How to run this code? I dont know what I am missing?

Indium Composition (Variable Definition)

Lattice Constans

cInGaN =5.2142 ; c0GaN = 5.1864; c0InN = 5.7033;
aInGaN = 3.2112; a0GaN = 3.1890; a0InN = 3.5378;

Stiffness Constants

C13InN =6; C13GaN = 15.8;
C33InN = 12.1; C33GaN = 18.2;

 D = x*c0InN+(1-x)*c0GaN;
 E = x*C13InN+(1-x)*C13GaN;
 F = x*C33InN+(1-x)*C33GaN;
 G = x*cInGaN+(1-x)*c0GaN;
 H =(cInGaN-D)/D + 2*E*(aInGaN-G)/(F*G);
 solve (H,x);
 
 

[Geoff Hayes]

Mohammed - what should x be initialized to since you reference it when initializing D? Or is there some other problem that you are having with the code?

[Mohammed Najmi]

Thank you Geoff for the interaction. Actually I am trying to solvee for x. All other variables are constants.

How should I define it? I am novie in programming.

[Mohammed Najmi]

H should equal 0 and I want to solve for x

[Geoff Hayes]

Perhaps you need to define x as a syms like

syms x

cInGaN =5.2142 ; c0GaN = 5.1864; c0InN = 5.7033;
aInGaN = 3.2112; a0GaN = 3.1890; a0InN = 3.5378;

% etc.

Unfortunately, I don't have experince with the Symbolic Toolbox so can't say for certain if the above will help.

[Image Analyst]

I'm not sure I understand. For any x you give it, you get various values for D, E, F, G, and H, so what is there so solve for?

cInGaN =5.2142 ; c0GaN = 5.1864; c0InN = 5.7033;
aInGaN = 3.2112; a0GaN = 3.1890; a0InN = 3.5378;
C13InN =6; C13GaN = 15.8;
C33InN = 12.1; C33GaN = 18.2;

allx = linspace(-15, 10, 100);
for k = 1 : 100
	x = allx(k);
	D(k) = x * c0InN+(1-x) * c0GaN
	E(k) = x * C13InN+(1-x) * C13GaN
	F(k) = x * C33InN+(1-x) * C33GaN
	G(k) = x * cInGaN+(1-x) * c0GaN
	H(k) =(cInGaN-D(k))/D(k) + 2 * E(k) * (aInGaN-G(k))/(F(k) * G(k))
end
plot(allx, D, '-', 'LineWidth', 2);
hold on;
plot(allx, E, '-', 'LineWidth', 2);
plot(allx, F, '-', 'LineWidth', 2);
plot(allx, G, '-', 'LineWidth', 2);
plot(allx, H, '-', 'LineWidth', 2);
grid on;
legend('D', 'E', 'F', 'G', 'H');
title('D, E, F, G, and H vs. x', 'FontSize', 20);
xlabel('x', 'FontSize', 20);
ylabel('D, E, F, G, or H', 'FontSize', 20);

You say you're trying to solve for x, so in the above plot, which value of x do you think would be the solution you are seeking? There are 4 x values where H is zero. Do you want them all? If so try ismembertol().

Answer 1

[Image Analyst]

Try this to solve it numerically just by looking for the peak in H:

cInGaN =5.2142 ; c0GaN = 5.1864; c0InN = 5.7033;
aInGaN = 3.2112; a0GaN = 3.1890; a0InN = 3.5378;
C13InN =6; C13GaN = 15.8;
C33InN = 12.1; C33GaN = 18.2;

allx = linspace(-15, 10, 1000000);
for k = 1 : length(allx)
	x = allx(k);
	D(k) = x * c0InN+(1-x) * c0GaN;
	E(k) = x * C13InN+(1-x) * C13GaN;
	F(k) = x * C33InN+(1-x) * C33GaN;
	G(k) = x * cInGaN+(1-x) * c0GaN;
	H(k) =(cInGaN-D(k))/D(k) + 2 * E(k) * (aInGaN-G(k))/(F(k) * G(k));
end
plot(allx, D, '-', 'LineWidth', 2);
hold on;
plot(allx, E, '-', 'LineWidth', 2);
plot(allx, F, '-', 'LineWidth', 2);
plot(allx, G, '-', 'LineWidth', 2);
plot(allx, H, '-', 'LineWidth', 2);
grid on;
legend('D', 'E', 'F', 'G', 'H');
title('D, E, F, G, and H vs. x', 'FontSize', 20);
xlabel('x', 'FontSize', 20);
ylabel('D, E, F, G, or H', 'FontSize', 20);
H(H<0) = 0;
[peakValues, peakIndexes] = findpeaks(H)
allx(peakIndexes)
x1 = allx(peakIndexes(1)-1)
x2 = allx(peakIndexes(2)+1)
H(peakIndexes(1)-1)
H(peakIndexes(2)+1)
fprintf('H = 0 at x=%f and %f\n', x1, x2);

You'll see in the command window:

H = 0 at x=-10.033670 and 2.983618

[Mohammed Najmi]

Thank you so much for the great effort. All variables are dummy variablaes exept H. I need to solve the equation H to get 3 values of x since the equation will be in the third order, so I expect to have 3 roots of x. I was not sure about how there are two roots only. Thanks a lot again.

[Image Analyst]

If you expand the plotting region you see there is another root at -186.56.

[Mohammed Najmi]

Could you please help me to include that in the code.

I am really grateful for your support.

[Image Analyst]

Just change the limits in linspace() to include -186.56 and you'll see it.

cInGaN =5.2142 ; c0GaN = 5.1864; c0InN = 5.7033;
aInGaN = 3.2112; a0GaN = 3.1890; a0InN = 3.5378;
C13InN =6; C13GaN = 15.8;
C33InN = 12.1; C33GaN = 18.2;

allx = linspace(-200, 10, 100000);
for k = 1 : length(allx)
	x = allx(k);
	D(k) = x * c0InN+(1-x) * c0GaN;
	E(k) = x * C13InN+(1-x) * C13GaN;
	F(k) = x * C33InN+(1-x) * C33GaN;
	G(k) = x * cInGaN+(1-x) * c0GaN;
	H(k) =(cInGaN-D(k))/D(k) + 2 * E(k) * (aInGaN-G(k))/(F(k) * G(k));
end
plot(allx, D, '-', 'LineWidth', 2);
hold on;
plot(allx, E, '-', 'LineWidth', 2);
plot(allx, F, '-', 'LineWidth', 2);
plot(allx, G, '-', 'LineWidth', 2);
plot(allx, H, '-', 'LineWidth', 2);
grid on;
legend('D', 'E', 'F', 'G', 'H');
title('D, E, F, G, and H vs. x', 'FontSize', 20);
xlabel('x', 'FontSize', 20);
ylabel('D, E, F, G, or H', 'FontSize', 20);
fprintf('Done running %s.m.\n', mfilename);

[Mohammed Najmi]

Wonderful!! Thank you sooo much!!!!