In [2]:
import numpy as np
import escape as esc
from escape.utils.widgets import show
esc.require('0.9.7')

Loading material database from /home/dkor/Data/Development/workspace_escape/escape/python/src/escape/scattering/../data/mdb/materials.db

Interfacial Roughness and Proximity Effects in Superconductor/Ferromagnet CuNi/Nb Heterostructures¶

Authors: Yu. Khaydukov, R. Morari, O. Soltwedel, T. Keller, G. Christiani, G. Logvenov, M. Kupriyanov, A. Sidorenko, and B. Keimer

Citation: Journal of Applied Physics 118, 213905 (2015); doi: 10.1063/1.4936789

In this study, we present the results of fitting experimental data from the publication mentioned above. We selected data from two samples, where the CuNi layers differ in terms of thickness and roughness, to showcase the capabilities of a simultaneous fit with shared parameters. Rather than fitting the Scattering Length Densities (SLDs), we will focus on fitting the mass densities of the layer compounds.

This notebook also demonstrates how to add temporary records to the default material database. This approach allows new material records to be kept within the notebook alongside the code, rather than creating a new local material database.

In [3]:
src = esc.xrays(0.1540562, "nm")

Capping = {
    "name": "Capping",
    "type": "amorphous",
    "density": 2.32,
    "atoms": [
        {"Si": {"repeat": 1}},
    ],
}

CuNi = {
    "name": "CuNi",
    "type": "amorphous",
    "density": 8.93,
    "atoms": [
        {"Cu": {"repeat": 1}},
        {"Ni": {"repeat": 1}},
    ],
}

SiO2 = {
    "name": "SiO2",
    "type": "amorphous",
    "density": 2.62,
    "atoms": [
        {"Si": {"repeat": 1}},
        {"O": {"repeat": 2}},
    ],
}

from escape.scattering.mdb import default_mdb
default_mdb.add(Capping)
default_mdb.add(CuNi)
default_mdb.add(SiO2)
In [5]:
Cap_common = esc.amorphous("Capping", density="mdb")
CuNi_common = esc.amorphous("CuNi", density="mdb")

SiO2Lay = esc.layer("Layer: SiO2", "SiO2", thkn="3+-2nm", rough="1+-1nm", bydensity=True)
NbLay = esc.layer("Layer: nb", "Nb", thkn="10+-2nm", rough="1+-1nm", bydensity=True)
Sub = esc.substrate("Substrate: Si", "Si", rough="1+-1nm", bydensity=True)

sample_10 = esc.multilayer("CuNi/Nb/Si_10", formula="Cap_common(10+-8nm,1+-1nm)/CuNi_common(10+-5nm,1+-1nm)/NbLay/SiO2Lay//Sub", bydensity=True, globals=globals())
sample_21 = esc.multilayer("CuNi/Nb/Si_21", formula="Cap_common(10+-8nm,1+-1nm)/CuNi_common(30+-5nm,1+-1nm)/NbLay/SiO2Lay//Sub", bydensity=True, globals=globals())

show(sample_10, source=src, figtitle="Sample 10")
show(sample_21, source=src, figtitle="Sample 21")
In [6]:
Qz=esc.var("qz")
Qz0=esc.var("qz0")
fwhm_10=esc.par("FWHM_10", 0.005, userlim=[0.003, 0.03], fixed=False)
fwhm_21=esc.par("FWHM_21", 0.005, userlim=[0.003, 0.03], fixed=False)

specrefl_10 = esc.specrefl("Specrefl_10", Qz, sample_10, "matrix", source=src)
specrefl_10 = esc.average_normal(specrefl_10, fwhm_10, Qz, Qz0)

specrefl_21 = esc.specrefl("Specrefl_21", Qz, sample_21, "matrix", source=src)
specrefl_21 = esc.average_normal(specrefl_21, fwhm_21, Qz, Qz0)
In [7]:
B10=esc.par("Bgr 10", 1, scale=1e-6, userlim=[0, 5])
B21=esc.par("Bgr 21", 1, scale=1e-6, userlim=[0, 5])
I10=specrefl_10+B10
I21=specrefl_21+B21
In [8]:
qz, y, err=np.loadtxt("data/JAP15/XRR/Silicon/s10/ASCII/Si10.dat", unpack=True, skiprows=2)
qz=qz*10
dobj10 = esc.data("S10.dat", qz, y, err, copy=True)


qz, y, err=np.loadtxt("data/JAP15/XRR/Silicon/s21/ASCII/Si21.dat", unpack=True, skiprows=2)
qz=qz*10
dobj21 = esc.data("S21.dat", qz, y, err, copy=True)
In [9]:
mobj10 = esc.model("Model 10", I10, dobj10, residuals_scale="q4", weight_type="data")
mobj21 = esc.model("Model 21", I21, dobj21, residuals_scale="q4", weight_type="data")
In [10]:
opt = esc.diffevol("DiffEvol", [mobj10, mobj21], popsize=5, maxiter=70, 
                   mutation=0.5, crossover=0.5, minconv=1e-3, nupdate=5, 
                  polish_final_maxiter=50, polish_candidate_maxiter=0)
#opt()
show(opt, ylog=True)
In [11]:
opt
Out[11]:
Name: DiffEvol            	Parameters number:         22
Parameter           	Value          	+-	Error     	Units     	Fixed
FWHM_10             	       0.011843	+-	0.0009844 	          	    0
Capping density     	         3.2719	+-	0.0070195 	g/cm^3    	    0
Layer-Capping: Thickness	         12.293	+-	0.0092808 	nm        	    0
Layer-Capping: Roughness Sigma	         1.5528	+-	0.0062791 	nm        	    0
CuNi density        	         9.4879	+-	0.0021899 	g/cm^3    	    0
Layer-CuNi: Thickness	         13.648	+-	0.0062589 	nm        	    0
Layer-CuNi: Roughness Sigma	        0.55935	+-	0.0010004 	nm        	    0
Nb density          	         9.1846	+-	0.0062983 	g/cm^3    	    0
Layer: nb: Thickness	             12	+-	0         	nm        	    0
Layer: nb: Roughness Sigma	              2	+-	0         	nm        	    0
SiO2 density        	         3.0469	+-	0.070247  	g/cm^3    	    0
Layer: SiO2: Thickness	         4.3487	+-	0.034003  	nm        	    0
Layer: SiO2: Roughness Sigma	         1.2464	+-	0.0070056 	nm        	    0
Si density          	         2.5843	+-	0.11571   	g/cm^3    	    0
Substrate: Si: Roughness Sigma	        0.97898	+-	0.050044  	nm        	    0
Bgr 10              	         1.5168	+-	0.013591  	x1e-06	   	    0
FWHM_21             	       0.015814	+-	0.00045991	          	    0
Layer-Capping: Thickness	          8.728	+-	0.01174   	nm        	    0
Layer-Capping: Roughness Sigma	         1.6869	+-	0.0072767 	nm        	    0
Layer-CuNi: Thickness	         32.713	+-	0.0067099 	nm        	    0
Layer-CuNi: Roughness Sigma	        0.50413	+-	0.0011366 	nm        	    0
Bgr 21              	         1.4718	+-	0.030647  	x1e-06	   	    0
In [13]:
show(sample_10, source=src, figtitle="Sample 10")
show(sample_21, source=src, figtitle="Sample 21")
In [ ]: