Constant-volume x-ray study of solid argon and solid krypton

At constant volume the temperature variation of the vacancy concentration can be obtained by measuring solely x-ray lattice parameters as a function of temperature. Furthermore, at the elevated pressures required the concentration of vacancies is sensitive to lattice relaxation via the free volume of formation. X-ray lattice parameters sufficiently precise to extract values for the free volume of both argon and krypton have been measured in crystals held at almost constant volume. The molar volumes of the Ar crystals were 24.6, 23.8, and 23.6 ${\mathrm{cm}}^{3}$/mole with melting temperatures of 86, 112, and 118 K, respectively. These temperatures correspond to melting pressures of 9.0, 123.7, and 152.7 MPa, respectively. The molar volume of the Kr crystal was 29.6 ${\mathrm{cm}}^{3}$/mole with a melting temperature of 126 K. The corresponding melting pressure is 34.8 MPa. The analyses require a knowledge of the vacancy concentration at the saturated vapor pressure, and it is shown that available experimental values for krypton are consistent only with a free volume of formation equal to almost an atomic volume. For argon they lead to a free volume somewhat less than an atomic volume. In addition, two anomalous phenomena were found to occur in these high-pressure crystals. A dramatic variation in the lattice parameter was observed near to the melting lines of both argon and krypton (\ensuremath{\gtrsim} 2 K below). Also, solid argon appeared to flow under the action of small pressure gradients (\ensuremath{\sim} 1 MPa) at high temperatures.

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