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What rationale (purely theoretical/assumptive, or known by experience / backed by evidence) would you use in an attempt to effectively anticipate which other metal or elemental ions are most likely to co-crystalize with a given metal / elemental ion?

In other words, to generally anticipate which elements are likely to easily substitute for a certain element during crystalization (which, as we know, generally promotes the exclusion of anions/cations different from that constituting the bulk of the crystal)?

Please feel free to reword my question or its description if you have a better way to put it right.

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    $\begingroup$ Major factors are shared valency, similar ionic radius, shared relevant chemistry regarding counter-ions. Like Al, Cr and Fe(III) in alums. // The universal, but demanding good way is obtaining good chemistry background knowledge. There are usually no simple rules to know all in chemistry. (except this one) $\endgroup$
    – Poutnik
    Jul 21, 2022 at 6:56
  • $\begingroup$ Would you like to copy/paste your comment into a formal answer? $\endgroup$
    – Hans
    Jul 21, 2022 at 7:32
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    $\begingroup$ Apart from alums, there are not too many examples of co-crystalization. In usual alum $\ce{KAl(SO4)2·12H2O}$, $\ce{K}$ may be replaced by $\ce{Rb, Cs, Tl, NH4}$, and $\ce{Al}$ may be replaced by $\ce{Cr, Ga, In, Co(III), Mn(III)}$. But there are some strange situations. Iron may replace $\ce{Al}$ only with ammonium and $\ce{Tl}$. And thallium makes alums only with $\ce{Al, Cr, Fe}$. $\endgroup$
    – Maurice
    Jul 21, 2022 at 8:26
  • $\begingroup$ @Maurice: Can K not also be replaced by Au(I) which has a radius way closer to that of K than Cs does? Or is it because it has a different chemistry? $\endgroup$
    – Hans
    Jul 21, 2022 at 21:58
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    $\begingroup$ @Hans Au(I) is not stable in water solutions and disproportionates, unless in stable complexes like [Au(CN)2]-. $\endgroup$
    – Poutnik
    Jul 22, 2022 at 5:19

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Major factors for coprecipitation are shared valency, similar ionic radius, shared relevant chemistry regarding counter-ions. Like Al, Cr and Fe(III) in alums.

Note the various forms of co-precipitation (Quote form the above Wikipedia link):

There are three main mechanisms of coprecipitation: inclusion, occlusion, and adsorption.

  • An inclusion (incorporation in the crystal lattice) occurs when the impurity occupies a lattice site in the crystal structure of the carrier, resulting in a crystallographic defect; this can happen when the ionic radius and charge of the impurity are similar to those of the carrier.
  • An adsorbate is an impurity that is weakly, or strongly, bound (adsorbed) to the surface of the precipitate.
  • An occlusion occurs when an adsorbed impurity gets physically trapped inside the crystal as it grows.

Each of the above factors applies in various extent on them:

  • Inclusion is the most sensitive to the ion radius and valency.
  • Occlusion has almost no prerequisities to occur.

The universal, but demanding and unpopular good way to obtain predicting knowledge is obtaining good chemistry background knowledge. There are usually no simple rules to know all in chemistry. (except this one)

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  • $\begingroup$ I'm looking at atomic radio tables on wikipedia. They have two different ones: (1) Crystal ionic radii and (2) Effective ionic radii in pm of elements as a function of ionic charge and spin (ls = low spin, hs = high spin). Am I correct to assume that crystal ionic radii is what is relevent for the present purpose? $\endgroup$
    – Hans
    Jul 21, 2022 at 11:56
  • $\begingroup$ Is it the low spin or the high spin radius of an element that should be considered? $\endgroup$
    – Hans
    Jul 21, 2022 at 11:56
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    $\begingroup$ @Hans The ion spin and spin dependable radius would depend on the charge and geometry of anions and or the lattice geometry. But I do not know enough here to give an authoritative answer. $\endgroup$
    – Poutnik
    Jul 22, 2022 at 5:16

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