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\begin_body

\begin_layout Title
Sorting Criterion for Slip and Twin system in HCP
\end_layout

\begin_layout Author
YunJo Ro
\end_layout

\begin_layout Standard
This document attempts to show how we sort the order of the slip and twin
 system for Hex (or hcp) structure in lattice.f90.
 
\end_layout

\begin_layout Section
Slip system 
\end_layout

\begin_layout Standard
An intersection between slip and basal plane is used in order to sort the
 slip system as illustrated in Figures 
\begin_inset CommandInset ref
LatexCommand ref
reference "Fig:BasalPrismSlip"

\end_inset

 and 
\begin_inset CommandInset ref
LatexCommand ref
reference "Fig:Pyr<a><c+a>"

\end_inset

.
 Numbers in Figures 
\begin_inset CommandInset ref
LatexCommand ref
reference "Fig:BasalPrismSlip"

\end_inset

 and 
\begin_inset CommandInset ref
LatexCommand ref
reference "Fig:Pyr<a><c+a>"

\end_inset

 indicate the sequence of each slip system in 
\begin_inset Quotes eld
\end_inset

lattice.f90
\begin_inset Quotes erd
\end_inset

.
 In 
\begin_inset Quotes eld
\end_inset

lattice.f90
\begin_inset Quotes erd
\end_inset

, No.
 4 - 6 for basal and prism <a> slip do not include (Figure 
\begin_inset CommandInset ref
LatexCommand ref
reference "Fig:BasalPrismSlip"

\end_inset

).
 In Figure 
\begin_inset CommandInset ref
LatexCommand ref
reference "Fig:Pyr<a><c+a>"

\end_inset

, pyramidal slip <c+a> was used two criterions to sort the 12 slip systems;
 i) intersection between pyramidal slip plane and basal plnae, and ii) <a>
 direction.
 
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	filename figures/slipSystemForHCP.jpg
	lyxscale 15
	scale 18
	clip

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\begin_inset Caption

\begin_layout Plain Layout
Basal and prism <a> slip.
\end_layout

\end_inset


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LatexCommand label
name "Fig:BasalPrismSlip"

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\end_layout

\end_inset


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	filename figures/slipSystemForHCP-pyr.jpg
	lyxscale 10
	scale 18
	clip

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\begin_inset Caption

\begin_layout Plain Layout
Pyramical <a> and <c+a> slip.
\end_layout

\end_inset


\begin_inset CommandInset label
LatexCommand label
name "Fig:Pyr<a><c+a>"

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Newpage clearpage
\end_inset


\end_layout

\begin_layout Section
Twin system
\end_layout

\begin_layout Standard
An intersection between twin and basal plane is used in order to sort the
 twin system as illustrated in Figures 
\begin_inset CommandInset ref
LatexCommand ref
reference "Fig:TwinType1"

\end_inset

 and 
\begin_inset CommandInset ref
LatexCommand ref
reference "Fig:TwinType2"

\end_inset

.
 Numbers in Figures 
\begin_inset CommandInset ref
LatexCommand ref
reference "Fig:TwinType1"

\end_inset

 and 
\begin_inset CommandInset ref
LatexCommand ref
reference "Fig:TwinType2"

\end_inset

 indicate the sequence of each twin system in 
\begin_inset Quotes eld
\end_inset

lattice.f90
\begin_inset Quotes erd
\end_inset

.
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	filename figures/twinSystemForHCP-1.jpg
	lyxscale 15
	scale 18
	clip

\end_inset


\begin_inset Caption

\begin_layout Plain Layout
Tensile and compressive twin type 1
\end_layout

\end_inset


\begin_inset CommandInset label
LatexCommand label
name "Fig:TwinType1"

\end_inset


\end_layout

\end_inset


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	filename figures/twinSystemForHCP-2.jpg
	lyxscale 15
	scale 18
	clip

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\begin_inset Caption

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Tensile and compressive twin type 2
\end_layout

\end_inset


\begin_inset CommandInset label
LatexCommand label
name "Fig:TwinType2"

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\end_layout

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