ON THE ELECTRICAL PHENOMENA OF TOURMALINE AND OF HEMIEDRAL CRYSTALS WITH INCLINED FACES. Pgs. 18-21
SUR LES
PHENOMENES ELECTRIQUES DE LA TOURMALINE
ET DES
CRISTAUX HEMIEDRES A FACES INCLINEES.
En commun avec JACQUES CURIE.
Comptes rendus de V Academie des Sciences, t. XCII, p. 35o,
seance du 1/4 fevrier 1881.
ON THE
ELECTRICAL PHENOMENA OF TOURMALINE
AND OF
HEMIEDRAL CRYSTALS WITH INCLINED FACES.
In collaboration with JACQUES CURIE.
Proceedings of the French Academy of Sciences, vol. XCII, p. 350,
session of February 1, 1881.
I. Queiques annees apres la publication de ses belles recherches sur la tourmaline, Gaugain a donne une theorie chi phenomene de la pyro-electricite. D'apres lui, la tourmaline serait assimilable, pendant une variation de temperature, a une pile thermo-electrique d’une tres grande resistance et d’une tres grande force electromotrice. Pour montrer la possibilite de bexistence de semblables piles, il fit souder de petits cones de bismuth et de cuivre alternativement les uns aui autres et cela alternativement par les pointes et par les bases; lors d une variation de temperature, les soudures etroites etaientplus rapidement inliuencees cjue les soudures larges et le systeme constituait momentanement une pile thenno-electrique. Gaugain lui assimilait chaque file de molecules de la tour¬ maline; il est facile de voir en elfet que cette conception rend compte des lois cjuantitatives qu’il aA^ait etablies. Neanmoins elle ne nous semble pas admissible : i° elle ne rend pas compte des phenomenes electriques obtenus par pression; 2° elle n’est pas d’ accord avec ce fait que le degagement electrique n’a lieu que sur les bases des prismes de tourmaline et non sur les faces laterales, fait qui peut etre etabli par les experiences suivantes.
I. A few years after the publication of his excellent research on tourmaline, Gaugain proposed a theory regarding the phenomenon of pyroelectricity. According to him, tourmaline, when subjected to a temperature change, behaves like a thermoelectric cell with very high resistance and a very high electromotive force. To demonstrate the possibility of such cells, he had small cones of bismuth and copper soldered alternately to one another, connecting them alternately at the tips and at the bases; during a temperature change, the narrow solder joints were affected more rapidly than the wide ones, and the system momentarily constituted a thermoelectric cell. Gaugain likened each row of molecules to a tourmaline; it is easy to see, in fact, that this conception accounts for the quantitative laws he had established. Nevertheless, it does not seem acceptable to us: 1) it does not account for the electrical phenomena obtained by pressure; 2) it is inconsistent with the fact that electrical discharge occurs only at the bases of the tourmaline prisms and not on the lateral faces, a fact that can be established by the following experiments.
Si Ton recouvre les deux bases d une longue tourmaline avec deux feuilles d etain que Foil met en communication avec la terre, et si l’on provoque le degagement de Felectricite, onn’en peut pas constater lateralement a l aide d’un anneau metallique en communication avec un electrometre, meme quand cet anneau se trouve tres pres d’une des extremites du cristal. Au contraire, la quantite d’electricite degagee sur les bases est toujours la meme, que la surface Jaterale soit recouverte ou non par une feuille d’etain reliee a la terre.
If one covers the two bases of a long tourmaline with two tin foils that connects to the ground, and if one induces the discharge of electricity, it cannot be detected laterally using a metal ring connected to an electrometer, even when this ring is very close to one of the crystal’s ends. On the contrary, the amount of electricity released at the bases is always the same, whether or not the lateral surface is covered by a tin foil connected to the ground.
Gaugain, mettantune des bases en communication avec la terre, laissant l’autre isolee, entourait le milieu du cristal d’un fii de platine relie a un electrometre; il constatait, lors du refroidissement, un degagement d’electricite de meme nom que celle de la base isolee. Cette experience n’a rien de contradictoire avec ce qui precede ; Felectricite qui se degage sur la base isolee charge la derniere couche du cristal, et celle-ci joue Je role de l’armature d’un condensateur dont le cristal est la lame isolante. De l’electricite de meme nom se degage par le fil de platine; de Felectricite de nom contraire est attiree et condensee, ce qu ’il est facile de montrer. II suffi t pour cela, apres avoir decharge le fil de platine et F avoir .relie a l’electrometre, de decharger la base restee isolee jusqu’alors; Felectricite de nom contraire, qui etait condensee, donne a travers le fil de platine une deviation.
Gaugain, connecting one of the bases to ground while leaving the other isolated, surrounded the center of the crystal with a platinum wire connected to an electrometer; during cooling, he observed the release of electricity of the same nature as that from the isolated base. This experiment is in no way contradictory to what has been stated above; The electricity released from the isolated base charges the outermost layer of the crystal, and this layer acts as the plate of a capacitor, with the crystal serving as the insulating plate. Electricity of the same name is released through the platinum wire; electricity of the opposite name is attracted and condensed, which is easy to demonstrate. To do this, after discharging the platinum wire and connecting it to the electrometer, it suffices to discharge the base, which had remained isolated until then; the electricity of the opposite sign, which had been condensed, causes a deflection through the platinum wire.
II. Les hypotheses sur la polarisation des molecules qui avaient ete emises plus ou moins vaguement des 1826 (Becquerel, Forbes, etc.) peuvent, mieux que celle de Gaugain, rendre compte du phenomene. Telle est, du reste, I’opinion de M. Thomson : comme Forbes autrefois, il suppose que les molecules sont toujours polarisees et qu’une couche d’electrieite condensee sur la surface de la tourmaline neutralise leur action exterieure ; la chaleur faisant varier l’etat de polarisation, la neutralisation n’a plus lieu.
II. The hypotheses regarding the polarization of molecules that had been put forward in a more or less vague manner as early as 1826 (Becquerel, Forbes, etc.) may provide a better explanation of the phenomenon than Gaugain’s. This, moreover, is Mr. Thomson’s opinion: like Forbes before him, he assumes that molecules are always polarized and that a layer of condensed electricity on the surface of tourmaline neutralizes their external action; since heat alters the state of polarization, the neutralization no longer occurs.
Notre maniere de voir est analogue, car l’idee que les molecules sont polarisees est en parfait accord avec ce fait que Felectricite ne se montre libre que sur les bases. On sait en effet qu’un cylindre forme de molecules unifonnement polarisees parallelement a la generatrice peut etre remplace par deux couches electrisees sur les deux bases.
Our view is similar, since the idea that molecules are polarized is fully consistent with the fact that electricity manifests itself only at the ends. Indeed, we know that a cylinder composed of molecules uniformly polarized parallel to the generatrix can be replaced by two layers electrified at both ends.
Nous essayerons de preciser davantage les causes de la polarisa¬ tion et cedes de sa variation, en supposant qu’entre les faces opposees de deux couclies successives de molecules existe une difference de tension constante, ce qui entraine une condensation d’electricite qui depend de la distance des deux couches; si par une cause quelconque on change cette distance (variation de pression ou de temperature), la quantite condensee variera.
We will attempt to further clarify the causes of polarization and the mechanisms behind its variation, assuming that there is a constant voltage difference between the opposing faces of two successive layers of molecules, which results in an accumulation of electric charge that depends on the distance between the two layers; if, for any reason, this distance changes (due to a variation in pressure or temperature), the amount of accumulated charge will vary.
Un sy steme propre a faire concevoir ce qui precede serait une pile de lames zinc-cuivre sondees (elements de Volta), orientees de la meme maniere et separees les unes des autres par d’egales epaisseurs d’air.
A system that would illustrate the above would consist of a stack of zinc-copper plates (Voltaic cells), all oriented in the same direction and separated from one another by equal thicknesses of air.
Soient e cette epaisseur, v la force electromotrice de contact zinc-cuivre. Toutes les lames etant d’abord reunies a la terre, il y a une quantite q = vs/4πe d’electricite condensee sur cliaque face opposee entre deux couches successives, pourvu que ces couches soient suffisamment rapprochees. Lorsque la distance entre les couches varie, cette quantite devient
Let e be the thickness, and v the electromotive force of the zinc-copper contact. Since all the plates are initially grounded, there is a quantity q = vs/4πe of electricity concentrated on the opposite face between two successive layers, provided that these layers are sufficiently close together. When the distance between the layers varies, this quantity becomes
q + DELTAq = vs / 4PI (e + DELTAe)
S^es deux lames extremes laisseront done echapper des quantites d’electricite de noms contraires
The two outer blades will therefore release quantities of electricity of opposite polarities
DELTAq = vs/4PI [DELTAe/e^2(1+DELTAe/e)]
Quant aux lames interieures, les electricites de signes opposes niises en liber te dans chacune d’elles se neutralisant, les resnltats seraient les memes si elles etaient isolees, et c’est le cas qui nous interesse.
As for the inner blades, since the electric charges of opposite signs contained within each of them cancel each other out, the results would be the same if they were isolated, and that is the case that interests us.
Si l’on neglige dans la derniere formule DELTA e / e devant l’unite, la quantite d’electricite degagee est proportionnelle a la variation de distance de deux couches successives; elle est proportionnelle a la surface; elle est independante du nombre des couches et, par consequent, de l’epaisseur de la colonne. Ces lois sont cedes que fournissent les experiences faites sur la tourmaline.
If we neglect the term DELTA e / e preceding the unit in the last formula, the amount of electricity released is proportional to the change in distance between two successive layers; it is proportional to the surface area; it is independent of the number of layers and, consequently, of the thickness of the column. These laws are confirmed by experiments conducted on tourmaline.
111. Amenes, par la discussion des hypotheses que 1’on avait emises avant nous, a formuler la maniere de concevoir les phenomenes qui nous semble la plus plausible, holis en suivrons les consequences, tout en ne nous faisant pas dbllusion sur la fragilite d’un pared terrain.
111. By examining the hypotheses put forward by others before us, we will formulate what seems to us to be the most plausible way of understanding these phenomena; we will then explore the implications of this approach, while remaining fully aware of the fragility of such a theoretical framework.
L’hypothese dont nous sommes partis est qu’entre les faces opposees de deux couches successives existe une difference de tension constante.
Our starting assumption is that there is a constant difference in electrical potential between the opposing faces of two successive layers.
La tourmaline etant un corps compose, les diverses parties d’une molecule cristalline peuvent etre formees de matieres differentes, ce qui expliquerait la difference de tension des extremites opposees de deux molecules.
Since tourmaline is a compound, the various parts of a crystal molecule may be composed of different materials, which would explain the difference in voltage between the opposite ends of two molecules.
Mais il est possible que, la matiere etant homogene, la forme seule des molecules donne une raison suffisante pour justifier l’hypothese; on peut meme dire que b experience semble concorder avec cette explication bien plus qu’avec la precedente (les considerations ordinaires n’etant probablement plus applicables aux molecules elles-memes).
But it is possible that, since the matter is homogeneous, the shape of the molecules alone provides sufficient grounds to justify the hypothesis; indeed, one might say that the experiment seems to agree much more with this explanation than with the previous one (since ordinary considerations are probably no longer applicable to the molecules themselves).
En elfet, les theories cristallographiques, quelies qu’elles soient, sont d’accord pour faire remonter aux molecules meines Forigine de la dissymetrie qui se revele a nous par les particularities des formes cristallines. Or nous avons montre cjue, pour toutes les substances hemiedres non conductrices etudiees, le sens du degagement de l’electricite est toujours lie a la forme cristalline, de telle sorte cpie l’extremite correspondant a bangle solide le plus aigu est negative par dilatation. Cette relation constante n’etant probablement pas due au hasarcl, et les analogies entre la forme de la molecule et la forme hemiedre du crista! etant admises, on est conduit a remarquer que bextremite aigue d’une molecule joue toujours par rapport a la base opposee de la molecule suivante le role du zinc par rapport au cuivre dans l’exemple d’analogie que nous avons pris, c’est-a-dire est constamment chargee d’electricite positive. La nature de la matiere semble done ne pas entrer en ligne de compte, et la forme de la molecule parait avoir binlluence preponderante.
In fact, all crystallographic theories agree that the asymmetry revealed to us by the peculiarities of crystalline forms can be traced back to the molecules themselves. Now, we have shown that, for all the non-conductive hemihedral substances studied, the direction of electric charge separation is always linked to the crystalline form, such that the end corresponding to the sharpest solid edge is negative by expansion. Since this constant relationship is probably not due to chance, and given the analogies between the shape of the molecule and the hemihedral shape of the crystal, are accepted, we are led to observe that the acute end of a molecule always plays, relative to the opposite base of the next molecule, the role of zinc relative to copper in the example of analogy we have taken, that is to say, it is constantly charged with positive electricity. The nature of the matter therefore seems to be irrelevant, and the shape of the molecule appears to have a decisive influence.
Overview
In this paper, presented to the Academy of Sciences on February 1, 1881, Pierre and Jacques Curie accomplish three things: they disprove a competing theory by Gaugain, they refine an existing molecular theory by Thomson and Forbes, and they propose their own molecular model to explain why piezoelectricity and pyroelectricity occur.
1. Disproving Gaugain's "Thermoelectric Cell" Theory
Gaugain had previously proposed that tourmaline behaves like a stack of tiny thermoelectric cells — similar to a battery made of alternating copper and bismuth cones. The Curies demolish this theory with two elegant experiments:
The Ring Experiment: They show that electricity is only released at the flat ends (bases) of the tourmaline crystal, and never from the sides. If Gaugain's theory were correct, electricity should be detectable along the entire length of the crystal.
The Capacitor Experiment: They explain away Gaugain's own experimental evidence by showing that what he observed was simply a capacitor effect — the crystal's surface was acting as an insulating plate between two charged layers, not generating electricity along its length.
2. Refining the Molecular Polarization Theory
The Curies align themselves with an older idea proposed by Becquerel, Forbes, and Thomson (1826 onwards): that the molecules of tourmaline are always electrically polarized — that is, each molecule is permanently slightly positive at one end and negative at the other. Their key contribution is to explain why this only becomes visible at the crystal's ends:
A cylinder made of uniformly polarized molecules can be mathematically replaced by two charged layers at its two ends.
In other words, all the internal charges cancel each other out, and only the charges at the very top and bottom of the crystal are left "unpaired" and detectable.
3. The Molecular Model and the Mathematics
This is the most original section of the paper. The Curies propose a physical model using a stack of Voltaic cells (zinc-copper plates separated by air gaps) as an analogy for the crystal's molecular layers. Their key formula states:
Δq=vs4π⋅Δee2(1+Δe/e)Δq=4πvs⋅e2(1+Δe/e)Δe
Where:
$v$ = the electrical potential difference between molecular faces
$s$ = the surface area
$e$ = the distance between molecular layers
$\Delta e$ = the change in that distance (due to pressure or temperature)
From this formula, they mathematically derive the five laws they had stated experimentally in the previous paper:
Electricity is proportional to the change in distance between layers (i.e., proportional to pressure).
It is proportional to surface area.
It is independent of the total thickness (length) of the crystal.
4. The Shape of the Molecule as the Root Cause
The paper's most profound conclusion is its final one. The Curies argue that the electrical asymmetry of a crystal is not simply a property of its chemical composition, but of the shape of its molecules. Because the crystal's external hemihedral form (its "pointy" ends) reflects the shape of the molecules inside it, the acute end of each molecule always acts as the positive pole relative to the base of the next molecule — like zinc relative to copper in a battery.
"The nature of the matter therefore seems to be irrelevant, and the shape of the molecule appears to have a decisive influence."
This is a remarkably modern statement. It anticipates the 20th-century understanding of how crystal symmetry at the atomic level determines macroscopic electrical properties.
Why This Paper Matters
This paper represents the transition of piezoelectricity from an experimental curiosity into a theoretical framework. The Curies are essentially proposing the first molecular model of a polar dielectric material — a concept that would not be fully formalized until the development of quantum mechanics and solid-state physics in the 20th century.
