Unverified Commit ce7c3e68 authored by Axel Kohlmeyer's avatar Axel Kohlmeyer Committed by GitHub
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Merge pull request #1648 from athomps/add_w_l_orientorder 

Add w l orientorder
parents df63a537 3ec9317d

doc/src/compute_orientorder_atom.txt

+29 −6
Original line number Diff line number Diff line
@@ -19,6 +19,8 @@ keyword = {cutoff} or {nnn} or {degrees} or {components} 
  {cutoff} value = distance cutoff

  {nnn} value = number of nearest neighbors

  {degrees} values = nlvalues, l1, l2,...

  {wl} value = yes or no

  {wl/hat} value = yes or no

  {components} value = ldegree  :pre



:ule
@@ -27,7 +29,8 @@ keyword = {cutoff} or {nnn} or {degrees} or {components} 


compute 1 all orientorder/atom

compute 1 all orientorder/atom degrees 5 4 6 8 10 12 nnn NULL cutoff 1.5

compute 1 all orientorder/atom degrees 4 6 components 6 nnn NULL cutoff 3.0 :pre

compute 1 all orientorder/atom wl/hat yes

compute 1 all orientorder/atom components 6 :pre



[Description:]
@@ -48,7 +51,7 @@ neighbors of the central atom. 
The angles theta and phi are the standard spherical polar angles

defining the direction of the bond vector {rij}.

The second equation defines {Ql}, which is a

rotationally invariant scalar quantity obtained by summing

rotationally invariant non-negative amplitude obtained by summing

over all the components of degree {l}.



The optional keyword {cutoff} defines the distance cutoff
@@ -63,7 +66,7 @@ specified distance cutoff are used. 


The optional keyword {degrees} defines the list of order parameters to

be computed.  The first argument {nlvalues} is the number of order

parameters. This is followed by that number of integers giving the

parameters. This is followed by that number of non-negative integers giving the

degree of each order parameter. Because {Q}2 and all odd-degree order

parameters are zero for atoms in cubic crystals (see

"Steinhardt"_#Steinhardt), the default order parameters are {Q}4,
@@ -71,7 +74,20 @@ parameters are zero for atoms in cubic crystals (see 
= sqrt(7/3)/8 = 0.19094....  The numerical values of all order

parameters up to {Q}12 for a range of commonly encountered

high-symmetry structures are given in Table I of "Mickel et

al."_#Mickel.

al."_#Mickel, and these can be reproduced with this compute



The optional keyword {wl} will output the third-order invariants {Wl} 

(see Eq. 1.4 in "Steinhardt"_#Steinhardt) for the same degrees as

for the {Ql} parameters. For the FCC crystal with {nnn} =12,

{W}4 = -sqrt(14/143).(49/4096)/Pi^1.5 = -0.0006722136...



The optional keyword {wl/hat} will output the normalized third-order 

invariants {Wlhat} (see Eq. 2.2 in "Steinhardt"_#Steinhardt) 

for the same degrees as for the {Ql} parameters. For the FCC crystal 

with {nnn} =12, {W}4hat = -7/3*sqrt(2/429) = -0.159317...The numerical

values of {Wlhat} for a range of commonly encountered high-symmetry

structures are given in Table I of "Steinhardt"_#Steinhardt, and these

can be reproduced with this keyword.



The optional keyword {components} will output the components of the

normalized complex vector {Ybar_lm} of degree {ldegree}, which must be
@@ -82,7 +98,7 @@ particles, as discussed in "ten Wolde"_#tenWolde2. 


The value of {Ql} is set to zero for atoms not in the

specified compute group, as well as for atoms that have less than

{nnn} neighbors within the distance cutoff.

{nnn} neighbors within the distance cutoff, unless {nnn} is NULL.



The neighbor list needed to compute this quantity is constructed each

time the calculation is performed (i.e. each time a snapshot of atoms
@@ -108,6 +124,12 @@ This compute calculates a per-atom array with {nlvalues} columns, 
giving the {Ql} values for each atom, which are real numbers on the

range 0 <= {Ql} <= 1.



If the keyword {wl} is set to yes, then the {Wl} values for each

atom will be added to the output array, which are real numbers.



If the keyword {wl/hat} is set to yes, then the {Wl_hat} 

values for each atom will be added to the output array, which are real numbers.

 

If the keyword {components} is set, then the real and imaginary parts

of each component of (normalized) {Ybar_lm} will be added to the

output array in the following order: Re({Ybar_-m}) Im({Ybar_-m})
@@ -130,7 +152,8 @@ hexorder/atom"_compute_hexorder_atom.html 
[Default:]



The option defaults are {cutoff} = pair style cutoff, {nnn} = 12,

{degrees} = 5 4 6 8 10 12 i.e. {Q}4, {Q}6, {Q}8, {Q}10, and {Q}12.

{degrees} = 5 4 6 8 10 12 i.e. {Q}4, {Q}6, {Q}8, {Q}10, and {Q}12,

{wl} = no, {wl/hat} = no, and {components} off



:line

examples/steinhardt/in.bcc

0 → 100644
+91 −0
Original line number Diff line number Diff line 
# Steinhardt-Nelson bond orientational order parameters for BCC



variable  	rcut equal 3.0



boundary	p p p



atom_style	atomic

neighbor	0.3 bin

neigh_modify	delay 5



# create geometry



lattice		bcc 1.0

region		box block 0 3 0 3 0 3

create_box	1 box

create_atoms	1 box



mass		1 1.0



# LJ potentials



pair_style	lj/cut ${rcut}

pair_coeff	* * 1.0 1.0 ${rcut}



# 14 neighbors, perfect crystal 



compute 	qlwlhat all orientorder/atom degrees 6 2 4 6 8 10 12 nnn 14 wl/hat yes

compute 	avql all reduce ave c_qlwlhat[1] c_qlwlhat[2] c_qlwlhat[3] c_qlwlhat[4] c_qlwlhat[5] c_qlwlhat[6] 

compute 	avwlhat all reduce ave c_qlwlhat[7] c_qlwlhat[8] c_qlwlhat[9] c_qlwlhat[10] c_qlwlhat[11] c_qlwlhat[12] 



thermo_style    custom step temp epair etotal c_avql[*] c_avwlhat[*]



run		0



# check Q_l values



print " "

print "*******************************************************************"

print " "

print "Comparison with reference values of Q_l "

print "   [Table I in W. Mickel, S. C. Kapfer," 

print "   G. E. Schroeder-Turkand, K. Mecke, "

print "   J. Chem. Phys. 138, 044501 (2013).]"

print " "



variable 	q2ref equal 0.0

variable 	q4ref equal 0.036

variable 	q6ref equal 0.511

variable 	q8ref equal 0.429

variable 	q10ref equal 0.195

variable 	q12ref equal 0.405



variable 	q2 equal c_avql[1]

variable 	q4 equal c_avql[2]

variable 	q6 equal c_avql[3]

variable 	q8 equal c_avql[4]

variable 	q10 equal c_avql[5]

variable 	q12 equal c_avql[6]



print "q2     = $(v_q2:%10.6f) delta = $(v_q2-v_q2ref:%10.4f)"

print "q4     = $(v_q4:%10.6f) delta = $(v_q4-v_q4ref:%10.4f)"

print "q6     = $(v_q6:%10.6f) delta = $(v_q6-v_q6ref:%10.4f)"

print "q8     = $(v_q8:%10.6f) delta = $(v_q8-v_q8ref:%10.4f)"

print "q10    = $(v_q10:%10.6f) delta = $(v_q10-v_q10ref:%10.4f)"

print "q12    = $(v_q12:%10.6f) delta = $(v_q12-v_q12ref:%10.4f)"



# check W_l_hat values



print " "

print "Comparison with reference values of W_l_hat"

print "   [Table I in P. Steinhardt, D. Nelson, and M. Ronchetti, "

print "   Phys. Rev. B 28, 784 (1983).]"

print " "



variable 	w4hatref equal 0.159317

variable 	w6hatref equal 0.013161

variable 	w8hatref equal -0.058455

variable 	w10hatref equal -0.090130



variable 	w4hat equal c_avwlhat[2]

variable 	w6hat equal c_avwlhat[3]

variable 	w8hat equal c_avwlhat[4]

variable 	w10hat equal c_avwlhat[5]



print "w4hat  = $(v_w4hat:%10.6f) delta = $(v_w4hat-v_w4hatref:%10.6f)"

print "w6hat  = $(v_w6hat:%10.6f) delta = $(v_w6hat-v_w6hatref:%10.6f)"

print "w8hat  = $(v_w8hat:%10.6f) delta = $(v_w8hat-v_w8hatref:%10.6f)"

print "w10hat = $(v_w10hat:%10.6f) delta = $(v_w10hat-v_w10hatref:%10.6f)"

print " "

print "*******************************************************************"

print " "

examples/steinhardt/in.fcc

0 → 100644
+88 −0
Original line number Diff line number Diff line 
# Steinhardt-Nelson bond orientational order parameters for FCC



variable  	rcut equal 3.0



boundary	p p p



atom_style	atomic

neighbor	0.3 bin

neigh_modify	delay 5



# create geometry



lattice		fcc 1.0

region		box block 0 3 0 3 0 3

create_box	1 box

create_atoms	1 box



mass		1 1.0



# LJ potentials



pair_style	lj/cut ${rcut}

pair_coeff	* * 1.0 1.0 ${rcut}



# 12 neighbors, perfect crystal



compute 	qlwlhat all orientorder/atom wl/hat yes

compute 	avql all reduce ave c_qlwlhat[1] c_qlwlhat[2] c_qlwlhat[3] c_qlwlhat[4] c_qlwlhat[5] 

compute 	avwlhat all reduce ave c_qlwlhat[6] c_qlwlhat[7] c_qlwlhat[8] c_qlwlhat[9] c_qlwlhat[10]



thermo_style    custom step temp epair etotal c_avql[*] c_avwlhat[*]



run		0



# check Q_l values



print " "

print "*******************************************************************"

print " "

print "Comparison with reference values of Q_l "

print "   [Table I in W. Mickel, S. C. Kapfer," 

print "   G. E. Schroeder-Turkand, K. Mecke, "

print "   J. Chem. Phys. 138, 044501 (2013).]"

print " "



variable 	q4ref equal 0.190

variable 	q6ref equal 0.575

variable 	q8ref equal 0.404

variable 	q10ref equal 0.013

variable 	q12ref equal 0.600



variable 	q4 equal c_avql[1]

variable 	q6 equal c_avql[2]

variable 	q8 equal c_avql[3]

variable 	q10 equal c_avql[4]

variable 	q12 equal c_avql[5]



print "q4     = $(v_q4:%10.6f) delta = $(v_q4-v_q4ref:%10.4f)"

print "q6     = $(v_q6:%10.6f) delta = $(v_q6-v_q6ref:%10.4f)"

print "q8     = $(v_q8:%10.6f) delta = $(v_q8-v_q8ref:%10.4f)"

print "q10    = $(v_q10:%10.6f) delta = $(v_q10-v_q10ref:%10.4f)"

print "q12    = $(v_q12:%10.6f) delta = $(v_q12-v_q12ref:%10.4f)"



# check W_l_hat values



print " "

print "Comparison with reference values of W_l_hat"

print "   [Table I in P. Steinhardt, D. Nelson, and M. Ronchetti, "

print "   Phys. Rev. B 28, 784 (1983).]"

print " "



variable 	w4hatref equal -0.159316

variable 	w6hatref equal -0.013161

variable 	w8hatref equal 0.058454

variable 	w10hatref equal -0.090128



variable 	w4hat equal c_avwlhat[1]

variable 	w6hat equal c_avwlhat[2]

variable 	w8hat equal c_avwlhat[3]

variable 	w10hat equal c_avwlhat[4]



print "w4hat  = $(v_w4hat:%10.6f) delta = $(v_w4hat-v_w4hatref:%10.6f)"

print "w6hat  = $(v_w6hat:%10.6f) delta = $(v_w6hat-v_w6hatref:%10.6f)"

print "w8hat  = $(v_w8hat:%10.6f) delta = $(v_w8hat-v_w8hatref:%10.6f)"

print "w10hat = $(v_w10hat:%10.6f) delta = $(v_w10hat-v_w10hatref:%10.6f)"

print " "

print "*******************************************************************"

print " "

examples/steinhardt/in.icos

0 → 100644
+106 −0
Original line number Diff line number Diff line 
# Steinhardt-Nelson bond orientational order parameters for icosahedral cluster

# W_6_hat is sensitive to icosohedral order



variable        rcut equal 1.2 # a bit bigger than LJ Rmin 

variable        rcutred equal 0.75 # a bit bigger than 1/sqrt(2)



# create a perfect fcc crystallite



atom_style	atomic

boundary	s s s

lattice		fcc 1.0 # neighbors at LJ Rmin

region		box block 0 2 0 2 0 2

create_box	1 box

create_atoms	1 box

mass		1 1.0



region 		centralatom sphere 1 1 1 0.0 side in

group 		centralatom region centralatom



region 		mysphere sphere 1 1 1 ${rcutred} side out

delete_atoms 	region mysphere



# LJ potential



pair_style	lj/cut 100.0

pair_coeff	* * 1.0 1.0 100.0



# define output for central atom



compute 	qlwlhat all orientorder/atom wl/hat yes cutoff ${rcut} nnn NULL

compute 	avql centralatom reduce ave c_qlwlhat[1] c_qlwlhat[2] c_qlwlhat[3] c_qlwlhat[4] c_qlwlhat[5] 

compute 	avwlhat centralatom reduce ave c_qlwlhat[6] c_qlwlhat[7] c_qlwlhat[8] c_qlwlhat[9] c_qlwlhat[10] 

variable	q6 equal c_avql[2]

variable	w6hat equal c_avwlhat[2]



compute 	mype all pe/atom

compute 	centralatompe centralatom reduce ave c_mype



# gently equilibrate the crystallite



velocity     	all create 0.001 482748

fix	     	1 all nve

neighbor	0.3 bin

neigh_modify	every 1 check no delay 0

timestep	0.003

thermo_style    custom step temp epair etotal c_centralatompe v_q6 v_w6hat

thermo		10



run		10



# quench to icosehedral cluster



minimize      	1.0e-10 1.0e-6 100 1000



# check Q_l values



print " "

print "*******************************************************************"

print " "

print "Comparison with reference values of Q_l "

print "   [Table I in W. Mickel, S. C. Kapfer," 

print "   G. E. Schroeder-Turkand, K. Mecke, "

print "   J. Chem. Phys. 138, 044501 (2013).]"

print " "



variable 	q4ref equal 0.0

variable 	q6ref equal 0.663

variable 	q8ref equal 0.0

variable 	q10ref equal 0.363

variable 	q12ref equal 0.585



variable 	q4 equal c_avql[1]

variable 	q6 equal c_avql[2]

variable 	q8 equal c_avql[3]

variable 	q10 equal c_avql[4]

variable 	q12 equal c_avql[5]



print "q4     = $(v_q4:%10.6f) delta = $(v_q4-v_q4ref:%10.4f)"

print "q6     = $(v_q6:%10.6f) delta = $(v_q6-v_q6ref:%10.4f)"

print "q8     = $(v_q8:%10.6f) delta = $(v_q8-v_q8ref:%10.4f)"

print "q10    = $(v_q10:%10.6f) delta = $(v_q10-v_q10ref:%10.4f)"

print "q12    = $(v_q12:%10.6f) delta = $(v_q12-v_q12ref:%10.4f)"



# check W_l_hat values



print " "

print "Comparison with reference values of W_l_hat"

print "   [Table I in P. Steinhardt, D. Nelson, and M. Ronchetti, "

print "   Phys. Rev. B 28, 784 (1983).]"

print " "



variable 	w6hatref equal -0.169754

variable 	w10hatref equal -0.093967



variable 	w4hat equal c_avwlhat[1]

variable 	w6hat equal c_avwlhat[2]

variable 	w8hat equal c_avwlhat[3]

variable 	w10hat equal c_avwlhat[4]

variable 	w12hat equal c_avwlhat[5]



print "w6hat  = $(v_w6hat:%10.6f) delta = $(v_w6hat-v_w6hatref:%10.6f)"

print "w10hat = $(v_w10hat:%10.6f) delta = $(v_w10hat-v_w10hatref:%10.6f)"

print " "

print "*******************************************************************"

print " "

src/compute_orientorder_atom.cpp

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