You can simulate the diffraction pattern of a mineral from its crystal structure and atomic coordinates. There are programs available to do that, one of them is VESTA (http://www.jp-minerals.org/vesta/en/) which can visualize the structure and simulate the XRD. The calculated XRD pattern will have the same relative intensity and 2-theta position as the experimental pattern but the shape of the peaks will be different because the instrument contributes to it. Rietveld refinement is one way to simulate the experimental XRD that also accounts for the instrument effect and other parameters (e.g. size, substitutions). See for instance this site for a Rietveld refinement software: https://profex.doebelin.org/

Debora Berti, thank you very much for your valuable response. I am very much benefited by your answer.

Regards

Nityananda Das

As an extension, I want to mention that VESTA is free software. It cap open different file types i.e .cif, .xyz etc. .xyz file is easy to generate by hand for a particular crystal type.

Yes, and the example above is valid for standard files. However, up to a certain amount. The problem includes that diffraction is quantum -- neither particle nor classical wave -- whereas computers are deterministic.

Dear Ed Gerck,

That's a very good point to discuss.

So, how much the calculated value by software is different from the real time experimental value ?

Definitely, this error is different for different structures.

Can you please suggest me any reference so that I can understand how much error occurs for different systems ?

Another thing is - the available standard data for different systems are generated by real time experiments or calculated by software ?

Regards

Nityananda Das

Dear Ed Gerck

The XRD theory is based on Bragg's formula and Laue equations. All these are from classical theory. Do you think that those classical theories are unable to analyze the observed XRD patterns ?

Please clarify so that I can understand how much quantum theory is needed to analyze XRD pattern ?

Regards

Nityananda Das

ND and all: whatever a digital computer calculates is deterministic -- even so-called random numbers. We call that chaos -- looks random but is not. XRD patterns generated by chaos is one problem, another is lack of a full chain of reflections, as it must be finite to certain number (for space and time reasons). In addition, it is based on classical formulas. But, for standard situations it works, although you may have to correct the final distributions.

Essentially, it is a problem of different dimensionalities which, by a theorem in topology, must include solutions that are not uniform -- have discontinuities.

Also, more than one solution can correspond to the same, single, XRD pattern. Finding a XRD pattern does not uniquely solve the problem. Kekulé was a famous example, regarding the possible structures in the diffraction of benzene.

Therefore, software can help but not define. Even with corrections. Maybe AI can help test more configurations, but false negatives will be excluded, provably. There also false positives, which are possible to reduce to zero, in a second step.

A photon is quantum, a third case in a double slit experiment, neither a particle nor a wave. Different distributions, all three. A single photon at a time, can build an interference pattern. This is proven experimentally.

ND and all: Note that from a physics point of view, all one can ever have as a measurement is a rational number, which is all a ruler, computer, oscilloscope, or any device can produce. This is well-known, and infinities are nonphysical. QM as well as SR must provide a finite, rational number, and they do.