ELECTRIC EXPANSION OF QUARTZ. Pgs. 35-38
DILATATION ELECTRIQUE DU QUARTZ.
En commun avec JACQUES CURIE.
Journal de Physique, 2e serie, t. VIII, 1889, p. 149.
ELECTRIC EXPANSION OF QUARTZ.
In collaboration with JACQUES CURIE.
Journal de Physique, 2nd series, vol. VIII, 1889, p. 149.
La premiere partie cle ce travail se rapporte a des experiences deja anciennes ( 188 1 ) ( 1 ). Au moment ou elles ont ete entreprises, M. Lippmann (2), dans un travail sur les applications des principes fondamentanx de la conservation de Fenergie, de la conservation de Felectricite et du principe de Carnot, montrait en particulier qu’avec la connaissance des phenomenes de piezo-electricite que nous avions decou verts, on pouvait theoriquement prevoir la dilatation electrique de ce cristal, ainsi que la grandeur, le sens et la nature du phenomene.
(1) Comptes rendus des seances de V Academie des Sciences, t. XCIII, p. 1187 el t. XCV, p. 9 1 4 -
(2) Journ. de Phys., 1881 ; p. 387. Ann. de Chim. et de Phys., 1881.
The first key part of this work relates to experiments conducted some time ago (1881) (1). At the time these experiments were conducted, Mr. Lippmann (2), in a paper on the applications of the fundamental principles of energy conservation, electrical conservation, and the Carnot principle, demonstrated in particular that, based on our knowledge of the piezoelectric phenomena we had discovered, one could theoretically predict the electrical expansion of this crystal, as well as the magnitude, direction, and nature of the phenomenon.
(1) Proceedings of the Sessions of the Academy of Sciences, vol. XCIII, p. 1187, and vol. XCV, p. 914 -
(2) Journal of Physics, 1881; p. 387. Annals of Chemistry and Physics, 1881.
Nos experiences entreprises a ce moment en ont donne la consecration experimental.
Our experiments to date have provided experimental confirmation of this.
A cote de Finteret particulier qu’elles peuvent avoir, elles se sont amsi trouvees avoir Finteret plus general de verifier les consequences d une theorie cjui s applique a un grand nombre de phenomenes.
In addition to any specific interest they may have, they have also found themselves with a more general interest in verifying the implications of a theory that applies to a wide range of phenomena.
Nous donnerons d’abord une vue d’ensemble de la nature des phenomenes.
First, we will provide an overview of the nature of these phenomena.
Considerons un parallelepipede rectangle de quartz (Jig' 1) ajant quatre aretes, telles que AD, parallels a Fun des axes electriques, et quatre aretes, telles que AB, parallels a Faxe optique.
Consider a rectangular quartz parallelepiped (Fig. 1) with four edges, such as AD, parallel to the electric axes, and four edges, such as AB, parallel to the optical axes.
Premier cas. — Si Ton comprime le cristal normalement aux faces ABC, DEFG, c’est-a-dire si Ton exerce 1’effort dans le sens del’axe electrique, on obtient un degagement d’electricite sur les memes faces, donne par la formule
q = Kf
q, etant le degagement electrique, f, la force et K, la constante piezo-electrique.
Case 1. — If one applies a compressive force to the crystal along the faces ABC and DEFG—that is, if one applies a force in the direction of the electric axis—electricity is discharged from those same faces, as given by the formula
q = Kf
q is the piezoelectric displacement, f is the force, and K is the piezoelectric constant.
Nous avons trouve qu’une force de 1 kg degage, par effort direct dans ces conditions, une quantite d’electricite capable de poiter une sphere de 16.6 cm an potentiel d’un daniell, d’oii 1 on deduit, pour la constante piezo-electrique en unites absolues C. G. S. electrostatiques,
K = 6.32 × 10-8
0.0000000632
K. est la quantile absolue d’eleclricite degagee par un effort d’une dyne sur le quartz.
We have found that a force of 1 kg, when applied directly under these conditions, generates a quantity of electricity sufficient to charge a sphere of 16.6 cm in diameter to a potential of one daniell, from which we deduce, for the piezoelectric constant in absolute C.G.S. electrostatic units,
K = 6.32 × 10-8
0.0000000632
K. is the absolute quantile of the electricity generated by a force of one dyne applied to quartz.
A ce degagement piezo-electrique correspond un phenomene de dilatation electrique o dans le sens de l’axe electrique, lorsque l’on etablit une difference de potentiel V entre les deux faces qui lui sont normales (faces que 1’on peut supposer argentees ) ; on aura
δ = Kv = 6.32 × 10-8 V
δ est exprime ici en centimetres.
On voit qne la grandeur de la dilatation dans le sens de l’axe electrique est independante des dimensions du cristal.
This piezoelectric discharge corresponds to a phenomenon of electrical expansion along the electric axis when a potential difference V is applied between the two faces perpendicular to it (which we can assume are silver-plated); we will have
δ = Kv = 6.32 × 10-8 V
δ is expressed here in centimeters.
It can be seen that the magnitude of the expansion along the electric axis is independent of the crystal's dimensions.
Cette grandeur est dureste extremement petite pour les tensions dont nous disposons; pour V= 14.8, sort 4400 volts environ, tension correspondant a imm d’etincelle dans Fair, on a
δ = 0.935 x 10-6
soit 0.00935 en microns, de 1/100 micron environ.
This value is extremely small for the voltages we have available; for V = 14.8, the output is approximately 4,400 volts, a voltage corresponding to the spark gap in air, so we have
δ = 0.935 × 10⁻⁶
or 0.00935 microns, which is about 1/100 of a micron.
Deuxieme cas. — Si Ton comprime le cristal dans la direction de l’axeoptique, c’est-a-dire normalement aux faces ADBF, CFG, aucun degagement electrique ne prend naissance.
Reciproquement, lorsque Foil etablit une tension electrique quelconque, la longueur de Faxe optique ne varie pas.
Second case. — If the crystal is compressed along the optical axis, that is, perpendicular to the faces ADBF and CFG, no electrical discharge occurs.
Conversely, when Foil applies any electrical voltage, the length of the optical axis does not change.
Troisieme cas. — SiFon comprime le cristal dans une direction normale aux axes optique et electrique, c’est-a-dire normalement aux faces ADEC, BFG, un degagement electrique se produit sur les faces ABC, DFGE normales a Faxe electrique. Le degagement electrique est de signe contraire a celui qu’aurait donne une compression dans le sens de Faxe electrique ; il est donne par la formule dans laquelle K est la meme constante que precedemment
q =-K [L/e]f
K = 6.32 x 10— 8
Third case. — If one compresses the crystal in a direction perpendicular to the optical and electric axes, that is, perpendicular to the faces ADEC and BFG, an electric discharge occurs on the faces ABC and DFGE, which are perpendicular to the electric axis. The electric displacement has the opposite sign to that which would result from compression in the direction of the electric axis; it is given by the formula - where K is the same constant as before
q = -K [L/e]f
K = 6.32 x 10— 8
L est la longueur AB du parallelepipede dans la direction normale aux axes optique et electrique, e est la longueur de la dimension AD parallele a Faxe electrique dans le parallelepipede.
L is the length AB of the parallelepiped in the direction perpendicular to the optical and electrical axes, and e is the length of the dimension AD parallel to the electrical axis in the parallelepiped.
Reciproquement, lorsque Fon etablit une difference de potentiel entre les deux faces ABC, DFG, normales a Faxe electrique, le cristal tend a se dilater ou a se contracter dans la direction nor¬ male aux axes optique et electrique. Les elfets sont donnes par fa formule - δ etant exprime en centimetres et V en unites electrostatiques.
δ = -K [L/e]V= — 6.32 × 10-8 [L/e]V
Conversely, when a potential difference is applied between the two faces ABC and DFG, which are perpendicular to the electric axis, the crystal tends to expand or contract in the direction perpendicular to the optical and electric axes. The effects are given by the following formula - where δ is expressed in centimeters and V in electrostatic units.
δ = -K [L/e]V = — 6.32 × 10⁻⁸ [L/e]V
Ici le phenomene depend de deux des dimensions du cristal et pent etre considerablement ampiifie en prenant une lame tres mince dans le sens de baxe electrique et tres longue dans le sens normal aux axes optique et electrique.
Here, the phenomenon depends on two of the crystal's dimensions and can be significantly amplified by using a plate that is very thin in the direction of the electric axis and very long in the direction perpendicular to both the optical and electric axes.
En resume, lorsque I on etablit une difference de potentiel entre deux faces normales a baxe electrique du parallelepipede de quartz, le parallelepipede se deforme; laxe optique conserve toujours une longueur invariable, mais les autres dimensions changent. Pour un certain sens de la tension, 1 axe electrique se contracte et la direction normale aux axes optique et electrique se dilate. Pour une tension de sens inverse, baxe electrique se dilate et l’autre direction se contracte.
In summary, when a potential difference is applied between two faces perpendicular to the electric axis of the quartz parallelepiped, the parallelepiped deforms; the optical axis always retains a constant length, but the other dimensions change. For a certain direction of voltage, the electric axis contracts and the direction perpendicular to both the optical and electric axes expands. For a voltage in the opposite direction, the electric axis expands and the other direction contracts.
Les phenomenes piezo-electrique et de dilatation electrique sont lies entre eux par une loi de reaction analogue a la loi de Lenz. Le sens du phenomene de dilatation est, par consequent, en relation avec la forme cristalline du quartz. Le quartz se contracte suivant baxe electrique lorsque la charge positive se trouve a bextremite de cet axe, qui correspond a une arete duprisme hexagonal portant les facettes du ditriedre. Cette extremite se charge, an contraire, d’eleetricite negative lorsque bon comprime le cristal dans le sens de l axe (*).
(*) Nous avons, par une erreur de redaction, donne le sens inverse de celu i-ci vis-a-vis des facettes du cristal dans le Journ. de Phys., 1882, p. 245. Cette erreur ne se rencontre pas dans les publications anterieures, faites par nous. (Bull, de la Soc. miner., 1880, et Cornptes rendus des seances de I’Academie des Sciences, t. XCI, p. 294. )
The piezoelectric and electrical expansion phenomena are linked by a law of reaction analogous to Lenz's law. The direction of the expansion phenomenon is, therefore, related to the crystalline structure of quartz. Quartz contracts along the electric axis when the positive charge is located at one end of this axis, which corresponds to an edge of the hexagonal prism bearing the facets of the dihedron. This end, on the contrary, becomes negatively charged when the crystal is compressed along the axis (*).
(*) Due to a typographical error, we gave the opposite direction with respect to the crystal’s facets in the Journal of Physics, 1882, p. 245. This error does not appear in our earlier publications. (Bull. of the Mineralogical Society, 1880, and Proceedings of the Sessions of the Academy of Sciences, vol. XCI, p. 294.)
