## Abstract

Measurements have been made of the onset of the superconducting phase transition of tin whiskers (single crystals of diameter 1-2 $\mu $m and length several millimetres) as a function of temperature T, magnetic field H, and elastic strain $\epsilon $ up to 2%. For samples of this size (denoted 'moderately small' since they are larger than $\lambda $(0)), there is a range of temperatures, approximately 20-30 mK below the transition temperature T$_{\text{c}}$($\epsilon $), for which the transition is of second order in the Ehrenfest sense. Below the temperature denoted T$^{\prime}$($\epsilon $) the transition is of first order and may exhibit hysteresis. The phase diagram at constant strain is derived from the equation $\Delta $G = - A$\psi ^{2}$ + $\frac{1}{2}$B$\psi ^{4}$ + $\frac{1}{3}$C$\psi ^{6}$, where $\Delta $G is the free energy difference between the superconducting and normal states, $\psi $ is the wave function of the superconducting electrons, and the coefficients A, B and C each comprise two terms, of which one is field-dependent, being proportional to H$^{2}$. The other, field-independent, term is Ginzburg's (1958) expression for the zero-field energy difference, so that A contains a term proportional to (T$_{\text{c}}$ - T), and B is independent of T. Coefficient C contains a field-independent term, assumed independent of T, which we introduce for consistency. The condition A = 0 describes both the secondorder transition and limiting supercooling, while the transition at thermodynamic equilibrium in the first order region and limiting superheating are described by B$^{2}$ = - $\frac{16}{3}$AC and B$^{2}$ = - 4AC respectively. The Landau critical point (H$^{\prime}$,T$^{\prime}$) is given by B = 0, A = 0. If the limiting metastable transitions for a cylinder in parallel field are included on a phase diagram, then the supercooling curve is a continuation of the second order curve while the curve for thermodynamic equilibrium branches from it tangentially if C(H$^{\prime}$, T$^{\prime}$) > 0, or at a slope which is 1.32 times greater than this if C(H$^{\prime}$, T$^{\prime}$) = 0. The case C(H$^{\prime}$, T$^{\prime}$) < 0 is discussed elsewhere (Nabarro & Bibby 1974, following paper in this volume). The last case arises because our observations indicate that the field-independent term in C is negative. Estimates of the sample size were made by using the present theory and were in fair agreement with estimates made electron-microscopically. Expressions for the change at the superconducting transition of the specific heat and other second derivatives of the Gibbs free energy above and below T$^{\prime}$ are derived. It is shown theoretically that the transition remains of second order when the sample is strained elastically. Some of the Ehrenfest relations describing a second order transition with two independent variables are experimentally verified from our data.