## Abstract

The heat capacity of single crystals of magnesium oxide has been measured in the temperature range 3 to 270 $^{o}$K with estimated accuracies of $\pm $0$\cdot $5% for 10 < T < 20 degrees K and $\pm $ 0$\cdot $2% for T>20 $^{o}$K. Reliable results were not obtained below 10 $^{o}$K because of desorption of helium exchange gas in the calorimeter vessel. With the assumption that the effect of anharmonicity of the lattice vibrations may be neglected for T < $\frac{1}{3}\Theta _{D}$, the experimental results have been analyzed to obtain a number of properties of an effective harmonic frequency spectrum of magnesium oxide. In particular, several negative moments, three even positive moments, and the coefficients of the first three terms in the low-frequency expansion have been calculated. From the low-frequency expansion the apparent Debye characteristic temperature at 0 degrees K ($\Theta _{0}$) is calculated to be 946 $\pm $ 4 degrees K, in good agreement with the measured elastic constants ($\Theta $ (elastic) = 949 $^{o}$K). The zero-point energy is found to be 3455 $\pm $ 25 cal mole$^{-1}$ deg$^{-1}$; it is pointed out that zero-point energy will cause some anharmonic effects even at the lowest temperatures. A comparison with the heat capacities and elastic constants of the alkali halides suggests that the interatomic forces in magnesium oxide may be rather similar to those in lithium fluoride. The difference between the present heat capacity results and earlier results of Giauque & Archibald (1937) for small particles of magnesium oxide is much larger than that predicted by theoretical estimates of the effect of particle size on the heat capacity of solids. A simple theoretical approximation is derived for the change of $\Theta _{\infty}$ with particle size; here again the experimental change is found to be much larger.