If we have two XRD patterns obtained from the monoclinic and orthorhombic phases of Bi4V2O11, how can we distinguish between them without using software programs?
you must compare each to standard diffraction of monoclinic and standard diffraction of orthorombic Bi4V2O11. The standard diffraction can be found in ICSD or JCPDS or others. In order to know the suitability between your difrraction pattern with the standard, you must do refinement whether with Le Bail or Rietveld. Still, you need a software to do...