Monoclinic crystal system

<h2 id="bravais-lattices">Bravais lattices</h2>
<p class="note">Further information: <a href="/facts/Bravais_lattice/7gQKTsXk">Bravais lattice</a></p>
<p>Two monoclinic Bravais lattices exist: the primitive monoclinic and the base-centered monoclinic.
</p>
<table><tbody><tr><th>Bravais lattice</th><th>Primitivemonoclinic</th><th>Base-centeredmonoclinic</th></tr><tr><th><a href="/facts/Pearson_symbol/K3qljnNu">Pearson symbol</a></th><td>mP</td><td>mS</td></tr><tr><th><a href="/facts/Unit_cell/znygJqdx">Unit cell</a></th><td></td><td></td></tr></tbody></table>
<p>For the base-centered monoclinic lattice, the <a href="/facts/Primitive_cell/znygJqdx">primitive cell</a> has the shape of an oblique rhombic prism;<a class="footnote-ref" id="fnref:1" href="#fn:1"><sup>1</sup></a> it can be constructed because the two-dimensional centered rectangular base layer can also be described with primitive rhombic axes. The length 
  
    
      
        a
      
    
    {\displaystyle a}
  
 of the primitive cell below equals 
  
    
      
        
          
            1
            2
          
        
        
          
            
              a
              
                2
              
            
            +
            
              b
              
                2
              
            
          
        
      
    
    {\displaystyle {\frac {1}{2}}{\sqrt {a^{2}+b^{2}}}}
  
 of the conventional cell above.
</p>
Oblique rhombic prism primitive cellPrimitive cell of the base-centered monoclinic latticeRelationship between base layers of primitive and conventional cells
<h2 id="crystal-classes">Crystal classes</h2>
<p class="note">Further information: <a href="/facts/Crystallographic_point_group/43NqYrf0">Crystallographic point group</a></p>
<p>The table below organizes the space groups of the monoclinic crystal system by crystal class. It lists the International Tables for Crystallography space group numbers,<a class="footnote-ref" id="fnref:2" href="#fn:2"><sup>2</sup></a> followed by the crystal class name, its point group in <a href="/facts/Schoenflies_notation/c4y0GtEt">Schoenflies notation</a>, <a href="/facts/Hermann%25E2%2580%2593Mauguin_notation/NGHDFXKC">Hermann–Mauguin (international) notation</a>, <a href="/facts/Orbifold/KR6dQNzH">orbifold</a> notation, and Coxeter notation, type descriptors, mineral examples, and the notation for the <a href="/facts/Space_group/2XQx0J7M">space groups</a>.
</p>
<table><tbody><tr><th rowspan="2">#</th><th colspan="5">Point group</th><th rowspan="2">Type</th><th rowspan="2">Example</th><th colspan="2">Space groups</th></tr><tr><th>Name<a class="footnote-ref" id="fnref:3" href="#fn:3"><sup>3</sup></a></th><th><a href="/facts/Schoenflies_notation/c4y0GtEt">Schön.</a></th><th><a href="/facts/Hermann-Mauguin_notation/NGHDFXKC">Intl</a></th><th><a href="/facts/Orbifold_notation/HCbBoa2J">Orb.</a></th><th><a href="/facts/Coxeter_notation/ArUw6goe">Cox.</a></th><th>Primitive</th><th>Base-centered</th></tr><tr><th>3–5</th><td>Sphenoidal</td><td>C2</td><td>2</td><td>22</td><td>[2]+</td><td><a href="/facts/Enantiomorphic/p5a9pftB">enantiomorphic</a> <a href="/facts/Polar_point_group/2aeoGxhc">polar</a></td><td><a href="/facts/Halotrichite/jhfsJ6Km">halotrichite</a></td><td>P2, P21</td><td>C2</td></tr><tr><th>6–9</th><td>Domatic</td><td>Cs (C1h)</td><td>m</td><td>*11</td><td>[ ]</td><td><a href="/facts/Polar_point_group/2aeoGxhc">polar</a></td><td><a href="/facts/Hilgardite/keAoTRo2">hilgardite</a></td><td>Pm, Pc</td><td>Cm, Cc</td></tr><tr><th>10–12</th><td rowspan="2">Prismatic</td><td rowspan="2">C2h</td><td rowspan="2">2/m</td><td rowspan="2">2*</td><td rowspan="2">[2,2+]</td><td rowspan="2"><a href="/facts/Centrosymmetric/nIFJqujU">centrosymmetric</a></td><td rowspan="2"><a href="/facts/Gypsum/MItYU70n">gypsum</a></td><td>P2/m, P21/m</td><td>C2/m</td></tr><tr><th>13–15</th><td>P2/c, P21/c</td><td>C2/c</td></tr></tbody></table>
<p>Sphenoidal is also called monoclinic hemimorphic, domatic is also called monoclinic hemihedral, and prismatic is also called monoclinic normal.
</p><p>The three monoclinic hemimorphic space groups are as follows:
</p>
<ul><li>a prism with a <a href="/facts/Wallpaper_group/egxEaC8q">wallpaper group p2</a> cross-section</li>
<li>ditto with screw axes instead of axes</li>
<li>ditto with screw axes as well as axes, parallel, in between; in this case an additional translation vector is one half of a translation vector in the base plane plus one half of a perpendicular vector between the base planes.</li></ul>
<p>The four monoclinic hemihedral space groups include
</p>
<ul><li>those with pure reflection at the base of the prism and halfway</li>
<li>those with glide planes instead of pure reflection planes; the glide is one half of a translation vector in the base plane</li>
<li>those with both in between each other; in this case an additional translation vector is this glide plus one half of a perpendicular vector between the base planes.</li></ul>
<h2 id="in-two-dimensions">In two dimensions</h2>
<p class="note">Main article: <a href="/facts/Oblique_lattice/2ls9Iv9N">Oblique lattice</a></p>
<p>The only monoclinic Bravais lattice in two dimensions is the oblique lattice.
</p>
<table><tbody><tr><th>Bravais lattice</th><th>Oblique</th></tr><tr><th><a href="/facts/Pearson_symbol/K3qljnNu">Pearson symbol</a></th><td>mp</td></tr><tr><th><a href="/facts/Unit_cell/znygJqdx">Unit cell</a></th><td></td></tr></tbody></table>
<h2 id="see-also">See also</h2>
<ul><li><a href="/facts/Crystal_structure/bJ4bCeHd">Crystal structure</a></li>
<li><a href="/facts/Crystal_system/dMQLk1q4">Crystal system</a></li></ul>

<h2 id="further-reading">Further reading</h2>
<ul><li>Hahn, Theo, ed. (2002). <a href="http://it.iucr.org/A/"><i>International Tables for Crystallography</i></a>. Vol. A: <i>Space Group Symmetry</i> (5th ed.). Berlin; New York: Springer-Verlag. <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1107%2F97809553602060000100">10.1107/97809553602060000100</a>. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-0-7923-6590-7.</li>
<li>Hurlbut, Cornelius S.; Klein, Cornels (1985). <a href="https://archive.org/details/manualofmineralo00klei/page/69"><i>Manual of Mineralogy</i></a> (20th ed.). pp. <a href="https://archive.org/details/manualofmineralo00klei/page/69">69–73</a>. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0-471-80580-7.</li></ul>

<h2 id="references">References</h2>

<ol>
<li id="fn:1"><p>See Hahn (2002), p. 746, row mC, column Primitive, where the cell parameters are given as a1 = a2, α = β - Hahn, Theo, ed. (2002). International Tables for Crystallography. Vol. A: Space Group Symmetry (5th ed.). Berlin; New York: Springer-Verlag. doi:10.1107/97809553602060000100. ISBN 978-0-7923-6590-7. <a href="http://it.iucr.org/A/" target="_blank">http://it.iucr.org/A/</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li>
<li id="fn:2"><p>Prince, E., ed. (2006). International Tables for Crystallography. International Union of Crystallography. doi:10.1107/97809553602060000001. ISBN 978-1-4020-4969-9. S2CID 146060934. <a href="978-1-4020-4969-9" target="_blank">978-1-4020-4969-9</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li>
<li id="fn:3"><p>"The 32 crystal classes". Retrieved 2018-06-19. <a href="https://www.tulane.edu/~sanelson/eens211/32crystalclass.htm" target="_blank">https://www.tulane.edu/~sanelson/eens211/32crystalclass.htm</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li>
</ol>

Monoclinic crystal system open-in-new

Monoclinic crystal system