The problem of splitting a powder such as XTOL into two or more piles having similar compositions seems closely related to the problem of sampling of an inhomogeneous powder. It is a very difficult problem, and at least one book has been written about it (Powder sampling and particle size determination
By Terence Allen). I don't pretend to be an expert on powder sampling or an expert on statistics. However, I know a little about statistics, and a bit more about chemistry and physics, and I have at least given the problem a little thought, so I thought I post a few of my thoughts on the topic.
The first thought, which may or may not have been obvious to any one person, is that Kodak has very much the same problem when they fill bags of XTOL. They must somehow produce a set of bags, each bag having a similar composition to the next. If they premix a powder and then in a separate step attempt to load powder into separate bags they are faced with exactly the same (very difficult) sampling problem under discussion here.
Kodak has either solved the sampling problem for this case to a degree that it commercially acceptable, in which case the problem is solvable, or they use an altogether different process for filling the bags that avoids the problem of sampling a premixed powder.
What process might they use to fill bags to avoid the problem of non-uniform composition between the bags? There might be several candidate processes, but the one that comes most readily to mind is to "mix" the components of the powder at the time of bag filling, i.e. to fill the bags from two or more streams of pure component. For sake of discussion let us limit this to components A and B. The problem then is to adjust the manufacturing process so the bag is always loaded with the same mass of component A. The same can be said of component B.
There would seem to be two ways of doing this, one based on mass measurement and the other based on calibrated flows of powder. For example, one could add powder A to a weighing pan, adjust the amount until it has the correct weight, and add it to the bag. Alternatively one could add powder A to the bag and weigh the bag, and assuming the weight of the bag was previously known, one would top off the bag with just enough powder to bring it up to weight. One would then to the same with component B. These mass-based processes would be expensive, though it might be possible to automate it to bring the costs in line with commercial reality, and in any case they would likely be "gold standard" methods.
The other way would be to add components A and B using some kind of calibrated flow streams, i.e. there would be a stream of component A of known flow rate and a stream of component B in another flow stream. They would be either added to the bag without any premixing, or the streams could be mixed just as or just before they are added to the bag. If mixed before being added to the bag one would need to be sure the streams do not settle into a heap before being added to the bags. Otherwise the components will stratify and we are back to the problem of uniformly sampling an inhomogeneous heap.
I should add that calibrating a flow stream would itself face a similar problem. Before a powder is introduced into a flow stream it must surely exist in a bin or a heap. To get a uniform flow from the heap (which has surely been stratified into an inhomogeneous sample with respect to particle size) would not necessarily be an easy task and would probably require constant monitoring of and tinkering with the flow stream controller.
It would be interesting to know what method Kodak uses for mixing their components and adding them to the bag.
Now, back to the problem of splitting a bag of XTOL in the home darkroom. Here we don't have the mighty process engineering infrastructure developed at Kodak over many generations, but we do have the luxury of not needing to worry too much about the cost of the process. I think there are two general approaches, which could be applied either individually or in combination.
The first is to sample from a flowing stream. This is the general approach that seems to be strongly favored in the book referred to above. Please challenge me if you disagree, but it seems to me that one reasonably practical way of doing this would be to arrange some kind of vertical divider (a board or cardboard sheet), place the dry XTOL in some kind of container that is easy to pour from (a bottle perhaps), mix the powder as best as one can (by shaking and/or inversion) and then pour the powder on the divider in such a way as to produce two piles of nearly equal volume, and by inference nearly equal mass.
There are two directions that one might orient the flow with respect to the plane of the board. It should be obvious to you that one orientation will introduce a fractionation of the composition of one pile with respect to the other. Therefore, pour in the other direction. These two piles will not generally have the same mass, so weigh them. Then mix the two piles as best as you can, and assuming that the masses of the piles are not too much different, take a small amount of material from the large pile and add it to the smaller pile. As long as the two piles are not too different in mass, and as long as your crude remixing of a pile has not produced a pile that is too badly inhomogeneous, the mass adjustment step will not perturb the compositions very much.
There is another approach you could use. Mix the dry XTOL as well as you can. Then take a very small spoon or scoop and transfer a small amount of the dry XTOL into pile 1. Similarly, transfer a small amount into pile 2. Do this without any obvious bias between the process applied to pile 1 and pile 2. For example, avoid scooping from wildly different parts of the master pile. Repeat the process, i.e. a scoop goes into pile 1 and another scoop goes into pile 2. As you go you might want to weigh the two piles so you can make minor adjustments in the amounts being added to piles 1 and 2. When you are done you should have two piles of equal mass with closely matching compositions.
If you want to be a little more sure of things you could gather pile 1. Mix it as best as you can. Pour it into a conical pile. Flatten the pile. Divide the pile into two sections using a thin flat board to make the split. You now have piles 1a and 1b. Do the same to pile 2 to make piles 2a and 2b. Mix pile 1a with 2b. Mix pile 1b with pile 2a. The result should be two piles of composition somewhat more uniform compositions than before. Of course, you can expect to need to perform some minor mass adjustments of the piles, as discussed earlier, either at the 1a/1b stage (and 2a/2b stage) or after the final mixing.
Please comment on these schemes.
P.S Wear a respirator.
P.P.S There is one other possibility that I hesitate to mention, but it is basically making a master solution, splitting it, and then vacuum evaporating to dryness. That would be even more of a pain in the neck than the ones already discussed, and one would need to design the process to minimize the possibility of oxidation.