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CRYSTALLINE_DEFINITION

                                                February 18, 2012
In the classic definition
of a crystal, they have
"translational symmetry":
you can pick out a small
basic sub-pattern (the
"unit cell") and generate            Like using a stamp pad
the layout of the entire             to make wrapping paper.
crystal by duplicating
that sub-pattern end-to-end
throughout the region.
                                                  
   But really crystals are phenomena.  There are these     
   things we find in nature, that have a certain look      
   and shape to them (e.g. gemstones) and we've            
   classified them together as "crystals", then we         
   started looking at them more closely, thinking          
   about what underlying structure is implied by their     
   outward behavior, and using that we refined a           
   theory of what they are-- matter arranged in a          
   certain kind of regular way-- and then we started       
   using this knowledge to refine the category: things     
   that you might have once categorized as crystals        
   are now excluded (e.g. glass prisims), and things       
   that it wouldn't have occured to you to call            
   crystals now are included (e.g.  opague things like     
   crystalline silicon or aluminum).                       
                                                           
       Our physical understanding of what crystals       
       are worked so well that we could get dogmatic     
       about it.  Angles between faces, diffraction      
       patterns, diagrams of regular atomic lattices,    
       varying materials properties in different         
       directions...  it all tied together so nicely     
       that we could imagine that we had our finger      
       on the nature of reality.                         
                                                         
          Yes, there are some odd              
          aspects of physics off                                         
          in the corners of                Understanding and evidence 
          relativity or quantum            were all in sync to the   
          mechanics, but not with          point there was little    
          crystals.                        need to distinguish       
                                           
                                                  
                      But: using that nice, simple     
                      geometric definition of          
                      crystals, you can show that      
                      five-fold symmetry doesn't          
                      happen.                                          
                                                                       
                          And yet: you can get                         
                          x-ray diffraction            And rather than revise
                          patterns that show that      the meaning of the word 
                          it happens.  The             "crystal", we invented 
                          phenomena diverged from      a new category, something
                          our understanding...         sort of like them 
                                                       but not exactly.
                                                          
                                                         QUASICRYSTALS 



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