Googling "spherical pressure hull limit"
LEEAMITe: The Transport Vehicle
ScienceDirect - Marine Structures : An overview of buckling and ultimate strength of spherical pressure hull under external pressure
The first gives some nice equations, with this perhaps the most useful:
Pe = 1.22 e (t/r)^2
Pe = elastic buclking pressure
e = module of elasticity
t = spherical shell thickness
r = radius to shell midsurface
There is a second limit equation ... probably worth running numbers through that, too,
to see if there is a different limit which is reached.
For a number of materials:
Elastic Properties and Young Modulus for some Materials
Structural Steel: 200 GPa
Silicon Carbide: 450 GPa
Tungsten Carbide: 450 - 650 GPa
Diamond: 1,050 - 1,200 GPa
Is a diamond sphere practical? I have no idea, but lets plug in some numbers.
e set to 1x10^3 GPa for diamond
t = 1m (arbitrarily)
r = 5m (arbitrarily)
Pe = 1.22 * 1x10^3 GPa * (1/5)^2
= 1.22 * (1/25) * 10^3 * GPa
= 0.05 * 10^3 GPa
= 5 * 10 GPa
That gets us nicely into the middle of the gas layer (which ends at 10
* 10 GPa, the gas transitions to a liquid metal, at a depth of 10,000
kilometers.
If you increase that by a factory of 100 ... then you are well above
the pressure at the transition, and can enter the metallic region.
Still a problem of temperature.
I *think* I read that the gas layer is transparent. Not really sure,
but I don't think the metal layer would be transparent.
Now, that is for an ideal sphere of solid diamond! 1m thickness and
5m radius seems to give you about 8m of interial space (diameter),
about 25 feet across.
That is an unbroken sphere, too! Maybe it runs off an special
"projection" engine that allows the machinery to be permanently
installed in the center of the sphere. Putting in passengers seems to
be a problem ...
(Edit: Putting carbon in a high temperature high pressure bath of atomic hydrogen seems to be a short lived experiment ... as well, if the reaction can be avoided, hydrogen infiltration would seem to be a problem.)