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A Young's modulus graphene nanoribbons

  1. Jul 4, 2016 #1
    Young’s modulus is given as the second derivative of the total energy with respect to the strain divided
    by the equilibrium volume.
    Can help me for the calculate equilibrium volume and young's modulus?
     
  2. jcsd
  3. Jul 4, 2016 #2
    Do you have the expression for energy as a function of strain figured out already?
     
  4. Jul 4, 2016 #3
    Matlab code for calculate band structure graphene nanoribbons under strain is below:

    clear;
    clc;
    close all;

    NU=12; % Number of atoms in unit cell
    Nbnd=4*NU; % number of bands
    q=0.03;
    w=0.41;
    aa=2.232*(1+q);
    a=3.866*(1+q);

    X(1)=1.9330*(1+q);
    Y(1)=0;

    xswitch = 0;

    for ixy=2:NU
    if mod(ixy,2)==1
    Y(ixy)=Y(ixy-1)+aa;
    else
    Y(ixy)=Y(ixy-1)+aa*sind(30);

    X(ixy) = xswitch;

    if (ixy+1)<=NU
    X(ixy+1)=xswitch;
    end

    if xswitch == 0
    xswitch =aa*cosd(30);
    else
    xswitch = 0;
    end
    end
    end

    for iz=1:NU
    if mod(iz,2)==1
    Z(iz)=0.46152;
    else
    Z(iz)=0;
    end

    end

    sho=0;
    for is=[0,-1,1]
    for ks=1:NU
    sho=sho+1;
    XT(sho)=X(ks)+is*a;
    YT(sho)=Y(ks);
    ZT(sho)=Z(ks);
    Ax(sho)=is*a;
    No(sho)=ks;
    end
    end
    figure(1)
    plot(XT,YT,'*')
    Ax=Ax/a;


    for ik=1:101
    K(ik)=(-pi+(ik-1)*((2*pi)/100))*(1-q);

    H=H0(Nbnd);

    for is=1:NU
    for js=1:sho
    dis=sqrt(((XT(is)-XT(js))^2)+((YT(is)-YT(js))^2));
    if abs(dis-2.232)<0.1 & abs(No(is)-No(js))>0
    l=(XT(is)-XT(js))/dis;
    m=(YT(is)-YT(js))/dis;
    n=(ZT(is)-ZT(js))/dis;
    h1=hamiltonian1(l,m,n);
    h2=hamiltonian2(l,m,n);

    H((No(is)-1)*4+1:No(is)*4,(No(js)-1)*4+1:No(js)*4)=H((No(is)-1)*4+1:No(is)*4,(No(js)-1)*4+1:No(js)*4)+h1*exp(i*K(ik)*Ax(js))+h2*exp(i*K(ik)*Ax(js));

    end
    end

    end

    E(ik,1:Nbnd)=sort(real(eig(H)));


    pl(ik)=(ik-1)/100;

    end

    figure(2)
    plot(E)

    [V,D]=eig(H);
    f=diag(D);
    g=f<0;
    g1=f(g);
    r=sum(g1)
     
  5. Jul 4, 2016 #4
    So is this yes or no? :smile:
     
  6. Jul 4, 2016 #5

    jim mcnamara

    User Avatar

    Staff: Mentor

    A suggestion: learn about formatting code on PF. What you posted is HARD to read, IMO. And hopefully the real code does not look like what you posted.
     
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