Normal Melting Point Research Articles

Effect of Pressure on Self-Diffusion in Lead

Data are presented for the self-diffusion of lead as a function of temperature from 174° to 322° and for pressures from 1–8000 atmos. The decrease in the self-diffusion coefficient with pressure follows a relationship of the form (dlnD)/dζ=−(1/RT0)(Q0−ΔVactdTm/dP),where ζ = Tm/T, T0 and Q0 are the normal melting point and the zero pressure activation energy, respectively, and ΔVact is the activation volume. To first order the derivative is constant, deviations arising at high pressure because of the pressure dependence of dTm/dP. Several relationships are derived from thermodynamic considerations of the activated state, and are shown to be valid experimentally: (1) ΔHact = bRTm, with b = 20.7, and (2) ΔHact = ΔHm·(ΔVact/ΔVm), where ΔHm and ΔVm are the latent heat and volume change on fusion, respectively.

PHASE TRANSITIONS IN MULTIMOLECULAR LAYERS OF ADSORBED NITROGEN

The heat capacity of nitrogen adsorbed on titanium dioxide has been measured for amounts adsorbed corresponding to 2.2, 3.1, 4.0, and 4.8 molecular layers in the temperature range 14 ° to 75 °K. The occurrence in the adsorbed films of melting and of the transition in the solid phase of nitrogen is shown by maxima in the heat capacity. The melting process is completely reversible and takes place at temperatures below the normal melting point. The solid phase transition does not occur reversibly, the magnitude of the anomaly in the heat capacity depending upon the extent to which the system has been cooled prior to the measurement of the heat capacity. The experimental results are discussed in terms of current thermodynamic treatments of phase transitions in adsorbed films.

Melting Point of Adsorbed Liquids

Batchelor and Foster1 found, by examination of the vapour pressure – temperature curves, that dioxan adsorbed on a ferric oxide gel of pore radius ∼ 100 A. melts sharply about 6° C. below the normal melting point of the bulk liquid. During a recent investigation of the sorption of amines by silica gel, a similar effect has been observed with ethylenediamine.

Gallium Anisotropy and Crystal Structure

AN earlier communication1 directed attention to the ease with which single crystals of gallium could be produced and to the highly anisotropic properties of the specimens so obtained. The room temperature electrical conductivities as determined for the three mutually perpendicular axial directions were in the ratios of 1:3.2:7, and the corresponding expansion coefficients were in the ratios of 1:0.7:1.9. At that time, the axial directions had been related to the geometrical form and positioning of the seed crystal used when growing the specimens. The seed crystal had the symmetrical pyramidal form which is characteristic of crystals formed from liquid gallium when cooled to some 10° C. below the normal melting point. The axial direction giving the low conductivity had been found to coincide with the geometrical axis passing through the well-defined crystal point, while the other two axial directions coincided with the diagonals of the approximately square base of the pyramid.

The Thermodynamic Properties of Liquid Argon

The thermodynamic properties and equation-of-state data of liquid argon are interpreted in terms of a partition function previously derived. This partition function has a part due to vibratory motion of the atoms in the liquid and a part due to translational motion. The vibratory part contains the Debye characteristic temperature Θ for the solid, evaluated for a certain interatomic distance a0 which appears as a parameter in the partition function. a0 is interpreted as the average interatomic distance between nearest neighbors in the liquid, and is a function of a, the latter being defined as (2½V/N)⅓, where V is the molal volume and N Avogadro's number. With V set equal to the molal volume of the liquid at its normal melting point, a0 is assigned a value which appears reasonable from the atomic distribution curves obtained by x-ray studies of the liquid. With this value of a0, the partition function for this fixed value of V gives reasonably good values of the entropy over a large range of temperatures. A small, entirely reasonable change in the partition function improves the agreement with the experimental data. The parameters in the partition function have been evaluated for other values of V by using equation-of-state data. This leads to a calculation of the specific heats of saturated liquid argon over a range of temperatures. The agreement with experimental data is not exceedingly close, but is probably within experimental error. A calculation is also made of the free energies of the solid and liquid phases along the melting curve. They are found to be equal to within reasonably close limits. The application to various values of V leads to the evaluation of a0 as a function of a. The experimental curve for (∂S/∂V)T plotted against V appears to show a change of slope near the value of V characteristic of the liquid at its normal melting point. There is also a change in slope of the curve for da0/da vs. a, at the corresponding value of a. These facts are interpreted in terms of the atomic distribution curves, which appear to indicate a change in structure of the liquid which starts near the same value of V or a. The liquid appears to change from a distorted face-centered structure to a distorted body-centered structure as the volume increases. Information about the potential energy of liquid argon is obtained from the experimental data by application of the partition function. It is found that the potential energy of the liquid can be rather effectively correlated with the potential energy of the solid. Finally, certain peculiarities of the equation-of-state data are believed to indicate a pre-freezing phenomenon, in which particles containing appreciable numbers of atoms and having the structure of the solid, appear in the liquid. A state of this sort can be stabilized by the entropy of mixing of the solid particles with the liquid.

The Five Alkali Metals under High Pressure

Effect of high pressure on the melting constants, electrical resistance and volume of the alkali metals.---(1) New data for Rb and Cs, presented in detail elsewhere, are given in three tables. Then, since similar data have previously been obtained for Li, Na and K, the results of a comparative study of all five alkali metals under pressure are given and discussed. (2) Melting constants. The general character of the melting phenomena is the same for the alkali metals as for other substances; the melting curve continues to rise indefinitely with increasing pressure, with neither maximum nor critical point. Above 10000 kg/${\mathrm{cm}}^{2}$ there is a reversal of the normal melting points of Na and K, and a moderate graphical extrapolation indicates other reversals also, so that at high pressures we may expect a complete reversal of the order of normal melting temperatures, Cs being the highest and Li the lowest. The fractional change of volume on melting is the same within 25 percent for Na, K, Rb, and Cs, as is also the latent heat of melting per gm atom; for Li the values are only about one-fourth as large. (3) Electric resistance. K shows the greatest relative decrease of resistance with pressure above 1400 kg/${\mathrm{cm}}^{2}$; Rb occupies electrically an intermediate position between K and Cs. The effect of pressure on the resistance of Cs is unique in that there is a minimum (at 4000 kg/${\mathrm{cm}}^{2}$). This minimum seems to have no connection with the crystal structure of the solid, but will probably be shown by the liquid also at higher pressures. At low pressures Cs has the maximum negative pressure coefficient of resistance and at high pressures the maximum positive coefficient of all pure metals measured. At high pressures the curve of pressure coefficient of resistance of Cs against pressure has a point of inflection which could not be predicted from the behavior at lower pressures; if other metals behave similarly above the present experimental range, it is possible that the resistance of all metals will eventually pass through a minimum. Such a change for Rb may be expected below 20000 kg/${\mathrm{cm}}^{2}$. This reversal of resistance may be an indication of the first beginning of a quantum break-down, suggested more strongly by the volume relations. The discontinuity of resistance at melting is approximately constant for all the alkalies. (4) Volume. Cs is the most compressible solid element yet measured directly. Instead of the atom the electron seems to be the significant unit of structure for volume since the volume per electron and the compressibility per electron do not vary greatly throughout the alkali series, whereas atomic volume and atomic compressibility vary greatly. At atmospheric pressure the electronic volume of K is abnormal, standing between that of Li and Na, but at high pressures there is a reversal. At high pressures the electronic compressibilities of all the alkalies are roughly equal (2.2. to 3.5\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}29}$ at 12000 kg/${\mathrm{cm}}^{2}$), except for K, which is twice as compressible per electron (5.9\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}29}$). The initial high relative compressibilities of Cs and Rb decrease rapidly with pressure, crossing that for K below 8000 kg/${\mathrm{cm}}^{2}$, while the high compressibility of K persists over a wide pressure range with comparatively small drop. All the evidence indicates an abnormally open electronic structure for K. (5) Comparison with compressibility of electron gas. Numerically the compressibility of all the alkalies is of the order of magnitude of that of a perfect gas under a high internal pressure, taking the electron as the gas unit. For K, the compressibility has passed a turning point within the experimental range, and appears to be ultimately headed for the perfect gas value. This may be the beginning of the quantum break-down, which is complete only at remotely high pressures. On the theoretical side, Schottky's theorem, in conjunction with the extrapolated behavior of compressibility, indicates the same break-down at high pressures.