First, I do not understand the values of 24-27? Which  unit is it? I only know x-ray density as result of the mass of atoms devided by the volume of the unit cell. Doping commonly has not a big impact because of the tiny concentration of these elements. The impact of a slight lattice parameter change (mainly caused by experimental errors during the XRD measurement) is commonly bigger.

The bulk density is an experimental value measured e.g. by a pycnometer. For an ideal crystal xray density and bulk density should be identical, but commonly the bulk density is smaller, again because of experimental errors, surface effects (tiny bubbles), possible vacancies, dislocations. Theoretically, it could be also higher if a certain amount of interstitials exists (i.e. atoms in "holes" between other atoms). 

The mentioned holes do not have anything to do with pores whichare results of the production of mainly polycrystalline ceramics. During production there are volumes between grains which are not filled which reduced the experimental density further. How much porosity exists depends on the production process applied but is also a question of the respective ceramic. Consider further, that often binder of glass is used during the production of ceramc. All this will have an effect on the observed and measured density. The X-ray density, however, does not know any imperfectness or secondary phases.

Thanks,. clear answer.

Dear Robayat,

As Dr. Nolze indicated the X-ray density has no units. He also explaimned the theoretical density correctly (RhoTD).

If you meand radiographic density, then they are meaning less unless you specify what energy you used.

In general porosity is the volume fraction of missing material in the bulk. It is actually the comlimentary part between the actual density (Rho) and RhoTD.

Porosity has implications on physical properties such as thermal conductivity, stiffnes and strength.

In order to answer dircetly to your point, you need to specify the end use of your porous material, e.g mimicing a human bone, heat shield for rocket, etc.

I wish you succes in your quest.

Ori Yeheskel

Only some further additions to stated by dear colleagues:

1. Absolute density is related to the structural (or X-Ray) density. In a monocrystalline ceramic material the absolute and X-Ray densities are the same; but in a polycrystalline ceramic you must to calculate a mean value.

2. The real density is measured with the picnometric method, in which the open porosity is supressed by a fine conminution of the material. The real density and the absolute density give close estimates.

3. The apparent density is measured with the displacement method, in which the solid sample surface is covered with a non-permeating layer of parafine. Then all the pores (open and close) are taked into account.

4. Also is possible to measure the open porosity with water absorption, Hg-porosimetry, gas adsorption, etc. Then close porosity may be measured by difference.

The porosity is related with many physical, chemical and biological properties of the ceramics; and many technologies are based on these properties.