Failed to properly set size of tikzpicture in beamerposter

Question

I tried to insert a TikZ picture provided below into a beamerposter document.

It is generated by the following code (except the arrow in the middle of the "incident beam", it's an excessive detail):

\begin{tikzpicture}
    % axes and origin
    \coordinate (O) at (0, 0);
    \draw node[anchor=north east] {$O$};
    \draw [->] (-3,0)--(3,0) node [pos=0.98, below] {$x$};
    \draw [->] (0,-1)--(0,3) node [pos=0.98, left] {$z$};
    % orts
    \draw [thick, ->] (O)--(1,0) node[pos=1, below] {$\vc e_x$};
    \draw [thick, ->] (O)--(0,1) node[pos=1, left] {$\vc e_z$};
    % vector k and its angle chi
    \coordinate (K) at ({2.6*sin(30)},{2.6*cos(30)});
    \draw [thick, ->] (O)--(K) node[pos=1, right] {$\vc k$};
    \draw ([shift=(60:0.5)] O) arc (60:90:0.5) node[pos=0.35, above] {$\chi$};
    % k projections
    \coordinate (Kx) at (K |- O);
    \coordinate (Kz) at (K -| O);
    \draw [thick, ->](O)--(Kx) node[pos=1.15, below] {$\vc k_x$};
    \draw [thick, ->](O)--(Kz) node[pos=1, left] {$\vc k_z$};
    \draw [dashed] (K)--(Kz);
    \draw [dashed] (K)--(Kx);
    % foton beam
    \draw (-3, 2)--(O) node[pos=0.45, above] {$\ \hbar \omega$};
\end{tikzpicture}

When I insert this piece of code anywhere in the beamerposter document (either within \begin{block}...\end{block}, or just inside the frame), I get this ugly result (the image spans the whole poster width):

MWE

\documentclass[final, 24pt]{beamer}\usetheme{Frankfurt}\usecolortheme{orchid}\usefonttheme[onlymath]{serif}\mode<presentation>
\usepackage[orientation=portrait,size=a0,scale=1.4,debug]{beamerposter}
\usepackage[utf8]{inputenc}
\usepackage[T2A]{fontenc}
\usepackage[english, russian]{babel}
\usepackage{tikz}

\newcommand{\vc}[1]{\mathbf {#1}}
\begin{document}
    \begin{frame}{}
        \begin{center}
            \begin{tikzpicture} 
                 % ... picture code given above
            \end{tikzpicture}
        \end{center}
    \end{frame}
\end{document}

How do I make its appearance acceptable? Rescaling by means of

\scalebox{2.2}{
    \begin{tikzpicture}[scale=3] 
          % picture code
    \end{tikzpicture}
}

produces this output (spans the full paper width as well)

Then I can make some adjustments to line widths (\draw[..., line width=0.33ex] for example) manually to get reasonable output:

I want to ask the community whether there is another way to get the desired result (maybe it is a widely known issue but I have failed to google it directly) and why does direct 'porting' of nice image code from a4 document produce such a garbage?

Answer 1

Welcome to TeX-SE! You could append some directives to the every path and every node styles. Here is an example.

   \documentclass[final, 24pt]{beamer}\usetheme{Frankfurt}\usecolortheme{orchid}\usefonttheme[onlymath]{serif}\mode<presentation>
\usepackage[orientation=portrait,size=a0,scale=1.4,debug]{beamerposter}
\usepackage[utf8]{inputenc}
\usepackage[T2A]{fontenc}
\usepackage[english, russian]{babel}
\usepackage{tikz}

\newcommand{\vc}[1]{\mathbf {#1}}
\begin{document}
    \begin{frame}{}
        \begin{center}
         \begin{tikzpicture}[scale=12,every path/.append style={
         line width=4*\pgflinewidth},every node/.append style={scale=0.2,transform
         shape}]
             % axes and origin
             \coordinate (O) at (0, 0);
             \draw node[anchor=north east] {$O$};
             \draw [->] (-3,0)--(3,0) node [pos=0.98, below] {$x$};
             \draw [->] (0,-1)--(0,3) node [pos=0.98, left] {$z$};
             % orts
             \begin{scope}[thick]
             \draw [->] (O)--(1,0) node[pos=1, below] {$\vc e_x$};
             \draw [->] (O)--(0,1) node[pos=1, left] {$\vc e_z$};
             % vector k and its angle chi
             \coordinate (K) at ({2.6*sin(30)},{2.6*cos(30)});
             \draw [thick, ->] (O)--(K) node[pos=1, right] {$\vc k$};
             \end{scope}
             \draw ([shift=(60:0.5)] O) arc (60:90:0.5) node[pos=0.35, above] {$\chi$};
             % k projections
             \coordinate (Kx) at (K |- O);
             \coordinate (Kz) at (K -| O);
             \begin{scope}[thick]
             \draw [->](O)--(Kx) node[pos=1.15, below] {$\vc k_x$};
             \draw [->](O)--(Kz) node[pos=1, left] {$\vc k_z$};
             \end{scope}
             \draw [dashed] (K)--(Kz);
             \draw [dashed] (K)--(Kx);
             % foton beam
             \draw (-3, 2)--(O) node[pos=0.45, above] {$\ \hbar \omega$};
         \end{tikzpicture}
        \end{center}
    \end{frame}
\end{document}

Of course I do not know what you like best but you can adjust the scalings to your needs.

EDIT: Fixed the arrows. Because of the way TikZ parses the paths the arguably simplest option is to set the line width via scopes.