testCoincidentRotations.cpp

This example demonstrates the generation of CSLs using rotations about an axis of a 3D lattice

1. Define types

       using VectorDimI = LatticeCore<3>::VectorDimI;
       using VectorDimD = LatticeCore<3>::VectorDimD;
       using IntScalarType = LatticeCore<3>::IntScalarType;

2. Instantiate a lattice \(\mathcal A\)

       const auto A(TextFileParser("bicrystal_3d.txt").readMatrix<double,3,3>("A",true));
       Lattice<3> lattice(A);

3. Specify an axis in the form of a reciprocal lattice direction

       const auto axis (TextFileParser("bicrystal_3d.txt").readMatrix<double,3,1>("axis",true));
       ReciprocalLatticeVector<3> rv(axis,lattice);
       std::cout << "Miller indices of the tilt axis plane = " << std::endl;
       std::cout << rv << std::endl;

4. Generate a family of rotations about the given axis such that lattices \(\mathbf R\mathcal A\) and \(\mathbf R\mathcal A\) share a coincidence relation

       const auto& coincidentRotations= lattice.generateCoincidentLattices(rv);

5. Loop over the the above family of rotations and carry out SNF bicrystallography of bicrystals \(\mathcal A \cup \mathbf R\mathcal A\).

       for (const auto& rotation : coincidentRotations)
       {
           try
           {
               double theta= acos((rotation.trace()-1.0)/2.0)*180/M_PI;
               std::cout << "angle = " << theta << "; ";
               BiCrystal<3> bc(lattice,Lattice<3>(lattice.latticeBasis,rotation),false);
               std::cout << "Sigma = " << bc.sigma << std::endl;
           }
           catch(std::runtime_error& e)
           {
               std::cout << e.what() << "Moving on ..." << std::endl;
           }
       }

Full code:

#include <LatticeModule.h>
#include <TextFileParser.h>
 
using namespace gbLAB;
 
int main()
{
    using VectorDimI = LatticeCore<3>::VectorDimI;
    using VectorDimD = LatticeCore<3>::VectorDimD;
    using IntScalarType = LatticeCore<3>::IntScalarType;
    const auto A(TextFileParser("bicrystal_3d.txt").readMatrix<double,3,3>("A",true));
    Lattice<3> lattice(A);
    const auto axis (TextFileParser("bicrystal_3d.txt").readMatrix<double,3,1>("axis",true));
    ReciprocalLatticeVector<3> rv(axis,lattice);
    std::cout << "Miller indices of the tilt axis plane = " << std::endl;
    std::cout << rv << std::endl;
    const auto& coincidentRotations= lattice.generateCoincidentLattices(rv);
    for (const auto& rotation : coincidentRotations)
    {
        try
        {
            double theta= acos((rotation.trace()-1.0)/2.0)*180/M_PI;
            std::cout << "angle = " << theta << "; ";
            BiCrystal<3> bc(lattice,Lattice<3>(lattice.latticeBasis,rotation),false);
            std::cout << "Sigma = " << bc.sigma << std::endl;
        }
        catch(std::runtime_error& e)
        {
            std::cout << e.what() << "Moving on ..." << std::endl;
        }
    }
    return 0;
}