The word "crystals" is probably a reference to the crystalline structure of the iron itself, not to some foreign material.
The thing is, wrought iron shouldn't have
any kind of crystalline structure other than the slag, unless it's high enough in carbon to count as a near-steel. And in that case, you'd want to harden it like a steel, not like an iron.
For all metals, including steel without a heat treatment, pounding on it while cold work-hardens the metal. It will generally become harder and "stronger," but also more brittle. Most metals become rather "crumbly" if work-hardened to too great a degree, like if you bend a metal monowire back and forth repeatedly, the break won't be clean. That's also why many older bronze swords have edges that look crumbled. Corrosion played some part, but that's mainly repeated work-hardening and impact.
Also, pretty much every metal except steel (including iron) is
annealed by heating and quenching. I.e., if you heat copper up until it glows, then dunk it in water, it will be at its softest state. Then you hammer on it to make it harder.
Quenching and tempering of steel, on the other hand, is basically both more and less complicated than what you think.
The crystalline structure reaches the strongest possible point at a particular temperature (which varies by alloy; for the simple steels, you heat until the steel is no longer magnetic), but a slow cooling will cause the crystals to go back to the soft state (annealing). So a fast quench is used to keep the steel in the harder state. Yes, you could use a slower quench (like motor oil or air cooling) to get an intermediate stage, but that results in a steel rather different from a fully hardened and tempered one. The only steels that usually get a slow quench are the high-alloy ones, which will shatter like glass if they're water-quenched (and the appropriate cooling speed for the high-alloy ones will
still result in very hard, brittle metal).
After that the metal is
tempered by baking it at a moderate temperature (a modern kitchen stove can actually be used to temper some steels) for a long time, up to 12 hours in some cases. And in modern processes, the steel may be cryo-tempered after that.
Easiest way to think of it is there are 3 different types of steel crystals; "hard," "springy," and "soft." Obviously, for most weapons, armor, tools, etc., you want a balance between "hard" and "springy," with no soft at all. The main role of "soft" steel is shock absorption without vibrating, like in axe heads.
Heating and then cooling
very slowly (European smiths would bury blades in thick layers of wood ash, so that it would be a couple weeks or more before you could touch the steel without burning yourself) makes the steel 100% "soft." Heating then cooling as quickly as possible (for that particular steel) makes it 100% "hard" (if done properly; a bad quench can leave some "soft" behind). Taking a 100% "hard" object and then tempering it turns some of the "hard" into "springy;" how much depends on the temperature and time (and once again, a bad temper can turn some "hard" into "soft" instead). Finally, in a modern smithery, a cryro-temper will turn any remaining "soft" into "springy," so a cryo temper basically will only correct flaws in the steel, it won't improve it if it was done right the first time. Ancient smiths had to just do it right to begin with, otherwise a sword or armor would bend rather than flex back.
However, with the vast majority of metals (certainly every metal other than steel that people had prior to 1800), you can't get "springy," at all. All you can do is try to balance "soft" with "hard," thus the dominance of steel.
And preferential hardening of the edges pretty much didn't happen at all, with a simple quench. A self-hardened European steel sword will have an edge and spine within a couple percent of each other, hardness-wise (unlike the earlier bronze and iron swords, where the edges were work-hardened and the spine was left alone). Differential hardening was done different ways, like the vikings put high-carbon steel at the edge, lower-carbon in the middle (given the same heat treatment and temper, the high-carbon will be harder). The Japanese would put a thick layer of clay over the back of the sword, so that heat would escape through the clay slower during the quench. On the Indian subcontinent, they would pour water from a pitcher over the edge of a sword rather than dunking the whole thing.
And actually, the Japanese and Indian approaches are a bit sub-optimum, since as you can guess, that means there's "soft" steel in the back of the blade, rather than "springy." And
actually, yes, permanent bending is a
huge problem with Japanese katanas, despite the ridiculous hype. Poor technique with a katana, and you can
easily bend one permanently on a bad cut. Nepali khukuris also actually do not flex and return true, their bend tolerance is very low compared to European style sword heat treatments (of course, bending a 1/2" thick khukuri is pretty hard); but in the case of the khukuri, that's probably because the "soft" steel at the spine keeps the blade from vibrating.
The best way to differentially harden something for maximum resistance to bending would be to
temper it differenly, but that's basically impossible, even with modern manufacturing techniques. You'd need a water bath and a line of blowtorches, or something.
Edits: clarifying the role of "soft" steel in blademaking.