# Particles rotation

This tutorial gives an overview on how to rotate a particle in different ways.

### Initial orientation

The rotation of particles starts from a known standard orientation. This orientation is represented by the motionless reference coordinate system of the particle and it is defined in the User Manual. In this tutorial we are going to use a box shaped particle with defined length, width and height. The picture below represents the initial orientation of the box shape. For all implemented shapes, please refer to the User Manual (section "Particle form factors").

The following code will create a box particle of 30nmx20nmx6nm size made of a material whose refractive index roughly corresponds to Silver at 1-Angstrom wavelength.

length, width, height = 30.0*nanometer, 20.0*nanometer, 6.0*nanometer material = HomogeneousMaterial("Ag", 1.245e-5, 5.419e-7) particle = Particle(material, FormFactorBox(length, width, height))

### Rotation classes

There are 4 rotation classes in BornAgain:

# sequence of three rotations following Euler angles notation RotationEuler(alpha, beta, gamma) # rotation around X axis by given angle RotationX(angle) # rotation around Y axis by given angle RotationY(angle) # rotation around Z axis by given angle RotationZ(angle)

By default all angles are expressed in radians.

**Euler Angles**

Alpha, beta, gamma are Euler angles describing a rotation composed by three elemental rotations:

the object is first rotated along the Z axis by alpha. The following rotation is along the transformed X axis (i.e. x' axis), while the last rotation is along the transformed Z axis (i.e. z' axis). This is commonly denoted as the z-x'-z' convention.

### Setting a particle rotation

To set the rotation, use the following constructor

# non rotated box particle = Particle(material, FormFactorBox(30, 20, 6)) # box rotated around X by 90. degrees particle = Particle(material, FormFactorBox(30, 20, 6), RotationX(90.*degree)) # box rotated around Y by 90. degrees particle = Particle(material, FormFactorBox(30, 20, 6), RotationY(90.*degree)) # box rotated around Z by 90. degrees particle = Particle(material, FormFactorBox(30, 20, 6), RotationZ(90.*degree))

The following plot shows the reference box at the top as well as the 3 rotated boxes at the bottom

Please note, that the rotation doesn't change the reference coordinate system of the box. The initial box reference point stays in the same place. This has to be taken into account when positioning of the rotated particle (see below).

### Alternative ways of defining the particle rotation

There are other ways of defining the rotation of a particle: via the particle's own methods and/or via a particle layout.

In the following code snippet we set the rotation of the particle using the particle's `setRotation`

method, then we apply an additional rotation via the particle's `applyRotation`

method and finally we add the resulting object to the layout.

particle = Particle(material, formfactor) # sets initial rotation of the particle particle.setRotation(RotationZ(90*degree)) # applies additional rotation on top of existing one particle.applyRotation(RotationY(90.0*degree)) layout.addParticle(particle, 1.0, kvector_t(0,0,0))

The following code snippet is equivalent to the previous one. We again set the initial rotation of the particle, and then we apply the additional rotation while adding the particle to the layout.

particle = Particle(material, formfactor) # sets initial rotation of the particle particle.setRotation(RotationZ(90*degree)) # adding particle to the layout with the additional rotation specified layout.addParticle(particle, 1.0, kvector_t(0,0,0), RotationY(90.0*degree))

### Important remark about positioning rotated particles

Consider a two-layer system (air, substrate) with a box shaped nanoparticle sitting in the air layer right on top of the interface:

box = Particle(particle_material, FormFactorBox(30., 20., 6.)) layout = ParticleLayout() layout.addParticle(box, 1, kvector_t(0, 0, 0)) air_layer = Layer(layer_material) air_layer.addLayout(layout) substrate_layer = Layer(substrate_material) multilayer = MultiLayer() multilayer.addLayer(air_layer) multilayer.addLayer(substrate_layer)

Suppose that you have decided to transform your box into a tower-like shape by rotating it by 90 degrees about the Y axis. In this case it is important to have in mind that the rotation of the box doesn't change the reference point of the box. In the plot below 3 different cases are illustrated.

# box on the left layout.addParticle(box, 1, kvector_t(0, 0, 0)) # box at the center layout.addParticle(box, 1, kvector_t(0, 0, 0), RotationY(90.*degree)) # box on the right layout.addParticle(box, 1, kvector_t(0, 0, 30.0/2.), RotationY(90.*degree))

The box on the left was added without specifying any rotation. The reference point of the box is not shifted with respect to the layer coordinate system. This setup is valid.

The box at the center was added with an extra rotation specified. As a result, the particle has turned with respect to its reference point and now crosses the interface. This means that the setup has become invalid as particles can not cross interfaces.

The box on the right was added with rotation and position specified. The position defines the location of box's reference point with respect to the coordinate system of the layer. The setup is again valid and the box has become a tower.

Of course, in this artificial example there is no need to create a box, then rotate it and finally shift it to get just another box. It is easier to directly create a tower as a box with the following set of dimensions (6 nm, 20 nm, 30 nm). In following tutorials we will show how to compose particles into complex shapes (e.g. box consisting from different materials), where such rotations will be necessary.