Reciprocal Mean Research Articles

Lattice thermal conductivity of antiferromagnetic MnF 2 below its néel temperature

The theoretical model of Callaway for lattice thermal conductivity at low temperatures has been used for MnF 2 to calculate the l ga(T) term in the reciprocal mean free path equation l −1 g = l −1 ga + l −1 ma . The l ga( T) part has also been calculated to get l g( T). The K g( T) value calculated from these K g( T) are compared with Slack's results. For satisfactory agreement it is necessary to conclude that, at low temperatures the boundary scattering term in the relaxation time formula of Callaway is temperature dependent and diverges from Casimir's model by a factor which changes from 6 to 1·2 in the temperature range 3–10°K.

Nuclear Spin-Lattice Relaxation in Superconducting Aluminum Alloys

The nuclear spin-lattice relaxation time, ${T}_{1}$, of superconducting aluminum alloys which contain up to 0.16% zinc or germanium has been measured in the range of 0.37\ifmmode^\circ\else\textdegree\fi{}K to 1.2\ifmmode^\circ\else\textdegree\fi{}K. A field cycling method was used. ${T}_{1}$ decreases slightly (less than 30%) with increasing-impurity concentration. The experimental data indicate that the anisotropy of the energy gap decreases with increasing reciprocal mean free path. The results are explained by means of the theory of dirty superconductors introduced by Anderson.

On the temperature-dependence of the distribution coefficient: The solid solubilities of tin in silicon and germanium

The solid solubility of tin in silicon has been determined in the range from 800°C to the melting point of silicon, using crystal-pulling and thermal-gradient crystallization techniques. The distribution coefficient, k, of tin in silicon falls from 0.016 at the melting point of silicon to about 6.5 × 10 −4 at 800°C. Earlier work on the tin-germanium system has also been extended. The form of the temperature-dependence of k is similar for both systems and does not fit into the correlation recently proposed by Hall ( J. Phys. Chem. Solids 3, 63 (1957)). For these two systems the observed temperature-dependence of k can be explained as being due in a large measure to departures from ideality in the liquid state. Binding energies of tin in germanium and silicon calculated from the solid-solubility data compare favorably with binding energies calculated using Allen's reciprocal mean postulate for covalent bond energies (J. Chem. Phys. 27, 810 (1957)).

Reciprocal Mean as a Measure of Covalent Bond Energy

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Markoff Random Processes and the Statistical Mechanics of Time-Dependent Phenomena. II. Irreversible Processes in Fluids

The procedures developed in a previous paper of the same main title are applied to the specific case of irreversible processes in fluids. The gross variables are chosen to be a finite number of the plane-wave expansion coefficients of the local particle, momentum and energy densities. As an example, the gross variables describing the local particle density are ∑ i=1Nexpik·xi,where pi and xi are the momentum and position of the ith molecule and N the total number. k runs over a finite number of values which are all small compared to the reciprocal mean distance between molecules. The phenomenonological equations are derived and expressions are given for the viscosity, diffusion, and heat conductivity in terms the autocorrelation coefficients of certain phase functions. These expressions are supposed to be valid for both liquids and gases. They are shown to coincide with the Chapman-Enskog expressions for dilute gases.

In re Cetuchinas.

456Treaties — Most-Favoured-Nation Clause — Meaning of Reciprocity.