From 79224374f68f283d4b48ad3c1611f73992c6ad2c Mon Sep 17 00:00:00 2001 From: sgbaird Date: Fri, 29 Oct 2021 01:04:57 -0600 Subject: [PATCH] initial files --- LatticePlane.m | 1077 ++++ LatticePlane.nb | 14133 ++++++++++++++++++++++++++++++++++++++++++++++ al.xyz | 10 + 3 files changed, 15220 insertions(+) create mode 100644 LatticePlane.m create mode 100644 LatticePlane.nb create mode 100644 al.xyz diff --git a/LatticePlane.m b/LatticePlane.m new file mode 100644 index 0000000..ae6d397 --- /dev/null +++ b/LatticePlane.m @@ -0,0 +1,1077 @@ +(* ::Package:: *) + +(************************************************************************) +(* This file was generated automatically by the Mathematica front end. *) +(* It contains Initialization cells from a Notebook file, which *) +(* typically will have the same name as this file except ending in *) +(* ".nb" instead of ".m". *) +(* *) +(* This file is intended to be loaded into the Mathematica kernel using *) +(* the package loading commands Get or Needs. Doing so is equivalent *) +(* to using the Evaluate Initialization Cells menu command in the front *) +(* end. *) +(* *) +(* DO NOT EDIT THIS FILE. This entire file is regenerated *) +(* automatically each time the parent Notebook file is saved in the *) +(* Mathematica front end. Any changes you make to this file will be *) +(* overwritten. *) +(************************************************************************) + + + +(* ::Input::Initialization:: *) +BeginPackage["LatticePlane`","NDSolve`FEM`","OpenCascadeLink`"(*,"CifImport`"*),"MaXrd`"]; +Unprotect@@Names[Evaluate[Context[]<>"*"]]; +Unprotect[Evaluate[Context[]<>"*"]]; +ClearAll@@Names[Evaluate[Context[]<>"*"]]; +ClearAll[Evaluate[Context[]<>"Private`*"]]; + + +(* ::Input::Initialization:: *) +ParseHKL::usage="ParseHKL[hklIn]"; +Reciprocal::usage="Reciprocal[hklIn"; +AssignAxis::usage="AssignAxis[n,valIn,\[Gamma]]"; +AssignAxes::usage="AssignAxes[\[ScriptCapitalI],\[Gamma]]"; +GetPositions::usage="GetPositions[\[ScriptCapitalI]]"; +OneDimension::usage="OneDimension[\[ScriptCapitalI],\[Gamma]]"; +TwoDimension::usage="TwoDimension[\[ScriptCapitalI],\[Gamma]]"; +MillerToPlane::usage="MillerToPlane[hkl,\[Gamma]]"; +UnitCell::usage="UnitCell[xyz]"; +InterplanarAngle::usage="InterplanarAngle[hkl1,hkl2,lattice]"; +DegenerateMesh::usage="DegenerateMesh[v]"; +TotalIntersectionArea::usage="TotalIntersectionArea[\[ScriptCapitalT],\[ScriptCapitalB]]"; +PlaneIntersection::usage="PlaneIntersection[\[ScriptCapitalP],\[ScriptCapitalU]]"; +RationalUnitCell::usage="RationalUnitCell[p]"; +QUC::usage="QUC[x]"; +ImportCrystalData2::usage="ImportCrystalData2[ciffile,name]"; +ExpandCrystal2::usage="ExpandCrystal2[crystalData,{n,n,n}]"; +AtomPolygonBallsIntersection::usage="AtomPolygonBallsIntersection[P,c,r]"; +PolygonBallsIntersection::usage="PolygonBallsIntersection[P,c,r]"; +AtomProbabilityIntersection::usage="AtomProbabilityIntersection[\[ScriptCapitalD],P]"; +ProbabilityIntersection::usage="ProbabilityIntersection[\[ScriptCapitalD],\[ScriptCapitalR],\[ScriptCapitalP]]"; +SetupDensityHKL::usage="SetupDensityHKL[mpid,n,hklMax,radiusFactor]"; +GetFullHKL::usage="GetFullHKL[valsIn,hklIn,pg]"; +DensityHKL::usage= +"{\!\(\*SubscriptBox[\(\[ScriptCapitalA]\), \(int, n\)]\),\!\(\*SubscriptBox[\(hkl\), \(list\)]\),\!\(\*SubscriptBox[\(\[ScriptCapitalE]\), \(unique\)]\)}=DensityHKL[mpid,n,hklMax,radiusFactorIn]; +{\!\(\*SubscriptBox[\(\[ScriptCapitalA]\), \(int, n\)]\),\!\(\*SubscriptBox[\(hkl\), \(list\)]\),\!\(\*SubscriptBox[\(\[ScriptCapitalE]\), \(unique\)]\)}=DensityHKL[mpid,n,hklMax,radiusFactorIn,\"Method\"\[Rule]\"PDF\"];" +PlotSetup::usage="{\!\(\*SubscriptBox[\(hkl\), \(list\)]\),reflectionList,pg}=PlotSetup[mpid,n,hklMax];" +PlotSymmetrizedHKL::usage="g=PlotSymmetrizedHKL[vals,hkl,o,legendLabel];" +PlotFullHKL::usage="g=PlotFullHKL[valsIn,hklIn,pg,o,legendLabel];" +PlotSymmetrizedFullHKL::usage="g=PlotSymmetrizedFullHKL[\!\(\*SubscriptBox[\(\[ScriptCapitalA]\), \(out, n\)]\),\!\(\*SubscriptBox[\(hkl\), \(list\)]\),pg,\!\(\*SubscriptBox[\(\[ScriptCapitalE]\), \(unique\)]\),tag];" + + +(* ::Input::Initialization:: *) +Begin["`Private`"]; + + +(* ::Input::Initialization:: *) +ParseHKL[hklIn_]:=Module[{hkl}, +hkl=hklIn/.{OverBar->Minus,0->Indeterminate}; +If[Length@hkl==4,hkl=hkl[[{1,2,4}]],hkl] +] + + +(* ::Input::Initialization:: *) +Reciprocal[hklIn_]:=1/ParseHKL@hklIn + + +(* ::Input::Initialization:: *) +MillerToPlane[hkl_,Rin_]:=Module[{\[ScriptCapitalI],R,negQ,\[ScriptCapitalO],pos,zeroPosition,finitePosition,axisIntersection}, +\[ScriptCapitalI]=Reciprocal[hkl]; +R=Rationalize[Rin,0];(*basis vectors*) +\[ScriptCapitalO]={0,0,0};(*reference point*) +negQ=Negative[\[ScriptCapitalI]/.Indeterminate->0];(*which ones are negative?*) +MapThread[If[#1,\[ScriptCapitalO]=\[ScriptCapitalO]+#2]&,{negQ,R}];(*if negative, shift the reference point in the positive direction along an axis*) +zeroPosition=Flatten@Position[hkl,0];(*which hkl values are 0?*) +finitePosition=Complement[Range@3,zeroPosition];(*which hkl values are finite?*) +axisIntersection=\[ScriptCapitalO]+#&/@(\[ScriptCapitalI][[finitePosition]]R[[finitePosition]]); (*using the finite hkl values, compute axis intersections*) +R=MapThread[If[#1,-#2,#2]&,{negQ,R}];(*if negative, flip the basis vector*) +If[Length@zeroPosition>0, +AppendTo[axisIntersection,axisIntersection[[1]]-R[[#]]]&/@zeroPosition]; (*get point(s) in plane (if any) for remaining hkl indices that are 0*) +InfinitePlane[axisIntersection] +] + + +(* ::Input::Initialization:: *) +ReadXYZ[xyzpath_]:=Import[xyzpath,"Table"][[3;;,2;;4]]; + + +(* ::Input::Initialization:: *) +UnitCell[xyz_]:=Module[{\[ScriptCapitalM],\[ScriptP],\[ScriptCapitalC],P,i,\[ScriptCapitalN],\[ScriptCapitalO]}, +\[ScriptCapitalM]=Region`Mesh`MergeCells@ConvexHullMesh@Rationalize[xyz,0]; +\[ScriptP]=MeshCoordinates@\[ScriptCapitalM]; +(*\[ScriptP]=\[ScriptP](1+$MachineEpsilon);*) +\[ScriptCapitalC]=MeshCells[\[ScriptCapitalM],1][[;;,1]]; +(*\[ScriptM]={\[ScriptCapitalC]\[LeftDoubleBracket]#\[RightDoubleBracket],\[ScriptP]\[LeftDoubleBracket]#\[RightDoubleBracket]}&/@Range@Length@\[ScriptP]; +\[ScriptCapitalN]=Select[\[ScriptM],ContainsAny[#\[LeftDoubleBracket]1\[RightDoubleBracket],{1}]&]\[LeftDoubleBracket];;,2\[RightDoubleBracket];*) +P=Position[\[ScriptCapitalC],_?(ContainsAny[#,{1}]&),1]//Flatten; +i=DeleteCases[Flatten[\[ScriptCapitalC][[P]]],1]; +\[ScriptCapitalN]=\[ScriptP][[i]]; +\[ScriptCapitalO]=\[ScriptP][[1]];(*\[ScriptCapitalN]=Nearest[\[ScriptP]\[LeftDoubleBracket]2;;\[RightDoubleBracket],\[ScriptCapitalO],3];*) +Parallelepiped[\[ScriptCapitalO],\[ScriptCapitalN]] +] + + +(* ::Input::Initialization:: *) +RationalUnitCell[R_,n_:1]:=Module[{R1,R2,R3,c,\[ScriptCapitalU]pts,\[ScriptCapitalU]}, +{R1,R2,R3}=R(1+100$MachineEpsilon);(*for some reason Kernel aborts unexpectedly without the machine precision factor*) +c=Floor[n/2](R1+R2+R3);(*corner*) +\[ScriptCapitalU]pts=#-c&/@(n{{0,0,0},R1,R2,R3,R1+R2,R2+R3,R1+R3,R1+R2+R3}); +\[ScriptCapitalU]=ConvexHullMesh@\[ScriptCapitalU]pts; +Polyhedron[Rationalize[MeshCoordinates@\[ScriptCapitalU],0],MeshCells[\[ScriptCapitalU],2][[;;,1]]] +] + + +(* ::Input::Initialization:: *) +InterplanarAngle[hkl1_,hkl2_,lattice_:"cubic"]:=Module[{h1,k1,l1,h2,k2,l2}, +{h1,k1,l1}=ParseHKL@hkl1/. Indeterminate\[RightArrow]0; +{h2,k2,l2}=ParseHKL@hkl2/. Indeterminate\[RightArrow]0;Switch[lattice,"cubic",ArcCos[ (h1 h2+k1 k2+l1 l2)/Sqrt[(h1^2+k1^2+l1^2)(h2^2+k2^2+l2^2)]],"hexagonal",Null,"tetragonal",Null,"trigonal",Null,"monoclinic",Null,"triclinic",Null,"orthorhombic",Null]] + + +(* ::Input::Initialization:: *) +DegenerateMesh[v_]:=Module[{\[ScriptCapitalR],\[ScriptCapitalN]},\[ScriptCapitalR]=DelaunayMesh@DimensionReduce@v; +\[ScriptCapitalN]=Range@Length@v; +\[ScriptCapitalT]=Last@MeshCells@\[ScriptCapitalR]/. Polygon\[RightArrow]Simplex/. MapThread[#1\[RightArrow]#2&,{\[ScriptCapitalN],v}]] + + +(* ::Input::Initialization:: *) +TotalIntersectionArea[\[ScriptCapitalT]_,\[ScriptCapitalB]_]:=Table[Area@RegionIntersection[t,b],{t,\[ScriptCapitalT]},{b,\[ScriptCapitalB]}]/. Undefined\[RightArrow]Sequence@@{}//Flatten//Total + + +(* ::Input::Initialization:: *) +PlaneIntersection[\[ScriptCapitalP]_,\[ScriptCapitalU]_]:=Module[{\[ScriptCapitalP]1,\[ScriptCapitalB],\[ScriptCapitalM],\[ScriptCapitalP]crop,\[ScriptCapitalP]int,shapes,bmesh,d,order,coords,TF}, +If[Head@\[ScriptCapitalP]===InfinitePlane,\[ScriptCapitalP]1={\[ScriptCapitalP]},\[ScriptCapitalP]1=\[ScriptCapitalP]]; +\[ScriptCapitalB]=RegionResize[BoundingRegion[\[ScriptCapitalU]],Scaled@Rationalize[1.1(*100$MachineEpsilon*)]];(*for cropping the plane*) +\[ScriptCapitalP]crop=RegionIntersection[#,\[ScriptCapitalB]]&/@\[ScriptCapitalP]1; +\[ScriptCapitalP]int=RegionIntersection[#,N@\[ScriptCapitalU]]&/@N[\[ScriptCapitalP]crop]; +shapes=OpenCascadeShape[#]&/@\[ScriptCapitalP]int; +bmesh=OpenCascadeShapeSurfaceMeshToBoundaryMesh[#]&/@shapes; +coords=#["Coordinates"]&/@bmesh; +TF=CoplanarPoints/@coords; +coords=MapThread[If[#1,#2,DimensionReduction[#2,2][#2,"ReconstructedData"]]&,{TF,coords}]; +{d,order}=(FindShortestTour[#]&/@coords)\[Transpose]; +\[ScriptCapitalP]int=MapThread[Polygon[#1[[#2[[;;-2]]]]]&,{coords,order}] +] + + +(* ::Input::Initialization:: *) +QUC[x_]:=QuantityMagnitude@UnitConvert@x + + +(* ::Input::Initialization:: *) +IsotropicMultinormal[pts_,r_]:=MapThread[MultinormalDistribution[#1,DiagonalMatrix@ConstantArray[#2,3]]&,{pts,r}] + + +(* ::Input::Initialization:: *) +ImportCrystalData2::subdataInteger="\"\!\(\* +StyleBox[\"ExtractSubdata\", \"Program\"]\)\" must be a positive integer."; +ImportCrystalData2::subdataLength="The \!\(\* +StyleBox[\".\", \"Program\"]\)\!\(\* +StyleBox[\"cif\", \"Program\"]\) file has a subdata length of `1`."; +ImportCrystalData2::latticeParameters="No lattice parameters were located, or they have an invalid form."; +ImportCrystalData2::atomData="No atom data was located."; +ImportCrystalData2::SG="Could not determine space group. 'P1' will be used."; +ImportCrystalData2::cell="Could not work out the unit cell properly."; +ImportCrystalData2::notMaXrd="Data collected using `1` radiation. Errors may occur."; +ImportCrystalData2::modulation="Modulated structure detected. Errors may occur."; +ImportCrystalData2::SpecialLabel="\[LeftGuillemet]`1`\[RightGuillemet] is a reserved label and should not be used."; + +Options@ImportCrystalData2={ +"DataFile"->"CrystalData2.m", +"ExtractSubdata"->1, +"IgnoreIonCharge"->False, +"Notes"-><||>, +"RoundAnglesThreshold"->0.001, +"Units"->True, +"OverwriteWarning"->True +}; + +SyntaxInformation@ImportCrystalData2={ +"ArgumentsPattern"->{___,OptionsPattern[]} +}; + + +(* ::Input::Initialization:: *) +ImportCrystalData2[ +{CrystalName_String, +ChemicalFormula:_?StringQ:"", +Z:_?IntegerQ:0, +SpaceGroup_:1, +Wavelength:_?NumericQ:-1 +}, +GetLatticeParameters_List, +AtomData_List, +OptionsPattern[] +]:=Block[ +{choice,name,sg,cell,\[Delta],fr,latticeItem,\[Lambda],itemAtomData,item,dataFile=OptionValue["DataFile"],temp}, + +(*---* Check if name already exists *---*) +If[CrystalName==="", +name="ImportedCrystal_"<>DateString["ISODate"],name=CrystalName]; +(*If[TrueQ@OptionValue["OverwriteWarning"], + If[KeyExistsQ[$CrystalData,name], + choice=ChoiceDialog["\[LeftGuillemet]"<>name<> +"\[RightGuillemet] already exists in $CrystalData.\nDo you want to overwrite this entry?"]]; + If[!choice,Return[]] +];*) + +(*--- Space Group *---*) +sg=InputCheck["GetPointSpaceGroupCrystal",SpaceGroup]; +sg=ToStandardSetting@sg; + +(*---* Lattice parameters *---*) +If[!AllTrue[GetLatticeParameters,NumericQ[#]&]|| +Length@GetLatticeParameters!=6, +Message[ImportCrystalData::latticeParameters]]; + + (* Optional: Round angles *) + cell=GetLatticeParameters; + \[Delta]=OptionValue["RoundAnglesThreshold"]; + Do[ + fr=FractionalPart@cell[[i]]; + If[fr>0.5,fr=1-fr]; + If[fr<=\[Delta],cell[[i]]=Round@cell[[i]]], + {i,4,6}]; + + (* Optional: Use units *) + If[OptionValue["Units"], + Do[ + Which[ + i<=3,cell[[i]]=Quantity[cell[[i]],"Angstroms"], + i>=4,cell[[i]]=Quantity[cell[[i]],"Degrees"]], + {i,6}]]; + + (* Prepare association entry *) + latticeItem=Association@ + Thread[{"a","b","c","\[Alpha]","\[Beta]","\[Gamma]"}->cell]; + +(*---* Wavelength *---*) + (* Optional: Use units *) + If[OptionValue["Units"], + \[Lambda]=Quantity[Wavelength,"Angstroms"], + \[Lambda]=Wavelength]; + +(*---* Atom data *---*) +If[AtomData==={}, +itemAtomData={<||>}, + +itemAtomData=Table[ +DeleteMissing@Part[AtomData[[i]],{ +"Element", +"OccupationFactor", +"SiteSymmetryMultiplicity", +"SiteSymmetryOrder", +"FractionalCoordinates", +"DisplacementParameters", +"Type"}], +{i,Length@AtomData}]; + +Do[ +If[KeyExistsQ[First@itemAtomData,k], +itemAtomData=MapAt[ +ToExpression,itemAtomData,{All,Key[k]}]], + {k,{ + "OccupationFactor", + "SiteSymmetryMultiplicity", + "SiteSymmetryOrder", + "DisplacementParameters"}} +]; + + (* Checking strings in coordinates *) + Do[itemAtomData[[i,"FractionalCoordinates"]]=itemAtomData[[i,"FractionalCoordinates"]]/.x_String:>ToExpression[x], + {i,Length@itemAtomData}] +]; + +(*---* Preparing item *---*) +item=<| + "ChemicalFormula"->ChemicalFormula, + "FormulaUnits"->Z, + "SpaceGroup"->sg, + "LatticeParameters"->latticeItem, + "Wavelength"->\[Lambda], + "AtomData"->itemAtomData, + "Notes"->OptionValue["Notes"] + |>; + +(* Delete certain keys *) + If[item["ChemicalFormula"]==="", + KeyDropFrom[item,"ChemicalFormula"]]; + + If[item["Notes"]===<||>, + KeyDropFrom[item,"Notes"]]; + + If[!Positive@item["Wavelength"], + KeyDropFrom[item,"Wavelength"]]; + + If[Z===0, + KeyDropFrom[item,"FormulaUnits"]]; + + (* If all occupation factors = 1, delete column *) + temp=item[["AtomData",All,"OccupationFactor"]]; + If[AllTrue[N@temp,#==1.&], + item[["AtomData",All]]=KeyDrop[ + item[["AtomData",All]],"OccupationFactor"]]; + + (* If all displacement parameters = 0, delete column *) + temp=item[["AtomData",All,"DisplacementParameters"]]; + If[AllTrue[N@temp,#==0.&], + item[["AtomData",All]]=KeyDrop[ + item[["AtomData",All]], + {"DisplacementParameters","Type"}]]; + + +(*InputCheck["Update$CrystalDataFile",dataFile,name,item]; +InputCheck["ShallowDisplayCrystal",name]*) +item +] + + +(* ::Input::Initialization:: *) +ImportCrystalData2[ciffile_,Name_String:"",OptionsPattern[]]:=Block[{ +(* A. Input check and setup *)name,specialLabels=Join[{"Void"},{"H","He","Li","Be","B","C","N","O","F","Ne","Na","Mg","Al","Si","P","S","Cl","Ar","K","Ca","Sc","Ti","V","Cr","Mn","Fe","Co","Ni","Cu","Zn","Ga","Ge","As","Se","Br","Kr","Rb","Sr","Y","Zr","Nb","Mo","Tc","Ru","Rh","Pd","Ag","Cd","In","Sn","Sb","Te","I","Xe","Cs","Ba","La","Ce","Pr","Nd","Pm","Sm","Eu","Gd","Tb","Dy","Ho","Er","Tm","Yb","Lu","Hf","Ta","W","Re","Os","Ir","Pt","Au","Hg","Tl","Pb","Bi","Po","At","Rn","Fr","Ra","Ac","Th","Pa","U","Np","Pu","Am","Cm","Bk","Cf","Es","Fm","Md","No","Lr","Rf","Db","Sg","Bh","Hs","Mt","Ds","Rg","Cn","Nh","Fl","Mc","Lv","Ts","Og"}],import,sub,endstring,enc,left,mid,right, +modulationQ=False, +(* B. Lattice parameters *)cell,x,X,multipleQ,parts,coordCount, +(* C. Atom data *)atomdata,atomtags,c, +(* D. Anisotropic displacement parameters (ADPs) *)anisodata,anisoOrder,P,atomoverview,tags,labels,disp,item, +(* E. Misc data labels (wavelength, formula units) *)\[Lambda],Z, +(* F. Chemical formula *)formula,chemicalformula,L,l,r,checkParentheses, +(* G. Space group *)sgTags,sgData,sg, +(* H. Adding item to dataset *)options, +(* Misc *)temp}, + +(*---* A. Input check and setup *---*) +If[Name=="",name=FileBaseName[ciffile],name=Name]; +If[MemberQ[specialLabels,name], +Message[ImportCrystalData2::SpecialLabel,name];Abort[]]; + +(* A.1. Check file *) +import=Check[Import[ciffile,"String"],Abort[]]; +sub=OptionValue["ExtractSubdata"]; + If[!(IntegerQ[#]&&Positive[#]&@sub), + Message[ImportCrystalData2::subdataInteger]; + Abort[]]; + +(* A.2. Auxiliary variables *) +endstring={"loop_","\n\n",";","#",EndOfString}; +enc={"'","\""};(* annotation/enclosing marks *) +{left,mid,right}={"\!\(\*SubscriptBox[\(","\), \(","\)]\)"}; + +(* A.3. Check radiation type *) +temp=StringCases[import, +Shortest[{ +"_diffrn_radiation_type","_diffrn_radiation_probe"} +~~Whitespace~~{"",enc}~~t:LetterCharacter..~~"\n"]:>t]; +If[MemberQ[temp,#],Message[ImportCrystalData2::notMaXrd,#]] +&/@{"neutron","electron"}; + +(* A.4. Check for modulation *) +temp=If[StringContainsQ[import,"_space_group_ssg_name"], +modulationQ=True; +Message[ImportCrystalData2::modulation]]; + +(*---* B. Lattice parameters *---*) +(* B.1. Extracting lattice parameters *) +cell=StringCases[import,Shortest[ +x:("_cell_"~~{"length","angle"}~~__~~ +{DigitCharacter,"."}..)~~ +{"(",Whitespace}]:>ToLowerCase@x, +IgnoreCase->True]; + + (* Check *) + If[cell=={}, + Message[ImportCrystalData2::latticeParameters]; + Abort[]]; + +(* B.2. Check for multiplue structures *) + cell=StringSplit[cell,Whitespace]; + Which[ + Length@cell>6, + multipleQ=True;parts=Length[cell]/6, + Length@cell==6, + multipleQ=False;parts=1, + True, + Message[ImportCrystalData2::cell]; + Return@cell + ]; + + (* Correct ordering *) + cell=Partition[cell, + Length@cell/Quotient[Length@cell,6]]; + + Do[ + X=cell[[i]]; + x=X[[All,1]]; + P=FindPermutation[x,{ + "_cell_length_a", + "_cell_length_b", + "_cell_length_c", + "_cell_angle_alpha", + "_cell_angle_beta", + "_cell_angle_gamma"}]; + cell[[i]]=Permute[X,P], + {i,Length@cell}]; + + cell=cell[[All,All,2]]; + +(* B.3. Check subdata extraction *) + (* Verify with fractional coordinates *) + coordCount=StringCount[import,"_atom_site_fract_x"]; + If[coordCount===0, + Message[ImportCrystalData2::atomData];Abort[]]; + + parts=Min[parts,coordCount]; + + If[(multipleQ&&sub>parts)||(!multipleQ&&sub!=1), + Message[ImportCrystalData2::subdataLength,parts]; + Abort[]]; + + If[!IntegerQ[parts], + Message[ImportCrystalData2::subdataInteger]; + Return@parts]; + + (* Extract subdata *) + cell=ToExpression@cell[[sub]]; + + +(*---* C. Atom data *---*) +Label["AtomData"]; + +(* C.1. Extracting relevant data block *) + (* Fractional coordinates *) + (* Occupation factor *) + (* Site symmetry multiplicity *) + + (* Extracting _atom_site loop *) + atomdata=StringCases[import,Shortest[ +labels:(Whitespace~~"_atom_site_"~~__~~"\n")~~data:(StartOfLine~~Whitespace...~~LetterCharacter~~__~~"\n") +~~{endstring,"_atom_site_aniso","_"~~Except["a"]}]:>{labels,data}]; + + (* No data? *) + If[atomdata=={}, + Message[ImportCrystalData2::atomData]; + Abort[]]; + + (* Delete cases containing anisotropy data *) + atomdata=DeleteCases[atomdata, + x_/;StringContainsQ[x[[1]],"aniso"]]; + + (* Specify sub-data *) + atomdata=atomdata[[sub]]; + +(* C.2. Organising data *) +atomtags=Flatten@StringCases[atomdata[[1]], +"_atom_site_"~~{WordCharacter,"_"}..]; + +atomdata=StringDelete[atomdata[[2]],"("~~DigitCharacter..~~")"]; +atomdata=Partition[StringSplit@atomdata,Length@atomtags]; +atomdata=DeleteCases[atomdata,x_/;Length[x]!=Length[atomtags]]; +atomdata=Association@Thread[atomtags->Transpose@atomdata]; + +(* C.3 Fixing entries *) +(* If 'site_type_symbol' is missing, copy 'site_label' *) +If[!KeyExistsQ[atomdata,"_atom_site_type_symbol"], +AppendTo[atomdata, +"_atom_site_type_symbol"->atomdata["_atom_site_label"]]]; + +(* Process and check elements *) +temp=atomdata["_atom_site_type_symbol"]; +temp=InputCheck["InterpretElement",temp]; + +(* Optional: Clear any ion charges *) +If[OptionValue["IgnoreIonCharge"], +temp=StringDelete[temp,{"+","-",DigitCharacter}]]; + +(* Update 'atomdata' with 'temp' *) +atomdata["_atom_site_type_symbol"]=temp; + + +(*---* D. Anisotropic displacement parameters *---*) +(* D.1. If missing, use default values for ADP *) +L=Length@First@atomdata; +If[!KeyExistsQ[atomdata,"_atom_site_adp_type"], +AppendTo[atomdata,"_atom_site_adp_type"->ConstantArray["Uiso",L]]]; +If[!KeyExistsQ[atomdata,"_atom_site_U_iso_or_equiv"], +AppendTo[atomdata,"_atom_site_U_iso_or_equiv"->ConstantArray[0,L]]]; + +(* D.2. Anisotropic displacement parameters *) +anisodata=StringCases[import, +Shortest["loop_"~~Whitespace~~ +x:("_atom_site_aniso"~~__)~~endstring]:>x]; + + (* Check *) + If[anisodata==={}, + Goto["OrganiseAtomdata"], + anisodata=anisodata[[sub]]]; + +(* D.3. Noting the order (permutation) *) +anisoOrder=Flatten@StringCases[anisodata,"U_"~~DigitCharacter..]; +P=FindPermutation[{"U_11","U_22","U_33","U_12","U_13","U_23"},anisoOrder]; + + (* Nothing there to extract? *) + temp=Flatten@StringCases[anisodata, + Shortest["_atom_site_aniso_"~~x__~~Whitespace]:>x]; + c=Flatten@Quiet@Position[temp, + x_/;StringContainsQ[x,"U"]]; + +(* D.4. Extracting relevant data and trimming *) +anisodata=StringCases[anisodata, +Shortest["_atom_site_aniso"~~__~~EndOfLine]~~Whitespace~~(* Last line *) +x:(WordCharacter~~__):>x(* Content *)]; + +(* Check if there is any actual data *) +If[anisodata==={},Goto["OrganiseAtomdata"]]; +anisodata=StringSplit[First@anisodata,Whitespace]; +anisodata=StringReplace[anisodata,x__~~"("~~__~~")":>x]; +anisodata=Partition[anisodata,Length@temp]; + +(* Correcting parameter order *) +anisodata[[All,c]]=Permute[#,P]&/@anisodata[[All,c]]; + +(* Associating each atom with values *) +anisodata=Association[ +Table[anisodata[[i,1]]->anisodata[[i,c]], +{i,Length@anisodata}]]; + +(* D.5. Organising the atom data *) +Label["OrganiseAtomdata"]; +atomoverview={}; +tags={ +"_atom_site_occupancy", +"_atom_site_site_symmetry_multiplicity", +"_atom_site_site_symmetry_order"}; +labels={ +"OccupationFactor", +"SiteSymmetryMultiplicity", +"SiteSymmetryOrder"}; + +Do[ +item=<||>; +AppendTo[item, +"Element"->atomdata[["_atom_site_type_symbol",i]]]; +Do[ +If[KeyExistsQ[atomdata,tags[[j]]], +AppendTo[item,labels[[j]]-> +atomdata[[tags[[j]],i]]]], +{j,Length@tags}]; + +AppendTo[item,"FractionalCoordinates"-> +Evaluate[atomdata[["_atom_site_fract_"<>#,i]]&/@{"x","y","z"}]]; +If[StringTake[ +atomdata[["_atom_site_adp_type",i]],-3]==="ani", +disp=Part[anisodata,atomdata[["_atom_site_label",i]]], +disp=atomdata[["_atom_site_U_iso_or_equiv",i]]]; + +AppendTo[item,"DisplacementParameters"->disp]; +AppendTo[item,"Type"->atomdata[["_atom_site_adp_type",i]]]; +AppendTo[atomoverview,item],{i,Length@First@atomdata}]; + + +(*---* E. Misc data labels *---*) +(* E.1. Wavelength *) +\[Lambda]=StringCases[import,Shortest["_diffrn_radiation_wavelength"~~ +Whitespace~~x:{DigitCharacter,"."}..~~Whitespace]:>x]; + +If[\[Lambda]=={},\[Lambda]=-1, +If[Length@\[Lambda]>1, +\[Lambda]=ToExpression@\[Lambda][[sub]], +\[Lambda]=ToExpression@First@\[Lambda]]]; + +(* E.2. Forumla units (Z) *) +Z=StringCases[import,Shortest["_cell_formula_units_Z"~~ +Whitespace~~z:DigitCharacter]:>z]; + +If[Z==={},Z=0,Z=ToExpression@First@Z]; + + +(*---* F. Chemical formula *---*) +(* F.1. Extracting formula *) +formula=StringCases[import, +Shortest[#~~{Whitespace,"\n"}..~~{"'","\""}~~f__~~ +{"'","\""}~~{Whitespace,"\n"}..]:>f]&/@{ +(* Prioritised order *) +"_chemical_formula_iupac", +"_chemical_formula_structural", +"_chemical_formula_sum"}; + +formula=Select[Flatten@formula,!StringContainsQ[#,{",","?"}]&]; +formula=StringDelete[formula,{"\r","~"}]; + +(* F.2. Check for simplest formula *) +temp=Select[formula,!StringContainsQ[#,"("]&]; +If[temp=!={},formula={First@temp}]; + +(* F.3. Misc treatmeant and possible subdata selection *) +If[formula==={}||formula==={""}, +chemicalformula="";Goto["SpaceGroup"]]; + +formula={StringDelete[StringTrim@First@formula,{"'","\""}]}; + +If[formula==={""}, +chemicalformula="";Goto["SpaceGroup"], +formula=StringSplit@formula]; + +If[Length@formula>1, +formula=formula[[sub]], +formula=Flatten@formula]; + +(* F.4. Loop for formatting the chemical formula *) +Label["FormatFormula"]; +If[AnyTrue[formula,StringContainsQ[#,{"(",")"}]&], +{l,r}=Flatten@Position[StringPosition[ +formula,{"(",")"}],{{_,_}}]; + checkParentheses=True]; + +chemicalformula={}; +Do[ +temp=Flatten@StringCases[formula[[i]], +x:LetterCharacter..~~ +y:({DigitCharacter,"."})..:>{x,y}]; +Which[ +temp=={},AppendTo[chemicalformula,formula[[i]]], +temp[[2]]=="1",AppendTo[chemicalformula,temp[[1]]], +True,AppendTo[chemicalformula,left<>temp[[1]]<>mid<>temp[[2]]<>right]], +{i,Length@formula}]; + +chemicalformula=StringDelete[chemicalformula,{"(",")"}]; + +(* Adding back parentheses *) +If[checkParentheses, +chemicalformula[[l]]="("<>chemicalformula[[l]]; +chemicalformula[[r]]=chemicalformula[[r]]<>")" +]; + +chemicalformula=StringJoin@chemicalformula; + + +(*---* G. Space group *---*) +Label["SpaceGroup"]; + +(* G.1. Prioritised list of data labels *) +sgTags={ +"_space_group_name_Hall", +"_space_group_name_H-M_alt", +"_space_group_IT_number", +"_symmetry_space_group_name_Hall", +"_symmetry_space_group_name_H-M", +"_symmetry_Int_Tables_number"}; + +(* G.2. Extract space group sections from imported data *) +sgData=StringCases[import,Shortest[sgTags~~__~~"loop_"]]; +If[Length[sgData]>0,sgData=sgData[[sub]]]; +sgData=StringTrim@StringDelete[sgData,"loop_"]; + +(* G.3. Make association of tags and corresponding info *) +sgData=StringCases[sgData,t:sgTags~~Whitespace~~sg:Shortest[Except[WhitespaceCharacter]~~__]~~{"\n",EndOfString}:>{t->sg}]; +sgData=Association@Flatten@sgData; +sgData=DeleteCases[sgData,"?"]; + +(* G.4. Go through priority order and validate *) +Do[ +sg=sgData[sgTags[[i]]]; +sg=Quiet@InputCheck["InterpretSpaceGroup",sg,False]; +If[sg=!=Null,Break[]], +{i,Length@sgTags}]; + +(* G.5. For modulated structures *) +If[sg===Null&&modulationQ, +sg=StringCases[import, +"_space_group_ssg_name"~~Whitespace~~ +{"'","\""}~~sg__~~{"'","\""}~~"\n":>sg]; +sg=StringCases[sg,Shortest[StartOfString~~___ +~~sg:(LetterCharacter~~__)~~"("]:>sg]; +If[sg=!={},sg=Quiet@InputCheck["InterpretSpaceGroup", +First@Flatten@sg,False]] +]; + +(* G.6. If missing space group, display message and use 'P1' *) +If[sg===Null,Message[ImportCrystalData2::SG];sg="P1"]; + + +(*---* H. Adding item to dataset *---*) +options=Thread[#->OptionValue[#],String]&/@( +First/@Options@ImportCrystalData2); + +ImportCrystalData2[ +{name,chemicalformula,Z,sg,\[Lambda]}, +cell,atomoverview, +options] +] + + +(* ::Input::Initialization:: *) +ExpandCrystal2::InvalidSize="The structure size must be a list of three natural numbers."; +ExpandCrystal2::DuplicateLabel="The new label must be different from the input."; + +Options@ExpandCrystal2={ +"DataFile"->FileNameJoin[{"CrystalData2.m"}], +"ExpandIntoNegative"->False, +"FirstTransformTo"->False, +"IgnoreSymmetry"->False, +"IncludeBoundary"->True, +"NewLabel"->"", +"StoreTemporarily"->False +}; + +SyntaxInformation@ExpandCrystal2={ +"ArgumentsPattern"->{_,_.,OptionsPattern[]} +}; + + +(* ::Input::Initialization:: *) +ExpandCrystal2[crystalData_,structureSize_List:{1,1,1}, +OptionsPattern[]]:=Block[{crystalCopy=crystalData, +dataFile=OptionValue["DataFile"], +newLabel=OptionValue["NewLabel"], +changeCell=OptionValue["FirstTransformTo"], +storeTempQ=TrueQ@OptionValue["StoreTemporarily"], +ignoreSymmetryQ=TrueQ@OptionValue["IgnoreSymmetry"], +atomData,coordinates,spaceGroup,generated, +copyTranslations,mid,atomDataMapUnitCell, +cutoffFunction,atomDataMapExpanded,lengths, +newAtomData +}, + +(* Input check and data acquisition *) +If[ +AllTrue[structureSize,Positive[#]&&IntegerQ[#]&]\[Nand] +Length[structureSize]===3, +Message[ExpandCrystal::InvalidSize];Abort[]]; + +(* Expand asymmetric unit to unit cell *) +atomData=crystalData["AtomData"]; +coordinates=atomData[[All,"FractionalCoordinates"]]; +spaceGroup=crystalData["SpaceGroup"]; + +(* Optional: Ignory symmetry and simply copy content as is *) +generated=N@If[ignoreSymmetryQ, +Partition[coordinates,1], +SymmetryEquivalentPositions[spaceGroup,#]&/@coordinates +]; + +(* Generate full content of the unit cell *) +atomDataMapUnitCell=Association@Thread[ +Range@Length@atomData->generated]; + +(* Copy by translation *) +copyTranslations=InputCheck["GenerateTargetPositions",structureSize+1]; +atomDataMapExpanded=Flatten[ +Outer[Plus,copyTranslations,#,1], +1]&/@atomDataMapUnitCell; + +(* Optional: Complete the outer boundary *) +cutoffFunction=If[TrueQ@OptionValue["IncludeBoundary"], +Greater,GreaterEqual]; + +(* Delete atoms whose coordinates are outside *) +atomDataMapExpanded=DeleteCases[atomDataMapExpanded,{x_,y_,z_}/; +Or@@MapThread[cutoffFunction,{{x,y,z},structureSize}], +{2}]; + +(* Optional: Center translations around origin *) +If[TrueQ@OptionValue["ExpandIntoNegative"], +mid=\[LeftFloor]structureSize/2.\[RightFloor]; +atomDataMapExpanded=Map[#-mid&,atomDataMapExpanded,{2}]; +]; + +(* Create new atom data structure *) +lengths=Values[Length/@atomDataMapExpanded]; +newAtomData=Table[ +ConstantArray[atomData[[i]],lengths[[i]]], +{i,Length@atomData}]; + +newAtomData[[All,All,"FractionalCoordinates"]]= +Values@atomDataMapExpanded; +newAtomData=Flatten[newAtomData,1]; + +(* Create new crystal entry *) +crystalCopy["AtomData"]=newAtomData; +AssociateTo[crystalCopy,"Notes"-><| +"StructureSize"->structureSize, +"UnitCellAtomsCount"->Total[Length/@generated], +"AsymmetricUnitAtomsCount"->Length@atomDataMapUnitCell +|>]; + +crystalCopy + +] + + +(* ::Input::Initialization:: *) +SetupDensityHKL::odd="supercell expansion (n) should be odd"; +SetupDensityHKL[mpid_String,n_Integer:1,hklMax_Integer:3,radiusFactor:(_Real|_Integer):1/3]:=Module[{crystalData,pg,latticeParameters,\[ScriptCapitalE],\[ScriptF]tmp,R,R1,R2,R3,\[ScriptCapitalO],\[ScriptCapitalE]Unique,\[ScriptF],rKey,r,\[ScriptCapitalE]Pos,\[ScriptCapitalU],\[ScriptCapitalU]pts,reflectionList,hklList,\[ScriptCapitalP],\[ScriptCapitalR],rList,\[ScriptF]List,\[ScriptCapitalD],npts,\[ScriptCapitalA]Sym}, + +crystalData=ImportCrystalData2[mpid<>".cif",mpid,"OverwriteWarning"->False]; +(*ExpandCrystal[mpid,{n,n,n},"NewLabel"\[Rule]mpid<>"_2","DataFile"\[Rule]mpid<>".m"];(*Defaults to 1x1x1*)*) +crystalData=ExpandCrystal2[crystalData,{n,n,n}]; + +(*CrystalData=Import[mpid<>".m"];*) +{\[ScriptCapitalE],\[ScriptF]tmp}=(Values/@crystalData[[(*mpid<>"_2",*)"AtomData",;;,{"Element","FractionalCoordinates"}]])\[Transpose]; +pg=crystalData[[(*mpid,*)"SpaceGroup"]]; +latticeParameters=Values@crystalData[[(*mpid,*)"LatticeParameters"]]; +R=GetCrystalMetric[latticeParameters,ToCartesian->True]; +(*R=GetCrystalMetric[mpid,ToCartesian\[Rule]True];*) +\[ScriptF]=\[ScriptF]tmp . R; +If[!OddQ@n,Message[SetupDensityHKL::odd]]; +{R1,R2,R3}=R; +\[ScriptCapitalO]=Floor[n/2](R1+R2+R3); +\[ScriptF]=#-\[ScriptCapitalO]&/@\[ScriptF]; +\[ScriptCapitalE]Unique=DeleteDuplicates@\[ScriptCapitalE]; + +covalentRadius=<|"H"->3.1`2.*^-11,"He"->2.8`2.*^-11,"Li"->1.28`3.*^-10,"Be"->9.6`2.*^-11,"B"->8.5`2.*^-11,"C"->7.6`2.*^-11,"N"->7.1`2.*^-11,"O"->6.6`2.*^-11,"F"->5.7`2.*^-11,"Ne"->5.8`2.*^-11,"Na"->1.66`3.*^-10,"Mg"->1.41`3.*^-10,"Al"->1.21`3.*^-10,"Si"->1.11`3.*^-10,"P"->1.07`3.*^-10,"S"->1.05`3.*^-10,"Cl"->1.02`3.*^-10,"Ar"->1.06`3.*^-10,"K"->2.03`3.*^-10,"Ca"->1.76`3.*^-10,"Sc"->1.7`3.*^-10,"Ti"->1.6`3.*^-10,"V"->1.53`3.*^-10,"Cr"->1.39`3.*^-10,"Mn"->1.39`3.*^-10,"Fe"->1.32`3.*^-10,"Co"->1.26`3.*^-10,"Ni"->1.24`3.*^-10,"Cu"->1.32`3.*^-10,"Zn"->1.22`3.*^-10,"Ga"->1.22`3.*^-10,"Ge"->1.2`3.*^-10,"As"->1.19`3.*^-10,"Se"->1.2`3.*^-10,"Br"->1.2`3.*^-10,"Kr"->1.16`3.*^-10,"Rb"->2.2`3.*^-10,"Sr"->1.95`3.*^-10,"Y"->1.9`3.*^-10,"Zr"->1.75`3.*^-10,"Nb"->1.64`3.*^-10,"Mo"->1.54`3.*^-10,"Tc"->1.47`3.*^-10,"Ru"->1.46`3.*^-10,"Rh"->1.42`3.*^-10,"Pd"->1.39`3.*^-10,"Ag"->1.45`3.*^-10,"Cd"->1.44`3.*^-10,"In"->1.42`3.*^-10,"Sn"->1.39`3.*^-10,"Sb"->1.39`3.*^-10,"Te"->1.38`3.*^-10,"I"->1.39`3.*^-10,"Xe"->1.4`3.*^-10,"Cs"->2.44`3.*^-10,"Ba"->2.15`3.*^-10,"La"->2.07`3.*^-10,"Ce"->2.04`3.*^-10,"Pr"->2.03`3.*^-10,"Nd"->2.01`3.*^-10,"Pm"->1.99`3.*^-10,"Sm"->1.98`3.*^-10,"Eu"->1.98`3.*^-10,"Gd"->1.96`3.*^-10,"Tb"->1.94`3.*^-10,"Dy"->1.92`3.*^-10,"Ho"->1.92`3.*^-10,"Er"->1.89`3.*^-10,"Tm"->1.9`3.*^-10,"Yb"->1.87`3.*^-10,"Lu"->1.87`3.*^-10,"Hf"->1.75`3.*^-10,"Ta"->1.7`3.*^-10,"W"->1.62`3.*^-10,"Re"->1.51`3.*^-10,"Os"->1.44`3.*^-10,"Ir"->1.41`3.*^-10,"Pt"->1.36`3.*^-10,"Au"->1.36`3.*^-10,"Hg"->1.32`3.*^-10,"Tl"->1.45`3.*^-10,"Pb"->1.46`3.*^-10,"Bi"->1.48`3.*^-10,"Po"->1.4`3.*^-10,"At"->1.5`3.*^-10,"Rn"->1.5`3.*^-10,"Fr"->2.6`3.*^-10,"Ra"->2.21`3.*^-10,"Ac"->2.15`3.*^-10,"Th"->2.06`3.*^-10,"Pa"->2.`3.*^-10,"U"->1.96`3.*^-10,"Np"->1.9`3.*^-10,"Pu"->1.87`3.*^-10,"Am"->1.8`3.*^-10,"Cm"->1.69`3.*^-10|>; (*produced via Association[ElementData[#,"Abbreviation"]\[Rule]QUC@ElementData[#,"CovalentRadius"]&/@Range@96]*) + +rKey=covalentRadius[#]&/@\[ScriptCapitalE]Unique; +r=radiusFactor*ReplaceAll[\[ScriptCapitalE],Thread[\[ScriptCapitalE]Unique->rKey]]*1*^10(*conversion to Angstroms*); +\[ScriptCapitalE]Pos=PositionIndex@\[ScriptCapitalE]; +\[ScriptCapitalU]=RationalUnitCell[R,n]; + +reflectionList=ReflectionList@hklMax; +hklList=MergeSymmetryEquivalentReflections[pg,reflectionList]; +\[ScriptCapitalP]=MillerToPlane[#,R]&/@hklList; +\[ScriptCapitalR]=PlaneIntersection[\[ScriptCapitalP],\[ScriptCapitalU]]; +\[ScriptF]List=\[ScriptF][[#/.\[ScriptCapitalE]Pos]]&/@\[ScriptCapitalE]Unique; +rList=r[[#/.\[ScriptCapitalE]Pos]]&/@\[ScriptCapitalE]Unique; + +\[ScriptCapitalD]=MapThread[Rationalize@IsotropicMultinormal[#1,#2]&,{\[ScriptF]List,rList}]; +npts=Length@Subscript[hkl, list2]; +\[ScriptCapitalA]Sym=Area/@\[ScriptCapitalR]; (*/@\[ScriptCapitalR]*) +{\[ScriptCapitalD],\[ScriptCapitalR],\[ScriptCapitalP],\[ScriptCapitalA]Sym,\[ScriptF]List,rList,hklList,\[ScriptCapitalE]Unique,pg} +] + + +(* ::Input::Initialization:: *) +DistanceRadiusComparison[i_,j_,n_:3.99]:=Thread[##2]&,{ids,c}]; +r2=MapThread[#1/.Thread[Range@Length@#2->#2]&,{ids,r}]; +(*{c2,r2}={c,r};*) +(*{c2,r2,P}*) +(*\[ScriptCapitalI]b=MapThread[Table[AtomPolygonBallsIntersection[i,#1,#2],{i,P}]&,{c2,r2}];*) +\[ScriptCapitalI]b=MapThread[AtomPolygonBallsMap[P,#1,#2]&,{c2,r2}]; +(*\[ScriptCapitalI]b=Table[MapThread[If[#1\[LeftDoubleBracket]1\[RightDoubleBracket]\[NotEqual]{},Flatten@AtomPolygonBallsIntersection[{#2},#1\[LeftDoubleBracket]1\[RightDoubleBracket],#1\[LeftDoubleBracket]2\[RightDoubleBracket]],0]&,{i,P}],{i,{c2,r2}\[Transpose]}]*) +\[ScriptCapitalA]b=Total[#,{2}]&/@\[ScriptCapitalI]b +] + + +(* ::Input::Initialization:: *) +AtomProbabilityIntersection[\[ScriptCapitalD]_,P_]:=(*Parallel*)Table[Quiet[NIntegrate[PDF[i,{x,y,z}]/.PDF[0,{x,y,z}]->0(*for region distance filtering*),{x,y,z}\[Element]j,AccuracyGoal->10],{General::munfl,NIntegrate::slwcon,NIntegrate::precw}],{i,\[ScriptCapitalD]},{j,P}] + + +(* ::Input::Initialization:: *) +ProbabilityIntersection[\[ScriptCapitalD]_,\[ScriptCapitalR]_,\[ScriptCapitalP]_,n:(_Real|_Integer):3.99,radiusFactor:(_Real|_Integer):1/4]:=Module[{\[ScriptF]List,rList,distances,d,id,\[ScriptCapitalD]2,\[ScriptCapitalI]int,ids,\[ScriptCapitalA]int}, +\[ScriptF]List=\[ScriptCapitalD][[;;,;;,1]]; +rList=\[ScriptCapitalD][[;;,;;,2,1,1]][[;;,1]];(*assumes isotropic radius and assumes constant radius for a particular element*) +d=Table[RegionDistance[i,j],{i,\[ScriptCapitalP]},{j,#}]&/@\[ScriptF]List; +TF=MapThread[DistanceRadiusComparison[#1,#2,n]&,{d,rList}]; +ids=TruePosition[#]&/@TF; +\[ScriptCapitalD]2=MapThread[#1/.Thread[Range@Length@#2->#2]&,{ids,\[ScriptCapitalD]}]/.{}->0; +\[ScriptCapitalI]int=Table[MapThread[Flatten@AtomProbabilityIntersection[#1,{#2}]&,{i,\[ScriptCapitalR]}],{i,\[ScriptCapitalD]2}]; +ids=Position[\[ScriptCapitalI]int,Except[_Real|_Integer],{3},Heads->False]; +ReplacePart[\[ScriptCapitalI]int,ids->0]; +\[ScriptCapitalA]int=Total[#,{2}]&/@\[ScriptCapitalI]int; +\[ScriptCapitalA]int=\[ScriptCapitalA]int \[Pi] (1/radiusFactor rList)^2(*weight the probabilities by the area of the atoms*) +] + + +(* ::Input::Initialization:: *) +GetFullHKL[valsIn_,hklIn_,pg_]:=Module[{max,\[ScriptR],pi,reflectionList,hklList,valsReplace,n,npts,vals2,hklListSub,valsSub}, +max=Max@hklIn; +\[ScriptR]=ReflectionList@max; +pi=PositionIndex[ToStandardSetting[pg,#]&/@\[ScriptR]];(*degenerate sets*) +hklList=MergeSymmetryEquivalentReflections[pg,\[ScriptR]]; +valsReplace=Thread[Keys@PositionIndex[hklList]->valsIn]/.pi; +n=Length/@Keys@valsReplace; +npts=Length@\[ScriptR]; +vals2=Range@npts/.(Thread[Keys@#->Values@#]&/@valsReplace//Flatten); +{\[ScriptR],vals2} +] + + +(* ::Input::Initialization:: *) +DensityHKL::mpidNotString="A string was expected for mpid."; +DensityHKL[mpid_:"mp-134",n_Integer:1,hklMax_Integer:3,dFactor:(_Real|_Integer):0.01,radiusFactorIn:(_Real|_Integer):0,OptionsPattern[{"Method"->"PDF","Output"->"PackingFraction","PrintID"->False,"PrintMethod"->False}]]:=Module[{method,radiusFactor,\[ScriptCapitalD],\[ScriptCapitalR],\[ScriptCapitalP],\[ScriptCapitalA]Sym,\[ScriptF]List,rList,hklList,\[ScriptCapitalE]Unique,\[ScriptCapitalA]out,\[ScriptCapitalA]outn,\[ScriptCapitalA]outCt,pg,hklFull,outCt,outn,\[ScriptCapitalA]fulln,\[ScriptCapitalA]fullCt}, +(*If[Head@mpid=!=String,Message[DensityHKL::mpidNotString];Abort[]];*) +If[OptionValue["PrintID"],Print@mpid]; +method=OptionValue["Method"]; +If[OptionValue["PrintMethod"],Print@method]; +If[radiusFactorIn==0,Switch[method,"PDF",radiusFactor=1/4,"HardSphere",radiusFactor=1],radiusFactor=radiusFactorIn]; +{\[ScriptCapitalD],\[ScriptCapitalR],\[ScriptCapitalP],\[ScriptCapitalA]Sym,\[ScriptF]List,rList,hklList,\[ScriptCapitalE]Unique,pg}=SetupDensityHKL[mpid,n,hklMax,radiusFactor]; +Switch[method, +"PDF",\[ScriptCapitalA]out=ProbabilityIntersection[\[ScriptCapitalD],\[ScriptCapitalR],\[ScriptCapitalP],dFactor], +"HardSphere",\[ScriptCapitalA]out=PolygonBallsIntersection[\[ScriptCapitalR],\[ScriptF]List,rList,dFactor] +]; +\[ScriptCapitalA]outn=#/\[ScriptCapitalA]Sym&/@\[ScriptCapitalA]out;(*normalize by lattice plane area*) +\[ScriptCapitalA]outCt=MapThread[#1/(\[Pi] #2^2)&,{\[ScriptCapitalA]outn,rList[[;;,1]]}]; +outn=GetFullHKL[#,hklList,pg]&/@\[ScriptCapitalA]outn; +hklFull=outn[[1,1]];(*extract a single hklListSub*) +\[ScriptCapitalA]fulln=outn[[;;,2]];(*extract just valsSub*) +outCt=GetFullHKL[#,hklList,pg]&/@\[ScriptCapitalA]outCt; +\[ScriptCapitalA]fullCt=outCt[[;;,2]];(*extract just valsSub*) +{\[ScriptCapitalA]outn,\[ScriptCapitalA]outCt,hklList,\[ScriptCapitalA]fulln,\[ScriptCapitalA]fullCt,hklFull,\[ScriptCapitalE]Unique} +] + + +(* ::Input::Initialization:: *) +PlotSetup[mpid_,n_:3,hklMax_:4]:=Module[{pg,reflectionList,hklList}, +crystalData=ImportCrystalData2[mpid<>".cif",mpid,"OverwriteWarning"->False]; +crystalData=ExpandCrystal2[crystalData,{n,n,n}]; +pg=crystalData[["SpaceGroup"]]; +reflectionList=ReflectionList@hklMax; +hklList=MergeSymmetryEquivalentReflections[pg,reflectionList]; +{hklList,reflectionList,pg} +] + + +(* ::Code::Initialization::Bold:: *) +PlotSymmetrizedHKL[vals_,hkl_,o_Integer:1,legendLabel_:"\!\(\*FractionBox[SubscriptBox[\(\[ScriptCapitalA]\), \(\[Integral]\)], SubscriptBox[\(\[ScriptCapitalA]\), \(hkl\)]]\)(\!\(\*SuperscriptBox[\(\[CapitalARing]\), \(-2\)]\))"]:=Module[{max,c,g1}, +max=Max@hkl; +c=ColorData[{"AvocadoColors",{0,Max@vals}}]; +g1=Graphics3D[{Opacity[o],PointSize[0.05],Point[hkl,VertexColors->c/@vals]},Axes->True,BoxRatios->Automatic,AxesLabel->{"h","k","l"},PlotRange->ConstantArray[{0,max},3],ImageSize->Medium]; +Show[Legended[g1,BarLegend[{c,c[[3]]},LegendLabel->legendLabel]],Graphics3D@{FaceForm[None],ConvexHullMesh@hkl}] +] + + +(* ::Code::Initialization::Bold:: *) +PlotFullHKL[valsIn_,hklIn_,pg_,o_Integer:0.75,legendLabel_:"\!\(\*FractionBox[SubscriptBox[\(\[ScriptCapitalA]\), \(\[Integral]\)], SubscriptBox[\(\[ScriptCapitalA]\), \(hkl\)]]\)(\!\(\*SuperscriptBox[\(\[CapitalARing]\), \(-2\)]\))"]:=Module[{c,max,hklFull,vals2,\[ScriptR],hklListSub,valsSub,g1}, +c=ColorData[{"AvocadoColors",{0,Max@valsIn}}]; +max=Max@hklIn; +{\[ScriptR],vals2}=GetFullHKL[valsIn,hklIn,pg]; +{hklListSub,valsSub}=DeleteCases[{\[ScriptR],vals2}\[Transpose],{{x_,y_,z_},_}/;AllTrue[Thread[{x,y,z}>0],TrueQ]]\[Transpose];(*remove a corner of the cube for visualization*) +g1=Graphics3D[{Opacity[o],PointSize[0.08],Point[hklListSub,VertexColors->c/@valsSub]},Axes->True,BoxRatios->Automatic,AxesLabel->{"h","k","l"},ViewPoint->{max,0.6max,0.6max},AxesEdge->{{1,-1},{1,-1},{1,-1}}, PlotRange->ConstantArray[{-max,max},3],ImageSize->Medium]; +Show[Legended[g1,BarLegend[{c,c[[3]]},LegendLabel->legendLabel]],Graphics3D@{EdgeForm[White],FaceForm[None],ConvexHullMesh@Permutations[{0,0,0,max,max,max},{3}](*ConvexHullMesh@Complement[hklList,hklListSub]*)}] +] + + +(* ::Input::Initialization:: *) +PlotSymmetrizedFullHKL[\[ScriptCapitalA]outNorm:_,hklList:_,pg_,\[ScriptCapitalE]Unique:_,tag_:"\[Integral]"]:=Module[{str,x}, +str[x_]:=StringTemplate["\!\(\*FractionBox[SubscriptBox[\(\[ScriptCapitalA]\), \(`tag`, `element`\)], SubscriptBox[\(\[ScriptCapitalA]\), \(hkl\)]]\)(\!\(\*SuperscriptBox[\(\[CapitalARing]\), \(-2\)]\))"][<|"element"->x,"tag"->tag|>]; +Grid[MapThread[{PlotSymmetrizedHKL[#1,hklList,str[#2]][[1]],PlotFullHKL[#1,hklList,pg,str[#2]]}&, +{\[ScriptCapitalA]outNorm,\[ScriptCapitalE]Unique}]] +] + + +(* ::Input::Initialization:: *) +End[]; +Protect@@Names[Evaluate[Context[]<>"*"]]; +Protect[Evaluate[Context[]<>"*"]]; +EndPackage[]; + + +(* ::Input::Initialization:: *) 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