Technology for reaching high pressure has been refined for many years.  It is central to the efforts of the CNC.  Relevant pressure apparatus can be broken down into to types:

Opposed Anvil

Opposed anvil apparatus apply opposed force in opposite directions to two anvils.  Examples include the diamond anvil cell and the Paris-Edinburgh press, which have both been used to synthesize nanothreads. There is generally a uniaxial stress component applied to the sample, a slightly higher stress in the direction of the applied load (vertical in the image below).  This uniaxial stress component aligns the nanothreads to it, such that the hexagonal c axis of nanothreads will be vertical in the apparatus below.

This web page from SNAP, where nanothreads were first synthesized by Fitzgibbons et.al., outlines some of the capabilities of the Paris-Edinburgh press. Single toriodal anvils can synthesize "non-encapsulated" samples up to 87 mm³ under favorable conditions at pressures up 10 GPa and "encapsulated" ones up to 55.5 mm³. Double toroidal anvils can synthesize volumes up to 31 mm³ for non-encapsulated samples under favorable conditions at pressures up to 20 GPa or so. For nanothread synthesis benzene is encapsulated in a metal gasket, which reduces the sample volume to around 20 mm³. The size of the encapsulated double toroidal sample is shown at left. For example, using the formula for the volume of a spherical cap: $$V = \frac {\pi h^2}{3} (3r-h)\,$$ the volume of the sample in the figure at the left is 21.8 mm³. h is the height of the spherical cap and r is the radius. Commercial pressure apparatus synthesizes >10⁶ kg of diamond/yr at 5 to 6 GPa.

The CNC is purchasing a 450 ton V7 Paris-Edinburgh press from MG63. Here is a list of their presses and a picture.

Conventional diamond anvil cells compress much smaller quantities, <0.05mm³.  However, new developments with large single crystal diamonds are increasing the sample size considerably to ~0.15mm³. Diamond cells are advantageous for in-situ measurements, despite the smaller sample volumes. For example, we have investigated the formation of nanothreads in-situ at high pressure using a diamond anvil cell and synchrotron x-ray diffraction at the Advanced Photon Source.

Multianvil

This web page describes multianvil apparatus that compress samples that may be larger than those in opposed anvil apparatus to pressures of up to 25 GPa or more. A V7 Paris-Edinburgh press can be used for multianvil experiments. Here is a youtube video showing a multi anvil press in Yingwei Fei's lab at the Carnegie Institution Geophysical Laboratory.  It has a Walker first stage and an octahedral second stage.  See Fei's facilities here.  The video is of the green press shown on this web page.  The two other presses typically use a split-cylinder configuration for the first stage instead of the Walker configuration.