Question

Using the simplified phase diagram, which substitutes straight lines for the curved lines typical of phase diagrams, write a MATLAB program that takes as input the mass percent of B and the temperature in units of degrees Celsius and returns the phases that may exist under those conditions. The equation of the line dividing the phases must be found in the program using polyfit. The program should produce a formatted output statement to the command window, similar to "For the composition of x% A, y% B and a temperature of T degrees Celsius, the phase is PHASE, " where x, y, T and Phase are replaced by the actual values. The program should also reproduce the graph as shown here with all phase division lines, and indicate the point entered by the user with a symbol. Your MATLAB program should include special notes if the provided conditions are on the eutectic line or at the eutectic point.

Answer 1

%Problem Statement: Take a user-set percent composition for a solution and
%its temperature, then determine its phase.

%Variables
%point11-point62 - reference points to calculate the phase lines
%point71-point72 - reference points for the eutectic point & line
%line1-line6 - coefficients for the phase lines
%m1-m6 - slope of the phase lines
%b1-b2 - y-intercepts of the phase lines
%xpf1-xpf6 - points to use for the phase lines
%ypf1-ypf6 - lines to divide the phases
%b - mass percent of B
%t - temperature of the solution [deg C]
%a - mass percent of A
%phase - phase of the solution based on percent B and temperature

clear
clc
close all

%Use polyfit to solve for the phase lines

point11=[0,15];
point12=[0,300];
line1=polyfit(point11,point12,1);
m1=line1(1);
b1=line1(2);
xpf1=linspace(min(point11),max(point11),100);
ypf1=m1*xpf1+b1;
point21=[0,15];
point22=[700,300];
line2=polyfit(point21,point22,1);
m2=line2(1);
b2=line2(2);
xpf2=linspace(min(point21),max(point21),100);
ypf2=m2*xpf2+b2;
point31=[0,50];
point32=[700,300];
line3=polyfit(point31,point32,1);
m3=line3(1);
b3=line3(2);
xpf3=linspace(min(point31),max(point31),100);
ypf3=m3*xpf3+b3;
point41=[50,100];
point42=[300,800];
line4=polyfit(point41,point42,1);
m4=line4(1);
b4=line4(2);
xpf4=linspace(min(point41),max(point41),100);
ypf4=m4*xpf4+b4;
point51=[100,85];
point52=[800,300];
line5=polyfit(point51,point52,1);
m5=line5(1);
b5=line5(2);
xpf5=linspace(min(point51),max(point51),100);
ypf5=m5*xpf5+b5;
point61=[85,100];
point62=[300,0];
line6=polyfit(point61,point62,1);
m6=line6(1);
b6=line6(2);
xpf6=linspace(min(point61),max(point61),100);
ypf6=m6*xpf6+b6;
point71=[15,85];
point72=[300,300];

%Allow the user to set the percent of B

b=input('Enter the mass percent of B: ');

%Return an error if the percent of B is not a valid number

if b<0 || b>100
    error('Please enter a value between 0 and 100.')
end

%Allow the user to set the temperature

t=input('Enter the temperature [deg C]: ');

%Solve for percent composition of A

a=100-b;

%Determine phase based on temperature and percent composition of B using
%the phase lines

if t<300
       if b<15 && t>m1*b+b1
           phase='alpha';
       elseif b<15 && t<m1*b+b1
           phase='alpha + beta';
       elseif b>=15 && b<=85
           phase='alpha + beta';
       elseif b>85 && t>m6*b+b6
           phase='beta';
       else phase='alpha + beta';
       end
elseif b<15
    if t<m2*b+b2
        phase='alpha';
    elseif t<m3*b+b3
        phase='alpha + Liquid';
    else phase='Liquid';
    end
elseif b>=15 && b<=50
    if t<m3*b+b3
        phase='alpha + Liquid';
    else phase='Liquid';
    end
elseif b>50 && b<=85
    if t<m4*b+b4
        phase='beta + Liquid';
    else phase='Liquid';
    end
else
    if t<m5*b+b5
        phase='beta';
    elseif t<m4*b+b4
        phase='beta + Liquid';
    else phase='Liquid';
    end
end

%Print out a message if the point falls on the eutectuc line or point

if b>=15 && b<=85 && t==300
    fprintf('The provided conditions fall on the eutectic line.\n')
end
if b==50 && t==300
    fprintf('The provided conditions fall on the eutectic point.\n')
end

%Output a formatted statement to display the phase

fprintf('For the composition of %0.2f%% A, %0.2f%% B and a temperature of %0.0f degrees Celsius, the phase is %s.\n',a,b,t,phase)

%Create a plot of the phase lines and the user's set point

figure('color','white')

%Set axes

axis([0 100 0 1000])

%Plot the phase lines, eutectic line, eutectic point, and the user's point

plot(xpf1,ypf1,'-b')
hold on
plot(xpf2,ypf2,'-b')
plot(xpf3,ypf3,'-b')
plot(xpf4,ypf4,'-b')
plot(xpf5,ypf5,'-b')
plot(xpf6,ypf6,'-b')
plot(point71,point72,'-k')
plot(b,t,'ro','MarkerFaceColor','r')

%Assign a title and axes labels

title('Phase Diagram of Elements A and B')
xlabel('Percent Composition of B')
ylabel('Temperature (T) [deg C]')

%Set scaling for the axes

set(gca,'XTick',0:10:100,'YTick',0:100:1000)

%Place the phase names on the graph

text(40,200,'alpha+beta')
text(45,600,'Liquid')
text(90,300,'beta')
text(3,300,'alpha')
text(15,375,'alpha + Liquid')
text(62,375,'beta + Liquid')

Enter the mass percent of B: 67 Enter the temperature [deg C]: 45 For the composition of 33.00% A, 67.00% B and a temperature of 45 degrees Celsius, the phase is alpha + beta. sh-4.3s