testGb.cpp

This example demonstrates the computation of step heights and the use of Gb class

1. Initialize two lattices

       const auto A(TextFileParser("bicrystal_2d.txt").readMatrix<double,2,2>("A",true));
       const auto B(TextFileParser("bicrystal_2d.txt").readMatrix<double,2,2>("B",true));
       const auto F(TextFileParser("bicrystal_2d.txt").readMatrix<double,2,2>("F",true));
    
       Lattice<2> L1(A);
       Lattice<2> L2(B,F);

2. Form the bicrystal

           BiCrystal<2> bc(L1,L2);

3. Define the grain boundary normal (w.r.t lattice 2) and form the GB

           ReciprocalLatticeVector<2> rvec(L2);
           rvec << 1,1;
           ReciprocalLatticeDirection<2> n(rvec);
           Gb<2> gb(bc,n);

4. Define the Burgers vector \(b\) of a disconnection and compute the two step heights, \(h_{\mathcal A}\) and \(h_{\mathcal B}\).

           LatticeVector<2> b(bc.dscl);
           b << 1,1;
           std::cout << "Step height A: ";
           double stepHeightA= gb.stepHeightA(b);
           std::cout << stepHeightA << std::endl;
           std::cout << "Step height B: ";
           double stepHeightB= gb.stepHeightB(b);
           std::cout << stepHeightB << std::endl;

5. Compute the CSL plane spacing \(H\) parallel to the grain boundary

           auto dir= gb.bc.getReciprocalLatticeDirectionInC(n.reciprocalLatticeVector());
           double cslPlaneSpacing= dir.planeSpacing();

6. Check the conditions: \( \mod(h_{\mathcal A} - h_{\mathcal B} - \textbf{b} \cdot \hat{\textbf{n}}_{\mathcal A}, H) = 0 \), where \(\hat{\textbf{n}}_{\mathcal A}\) and \(\hat{\textbf{n}}_{\mathcal B}\) are the outward unit normals to lattices \(\mathcal A\) and \(\mathcal B\), respectively.

           double error= abs(stepHeightA-stepHeightB - b.cartesian().dot(gb.nA.cartesian().normalized()));
           error= std::remainder(error,cslPlaneSpacing);
    
           if((gb.nA.cartesian().normalized()+gb.nB.cartesian().normalized()).norm() > 1e-5)
               throw std::runtime_error("Cartesian coordinates of normalized nA and nB are not anti-parallel");
           if(error > 1e-6)
               throw std::runtime_error("Error in step height calculation");

Full code:

#include <LatticeModule.h>
#include <TextFileParser.h>
 
using namespace gbLAB;
int main()
{
    const auto A(TextFileParser("bicrystal_2d.txt").readMatrix<double,2,2>("A",true));
    const auto B(TextFileParser("bicrystal_2d.txt").readMatrix<double,2,2>("B",true));
    const auto F(TextFileParser("bicrystal_2d.txt").readMatrix<double,2,2>("F",true));
 
    Lattice<2> L1(A);
    Lattice<2> L2(B,F);
    try
    {
        BiCrystal<2> bc(L1,L2);
        ReciprocalLatticeVector<2> rvec(L2);
        rvec << 1,1;
        ReciprocalLatticeDirection<2> n(rvec);
        Gb<2> gb(bc,n);
        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<2> b(bc.dscl);
        b << 1,1;
        std::cout << "Step height A: ";
        double stepHeightA= gb.stepHeightA(b);
        std::cout << stepHeightA << std::endl;
        std::cout << "Step height B: ";
        double stepHeightB= gb.stepHeightB(b);
        std::cout << stepHeightB << std::endl;
        auto dir= gb.bc.getReciprocalLatticeDirectionInC(n.reciprocalLatticeVector());
        double cslPlaneSpacing= dir.planeSpacing();
        double error= abs(stepHeightA-stepHeightB - b.cartesian().dot(gb.nA.cartesian().normalized()));
        error= std::remainder(error,cslPlaneSpacing);
 
        if((gb.nA.cartesian().normalized()+gb.nB.cartesian().normalized()).norm() > 1e-5)
            throw std::runtime_error("Cartesian coordinates of normalized nA and nB are not anti-parallel");
        if(error > 1e-6)
            throw std::runtime_error("Error in step height calculation");
        auto nC= gb.bc.getReciprocalLatticeDirectionInC(gb.nA.reciprocalLatticeVector());
        auto planeParallelBasis= bc.csl.planeParallelLatticeBasis(nC,true);
        std::vector<LatticeVector<2>> boxVectors;
        boxVectors.push_back(planeParallelBasis[0].latticeVector());
        boxVectors.push_back(planeParallelBasis[1].latticeVector());
        gb.box(boxVectors,0.9,1,"gb.txt", true);
 
    }
    catch(std::runtime_error& e)
    {
        std::cout << e.what() << std::endl;
        return -1;
    }
    return 0;
}