ELECTRICAL DEFORMATIONS OF QUARTZ. Pgs. 30-32.
DEFORMATIONS ELECTRIQUES DU QUARTZ.
En commun avec JACQUES CURIE.
Comptes rendus de L’Ac'ademie des Sciences, t. XCV , p. 914, seance clu i3 novembre 1882.
ELECTRICAL DEFORMATIONS OF QUARTZ.
In collaboration with JACQUES CURIE.
Proceedings of the Academy of Sciences, vol. XCV, p. 914, session held on November 13, 1882.
A chaque maniere (1) de provoquer par pression le degagement electrique dans le quartz correspond nn phenomene reciproque particular. Soil un parallelepipede a yant deux faces normales a un axe electrique et deux normales afaxe optique; lorsqu’il y a entre les deux faces normales a faxe electrique une difference de potentiel, le quartz se dilate suivant l’axe electrique et se contracte dans la direction normale aux axes optique et electrique, ou inversement se contracte suivant la premiere direction et se dilate suivant la premiere direction et se dilate suivant la seconde, selon le sens de la tension. La troisieme direction ne varie pas. Les sens des phenomenes reciproque et direct sont lies entre eux par une loi de reaction analogue a la loi de Lenz. Chacune des deformations est proportionnelle a la difference de potentiel. Enfin, dans chaque direction, la grandeur de la dilatation est donnee en centimetres, pour une difference de potentiel egale a funite absolue G.G.S. electrostatique, par le meme nombre que celui qui exprime en valeur absolue la quantite d’electricite degagee par une pression d7une dyne exercee dans la direction consideree.
(1) Voir Journal de Physique, 1882^ p. 245.
Each method (1) of inducing an electrical discharge in quartz by pressure corresponds to a specific reciprocal phenomenon. Consider a rectangular prism with two faces perpendicular to an electric axis and two faces perpendicular to an optical axis; when there is a potential difference between the two faces perpendicular to the electric axis, the quartz expands along the electric axis and contracts in the direction perpendicular to both the optical and electric axes, or conversely, contracts along the first direction and expands along the second, depending on the direction of the voltage. The third direction remains unchanged. The directions of the reciprocal and direct phenomena are linked by a reaction law analogous to Lenz’s law. Each deformation is proportional to the potential difference. Finally, in each direction, the magnitude of the expansion is given in centimeters, for a potential difference equal to the absolute electrostatic G.G.S. constant, by the same number that expresses in absolute value the quantity of electricity released by a pressure of one dyne exerted in the direction under consideration.
(1) See Journal de Physique, 1882, p. 245.
La dilatation suivant faxe electrique est independante des dimensions de la plaque; el le est trop faible pour etre constatee directement, mais, pour la mettre en evidence, on peut s’opposer a ce que la deformation se produise, employer de grandes surfaces et utiliser la variation de pression assez considerable qui en resulle. C’est ce qae nous avons deja fait. La methode est des plus sensibles, mais la connaissance imparfaite on nulle que l’on a des coefficients d’elasticite ne nous a pas permis de faire des experiences quantitatives. Au contraire, la dilatation normalement a l’axe varie avec les dimensions du parallelepipede ; elle est egale a la dilatation suivant l’axe, lorsque le rapport des dimensions actives est egal a i ; en faisant varier ces dimensions, on peut la rendre beaucoup plus grande; elle peut devenir visible et mesurable au microscope, surtout apres amplification a l’aide d’un levier.
The expansion caused by an electric field is independent of the plate’s dimensions; it is too small to be observed directly, but to demonstrate it, one can prevent the deformation from occurring, use large surfaces, and take advantage of the resulting significant pressure variation. This is what we have already done. The method is highly sensitive, but our imperfect or even non-existent knowledge of the coefficients of elasticity has not allowed us to conduct quantitative experiments. On the contrary, the expansion perpendicular to the axis varies with the dimensions of the parallelepiped; it is equal to the expansion along the axis when the ratio of the active dimensions is equal to 1; by varying these dimensions, it can be made much greater; it can become visible and measurable under a microscope, especially after magnification using a lever.
L’appareil dont nous nous sommes servis etait dispose de la facon suivante : une plaque de quartz, revetue de deux feuilles d’etain sur les faces normales a l’axe electrique (et tres peu epaisse suivant la direction de cet axe), etait fixee par Tune des extremites de sa grande longueur (normaie aux deux axes optique et electrique) a un montant solide.
The apparatus we used was arranged as follows: a quartz plate, coated with two sheets of tin on the faces perpendicular to the electrical axis (and very thin in the direction of that axis) [a-axis or x-axis], was secured at one end of its long side (perpendicular to both the optical [c-axis or Z-axis] and electrical axes) to a sturdy support.
L’autre extremite, munie d’une petite piece rigide, retenait le petit bras d’un levier. Le grand bras portait une petite toile d’araignee que Ton regardait avec un microscope muni d’un micrometre oculaire.
The other end, fitted with a small rigid piece, held the short arm of a lever. The long arm supported a small spiderweb [used as a crosshair reference in the microscope eyepiece], which was examining through a microscope equipped with an ocular micrometer.
Les variations de longueur de la plaque de quartz etaient amplifiees une cinquantaine de fois. On produisait la tension electrique en chargeant les deux feuilles d’etain a 1 ’aide d’une machine de Holtz reliee a une batterie de six bouteilles de Leyde. La tension s’etablissait ainsi assez lentement et l’on notait le deplacement du levier a l’instant oil l’etincelle partait entre deux boules.
Variations in the length of the quartz plate were amplified about fiftyfold. Electric voltage was generated by charging the two tin sheets using a Holtz machine connected to a battery of six Leyden jars. The voltage built up fairly slowly, and the displacement of the lever was recorded at the moment the spark jumped between the two spheres.
La mesure se compose de deux parties distinctes :
The measure consists of two distinct parts
i° On determine experimentalement, par ies procedes que nous avons precedemment publies, la quantite absolue d’electricite degagee par la lame revetue de ses feuilles d’etam et telle qu’elle va etre employee dans la seconde partie ;
1. We determine experimentally, using the methods we have previously published, the absolute quantity of electricity released by the blade coated with its tin sheets, as it will be used in the second part;
2° On mesure, a l’aide de l’appareil ci-dessus decrit, les variations de longueur correspondant a une serie de differences de potentiel donnees par les distances explosives entre des boules de 0.06 m d’apres les determinations de M. Bailie.
(i) Les epaisseurs des lames etaient 2.4 mm et 0.65 mm; les longueurs de 1’etain environ 27.8 mm et 40 mm
2. Using the apparatus described above, we measure the changes in length corresponding to a series of potential differences determined by the spark gap distances between spheres 0.6 cm apart, as measured by Mr. Baille. [Jules Baille].
(i) The thicknesses of the blades were 2.4 mm and 0.65 mm; the lengths of the tin strips were approximately 27.8 mm and 40 mm
Traction necessaire pour charger une capacite de om,5o a la tension d’un daniell .
D’ou une traction de i dyne degagerait une quantity absolue d’electricite egale a
D’oii dilatation calculee en centimetres pour 1 unite de difference de potentiel
D’ou dilatation calculee en millimetres pour une difference de potentiel egale a i4,8, correspondant a une etincelle de imm dans l’air, entre boules de om,o6 .
D’oii dilatation calculee en millimetres pour une difference de potentiel de 65,2 (etincelle de 6mm).
Deplacement de l’extremite du levier exprime en divisions du micrometre, pour tension correspond ant a imm d 'etincelle
Deplacement pour tension correspondant a 6mm d’etincelle
Valeurs de ces deplacements en millimetres
Rapport des bras du levier
D’ou dilatation mesuree
Sample Dimensions
Sample 1
2.4 mm x 0.65 mm
Sample 2
27.8 mm x 40 mm
The force required to charge a capacitance of 0.5 cm to the voltage of a Daniell cell.
Sample 1: 258
Sample 2: 48.5
Hence, a force of 1 dyne would release an absolute quantity of electricity equal to
0.000000739
0.000000393
Hence, the expansion calculated in centimeters per unit of potential difference
0.000000739
0.000000393
Hence, the expansion calculated in millimeters for a potential difference equal to 14.8, corresponding to a 1 mm spark in air, between spheres of 0.06 mm.
no value
0.00058
Hence, the expansion calculated in millimeters for a potential difference of 65.2 (6 mm spark).
0.00048
no value
Displacement of the lever arm tip expressed in micrometer divisions, for a voltage corresponding to a 1 mm spark
no value
6.7
Displacement for a voltage corresponding to a 6 mm spark
5
no value
Values of these displacements in millimeters
0.0206
0.0276
Ratio of the lever arms
40.8
46.5
Hence, measured expansion
0.0005
0.00061
Ides dilatations mesurees etant de 0.00050 mm et de oun 0.00061 mm , les dilatations caleulees par les quantites d’electricite degagees sont on 0.00048 mm et 0.00058 mm. Ces resultats doivent etre considers co mine satisfaisants. Sans meme considerer les facteurs nombreux entrant en cause, les differences s’expliquent simplement par l’erreur de lecture dans la mesure des dilatations electriques. Ces determinations sont done des verifications non settlement qualitative s , mais aussi numeriques des consequences auxquelles les principes de la conservation de l’energie et de la conservation de l’electricite ont conduit M. Lippmann. La proportionnalite de la dilatation a la difference de potentiel se veriffe egalement bien; toutefois nos experiences n’ont pu etre faites que sur des echelles de tension tres iimitees.
Since the measured expansions are 0.00050 mm and 0.00061 mm, the expansions calculated based on the amounts of electricity released are 0.00048 mm and 0.00058 mm. These results must be considered satisfactory. Without even considering the numerous factors involved, the differences can be explained simply by reading errors in the measurement of electrical expansions. These determinations are therefore not only qualitative verifications but also numerical verifications of the conclusions to which the principles of energy conservation and electrical conservation led Mr. Lippmann. The proportionality of the expansion to the potential difference is also well verified; however, our experiments could only be conducted over very limited voltage ranges.
Summary
Presented to the Academy of Sciences on November 13, 1882, this paper by Pierre and Jacques Curie provides the first complete quantitative verification of the converse piezoelectric effect in quartz. It represents the culmination of two years of experimental work begun with the discovery of piezoelectricity in August 1880, and delivers the definitive numerical confirmation of Lippmann's thermodynamic prediction.
The paper opens by stating the full geometry of piezoelectric deformation in quartz with a clarity that had not appeared in previous papers. For a rectangular quartz prism:
Along the electrical axis (a-axis): The crystal expands or contracts depending on the direction of the applied voltage.
Perpendicular to both axes (b-axis/mechanical axis): The crystal deforms in the opposite direction — if it expands along the electrical axis, it contracts here, and vice versa.
Along the optical axis (c-axis):No deformation occurs in this direction at all.
This three-axis description is the first complete statement of what modern physics calls the piezoelectric tensor for quartz — the full mathematical description of how electrical and mechanical effects are coupled in all three dimensions simultaneously.
The experiment is divided into two carefully separated parts, reflecting the Curies' rigorous experimental design:
Part 1 (Direct Effect): Using their previously published methods, they measure the absolute quantity of electricity released by each quartz plate under a known pressure. This calibrates the crystal as an electrical standard.
Part 2 (Converse Effect): Using the cantilever and lever apparatus described in the paper, they apply known voltages (calibrated using Baille's spark gap tables) and measure the resulting physical deformation of the crystal under a microscope with an ocular micrometer, amplified approximately fiftyfold by the lever system.
The use of spider silk as a crosshair in the microscope eyepiece, and the recording of lever displacement at the precise moment of spark discharge, reflect the extraordinary experimental ingenuity the Curies brought to measurements at the edge of what was physically detectable in 1882.
The Results Sample 1 Sample 2
Dimensions 2.4 mm × 0.65 mm 27.8 mm × 40 mm
Calculated expansion 0.00048 mm 0.00058 mm
Measured expansion 0.0005 mm 0.00061 mm
Agreement~4%~5%
The agreement between the theoretically calculated and experimentally measured values is within 4-5% for both samples — well within the experimental error of the apparatus. The Curies note that the remaining discrepancy is fully explained by reading errors in the micrometer measurements.
Critically, the piezoelectric coefficient — the number expressing both the charge released per unit force AND the expansion per unit potential difference — is identical for both directions of the effect, confirming Lippmann's thermodynamic prediction experimentally for the first time.
Conclusions
The Curies draw three explicit conclusions:
Qualitative verification: The converse effect exists exactly as Lippmann predicted — electricity makes quartz physically move.
Quantitative verification: The magnitude of the effect matches the theoretical prediction derived from energy and charge conservation to within experimental error.
Proportionality: The deformation is proportional to the applied voltage, though the Curies honestly note this was only verified over a limited voltage range.
Why This Paper Matters
This paper closes the loop on one of the most elegant experimental programs in the history of physics. In just over two years, Pierre and Jacques Curie had:
August 1880 Discovered piezoelectricity (pressure → electricity)
August 1880 Linked the effect to crystal symmetry
January 1881 Established five quantitative laws
February 1881 Proposed the first molecular theory
July 1881 Built the first piezoelectric instrument
December 1881 Discovered the converse effect (electricity → movement)
November 1882 Quantitatively verified the full reciprocal relationship
The instrument they designed to make these measurements — the piezoelectric quartz electrometer — went on to become one of the most important scientific instruments of the late 19th and early 20th centuries. It was the device Marie Curie used to measure radioactivity with precision, work that led directly to her two Nobel Prizes and the founding of nuclear physics.
