I couldn't find any write-up of these, so I thought I'd have a go.
They may or may not be canon in your campaign, or in Traveller-at-large.
Feel free to modify TLs and so forth. Feedback welcome. Hope that this
is useful...

Jonathan
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Vibro-knife
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This type of blade is very illegal in almost all jurisdictions where there
is actually a functioning law level, and requires its owner to either be a
Noble, or to have a permit signed by one (usually the character must be
working for the Noble as a bodyguard or equivalent). These blades have two
modifications from a 'normal' knife.

First, the blade is made from some sort of exotic material. There are
four main options, in order of (significantly) increasing cost:

- CrystalIron. Iron treated at the atomic level to form a single crystalline
complex. This metal is commonly used for starship hulls. The crystal matrix
is unstable, so requires a stabilizing field, supplied by a power system
set into the handle, and a realignment system, usually a stand into which
the blade must be inserted every so often (after use, and every week or so).
Loss of power to the stabilizing system causes the blade to suddenly lose
its edge and shape, at which point it cannot be repaired. Typical standby
battery life is 90 days. CrystalIron blades are TL-12 items.

- Diamond. The actual diamond blade is usually set into a sanmei (three-layer)
construction with tungsten side plates. Diamond is statically stable, so
requires no external stabilizing field. Lightest of all the listed blade types.
Diamond blades are TL-14 items.

- Bonded Superdense. Military starship hull material, usually set into a
wumei (five-layer) construction with crystalIron internal, and tungsten
external, side plates. Requires two powered stabilizing fields, supplied
by a power system set into the handle. Loss of the stabilizing field leads
to loss of the blade by (relatively minor) explosion. Typical standby battery
life is 60 days. Heavier than CrystalIron. Typically these are TL-16 items.

- Neutronium. Usually a coating of one or two atomic-radius equivalent
thickness on an existing edge, carefully milled to provide bonding sites.
The underlying blade is usually diamond or bonded superdense, onto which the
neutronium is deposited. Sometimes sanmei but more often wumei construction
is typically used. Neutronium requires its own active stabilizing field,
again with the power system set into the handle. Loss of the stabilizing
field leads to loss of the blade by usually fairly major explosion (strictly,
a gravity-based implosion followed by a strong force-based explosion, but
the results are pretty messy, however they are caused). Typical standby
battery life is 30 days. Much heavier than the other types, but still
designed for one-handed operation. May require minimum STR levels for proper
(or optimal) operation. These are TL-18 items.

As far as cutting ability goes, neutronium cuts bonded superdense, which
in turn cuts diamond, which cuts crystaliron, which cuts everything else.
That's bit simplistic, but will serve. It is rumoured that some Ancient
artefacts will cut through even a neutronium/bonded superdense blade like
it was warm butter, but there are all sorts of rumours about Ancient
artefacts.

The second change from a regular blade is that the power supply, in addition
to any necessary stabilizing effect it may have, also (when the 'on' button
is pressed), causes resonant vibrations in the blade itself. This allows it
to cut through anything it could normally cut through without any real effort,
just rest the blade against the surface, turn it on, and the blade will
usually cut through using only its own mass. (There are exceptions, such
as things like Chobham armour, and starship hulls, but you get the idea.)
Obviously the more you use the vibro facility, the more you use the battery,
but these are typically well equipped with warning lights, buzzers, and so on.
When the vibro is turned on, the blade typically hums, unless it is damped
somehow. Holding the blade in a chef's grip (thumb and forefinger holding
the actual blade, not the pommel) is a quick'n'easy way to silence it,
although this may cause stress fractures in the thumb- and finger-bones.