Question

if the coordinates of a point are (1, 0,2) what will the miller index be? if the answer comes as (2, infinty, 1)

Answer 1

first of all, the miller indices refer to planes making intercepts on the axes, and not just to any random point of the lattice... do you see the fault in your question now...? and if we take the intercepts as (1,0,2), even then it is wrong... no plane can cut the x-axis at 1, z-axis at 2 and the "y-axis at 0"... no way... try drawing this weird plane and you will see the fault... the y-intercept could be anything but strictly can never be zero... the prof refers to a plane which does pass through the origin but did you notice, any plane which passes through the origin can never cut any of the three axes... of course we can shift the origin and can get those intercepts, but that is a completely different concept... I can see you have learnt the math of finding the miller indices properly, but the sense, we have to find it first friend... as the prof says, let the math work for you, you don't work for the math... i hope this will help... have fun...

Answer 2

diffrence between allotopy and polymorphism

Answer 3

If the plane intercepts the axis at 1, infinity and 1/2 then the miller indices would be (102) and would look like the diagram. A coordinate has no miller indices because the numbers you get from a point describe it's position perfectly, Miller indices allow you to visulaise a projection of the plane without having to draw/imagine multiple cells. You can spot a plane from a vector from a point by their brackets or, lack there of for a point.