

   PYRAMID MAKER v2                    7th October 2002

   CONTENTS

     1.	WHAT IS PYRAMID MAKER?
     2.	PYRAMIDAL ICE CRYSTALS    
     3.	CRYSTAL FILES
     4.	SHAPING THE CRYSTAL
       4.1.    HEIGHTS 
       4.2.    PYRAMID ANGLES & MILLER INDICES
     5      MAKING THE CRYSTAL FILES 
     6.     READING


   1.  WHAT IS PYRAMID MAKER?

   'Pyramid Maker' is a stand-alone program that runs on 
   Windows95 and higher.

   Pyramid Maker generates files used by HALOSIM to 
   simulate the atmospheric halos produced by pyramidal 
   ice crystals.


   2.  PYRAMIDAL ICE CRYSTALS  

   Common water ice crystals belong to the hexagonal 
   system.  

   The usual form is right hexagonal prisms and these 
   are responsible for most halos.

   A less common form, still belonging to the hexagonal
   system, is pyramidal.   These produce the less frequent 
   'odd radius circular halos' and - if preferentially 
   oriented - parhelia and other arcs.

   The general pyramidal cystal has a central hexagonal 
   prism section with its flat end faces replaced by
   hexagonal pyramids.  Each pyramid can be truncated with 
   its apex substituted by a flat face.  

   The sloping faces represent the directions of planes in 
   the internal structure and they have fixed and constant
   angles determined by the atomic and molecular structure
   of ice.   

   Not all 'rings' of faces are present in individual 
   'habits' and 18 different variations are possible.  
   'Pyramid Maker' can produce files representing all these 
   habits.



   3.  CRYSTAL FILES

   HALOSIM needs the locations of each face and the 
   direction it faces.   These are stored in *.XSH files and 
   are unique for each particular pyramidal crystal.   

   A second file type, FCT, is associated with each XSH
   file.  The second file stores data about the face 
   numbering system to ensure that when ray tracing or 
   filtering, HALOSIM accepts and displays face numbers 
   that are in general use rather than the ones it uses 
   internally.  

      The generally used face numbers are as used by 
      Tape (see reading).   When using ray filters or ray 
      tracing tools in HALOSIM the face numbers can be seen 
      on a diagram of the crystal by clicking the 'View 
      Crystal' button. 

   The FCT file contains other data about the crystal 
   parameters and name of associated image files. 

   The XSH and FCT files should >not< be modified.



   4.  SHAPING THE CRYSTAL

   When 'Pyramid Maker' is first run it shows an elevation 
   (perpendicular to the crystal 'c' axis) of a pyramidal
   ice crystal.   The angles of the crystal facets are 
   accurate representations.  The crystal proportions are 
   randomly chosen.

      Pyramidal crystals can be completely characterised by 
      four parameters.  These are:
        (1) the reduced height of the upper section (beta),
        (2) the mid section height (alpha),
        (3) the lower section height(gamma),
        (4) the angle that the pyramidal faces make to the
            crystal c axis - vertical in the graphic.

      4.1. SECTION HEIGHTS   
      The parameter for the mid section (alpha) is just 
      the c/a ratio of the equivalent hexagonal prism  
      crystal - it is the ratio of the height to the 
      distance across an end face between opposite vertices.

      The parameters for the upper and lower pyramidal 
      sections (beta and gamma) are the ratios of the actual 
      pyramid (or fustrum) height to the height of the 
      complete perfect pyramid.

      When present (beta, gamma <1), the uppermost and 
      lowermost end faces are regular hexagons.  they are 
      not visible in the view.   

      The three height parameters can be selected by 
      entering their values in the data boxes.  The crystal
      will be immediately redrawn.  Play with the numbers 
      and examine the possible crystal habits .

        Zero values will remove whole 'rings' or sets of 
        faces - this is quite legitimate.

        Non physical values will cause the crystal to 
        dissapear and the 'offending' value to be 
        highlighted.

      4.2. PYRAMID FACE TILTS
      The pyramid face angles (4) have a default value of
      27.98 degrees corresponding to those which generate
      pyramidal crystal displays.  However, the angle
      is adjustable.   

      The last integer of the 'Miller Indices' of the 
      pyramidal faces is also shown.   The Miller
      Index and the Face Angle are coupled displays and 
      either can be adjusted - the other changes at the same
      time.   

      A Miller Index of one corresponds to 'normal' 
      pyramidal crystals with faces inclined 27.98 degrees.
   
         The crystallographic description of a crytal face
         is via Miller Indices.  For the hexagonal system
         these are of the form {l,m,n,p} where l,m,n,p are 
         integers and are each the reciprocal of the 
         intercepts of the face with the four crystal axes 
         a1,a2,a3 and c.  They therefore uniquely define 
         the orientation in space of the face.  The values
         are always integer because the underlying dis-
         continuous atomic structure imposes a spatial 
         'quantisation' making only particular face 
         orientations possible.

         Non zero values of the last integer produce the
         tilting pyramidal faces.  Values like 2,3, 
         0.5 = 1/2, 0.3333 = 1/3 are crystallographically
         legitimate.

      When the face angle or its Miller Index are changed 
      the crystal is redrawn.    

      The default tilt of 27.98 can be regained by clicking
      the reset button.
        
   5.   MAKING THE CRYSTAL FILES 

   When the crystal has been shaped, the next step is to 
   make the XSH and FCT files.  Click the button
   'Make Crystal Files'.   A new display is produced that 
   suggests the file names.  The names are perhaps clumsy 
   but they contain the four parameters that determine the 
   crystal and are therefore both descriptive and unique.

   Press 'OK' to generate and store the files in the folder 
   that contains HALOSIM.  

   That's it!  


      Changing file names or locations

      Click 'Change name' to alter the file name or its 
      storage location.   

      The program will always give the XSH and FCT the same 
      name.  HALOSIM will NOT run properly if the names are 
      different.
  

 
   6.  READING

       Chapter 10
       "Atmospheric Halos" by W. Tape    
       Antarctic Research Series, Vol. 64, 
       American Geophysical Union, Washington, 1994



   


