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Commit cef4ee70 authored by Gareth Tribello's avatar Gareth Tribello
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Fixes to manual for FCCUBIC and SIMPLECUBIC

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...@@ -45,7 +45,8 @@ s_i = \frac{ \sum_{i \ne j} \sigma(r_{ij}) \left\{ a\left[ \frac{(x_{ij}y_{ij})^ ...@@ -45,7 +45,8 @@ s_i = \frac{ \sum_{i \ne j} \sigma(r_{ij}) \left\{ a\left[ \frac{(x_{ij}y_{ij})^
In this expression \f$x_{ij}\f$, \f$y_{ij}\f$ and \f$z_{ij}\f$ are the \f$x\f$, \f$y\f$ and \f$z\f$ components of the vector connecting atom \f$i\f$ to In this expression \f$x_{ij}\f$, \f$y_{ij}\f$ and \f$z_{ij}\f$ are the \f$x\f$, \f$y\f$ and \f$z\f$ components of the vector connecting atom \f$i\f$ to
atom \f$j\f$ and \f$r_{ij}\f$ is the magnitude of this vector. \f$\sigma(r_{ij})\f$ is a \ref switchingfunction that acts on the distance between atom \f$j\f$ and \f$r_{ij}\f$ is the magnitude of this vector. \f$\sigma(r_{ij})\f$ is a \ref switchingfunction that acts on the distance between
atom \f$i\f$ and atom \f$j\f$ and its inclusion in the numerator and the denominator of the above expression ensures that we are calculating an average atom \f$i\f$ and atom \f$j\f$ and its inclusion in the numerator and the denominator of the above expression as well as the fact that we are summing
over all of the other atoms in the system ensures that we are calculating an average
of the function of \f$x_{ij}\f$, \f$y_{ij}\f$ and \f$z_{ij}\f$ for the atoms in the first coordination sphere around atom \f$i\f$. Lastly, \f$\alpha\f$ of the function of \f$x_{ij}\f$, \f$y_{ij}\f$ and \f$z_{ij}\f$ for the atoms in the first coordination sphere around atom \f$i\f$. Lastly, \f$\alpha\f$
is a parameter that can be set by the user, which by default is equal to three. The values of \f$a\f$ and \f$b\f$ are calculated from \f$\alpha\f$ using: is a parameter that can be set by the user, which by default is equal to three. The values of \f$a\f$ and \f$b\f$ are calculated from \f$\alpha\f$ using:
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...@@ -35,6 +35,22 @@ namespace crystallization{ ...@@ -35,6 +35,22 @@ namespace crystallization{
Calculate whether or not the coordination spheres of atoms are arranged as they would be in a simple Calculate whether or not the coordination spheres of atoms are arranged as they would be in a simple
cubic structure. cubic structure.
We can measure how similar the environment around atom $i$ is to a simple cubic structure is by evaluating
the following quantity:
\f[
s_i = \frac{ \sum_{i \ne j} \sigma(r_{ij}) \left[ \frac{ x_{ij}^4 + y_{ij}^4 + z_{ij}^4 }{r_{ij}^4} \right] }{ \sum_{i \ne j} \sigma(r_{ij}) }
\f]
In this expression \f$x_{ij}\f$, \f$y_{ij}\f$ and \f$z_{ij}\f$ are the \f$x\f$, \f$y\f$ and \f$z\f$ components of the vector connecting atom \f$i\f$ to
atom \f$j\f$ and \f$r_{ij}\f$ is the magnitude of this vector. \f$\sigma(r_{ij})\f$ is a \ref switchingfunction that acts on the distance between atom \f$i\f$ and atom \f$j\f$ and its inclusion in the numerator and the denominator of the above expression as well as the fact that we are summing
over all of the other atoms in the system ensures that we are calculating an average
of the function of \f$x_{ij}\f$, \f$y_{ij}\f$ and \f$z_{ij}\f$ for the atoms in the first coordination sphere around atom \f$i\f$.
This quantity is once again a multicolvar so you can compute it for multiple atoms using a single PLUMED action and then compute
the average value for the atoms in your system, the number of atoms that have an \f$s_i\f$ value that is more that some target and
so on. Notice also that you can rotate the reference frame if you are using a non-standard unit cell.
\par Examples \par Examples
The following input tells plumed to calculate the simple cubic parameter for the atoms 1-100 with themselves. The following input tells plumed to calculate the simple cubic parameter for the atoms 1-100 with themselves.
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