This examples demonstrates the construction of a grain boundary in a 3D bicrystal. We will construct a [111] tilt \(\Sigma 273\) - STGB (5 6 -11) and an ATGB (17 23 -40)(145 136 -281).

Initialize the first lattice L1
Eigen::Matrix3d A;

A << 0.0, 0.5, 0.5, 0.5, 0.0, 0.5, 0.5, 0.5, 0.0;

Lattice<dim> L1(A);
Define the tilt axis \([1\,1\,1]\) as a reciprocal vector in L1
Eigen::Vector3d axis;

axis << 1, 1, 1;

ReciprocalLatticeVector<dim> rv(

L1.reciprocalLatticeDirection(axis).reciprocalLatticeVector());
Form the second lattice L2 by rotating L1 about the tilt axis
double angle = 6.0089831977661480877 * std::numbers::pi / 180;

Eigen::AngleAxisd rotation(angle, axis.normalized());

Lattice<dim> L2(A, rotation.matrix());
Define the grain boundary normal (w.r.t lattice 1) and form the GB
ReciprocalLatticeVector<dim> normal(L1);

normal << 17, 23, -40;

// normal << 5,6,-11;

Gb<dim> gb(bc, normal);
To print, construct a grain boundary bounded by a box formed by three CSL vectors - period vector and vectors along the tilt axis and the grain boundary normal. Period vector is the shortest CSL vector normal to the tilt axis and the grain boundary normal.
1. Calculate the period vector (periodC). glideA is a vector in lattice L1, and periodC is the shortest CSL vector along glideA.
  LatticeVector<dim> glideA(
  
  rv.cross(gb.nA.reciprocalLatticeVector()).latticeVector());
  
  LatticeVector<dim> periodC(
  
  bc.getLatticeDirectionInC(glideA).latticeVector());
2. Calculate the CSL vector along the normal (normalC). normalA is a vector in lattice L1, and normalC is the shortest CSL vector along normalA.
  auto basis = bc.csl.planeParallelLatticeBasis(
  
  gb.bc.getReciprocalLatticeDirectionInC(gb.nA.reciprocalLatticeVector()),
  
  true);
  
  LatticeVector<dim> nonParallelC(basis[0].latticeVector());
3. Calculate the CSL vector along the tilt axis (vectorAlongAxisC). vectorAlongAxisA is a vector in lattice L1, and vectorAlongAxisC is the shortest CSL vector along vectorAlongAxisA.
  LatticeVector<dim> vectorAlongAxisA(
  
  bc.A.latticeDirection(rv.cartesian()).latticeVector());
  
  LatticeVector<dim> vectorAlongAxisC(
  
  bc.getLatticeDirectionInC(vectorAlongAxisA).latticeVector());
Form the box vectors and output the grain boundary to a file
std::vector<LatticeVector<dim>> boxVectors;

boxVectors.push_back(nonParallelC);

boxVectors.push_back(periodC);

boxVectors.push_back(vectorAlongAxisC);

std::cout << "Input box vectors = " << std::endl;

std::cout << boxVectors[0].cartesian().transpose() << std::endl;

std::cout << boxVectors[1].cartesian().transpose() << std::endl;

std::cout << boxVectors[2].cartesian().transpose() << std::endl;

gb.box(boxVectors, 0.5, 2, "gb.txt", true);

std::cout << "Output box vectors = " << std::endl;

std::cout << boxVectors[0].cartesian().transpose() << std::endl;

std::cout << boxVectors[1].cartesian().transpose() << std::endl;

std::cout << boxVectors[2].cartesian().transpose() << std::endl;

Full code:

#include "../../include/IO/TextFileParser.h"
#include "../../include/Lattices/LatticeModule.h"
#include <numbers>
 
/* This examples demonstrates the construction of a grain boundary in a 3D
bicrystal.
 * The following is a snippet from the output generated by testGenerateGBs. In
this example,
 * we will construct a [111] tilt Sigma 273 - STGB (5 6 -11) and an
 * ATGB (17  23 -40)(145  136 -281).
Lattice A =
  0 0.5 0.5
0.5   0 0.5
0.5 0.5   0
maxis=
1
1
1
Cartesian coordinates of axis =
1 1 1
###################################################
Misorientation angle = 6.0089831977661480877; Sigma = 273
 
Lattice B =
0.001831501831501824995  0.52930402930402931094  0.46886446886446891957
 0.46886446886446891957 0.001831501831501824995  0.52930402930402931094
 0.52930402930402931094  0.46886446886446891957 0.001831501831501824995
 
Parallel CSL basis Cp=
                    272.5                      -7.5                    -136.5
                      145                        -8                    -136.5
                    128.5                       0.5 8.8817841970012523234e-16
 
Parallel DSCL basis Dp =
      0.998168498168498175                       -7.5                        0.5
    0.53113553113553113594                         -8                        0.5
    0.47069597069597068906                        0.5 -3.2534008047623634856e-18
 
Reduced DSCL basis vectors:
d1 =  0.001831501831501824995 -0.031135531135531135938  0.029304029304029310943
Integer coordinates of d1:-1  1 17
 
d2 =   0.02930402930402919992  0.001831501831501824995 -0.031135531135531024916
Integer coordinates of d2:-16  15 257
 
Reduced shift vectors:
s1 = 0.0018315018315023801065    0.4688644688644695302   0.52930402930402986605
s2 =   0.52930402930402831174 0.0018315018315036013519   0.46886446886445387605
 
GBs of varying inclination (measured with respect to the first grain boundary)
-----------------------------------------------------------------------------
-- CAUTION: The integer coordinates of GB normals are w.r.t the reciprocal --
--          basis of the primitive unit cell.                              --
-----------------------------------------------------------------------------
1) Inclination = 0
nA =   5   6 -11
nB =   6   5 -11
GB period = 11.68332144554794283
CSL plane distance (Height)= 3.3726843908079144896
Glide disconnection Burgers vector =   0.031135531135532801272
-0.02930402930402919992 -0.0018315018315027131734; norm =
0.042796049251092468935 Step height of glide disconnection =
0.40768712416676056165 Step height of non-glide disconnection 1=
0.22237479499852241815 Step height of non-glide disconnection 2=
0.18531232916825057799
-----------------------------------------------------------------------------
2) Inclination = 1.9451190845039707522
nA =  17  23 -40
nB =  145  136 -281
GB period = 99.36548696604899078
CSL plane distance (Height)= 0.39655776945623399943
Glide disconnection Burgers vector =  0.80769230769237765344
-0.7307692307690558664 -0.07692307692309441336; norm = 1.0919284281982737372
Step height of glide disconnection = 0.091513331645593942731
Step height of non-glide disconnection 1= -0.18593184794961481465
Step height of non-glide disconnection 2= 0.19755258845548662183
 
*/
 
using namespace oILAB;
int main() {
  const int dim = 3;
  Eigen::Matrix3d A;
  A << 0.0, 0.5, 0.5, 0.5, 0.0, 0.5, 0.5, 0.5, 0.0;
  Lattice<dim> L1(A);
  Eigen::Vector3d axis;
  axis << 1, 1, 1;
  ReciprocalLatticeVector<dim> rv(
      L1.reciprocalLatticeDirection(axis).reciprocalLatticeVector());
  double angle = 6.0089831977661480877 * std::numbers::pi / 180;
  Eigen::AngleAxisd rotation(angle, axis.normalized());
  Lattice<dim> L2(A, rotation.matrix());
  try {
    BiCrystal<dim> bc(L1, L2);
    std::cout << "Sigma = " << bc.sigma << std::endl;
    ReciprocalLatticeVector<dim> normal(L1);
    normal << 17, 23, -40;
    // normal << 5,6,-11;
    Gb<dim> gb(bc, normal);
    std::cout << "Miller indices w.r.t A: ";
    std::cout << gb.nA << std::endl;
    std::cout << "Miller indices w.r.t B: ";
    std::cout << gb.nB << std::endl;
 
    LatticeVector<dim> glideA(
        rv.cross(gb.nA.reciprocalLatticeVector()).latticeVector());
    LatticeVector<dim> periodC(
        bc.getLatticeDirectionInC(glideA).latticeVector());
    auto basis = bc.csl.planeParallelLatticeBasis(
        gb.bc.getReciprocalLatticeDirectionInC(gb.nA.reciprocalLatticeVector()),
        true);
    LatticeVector<dim> nonParallelC(basis[0].latticeVector());
    LatticeVector<dim> vectorAlongAxisA(
        bc.A.latticeDirection(rv.cartesian()).latticeVector());
    LatticeVector<dim> vectorAlongAxisC(
        bc.getLatticeDirectionInC(vectorAlongAxisA).latticeVector());
    std::vector<LatticeVector<dim>> boxVectors;
    boxVectors.push_back(nonParallelC);
    boxVectors.push_back(periodC);
    boxVectors.push_back(vectorAlongAxisC);
    std::cout << "Input box vectors = " << std::endl;
    std::cout << boxVectors[0].cartesian().transpose() << std::endl;
    std::cout << boxVectors[1].cartesian().transpose() << std::endl;
    std::cout << boxVectors[2].cartesian().transpose() << std::endl;
    gb.box(boxVectors, 0.5, 2, "gb.txt", true);
    std::cout << "Output box vectors = " << std::endl;
    std::cout << boxVectors[0].cartesian().transpose() << std::endl;
    std::cout << boxVectors[1].cartesian().transpose() << std::endl;
    std::cout << boxVectors[2].cartesian().transpose() << std::endl;
  } catch (std::runtime_error &e) {
    std::cout << e.what() << std::endl;
    return -1;
  }
  return 0;
}