HAL Id: jpa-00217983
https://hal.archives-ouvertes.fr/jpa-00217983
Submitted on 1 Jan 1978
HAL is a multi-disciplinary open access
archive for the deposit and dissemination of
sci-entific research documents, whether they are
pub-lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d’enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.
THE TRANSITION BETWEEN THE
CLOSE-PACKED PHASES OF 4He
J. Franck
To cite this version:
JOURNAL DE PHYSIQUE Colloque C6, supplkment au
no
8, Tome 39, aoat 1978, page (26-1 10THE
TRANSITIONBETWEEN THE
CLOSE-PACKED PHASES O F 4 ~ e J.P. FranckDepartment of Physics, University of Alberta, Edmonton, Alberta, Canada T6G 2J1
R6suml.- Une ltude thermique de la transition hexagonale compact
-
cubique 1 faces centrdes de 4 ~ e a ltd effectude depuis le voisinage du point triple jusqu's environ 3,7 kbar. La transition prlsen- te un cycle d'hystlrgsis de tempdrature dans toute la rlgion. Le caractsre ggndral de la transition suggzre une transformation martensitique. Des mesures de chaleur latente montrent que la transfor- mation est partielle au-dessus de 16 K.Abstract.- The transition hcp
-
fcc 4 ~ e was studied thermally from the vicinity of the triple point to about 3.7 kbar. It was found that the transition shows temperature hysteresis over the whole ran- ge. The general character of the transition suggests a martensitic transformation. Latent heat mea- surements show that above 16 K only partial transformation takes place.The transition hcp
-
fcc 4 ~ e /I/ was studied and is assumed to close to T = 1/2(T +T ) . Thistr L h
thermally from the vicinity of the triple point to line is also shown in figure 1. about 3.7 kbar. The helium crystals were contained
ting and cooling curves could be taken, during hea- ting the latent heat of transition could also be ob- in a pressure bomb of 7.44 cm3 internal volume and
3 5
,
I I I Itained. The density of the crystals was obtained from the melting point, making use of published ther- modynamical data of 4 ~ e 121.
grown at essentially constant pressure. Both hea-
It was found that both heating and cooling transition have finite width ; the heating transi- tion temperature, Th, was taken as the lower limit of the heating transition range, and the cooling transition, Tc, as the upper limit of the cooling transition range. In all cases it was found that T is lower than Th ; the amount of temperature hyste- resis T -T varies along the transition line. The
h c
width of the heating and cooling transition also varies along the transition line, generally a large temperature hysteresis is observed when the transi- tion widths are also large.
The phasediagram in the (P,T) plane is shown in figure 1. Cooling transitions have so far only been observed up to a pressure of 3 kbar, where the temperature hysteresis is a maximum of 450 mK. Hea- tin& transitions were observed up to 3.7 kbar, they were found on the linear extrapolation of the hea- ting transition line shown in figure l. The thermo- dynamical equilibrium transition temperature (equa- lity of Gibbs free energy) is bracketed by Tc and Th
Fig. 1 : Phase diagram of 4 ~ e . Solid lines : hea- ting and cooling transition. Dashed line : estima- ted equilibrium transition. Open triangle : Dugdale and Franck (Reference 141) ; open square : Mills and Schuch (Reference 1 5 1 ) .
The slope of the transition line above about 16.5 K is constant at dP/dT = 508 bar/K. Below 16.5 K the slope continuously increases, at the triple point it is at least 2300 bar/^ and might in fact be in- finite. The latent heat was measured for a number
of crystals, from which the transition entropy ( A S ) ~ ~ = = L / T ~ ~ was obtained, this is shown in figure 2.
Fig. 2 : Transition entropy (AS) and molar volume change (AV) tr. (AV) is calculaEZd from the Clapey- ron equation. (AS) Eglc. and (AV) calc. : theoreti- cal estimates of Holian et al. (Reference /3/) ;
Open triangle : Dugdale and Franck (Reference /4/).
Up to about 16 K, the transition entropy is nearly constant at 4.1 mcal/mole.K. Above 16 K, the transi- tion entropy decreases rapidly. Above 18 K no relia- ble measurements of the transition temperature could be made. It is suggested that the data indicate com- plete or almost complete transformation from hcp to fcc 4 ~ e below I6 K. Above this temperature, only par- tial transformation to the low temperature phase ta- kes place, the amount transformed being at most 25 %
at 18.5 K and probably even less at higher tempera- tures. Since it is believed that up to 16 K the tansition entropy represents a true molar quantity, one could obtain the molar volume change from the Clapeyron equation, this is also shown in figure 2.
The temperature hysteresis decreases from about 450 mK at 3 kbar to about 25 mK at a pressure about 50 bar above the triple point (1126 bar). The tran- sition width over the same range changes from 100 mK
to about 5 mK. Cooling and heating transition width are nearly the same.
the temperature hysteresis increases again, beco- ming about 150 mK when the transition is observed on the melting line. In chis range the heating transition retains a rather small width (a 8 mK)
but the cooling transition becomes very large, up to a width of 150 mK on the melting line. In this interval the transition also shows increasingly ir- reversible behaviour, sometimes occurring in seve- ral separate stages. Self-cooling during heating and self-heating during cooling were also commonly observed in this range.
The general characteristics of the transi- tion are those found in martensitic transitions, and it is proposed that the transition is of this type. A diffusionless transition is made highly li- kely because of the extreme smallness of the tran- sition entropy ((AS) =2.9x10-~ erg/atom.K)
.
Tem-tr
perature hysteresis and transition width are gover- ned by the nature of the martensitic nuclei belie- ved to be present in the high temperature phase. The very pronouncedchargesin the equilibrium data as well as the kinetics of the transition close to the triple point are believed to be caused by pre- melting phenomena (e.g. creation of equilibrium vacancies) in the solid. The transition will be susceptible to such effects because of its extreme weakness.
The transition entropy up to 16 K is in excellent agreement vith the predictions of Holian et al. /3/, the same is true for the molar volume change. The predicted upwards curvature of the transition line is, however, not found. The behaviour close to the melting point is so far also not predicted by theo- ry. Earlier experimental investigations /4/ are in good agreement with the present data. Crystals sho- wing both fcc and hcp in X-ray work /5/ are now believed to indicate the partial transformation at higher pressures rather than thermodynamical equilibrium between the two phases.
Acknowledgements.- I would like to thank P.W. Wright A. O'Shea and I.D. Calder for help with the experi- ments and J.S. Dugdale for valuable correspondence.
References
/I/ Dugdale,J.S. and Simon, F.E., Proc. R. Soc.
218A
(1953) 291 121 Spain, I . L . and Segall, S.,Cryogenics (1971) 26
/3/ Holian, B.L., Gwinn, W.D., Luntz, A.C. and Alder, B.J.,
J. Chem. Phys.
59
(1973) 5444 /4/ Dugdale, J.S. and Franck, J.P.,Phil. Trans. R. Soc.
