Normal double-acting baking powder makes CO2 (thus giving a rising effect) in two ways: when it gets wet, and when it is heated.
Baking soda only makes CO2 when it gets wet.
From Wikipedia:
The acid in a baking powder can be
either fast-acting or slow-acting.[6]
A fast-acting acid reacts in a wet
mixture with baking soda at room
temperature, and a slow-acting acid
will not react until heated in an
oven. Baking powders that contain both
fast- and slow-acting acids are double
acting; those that contain only one
acid are single acting. By providing a
second rise in the oven, double-acting
baking powders increase the
reliability of baked goods by
rendering the time elapsed between
mixing and baking less critical, and
this is the type most widely available
to consumers today.
1. Chemical leaveners
There are two "oldfashioned" chemical leaveners, both still used today in traditional German and Scandinavian gingerbread recipes:
- Potassium carbonate (potash or pearl ash) and
- Ammonium bicarbonate (salt of heartshorn)
They do have their own quirks and pitfalls, but if nothing else is available...
If you can get baking soda, mix with cream of tartar to make baking powder.
If your store does not stock it, you pharmacy most likely will carry "sodium hydrogen carbonate" (which is another name for baking soda) either as treatment for heartburn, it's an antacid (because it reacts with acid, neutralzing it and making these nice bubbles, as we know from baking...) or as topical treatment for allergic reactions of the skin (poison ivy and others).
2. Biological leaveners
This boils down to Saccharomyces cerevisiae, aka. baker's yeast or brewer's yeast. Of course you get very different results and have to follow a different procedure. But here are some recipes where they are used somewhat interchangeably, e.g. some types of pancakes or waffles and, obviously, bread (vs. sodabread).
The charming thing about yeast is, that if your are really, really far from a store, you can still get your hands on yeast: Start a sourdough using the yeasts naturally occuring on fruits or the air around you.
Probably not the kind of substitution you had in mind, though.
3. No leaveners
With good technique, you can incorporate a lot of air (because that's what all leaveners are supposed to do) in your baking goods by whipping your eggs well. There are various approaches:
- You can whip the whole eggs.
- Whip the yolks (with hot water or over a water bath to stabilize them) to Zabaione-like consistency.
- Whip the whites and fold into your batter.
You will want to bake these batters right away before the bubbles get a chance to burst. The air will expand during baking and the hardening egg/flour-mixture will trap them in the baked goods. Contrary to many recipes out there there is no real need to bake a pound cake or even sponge cake with baking powder if it's done right.
Other recipes without leavener (or rather with the egg trapping steam generated by a rather high water content) are the members of the popover family (Yorkshire pudding in the UK, Pfitzauf in Swabia, some dutch pancakes) and pâté a choux.
Puff pastry relies on thin layers of butter separating the layers of floury dough and trapping steam between them.
Best Answer
You don't strictly need to use any leavener in this type of cookie. You can certainly get a firm, nonchewy texture without it, although it is unlikely to be "crunchy" and not very airy - it is more sandy, melts-on-the-tongue thing. Of course, if you use crystal sugar (as opposed to powdered sugar) you will experience some crunch from the non-melted sugar crystals, which might be what you wanted.
If you want to try a leavener, a typical amount would be 1 teaspoon (around 5 g) of baking powder for 250 g of flour. Use that as a starting point for the recipe development - I don't think you have to reduce it to 4 g from the start, since 1) traditional recipes are not that accurate anyway, and 2) the cocoa powder also adds starch, which kinda "counts as flour" for the purpose of calculating leavening. There is no reason to use any baking soda. And of course, remove the ammonium bicarbonate - if you really want to experiment with a combination, do it after you have created a working simpler version of the recipe with just baking powder.