CONTRACTIONS AND EXPANSIONS CAUSED BY ELECTRICAL TENSIONS IN HEMIHEDRAL CRYSTALS WITH INCLINED FACES. Pgs. 26-29
CONTRACTIONS ET DILATATIONS
PRODU1TES PAR RES TENSIONS ELECTRIQUES
DANS LES
CRISTAUX HEMIEDRES A FACES 1NCLINEES.
En commun avec JACQUES CURIE.
Comptes rendus de I’Academie des Sciences, t. XCIII, p. 1187,
seance du 26 decembre 1881.
CONTRACTIONS AND EXPANSIONS
CAUSED BY ELECTRICAL TENSIONS
IN
HEMIHEDRAL CRYSTALS WITH INCLINED FACES.
In collaboration with JACQUES CURIE.
Proceedings of the Academy of Sciences, vol. XCIII, p. 1187,
session of December 26, 1881.
Supposons qu’un corps solide, un prisme de verre, par exemple, ayant 1 cm2 de surface, eprouve une variation egale au millionieme de sa longueur. Cette quantite sera tres difficilement constatable par un procede direct.
Suppose that a solid object, a glass prism, for example, with a surface area of 1 cm² undergoes a change equal to one-millionth of its length. It would be very difficult to measure this quantity using a direct method.
Mais, si l’on s’oppose d’une maniere absolue a cette variation de longueur, le solide eprouvera une variation de pression de pres de 1 kg. Un systeme sensible, permettant de constater ou de mesurer cette pression, donnerait done la possibility de conclure d’une facon indirecte a la variation de longueur qui aurait pu se produire. On voit que cette methode est basee sur la faiblesse du coefficient de compressibilite des corps solides.
However, if this change in length is completely prevented, the solid will experience a pressure change of nearly 1 kg. A sensitive system capable of detecting or measuring this pressure would therefore make it possible to indirectly infer the change in length that might have occurred. It is clear that this method is based on the low compressibility coefficient of solid bodies.
Nous avons realise un appareil remplissant ces conditions, en nous servant de la propriete que possede le quartz de degager, lorsqu’on exerce sur lui un effort dans certaines directions, des quantites d’electricite proportionnelles aux pressions qu’on lui fait subir.
We have developed a device that meets these requirements, taking advantage of the property that quartz has of generating, when a force is applied to it in certain directions, amounts of electricity proportional to the pressures exerted upon it.
Nous decrirons cet appareil, en detaillant l’application que nous en avons faite pour mettre au jour le phenomene reciproque de la polarite electrique des cristaux bemiedres.
We will describe this device, detailing how we used it to uncover the reciprocal phenomenon of the electrical polarity of hemihedra crystals.
On sait que, lorsqu’on fait subir a un cristal hemiedre a faces inclinees une variation de pression suivant un axe d’hemiedrie, il se developpe aux deux extremites de cet axe des quantiles d’electricite egales et de signes contraires, le sens du degagement etant lie an signe de la variation de pression.
It is known that when a hemihedral crystal with inclined faces is subjected to a pressure variation along a hemiedral axis, electric charges of equal magnitude and opposite signs develop at both ends of that axis, with the direction of the charge discharge being related to the sign of the pressure variation.
Nos experiences actuelles viennent prouver que, reciproquement, lorsqu’on charge d’electricites contraires les deux extremites de l’axe d’uncristal hemiedre, il eprouve, suivant cet axe, soit une contraction, soit une dilatation, selon le sens dans lequel la tension electrique 1 ui a ete appliquee.
Our current experiments demonstrate that, conversely, when opposite electric charges are applied to the two ends of the axis of a hemihedral crystal, it undergoes either contraction or expansion along that axis, depending on the direction in which the electric voltage was applied.
Les sens des deux phenomenes reciproques sont lies entre eux par la loi generale suivante, dont nous empruntons Fenonce a M. Lippmann, et qui n’est autre chose qu’une generalisation de la loi de Lenz :
« Le sens est toujours tel que le phenomene reciproque tende a s’opposer a la production du phenomene primitif. »
The directions of the two reciprocal phenomena are linked by the following general law, the wording of which we borrow from Mr. Lippmann, and which is nothing other than a generalization of Lenz’s law:
“The direction is always such that the reciprocal phenomenon tends to oppose the occurrence of the original phenomenon.”
M. Lippmann, se basant a la fois sur les principes de la conservation de l'electricite et de la conservation de l’energie, et sur les proprietes du phenomene direct, avait pu prevoir et demontrer d’avance toutes les particularites du phenomene reciproque (1). Il avait meme donne le moyen d’en calculer cFavance la grandeur pour une difference de potentiel determinee, lorsque Fon connait la quantite d’electricite degagee par une pression determinee.
( 1 ) Principe de la conservation de l’electricite ( A /males de Chimie et de Physique, 1881, p. i45).
Mr. Lippmann, drawing on both the principles of the conservation of charge and the conservation of charge, as well as on the properties of the direct phenomenon, was able to predict and demonstrate in advance all the characteristics of the reciprocal phenomenon (1). He had also provided a method for calculating its magnitude in advance for a given potential difference, when one knows the quantity of electricity released by a given pressure.
(1) Principle of the conservation of charge (Annales de Chimie et de Physique, 1881, p. 145).
Nous avons anterieurement mesure la quantite d’electricite degagee pur la tourmaline et par le quartz pour une pression de ikg; on trou ve, en faisant le calcul, que des prismes de ces substances eprouveront des variations de longueurs d’environ 1/20000 de millimetre pour une difference de potentiel correspondant a une etincelle de om,oi dans Fair.
We have previously measured the amount of electricity discharged by tourmaline and quartz at a pressure of 1 kg; calculation shows that prisms of these substances will undergo length changes of about 1/20,000 of a millimeter for a potential difference corresponding to a spark of 0.01 volt in air.
Voici comment les experiences ont ete disposees : Fappareil est forme de deux plaques massives en bronze, unies par trois grosses colonnes qui font corps avec l’une des plaques, traversent 1 autre et sont terminees par des vis munies d’ecrous (2).
(2) (E) Voir la figure 2, page 4o*
Here is how the experiments were set up: The apparatus consists of two solid bronze plates joined by three large columns that are integral with one of the plates, pass through the other, and are topped with screws fitted with nuts (2).
(2) (E) See Figure 2, page 40*
On pent ainsi, a l’aide des ecrous, serrer entre les deux plaques une pile d’objets places les uns au-dessus des autres. Les objets sont partages en deux systemes distincts :
Using the nuts, you can thus clamp a stack of objects placed one on top of the other between the two plates. The objects are divided into two separate systems:
Le système inférieur sert uniquement à mesurer les variations de pression : il se compose de trois larges plaques de quartz minces, séparées par des plaques métalliques reliées à un électromètre, qui enregistre l'électricité générée par les variations de pression subies par les plaques de quartz.
The lower system is used solely to measure pressure variations: it consists of three wide, thin quartz plates, separated by metal plates that are connected to an electrometer, which registers the electricity generated by the pressure variations experienced by the quartz plates.
Le systeme superieur sert a produire le phenomene que bon veut etudier. Dans le cas qui nous occupe, il se composait de trois cristaux hemiedres aussi volumineux que possible, et separes les uns des autres par deux rondelles de cuivre. Les trois cristaux avaient leurs axes d’hemiedrie paralleles a la direction du serrage. Les deux cristaux des bouts etaient retournes par rapport a celui du milieu, c’est-a-dire que, sur bune des rondelles de cuivre, se trouvaient appliquees rleux bases positives par pression, surbautre deux bases negatives.
The experimental setup is designed to produce the phenomenon that one wishes to study. In the case at hand, it consisted of three hemiedral crystals as large as possible, separated from one another by two copper washers. The three crystals had their hemiedral axes parallel to the direction of clamping. The two crystals at the ends were reversed relative to the one in the middle; that is to say, on one of the copper washers, their positive bases were pressed against it, while on the other two, the negative bases were pressed against it.
Les deux bases exterieures des trois cristaux communiquaient avec la terre. Les deux rondelles de cuivre pouvaient etre reliees aux deux poles d une machine de Holtz.
The two outer bases of the three crystals were connected to the ground. The two copper washers could be connected to the two poles of a Holtz machine.
Nous avons opere sur la tourmaline et sur le quartz. Pour ees deux substances, lorsque bon unit la branche positive d une machine de Holtz a la rondelie de cuivre attenante aux faces des cristaux positives par pression, et la branche negative a la rondelie attenante aux faces negatives, les cristaux tendent a se dilater suivant baxe de serrage et, par bmtermediaire du systeme inferieur, qui subit une augmentation de pression, belectrometre indique cette dilatation; quand baction de la machine cesse, belectrometre bindique encore. Enfin, quand on renverse le sens de la tension, les cristaux se contractent et tons les eflets se produisent en sens inverse.
We conducted experiments on tourmaline and quartz. For both substances, when one connects the positive terminal of a Holtz machine to the copper disc adjacent to the positive faces of the crystals by pressure, and the negative terminal to the disc adjacent to the negative faces, the crystals tend to expand along the axis of compression, and through the lower system, which undergoes an increase in pressure, the electrometer indicates this expansion; when the machine’s action ceases, the electrometer still indicates a reading. Finally, when the direction of the voltage is reversed, the crystals contract and all the effects occur in the opposite direction.
Le phenomene est deja sensible pour une tension correspondant a une etincelle d’un demi-millimetre ; il semble etre proportionnel a la difference de tension.
The phenomenon is already noticeable at a voltage corresponding to a spark of half a millimeter; it appears to be proportional to the voltage difference.
11 nous est impossible, pour le moment, de donner une mesure; mais un calcul que nous avons fait pour le quartz, calcul grossierement approximatif, vu les donnees imparfaites que nous avons employees, nous a montre que le phenomene est du memo ordre de grandeur que le phenomene calcule theoriquement (1 ).
(1) Les deux systemes, celui qui servait a produire le phenomene electiiquc et celui qui servait a le mesurer, etaient sepai’es l’un de l’autre, au point de vue electrique, d’une facon parfaite; ils etaient chacun parfaitement enfermes dans des enveloppes metalliques communiquant avec la terre.
Nous n’avons pas neglige toutefois les nonabreuses verifications qui peimcltent de s'assurer que l’on n’a pas affaire a un phenomene d’influence. Ces precautions sont necessaires, puisqu’il s’agit de constater de tres petites quantites delectricite qui se degagent en presence des tensions enormes des machines de lloltz.
It is impossible for us, at present, to provide a measurement; but a calculation we have made for quartz—a rough approximation, given the imperfect data we have used—has shown us that the phenomenon is of the same order of magnitude as the phenomenon calculated theoretically (1).
(1) The two systems—the one used to produce the electrical phenomenon and the one used to measure it—were perfectly isolated from one another electrically; each was completely enclosed in metal casings connected to ground.
We have not, however, neglected the numerous checks required to ensure that we are not dealing with a phenomenon of influence. These precautions are necessary, since the task is to detect very small quantities of electricity released in the presence of the enormous voltages of the Holtz machines.
Overview
Presented to the Academy of Sciences on December 26, 1881, this paper by Pierre and Jacques Curie announces the experimental discovery of the converse piezoelectric effect: the physical deformation of a crystal in response to an applied electrical voltage. This completes the theoretical framework of piezoelectricity, establishing it as a fully reversible physical phenomenon.
1. The Problem of Measuring Tiny Deformations
The paper opens with a beautifully clear statement of the experimental challenge. A change of one-millionth of the length of a solid object is essentially impossible to measure directly. However, if that same deformation is physically prevented, it manifests as a measurable pressure change of approximately 1 kg per cm². The Curies exploit this principle by using a quartz pressure sensor as an indirect measuring device — detecting deformations too small to see by converting them into electrical signals.
2. The Converse Effect — Electricity Makes Crystals Move
The central discovery of the paper is stated clearly and concisely:
"When opposite electric charges are applied to the two ends of the axis of a hemihedral crystal, it undergoes either contraction or expansion along that axis, depending on the direction in which the electric voltage was applied."
This is the converse piezoelectric effect. The direct effect (pressure → electricity) had been established in 1880. This paper proves the reverse is equally true: electricity → mechanical deformation.
3. Lippmann's Law — A Theoretical Prediction Confirmed
Critically, this discovery was not entirely unexpected. The Curies credit Gabriel Lippmann (who would later win the 1908 Nobel Prize in Physics for colour photography) with having predicted the converse effect mathematically from first principles, using:
The conservation of energy
The conservation of electric charge
The known properties of the direct piezoelectric effect
The governing law — borrowed directly from Lippmann — is a generalization of Lenz's Law:
"The direction is always such that the reciprocal phenomenon tends to oppose the occurrence of the original phenomenon."
In practical terms: if squeezing a crystal creates a positive charge at the top, then applying a positive charge to the top will make the crystal expand (resist being squeezed). This is a statement of thermodynamic reversibility applied to piezoelectricity.
4. The Experimental Apparatus
The Curies describe an ingenious two-part apparatus:
The Lower System (Measuring): Three thin quartz plates connected to a Thomson-Mascart electrometer. This acts as the pressure sensor, converting any mechanical deformation into a measurable electrical signal.
The Upper System (Producing): Three hemihedral crystals arranged in a stack with alternating orientations, connected to a Holtz electrostatic machine (a high-voltage generator). When the machine is activated, the crystals expand or contract; this deformation is transmitted to the lower quartz system, which registers it electrically.
Both systems were fully enclosed in grounded metal casings to prevent electrical interference — a remarkably modern approach to electromagnetic shielding.
5. Results
The converse effect was observed in both tourmaline and quartz.
It was detectable at voltages as low as a 0.5 mm spark gap.
The effect appeared proportional to the applied voltage.
The measured magnitude was consistent with Lippmann's theoretical prediction.
The Curies explicitly confirm they ruled out electrostatic induction as a confounding factor — showing their experimental rigour.
This paper completes what the 1880 papers began. Together, the six papers establish piezoelectricity as a fully reversible, mathematically predictable, and practically measurable physical phenomenon.
