8);

Lattice expansion

The most crucial operation to vegas lattice is expand, this is the one that takes a lattice (usually a unitcell) and expands it to a bigger lattice, for example, if you take a cubic lattice and apply the following operation:

use vegas_lattice::{Axis, Lattice};

let lattice = Lattice::sc(1.0).expand_along(Axis::X, 2);

assert_eq!(lattice.size(), (2.0, 1.0, 1.0));
assert_eq!(lattice.sites().len(), 2);
assert_eq!(lattice.vertices().len(), 6);

You will end up with a lattice that is twice as big in the x direction. Notice how the number of sites and vertices is also doubled. This is because the lattice is expanded by replicating the original lattice in the x direction. The same operation can be applied to the y and z. The vertices of the lattice are also replicated.

Vertex dropping

Well, as you saw in the expand operation, we keep the vertices that have a delta those belong to neighboring cells and can be interpreted as periodic boundary conditions, they also allow for future expansions of the lattice, if you want to drop this behavour you can use the drop operation. Let’s remove the periodic boundary conditions of the cubic lattice example we did before:

use vegas_lattice::{Axis, Lattice};

let lattice = Lattice::sc(1.0).drop(Axis::X);
assert_eq!(lattice.size(), (1.0, 1.0, 1.0));
assert_eq!(lattice.sites().len(), 1);
assert_eq!(lattice.vertices().len(), 2);

Masking

The apply_mask operation allows you to remove sites from the lattice according to a mask. The mask is a function that takes the coordinates of a site and returns a boolean. If the function returns true, the site is kept, otherwise it is removed. This is useful to create composite materials by drawing an image of them.

extern crate rand;

use vegas_lattice::{Axis, Lattice, Mask};
use rand::thread_rng;
use std::path::Path;

let lattice = Lattice::sc(1.0)
    .expand_along(Axis::X, 2)
    .expand_along(Axis::Y, 2)
    .expand_along(Axis::Z, 2)
    .apply_mask(Mask::new(Path::new("docs/pattern.png"), 100.0).unwrap());
assert_eq!(lattice.size(), (2.0, 2.0, 2.0));
assert!(lattice.sites().len() <= 8);
assert!(lattice.vertices().len() <= 24);

Alloying

The alloy_sites operation allows you to replace sites labeled as source with sites in the target alloy. This is useful to create alloy materials by mixing different materials.

use vegas_lattice::{Alloy, Lattice};

let lattice = Lattice::sc(1.0).alloy_sites("A", Alloy::new(vec!["B", "C"], vec![50, 50]));
assert_eq!(lattice.sites().len(), 1);
assert!(lattice.sites()[0].kind() == "B" || lattice.sites()[0].kind() == "C");

Modules

• error
  Error handling for the lattice crate
• io
  Defines the to_writer_lattice function for serializing a type to a writer

Structs

• Alloy
  An alloy is a collection of kinds of atoms and their ratios
• Lattice
  A lattice is a collection of sites and vertices.
• Mask
  A mask represents a 2D image that can be used to filter out points
• Site
  Represetns a site in a lattice.
• Vertex
  Represents a vertex in a lattice.

Enums

• Axis
  Represents a 3D axis

Traits

• Tagged
  A trait for tagged objects