In this paper we present a review of high-gas-pressure single crystal growth studies of YBa2Cu4O8 and Y2Ba4Cu7O15-x performed in oxygen pressure up to 3000 bar and Hg1-xMxBa2Can-1CunO2n+2+ (M = Pb, Re; n = 1-7) compounds in argon pressure up 11 000 bar at temperature up to 1200 °C. Chain compounds A1-xCuO2 (A = Sr, Ca, Ba) have been synthesized at high oxygen pressure up to 2000 bar. High-pressure phase diagram studies of the investigated systems are also discussed. Structure analyses of Y2Ba4CunO2n+x (n = 6-8), Hg1-xMxBa2Can-1CunO2n+2+ (M = Pb, Re; n = 1-8), Sr0.73CuO2 and (Sr,Ca)4Cu6O10 single crystals have been performed. The effects of substitutions and trends in bondlengths are discussed. The vortex state properties of HgBa2Ca2Cu3O8+ and YBa2Cu4O8 single crystals are compared. For Hg-based compounds, the influence of oxygen content, chemical substitutions and radiation defects on vortex pinning were determined. The quasi-one-dimensional cuprates Ca0.83CuO2 and Sr0.73CuO2 show an antiferromagnetically ordered state of long-range 3D character at T < 10 K. The spin dynamics of Sr0.73CuO2, measured by inelastic neutron scattering, indicate that this ordered state coexists with a dimerized singlet ground state.
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