rguil...
Most very high performance military turbine engines have fixed abradable seals around the blade path. I have seen high density light weight honeycomb core potted with the bonding adhesive used for this purpose.
NOTE: although 0.0000001" blade-tip clearance is desirable, it is also impractical. Typical maintenance practices call for a STATIC [no-load] clearance all-around between the blades and case-half-seals... otherwise undesirable damage during assembly/installation and start-up WILL OCCUR. High precision blade and disk diametrical measurements are taken of the assembly; then the outer-case abraidable seal(s) are machined to provide a very slight static clearance. The engine is then started and slowly advanced to full power. At this time, the blades stretch and distort due to centrifugal loads, air loads, thermal loads, etc... up-to a maximum. During the "break-in" period leading up to full power, the blade tip-path "grows" until it "gently" and deliberately abrades into the seal... setting the final clearance [and pattern]. A final visual inspection [Borescope] is used to confirm that the seals have been uniformly abraded around the circumference... and they are otherwise undamaged.
NOTE: the Blade tip path is usually "set" slightly outside of the desired airflow-path, by a small amount, to minimize airflow distortion at the very tips and enhance sealing.
Regards, Wil Taylor