@@ -2766,7 +2766,10 @@ \subsection{Tutorial 5: Reactive silicon dioxide}
27662766\centering 
27672767\includegraphics [width=0.55\linewidth ]{SIO}
27682768\caption {A portion of the silicon dioxide structure as simulated during
2769- \hyperref [reactive-silicon-dioxide-label]{Tutorial 5}.  Atoms are colored by their charges.}
2769+ \hyperref [reactive-silicon-dioxide-label]{Tutorial 5}.  Atoms are colored
2770+ by their charges: the hydrogen atoms appear as small greenish spheres, silicon
2771+ atoms as large orange spheres, and oxygen atoms as blue spheres of intermediate
2772+ size.}
27702773\label {fig:SIO }
27712774\end {figure }
27722775
@@ -3124,9 +3127,8 @@ \subsubsection{Decorate the surface}
31243127\includegraphics [width=\linewidth ]{SIO-decorated}
31253128\caption {Cracked silicon oxide after the addition of hydrogen atoms
31263129during \hyperref [reactive-silicon-dioxide-label]{Tutorial 5}.  The atoms
3127- are colored by their charges.  Dangling oxygen groups appear in greenish, bulk
3128- Si atoms with a charge of about $ 1.8 ~\text {e}$ 
3129- O atoms with a charge of about $ -0.9  ~ \text {e}$ 
3130+ are colored by their charges, with the newly added hydrogen atoms appearing as small
3131+ greenish spheres.}
31303132\label {fig:SIO-decorated }
31313133\end {figure }
31323134
@@ -3135,10 +3137,11 @@ \subsection{Tutorial 6: Water adsorption in silica}
31353137
31363138\begin {figure }
31373139\centering 
3138- \includegraphics [width=0.55\linewidth ]{GCMC}
3139- \caption {Water molecules adsorbed in cracked silica (SiO$ _2 $ 
3140- during \hyperref [gcmc-silica-label]{Tutorial 6}.  Water molecules are colored in
3141- cyan and white, oxygen (O) atoms from SiO$ _2 $ 
3140+ \includegraphics [width=0.6\linewidth ]{GCMC}
3141+ \caption {Water molecules (H$ _2 $ $ _2 $ 
3142+ during \hyperref [gcmc-silica-label]{Tutorial 6}.  The oxygen atoms of the water
3143+ molecules are represented in cyan, the silicon atoms in yellow, and the oxygen
3144+ atoms of the solid in red.}
31423145\label {fig:GCMC }
31433146\end {figure }
31443147
@@ -3208,11 +3211,6 @@ \subsubsection{Generation of the silica block}
32083211thermo_style custom step temp etotal vol density
32093212\end {lstlisting }
32103213
3211- %  SG
3212- %  FROM . Chem. Phys. 97, 2682–2689 (1992)
3213- %  https://doi.org/10.1063/1.463056
3214- %  3 steps only. Say that its too fast to be correct. Show density.
3215- %  Show rdf instead of box size?
32163214Finally, let us implement the annealing procedure which
32173215consists of three consecutive runs.  This procedure was inspired
32183216by Ref.\, \cite {della1992molecular }.  First, to melt the system,
@@ -3255,12 +3253,10 @@ \subsubsection{Generation of the silica block}
32553253\begin {figure }
32563254\centering 
32573255\includegraphics [width=\linewidth ]{GCMC-dimension}
3258- \caption {a) Temperature $ T$ $ t$ 
3259- during the annealing of the silica system
3260- from \hyperref [gcmc-silica-label]{Tutorial 6}.
3261- b) System density $ \rho $ 
3262- annealing.  The vertical dashed lines mark the transition between the different
3263- phases of the simulation.}
3256+ \caption {a) Temperature $ T$ $ t$ 
3257+ of the silica system from \hyperref [gcmc-silica-label]{Tutorial 6}.
3258+ b) System density $ \rho $ 
3259+ mark the transition between the different phases of the simulation.}
32643260\label {fig:GCMC-dimension }
32653261\end {figure }
32663262
@@ -3269,7 +3265,7 @@ \subsubsection{Generation of the silica block}
32693265\includegraphics [width=0.9\linewidth ]{GCMC-generate}
32703266\caption {Amorphous silica ($ \text {SiO}_2 $ 
32713267during \hyperref [gcmc-silica-label]{Tutorial 6}.  Silicon atoms are
3272- represented in yellow, and the  oxygen atoms in red.}
3268+ represented in yellow, and oxygen atoms in red.}
32733269\label {fig:GCMC-snapshot }
32743270\end {figure }
32753271
@@ -3313,16 +3309,17 @@ \subsubsection{Cracking the silica}
33133309\end {lstlisting }
33143310The \lmpcmd {fix nvt} command is employed to control the temperature of the system.
33153311As observed from the generated images, the atoms
3316- progressively adjust to the changing box dimensions. At some point, bonds begin to break,
3317- leading to the appearance of dislocations (Fig.~\ref {fig:GCMC-cracked }).
3312+ progressively adjust to the changing box dimensions.  At some point,
3313+ bonds begin to break, leading to the appearance of
3314+ dislocations (Fig.~\ref {fig:GCMC-cracked }).
33183315
33193316\begin {figure }
33203317\centering 
33213318\includegraphics [width=\linewidth ]{GCMC-cracked}
33223319\caption {Block of silica from \hyperref [gcmc-silica-label]{Tutorial 6}
33233320after deformation.  Silicon atoms are represented in yellow,
3324- and the  oxygen atoms in red.  The crack was induced by the
3325- imposed deformation of the box along the $ x$ 
3321+ and oxygen atoms in red.  The crack was induced by the
3322+ imposed deformation of the box along the $ x$  (i.e.,~the horizontal axis) .}
33263323\label {fig:GCMC-cracked }
33273324\end {figure }
33283325
@@ -3332,7 +3329,7 @@ \subsubsection{Adding water}
33323329the Monte Carlo method in the grand canonical ensemble (GCMC).  In short, the
33333330system is placed into contact with a virtual reservoir of a given chemical potential
33343331$ \mu $ 
3335- made. Each attempt is either accepted or rejected based on energy considerations.
3332+ made.   Each attempt is either accepted or rejected based on energy considerations.
33363333For further details, please refer to classical textbooks like Ref.~\citenum {frenkel2023understanding}.
33373334
33383335\paragraph {Using hydrid potentials }
@@ -3539,7 +3536,7 @@ \subsubsection{Adding water}
35393536\begin {figure }
35403537\centering 
35413538\includegraphics [width=\linewidth ]{GCMC-number}
3542- \caption {Number of water molecules $ N_\text {H2O}$ the  time $ t$ 
3539+ \caption {Number of water molecules,  $ N_\text {H2O}$ ,  as a function of time,  $ t$ , 
35433540as extracted from \hyperref [gcmc-silica-label]{Tutorial 6}.}
35443541\label {fig:GCMC-number }
35453542\end {figure }
@@ -3568,10 +3565,10 @@ \subsection{Tutorial 7: Free energy calculation}
35683565
35693566\begin {figure }
35703567\centering 
3571- \includegraphics [width=0.55 \linewidth ]{US}
3572- \caption {Atoms as  simulated during \hyperref [umbrella-sampling-label]{Tutorial 7}.
3573- Only the  atom colored in pink feels  the additional force used for  the umbrella 
3574- sampling method .}
3568+ \includegraphics [width=0.7 \linewidth ]{US}
3569+ \caption {System  simulated during \hyperref [umbrella-sampling-label]{Tutorial 7}.
3570+ The pink  atom explores  the energetically unfavorable central area of  the simulation 
3571+ box thanks to the additional potential imposed during umbrella sampling .}
35753572\label {fig:US }
35763573\end {figure }
35773574
@@ -3747,8 +3744,8 @@ \subsubsection{Method 1: Free sampling}
37473744\includegraphics [width=\linewidth ]{US-density-evolution}
37483745\caption {Evolution of the number of atoms $ n_\text {center}$ 
37493746region \lmpcmd {mymes} as a function of time $ t$ 
3750- is $ n_\text {center} = 22  \exp (-t/160 )+5 $   Here,  $ U_ 0  =  0.36 ~ \text {kcal/mol} $ , 
3751- $ \ delta0.5 ~\text {\AA {}}$ $ x_0  = 5 ~\text {\AA {}}$ 
3747+ is $ n_\text {center} = 22  \exp (-t/160 )+5 $ 
3748+ Here,  $ U_ 0  =  0.36 ~ \text {kcal/mol} $ ,  $ \ delta1.0 ~\text {\AA {}}$ $ x_0  = 10 ~\text {\AA {}}$ 
37523749\label {fig:US-density-evolution }
37533750\end {figure }
37543751
@@ -3962,9 +3959,10 @@ \subsubsection{Method 2: Umbrella sampling}
39623959\begin {figure }
39633960\centering 
39643961\includegraphics [width=\linewidth ]{US-free-energy}
3965- \caption {The potential $ U$ $ x$ 
3966- (blue disks), is compared to the imposed potential given in Eq.~\eqref {eq:U }
3967- (dark line). Parameters are $ U_0  = 2.38 ~\text {kcal/mol}$ $ \delta  = 1.0 ~\text {\AA {}}$ 
3962+ \caption {The potential $ U$ $ x$ 
3963+ sampling during \hyperref [umbrella-sampling-label]{Tutorial 7} (blue disks),
3964+ is compared to the imposed potential given in Eq.~\eqref {eq:U }
3965+ (dark line).  Parameters are $ U_0  = 2.38 ~\text {kcal/mol}$ $ \delta  = 1.0 ~\text {\AA {}}$ 
39683966and $ x_0  = 10 ~\text {\AA {}}$ 
39693967\label {fig:US-freenergy }
39703968\end {figure }
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