"Any idea why the plot comes up all black?"
Because your mesh is extremely dense. I have increased the mesh density by 5 times, so to can see the corresponding result.
Also, note that you should not hard code values, as that is likely to cause issues - In this case while defining Z. And you can use logical indexing instead of find(), as it is more efficient.
x = -1:2*5/511:1;
[X,Y] = meshgrid(x);
R = sqrt(X.^2 + Y.^2);
Phi = atan2(X,Y);
%Define Z according to the size of R, instead of hard-coding
Z = zeros(size(R));
%logical indexing
index1 = (Phi<pi/20 & Phi>-pi/20);
Z(index1)=6;
index2 = (R<0.0142);
Z(index2)=50;
index3 = (R>0.425);
Z(index3)=0;
surf(X,Y,Z)
colorbar
%view(2)
