For density, you need a measure of volume (physical thickness) and mass.  We generally use XRF that has been calibrated by RBS or ICP-MS to determine the number of Al and Zr atoms/cm2.  Then we assume a mixture of Al2O3 and ZrO2 to determine the number of O atoms/cm2.  XRR is a good method for determining a physical thickness on a Si substrate with native oxide as long as the films are very smooth.  (If the films are not smooth, any measure of density will have problems.)  I have also used 3 angle spectroscopic ellipsometry to measure thickness, but I would prefer films of at least 30nm to have accurate fitting of the optical properties. 

One possible method would be X-ray tomography to quantitatively identify any and all voids. This way you can determine the effective volume of your sample. Another faster method to do the same would be low-angle XRD analysis.

At the moment I cannot think of a better method.

I hope it helps.

For density, you need a measure of volume (physical thickness) and mass.  We generally use XRF that has been calibrated by RBS or ICP-MS to determine the number of Al and Zr atoms/cm2.  Then we assume a mixture of Al2O3 and ZrO2 to determine the number of O atoms/cm2.  XRR is a good method for determining a physical thickness on a Si substrate with native oxide as long as the films are very smooth.  (If the films are not smooth, any measure of density will have problems.)  I have also used 3 angle spectroscopic ellipsometry to measure thickness, but I would prefer films of at least 30nm to have accurate fitting of the optical properties. 

refer

www.nature.com/articles/2181179a0

www.sciencedirect.com/science/article/pii/004060909390499F

www.icdd.com/resources/axa/vol42/v42_64.pdf

You may be based on XRD results to identify the crystal structure and unit cell parameters to calculate the thin film density. 

by (GIXRR)  Grazing Incidence X-Ray Reflectometry technique

The colleagues above have answered this question, but I can add some more points:

Thin films with 10nm do not have the same density as bulk materials. They are full of voids , surface deffects, stress and strain. Normal bulk analysis will not work for them.

The XRR measurements and a good fitting will provide thickness and density information. XPS and XRF  could also be used to determine the relative number of atoms of each element and double check the XRR results for density.

good luck

Hello Baek, I would like to add a suggestion.

If the density is important to you because you are interested on porosity and surface area, you may also want to try BET analysis which gives you pore size, pore distribution, and surface area.

Success

Alejandra

It is impossible to measure the density of nanostructured materials in thin films or materials 2D by BET!

These 2D materials have physical, chemical and morphological properties different from  3D materials or bulk materials.

A piece of Gold melts at 1064C, but if deposited with nanometer dimensions can be melted at 700C or less!

The graphite is an electrical conductor material, but if  it is nanostructured in thin films or in nanotubes it  can becomes a semiconductor or even an insulator!

Techniques for physical characterization of bulk materials do not work for nanostructured materials in most cases.

Alexandre, thank you for the kind clarification.

In fact the BET surface areas of porous thin films could be Determined. However in this case surface acoustic wave devices is implemented.

You may refer to patent # US4,947,677 (SAW DETERMINATION OF URFACE AREA OF THIN FILMS)

or http://pubs.acs.org/doi/abs/10.1021/la00085a053

Dear Hayk

Surface acoustic wave (SAW) is a powerful technique for analysis of adsorption of organic compounds, proteins, nanoparticles, etc. onto nanometer surfaces . BET is a technique that requires a large amount of material and area in comparison with nanometric marterials. In the case of that patent (very interesting  and thanks for share) the authors used a BET machine only to control the inlet gas and temperature to the samples. They also  compare the results of a bulk sample. The measurements of the films were made in a SAW device. So call this new technique BET was a scientific freedom of the authors.