A vessel system for high temperature, high-pressure, microwave-assisted chemistry methods, the improvement comprising: a rigid liner cylinder that includes one closed end and one open end defining a mouth; a liner cap positioned in said mouth of said rigid liner cylinder for closing said rigid liner cylinder; said liner cap including a depending column that seats within the inside diameter of said rigid liner cylinder, a disk at one end of said depending column and having a diameter sufficient to rest upon the rigid liner cylinder without falling into the rigid liner cylinder so that said liner cap can rest in said rigid liner cylinder at said mouth of said rigid liner cylinder, and a gas venting passage as part of said depending column to provide gas venting at said liner cap and from said rigid liner cylinder; a cylindrical reaction vessel, wherein said rigid liner cylinder is positioned inside of a cylindrical reaction vessel, said rigid liner cylinder having an outer diameter that together with the inner diameter of said cylindrical reaction vessel defines an interstitial space between said cylindrical reaction vessel and said rigid liner cylinder; a microwave-transparent reaction vessel floating plug that rests in a defined position above said mouth of said rigid liner cylinder and coaxial with but not bearing against said cylindrical liner cap; a female threaded cap that engages male threads on said cylindrical reaction vessel at said mouth of said cylindrical reaction vessel and that bears against said reaction vessel plug to thereby provide a pressure resistant closure connection for said vessel system; and a vent opening in said female threaded cap, so that when the pressure inside the reaction vessel exceeds a mechanically defined set point, the top of the female threaded cap can flex to allow the reaction vessel floating plug to move slightly and release gas pressure from the reaction vessel while the digestion reaction continues and excess gas can then vent through said vent opening. a rigid liner cylinder that includes one closed end and one open end defining a mouth; a liner cap positioned in said mouth of said rigid liner cylinder for closing said rigid liner cylinder; said liner cap including a depending column that seats within the inside diameter of said rigid liner cylinder, a disk at one end of said depending column and having a diameter sufficient to rest upon the rigid liner cylinder without falling into the rigid liner cylinder so that said liner cap can rest in said rigid liner cylinder at said mouth of said rigid liner cylinder, and a gas venting passage as part of said depending column to provide gas venting at said liner cap and from said rigid liner cylinder; a cylindrical reaction vessel, wherein said rigid liner cylinder is positioned inside of a cylindrical reaction vessel, said rigid liner cylinder having an outer diameter that together with the inner diameter of said cylindrical reaction vessel defines an interstitial space between said cylindrical reaction vessel and said rigid liner cylinder; a microwave-transparent reaction vessel floating plug that rests in a defined position above said mouth of said rigid liner cylinder and coaxial with but not bearing against said cylindrical liner cap; a female threaded cap that engages male threads on said cylindrical reaction vessel at said mouth of said cylindrical reaction vessel and that bears against said reaction vessel plug to thereby provide a pressure resistant closure connection for said vessel system; and a vent opening in said female threaded cap, so that when the pressure inside the reaction vessel exceeds a mechanically defined set point, the top of the female threaded cap can flex to allow the reaction vessel floating plug to move slightly and release gas pressure from the reaction vessel while the digestion reaction continues and excess gas can then vent through said vent opening.