Dear Philipi,

there are many ways to distinguish the two substances. The most common are: X-ray  diffraction or TGA/DSC.

Regards,

Fernando

It depends on the purity you are looking for. This is not my primary field of expertise but  you could take a powder diffraction measurement and look for the respective signals. The most reliable way would possibly be elemental analysis if you have that available for oxygen.

Dear Philpi,

a bulk sample of about 100% Cu and another consisting of about 100% CuO can be easily destinguished by their density;  rhoCU = 8,96g/cm³ and rhoCuO = 6,31g/cm³.

However powder samples will be challenging with respect  to density measurement.

Although I am a friend of x-rays, but in this case x-ray application seems to be overkill here.

Or simply scratch (better cut) the sample. If the scratch/cut face appears reddish brown; then you have metallic Copper. The CuO (black) is only at the surface of a Copper block.

XRD or EDS

in order to distinguish Cu from CuO we have to analyze the samples with XRD, EDX, XPS, the densities of the two materials may also help to identify them

Thank you all! I'll use the density to determine purity. 

XPS should be enough to determine the purity and oxidation state in your sample

Although it's a semicuantiative technique, a XPS should be enough to determine oxidation state https://en.wikipedia.org/wiki/X-ray_photoelectron_spectroscopy If you need more detailed analyses, I think that you can use an X-RAY diffraction or even a TOF-SIMS (Time of flight secondary ion mass spectrometry).