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Critical Temperature

physicsthermodynamicsphase-transitionstemperaturecritical-temperaturepgfplotscetztikz

A plot illustrating the temperature-dependent phase transitions of a material as a function of the critical temperature (TcT_c). The blue curve represents the low-temperature phase, the red curve represents the high-temperature phase, and the orange curve shows the critical mass (mcm_c) as a function of temperature. This visualization helps to understand the behavior of materials as they undergo phase transitions due to changes in temperature.


Critical Temperature

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  Code

  LaTeX

critical-temperature.tex (30 lines)

\documentclass{standalone}

\usepackage{pgfplots}
\pgfplotsset{compat=newest}

\begin{document}
\begin{tikzpicture}
  \begin{axis}[
      xlabel = $T$,
      smooth,thick,
      domain=0:1.1,
      ymax=2.8,
      axis lines = center,
      every tick/.style = {thick},
      legend cell align=left,
      legend style={font=\tiny}]

    \def\Tc{1}
    \addplot[color=blue,samples=75]{sqrt(3)*(\Tc/x - 1)^(1/2)};
    \addplot[color=red]{sqrt(3)*(x/\Tc)^(3/2)};
    \addplot[color=orange,samples=75]{sqrt(3)*(x/\Tc)^(3/2)*(\Tc/x - 1)^(1/2)};

    \legend{$\sqrt{3} \left(T_c/T - 1\right)^{1/2}$,
      $\sqrt{3} \left(T/T_c\right)^{3/2}$,
      $m_c(T)$}

  \end{axis}
\end{tikzpicture}
\end{document}

  Typst

critical-temperature.typ (71 lines)

#import "@preview/cetz:0.3.2": canvas, draw
#import "@preview/cetz-plot:0.1.1": plot

#set page(width: auto, height: auto, margin: 8pt)

#let tc = 1

// Define the three functions
#let f1(x) = {
  if x == tc { return 0 }
  calc.sqrt(3) * calc.pow(tc / x - 1, 1 / 2)
}

#let f2(x) = calc.sqrt(3) * calc.pow(x / tc, 3 / 2)

#let f3(x) = {
  if x == tc { return 0 }
  calc.sqrt(3) * calc.pow(x / tc, 3 / 2) * calc.pow(tc / x - 1, 1 / 2)
}

#canvas({
  draw.set-style(
    axes: (
      y: (label: (anchor: "north-west", offset: -0.2), mark: (end: "stealth", fill: black)),
      x: (label: (anchor: "north", offset: 0.2), mark: (end: "stealth", fill: black)),
    ),
  )

  plot.plot(
    size: (10, 8),
    x-label: $T$,
    x-min: 0,
    x-max: 1.1,
    y-min: 0,
    y-max: 2.8,
    axis-style: "left",
    x-tick-step: 0.2,
    y-tick-step: 0.5,
    legend: (6.5, 8.5),
    legend-style: (item: (spacing: 0.15), padding: 0.25, stroke: .5pt),
    {
      // First function (blue)
      plot.add(
        style: (stroke: blue + 1.5pt),
        samples: 100,
        domain: (0.01, 1),
        f1,
        label: $sqrt(3)(T_c \/ T - 1)^(1 / 2)$,
      )

      // Second function (red)
      plot.add(
        style: (stroke: red + 1.5pt),
        samples: 50,
        domain: (0, 1.1),
        f2,
        label: $sqrt(3)(T \/ T_c)^(3 / 2)$,
      )

      // Third function (orange)
      plot.add(
        style: (stroke: orange + 1.5pt),
        samples: 125,
        domain: (0.01, 1),
        f3,
        label: $m_c(T)$,
      )
    },
  )
})