I am trying to grasp what new discovery you may find in this experiment—snip
Me too. An incomplete wipe will certainly allow you to carve out files or, depending on the FS, use backup catalogue structures for recovery. FTK is only "seeing" free space as you have wiped out the MFT or other catalogue structure - dependant on the file system.
An experiment is designed to test a hypothesis in formal scientific disciplines. Do you have a hypothesis that you are trying to test or are you only observing the effectiveness of the tools?
As per some posts above, it would be helpful to further clarify your objective. From your original post, your statement of problem seems to be to "attempt to determine if any data is still present on a hard disk after using a secure wipe", and my first observation would be that your methods of analysis are only at the same level (or higher) than the level the wipe is being performed at, which is unlikely to be sufficient; I would suggest you need to consider all the levels and processes involved from the physical through to the logical.
If you have demonstrated that binary data is initially present and correct at a logical OS/application level and that data read from the same location is read as all zero at the same OS/application level following your "secure wipe", then any further processing above that level of the all-zero data would be pointless (since you already know there is zero information content) and would not really constitute a 'further' attempt to recover data. Only further techniques at the same or lower levels might be worthwhile (and in terms of 'at the same level, minimally likely in this case, but could include e.g. repeated reads etc, in case of borderline variations etc). Frankly, if you are using standard secure-wipe tools, I would consider a repeatable logical all-zero read at the application/OS level to be the problem definition start point, which would mandate (following verification) examination at a lower level in order to make any further attempt to recover data.
I would suggest considering the detailed low-level processes and methods involved to perform reading/writing from/to the media under consideration (such as the physical processes on the end media itself, the use of any controller for management of data areas abstracted from any accessing external entity such as the OS). Depending on hard disk type (age, physical structure - platters, SSD, controllers) these factors may differ, and therefore so may your examination options and results, depending on the equipment you have access to and the time available for examination (for example depending whether you might decide to implement bespoke control or interfacing to the underlying physical media involved).
In addition to the above, complementary consideration of the wiping process (with all options therein, i.e. what do you/others mean by 'secure' wipe) would be worthwhile. You appear to already be aware of the potential for limited success, but by consideration of all factors there may be some circumstances and combinations where you can demonstrate recovery, depending on equipment and techniques, or at least to demonstrate to a more rigorous degree that there is no recoverable data for the items and equipment available to you.
Phil.