You have two different question in the same post.
how can I simulate the powder XRD spectra?
To just simulate the XRD spectra you can use this answer https://mattermodeling.stackexchange.com/a/146/24.
can I use the powder XRD to further refine the lattice constants of the structure?
The short answer: yes.
The long answer:
For the fitting process, or ...
The Crystallography Open Database is a good database of experimental crystal structures, take a look at their .hkl files which contain structure factors.
The Materials Project, a computational database, also calculations X-ray diffraction patterns and absorption patterns (disclosure, I'm on the Materials Project staff).
You can also generate your own once ...
In Bragg's law, $n\lambda=2d\sin(\theta)$. Here, $n$ is the order of the reflection, and corresponds to the path length difference between X-rays diffracted from two different layers of atoms, in terms of the number of wavelengths. So if the path lengths differ by exactly one wavelength, it is a first order reflection.
By convention, we treat all reflections ...
For x-ray diffraction and Raman spectroscopy data of minerals, you may try https://rruff.info/
According to their site, "The RRUFF™ Project is creating a complete set of high quality spectral data from well characterized minerals and is developing the technology to share this information with the world. Our collected data provides a standard for ...