% This file has been produced for use with REVTEX 3.0.
%
\documentstyle[aps,preprint,epsfig]{revtex}

\begin{document}

\input amssym.def
\input amssym.tex

\title{Results from the DOS analysis for AlCoNi QC}

\author{Ibrahim Al-Lehyani$^{a,b}$ and Mike Widom$^{a}$}

\address{$^{a}$Department of Physics, Carnegie Mellon University,
Pittsburgh, Pennsylvania 15213}
\address{$^{b}$Department of Physics, King AbdulAziz University, Jeddah, Saudi Arabia}

\author{Yang Wang}

\address{Pittsburgh Supercomputer Center, Pittsburgh, Pennsylvania 15213}

\author{Nassrin Moghadam and G.~Malcolm Stocks}

\address{Oak Ridge National Laboratory, Oak Ridge, TN 37831-6114}

\date{\today}

\maketitle

\section{The problem}
The forces on TM atoms in decagonal QC were studied in a previous paper. The TM atoms were found to repel each other consistent with expectations but in contradiction to the prediction of GPT. We found that in AlCoNi QC similar TM atoms like to be adjacent to each other. The GPT pair potentials were corrected at short distance to comply with the VASP calculation. To get insight into the forces and to understand the root cause for such TM atoms behavior, the densities of states of the QC are studied. Band narrowing and peak shifts in local and total DOS are expected under moving the TM atoms away from each other.

\section{Summary}
\label{sec:summ}

The total and band energy were calculated for four structures. The basic structure in Fig.~\ref{fig:strn} (d0c0s0) is our same structure we used for the pair potential correction. It is Al$_{34}$Co$_{10}$Ni$_{6}$ with CoNi pairs on the tile edges and two Co atoms surrounding the central Al atom. The unit cell is shown with the atoms numbered. Dark gray atoms are Co, light gray are Ni and white are Al. Moving the pair 23 and 26  away from each other by 0.2 au and similarly for the pair 3 and 49 (adjacent through cell repetition) produces the basic-displaced (d200c0s0)structure. Swapping atom 23 (Ni) with atom 3 (Co) produces the swapped (d0s2303) structure and performing  the same displacement ,as in d200c0s0 but this time it is CoCo and NiNi pairs, results in the swapped-displaced (d200s2303) structure. In all, the displacement was performed on two CoNi pairs, one CoCo pair and one NiNi pair. The total and atomic densities of states were calculated for all structures. 
*********************************************
Table ~\ref{tab:ef} shows raw data for each structre. Note that the Fermi energis differ by less 0.01. In all comming graphs the difference between the fermi energies will not be noticable. Table ~\ref{tab:diff} shows the differences in energies between the structures. As expected and calculated before, the swapping lowered the energy, reflecting the fact that TM atoms prefer to be close to similar species (slightly). The displacement lowered the energies for both basic and swapped structures. The band energy differences were always much larger than the total energy differences.


Fig.[~\ref{fig:d0c0s0}-\ref{fig:d200s2303}] show the averaged elemental and total DOS for the four structures. The Al DOS is flat because it doesn't tend to have d-electrons. Co curve peaks are always higher than Ni in magnitude and position at higher energies ( dE ~ 1-2 eV).  Co peak in the swapped structure is split. That splitting is kind of removed after displacing the Co atoms away from each other.  All the DOS graphs were obtained from the VASP calculated DOS and smoothed with a Gaussian for clarity.

In Fig.~\ref{fig:d0c0s0both}, the total DOS for the basic and the basic-displaced structures were plotted on the same graph for comparison. Fig.~\ref{fig:d0s2303both} is the same but for the swapped structures. Fig.~\ref{fig:d0c0s0both} shows clearly the d-band narrowing for the basic structure after displacing the TM atoms away from each other. The shift in peak energy is also pronounced. The swapped structure shows almost no shift after displacing the CoCo and NiNi pairs away from each other as seen in Fig.~\ref{fig:d0s2303both}. Even though the calculated VASP E-band show a decrease in E-band by 1.7 eV, the graph shows the opposite. We checked the visual appearance of the increase in band energy after displacement by integrating the total DOS data calculated from VASP. It confirmed what is seen on the graph. This is puzzling and we don't have an interpretation for it. 

The rest of the figures[~\ref{fig:b1}-\ref{fig:b3}] show the difference in atomic density of states between the displaced-basic and the basic structures. It should be noted that our DOS data sets contain 301 points each. There is an offset between the sets of about 0.04 in worst case. In calculating the differences, we mapped the points by their order in the sets. The variation over intervals between the points doesn't seem to be sharp.  The local TM-atoms DOS difference plots show a signature of w-shape. In simple cases the symmetric w-shape is a sign of band narrowing and asymmetric w-shape is an indicator of peak shift. All the TM atoms show the w-shape, not only the ones that moved. The Al atoms show minimal differences (~0.02 on the vertical scale).


\begin{table}
\caption{Fermi Energies for the different structures}
\vspace{10pt}
\begin{tabular}{|l|l|r|r|r|}
%%
Structure &Name 		&E$_{tot}$(eV)&E$_{band}$(eV)	& E$_{Fermi}$ (eV) \\
\hline
\hline
d0c0s0  & basic 		& -281.89555  &    677.953444   & 5.76196136 \\
d200c0s0& basic displaced 	& -282.28488  &    675.959517   & 5.76293886 \\
d0s2303 & swapped 		& -281.92761  &    677.077513   & 5.77698429 \\
d200s2303 & swapped displaced 	& -282.31411  &    675.349705   & 5.77475059 \\
%%
\end{tabular}
\label{tab:ef}
\end{table}

\begin{table}
\caption{Energy differences between the structures}
\vspace{10pt}
\begin{tabular}{|l|l|r|r|}
Structure  		&Comments			& Tot E (eV)   & E-band (eV) \\
\hline
\hline
 d0s2303-d0c0s0  	& Swap energy      		& -.03206 	& -.875931  \\ 
\hline
d200c0s0-d0c0s0  	& 2 CoNi bonds stretched     	& -.38933  	& -1.993927  \\  
d200s2303-d0s2303	& CoCo + NiNi bonds stretched 	& -.3865  	& -1.727808  \\ 
\end{tabular}
\label{tab:diff}
\end{table}


\begin{figure}
%%\vspace{5pt}
\epsfig{figure=strn_right.eps}
\caption{The unit cell with the atoms numbered for clarity. Black atoms are Ni, gray are Co and white are Al. }
\label{fig:strn}
\end{figure}


\begin{figure}
\epsfig{figure=forces.eps,width=5.5in}
\caption{The forces calculated by VASP and GPT. Columns from left to right correspond to diplaced pairs, undisplaced pairs and GPT.}
\label{fig:forces}
\end{figure}



\begin{figure}
\epsfig{figure= d0c0s0.eps,width=7in}
\vspace{100pt}
\caption{The total and elemental  density fo states for the basic structure.}
\label{fig:d0c0s0}
\end{figure}
 
 
\begin{figure}
\epsfig{figure= d200c0s0.eps,width=7in}
\vspace{100pt}
\caption{The total and elemental  density fo states for the basic-displaced structure.}
\label{fig:d200c0s0}
\end{figure}
 
\begin{figure}
\epsfig{figure= d0s2303.eps,width=7in}
\vspace{100pt}
\caption{The total and elemental  density fo states for the swapped structure.}
\label{fig:d0s2303}
\end{figure}
 
 
\begin{figure}
\epsfig{figure= d200s2303.eps,width=7in}
\vspace{100pt}
\caption{The total and elemental  density fo states for the swapped-displaced structure.}
\label{fig:d200s2303}
\end{figure}

 
\begin{figure}
\epsfig{figure= d0c0s0both.eps,width=7in}
\vspace{100pt}
\caption{The total density of states for both basic and basic-displaced structures. Some states with energies right below the fermi energy moved to lower energies after displacement. They moved down to the first peak from right and lower. This is an energy lowering mechanisem}
\label{fig:d0c0s0both}
\end{figure}
 
 
\begin{figure}
\epsfig{figure= d0s2303both.eps,width=7in}
\vspace{100pt}
\caption{The total density of states for both swapped and swapped-displaced structures. As in the case of the basic structure, states moved from right below the fermi energy to lower-energy states. Some of the states moved from energies higher than the fermi energy to the band. This raises the energy but the number is small here  and it is overbalanced by states in the band moving to lower energies.}
\label{fig:d0s2303both}
\end{figure}

 
 
\begin{figure}
\epsfig{figure= swappedandbasic.eps,width=7in}
\vspace{100pt}
\caption{The total density of states for both swapped and the basic strucutres}
\label{fig:swappedandbasic}
\end{figure}
 
\begin{figure}
\epsfig{figure= d0c0s0diff.eps,width=7in}
\vspace{100pt}
\caption{The difference between the density of states for the basic-displaced and the basic strucutres. This figure show the energy-lowering mechanism discussed in fig~\ref{fig:d0c0s0both}. State are moving from the right of the band to the left.}
\label{fig:d0c0s0diff}
\end{figure}
 
 
\begin{figure}
\epsfig{figure= d0s2303diff.eps,width=7in}
\vspace{100pt}
\caption{The difference between the density of states for the swapped-displaced and the swapped structures.  Again this shows the states move to lower the energy.}
\label{fig:d0s2303diff}
\end{figure}

 
 
\begin{figure}
\epsfig{figure= swappedmbasic.eps,width=7in}
\vspace{100pt}
\caption{The difference between the density of states for the swapped and the basic strucutres. The graph shows the assymmetric w-shape. As discussed in the text the w-shape is a signature of band narrowing and the assymetry is an indication of a peak shift. The difference in band energy is small as shown in table table~\ref{tab:diff}. It is as clear as in figures~\ref{fig:d0c0s0diff} and ~\ref{fig:d0s2303} that the energy-lowering mechanisem is winning which refelcts the small difference in band and total energies between the two strucutres.}
\label{fig:swappedmbasic}
\end{figure}



\begin{figure}
\epsfig{figure=b1.eps,width=6in}
\vspace{10pt}
\caption{The local density of states differences between the displaced-basic and the basic structures. All atoms are drown to the same scale. Atoms moved were pairs 3(Co),49(Ni) and 23(Ni),26(Co). For the atom numbers see fig.~`\ref{fig:strn}.The Al atoms show alomst no differences. The only clear differences are in the atoms that moved and slightly in the other TM atoms around. This might be an evidence of d-band extension over the unit cell. This figure shows atoms 0-17}
\label{fig:b1}
\end{figure}
 
 
\begin{figure}
\epsfig{figure=b2.eps,width=6in}
\vspace{10pt}
\caption{Local DOS basic-displaced - basic atoms 18-35}
\label{fig:b2}
\end{figure}
 
\begin{figure}
\epsfig{figure=b3.eps,width=6in}
\vspace{10pt}
\caption{Local DOS basic-displaced - basic atoms 36-49}
\label{fig:b3}
\end{figure}




\begin{figure}
\epsfig{figure=s1.eps,width=6in}
\vspace{10pt}
\caption{local DOS swapped-displaced - swapped atoms 0-17}
\label{fig:s1}
\end{figure}
 
 
\begin{figure}
\epsfig{figure=s2.eps,width=6in}
\vspace{10pt}
\caption{local DOS swapped-displaced - swapped atoms 18-35}
\label{fig:s2}
\end{figure}
 
\begin{figure}
\epsfig{figure=s3.eps,width=6in}
\vspace{10pt}
\caption{local DOS swapped-displaced - swapped atoms 35-49}
\label{fig:s3}
\end{figure}




\begin{figure}
\epsfig{figure=smb1.eps,width=6in}
\vspace{10pt}
\caption{Local DOS swapped - absic atoms 0-17. The swapped atoms 3 and 23 in the swapped were compared with atoms 23 and 3 in the basic. Atoms 3 and 23 here correspond to the atoms in the basic strucutre.}
\label{fig:smb1}
\end{figure}
 
 
\begin{figure}
\epsfig{figure=smb2.eps,width=6in}
\vspace{10pt}
\caption{Local DOS swapped - absic atoms 18-35.}
\label{fig:smb2}
\end{figure}
 
\begin{figure}
\epsfig{figure=smb3.eps,width=6in}
\vspace{10pt}
\caption{Local DOS swapped - absic atoms 36-49.}
\label{fig:smb3}
\end{figure}

\end{document}  