Freeform structures

The following is a freeform superlattice floating in a solvent and anchored with a tether molecule. The tether is anchored via a thiol group to a multilayer of Si/Cr/Au. The sulphur in the thiol attaches well to gold, but not silicon. Gold will stick to chrome which sticks to silicon.

Here is the plot using a random tether, membrane and tail group:

(Source code)

The model is defined by

The materials are straight forward:

from refl1d.names import *

chrome = Material('Cr')
gold = Material('Au')
solvent = Material('H2O', density=1)

The sample description is more complicated. When we define a freeform layer we need to anchor the ends of the freeform layer to a known material. Usually, this is just the material that makes up the preceding and following layer. In case we have freeform layers connected to each other, though, we need an anchor material that controls the SLD at the connection point. For this purpose we introduce the dummy material wrap

wrap = SLD(name="wrap", rho=0)

Each section of the freeform layer has a different number of control points. The value should be large enough to give the profile enough flexibility to match the data, but not so large that it over fits the data. Roughly the number of control points is the number of peaks and valleys allowed. We want a relatively smooth tether and tail, so we keep n1 and n3 small, but make n2 large enough to define an interesting repeat structure.

n1, n2, n3 = 3,9,3

Free layers have a thickness, horizontal control points z varying in \([0,1]\), real and complex SLD \(\rho\) and \(\rho_i\), and the material above and below.

tether = FreeLayer(below=gold, above=wrap, thickness=10,
bilayer = FreeLayer(below=wrap, above=wrap, thickness=80,
tail = FreeLayer(below=wrap, above=solvent, thickness=10,

With the predefined free layers, we can quickly define a stack, with the bilayer repeat structure. Note that we are setting the thickness for the free layers when we define the layers, so there is no need to set it when composing the layers into a sample.

sample = (silicon(0,5) | chrome(20,2) | gold(50,5)
          | tether | bilayer*10 | tail | solvent)

Finally, simulate the resulting model.

T = numpy.linspace(0, 5, 100)
probe = NeutronProbe(T=T, dT=0.01, L=4.75, dL=0.0475,
M = Experiment(probe=probe, sample=sample, dA=5)
problem = FitProblem(M)