Which compound is responsible for the borax bead test?

When borax is heated, the reaction that takes place is :


$$\ce{Na\_2B\_4O\_7.10H\_2O \ce{->} 2NaBO\_2 + B\_2O\_3 + 10H\_2O}$$
And the compounds that are responsible for the colors are $\ce{M\_x(BO\_2)\_y}$ salts, like $\ce{Co(BO\_2)\_2}$. My question is, does this $\ce{BO\_2}$ come from $\ce{NaBO\_2}$ or from $\ce{B\_2O\_3}$ or do both of them react?




A little chemical detective work gives a plausible answer.


Say the metal is cobalt and it's oxidation state is +2. Then, with the cobalt calcined to the oxide, you have two possible acid-base reactions:


$\ce{CoO + 2 NaBO2 -> Co(BO2)2 + Na2O}$


$\ce{CoO + B2O3 -> Co(BO2)2}$


Both reactions look good, but upon further review the first one gives something we recognize as a powerful base, more likely to be a reactant than a product. Moreover, a quick check [here](https://en.m.wikipedia.org/wiki/Boron_trioxide) reveals that boric oxide has a low enough melting point to liquefy in the flame, favoring the second reaction kinetically.


So the second reaction above is really the only plausible one.


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