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geant4/source/materials/src/G4CrystalUnitCell.cc
T
Gabriele Cosmo a3452e42ac Import Geant4 10.3.0 source tree
2016-12-09 12:35:28 +01:00

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//
// ********************************************************************
// * License and Disclaimer *
// * *
// * The Geant4 software is copyright of the Copyright Holders of *
// * the Geant4 Collaboration. It is provided under the terms and *
// * conditions of the Geant4 Software License, included in the file *
// * LICENSE and available at http://cern.ch/geant4/license . These *
// * include a list of copyright holders. *
// * *
// * Neither the authors of this software system, nor their employing *
// * institutes,nor the agencies providing financial support for this *
// * work make any representation or warranty, express or implied, *
// * regarding this software system or assume any liability for its *
// * use. Please see the license in the file LICENSE and URL above *
// * for the full disclaimer and the limitation of liability. *
// * *
// * This code implementation is the result of the scientific and *
// * technical work of the GEANT4 collaboration. *
// * By using, copying, modifying or distributing the software (or *
// * any work based on the software) you agree to acknowledge its *
// * use in resulting scientific publications, and indicate your *
// * acceptance of all terms of the Geant4 Software license. *
// ********************************************************************
//
//
//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
// 21-04-16, created by E.Bagli
//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
#include "G4CrystalUnitCell.hh"
#include "G4PhysicalConstants.hh"
#include <cmath>
G4CrystalUnitCell::G4CrystalUnitCell(G4double sizeA,
G4double sizeB,
G4double sizeC,
G4double alpha,
G4double beta,
G4double gamma,
G4int spacegroup):
theSpaceGroup(spacegroup),
theSize(G4ThreeVector(sizeA,sizeB,sizeC)),
theAngle(G4ThreeVector(alpha,beta,gamma))
{
nullVec = G4ThreeVector(0.,0.,0.);
theUnitBasis[0] = CLHEP::HepXHat;
theUnitBasis[1] = CLHEP::HepYHat;
theUnitBasis[2] = CLHEP::HepZHat;
theRecUnitBasis[0] = CLHEP::HepXHat;
theRecUnitBasis[1] = CLHEP::HepYHat;
theRecUnitBasis[2] = CLHEP::HepZHat;
cosa=std::cos(alpha), cosb=std::cos(beta), cosg=std::cos(gamma);
sina=std::sin(alpha), sinb=std::sin(beta), sing=std::sin(gamma);
cosar = (cosb*cosg-cosa)/(sinb*sing);
cosbr = (cosa*cosg-cosb)/(sina*sing);
cosgr = (cosa*cosb-cosg)/(sina*sinb);
theVolume = ComputeCellVolume();
theRecVolume = 1. / theVolume;
theRecSize[0] = sizeB * sizeC * sina / theVolume;
theRecSize[1] = sizeC * sizeA * sinb / theVolume;
theRecSize[2] = sizeA * sizeB * sing / theVolume;
theRecAngle[0] = std::acos(cosar);
theRecAngle[1] = std::acos(cosbr);
theRecAngle[2] = std::acos(cosgr);
G4double x3,y3,z3;
switch (GetLatticeSystem(theSpaceGroup)) {
case Amorphous:
break;
case Cubic: // Cubic, C44 set
break;
case Tetragonal:
break;
case Orthorhombic:
break;
case Rhombohedral:
theUnitBasis[1].rotateZ(gamma-CLHEP::halfpi); // X-Y opening angle
// Z' axis computed by hand to get both opening angles right
// X'.Z' = cos(alpha), Y'.Z' = cos(beta), solve for Z' components
x3=cosa, y3=(cosb-cosa*cosg)/sing, z3=std::sqrt(1.-x3*x3-y3*y3);
theUnitBasis[2] = G4ThreeVector(x3, y3, z3).unit();
break;
case Monoclinic:
theUnitBasis[2].rotateX(beta-CLHEP::halfpi); // Z-Y opening angle
break;
case Triclinic:
theUnitBasis[1].rotateZ(gamma-CLHEP::halfpi); // X-Y opening angle
// Z' axis computed by hand to get both opening angles right
// X'.Z' = cos(alpha), Y'.Z' = cos(beta), solve for Z' components
x3=cosa, y3=(cosb-cosa*cosg)/sing, z3=std::sqrt(1.-x3*x3-y3*y3);
theUnitBasis[2] = G4ThreeVector(x3, y3, z3).unit();
break;
case Hexagonal: // Tetragonal, C16=0
theUnitBasis[1].rotateZ(30.*CLHEP::deg); // X-Y opening angle
break;
default:
break;
}
for(auto i:{0,1,2}){
theBasis[i] = theUnitBasis[i] * theSize[i];
theRecBasis[i] = theRecUnitBasis[i] * theRecSize[i];
}
// Initialize sgInfo
/* at first some initialization for SgInfo */
/*
const T_TabSgName *tsgn = NULL;
SgInfo.MaxList = 192;
SgInfo.ListSeitzMx = malloc( SgInfo.MaxList * sizeof(*SgInfo.ListSeitzMx) );
// no list info needed here
SgInfo.ListRotMxInfo = NULL;
tsgn = FindTabSgNameEntry(SchoenfliesSymbols[theSpaceGroup], 'A');
// initialize SgInfo struct
InitSgInfo( &SgInfo );
SgInfo.TabSgName = tsgn;
if ( tsgn ){
SgInfo.GenOption = 1;
}
ParseHallSymbol( SchoenfliesSymbols[theSpaceGroup], &SgInfo );
CompleteSgInfo( &SgInfo );
Set_si( &SgInfo );
*/
}
//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
G4CrystalUnitCell::~G4CrystalUnitCell(){;}
//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
theLatticeSystemType G4CrystalUnitCell::GetLatticeSystem(G4int aGroup){
if( aGroup >= 1 && aGroup <= 2 ) {return Triclinic;}
else if(aGroup >= 3 && aGroup <= 15 ) {return Monoclinic;}
else if(aGroup >= 16 && aGroup <= 74 ) {return Orthorhombic;}
else if(aGroup >= 75 && aGroup <= 142) {return Tetragonal;}
else if(aGroup == 146 || aGroup == 148 ||
aGroup == 155 || aGroup == 160 ||
aGroup == 161 || aGroup == 166 ||
aGroup == 167) {return Rhombohedral;}
else if(aGroup >= 143 && aGroup <= 167) {return Hexagonal;}
else if(aGroup >= 168 && aGroup <= 194) {return Hexagonal;}
else if(aGroup >= 195 && aGroup <= 230) {return Cubic;}
return Amorphous;
}
//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
/*
theBravaisLatticeType G4CrystalUnitCell::GetBravaisLattice(G4int aGroup){
;
}
*/
//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
const G4ThreeVector& G4CrystalUnitCell::GetUnitBasis(G4int idx) const {
return (idx>=0 && idx<3 ? theUnitBasis[idx] : nullVec);
}
//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
const G4ThreeVector& G4CrystalUnitCell::GetBasis(G4int idx) const {
return (idx>=0 && idx<3 ? theBasis[idx] : nullVec);
}
//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
const G4ThreeVector& G4CrystalUnitCell::GetRecUnitBasis(G4int idx) const {
return (idx>=0 && idx<3 ? theRecUnitBasis[idx] : nullVec);
}
//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
const G4ThreeVector& G4CrystalUnitCell::GetRecBasis(G4int idx) const {
return (idx>=0 && idx<3 ? theRecBasis[idx] : nullVec);
}
//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
G4ThreeVector G4CrystalUnitCell::GetUnitBasisTrigonal(){
// Z' axis computed by hand to get both opening angles right
// X'.Z' = cos(alpha), Y'.Z' = cos(beta), solve for Z' components
G4double x3=cosa, y3=(cosb-cosa*cosg)/sing, z3=std::sqrt(1.-x3*x3-y3*y3);
return G4ThreeVector(x3, y3, z3).unit();
}
//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
G4bool G4CrystalUnitCell::FillAtomicUnitPos(G4ThreeVector& pos, std::vector<G4ThreeVector>& vecout){
// Just for testing the infrastructure
G4ThreeVector aaa = pos;
vecout.push_back(aaa);
vecout.push_back(G4ThreeVector(2.,5.,3.));
return true;
}
//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
G4bool G4CrystalUnitCell::FillAtomicPos(G4ThreeVector& posin, std::vector<G4ThreeVector>& vecout){
FillAtomicUnitPos(posin,vecout);
for(auto &vec:vecout){
vec.setX(vec.x()*theSize[0]);
vec.setY(vec.y()*theSize[1]);
vec.setZ(vec.z()*theSize[2]);
}
return true;
}
//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
G4bool G4CrystalUnitCell::FillElReduced(G4double Cij[6][6]) {
switch (GetLatticeSystem()) {
case Amorphous:
return FillAmorphous(Cij);
break;
case Cubic: // Cubic, C44 set
return FillCubic(Cij);
break;
case Tetragonal:
return FillTetragonal(Cij);
break;
case Orthorhombic:
return FillOrthorhombic(Cij);
break;
case Rhombohedral:
return FillRhombohedral(Cij);
break;
case Monoclinic:
return FillMonoclinic(Cij);
break;
case Triclinic:
return FillTriclinic(Cij);
break;
case Hexagonal: // Tetragonal, C16=0
return FillHexagonal(Cij);
break;
default:
break;
}
return false;
}
//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
G4bool G4CrystalUnitCell::FillAmorphous(G4double Cij[6][6]) const {
Cij[3][3] = 0.5*(Cij[0][0]-Cij[0][1]);
return true;
}
//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
G4bool G4CrystalUnitCell::FillCubic(G4double Cij[6][6]) const {
G4double C11=Cij[0][0], C12=Cij[0][1], C44=Cij[3][3];
for (size_t i=0; i<6; i++) {
for (size_t j=i; j<6; j++) {
if (i<3 && j<3) Cij[i][j] = (i==j) ? C11 : C12;
else if (i==j && i>=3) Cij[i][i] = C44;
else Cij[i][j] = 0.;
}
}
ReflectElReduced(Cij);
return (C11!=0. && C12!=0. && C44!=0.);
}
//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
G4bool G4CrystalUnitCell::FillTetragonal(G4double Cij[6][6]) const {
G4double C11=Cij[0][0], C12=Cij[0][1], C13=Cij[0][2], C16=Cij[0][5];
G4double C33=Cij[2][2], C44=Cij[3][3], C66=Cij[5][5];
Cij[1][1] = C11; // Copy small number of individual elements
Cij[1][2] = C13;
Cij[1][5] = -C16;
Cij[4][4] = C44;
ReflectElReduced(Cij);
// NOTE: Do not test for C16 != 0., to allow calling from Hexagonal
return (C11!=0. && C12!=0. && C13!=0. && C33!=0. && C44!=0. && C66!=0.);
}
//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
G4bool G4CrystalUnitCell::FillOrthorhombic(G4double Cij[6][6]) const {
// No degenerate elements; just check for all non-zero
ReflectElReduced(Cij);
G4bool good = true;
for (size_t i=0; i<6; i++) {
for (size_t j=i+1; j<3; j++)
good &= (Cij[i][j] != 0);
}
return good;
}
//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
G4bool G4CrystalUnitCell::FillRhombohedral(G4double Cij[6][6]) const {
G4double C11=Cij[0][0], C12=Cij[0][1], C13=Cij[0][2], C14=Cij[0][3];
G4double C15=Cij[0][4], C33=Cij[2][2], C44=Cij[3][3], C66=0.5*(C11-C12);
Cij[1][1] = C11; // Copy small number of individual elements
Cij[1][2] = C13;
Cij[1][3] = -C14;
Cij[1][4] = -C15;
Cij[3][5] = -C15;
Cij[4][4] = C44;
Cij[4][5] = C14;
// NOTE: C15 may be zero (c.f. rhombohedral(I) vs. (II))
return (C11!=0 && C12!=0 && C13!=0 && C14!=0. &&
C33!=0. && C44!=0. && C66!=0.);
}
//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
G4bool G4CrystalUnitCell::FillMonoclinic(G4double Cij[6][6]) const {
// The monoclinic matrix has 13 independent elements with no degeneracies
// Sanity condition is same as orthorhombic, plus C45, C(1,2,3)6
return (FillOrthorhombic(Cij) && Cij[0][5]!=0. && Cij[1][5]!=0. &&
Cij[2][5] != 0. && Cij[3][4]!=0.);
}
//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
G4bool G4CrystalUnitCell::FillTriclinic(G4double Cij[6][6]) const {
// The triclinic matrix has the entire upper half filled (21 elements)
ReflectElReduced(Cij);
G4bool good = true;
for (size_t i=0; i<6; i++) {
for (size_t j=i; j<6; j++) good &= (Cij[i][j] != 0);
}
return good;
}
//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
G4bool G4CrystalUnitCell::FillHexagonal(G4double Cij[6][6]) const {
Cij[0][5] = 0.;
Cij[4][5] = 0.5*(Cij[0][0] - Cij[0][1]);
return true;
}
//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
G4bool G4CrystalUnitCell::ReflectElReduced(G4double Cij[6][6]) const {
for (size_t i=1; i<6; i++) {
for (size_t j=i+1; j<6; j++) {
Cij[j][i] = Cij[i][j];
}
}
return true;
}
//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
G4double G4CrystalUnitCell::ComputeCellVolume(){
G4double a = theSize[0], b = theSize[1], c = theSize[2];
switch(GetLatticeSystem())
{
case Amorphous:
return 0.;
break;
case Cubic:
return a * a * a;
break;
case Tetragonal:
return a * a * c;
break;
case Orthorhombic:
return a * b * c;
break;
case Rhombohedral:
return a*a*a*std::sqrt(1.-3.*cosa*cosa+2.*cosa*cosa*cosa);
break;
case Monoclinic:
return a*b*c*sinb;
break;
case Triclinic:
return a*b*c*std::sqrt(1.-cosa*cosa-cosb*cosb-cosg*cosg*2.*cosa*cosb*cosg);
break;
case Hexagonal:
return std::sqrt(3.0)/2.*a*a*c;
break;
default:
break;
}
return 0.;
}
//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
G4double G4CrystalUnitCell::GetIntSp2(G4int h,
G4int k,
G4int l){
/* Reference:
Table 2.4, pag. 65
@Inbook{Ladd2003,
author="Ladd, Mark and Palmer, Rex",
title="Lattices and Space-Group Theory",
bookTitle="Structure Determination by X-ray Crystallography",
year="2003",
publisher="Springer US",
address="Boston, MA",
pages="51--116",
isbn="978-1-4615-0101-5",
doi="10.1007/978-1-4615-0101-5_2",
url="http://dx.doi.org/10.1007/978-1-4615-0101-5_2"
}
*/
G4double a = theSize[0], b = theSize[1], c = theSize[2];
G4double a2 = a*a, b2 = b*b, c2 = c*c;
G4double h2 = h*h, k2 = k*k, l2 = l*l;
G4double cos2a,sin2a,sin2b;
G4double R,T;
switch(GetLatticeSystem())
{
case Amorphous:
return 0.;
break;
case Cubic:
return a2 / ( h2+k2+l2 );
break;
case Tetragonal:
return 1.0 / ( (h2 + k2)/a2 + l2/c2 );
break;
case Orthorhombic:
return 1.0 / ( h2/a2 + k2/b2 + l2/c2 );
break;
case Rhombohedral:
cos2a=cosa*cosa; sin2a=sina*sina;
T = h2+k2+l2+2.*(h*k+k*l+h*l) * ((cos2a-cosa)/sin2a);
R = sin2a / (1. - 3*cos2a + 2.*cos2a*cosa);
return a*a / (T*R);
break;
case Monoclinic:
sin2b=sinb*sinb;
return 1./(1./sin2b * (h2/a2+l2/c2-2*h*l*cosb/(a*c)) + k2/b2);
break;
case Triclinic:
return 1./GetRecIntSp2(h,k,l);
break;
case Hexagonal:
return 1. / ( (4.*(h2+k2+h*k) / (3.*a2)) + l2/c2 );
break;
default:
break;
}
return 0.;
}
//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
G4double G4CrystalUnitCell::GetRecIntSp2(G4int h,
G4int k,
G4int l){
/* Reference:
Table 2.4, pag. 65
@Inbook{Ladd2003,
author="Ladd, Mark and Palmer, Rex",
title="Lattices and Space-Group Theory",
bookTitle="Structure Determination by X-ray Crystallography",
year="2003",
publisher="Springer US",
address="Boston, MA",
pages="51--116",
isbn="978-1-4615-0101-5",
doi="10.1007/978-1-4615-0101-5_2",
url="http://dx.doi.org/10.1007/978-1-4615-0101-5_2"
}
*/
G4double a = theRecSize[0], b = theRecSize[1], c = theRecSize[2];
G4double a2 = a*a, b2 = b*b, c2 = c*c;
G4double h2 = h*h, k2 = k*k, l2 = l*l;
switch(GetLatticeSystem())
{
case Amorphous:
return 0.;
break;
case Cubic:
return a2 * (h2+k2+l2);
break;
case Tetragonal:
return (h2+k2)*a2 + l2*c2 ;
break;
case Orthorhombic:
return h2*a2 + k2+b2 + h2*c2;
break;
case Rhombohedral:
return (h2+k2+l2+2.*(h*k+k*l+h*l) * cosar)*a2;
break;
case Monoclinic:
return h2*a2+k2*b2+l2*c2+2.*h*l*a*c*cosbr;
break;
case Triclinic:
return h2*a2+k2*b2+l2*c2+2.*k*l*b*c*cosar+2.*l*h*c*a*cosbr+2.*h*k*a*b*cosgr;
break;
case Hexagonal:
return (h2+k2+h*k)*a2 + l2*c2;
break;
default:
break;
}
return 0.;
}
//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
G4double G4CrystalUnitCell::GetIntCosAng(G4int h1,
G4int k1,
G4int l1,
G4int h2,
G4int k2,
G4int l2){
/* Reference:
Table 2.4, pag. 65
@Inbook{Kelly2012,
author="Anthony A. Kelly and Kevin M. Knowles",
title="Appendix 3 Interplanar Spacings and Interplanar Angles",
bookTitle="Crystallography and Crystal Defects, 2nd Edition",
year="2012",
publisher="John Wiley & Sons, Ltd.",
isbn="978-0-470-75014-8",
doi="10.1002/9781119961468",
url="http://onlinelibrary.wiley.com/book/10.1002/9781119961468"
}
*/
G4double a = theRecSize[0], b = theRecSize[1], c = theRecSize[2];
G4double a2 = a*a, b2 = b*b, c2 = c*c;
G4double dsp1dsp2;
switch(GetLatticeSystem())
{
case Amorphous:
return 0.;
break;
case Cubic:
return (h1*h2 + k1*k2 + l1+l2) / (std::sqrt(h1*h1 + k1*k1 + l1*l1) * std::sqrt(h2*h2 + k2*k2 + l2*l2));
break;
case Tetragonal:
dsp1dsp2 = std::sqrt(GetIntSp2(h1,k1,l1)*GetIntSp2(h2,k2,l2));
return 0. ;
break;
case Orthorhombic:
dsp1dsp2 = std::sqrt(GetIntSp2(h1,k1,l1)*GetIntSp2(h2,k2,l2));
return dsp1dsp2 * (h1*h2*a2 + k1*k2*a2 + l1*l2*c2);
break;
case Rhombohedral:
dsp1dsp2 = std::sqrt(GetIntSp2(h1,k1,l1)*GetIntSp2(h2,k2,l2));
return dsp1dsp2 * (h1*h2*a2 + k1*k2*b2 + l1*l2*c2+
(k1*l2+k2*l1)*b*c*cosar+
(h1*l2+h2*l1)*a*c*cosbr+
(h1*k2+h2*k1)*a*b*cosgr);
break;
case Monoclinic:
dsp1dsp2 = std::sqrt(GetIntSp2(h1,k1,l1)*GetIntSp2(h2,k2,l2));
return dsp1dsp2 * (h1*h2*a2 + k1*k2*b2 + l1*l2*c2+
(k1*l2+k2*l1)*b*c*cosar+
(h1*l2+h2*l1)*a*c*cosbr+
(h1*k2+h2*k1)*a*b*cosgr);
break;
case Triclinic:
dsp1dsp2 = std::sqrt(GetIntSp2(h1,k1,l1)*GetIntSp2(h2,k2,l2));
return dsp1dsp2 * (h1*h2*a2 + k1*k2*b2 + l1*l2*c2+
(k1*l2+k2*l1)*b*c*cosar+
(h1*l2+h2*l1)*a*c*cosbr+
(h1*k2+h2*k1)*a*b*cosgr);
break;
case Hexagonal:
dsp1dsp2 = std::sqrt(GetIntSp2(h1,k1,l1)*GetIntSp2(h2,k2,l2));
return dsp1dsp2 *( (h1*h2 + k1*k2 + 0.5*(h1*k2+k1*h2))*a2 + l1*l2*c2);
break;
default:
break;
}
return 0.;
}
//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
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