Q:

Can a "distributed gap" powdered-iron or ferrite toroidal core be used for a flyback converter's coupled inductor?

As just about all of us who deal with switching power supplies know, flyback converter designs use an air-gapped coupled inductor instead of a transformer.  Typically, this gap is an explicit gap in an E-I type core.
Nick Alexeev points out in a comment, though, that:

Transformer cores are usually not gapped. Inductor cores tend to be gapped. Toroid cores of power inductors have what's called "distributed gap", which you can't see.

Can a "distributed gap" toroid core yield satisfactory results when used for a flyback converter's coupled inductor, or will it cause undesirable effects when used instead of an E-I core with an explicit gap?

A:

I believe the type of "distributed gap" that Nick Alexeev comment refers to in This question , is regarding a "Powder Core" material.  
Powder Iron Core material is, loosely speaking, granules of Iron emulsified in a binder (the stuff that holds the material together), similar to an epoxy. So the iron granules literally have a physical separation from each other by virtue of the binder material. This is the "distributed gap". Literally a large number of small gaps.  
With laminated iron cores, the gap is explicit and at one section of the core.  
Ferrite cores for the most part do not have a distributed gap.  
Providing a gap is a technique to avoid saturation of the core material. 

For power module designs, the inductor's saturation level is critical. Saturation level is typically defined as the dc current level at which the device's inductance declines to 75% to 80% of its nominal inductance. The dc current can saturate the inductor quickly if an air gap is not introduced into the core's magnetic path. Powdered iron materials have an inherent air gap that is distributed throughout the core, which gives them a soft saturation curve. Ferrite material must have an air gap physically inserted or ground between the mating surfaces of the core halves.
  [Taken from Power Electronics ]

Since the "distributed gap" of a powdered iron core material is literally a gap, yes, a powdered iron core can be used as if the core were literally gapped.  
Powder Iron cores are lossy, and that should definitely be a consideration. In most cases the core loss will be too high to use in most high frequency transformer applications. But the distributed gap is still valid as a gap. The losses in powdered iron core material may make it an unsuitable candidate, but that would depend upon the application.

