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If you stop the coals from completely becoming ash it's called biochar. You can spray some water on the coals after your wood has burnt down and it will stay like a charcoal. It's supposed to have a lot of benefits for the soil too along with the ash.

Yes, just be sure that you are using it for alkaline or ph neutral plants, not acid loving plants. Calcium raises the ph in soil slowly and wood ash is alkaline. It should not be used in compost too heavily because it can disrupt the microbial activity. Also, avoid using with nitrogen fertilizers like urea because it creates ammonia gas. 😉 Biochar is great for many plants in the garden and you will find many companies using it in bagged soil. Thanks for sharing @rakkasan84 and great tip:

You can spray some water on the coals after your wood has burnt down and it will stay like a charcoal.

Just be sure to use hardwoods - they contain as much as 5x more nutrients than soft woods. Oak & maple work great, but I recommend readers avoid using chemically treated wood like pallets and construction​ debris.

Indeed. We have a very low pH soil here around 5.3 and I'm working to raise it to around 6.0 in the garden to grow a wider variety. Fortunately we have a lot of oak and hickory here.

That's perfect! In that application, it'll work great. Many fruiting plants will enjoy the potash and phosphorous added. I have to amend my soil down a bit, I'm totally neutral here at 7. My well water is slightly acidic (6.8), so I do not amend much unless I notice nutrient lockout/deficiencies. I'm a tomato grower, so 6.2 is where I would prefer to have the soil. But.. I do my best with what I've got 😋

You can also make biochar by heating the wood in an anaerobic environment -- there are instructions on the net about making biochar crucibles from metal cans.