Added triclinic cell keywords and tilt factor scaling options

git-svn-id: svn://svn.icms.temple.edu/lammps-ro/trunk@6429 f3b2605a-c512-4ea7-a41b-209d697bcdaa

doc/Section_howto.html

@@ -755,8 +755,8 @@ See the <A HREF = "dump.html">dump</A> command for more information on XTC files
 particles.  The <A HREF = "boundary.html">boundary</A> command sets the boundary
 conditions of the box (periodic, non-periodic, etc).  The orthogonal
 box has its "origin" at (xlo,ylo,zlo) and is defined by 3 edge vectors
-starting from the origin given by A = (xhi-xlo,0,0); B =
-(0,yhi-ylo,0); C = (0,0,zhi-zlo).  The 6 parameters
+starting from the origin given by <B>a</B> = (xhi-xlo,0,0); <B>b</B> =
+(0,yhi-ylo,0); <B>c</B> = (0,0,zhi-zlo).  The 6 parameters
 (xlo,xhi,ylo,yhi,zlo,zhi) are defined at the time the simluation box
 is created, e.g. by the <A HREF = "create_box.html">create_box</A> or
 <A HREF = "read_data.html">read_data</A> or <A HREF = "read_restart.html">read_restart</A>
@@ -768,14 +768,14 @@ custom</A> command.
 <P>LAMMPS also allows simulations to be perfored in non-orthogonal
 simulation boxes shaped as a parallelepiped with triclinic symmetry.
 The parallelepiped has its "origin" at (xlo,ylo,zlo) and is defined by
-3 edge vectors starting from the origin given by A = (xhi-xlo,0,0); B
-= (xy,yhi-ylo,0); C = (xz,yz,zhi-zlo).  <I>Xy,xz,yz</I> can be 0.0 or
+3 edge vectors starting from the origin given by <B>a</B> = (xhi-xlo,0,0); <B>b</B>
+= (xy,yhi-ylo,0); <B>c</B> = (xz,yz,zhi-zlo).  <I>Xy,xz,yz</I> can be 0.0 or
 positive or negative values and are called "tilt factors" because they
 are the amount of displacement applied to faces of an originally
 orthogonal box to transform it into the parallelepiped.  Note that in
-LAMMPS the triclinic simulation box edge vectors A,B,C cannot be
-arbitrary vectors.  As indicated, A must be aligned with the x axis, B
-must be in the xy plane, and C is arbitrary.  However, this is not a
+LAMMPS the triclinic simulation box edge vectors <B>a</B>, <B>b</B>, and <B>c</B> cannot be
+arbitrary vectors.  As indicated, <B>a</B> must be aligned with the x axis, <B>b</B>
+must be in the xy plane, and <B>c</B> is arbitrary.  However, this is not a
 restriction since it is possible to rotate any set of 3 crystal basis
 vectors so that they meet this restriction.
 </P>
@@ -817,14 +817,25 @@ equivalent.
 </P>
 <P>Triclinic crystal structures are often defined using three lattice
 constants <I>a</I>, <I>b</I>, and <I>c</I>, and three angles <I>alpha</I>, <I>beta</I> and
-<I>gamma</I>.  Note that in this nomenclature, the a,b,c lattice constants
-are the scalar lengths of the 3 A,B,C edge vectors defined above.  The
+<I>gamma</I>. Note that in this nomenclature, the a, b, and c lattice constants
+are the scalar lengths of the edge vectors <B>a</B>, <B>b</B>, and <B>c</B> defined 
+above.  The
 relationship between these 6 quantities (a,b,c,alpha,beta,gamma) and
 the LAMMPS box sizes (lx,ly,lz) = (xhi-xlo,yhi-ylo,zhi-zlo) and tilt
 factors (xy,xz,yz) is as follows:
 </P>
 <CENTER><IMG SRC = "Eqs/box.jpg">
 </CENTER>
+<P>The inverse relationship can be written as follows:
+</P>
+<CENTER><IMG SRC = "Eqs/box_inverse.jpg">
+</CENTER>
+<P>The values of <I>a</I>, <I>b</I>, <I>c</I> , <I>alpha</I>, <I>beta</I> , and <I>gamma</I> can be printed 
+out or accessed by computes using the 
+<A HREF = "thermo_style.html">thermo_style custom</A> keywords 
+<I>cella</I>, <I>cellb</I>, <I>cellc</I>, <I>cellalpha</I>, <I>cellbeta</I>, <I>cellgamma</I>,
+respectively. 
+</P>
 <P>As discussed on the <A HREF = "dump.html">dump</A> command doc page, when the BOX
 BOUNDS for a snapshot is written to a dump file for a triclinic box,
 an orthogonal bounding box which encloses the triclinic simulation box
@@ -1158,7 +1169,7 @@ discussed below, it can be referenced via the following bracket
 notation, where ID in this case is the ID of a compute.  The leading
 "c_" would be replaced by "f_" for a fix, or "v_" for a variable:
 </P>
-<DIV ALIGN=center><TABLE  BORDER=1 >
+<DIV ALIGN=center><TABLE  WIDTH="0%"  BORDER=1 >
 <TR><TD >c_ID </TD><TD > entire scalar, vector, or array</TD></TR>
 <TR><TD >c_ID[I] </TD><TD > one element of vector, one column of array</TD></TR>
 <TR><TD >c_ID[I][J] </TD><TD > one element of array 
@@ -1357,7 +1368,7 @@ data and scalar/vector/array data.
 input, that could be an element of a vector or array.  Likewise a
 vector input could be a column of an array.
 </P>
-<DIV ALIGN=center><TABLE  BORDER=1 >
+<DIV ALIGN=center><TABLE  WIDTH="0%"  BORDER=1 >
 <TR><TD >Command</TD><TD > Input</TD><TD > Output</TD><TD ></TD></TR>
 <TR><TD ><A HREF = "thermo_style.html">thermo_style custom</A></TD><TD > global scalars</TD><TD > screen, log file</TD><TD ></TD></TR>
 <TR><TD ><A HREF = "dump.html">dump custom</A></TD><TD > per-atom vectors</TD><TD > dump file</TD><TD ></TD></TR>