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XRD_file_interpreter.tex
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\documentclass[11pt]{article}
\usepackage[breakable]{tcolorbox}
\usepackage{parskip} % Stop auto-indenting (to mimic markdown behaviour)
% Basic figure setup, for now with no caption control since it's done
% automatically by Pandoc (which extracts  syntax from Markdown).
\usepackage{graphicx}
% Maintain compatibility with old templates. Remove in nbconvert 6.0
\let\Oldincludegraphics\includegraphics
% Ensure that by default, figures have no caption (until we provide a
% proper Figure object with a Caption API and a way to capture that
% in the conversion process - todo).
\usepackage{caption}
\DeclareCaptionFormat{nocaption}{}
\captionsetup{format=nocaption,aboveskip=0pt,belowskip=0pt}
\usepackage{float}
\floatplacement{figure}{H} % forces figures to be placed at the correct location
\usepackage{xcolor} % Allow colors to be defined
\usepackage{enumerate} % Needed for markdown enumerations to work
\usepackage{geometry} % Used to adjust the document margins
\usepackage{amsmath} % Equations
\usepackage{amssymb} % Equations
\usepackage{textcomp} % defines textquotesingle
% Hack from http://tex.stackexchange.com/a/47451/13684:
\AtBeginDocument{%
\def\PYZsq{\textquotesingle}% Upright quotes in Pygmentized code
}
\usepackage{upquote} % Upright quotes for verbatim code
\usepackage{eurosym} % defines \euro
\usepackage{iftex}
\ifPDFTeX
\usepackage[T1]{fontenc}
\IfFileExists{alphabeta.sty}{
\usepackage{alphabeta}
}{
\usepackage[mathletters]{ucs}
\usepackage[utf8x]{inputenc}
}
\else
\usepackage{fontspec}
\usepackage{unicode-math}
\fi
\usepackage{fancyvrb} % verbatim replacement that allows latex
\usepackage{grffile} % extends the file name processing of package graphics
% to support a larger range
\makeatletter % fix for old versions of grffile with XeLaTeX
\@ifpackagelater{grffile}{2019/11/01}
{
% Do nothing on new versions
}
{
\def\Gread@@xetex#1{%
\IfFileExists{"\Gin@base".bb}%
{\Gread@eps{\Gin@base.bb}}%
{\Gread@@xetex@aux#1}%
}
}
\makeatother
\usepackage[Export]{adjustbox} % Used to constrain images to a maximum size
\adjustboxset{max size={0.9\linewidth}{0.9\paperheight}}
% The hyperref package gives us a pdf with properly built
% internal navigation ('pdf bookmarks' for the table of contents,
% internal cross-reference links, web links for URLs, etc.)
\usepackage{hyperref}
% The default LaTeX title has an obnoxious amount of whitespace. By default,
% titling removes some of it. It also provides customization options.
\usepackage{titling}
\usepackage{longtable} % longtable support required by pandoc >1.10
\usepackage{booktabs} % table support for pandoc > 1.12.2
\usepackage{array} % table support for pandoc >= 2.11.3
\usepackage{calc} % table minipage width calculation for pandoc >= 2.11.1
\usepackage[inline]{enumitem} % IRkernel/repr support (it uses the enumerate* environment)
\usepackage[normalem]{ulem} % ulem is needed to support strikethroughs (\sout)
% normalem makes italics be italics, not underlines
\usepackage{soul} % strikethrough (\st) support for pandoc >= 3.0.0
\usepackage{mathrsfs}
% Colors for the hyperref package
\definecolor{urlcolor}{rgb}{0,.145,.698}
\definecolor{linkcolor}{rgb}{.71,0.21,0.01}
\definecolor{citecolor}{rgb}{.12,.54,.11}
% ANSI colors
\definecolor{ansi-black}{HTML}{3E424D}
\definecolor{ansi-black-intense}{HTML}{282C36}
\definecolor{ansi-red}{HTML}{E75C58}
\definecolor{ansi-red-intense}{HTML}{B22B31}
\definecolor{ansi-green}{HTML}{00A250}
\definecolor{ansi-green-intense}{HTML}{007427}
\definecolor{ansi-yellow}{HTML}{DDB62B}
\definecolor{ansi-yellow-intense}{HTML}{B27D12}
\definecolor{ansi-blue}{HTML}{208FFB}
\definecolor{ansi-blue-intense}{HTML}{0065CA}
\definecolor{ansi-magenta}{HTML}{D160C4}
\definecolor{ansi-magenta-intense}{HTML}{A03196}
\definecolor{ansi-cyan}{HTML}{60C6C8}
\definecolor{ansi-cyan-intense}{HTML}{258F8F}
\definecolor{ansi-white}{HTML}{C5C1B4}
\definecolor{ansi-white-intense}{HTML}{A1A6B2}
\definecolor{ansi-default-inverse-fg}{HTML}{FFFFFF}
\definecolor{ansi-default-inverse-bg}{HTML}{000000}
% common color for the border for error outputs.
\definecolor{outerrorbackground}{HTML}{FFDFDF}
% commands and environments needed by pandoc snippets
% extracted from the output of `pandoc -s`
\providecommand{\tightlist}{%
\setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}}
\DefineVerbatimEnvironment{Highlighting}{Verbatim}{commandchars=\\\{\}}
% Add ',fontsize=\small' for more characters per line
\newenvironment{Shaded}{}{}
\newcommand{\KeywordTok}[1]{\textcolor[rgb]{0.00,0.44,0.13}{\textbf{{#1}}}}
\newcommand{\DataTypeTok}[1]{\textcolor[rgb]{0.56,0.13,0.00}{{#1}}}
\newcommand{\DecValTok}[1]{\textcolor[rgb]{0.25,0.63,0.44}{{#1}}}
\newcommand{\BaseNTok}[1]{\textcolor[rgb]{0.25,0.63,0.44}{{#1}}}
\newcommand{\FloatTok}[1]{\textcolor[rgb]{0.25,0.63,0.44}{{#1}}}
\newcommand{\CharTok}[1]{\textcolor[rgb]{0.25,0.44,0.63}{{#1}}}
\newcommand{\StringTok}[1]{\textcolor[rgb]{0.25,0.44,0.63}{{#1}}}
\newcommand{\CommentTok}[1]{\textcolor[rgb]{0.38,0.63,0.69}{\textit{{#1}}}}
\newcommand{\OtherTok}[1]{\textcolor[rgb]{0.00,0.44,0.13}{{#1}}}
\newcommand{\AlertTok}[1]{\textcolor[rgb]{1.00,0.00,0.00}{\textbf{{#1}}}}
\newcommand{\FunctionTok}[1]{\textcolor[rgb]{0.02,0.16,0.49}{{#1}}}
\newcommand{\RegionMarkerTok}[1]{{#1}}
\newcommand{\ErrorTok}[1]{\textcolor[rgb]{1.00,0.00,0.00}{\textbf{{#1}}}}
\newcommand{\NormalTok}[1]{{#1}}
% Additional commands for more recent versions of Pandoc
\newcommand{\ConstantTok}[1]{\textcolor[rgb]{0.53,0.00,0.00}{{#1}}}
\newcommand{\SpecialCharTok}[1]{\textcolor[rgb]{0.25,0.44,0.63}{{#1}}}
\newcommand{\VerbatimStringTok}[1]{\textcolor[rgb]{0.25,0.44,0.63}{{#1}}}
\newcommand{\SpecialStringTok}[1]{\textcolor[rgb]{0.73,0.40,0.53}{{#1}}}
\newcommand{\ImportTok}[1]{{#1}}
\newcommand{\DocumentationTok}[1]{\textcolor[rgb]{0.73,0.13,0.13}{\textit{{#1}}}}
\newcommand{\AnnotationTok}[1]{\textcolor[rgb]{0.38,0.63,0.69}{\textbf{\textit{{#1}}}}}
\newcommand{\CommentVarTok}[1]{\textcolor[rgb]{0.38,0.63,0.69}{\textbf{\textit{{#1}}}}}
\newcommand{\VariableTok}[1]{\textcolor[rgb]{0.10,0.09,0.49}{{#1}}}
\newcommand{\ControlFlowTok}[1]{\textcolor[rgb]{0.00,0.44,0.13}{\textbf{{#1}}}}
\newcommand{\OperatorTok}[1]{\textcolor[rgb]{0.40,0.40,0.40}{{#1}}}
\newcommand{\BuiltInTok}[1]{{#1}}
\newcommand{\ExtensionTok}[1]{{#1}}
\newcommand{\PreprocessorTok}[1]{\textcolor[rgb]{0.74,0.48,0.00}{{#1}}}
\newcommand{\AttributeTok}[1]{\textcolor[rgb]{0.49,0.56,0.16}{{#1}}}
\newcommand{\InformationTok}[1]{\textcolor[rgb]{0.38,0.63,0.69}{\textbf{\textit{{#1}}}}}
\newcommand{\WarningTok}[1]{\textcolor[rgb]{0.38,0.63,0.69}{\textbf{\textit{{#1}}}}}
% Define a nice break command that doesn't care if a line doesn't already
% exist.
\def\br{\hspace*{\fill} \\* }
% Math Jax compatibility definitions
\def\gt{>}
\def\lt{<}
\let\Oldtex\TeX
\let\Oldlatex\LaTeX
\renewcommand{\TeX}{\textrm{\Oldtex}}
\renewcommand{\LaTeX}{\textrm{\Oldlatex}}
% Document parameters
% Document title
\title{XRD\_file\_interpreter}
% Pygments definitions
\makeatletter
\def\PY@reset{\let\PY@it=\relax \let\PY@bf=\relax%
\let\PY@ul=\relax \let\PY@tc=\relax%
\let\PY@bc=\relax \let\PY@ff=\relax}
\def\PY@tok#1{\csname PY@tok@#1\endcsname}
\def\PY@toks#1+{\ifx\relax#1\empty\else%
\PY@tok{#1}\expandafter\PY@toks\fi}
\def\PY@do#1{\PY@bc{\PY@tc{\PY@ul{%
\PY@it{\PY@bf{\PY@ff{#1}}}}}}}
\def\PY#1#2{\PY@reset\PY@toks#1+\relax+\PY@do{#2}}
\@namedef{PY@tok@w}{\def\PY@tc##1{\textcolor[rgb]{0.73,0.73,0.73}{##1}}}
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% for compatibility with earlier versions
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% For linebreaks inside Verbatim environment from package fancyvrb.
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\def\PYGZcb{\discretionary{\char`\}}{\Wrappedafterbreak}{\char`\}}}%
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\catcode`\.\active
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\catcode`\?\active
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\lccode`\~`\~
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%\parskip\z@skip
\sbox\Wrappedcontinuationbox {\Wrappedcontinuationsymbol}%
\sbox\Wrappedvisiblespacebox {\FV@SetupFont\Wrappedvisiblespace}%
\def\FancyVerbFormatLine ##1{\hsize\linewidth
\vtop{\raggedright\hyphenpenalty\z@\exhyphenpenalty\z@
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% If the linebreak is at a space, the latter will be displayed as visible
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% prompt
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% Prevent overflowing lines due to hard-to-break entities
\sloppy
% Setup hyperref package
\hypersetup{
breaklinks=true, % so long urls are correctly broken across lines
colorlinks=true,
urlcolor=urlcolor,
linkcolor=linkcolor,
citecolor=citecolor,
}
% Slightly bigger margins than the latex defaults
\geometry{verbose,tmargin=1in,bmargin=1in,lmargin=1in,rmargin=1in}
\begin{document}
\maketitle
\section{XRD File reader and plotter}\label{xrd-file-reader-and-plotter}
\begin{tcolorbox}[breakable, size=fbox, boxrule=1pt, pad at break*=1mm,colback=cellbackground, colframe=cellborder]
\prompt{In}{incolor}{1}{\boxspacing}
\begin{Verbatim}[commandchars=\\\{\}]
\PY{c+c1}{\PYZsh{} Importamos librerias necesarias para nuestro programa}
\PY{k+kn}{import} \PY{n+nn}{pandas} \PY{k}{as} \PY{n+nn}{pd}
\PY{k+kn}{import} \PY{n+nn}{numpy} \PY{k}{as} \PY{n+nn}{np}
\PY{k+kn}{import} \PY{n+nn}{plotly}\PY{n+nn}{.}\PY{n+nn}{express} \PY{k}{as} \PY{n+nn}{px}
\PY{k+kn}{import} \PY{n+nn}{plotly}\PY{n+nn}{.}\PY{n+nn}{graph\PYZus{}objects} \PY{k}{as} \PY{n+nn}{go} \PY{c+c1}{\PYZsh{} Ensure plotly.graph\PYZus{}objects is imported}
\PY{k+kn}{from} \PY{n+nn}{IPython}\PY{n+nn}{.}\PY{n+nn}{display} \PY{k+kn}{import} \PY{n}{display}\PY{p}{,} \PY{n}{Markdown}
\PY{k+kn}{from} \PY{n+nn}{scipy}\PY{n+nn}{.}\PY{n+nn}{signal} \PY{k+kn}{import} \PY{n}{find\PYZus{}peaks}
\PY{k+kn}{from} \PY{n+nn}{sklearn}\PY{n+nn}{.}\PY{n+nn}{metrics} \PY{k+kn}{import} \PY{n}{r2\PYZus{}score}
\PY{k+kn}{from} \PY{n+nn}{sklearn}\PY{n+nn}{.}\PY{n+nn}{linear\PYZus{}model} \PY{k+kn}{import} \PY{n}{LinearRegression}
\end{Verbatim}
\end{tcolorbox}
\begin{center}\rule{0.5\linewidth}{0.5pt}\end{center}
\subsection{Se lee el archivo crudo}\label{se-lee-el-archivo-crudo}
En esta parte del código se lee el archivo crudo proveniente del equipo
de xrd y se trata para obtener una salida csv
\begin{tcolorbox}[breakable, size=fbox, boxrule=1pt, pad at break*=1mm,colback=cellbackground, colframe=cellborder]
\prompt{In}{incolor}{2}{\boxspacing}
\begin{Verbatim}[commandchars=\\\{\}]
\PY{n}{file} \PY{o}{=} \PY{n+nb}{open}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{../SrTiO3.uxd}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{mode}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{r}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{n}{content} \PY{o}{=} \PY{n}{file}\PY{o}{.}\PY{n}{read}\PY{p}{(}\PY{p}{)}
\PY{n}{partes\PYZus{}importantes} \PY{o}{=} \PY{n}{content}\PY{o}{.}\PY{n}{split}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{;}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{n}{tabla\PYZus{}contenido} \PY{o}{=} \PY{n}{partes\PYZus{}importantes}\PY{p}{[}\PY{l+m+mi}{7}\PY{p}{]}
\PY{n}{titles} \PY{o}{=} \PY{n}{tabla\PYZus{}contenido}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{:}\PY{l+m+mi}{15}\PY{p}{]}
\PY{n}{tabla\PYZus{}contenido} \PY{o}{=} \PY{n}{tabla\PYZus{}contenido}\PY{o}{.}\PY{n}{replace}\PY{p}{(}\PY{n}{titles}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{2THETA, PSD}\PY{l+s+se}{\PYZbs{}n}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{n}{tabla\PYZus{}contenido} \PY{o}{=} \PY{n}{tabla\PYZus{}contenido}\PY{o}{.}\PY{n}{replace}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{ }\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{, }\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{n}{tabla\PYZus{}contenido} \PY{o}{=} \PY{n}{tabla\PYZus{}contenido}\PY{o}{.}\PY{n}{replace}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{ }\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{, }\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{n}{file}\PY{o}{.}\PY{n}{close}\PY{p}{(}\PY{p}{)}
\end{Verbatim}
\end{tcolorbox}
\begin{center}\rule{0.5\linewidth}{0.5pt}\end{center}
\subsection{Se convierte el archivo}\label{se-convierte-el-archivo}
En esta parte del código el contenido del archivo crudo se convierte en
un archivo CSV para posteriormete abrirlo con pandas
\begin{tcolorbox}[breakable, size=fbox, boxrule=1pt, pad at break*=1mm,colback=cellbackground, colframe=cellborder]
\prompt{In}{incolor}{3}{\boxspacing}
\begin{Verbatim}[commandchars=\\\{\}]
\PY{n}{output\PYZus{}file} \PY{o}{=} \PY{n+nb}{open}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{data.csv}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{w}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{n}{output\PYZus{}file}\PY{o}{.}\PY{n}{write}\PY{p}{(}\PY{n}{tabla\PYZus{}contenido}\PY{p}{)}
\PY{n}{output\PYZus{}file}\PY{o}{.}\PY{n}{close}\PY{p}{(}\PY{p}{)}
\end{Verbatim}
\end{tcolorbox}
\begin{center}\rule{0.5\linewidth}{0.5pt}\end{center}
\subsection{Creamos la gráfica interactiva para la formula de
Debye-Scherrer}\label{creamos-la-gruxe1fica-interactiva-para-la-formula-de-debye-scherrer}
En esta parte del código se obtienen los puntos más relevantes de la
gráfica y se les da un tratamiento para poder trabajar con ellos.
\begin{tcolorbox}[breakable, size=fbox, boxrule=1pt, pad at break*=1mm,colback=cellbackground, colframe=cellborder]
\prompt{In}{incolor}{4}{\boxspacing}
\begin{Verbatim}[commandchars=\\\{\}]
\PY{n}{df} \PY{o}{=} \PY{n}{pd}\PY{o}{.}\PY{n}{read\PYZus{}csv}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{data.csv}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{n}{y\PYZus{}position\PYZus{}value\PYZus{}global} \PY{o}{=} \PY{l+m+mi}{100}
\PY{n}{beta\PYZus{}constant\PYZus{}value} \PY{o}{=} \PY{l+m+mi}{0}
\PY{n}{fig} \PY{o}{=} \PY{n}{px}\PY{o}{.}\PY{n}{line}\PY{p}{(}\PY{n}{df}\PY{p}{,} \PY{n}{x}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{ 2THETA}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{y}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{ PSD}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{labels}\PY{o}{=}\PY{p}{\PYZob{}}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Name}\PY{l+s+s1}{\PYZsq{}}\PY{p}{:} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{2theta}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Value}\PY{l+s+s1}{\PYZsq{}}\PY{p}{:} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{values}\PY{l+s+s1}{\PYZsq{}}\PY{p}{\PYZcb{}}\PY{p}{,} \PY{n}{title}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{SrTiO3 difractograma}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{n}{fig}\PY{o}{.}\PY{n}{update\PYZus{}traces}\PY{p}{(}\PY{n}{line}\PY{o}{=}\PY{n+nb}{dict}\PY{p}{(}\PY{n}{color}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{blue}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}\PY{p}{)}
\PY{c+c1}{\PYZsh{} Add a line parallel to x\PYZhy{}axis at y\PYZus{}position\PYZus{}value}
\PY{n}{fig}\PY{o}{.}\PY{n}{add\PYZus{}shape}\PY{p}{(}
\PY{n+nb}{type}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{line}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,}
\PY{n}{x0}\PY{o}{=}\PY{n}{df}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{ 2THETA}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{o}{.}\PY{n}{min}\PY{p}{(}\PY{p}{)}\PY{p}{,}
\PY{n}{y0}\PY{o}{=}\PY{n}{y\PYZus{}position\PYZus{}value\PYZus{}global}\PY{p}{,}
\PY{n}{x1}\PY{o}{=}\PY{n}{df}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{ 2THETA}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{o}{.}\PY{n}{max}\PY{p}{(}\PY{p}{)}\PY{p}{,}
\PY{n}{y1}\PY{o}{=}\PY{n}{y\PYZus{}position\PYZus{}value\PYZus{}global}\PY{p}{,}
\PY{n}{line}\PY{o}{=}\PY{n+nb}{dict}\PY{p}{(}\PY{n}{color}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{red}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{width}\PY{o}{=}\PY{l+m+mi}{2}\PY{p}{,} \PY{n}{dash}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{solid}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{p}{)}
\PY{c+c1}{\PYZsh{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}}
\PY{c+c1}{\PYZsh{}Se calcula la altura máxima en de la reflexión más grande:}
\PY{n}{altura\PYZus{}reflexion\PYZus{}max} \PY{o}{=} \PY{n+nb}{max}\PY{p}{(}\PY{n}{df}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{ PSD}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{o}{.}\PY{n}{values}\PY{p}{)} \PY{o}{\PYZhy{}} \PY{n}{y\PYZus{}position\PYZus{}value\PYZus{}global}
\PY{c+c1}{\PYZsh{} indice reflexión más alta}
\PY{n}{indice\PYZus{}refle\PYZus{}mas\PYZus{}alta} \PY{o}{=} \PY{n}{df}\PY{p}{[}\PY{n}{df}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{ PSD}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]} \PY{o}{==} \PY{n+nb}{max}\PY{p}{(}\PY{n}{df}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{ PSD}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{o}{.}\PY{n}{values}\PY{p}{)}\PY{p}{]}\PY{o}{.}\PY{n}{index}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{]}
\PY{c+c1}{\PYZsh{}print(indice\PYZus{}refle\PYZus{}mas\PYZus{}alta)}
\PY{c+c1}{\PYZsh{} Obtenemos la mitad de la distancia con de la reflexión mas grande usando el punto de referencia}
\PY{n}{given\PYZus{}PSD\PYZus{}value} \PY{o}{=} \PY{n}{altura\PYZus{}reflexion\PYZus{}max}\PY{o}{/}\PY{l+m+mi}{2}
\PY{c+c1}{\PYZsh{} Se calcula la diferencia absoluta entre los dos valores dados y todos los datos de la columna PSD.}
\PY{n}{df}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Absolute\PYZus{}Difference}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]} \PY{o}{=} \PY{n+nb}{abs}\PY{p}{(}\PY{n}{df}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{ PSD}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]} \PY{o}{\PYZhy{}} \PY{n}{given\PYZus{}PSD\PYZus{}value}\PY{p}{)}
\PY{c+c1}{\PYZsh{} Encuentra la fila con la menor diferencia encontrada}
\PY{n}{closest\PYZus{}index} \PY{o}{=} \PY{n}{df}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Absolute\PYZus{}Difference}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{o}{.}\PY{n}{idxmin}\PY{p}{(}\PY{p}{)}
\PY{n}{closest\PYZus{}2THETA\PYZus{}value} \PY{o}{=} \PY{n}{df}\PY{o}{.}\PY{n}{loc}\PY{p}{[}\PY{n}{closest\PYZus{}index}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{ 2THETA}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}
\PY{n}{closest\PYZus{}PSD\PYZus{}value} \PY{o}{=} \PY{n}{df}\PY{o}{.}\PY{n}{loc}\PY{p}{[}\PY{n}{closest\PYZus{}index}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{ PSD}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}
\PY{c+c1}{\PYZsh{} Encontramos el siguiente valor más cercano}
\PY{n}{next\PYZus{}upper\PYZus{}values} \PY{o}{=} \PY{n}{df}\PY{p}{[}\PY{n}{df}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{ PSD}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]} \PY{o}{\PYZgt{}} \PY{n}{given\PYZus{}PSD\PYZus{}value}\PY{p}{]}
\PY{k}{if} \PY{o+ow}{not} \PY{n}{next\PYZus{}upper\PYZus{}values}\PY{o}{.}\PY{n}{empty}\PY{p}{:}
\PY{n}{next\PYZus{}upper\PYZus{}index} \PY{o}{=} \PY{n}{next\PYZus{}upper\PYZus{}values}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{ PSD}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{o}{.}\PY{n}{idxmin}\PY{p}{(}\PY{p}{)}
\PY{n}{next\PYZus{}upper\PYZus{}2THETA} \PY{o}{=} \PY{n}{df}\PY{o}{.}\PY{n}{loc}\PY{p}{[}\PY{n}{next\PYZus{}upper\PYZus{}index}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{ 2THETA}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}
\PY{n}{next\PYZus{}upper\PYZus{}PSD} \PY{o}{=} \PY{n}{df}\PY{o}{.}\PY{n}{loc}\PY{p}{[}\PY{n}{next\PYZus{}upper\PYZus{}index}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{ PSD}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}
\PY{c+c1}{\PYZsh{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}}
\PY{n}{promedio\PYZus{}de\PYZus{}dos\PYZus{}puntos} \PY{o}{=} \PY{p}{(}\PY{p}{(}\PY{n}{df}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{ 2THETA}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{[}\PY{n}{next\PYZus{}upper\PYZus{}index}\PY{p}{]} \PY{o}{+} \PY{n}{df}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{ 2THETA}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{[}\PY{n}{next\PYZus{}upper\PYZus{}index} \PY{o}{+} \PY{l+m+mi}{1}\PY{p}{]}\PY{p}{)}\PY{o}{/}\PY{l+m+mi}{2}\PY{p}{)} \PY{o}{+} \PY{l+m+mf}{0.003}
\PY{c+c1}{\PYZsh{} Agregamos dos puntos con las coordenadas de closes index y el promedio de 2theta en el next\PYZus{}upper\PYZus{}index y next\PYZus{}upper\PYZus{}index + 1}
\PY{n}{fig}\PY{o}{.}\PY{n}{add\PYZus{}trace}\PY{p}{(}\PY{n}{go}\PY{o}{.}\PY{n}{Scatter}\PY{p}{(}\PY{n}{x}\PY{o}{=}\PY{p}{[}\PY{n}{df}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{ 2THETA}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{[}\PY{n}{closest\PYZus{}index}\PY{p}{]}\PY{p}{]}\PY{p}{,} \PY{n}{y}\PY{o}{=}\PY{p}{[}\PY{n}{df}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{ PSD}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{[}\PY{n}{closest\PYZus{}index}\PY{p}{]}\PY{p}{]}\PY{p}{,} \PY{n}{mode}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{markers+text}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{text}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Punto A}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{textposition}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{bottom center}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{marker}\PY{o}{=}\PY{n+nb}{dict}\PY{p}{(}\PY{n}{color}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{blue}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}\PY{p}{)}\PY{p}{)}
\PY{n}{fig}\PY{o}{.}\PY{n}{add\PYZus{}trace}\PY{p}{(}\PY{n}{go}\PY{o}{.}\PY{n}{Scatter}\PY{p}{(}\PY{n}{x}\PY{o}{=}\PY{p}{[}\PY{n}{promedio\PYZus{}de\PYZus{}dos\PYZus{}puntos}\PY{p}{]}\PY{p}{,} \PY{n}{y}\PY{o}{=}\PY{p}{[}\PY{n}{df}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{ PSD}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{[}\PY{n}{closest\PYZus{}index}\PY{p}{]}\PY{p}{]}\PY{p}{,} \PY{n}{mode}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{markers+text}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{text}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Punto B}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{textposition}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{bottom center}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{marker}\PY{o}{=}\PY{n+nb}{dict}\PY{p}{(}\PY{n}{color}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{red}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}\PY{p}{)}\PY{p}{)}
\PY{c+c1}{\PYZsh{} Creamos una linea entre esos cos puntos}
\PY{n}{fig}\PY{o}{.}\PY{n}{add\PYZus{}trace}\PY{p}{(}\PY{n}{go}\PY{o}{.}\PY{n}{Scatter}\PY{p}{(}\PY{n}{x}\PY{o}{=}\PY{p}{[}\PY{n}{df}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{ 2THETA}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{[}\PY{n}{closest\PYZus{}index}\PY{p}{]}\PY{p}{,} \PY{n}{promedio\PYZus{}de\PYZus{}dos\PYZus{}puntos}\PY{p}{]}\PY{p}{,} \PY{n}{y}\PY{o}{=}\PY{p}{[}\PY{n}{df}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{ PSD}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{[}\PY{n}{closest\PYZus{}index}\PY{p}{]}\PY{p}{,} \PY{n}{df}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{ PSD}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{[}\PY{n}{closest\PYZus{}index}\PY{p}{]}\PY{p}{]}\PY{p}{,} \PY{n}{mode}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{lines}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{line}\PY{o}{=}\PY{n+nb}{dict}\PY{p}{(}\PY{n}{color}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{green}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{dash}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{dash}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}\PY{p}{)}\PY{p}{)}
\PY{c+c1}{\PYZsh{} Se calcula la distancia con la formula euclidiana}
\PY{k}{def} \PY{n+nf}{calculate\PYZus{}fwhm}\PY{p}{(}\PY{n}{index}\PY{p}{)}\PY{p}{:}
\PY{n}{half\PYZus{}max} \PY{o}{=} \PY{n}{df}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{ PSD}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{[}\PY{n}{index}\PY{p}{]} \PY{o}{/} \PY{l+m+mi}{2} \PY{c+c1}{\PYZsh{} Half of the peak\PYZsq{}s maximum value}
\PY{n}{left\PYZus{}bound} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{where}\PY{p}{(}\PY{n}{df}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{ PSD}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{[}\PY{p}{:}\PY{n}{index}\PY{p}{]} \PY{o}{\PYZlt{}} \PY{n}{half\PYZus{}max}\PY{p}{)}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{]}\PY{p}{[}\PY{o}{\PYZhy{}}\PY{l+m+mi}{1}\PY{p}{]} \PY{c+c1}{\PYZsh{} Left boundary}
\PY{n}{right\PYZus{}bound} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{where}\PY{p}{(}\PY{n}{df}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{ PSD}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{[}\PY{n}{index}\PY{p}{:}\PY{p}{]} \PY{o}{\PYZlt{}} \PY{n}{half\PYZus{}max}\PY{p}{)}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{]}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{]} \PY{o}{+} \PY{n}{index} \PY{c+c1}{\PYZsh{} Right boundary}
\PY{n}{fwhm} \PY{o}{=} \PY{n}{df}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{ 2THETA}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{[}\PY{n}{right\PYZus{}bound}\PY{p}{]} \PY{o}{\PYZhy{}} \PY{n}{df}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{ 2THETA}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{[}\PY{n}{left\PYZus{}bound}\PY{p}{]} \PY{c+c1}{\PYZsh{} FWHM calculation}
\PY{k}{return} \PY{n}{fwhm}
\PY{n}{beta\PYZus{}constant\PYZus{}value} \PY{o}{=} \PY{n}{calculate\PYZus{}fwhm}\PY{p}{(}\PY{n}{indice\PYZus{}refle\PYZus{}mas\PYZus{}alta}\PY{p}{)} \PY{c+c1}{\PYZsh{}Se guardan los datos en la variable global}
\PY{n}{distance\PYZus{}two\PYZus{}points} \PY{o}{=} \PY{n}{beta\PYZus{}constant\PYZus{}value}
\PY{c+c1}{\PYZsh{} Se agrega una anotación con esta distancia}
\PY{n}{fig}\PY{o}{.}\PY{n}{add\PYZus{}annotation}\PY{p}{(}
\PY{n}{x}\PY{o}{=}\PY{p}{(}\PY{n}{next\PYZus{}upper\PYZus{}2THETA} \PY{o}{+} \PY{n}{closest\PYZus{}2THETA\PYZus{}value}\PY{p}{)}\PY{o}{/}\PY{l+m+mi}{2}\PY{p}{,}
\PY{n}{y}\PY{o}{=}\PY{n}{df}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{ PSD}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{[}\PY{n}{closest\PYZus{}index}\PY{p}{]}\PY{p}{,}
\PY{n}{text}\PY{o}{=}\PY{l+s+sa}{f}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Distancia: }\PY{l+s+si}{\PYZob{}}\PY{n}{distance\PYZus{}two\PYZus{}points}\PY{l+s+si}{:}\PY{l+s+s1}{.5f}\PY{l+s+si}{\PYZcb{}}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{c+c1}{\PYZsh{} Ponemos la distancia con 3 puntos decimales}
\PY{n}{showarrow}\PY{o}{=}\PY{k+kc}{True}\PY{p}{,}
\PY{n}{arrowhead}\PY{o}{=}\PY{l+m+mi}{1}\PY{p}{,}
\PY{p}{)}
\PY{n}{fig}\PY{o}{.}\PY{n}{add\PYZus{}annotation}\PY{p}{(}
\PY{n}{x}\PY{o}{=}\PY{p}{(}\PY{n}{next\PYZus{}upper\PYZus{}2THETA} \PY{o}{+} \PY{n}{closest\PYZus{}2THETA\PYZus{}value}\PY{p}{)}\PY{o}{/}\PY{l+m+mi}{2}\PY{p}{,}
\PY{n}{y}\PY{o}{=}\PY{n}{df}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{ PSD}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{[}\PY{n}{closest\PYZus{}index} \PY{o}{+} \PY{l+m+mi}{3}\PY{p}{]}\PY{p}{,}
\PY{n}{text}\PY{o}{=}\PY{l+s+sa}{f}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Distancia entre linea y pico: }\PY{l+s+si}{\PYZob{}}\PY{n}{altura\PYZus{}reflexion\PYZus{}max}\PY{l+s+si}{\PYZcb{}}\PY{l+s+s1}{ y distancia mitad }\PY{l+s+si}{\PYZob{}}\PY{n}{altura\PYZus{}reflexion\PYZus{}max}\PY{o}{/}\PY{l+m+mi}{2}\PY{l+s+si}{\PYZcb{}}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{c+c1}{\PYZsh{} Ponemos la distancia con 3 puntos decimales}
\PY{n}{showarrow}\PY{o}{=}\PY{k+kc}{True}\PY{p}{,}
\PY{n}{arrowhead}\PY{o}{=}\PY{l+m+mi}{1}\PY{p}{,}
\PY{p}{)}
\PY{n}{fig}\PY{o}{.}\PY{n}{show}\PY{p}{(}\PY{n}{renderer}\PY{o}{=}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{notebook}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)}
\end{Verbatim}
\end{tcolorbox}
\subsubsection{Cálculo de tamaño de cristalito a partir de la formula de
Debye-Scherrer}\label{cuxe1lculo-de-tamauxf1o-de-cristalito-a-partir-de-la-formula-de-debye-scherrer}
~
\[D = \frac{K \lambda}{\beta cos(\theta)}\]
Donde: - K: Factor de estructura (0.89 para cúbicas
{[}\href{https://www.sciencedirect.com/science/article/pii/S2590182621000175\#fo0015}{2}{]})
- \(\lambda\): Longitud de onda CuK\(\alpha\) (1.5406 Å) - \(\beta\):
Distancia entre \textbf{Punto A} y \textbf{Punto B} - D: Tamaño de
cristalito
\begin{tcolorbox}[breakable, size=fbox, boxrule=1pt, pad at break*=1mm,colback=cellbackground, colframe=cellborder]
\prompt{In}{incolor}{5}{\boxspacing}
\begin{Verbatim}[commandchars=\\\{\}]
\PY{k}{def} \PY{n+nf}{calc\PYZus{}tamanio\PYZus{}cristalito\PYZus{}scherrer} \PY{p}{(}\PY{n}{beta}\PY{p}{,} \PY{n}{theta}\PY{p}{)}\PY{p}{:}
\PY{n}{K} \PY{o}{=} \PY{l+m+mf}{0.89} \PY{c+c1}{\PYZsh{} Para cúbicas según la referencia}
\PY{n}{LAMBDA} \PY{o}{=} \PY{l+m+mf}{1.5406} \PY{c+c1}{\PYZsh{} Longitud de onda Cobre K alfa}
\PY{c+c1}{\PYZsh{}print(theta)}
\PY{n}{theta\PYZus{}rads} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{deg2rad}\PY{p}{(}\PY{n}{theta}\PY{p}{)}
\PY{n}{angulo} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{cos}\PY{p}{(}\PY{n}{theta\PYZus{}rads}\PY{p}{)}
\PY{c+c1}{\PYZsh{}print(angulo)}
\PY{n}{cristalito\PYZus{}size} \PY{o}{=} \PY{p}{(}\PY{n}{K} \PY{o}{*} \PY{n}{LAMBDA}\PY{p}{)}\PY{o}{/}\PY{p}{(}\PY{n}{beta} \PY{o}{*} \PY{n}{angulo}\PY{p}{)}
\PY{c+c1}{\PYZsh{}print(f\PYZsq{}Tamaño de cristalito calculado: \PYZob{}cristalito\PYZus{}size.values[0]\PYZcb{} Å\PYZsq{})}
\PY{k}{return} \PY{n}{cristalito\PYZus{}size}\PY{o}{.}\PY{n}{values}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{]} \PY{o}{*} \PY{l+m+mf}{0.1} \PY{c+c1}{\PYZsh{} Se multiplica por 0.1 para convertir A a nm}
\PY{n}{theta\PYZus{}scherrer} \PY{o}{=} \PY{n}{df}\PY{p}{[}\PY{n}{df}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{ PSD}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]} \PY{o}{==} \PY{n+nb}{max}\PY{p}{(}\PY{n}{df}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{ PSD}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{o}{.}\PY{n}{values}\PY{p}{)}\PY{p}{]}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{ 2THETA}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}
\PY{c+c1}{\PYZsh{}print(theta\PYZus{}scherrer/2)}
\PY{n}{display}\PY{p}{(}\PY{n}{Markdown}\PY{p}{(}\PY{l+s+sa}{f}\PY{l+s+s1}{\PYZsq{}\PYZsq{}\PYZsq{}}
\PY{l+s+s1}{\PYZam{}nbsp;}
\PY{l+s+s1}{\PYZlt{}div align=}\PY{l+s+s1}{\PYZdq{}}\PY{l+s+s1}{center}\PY{l+s+s1}{\PYZdq{}}\PY{l+s+s1}{\PYZgt{} Tamaño de cristalito calculado: \PYZlt{}b\PYZgt{} }\PY{l+s+si}{\PYZob{}}\PY{n}{calc\PYZus{}tamanio\PYZus{}cristalito\PYZus{}scherrer}\PY{p}{(}\PY{n}{np}\PY{o}{.}\PY{n}{deg2rad}\PY{p}{(}\PY{n}{distance\PYZus{}two\PYZus{}points}\PY{p}{)}\PY{p}{,}\PY{p}{(}\PY{n}{theta\PYZus{}scherrer}\PY{o}{/}\PY{l+m+mi}{2}\PY{p}{)}\PY{p}{)}\PY{l+s+si}{\PYZcb{}}\PY{l+s+s1}{ nm \PYZlt{}/b\PYZgt{}\PYZlt{}/div\PYZgt{}}
\PY{l+s+s1}{\PYZam{}nbsp;}
\PY{l+s+s1}{\PYZsq{}\PYZsq{}\PYZsq{}}\PY{p}{)}\PY{p}{)}
\end{Verbatim}
\end{tcolorbox}
~
Tamaño de cristalito calculado: 24.886226598966275 nm
~
\begin{center}\rule{0.5\linewidth}{0.5pt}\end{center}
\subsection{Creamos la gráfica interactiva para la formula de
Williamson-Hall}\label{creamos-la-gruxe1fica-interactiva-para-la-formula-de-williamson-hall}
En esta parte del código se obtienen los puntos más relevantes de la
gráfica y se les da un tratamiento para poder trabajar con ellos, sin
embargo ahora el tratamiento se hace con base a obtener los datos para
calcular el tamaño de cristalito a través de Williamson-Hall
\begin{tcolorbox}[breakable, size=fbox, boxrule=1pt, pad at break*=1mm,colback=cellbackground, colframe=cellborder]
\prompt{In}{incolor}{6}{\boxspacing}
\begin{Verbatim}[commandchars=\\\{\}]
\PY{n}{df} \PY{o}{=} \PY{n}{pd}\PY{o}{.}\PY{n}{read\PYZus{}csv}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{data.csv}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{c+c1}{\PYZsh{} Encontramos los picos más altos en la gráfica}
\PY{n}{peaks}\PY{p}{,} \PY{n}{\PYZus{}} \PY{o}{=} \PY{n}{find\PYZus{}peaks}\PY{p}{(}\PY{n}{df}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{ PSD}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{,} \PY{n}{prominence}\PY{o}{=}\PY{l+m+mi}{50} \PY{p}{,} \PY{n}{distance}\PY{o}{=} \PY{l+m+mi}{90}\PY{p}{)} \PY{c+c1}{\PYZsh{} Adjust prominence as needed}
\PY{n}{peaks} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{delete}\PY{p}{(}\PY{n}{peaks}\PY{p}{,} \PY{l+m+mi}{0}\PY{p}{)}
\PY{n}{peaks} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{delete}\PY{p}{(}\PY{n}{peaks}\PY{p}{,} \PY{l+m+mi}{1}\PY{p}{)}
\PY{n}{peaks} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{delete}\PY{p}{(}\PY{n}{peaks}\PY{p}{,} \PY{l+m+mi}{7}\PY{p}{)}
\PY{n}{y\PYZus{}position\PYZus{}value\PYZus{}global} \PY{o}{=} \PY{l+m+mi}{100}
\PY{n}{beta\PYZus{}constant\PYZus{}value} \PY{o}{=} \PY{l+m+mi}{0}
\PY{n}{lista\PYZus{}picos\PYZus{}index} \PY{o}{=} \PY{p}{[}\PY{p}{]}
\PY{k}{for} \PY{n}{i} \PY{o+ow}{in} \PY{n}{peaks}\PY{p}{:}
\PY{n}{lista\PYZus{}picos\PYZus{}index}\PY{o}{.}\PY{n}{append}\PY{p}{(}\PY{n}{i}\PY{p}{)}
\PY{n}{fig} \PY{o}{=} \PY{n}{px}\PY{o}{.}\PY{n}{line}\PY{p}{(}\PY{n}{df}\PY{p}{,} \PY{n}{x}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{ 2THETA}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{y}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{ PSD}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{labels}\PY{o}{=}\PY{p}{\PYZob{}}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Name}\PY{l+s+s1}{\PYZsq{}}\PY{p}{:} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{2theta}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Value}\PY{l+s+s1}{\PYZsq{}}\PY{p}{:} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{values}\PY{l+s+s1}{\PYZsq{}}\PY{p}{\PYZcb{}}\PY{p}{,} \PY{n}{title}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{SrTiO3 difractograma}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{n}{fig}\PY{o}{.}\PY{n}{add\PYZus{}scatter}\PY{p}{(}\PY{n}{x}\PY{o}{=}\PY{n}{df}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{ 2THETA}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{[}\PY{n}{peaks}\PY{p}{]}\PY{p}{,} \PY{n}{y}\PY{o}{=}\PY{n}{df}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{ PSD}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{[}\PY{n}{peaks}\PY{p}{]}\PY{p}{,} \PY{n}{mode}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{markers}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{marker}\PY{o}{=}\PY{n+nb}{dict}\PY{p}{(}\PY{n}{color}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{red}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{size}\PY{o}{=}\PY{l+m+mi}{8}\PY{p}{)}\PY{p}{,} \PY{n}{name}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Peaks}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{n}{fig}\PY{o}{.}\PY{n}{update\PYZus{}traces}\PY{p}{(}\PY{n}{line}\PY{o}{=}\PY{n+nb}{dict}\PY{p}{(}\PY{n}{color}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{blue}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}\PY{p}{)}
\PY{c+c1}{\PYZsh{} Agregamos una linea horizontal que sirve como punto de referencia}
\PY{n}{fig}\PY{o}{.}\PY{n}{add\PYZus{}shape}\PY{p}{(}
\PY{n+nb}{type}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{line}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,}
\PY{n}{x0}\PY{o}{=}\PY{n}{df}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{ 2THETA}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{o}{.}\PY{n}{min}\PY{p}{(}\PY{p}{)}\PY{p}{,}
\PY{n}{y0}\PY{o}{=}\PY{n}{y\PYZus{}position\PYZus{}value\PYZus{}global}\PY{p}{,}
\PY{n}{x1}\PY{o}{=}\PY{n}{df}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{ 2THETA}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{o}{.}\PY{n}{max}\PY{p}{(}\PY{p}{)}\PY{p}{,}
\PY{n}{y1}\PY{o}{=}\PY{n}{y\PYZus{}position\PYZus{}value\PYZus{}global}\PY{p}{,}
\PY{n}{line}\PY{o}{=}\PY{n+nb}{dict}\PY{p}{(}\PY{n}{color}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{red}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{width}\PY{o}{=}\PY{l+m+mi}{2}\PY{p}{,} \PY{n}{dash}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{solid}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{p}{)}
\PY{c+c1}{\PYZsh{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}\PYZhy{}}
\PY{c+c1}{\PYZsh{}Se calcula la altura máxima en de la reflexión más grande:}
\PY{c+c1}{\PYZsh{}altura\PYZus{}reflexion\PYZus{}max = max(df[\PYZsq{} PSD\PYZsq{}].values) \PYZhy{} y\PYZus{}position\PYZus{}value\PYZus{}global}
\PY{k}{def} \PY{n+nf}{calculate\PYZus{}fwhm}\PY{p}{(}\PY{n}{index}\PY{p}{)}\PY{p}{:}
\PY{n}{half\PYZus{}max} \PY{o}{=} \PY{n}{df}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{ PSD}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{[}\PY{n}{index}\PY{p}{]} \PY{o}{/} \PY{l+m+mi}{2} \PY{c+c1}{\PYZsh{} Half of the peak\PYZsq{}s maximum value}
\PY{n}{left\PYZus{}bound} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{where}\PY{p}{(}\PY{n}{df}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{ PSD}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{[}\PY{p}{:}\PY{n}{index}\PY{p}{]} \PY{o}{\PYZlt{}} \PY{n}{half\PYZus{}max}\PY{p}{)}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{]}\PY{p}{[}\PY{o}{\PYZhy{}}\PY{l+m+mi}{1}\PY{p}{]} \PY{c+c1}{\PYZsh{} Left boundary}
\PY{n}{right\PYZus{}bound} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{where}\PY{p}{(}\PY{n}{df}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{ PSD}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{[}\PY{n}{index}\PY{p}{:}\PY{p}{]} \PY{o}{\PYZlt{}} \PY{n}{half\PYZus{}max}\PY{p}{)}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{]}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{]} \PY{o}{+} \PY{n}{index} \PY{c+c1}{\PYZsh{} Right boundary}
\PY{n}{fwhm} \PY{o}{=} \PY{n}{df}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{ 2THETA}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{[}\PY{n}{right\PYZus{}bound}\PY{p}{]} \PY{o}{\PYZhy{}} \PY{n}{df}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{ 2THETA}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{[}\PY{n}{left\PYZus{}bound}\PY{p}{]} \PY{c+c1}{\PYZsh{} FWHM calculation}
\PY{k}{return} \PY{n}{fwhm}
\PY{k}{def} \PY{n+nf}{largo\PYZus{}pico}\PY{p}{(}\PY{n}{distancia}\PY{p}{,} \PY{n}{df\PYZus{}f}\PY{p}{,} \PY{n}{peaks}\PY{p}{)}\PY{p}{:}
\PY{n}{fig}\PY{o}{.}\PY{n}{add\PYZus{}annotation}\PY{p}{(}
\PY{n}{x}\PY{o}{=}\PY{n}{df\PYZus{}f}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{ 2THETA}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{[}\PY{n}{peaks}\PY{p}{]}\PY{p}{,}
\PY{n}{y}\PY{o}{=}\PY{n}{df\PYZus{}f}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{ PSD}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{[}\PY{n}{peaks} \PY{o}{\PYZhy{}} \PY{l+m+mi}{2}\PY{p}{]}\PY{p}{,}
\PY{n}{text}\PY{o}{=}\PY{l+s+sa}{f}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{FWHM }\PY{l+s+si}{\PYZob{}}\PY{n}{distancia}\PY{l+s+si}{:}\PY{l+s+s1}{.3f}\PY{l+s+si}{\PYZcb{}}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{c+c1}{\PYZsh{} Ponemos la distancia con 3 puntos decimales}
\PY{n}{showarrow}\PY{o}{=}\PY{k+kc}{True}\PY{p}{,}
\PY{n}{arrowhead}\PY{o}{=}\PY{l+m+mi}{1}\PY{p}{,}
\PY{p}{)}
\PY{n}{fwhm\PYZus{}values} \PY{o}{=} \PY{p}{[}\PY{p}{]}
\PY{n}{angulos\PYZus{}peaks} \PY{o}{=} \PY{p}{[}\PY{p}{]}
\PY{k}{for} \PY{n}{peak\PYZus{}index} \PY{o+ow}{in} \PY{n}{peaks}\PY{p}{:}
\PY{n}{fwhm} \PY{o}{=} \PY{n}{calculate\PYZus{}fwhm}\PY{p}{(}\PY{n}{peak\PYZus{}index}\PY{p}{)}
\PY{n}{angulos\PYZus{}peaks}\PY{o}{.}\PY{n}{append}\PY{p}{(}\PY{n}{df}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{ 2THETA}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{[}\PY{n}{peak\PYZus{}index}\PY{p}{]}\PY{p}{)}
\PY{n}{fwhm\PYZus{}values}\PY{o}{.}\PY{n}{append}\PY{p}{(}\PY{n}{fwhm}\PY{p}{)}
\PY{c+c1}{\PYZsh{}print(f\PYZdq{}Peak at index \PYZob{}peak\PYZus{}index\PYZcb{}: FWHM = \PYZob{}fwhm\PYZcb{}\PYZdq{})}
\PY{k}{for} \PY{n}{i} \PY{o+ow}{in} \PY{n+nb}{range}\PY{p}{(}\PY{n+nb}{len}\PY{p}{(}\PY{n}{lista\PYZus{}picos\PYZus{}index}\PY{p}{)}\PY{p}{)}\PY{p}{:}
\PY{n}{largo\PYZus{}pico}\PY{p}{(}\PY{n}{fwhm\PYZus{}values}\PY{p}{[}\PY{n}{i}\PY{p}{]}\PY{p}{,} \PY{n}{df}\PY{p}{,} \PY{n}{lista\PYZus{}picos\PYZus{}index}\PY{p}{[}\PY{n}{i}\PY{p}{]}\PY{p}{)}
\PY{c+c1}{\PYZsh{}largo\PYZus{}pico(lista\PYZus{}distancia\PYZus{}entre\PYZus{}picos[1], df,1,1)}
\PY{c+c1}{\PYZsh{}print(lista\PYZus{}picos\PYZus{}index[1])}
\PY{c+c1}{\PYZsh{}print(calculate\PYZus{}fwhm(lista\PYZus{}picos\PYZus{}index[1]))}
\PY{n}{fig}\PY{o}{.}\PY{n}{show}\PY{p}{(}\PY{n}{renderer}\PY{o}{=}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{notebook}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)}
\end{Verbatim}
\end{tcolorbox}
\begin{center}\rule{0.5\linewidth}{0.5pt}\end{center}
\#\#~Se obtienen los datos necesarios para hacer la gráfica
\(\beta cos\theta\) vs \(sen\theta\)
\begin{tcolorbox}[breakable, size=fbox, boxrule=1pt, pad at break*=1mm,colback=cellbackground, colframe=cellborder]
\prompt{In}{incolor}{7}{\boxspacing}
\begin{Verbatim}[commandchars=\\\{\}]
\PY{n}{lista\PYZus{}de\PYZus{}angulos\PYZus{}2theta} \PY{o}{=} \PY{n}{angulos\PYZus{}peaks}
\PY{n}{lista\PYZus{}de\PYZus{}angulos\PYZus{}theta} \PY{o}{=} \PY{p}{[}\PY{p}{]}
\PY{k}{for} \PY{n}{angulo} \PY{o+ow}{in} \PY{n}{lista\PYZus{}de\PYZus{}angulos\PYZus{}2theta}\PY{p}{:}
\PY{n}{lista\PYZus{}de\PYZus{}angulos\PYZus{}theta}\PY{o}{.}\PY{n}{append}\PY{p}{(}\PY{n}{angulo}\PY{o}{/}\PY{l+m+mi}{2}\PY{p}{)}
\end{Verbatim}
\end{tcolorbox}
\begin{tcolorbox}[breakable, size=fbox, boxrule=1pt, pad at break*=1mm,colback=cellbackground, colframe=cellborder]
\prompt{In}{incolor}{8}{\boxspacing}
\begin{Verbatim}[commandchars=\\\{\}]
\PY{n}{sen\PYZus{}angulos\PYZus{}plot} \PY{o}{=} \PY{p}{[}\PY{p}{]}
\PY{n}{cos\PYZus{}angulos\PYZus{}plot} \PY{o}{=} \PY{p}{[}\PY{p}{]}
\PY{c+c1}{\PYZsh{}print(beta\PYZus{}constant\PYZus{}value)}
\PY{c+c1}{\PYZsh{}beta\PYZus{}constant\PYZus{}value = 3}
\PY{n}{contador} \PY{o}{=} \PY{l+m+mi}{0}
\PY{k}{for} \PY{n}{angulo} \PY{o+ow}{in} \PY{n}{lista\PYZus{}de\PYZus{}angulos\PYZus{}theta}\PY{p}{:}
\PY{c+c1}{\PYZsh{}print(fwhm\PYZus{}values[contador])}
\PY{c+c1}{\PYZsh{}print(np.deg2rad(angulo))}
\PY{c+c1}{\PYZsh{} Convert the angle from degrees to radians}
\PY{n}{deg\PYZus{}angle\PYZus{}sen} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{sin}\PY{p}{(}\PY{n}{np}\PY{o}{.}\PY{n}{deg2rad}\PY{p}{(}\PY{n}{angulo}\PY{p}{)}\PY{p}{)}
\PY{n}{deg\PYZus{}angle\PYZus{}cos} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{cos}\PY{p}{(}\PY{n}{np}\PY{o}{.}\PY{n}{deg2rad}\PY{p}{(}\PY{n}{angulo}\PY{p}{)}\PY{p}{)}
\PY{n}{sen\PYZus{}angulos\PYZus{}plot}\PY{o}{.}\PY{n}{append}\PY{p}{(}\PY{l+m+mi}{4} \PY{o}{*} \PY{n}{deg\PYZus{}angle\PYZus{}sen}\PY{p}{)}
\PY{n}{cos\PYZus{}angulos\PYZus{}plot}\PY{o}{.}\PY{n}{append}\PY{p}{(}\PY{n}{fwhm\PYZus{}values}\PY{p}{[}\PY{n}{contador}\PY{p}{]} \PY{o}{*} \PY{n}{deg\PYZus{}angle\PYZus{}cos}\PY{p}{)}
\PY{c+c1}{\PYZsh{}print(np.cos(angulo) * beta\PYZus{}constant\PYZus{}value)}
\PY{n}{contador} \PY{o}{+}\PY{o}{=} \PY{l+m+mi}{1}
\PY{c+c1}{\PYZsh{}print(sen\PYZus{}angulos\PYZus{}plot)}
\end{Verbatim}
\end{tcolorbox}
\subsection{\texorpdfstring{Se grafíca \(\beta cos\theta\) vs
\(sen\theta\)}{Se grafíca \textbackslash beta cos\textbackslash theta vs sen\textbackslash theta}}\label{se-grafuxedca-beta-costheta-vs-sentheta}
\begin{tcolorbox}[breakable, size=fbox, boxrule=1pt, pad at break*=1mm,colback=cellbackground, colframe=cellborder]
\prompt{In}{incolor}{9}{\boxspacing}
\begin{Verbatim}[commandchars=\\\{\}]
\PY{c+c1}{\PYZsh{} Add a scatter plot of the list values}
\PY{c+c1}{\PYZsh{} Create a Plotly figure}
\PY{n}{fig} \PY{o}{=} \PY{n}{go}\PY{o}{.}\PY{n}{Figure}\PY{p}{(}\PY{p}{)}
\PY{n}{fig}\PY{o}{.}\PY{n}{add\PYZus{}trace}\PY{p}{(}\PY{n}{go}\PY{o}{.}\PY{n}{Scatter}\PY{p}{(}\PY{n}{x}\PY{o}{=}\PY{n}{sen\PYZus{}angulos\PYZus{}plot}\PY{p}{,} \PY{n}{y}\PY{o}{=}\PY{n}{cos\PYZus{}angulos\PYZus{}plot}\PY{p}{,} \PY{n}{mode}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{markers}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{marker}\PY{o}{=}\PY{n+nb}{dict}\PY{p}{(}\PY{n}{color}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{blue}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}\PY{p}{)}\PY{p}{)}
\PY{c+c1}{\PYZsh{} Update layout if needed (e.g., title, axis labels)}
\PY{n}{fig}\PY{o}{.}\PY{n}{update\PYZus{}layout}\PY{p}{(}\PY{n}{title}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{SrTiO3 ßcosø vs senø}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{xaxis\PYZus{}title}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{4senø}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{yaxis\PYZus{}title}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{ßcosø}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{c+c1}{\PYZsh{} Show the plot}
\PY{n}{fig}\PY{o}{.}\PY{n}{show}\PY{p}{(}\PY{n}{renderer}\PY{o}{=}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{notebook}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)}
\end{Verbatim}
\end{tcolorbox}
\subsection{Regresión lineal de los
datos}\label{regresiuxf3n-lineal-de-los-datos}
\begin{tcolorbox}[breakable, size=fbox, boxrule=1pt, pad at break*=1mm,colback=cellbackground, colframe=cellborder]
\prompt{In}{incolor}{10}{\boxspacing}
\begin{Verbatim}[commandchars=\\\{\}]
\PY{c+c1}{\PYZsh{} Sample XRD data (replace this with your actual data)}
\PY{n}{x} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{array}\PY{p}{(}\PY{n}{sen\PYZus{}angulos\PYZus{}plot}\PY{p}{)} \PY{c+c1}{\PYZsh{} X\PYZhy{}axis data (e.g., angles)}
\PY{n}{y} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{array}\PY{p}{(}\PY{n}{cos\PYZus{}angulos\PYZus{}plot}\PY{p}{)} \PY{c+c1}{\PYZsh{} Y\PYZhy{}axis data (e.g., intensity)}
\PY{c+c1}{\PYZsh{} Perform linear regression using NumPy}
\PY{n}{slope}\PY{p}{,} \PY{n}{intercept} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{polyfit}\PY{p}{(}\PY{n}{x}\PY{p}{,} \PY{n}{y}\PY{p}{,} \PY{l+m+mi}{1}\PY{p}{)} \PY{c+c1}{\PYZsh{} 1 for linear regression}
\PY{c+c1}{\PYZsh{} Create the regression line using the slope and intercept}
\PY{n}{regression\PYZus{}line} \PY{o}{=} \PY{n}{slope} \PY{o}{*} \PY{n}{x} \PY{o}{+} \PY{n}{intercept}
\PY{c+c1}{\PYZsh{} Create a scatter plot with regression line using Plotly}
\PY{n}{fig} \PY{o}{=} \PY{n}{go}\PY{o}{.}\PY{n}{Figure}\PY{p}{(}\PY{p}{)}
\PY{c+c1}{\PYZsh{} Plot the original data points}
\PY{n}{fig}\PY{o}{.}\PY{n}{add\PYZus{}trace}\PY{p}{(}\PY{n}{go}\PY{o}{.}\PY{n}{Scatter}\PY{p}{(}\PY{n}{x}\PY{o}{=}\PY{n}{x}\PY{p}{,} \PY{n}{y}\PY{o}{=}\PY{n}{y}\PY{p}{,} \PY{n}{mode}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{markers}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{name}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Original Data}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}\PY{p}{)}
\PY{c+c1}{\PYZsh{} Plot the regression line}
\PY{n}{fig}\PY{o}{.}\PY{n}{add\PYZus{}trace}\PY{p}{(}\PY{n}{go}\PY{o}{.}\PY{n}{Scatter}\PY{p}{(}\PY{n}{x}\PY{o}{=}\PY{n}{x}\PY{p}{,} \PY{n}{y}\PY{o}{=}\PY{n}{regression\PYZus{}line}\PY{p}{,} \PY{n}{mode}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{lines}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,} \PY{n}{name}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Regression Line}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}\PY{p}{)}
\PY{c+c1}{\PYZsh{} Add labels and title}
\PY{n}{fig}\PY{o}{.}\PY{n}{update\PYZus{}layout}\PY{p}{(}
\PY{n}{title}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{SrTiO3 ßcosø vs senø con Regresion lineal}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,}
\PY{n}{xaxis\PYZus{}title}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{X\PYZhy{}axis (e.g., Angles)}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,}
\PY{n}{yaxis\PYZus{}title}\PY{o}{=}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Y\PYZhy{}axis (e.g., Intensity)}\PY{l+s+s1}{\PYZsq{}}
\PY{p}{)}
\PY{n}{equation} \PY{o}{=} \PY{l+s+sa}{f}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{y = }\PY{l+s+si}{\PYZob{}}\PY{n}{slope}\PY{l+s+si}{\PYZcb{}}\PY{l+s+s1}{x + }\PY{l+s+si}{\PYZob{}}\PY{n}{intercept}\PY{l+s+si}{\PYZcb{}}\PY{l+s+s1}{\PYZsq{}}
\PY{c+c1}{\PYZsh{} Calculate R\PYZhy{}squared value}
\PY{n}{r\PYZus{}squared} \PY{o}{=} \PY{n}{r2\PYZus{}score}\PY{p}{(}\PY{n}{y}\PY{p}{,} \PY{n}{regression\PYZus{}line}\PY{p}{)}
\PY{c+c1}{\PYZsh{} Show the plot}
\PY{n}{fig}\PY{o}{.}\PY{n}{show}\PY{p}{(}\PY{n}{renderer}\PY{o}{=}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{notebook}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)}
\PY{n}{display}\PY{p}{(}\PY{n}{Markdown}\PY{p}{(}\PY{l+s+sa}{f}\PY{l+s+s1}{\PYZsq{}\PYZsq{}\PYZsq{}}
\PY{l+s+s1}{\PYZam{}nbsp;}
\PY{l+s+s1}{\PYZlt{}div align=}\PY{l+s+s1}{\PYZdq{}}\PY{l+s+s1}{center}\PY{l+s+s1}{\PYZdq{}}\PY{l+s+s1}{\PYZgt{} Ecuación obtenidad: }\PY{l+s+si}{\PYZob{}}\PY{l+s+sa}{f}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{y = }\PY{l+s+si}{\PYZob{}}\PY{n}{slope}\PY{l+s+si}{\PYZcb{}}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+si}{\PYZcb{}}\PY{l+s+s1}{\PYZlt{}b\PYZgt{} x \PYZlt{}/b\PYZgt{}+ }\PY{l+s+si}{\PYZob{}}\PY{l+s+sa}{f}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+si}{\PYZob{}}\PY{n}{intercept}\PY{l+s+si}{\PYZcb{}}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+si}{\PYZcb{}}\PY{l+s+s1}{ \PYZlt{}/b\PYZgt{}\PYZlt{}/div\PYZgt{}}
\PY{l+s+s1}{\PYZlt{}div align=}\PY{l+s+s1}{\PYZdq{}}\PY{l+s+s1}{center}\PY{l+s+s1}{\PYZdq{}}\PY{l+s+s1}{\PYZgt{} \PYZdl{}R\PYZca{}2\PYZdl{}= }\PY{l+s+si}{\PYZob{}}\PY{n}{r\PYZus{}squared}\PY{l+s+si}{\PYZcb{}}\PY{l+s+s1}{ \PYZlt{}/b\PYZgt{}\PYZlt{}/div\PYZgt{}}
\PY{l+s+s1}{\PYZam{}nbsp;}
\PY{l+s+s1}{\PYZsq{}\PYZsq{}\PYZsq{}}\PY{p}{)}\PY{p}{)}
\end{Verbatim}
\end{tcolorbox}
~
Ecuación obtenidad: y = 0.07948605932788505 x + 0.2832693357361943
\(R^2\)= 0.6759802329862871
~
\subsection{Calculo del cristalito utilizando la fórmula de
Williamson-hall}\label{calculo-del-cristalito-utilizando-la-fuxf3rmula-de-williamson-hall}
Para calcular el cristralito a través de este método tenemos que
utilizar la siguiente expresión
\[ \beta_{hkl}cos\theta = \frac{K\lambda}{D} + 4\epsilon sen\theta\]
si observamos bien podemos darnos cuenta que la fórmula adopta la forma:
\[ y = mx+b \]
Haciendo la regresión lineal de nuestros datos podemos obtener la
siguiente expresión
\[ y = 0.11535040977386593 x + 0.24479779320473088 \]
por lo que podemos asumir que:
\[ \frac{K\lambda}{D} = 0.24479779320473088 \]
Asumiendo que: - K = 0.89 - \(\lambda\) = 1.5406 Å
Podemos despejar y obtener el resultado, tal que:
\begin{tcolorbox}[breakable, size=fbox, boxrule=1pt, pad at break*=1mm,colback=cellbackground, colframe=cellborder]
\prompt{In}{incolor}{11}{\boxspacing}
\begin{Verbatim}[commandchars=\\\{\}]
\PY{n}{K} \PY{o}{=} \PY{l+m+mf}{0.9} \PY{c+c1}{\PYZsh{} Para cúbicas según la referencia}
\PY{n}{LAMBDA} \PY{o}{=} \PY{l+m+mf}{1.5406} \PY{c+c1}{\PYZsh{} Longitud de onda Cobre K alfa}
\PY{n}{wh\PYZus{}cristalito} \PY{o}{=} \PY{p}{(}\PY{n}{K} \PY{o}{*} \PY{n}{LAMBDA}\PY{p}{)}\PY{o}{/}\PY{n}{intercept}
\PY{n}{display}\PY{p}{(}\PY{n}{Markdown}\PY{p}{(}\PY{l+s+sa}{f}\PY{l+s+s1}{\PYZsq{}\PYZsq{}\PYZsq{}}
\PY{l+s+s1}{\PYZam{}nbsp;}
\PY{l+s+s1}{\PYZlt{}div align=}\PY{l+s+s1}{\PYZdq{}}\PY{l+s+s1}{center}\PY{l+s+s1}{\PYZdq{}}\PY{l+s+s1}{\PYZgt{} Tamaño de cristalito calculado por Williamson\PYZhy{}hall : \PYZlt{}b\PYZgt{} }\PY{l+s+si}{\PYZob{}}\PY{n}{wh\PYZus{}cristalito}\PY{l+s+si}{\PYZcb{}}\PY{l+s+s1}{ nm \PYZlt{}/b\PYZgt{}\PYZlt{}/div\PYZgt{}}
\PY{l+s+s1}{\PYZam{}nbsp;}
\PY{l+s+s1}{\PYZsq{}\PYZsq{}\PYZsq{}}\PY{p}{)}\PY{p}{)}
\end{Verbatim}
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Tamaño de cristalito calculado por Williamson-hall : 4.894776190287218
nm
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