Are my " diamond " tweeters really diamond

A breakup node that is outside the audible band will impact the audible band by IM distortion. Using red book, most metal domes will have a breakup above the FR range. Analog and true hires recordings can have energy that may cause the driver distort. Typically, these ranges are lower in level and thus the IM distortion will be accordingly lower. The use of exotic materials is one way to push the breakup out the range of most content. Another is engineering design, which can take a material quite a far with shape, variable thickness and stiffness, and other design features.

Soft domes will breakup quite a bit earlier, and the exact degree will vary based on the doping materials. The distortion will be more benign due to the internal damping properties. Other distortions are more present with soft domes as compared to other more rigid domes, but the internal damping does help to keep the issues generally benign. You don't have this kind of forgiveness in most rigid domes.

The exotic material choices is an effort to get a more ideal driver. Still, its only a single piece, or a single chapter, in describing a drivers performance. 

Is an interesting comparison as to which method of damping produces the best result in dealing with certain distortions, high damping or internal damping. High damping meaning the ability to resist distortions due to increased rigidity or internal damping so that distortions are instead dissipated via friction in the fabric and doping material.

With a very rigid dome, even energy going back into the cavity behind the dome requires damping as the dome will be impacted by return energy. Fabric domes will be affected as well, but will further dissipate this energy as it propagates through. While its important to either side, its less of an issue for soft domes. This doesn't imply one being clearly superior, just that an engineer has different set of issue priorities based on material selection. But I do feel that fabric domes can be more forgiving in designs with the understanding that your accepting certain performance limitations.

As for the dispositions of sound quality based on given material, its being given more weight then it should by many.  We see many different designs show considerable ranges performance with very similar raw materials. The extra effort in thought and engineering really make all the difference. The engineers experience with certain materials can allow them to achieve more due to better understanding of material properties and solutions.