<p>The short answer: <em>cubic cleavage</em> is a specific example of <em>3D cleavage</em>.</p>
<ul>
<li><p>A cleavage plane is a direction along a crystal splits <em>preferentially</em> when exposed to mechanical stress.</p>
</li>
<li><p>3D crystals are objects where the spatial arrangement of atoms is described in  a parallelepiped (a unitcell) with three outer dimensions <span class="math-container">$\vec{a}$</span>, <span class="math-container">$\vec{b}$</span>, and <span class="math-container">$\vec{c}$</span>.  The crystal literally builds by translating this unit cell along <span class="math-container">$\vec{a}$</span>, <span class="math-container">$\vec{b}$</span>, and <span class="math-container">$\vec{c}$</span>.</p>
</li>
<li><p>The relative lengths of <span class="math-container">$\vec{a}$</span>, <span class="math-container">$\vec{b}$</span>, and <span class="math-container">$\vec{c}$</span> and the angles these vectors enclose define the outer symmetry of this unit cell.  Any of the following seven crystal classes is possible: triclinic, monoclinic, orthorhombic, tetragonal, rhombohedral, hexagonal, and cubic.  In this set, starting from triclinic and moving to cubic, the inherent symmetry increases.</p>
</li>
<li><p>With <span class="math-container">$\vec{a}$</span>, <span class="math-container">$\vec{b}$</span>, and <span class="math-container">$\vec{c}$</span>, equally crystallographic planes may be defined; <em>some</em> of them parallel to / coincide with the cleavage planes observed at macroscopic scale.</p>
</li>
</ul>
<p>Thus, as listed e.g., in <a href="https://en.wikipedia.org/wiki/Cleavage_(crystal)#Types_of_cleavage" rel="nofollow noreferrer">Wikipedia</a> you may discern:</p>
<blockquote>
<ul>
<li><p>Basal or pinacoidal cleavage occurs when there is only one cleavage plane. Graphite has basal cleavage. Mica (like muscovite or biotite) also has basal cleavage; this is why mica can be peeled into thin sheets.</p>
</li>
<li><p>Cubic cleavage occurs when there are three cleavage planes intersecting at 90 degrees. Halite (or salt) has cubic cleavage, and therefore, when halite crystals are broken, they will form more cubes.</p>
</li>
<li><p>Octahedral cleavage occurs when there are four cleavage planes in a crystal. Fluorite exhibits perfect octahedral cleavage. Octahedral cleavage is common for semiconductors. Diamond also has octahedral cleavage.</p>
</li>
<li><p>Rhombohedral cleavage occurs when there are three cleavage planes intersecting at angles that are not 90 degrees. Calcite has rhombohedral cleavage.</p>
</li>
<li><p>Prismatic cleavage occurs when there are two cleavage planes in a crystal. Spodumene exhibits prismatic cleavage.</p>
</li>
<li><p>Dodecahedral cleavage occurs when there are six cleavage planes in a crystal. Sphalerite has dodecahedral cleavage.</p>
</li>
</ul>
</blockquote>
<p>Intentionally, the description above was constrained to 3D crystals which eventually are (typically) described in one of 230 3D space groups. Note, there equally are seven <a href="https://www.iucr.org/education/pamphlets/21/supplement" rel="nofollow noreferrer">planar space groups</a>, and a growing body of work about <a href="https://journals.iucr.org/d/issues/2000/10/00/ba0045/" rel="nofollow noreferrer">2D crystals</a>, too.</p>

CC BY-SA 4.0
2021-02-24T21:26:33.020Z
2021-02-24T21:26:33.020Z
Buttonwood
<p>What is the difference between 3-dimensional cleavage and cubic cleavage?</p>
<p>I think, they are the same, but I am not sure about if I was right or not.</p>

<geology><mineralogy><minerals>
Cleavage of minerals
Kiroloes Amir
# Cleavage of minerals

(Asked by: username_0 on 2021-02-23)

What is the difference between 3-dimensional cleavage and cubic cleavage?

I think, they are the same, but I am not sure about if I was right or not.

**Tags:** geology, mineralogy, minerals


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## 1 answers

### Answer by username_1 on 2021-02-24. Score: 1

The short answer: *cubic cleavage* is a specific example of *3D cleavage*.

* A cleavage plane is a direction along a crystal splits *preferentially* when exposed to mechanical stress.
* 3D crystals are objects where the spatial arrangement of atoms is described in a parallelepiped (a unitcell) with three outer dimensions $\vec{a}$, $\vec{b}$, and $\vec{c}$. The crystal literally builds by translating this unit cell along $\vec{a}$, $\vec{b}$, and $\vec{c}$.
* The relative lengths of $\vec{a}$, $\vec{b}$, and $\vec{c}$ and the angles these vectors enclose define the outer symmetry of this unit cell. Any of the following seven crystal classes is possible: triclinic, monoclinic, orthorhombic, tetragonal, rhombohedral, hexagonal, and cubic. In this set, starting from triclinic and moving to cubic, the inherent symmetry increases.
* With $\vec{a}$, $\vec{b}$, and $\vec{c}$, equally crystallographic planes may be defined; *some* of them parallel to / coincide with the cleavage planes observed at macroscopic scale.

Thus, as listed e.g., in [Wikipedia](https://en.wikipedia.org/wiki/Cleavage_(crystal)#Types_of_cleavage) you may discern:

> * Basal or pinacoidal cleavage occurs when there is only one cleavage plane. Graphite has basal cleavage. Mica (like muscovite or biotite) also has basal cleavage; this is why mica can be peeled into thin sheets.
> * Cubic cleavage occurs when there are three cleavage planes intersecting at 90 degrees. Halite (or salt) has cubic cleavage, and therefore, when halite crystals are broken, they will form more cubes.
> * Octahedral cleavage occurs when there are four cleavage planes in a crystal. Fluorite exhibits perfect octahedral cleavage. Octahedral cleavage is common for semiconductors. Diamond also has octahedral cleavage.
> * Rhombohedral cleavage occurs when there are three cleavage planes intersecting at angles that are not 90 degrees. Calcite has rhombohedral cleavage.
> * Prismatic cleavage occurs when there are two cleavage planes in a crystal. Spodumene exhibits prismatic cleavage.
> * Dodecahedral cleavage occurs when there are six cleavage planes in a crystal. Sphalerite has dodecahedral cleavage.

Intentionally, the description above was constrained to 3D crystals which eventually are (typically) described in one of 230 3D space groups. Note, there equally are seven [planar space groups](https://www.iucr.org/education/pamphlets/21/supplement), and a growing body of work about [2D crystals](https://journals.iucr.org/d/issues/2000/10/00/ba0045/), too.


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