Peak intensities refers to how much the matter can be seen by comparing isotypic substances; substances with identical unit cell and atom distribution. ZrO2 and HfO2 are two examples.
While the peak positions are clearly as identical as the structure, there are some differences as to the intensities:
Two factors affecting peak intensity:
Atomic number of the atoms.
The Way X-Rays Interact With Matter
While crystal planes and lattices are helpful to understand the laws of diffraction, they are not what X-rays “see”. X-rays interact with the electrons around the atoms. What scatter them are regular patterns in the electron density distribution.
In the case of HfO2 and ZrO2 the different intensities are a consequence of the different electron number of Zr (40) and Hf (72). Generally, the heavier an element, that is, the more electrons it has the stronger it scatters X-rays.
Orientation of the particles in a powdered sample.
It is generally assumed that powder particles are randomly oriented (left below). Sometimes the particles are needles or platelets that are aomewhat aligned (right below). This has a very strong effect on intensities. Actually you might think of a single crystal as a perfectly oriented powder.