I have a powder which is made from Co and Ni (without any other impurity). I will be appreciate if you tell me your suggestion to separate these metals and obtain pure Ni and Co.
Assuming each powder grain is either Co or Ni, a magnetic field gradient transversal to a dropping stream of the powder might split it into two streams, since Ni is substantially more paramagnetic than Co.
If, instead, the powder grains are individual composites, or even an alloy, then the only way that I see is chemical or electrochemical.
Cobalt and nickel both have the same density, so it seems gravity separation which works based on the difference between density of materials is not a proper method. Also, these two elements are categorized as ferromagnetic, making their separation via magnetic field possible.
I think the only way might be selective dissolution of Ni in highly oxidan conditions and precipitation of Co3+.
Stan Sykora is correct in stating that Ni and Co must exist as separate particles in order to make a direct physical separation possible in their solid state . Farhad Moosakazemi is correct regarding density and ferromagnetism of the 2 metals. They also have very close melting points and weights.
If there is a significant difference in particle size between the Ni and Co, then any method that separates particles by size (screening) or particle weight (elutriation, etc.) might work.
Otherwise, chemical conversion of the metals is necessary. Most commonly, nickel and cobalt are dissolved in an acidic solution and separated by solvent extraction. There are many papers describing this process.
It may also be possible to heat the powder in an oxidizing atmospher to convert the metals to oxides. They then become paramagnetic and may be separable via magnetic separation.
Chemically , neodecanoic acid as extractant in a sulfate solution can be used to separate cobalt and nickel. Nickel, cobalt and iron(II) can be separated easily from magnesium via selective extraction using 20% Versatic 10(neodecanoic acid) as extractant and 5% tri-n-butyl phosphate (TBP) as phase modifier at pH 7.0, while the nickel and cobalt in the loaded organic phase can be separated from iron(II) by selective stripping of the two metals using 0.1 mol/L sulfuric acid solution leaving iron(II) in the organic phase.