Diffraction on a crystal lattice shows its period according to Bragg's law. If the lattice period is ideal and has no deviations, then a narrow peak appears in the diffraction spectrum. Broadening of this peak indicates that there are deviations from the average period. They are caused by the formation of new structures during melting and ablation. This is like in a radio signal - there is a carrier frequency (the main lattice) and a deviation of the carrier frequency (changes in the main lattice). Similar phenomena are known in holography: Photonics 2021, 8(10), 448; https://doi.org/10.3390/photonics8100448 (Figure 3, Figure 6).

At the time during MD simulation, where the peak pressures were generated in the solid+liquid system, the broadening of the peaks was the highest. Was there an effect on the gradient of pressure in the system causing peak broadening for the virtual diffraction pattern obtained? Does temperature gradient also produce broadening of the diffraction pattern?

The width of a diffraction peak indicates the size scale over which the exact periodicity holds.

Consider a two slit experiment. The diffraction pattern looks sort of like a sine wave. At the peak the contribution from the two slits are exactly in phase and they add together. At the minimum they are exactly out of phase and the cancel. What is interesting is between those points. In between they aren’t perfectly out of phase and so they don’t cancel.

Now consider 4 slits. The pattern starts to look like broad peaks with dark regions between. In each of those dark regions there are now three places where the four contributions exactly cancel. Elsewhere they come close to cancelling. This is because any Given point experiences a range of phases between 0 and 2 pi. With only 4 phases you don’t get perfect cancellation everywhere, but the phases do cover the gamut until you get close to the peak. Near the peak you reach a place where all 4 phases are within 2 pi of each other and they start to not cancel. Closer to the peak the range of phases compresses further and further until they are in phase at the peak.

Now consider a large number of slits. Now you have sharp peaks and broad dark regions. Everywhere in the dark region a large number of phases are represented ranging uniformly across 2 pi. For every contribution at some phase, there is another contribution that is out of phase with it. Once again near the peak all the phases fall within 2 pi and they stop cancelling so perfectly. How close to the peak that happens depends on how many slits are contributing, or, equivalently, how large of a region of slits are contributing. That is, the peak width is inversely proportional to the length of coherent sources contributing.

Now consider what happens when you start to randomly cover some of the slits. Now some of the uniform distribution of phases aren’t represented. The dark only happened because the phases were more or less pair wise cancelling. Now some contributions don’t cancel, and it isn’t fully dark. This is not as important in the middle where the uniform range of phases was selected from a range of many pi. Statistically all phases are still well represented and it’s still dark. However, nearer the peak where the entire range of phases is only a few pi, these missing contributions matter more because statistically each contribution is a larger fraction of all contributors at that specific phase and so matters more in the sum. The net effect is that the peak gets wider. So the peak width is determined not just by the maximum extent of the periodicity, but also on the perfection of the periodicity.

Anything that spoils the extent of the periodicity (say, grain size in an alloy, or dislocations that make one region be not on the same periodicity as neighboring region) or the perfection of the periodicity (say voids or interstitials) will make the diffraction peak wider.

So in regards to your question, for the various phenomena you list, think about the perfect crystal lattice, and then think about how that phenomenon affects the extent of the order (for example “amorphous” is really just a statement about the size scale over which periodicity holds), or the perfection of the order. Anything that spoils the periodicity spoils the uniform representation of all phases and so spoils the cancellation and makes the peaks broader (and the dark areas less dark)