Skip to main content
Engineering LibreTexts

9.2: When do atomic bonds break?

  • 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}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\)

    \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)

    \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\)

    \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)

    \( \newcommand{\Span}{\mathrm{span}}\)

    \( \newcommand{\id}{\mathrm{id}}\)

    \( \newcommand{\Span}{\mathrm{span}}\)

    \( \newcommand{\kernel}{\mathrm{null}\,}\)

    \( \newcommand{\range}{\mathrm{range}\,}\)

    \( \newcommand{\RealPart}{\mathrm{Re}}\)

    \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)

    \( \newcommand{\Argument}{\mathrm{Arg}}\)

    \( \newcommand{\norm}[1]{\| #1 \|}\)

    \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)

    \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\)

    \( \newcommand{\vectorA}[1]{\vec{#1}}      % arrow\)

    \( \newcommand{\vectorAt}[1]{\vec{\text{#1}}}      % arrow\)

    \( \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

    \( \newcommand{\vectorC}[1]{\textbf{#1}} \)

    \( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \)

    \( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \)

    \( \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} \)

    \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

    \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)

    Fracture is the separation of atoms. We normally do this by applying a force to the body. How big a force should we need?

    We want to know how the energy, U, changes with distance, r, between two atoms. A commonly used expression (known as the Lennard-Jones potential is

    \[U(r)=4 \varepsilon\left[\left(\frac{\beta^{12}}{r^{12}}\right)-\left(\frac{\beta^{6}}{r^{6}}\right)\right]\]

    Other potentials exist, but the argument is essentially the same.

    This contains a short range repulsive term, and a long range attractive term. The parameter ε is a measure of the depth of the potential well, and β is the non-infinite distance where the interparticle potential equals zero.

    Use the animation to see how the energy changes as the distance between two atoms is varied.

    The force between a pair of atoms is calculated by taking the derivative of the energy function, giving:

    \[\boldsymbol{F}=\frac{\mathrm{d} U(\mathrm{r})}{\mathrm{d} r}=24 \varepsilon\left[-2\left(\frac{\beta^{12}}{r^{13}}\right)+\left(\frac{\beta^{6}}{r^{7}}\right)\right]\]

    Now see how the force between the atoms changes with distance. What is the force needed to separate the atoms in a crystal?

    Because we are interested in the material’s properties we normally think of failure stresses, so in a unit area of crystal we need to know how many bonds in an area of crystal normal to the applied force are carrying the load, say 6.25 × 10−22 m2.

    From the animation it is clear that materials should have breaking stresses of the order of 10 GPa, but a piece of glass normally breaks at a stress of 70 MPa.

    Where have we gone wrong?

    What have we just estimated? It is the stress required to break the bonds on a given plane simultaneously, what becomes the fracture surface. So do all the bonds on a given plane break at once?

    Anybody who has opened a packet of crisps or torn a sheet of paper knows the answer is ‘no’ – the bonds break a few at a time – at the tip of a growing crack.

    So the analysis above does not describe what actually happens when a material breaks, which is a relief as the predictions were no good anyway.

    This page titled 9.2: When do atomic bonds break? is shared under a CC BY-NC-SA 2.0 license and was authored, remixed, and/or curated by Dissemination of IT for the Promotion of Materials Science (DoITPoMS) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.

    • Was this article helpful?