Theoretically, it's possible I think. if you can measure temperature of melting with high precision you can compare it with tables data. But you should use another methods because it's very easy to make a mistake. I wouldn't reccomed it to you.
If you're interested in very small crystals, Electron Back Scatter Diffraction (EBSD) in the SEM is a powerful tool for determining whether grains or particles are single crystal. It's invaluable for some of the nanomechanical testing I do. Perhaps not as useful for macroscopic single crystals though...
A petrographic polarizing microscope is certainly the first choice instrument to identify single crystals without X-ray diffraction.
In the transmission mode (transparent crystals) you can observe crystals up to 500X, hence the size limit could be around 1/1000 of a mm (or 1µm).
In the reflection mode (opaque crystals) magnification can be pushed up to almost 1000X hence roughly halving the size limit of the object to be examined. In this case a limitation may be that of the sample preparation (the crystals must be polished to a smooth metallographic finish).
Such microscopes are the common work-horse of any Mineralogy - Petrology section of any Univ. Geology Department. The simplest models of such microscopes are in use by all Mineralogy, Petrology and Geology students. Their cost is in the several hundreds of Euro range. A research polarizing microscope could rate in a few thousands of Euro.
Thiru! "I am interested in the process of identification of single crystals". If so, one Thiru to another, you've created the biggest handicap for yourself (we are not talking about the race tracks either) possible, by excluding XRD. Imagine if the Braggs were forced to do the same, DNA would still be an enigma. We'd still be "flat earthers"! One exception being, if you anticipate the X-rays damaging the crystals in the data acquisition time frame (30-300 fps).
This question is interesting in the sense that it is "fundamental"! XRD is the only tool to get an unequivocal answer with out a vacuum and in situ.
Release yourself from those self imposed sanctions. Find the nearest XRD lab. Plenty in India. Run! Run! Odunge! Odu! Lol!
It is certainly dependent on the size of the crystal or coherent domains. A wide range is covered by EBSD as mentioned already by Philip. In contrast to TEM it allows single scans from several 100nm² up to 1 cm². Multiple measurements can even cover bigger areas. Below the 100nm² Transmission Kikuchi Diffraction or better TEM is the best choice.
The background to the question is not entirely obvious to me. It may be so, when for example you work with alloys, that there is no help at all from the outer form of a fragment that you have retrieved from the "debris" of smashing an arc-melted pellet, i.e. whether it is a single crystal or not. I now suppose that structure analysis is the outcome wished for? Even with X-rays at hand, it is very time-consuming to investigate each particle that you pick out; after twenty trials you tend to give up.
I made my first faltering steps with the Weissenberg camera technique where the fragments had to be more or less correctly oriented in order to make any sense for the interpreter. To save time,
I devised a program where a powder pattern(!) was simulated in the Weissenberg geometry. (Of course the cell had to be known.) Then, for any orientation of a single crystal, its spots had to fall on the diffraction traces (almost ellipses). If the fragment was two-phase spots would appear that did not fit.This method saved weeks of time otherwise spent in vain!
This does not answer your question but is a comment on that X-rays may give you an answer but sometimes only after much effort. Choosing material with nice morphology is quite something else -- and if you can use a polarizing microscope. Using TEM does not solve the problem of picking out crystals that are good for forthcoming structure solution, because you cannot retrieve those which will do....
Rolf! "X-rays may give you an answer but sometimes only after much effort" only if you do not have a way to observe real time XRD images. There is no mystery in detecting the single crystal of HgMnTe in the image below. I've used the real time method since 1984 to detect "mono" crystallinity of grown crystals (large ones). Others have used low tech high spatial resolution film for essentially the same purpose.
A fairly wide range of possibilities has so far been described in order to answer the original question: "which tool can be used to identify single crystals without x-ray diffraction". So each one of us has had a chance to offer an answer along the lines of one's personal experience. However what seems to be missing here is some feed back from the initiator of the discussion. As a matter of fact, in order to provide the best possible advice it is also very important to have more details related to the original problem. Such as for instance, the nature of the crystals to be investigted i.e.: opaque or translucent; what size; isolated or within a matrix, etc., etc.. Another important piece of information is the reason why x-rays are excluded as a tool. Is it because they failed to provide the right information in the first place or because the lab in question has no access to x-ray techniques? Are we looking for the simplest possible method or are we including the most sophisticated technology available to solve the problem? etc.
In other words, without further knowledge on why the original question was posed, I feel the discussion may take off at a tangent and fantasy could become the limit.
I would therfore urge the question to be posed within a reasonable frame of constrains such as those mentioned above or others that seem appropriate, in order to help solve the problem within the real scenario that triggered the question in the first place.
The variables are irrelevant. There is no other way to unequivocally establish the single crystallinity by any habitat/habitus or other studies as a general method. Romano is obviously right in the sense that if the material type is known then there may be some empirical method other than XRD to vaguely confirm single crystallinity, certainly NOT the deviation from "perfect" mono-crystallinity absent etching. So, just as the questioner is missing so is the entire logic behind this question. Could I eat beef without butchering a cow? :-) I do concede that there is no question that is illogical until one learns the answer. I just hope "Thiru" got the point. https://www.flickr.com/photos/85210325@N04/11487549683/
BTW very elegant work was done by the likes of Bragg, Ewald, Laue, Guinier etc. without fancy or expensive XRD equipment. They used photographic film, cannibalized clock parts (my exaggeration), adhesives, lead foil and antique "spatially blind" zero dimensional scintillation counters (still in use presently) to decipher the deepest secrets of crystals.
In my humble opinion, Larry is one hundred percent correct besides being succinct. I'm surprised he stopped with one and a half syllables. You have no clue what Larry meant. The negi Nelly better come out of the closet before going for the negi vote again in your own interest in learning. Make your objection know Caveliero! Show us how much you know about identifying "single crystals" (in general). What would be the precision of this other technique you may have knowledge of. Spit it up in the interest of science. LOL!
I hope you realize by now that I'm just having some fun learning. Heck with the conventional thought process. Let's think out of the box!