Skip to main content
Library homepage
Engineering LibreTexts

28.7: Temperature Dependence of the Hysteresis Loop

  • Page ID
  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

    We have now seen the way in which the hysteresis loop arises. However, there are more aspects to the hysteresis loop.

    We have only observed it at one particular temperature, one at which the material is ferroelectric. What happens if the temperature is raised? The hysteresis loop changes with temperature, becoming sharper and thinner, and eventually disappearing, i.e.:

    Hysteresis loops at different temperatures

    As you can see, the polarisation increases at 90°C, as a result of a phase transition. Between this temperature and room temperature, the polarisation increases steadily, as a direct relation with temperature, such that:

    ΔP = p ΔT

    where p = pyroelectric coefficient (C m-2 T-1).

    Click here to find out more about pyroelectrics.

    Why should this be?
    This is a general behaviour (that does not apply to KNO3) that can arise for two reasons depending on the material.

    1. Disorder. Each unit cell has its own dipole moment, which, when there is a net polarisation, are described as ordered. At high T, the direction of the dipole moments randomises, giving a disordered material with no net polarisation.
    2. Phase transitions that can open up new possibilities for dipole moments to form. In this case, there is a jump at 0°C, and at 90°C, where the loop becomes taller.

    This page titled 28.7: Temperature Dependence of the Hysteresis Loop is shared under a CC BY-NC-SA license and was authored, remixed, and/or curated by Dissemination of IT for the Promotion of Materials Science (DoITPoMS).

    • Was this article helpful?