Pierre Curie

How to use this course

Pierre Curie is often remembered as Marie Curie’s husband and partner in the discovery of radium. Before he met her he was already one of the most original physicists in France. With his brother Jacques he discovered piezoelectricity at 21. He then worked out a general theory of what symmetry permits in physics, gave the principle that governs the shapes of crystals, and found the laws by which magnetism changes with temperature. His name survives in Curie’s law, the Curie temperature, the Curie principle and the curie unit.

Part II takes these subjects in the order he did them. Lessons 04 to 06 treat crystals: piezoelectricity, symmetry and crystal growth. Lesson 07 treats his doctoral work on magnetism. Lessons 08 and 09 treat his contributions to radioactivity: the rays, the decay of the emanation, and the discovery, with Albert Laborde, that radium releases heat without end. Lesson 10 treats the physics of his precision instruments.

Each technical lesson opens with a paragraph for the general reader, then gives precise statements, derivations and exercises with folded solutions. The companion courses on Marie Curie and Henri Becquerel cover the discovery of radioactivity from their sides.

Timeline

A doctor’s son, taught at home, 1859–1877

Pierre Curie was born in Paris on 15 May 1859, the second son of Eugène Curie (1827–1910), a physician, and Sophie-Claire Depouilly (1832–1897). His grandfather Paul Curie was also a doctor. The family was Protestant and republican.

Pierre never attended a lycée. His parents judged that his slow, absorbed way of thinking would not suit the French school system, and they taught him at home, together with his elder brother Jacques. From the age of fourteen he studied mathematics with a private tutor named Bazille and made rapid progress, especially in geometry. In November 1875, aged sixteen, he passed the baccalauréat in science and entered the Faculty of Sciences of the University of Paris. He took the licence in the physical sciences at eighteen.

The home education left a mark. Pierre worked best on problems of his own choosing, followed them over years, and was uninterested in the competitive examinations and honours that organized French academic life. He never attended the École normale or the École polytechnique, which made his later career slower than his work deserved.

The Sorbonne and Jacques, 1878–1882

In 1878 Curie became a laboratory assistant to Paul Desains in the physics laboratory of the Sorbonne. His first research, with Desains, measured the wavelengths of infrared radiation. His brother Jacques (1855–1941) was then an assistant in the mineralogy laboratory of Charles Friedel, where crystals and pyroelectricity were studied.

Pyroelectricity, the appearance of electric charge on certain crystals when they are heated, had been known since the eighteenth century in tourmaline. The brothers asked whether mechanical pressure could have the same effect. In 1880 they showed that crystals such as tourmaline, quartz, topaz, cane sugar and Rochelle salt develop charges on their faces when compressed along certain directions, of opposite sign under tension, and proportional to the force. They named the effect piezoelectricity, from the Greek for pressing. In 1881 Gabriel Lippmann predicted from thermodynamics that the converse effect should exist: an electric field should deform the crystal. The Curies confirmed it within months and showed that the coefficients of the direct and converse effects are equal.

To measure the minute charges, they built a quartz plate that releases a known charge when loaded with a weight (Lesson 04). This instrument, the piezoelectric quartz, was used by Marie Curie fifteen years later to discover the radioactivity of thorium and the activity of pitchblende.

The School of Physics and Chemistry, 1882–1895

In 1882 the city of Paris founded the École municipale de physique et de chimie industrielles to train engineers for the chemical and electrical industries. Curie was appointed head of practical work in physics and stayed at the school for 22 years. In 1883 Jacques left to teach mineralogy at Montpellier, and the brothers’ collaboration ended.

Alone, Curie turned to theory. From 1884 he published on symmetry and crystal structure. In 1885 he proposed that the equilibrium form of a crystal is the one that minimizes its total surface energy (Lesson 06). In 1894 he published his memoir on symmetry in physical phenomena, which states the principle now called Curie’s principle (Lesson 05). He also designed instruments: an aperiodic precision balance with direct reading, in 1889, and an electrometer.

From about 1890 he studied the magnetic properties of matter over a wide range of temperatures, from room temperature to well above the transition of iron near 770 °C. The work became his doctoral thesis, defended on 6 March 1895 before the Faculty of Sciences (Lesson 07). William Thomson, Lord Kelvin, who knew and admired his work, supported his promotion, and after the doctorate the school made him professor. In the spring of 1894 he had met Maria Skłodowska, a young Polish physicist looking for laboratory space for a study of steels. They married on 26 July 1895, in a civil ceremony at Sceaux.

Piezoelectricity

For the general reader. Squeeze a quartz crystal and electric charges appear on its faces; put it in an electric field and it changes shape slightly. Pierre and Jacques Curie discovered the first effect in 1880 and confirmed the second in 1881. Every quartz watch and many sensors, loudspeakers and ultrasound probes now rely on it. The Curies used it at once to build an instrument that releases an exactly known charge.

The constitutive relations

Proof of the equality (Lippmann, 1881). Take the Gibbs free energy per unit volume \(G(T_{jk},E_i)\), with \(dG=-S_{jk}\,dT_{jk}-D_i\,dE_i\) at constant temperature. Then \(S_{jk}=-\partial G/\partial T_{jk}\) and \(D_i=-\partial G/\partial E_i\), and equality of mixed second derivatives gives

The left side is the direct coefficient and the right side the converse one. Lippmann’s argument used conservation of electric charge and energy in the same way, and the Curies’ measurements confirmed the equality.

Quartz

α-quartz belongs to the trigonal class 32. Its symmetry (Lesson 05) reduces the 18 independent components of \(d\) to two, conventionally \(d_{11}\) and \(d_{14}\) in the contracted notation, with \(d_{11}\approx2.3\) pC/N. For a plate whose faces are perpendicular to an electrical axis \(x_1\), with thickness \(e\) along \(x_1\) and length \(L\) along \(x_2\), a tension \(F\) applied along \(x_2\) on the end face of area \(e\,w\) produces the stress \(T_{22}=F/(ew)\). Since \(d_{12}=-d_{11}\) in class 32, the displacement on the large faces, of area \(Lw\), is \(D_1=-d_{11}T_{22}\), and the charge released is

The factor \(L/e\) is the point of the design: a long, thin plate multiplies the charge. The Curies’ piezoelectric quartz carried a pan from which weights were hung; each gram released a fixed, calculable charge. Used against an electrometer as a null instrument, it measured currents of \(10^{-11}\) A without calibrating the electrometer (see Lesson 05 of the Marie Curie course).

Symmetry in physical phenomena

For the general reader. Why can quartz become electric when squeezed, while table salt cannot? Pierre Curie answered with a general rule: an effect cannot be less symmetric than the situation that produces it. If a crystal looks the same after being turned inside out through a point, squeezing it cannot give it an electric polarity, because a polarity has a direction and the cause has none. His 1894 memoir made symmetry a working tool of physics.

Centrosymmetric crystals

Theorem. A crystal whose point group contains the inversion \(-I\) has \(d_{ijk}=0\).

Proof. Apply Neumann’s principle with \(R=-I\): \(d_{ijk}=(-1)^3d_{ijk}=-d_{ijk}\), so \(d=0\). In words, stress is unchanged by inversion (it is a second-rank tensor) while polarization reverses, so a stress cannot select a polarity in a medium that has none. Of the 32 crystal classes, 11 contain the inversion; of the remaining 21, all except the cubic class 432 are piezoelectric. Quartz (32) has no centre of symmetry; rock salt (\(m\bar3m\)) has one.

The symmetry of fields

Curie characterized the symmetry of the electric and magnetic fields by the infinite groups that now bear his name. A uniform electric field is a polar vector: it has the symmetry of a cone (\(\infty mm\) in modern notation), with an axis of rotation of any order and mirror planes containing it, but no mirror perpendicular to it. A magnetic field is an axial vector: it has the symmetry of a rotating cylinder (\(\infty/m\)), with a mirror plane perpendicular to the axis but none containing it. The distinction decides which effects are possible. A polar crystal (one of the 10 classes with a unique polar direction, such as tourmaline) can be pyroelectric, because a scalar cause, temperature, can produce a polar effect only where the medium is already polar.

Crystal growth and surface energy

For the general reader. A drop of liquid is round because surface tension pulls it into the shape with the least surface. Curie asked what the same idea means for a crystal, whose faces have different surface energies depending on their orientation. In 1885 he proposed that a crystal in equilibrium takes the shape that minimizes its total surface energy for its volume. George Wulff turned the idea into a geometric construction in 1901.

Proof for a fixed set of orientations. Let the faces have fixed unit normals \(\mathbf n_i\) and distances \(h_i\) from an origin inside the crystal. Decomposing the polyhedron into pyramids with apex at the origin gives \(V=\tfrac13\sum_ih_iA_i\). Moving face \(j\) outward by \(dh_j\) adds a slab of area \(A_j\), so \(\partial V/\partial h_j=A_j\). Differentiating the pyramid formula instead gives \(A_j=\tfrac13\big(A_j+\sum_ih_i\,\partial A_i/\partial h_j\big)\), that is,

Now minimize \(\sum_i\gamma_iA_i\) at fixed \(V\) with a Lagrange multiplier \(\mu\): the stationarity condition is \(\sum_i\gamma_i\,\partial A_i/\partial h_j=\mu A_j\) for every \(j\). The choice \(h_i=c\gamma_i\) turns the left side into \(c^{-1}\sum_ih_i\,\partial A_i/\partial h_j=2A_j/c\), so the condition holds with \(\mu=2/c\). Faces whose plane at \(h_i=c\gamma_i\) lies outside the polyhedron formed by the others have \(A_i=0\) and do not appear.

The constant \(\mu\) is related to the chemical potential excess of the small crystal, the solid analogue of the Laplace pressure \(2\gamma/r\) of a drop. Real crystals grown from solution are usually shaped by the growth rates of the faces rather than by equilibrium, a point Curie himself recognized; equilibrium shapes are reached in small crystals annealed for a long time.

Magnetism and temperature

For the general reader. Some substances are pushed out of a magnetic field (diamagnetic), some weakly pulled in (paramagnetic), and iron, nickel and cobalt strongly pulled in (ferromagnetic). For his doctorate, Curie measured all three kinds over hundreds of degrees. He found that diamagnetism does not depend on temperature, that paramagnetism falls in inverse proportion to the absolute temperature, and that iron loses its strong magnetism above a definite temperature, now called the Curie point. Langevin and Pierre Weiss explained these laws within twelve years.

The measurements

Curie placed a small sample in a nonuniform field and measured the force on it with a torsion balance. For a sample of volume \(V\) and small susceptibility \(\chi\) in a field \(B\) that varies along \(x\), the force is

The sample sat in a small furnace inside the field, so the susceptibility could be followed with temperature. He studied gases (oxygen), salts, metals, and the ferromagnets iron, nickel and magnetite.

Curie’s law from statistical mechanics

Paul Langevin, Curie’s former student, derived the law in 1905. Take \(n\) permanent moments \(\mu\) per unit volume in a field \(B\), with energy \(-\mu B\cos\theta\). The Boltzmann distribution gives the mean moment along the field:

For \(x\ll1\), \(L(x)\approx x/3\), so \(M=n\mu^2B/(3k_BT)\) and \(\chi=\mu_0M/B\) gives

For spin ½ the moment has only two orientations, \(\pm\mu_B\) with \(g=2\), and \(M=n\mu_B\tanh(\mu_BB/k_BT)\). At small fields \(\tanh x\approx x\), giving \(C=\mu_0n\mu_B^2/k_B\), which agrees with the general formula since \(g^2J(J+1)/3=1\). Diamagnetism, by contrast, comes from the orbital response of all electrons to the field; Langevin found \(\chi=-\mu_0ne^2\langle r^2\rangle/(6m)\) per electron, with no temperature in it, as Curie had measured.

The Curie–Weiss law

In 1907 Pierre Weiss supposed that each moment feels, besides the applied field, a molecular field proportional to the magnetization, \(B_{\text{eff}}=B+\lambda\mu_0M\). Above the transition, \(M=(C/\mu_0T)B_{\text{eff}}\), so \(M(1-\lambda C/T)=CB/(\mu_0T)\).

The figure at the head of this page plots both laws. Mean-field theory gets the exponents only approximately; near a real Curie point the magnetization vanishes as \((T_C-T)^{\beta}\) with \(\beta\approx0.33\) in three dimensions.

Rays, emanation and a clock

For the general reader. From 1898 Pierre Curie set his own research aside to join Marie’s search for new elements. He brought instruments and a physicist’s questions. What are the rays? Do they carry charge? Why do objects left near radium become radioactive themselves? He found that radium gives off a radioactive gas whose activity decays at a fixed rate, and proposed that such decay could serve as a clock independent of anything else in nature.

The rays carry charge

In 1899–1900 several groups found that part of the radiation of radium is deflected by a magnetic field. Pierre Curie showed that the radiation contains a deviable and a non-deviable part, and in 1900 Pierre and Marie Curie showed directly that the deviable rays carry negative charge. They let the rays fall on a metal plate surrounded by insulation and connected to an electrometer. The plate charged negatively at a steady rate, while the insulated radium source charged positively.

Induced radioactivity and the emanation

In 1899 the Curies noticed that any object kept near radium becomes active, and that the activity disappears after the object is removed. With André-Louis Debierne, Pierre showed in 1901 that the effect is carried through the air: it occurs in closed vessels, and its intensity depends on the gas space around the radium, not on the rays. Ernest Rutherford had found the same with thorium and named the cause an emanation, a radioactive gas. In closed vessels, Curie found, the activity of the emanation disappears by an exponential law with a time constant independent of the conditions.

In his Nobel lecture of 1905 Curie gave the emanation of radium a halving time of about four days, that of thorium about 55 seconds and that of actinium about 3 seconds. He pointed out that a radioactive decay gives an absolute measure of time, and that radioactive minerals could therefore date geological events. Rutherford put the suggestion to work from 1904 onward.

The heat of radium

For the general reader. On 16 March 1903 Pierre Curie and his student Albert Laborde announced that radium salts stay warmer than their surroundings, permanently, with no visible change. A gram of radium releases about a hundred calories each hour, enough to melt its own weight of ice in under an hour. The result made the energy of the atom tangible, and led within months to the recognition that radioactivity releases about a million times more energy per atom than any chemical reaction.

The measurement

Curie and Laborde compared the temperature of a radium-bearing barium chloride with that of an equal mass of inactive barium chloride under identical conditions, and also measured the heat directly by calorimetry. Both methods gave a release of about 100 calories per gram of radium per hour, or about 22 500 calories per hour per gram-atom on the atomic weight of 225. Marie Curie’s Nobel lecture of 1911 gives 118 calories per gram per hour for radium in equilibrium with its products.

For radium-226, the short-lived chain down to lead-210 contains four alpha decays (radium-226, radon-222, polonium-218, polonium-214) with total alpha-decay energy close to 24 MeV, plus two beta decays (lead-214, bismuth-214) whose energy is partly carried off by neutrinos and gamma rays. A freshly purified radium salt has only the first alpha decay; the others grow in with the radon over about a month (Exercise 8.3), so the heat output rises roughly fourfold. Curie and Laborde found this rise, and it showed that most of the heat comes from the emanation and its products.

Instruments: damping and the balance

For the general reader. A sensitive balance swings for a long time before it settles, and a weighing waits on the swinging. Curie designed in 1889 a balance damped by air pistons, which settles in one smooth motion and is read directly on a scale through a microscope. He applied the same idea, damping chosen to stop oscillation without slowing the response, to his electrometers. The physics is that of the damped oscillator, and his choice was critical damping.

Derivation. The homogeneous equation has solutions \(e^{st}\) with \(s^2+2\zeta\omega_0s+\omega_0^2=0\), so \(s=\omega_0(-\zeta\pm\sqrt{\zeta^2-1})\). For \(\zeta>1\) both roots are real and negative, and the slower one, \(s_+=\omega_0(-\zeta+\sqrt{\zeta^2-1})\), approaches 0 as \(\zeta\) grows, so heavy damping slows the approach. For \(\zeta<1\) the roots are complex with real part \(-\zeta\omega_0\). The slowest decay rate, \(\min|\mathrm{Re}\,s|\), is \(\omega_0(\zeta-\sqrt{\zeta^2-1})\) for \(\zeta\ge1\) and \(\zeta\omega_0\) for \(\zeta\le1\); it is largest at \(\zeta=1\), where it equals \(\omega_0\). Critical damping is therefore the fastest approach without oscillation. At \(\zeta=1\) the double root gives the solution \((A+Bt)e^{-\omega_0t}\), and the initial conditions \(\theta(0)=0\), \(\dot\theta(0)=0\) fix the form above.

Curie’s balance used air dampers, light pistons moving in cylinders with a small clearance, which produce a torque proportional to velocity. Combined with a scale on the beam read through a microscope, it allowed a weighing in a fraction of a minute instead of several minutes of watching swings. The same aperiodic principle governed the electrometer he built with a magnetic damper.

Radium and recognition, 1898–1905

When Marie Curie found in early 1898 that pitchblende was more active than its uranium content allowed, Pierre joined her in the search for the unknown substance. The note announcing polonium, on 18 July 1898, and the note on radium, on 26 December with Gustave Bémont, were joint. In the division of labour that followed, Marie led the chemical concentration of radium and Pierre the study of the properties of the radiation. Between 1898 and 1902 the couple published 32 papers, together and separately.

Money and positions remained scarce. In 1900 Pierre became assistant professor at the École polytechnique and taught the preparatory course in physics, chemistry and natural history for medical students at the Faculty of Sciences. That spring he declined a well-paid chair at the University of Geneva to keep working in Paris. In 1901 he tested the action of radium on his own skin, holding a sample against his arm for several hours and following the burn as it developed over weeks. With Becquerel he reported the physiological effects, and with the physicians Charles Bouchard and Victor Balthazard he later studied the effect of the emanation on animals. These studies opened the way to radium therapy.

Recognition came quickly from abroad. In June 1903 Pierre lectured on radium in London. In November the Royal Society awarded the Davy Medal to both Curies, and in December the Nobel Prize in Physics was divided between Becquerel and the Curies. Pierre had insisted that Marie be included when he learned that the first nomination named only him. The couple did not travel to Stockholm until June 1905, when Pierre delivered the lecture. He ended it by saying he was among those who believe “that mankind will derive more good than harm” from new discoveries. In 1903 he declined the Legion of Honour; what he wanted was a laboratory. In October 1904 the Faculty of Sciences created a chair of physics for him, with a laboratory of which Marie became head of work. On 3 July 1905 he was elected to the Académie des sciences.

Rue Dauphine, 1906, and legacy

By 1905 Curie was often ill, with pains and fatigue that may have owed something to radiation exposure. His hands were scarred by radium burns. On the rainy afternoon of 19 April 1906, crossing the busy rue Dauphine near the Quai de Conti, he slipped and fell in front of a heavy horse-drawn wagon, and a wheel ran over his head. He died instantly, aged 46. He was buried at Sceaux two days later.

The Faculty of Sciences gave his course to Marie, who became the first woman professor at the University of Paris. The Société française de physique published his collected papers in 1908. In 1910 the Radiology Congress at Brussels named the unit of radioactivity, the curie, in his honour. In April 1995 his remains and Marie’s were moved to the Panthéon.

Legacy

• Crystal physics: piezoelectricity underlies quartz oscillators, sonar, ultrasound imaging, inkjet printheads and the scanning tunnelling microscope. The Curie principle and his limiting symmetry groups remain the standard tools for deciding which effects a crystal can show.
• Magnetism: Curie’s law, the Curie constant and the Curie temperature are in every textbook of condensed matter. His student Paul Langevin and Pierre Weiss built the first theories of para- and ferromagnetism on his measurements.
• Radioactivity: co-discovery of polonium and radium; the charge of beta rays; the decay of the emanation as an absolute clock; the heat of radium.
• Family and school: his daughter Irène and son-in-law Frédéric Joliot-Curie won the Nobel Prize in Chemistry in 1935; the school where he worked is now ESPCI Paris. The element curium is named for Pierre and Marie.

Sources and further reading

Biography

1. Pierre Curie, Wikipedia (English), and Pierre Curie, Wikipédia (French).
2. Nobel Foundation, Pierre Curie: Biographical.
3. Curie, Pierre, Complete Dictionary of Scientific Biography, via Encyclopedia.com.
4. M. Curie, Pierre Curie, Macmillan, 1923; Dover reprint, 2012.
5. A. Pais, Inward Bound, Oxford University Press, 1986, chapters on radioactivity.
6. S. Katzir, The Beginnings of Piezoelectricity: A Study in Mundane Physics, Springer, 2006.

Physics

1. J. Curie and P. Curie, Développement par compression de l’électricité polaire dans les cristaux hémièdres à faces inclinées, Bulletin de la Société minéralogique de France 3 (1880), 90–93.
2. P. Curie, Sur la formation des cristaux et sur les constantes capillaires de leurs différentes faces, Bulletin de la Société minéralogique de France 8 (1885), 145–150.
3. P. Curie, Sur la symétrie dans les phénomènes physiques, symétrie d’un champ électrique et d’un champ magnétique, Journal de physique théorique et appliquée 3 (1894), 393–415.
4. P. Curie, Propriétés magnétiques des corps à diverses températures, thesis, Paris, 1895; Annales de chimie et de physique, 1895.
5. P. Curie and A. Laborde, Sur la chaleur dégagée spontanément par les sels de radium, Comptes rendus 136 (1903), 673–675.
6. P. Curie, Radioactive substances, especially radium, Nobel lecture, 6 June 1905.
7. Curie’s law and Curie’s principle, Wikipedia.
8. J. F. Nye, Physical Properties of Crystals, Oxford University Press, 1957, for the tensor treatment of piezoelectricity and Neumann’s principle.
9. Société française de physique, Œuvres de Pierre Curie, Gauthier-Villars, 1908.