Peter Debye

How to use this course

Peter Debye has more everyday units and laws named after him than almost any scientist of his century: the debye unit of dipole moment, the Debye temperature, the Debye \(T^3\) law, the Debye length, Debye relaxation, the Debye–Waller factor, the Debye–Scherrer camera and the Debye–Hückel theory. He was a theoretical physicist who received the Nobel Prize in Chemistry, and his ideas run through solid-state physics, physical chemistry and polymer science. His method was to find the simplest model that captured the physics and then push it to quantitative comparison with experiment.

Each technical lesson opens with a paragraph for the general reader, then gives precise statements, derivations in modern notation and exercises with folded solutions. Part III treats Debye’s directorship in Berlin from 1935 to 1939 and the public controversy that broke out in the Netherlands in 2006. It sets out the documented facts and the conclusions of the investigations, with sources, and separates them from interpretations that remain disputed.

Timeline

Maastricht and Aachen, 1884–1906

Petrus Josephus Wilhelmus Debije was born in Maastricht, in the Dutch province of Limburg, on 24 March 1884. His father, Johannes Wilhelmus Debije, was a foreman at a metalware factory; his mother, Maria Anna Barbara Ruemkens, worked as a cashier at the local theatre. The family was Catholic and of modest means, and he had a younger sister. He attended elementary and secondary schools in Maastricht, where he did well in mathematics and physics.

Maastricht lies a short distance from the German border, and the nearest technical university was not in the Netherlands but across it, in Aachen. In 1901 Debije enrolled at the Technische Hochschule there to study electrical engineering, then a fashionable and practical subject. He used the German spelling Debye for the rest of his life.

Sommerfeld

Aachen’s physics was led by Max Wien, and in 1900 Arnold Sommerfeld arrived as professor of technical mechanics. Sommerfeld recognized Debye’s talent and gave him theoretical problems beyond the engineering curriculum. After Debye’s degree in 1905 he became Sommerfeld’s assistant in technical mechanics. When Munich called Sommerfeld to its chair of theoretical physics in 1906, he took Debye with him as his assistant. The move turned an engineer into a theoretical physicist.

Munich with Sommerfeld, 1906–1911

Munich in 1906 had Wilhelm Röntgen in experimental physics and now Sommerfeld in theory. Sommerfeld’s small institute became the training ground for a generation of theorists, and Debye was its first star. Sommerfeld’s method of setting students hard problems from current research suited him perfectly.

His doctoral thesis, completed in July 1908, calculated the pressure of light on small spheres of arbitrary material, a problem in electromagnetic scattering theory. It built on the solution of Maxwell’s equations for scattering by a sphere, published by Gustav Mie the same year; the theory is sometimes called Lorenz–Mie–Debye. In 1910 Debye qualified as a university lecturer (Privatdozent) in Munich.

Planck’s law by counting modes

In 1910 Debye published a short derivation of Planck’s radiation law. Instead of material oscillators in the walls, he counted the standing electromagnetic waves of a cavity, gave each mode the mean energy of a Planck oscillator, and summed. The number of modes with frequency below \(\nu\) in a volume \(V\) is \(\frac{8\pi V\nu^3}{3c^3}\), and the energy density follows directly. Max Planck regarded the derivation as simpler than his own. The same idea, applied to sound waves in a solid, became Debye’s theory of specific heat two years later (Lesson 04).

Zurich, Utrecht, Göttingen, Zurich, 1911–1927

In 1911 Albert Einstein left the University of Zurich for Prague, and Debye, aged 27, succeeded him as professor of theoretical physics. A year later he moved to Utrecht, in his own country. In 1913 he married Mathilde Alberer. They had a son, Peter Paul Rupprecht (born 1916), who became a physicist and worked with his father, and a daughter, Mathilde Maria (born 1921).

The years 1912 to 1916 were extraordinarily productive. In 1912 alone he published the specific heat theory and the theory of polar molecules. In 1914 he moved to Göttingen, where he headed the theoretical department of the physics institute and later directed it. There, during the war, he and his student Paul Scherrer invented the powder method of X-ray diffraction. Hertha Sponer took her doctorate with him at Göttingen. From 1915 Debye edited the Physikalische Zeitschrift, one of the main German physics journals, for a quarter of a century.

Debye was a Dutch citizen throughout, and he moved readily between countries and between theory and experiment. In 1920 the ETH in Zurich appointed him professor of physics and director of its physics institute, an experimental post. His Göttingen chair went to Max Born. At the ETH his assistant Erich Hückel worked with him on the theory of electrolytes (Lesson 08), and in 1926 the young Norwegian Lars Onsager came to Zurich to work with him, having found that the theory of conductivity was incomplete. In 1927 Debye moved again, to Leipzig, as professor of experimental physics.

The heat capacity of solids

For the general reader. Heating a solid makes its atoms vibrate. Classical physics predicted that every solid should need the same amount of heat per atom to warm it by one degree, but at low temperatures solids need far less. Einstein explained part of this in 1907 with quantum theory. Debye saw what Einstein had missed: the vibrations of a solid are sound waves of all wavelengths, and the longest waves keep absorbing heat even when the solid is very cold. The result is the famous \(T^3\) law.

Debye’s paper Zur Theorie der spezifischen Wärmen appeared in the Annalen der Physik in 1912, a few months before the discrete lattice theory of Born and von Kármán. Einstein’s model gave all \(3N\) vibrations of a crystal the same frequency, and so predicted a heat capacity that falls exponentially at low temperature. Measurements in Walther Nernst’s laboratory showed a slower decline.

The model

Treat the crystal of \(N\) atoms in volume \(V\) as an elastic continuum with, for simplicity, one sound speed \(v\) for all three polarizations. Counting standing waves as in Lesson 02, the number of modes with angular frequency below \(\omega\) is \(\frac{V\omega^3}{2\pi^2v^3}\). A crystal has only \(3N\) degrees of freedom, so Debye cut the spectrum off at a frequency \(\omega_D\) chosen to give exactly \(3N\) modes:

Derivation

A mode of frequency \(\omega\) contributes \(k_B\,x^2e^x/(e^x-1)^2\) with \(x=\hbar\omega/k_BT\), as in Einstein’s theory. Integrating against \(g(\omega)\) and substituting \(\omega=k_BTx/\hbar\) gives the formula in the box. At low temperature the upper limit goes to infinity, and \(\int_0^\infty\frac{x^4e^x}{(e^x-1)^2}dx=\frac{4\pi^4}{15}\), which gives the coefficient \(\frac{12\pi^4}{5}\approx233.8\). Per mole, \(C_V\approx1944\,(T/\Theta_D)^3\) J mol\(^{-1}\) K\(^{-1}\).

The physical reason for \(T^3\) is that only modes with \(\hbar\omega\lesssim k_BT\) are excited, their number grows as \(T^3\), and each carries about \(k_BT\). The same counting gives the Stefan–Boltzmann \(T^4\) law for photons; phonons are the sound-wave analogue. Typical Debye temperatures are about 105 K for lead, 343 K for copper and about 2200 K for diamond. At low temperature in metals, the electrons add a term linear in \(T\), which Sommerfeld explained in 1927–28.

Polar molecules and dielectric relaxation

For the general reader. Some molecules, like water, have a positive end and a negative end. Debye realized in 1912 that such permanent dipoles would line up partly in an electric field, fighting against thermal agitation, so that their contribution to a material’s dielectric constant should fall as the temperature rises. Measuring that temperature dependence revealed the size of the dipole, and with it the shape of the molecule. This is the work for which he received the Nobel Prize.

Debye’s paper Einige Resultate einer kinetischen Theorie der Isolatoren (Physikalische Zeitschrift, 1912) adapted Paul Langevin’s 1905 theory of paramagnetism to electric dipoles.

Orientational polarization

A molecule with permanent dipole moment \(p\) in a field \(E\) has energy \(-pE\cos\theta\). With the Boltzmann distribution over orientations, the mean component along the field is

For ordinary fields \(pE\ll k_BT\), so each molecule contributes \(p^2E/3k_BT\), in addition to the induced moment \(\alpha E\) from distortion of its electron cloud.

The unit of dipole moment, the debye, is \(1\ \mathrm D=10^{-18}\) statcoulomb·cm \(\approx3.336\times10^{-30}\) C·m, about the moment of charges \(\pm e\) separated by 0.21 Å. Water has 1.85 D, hydrogen chloride 1.08 D. Carbon dioxide and methane have zero, which shows that CO\(_2\) is linear and CH\(_4\) symmetric. Measured dipole moments became a standard tool for determining molecular structure, for instance distinguishing cis and trans isomers. Debye collected the theory in Polar Molecules (1929).

Relaxation

Dipoles take time to reorient. If the orientational polarization relaxes exponentially with time constant \(\tau\) toward its equilibrium value, a field \(E_0e^{i\omega t}\) gives

The loss part \(\varepsilon''\) peaks at \(\omega=1/\tau\). For liquid water at room temperature this is near 20 GHz, in the microwave band, which is why microwave ovens heat water efficiently.

X-rays, thermal motion and gases

For the general reader. In 1912 Max von Laue showed that crystals diffract X-rays. A puzzle followed at once: the atoms of a warm crystal jiggle, so why are the diffraction spots still sharp? Debye showed that thermal motion does not blur the spots but weakens them, by an amount that grows with temperature and with the diffraction angle. He then showed that even a gas of randomly oriented molecules produces broad diffraction rings that reveal the distances between atoms within each molecule.

The temperature factor

Let atom \(j\) sit at \(\mathbf R_j+\mathbf u_j\), where \(\mathbf u_j\) is a thermal displacement. For scattering vector \(\mathbf q\), the Bragg intensity involves the average \(\langle e^{i\mathbf q\cdot\mathbf u}\rangle\). Debye computed this in 1913–14; Ivar Waller completed the treatment in 1923.

The key identity holds because in a harmonic crystal \(\mathbf q\cdot\mathbf u\) is a sum of many independent normal-mode coordinates and is Gaussian distributed. For a Gaussian variable \(X\) of mean zero, \(\langle e^{iX}\rangle=e^{-\langle X^2\rangle/2}\). The same factor, under the name Lamb–Mössbauer factor, gives the fraction of recoil-free gamma emission in the Mössbauer effect.

Randomly oriented molecules

In 1915, in Zerstreuung von Röntgenstrahlen (Annalen der Physik), Debye asked what a gas of identical molecules would show. Each molecule has atoms with scattering factors \(f_i\) at relative positions \(\mathbf r_{ij}\). The intensity from one molecule in a fixed orientation is \(\sum_{i,j}f_if_je^{i\mathbf q\cdot\mathbf r_{ij}}\). Averaging over all orientations of \(\mathbf r_{ij}\) gives:

The diffraction from a gas is therefore not uniform but has broad maxima that depend only on the interatomic distances. Debye and his collaborators later used X-ray and electron diffraction by gases to measure bond lengths. The same equation is used today to compute powder patterns of nanoparticles and the scattering from proteins in solution.

The powder method

For the general reader. To study a crystal with X-rays one needed a large, perfect single crystal, and most materials do not form one. In 1916 in Göttingen, Debye and Paul Scherrer turned a powder of tiny crystals into a diffraction instrument. Because the grains point in every direction, each family of atomic planes reflects X-rays into a cone, and a strip of film around the sample records a set of rings. Powder diffraction became the most widely used method for identifying crystalline materials.

The paper Interferenzen an regellos orientierten Teilchen im Röntgenlicht (Physikalische Zeitschrift, 1916) described the method and applied it to lithium fluoride and other substances. Albert Hull at General Electric developed the same method independently in 1917.

Selection rules

The intensity of reflection \((hkl)\) is proportional to \(|F_{hkl}|^2\), where the structure factor \(F_{hkl}=\sum_jf_je^{2\pi i(hx_j+ky_j+lz_j)}\) sums over atoms in the cubic cell. For a body-centred lattice \(F=0\) unless \(h+k+l\) is even. For a face-centred lattice \(F=0\) unless \(h,k,l\) are all even or all odd. So the sequence of allowed values of \(N=h^2+k^2+l^2\) identifies the lattice: simple cubic 1, 2, 3, 4, 5, 6, 8, …; body-centred 2, 4, 6, 8, 10, …; face-centred 3, 4, 8, 11, 12, 16, …

Electrolytes: Debye–Hückel

For the general reader. When salt dissolves in water it splits into positive and negative ions. Each ion attracts a cloud of opposite charge around itself, which screens its field and lowers its effective concentration. In 1923 Debye and Erich Hückel calculated this cloud and obtained exact laws for dilute solutions, explaining why the measured properties of salt solutions depend on the square root of the concentration. The same screening idea governs plasmas, semiconductors and colloids.

Their paper Zur Theorie der Elektrolyte appeared in the Physikalische Zeitschrift in 1923.

The ionic atmosphere

Let ion species \(i\) have charge \(z_ie\) and bulk number density \(n_i\), with \(\sum_in_iz_i=0\). The potential \(\phi\) around a chosen ion obeys Poisson’s equation, and the other ions follow Boltzmann distributions \(n_ie^{-z_ie\phi/k_BT}\). For \(|z_ie\phi|\ll k_BT\), linearizing gives

Derivation of the limiting law

For \(\kappa a\to0\), \(\phi=\frac{ze}{4\pi\varepsilon_0\varepsilon_r}\big(\frac{e^{-\kappa r}}{r}\big)\). Subtracting the ion’s own Coulomb potential, the atmosphere produces at the ion the potential \(-\frac{ze\kappa}{4\pi\varepsilon_0\varepsilon_r}\). Charging the ion from 0 to \(ze\) in this self-consistent field costs the extra free energy \(-\frac{z^2e^2\kappa}{8\pi\varepsilon_0\varepsilon_r}\), which equals \(k_BT\ln\gamma\) for that ion. Averaging over cation and anion gives the law in the box. Since \(\kappa\propto\sqrt I\), the correction is proportional to the square root of the concentration, as Friedrich Kohlrausch had found empirically for conductivity. Onsager corrected the conductivity theory in 1926–27, giving the Debye–Hückel–Onsager equation.

Compton, cold and sound

For the general reader. Debye’s range is shown by three ideas from the 1920s and early 1930s. He explained, at the same time as Arthur Compton, why X-rays change colour when they bounce off electrons. He proposed, at the same time as William Giauque, a way of reaching temperatures within a fraction of a degree of absolute zero by demagnetizing a salt. And with Francis Sears he showed that a sound wave in a liquid acts as a diffraction grating for light.

The Compton effect (1923)

Compton announced his measurements and theory in 1923. Debye, working independently, published the same quantum explanation in the Physikalische Zeitschrift that spring. Treat the X-ray as a photon of momentum \(h/\lambda\) colliding elastically with a free electron at rest.

Magnetic cooling (1926)

In a paramagnetic salt, the ionic magnetic moments are disordered at low temperature unless a field aligns them. The entropy of ideal non-interacting moments depends only on \(B/T\). Magnetize the salt isothermally at about 1 K in a strong field, so that the moments align and their entropy falls; then isolate it and lower the field. Constant entropy forces \(B/T\) to stay constant, so the temperature drops in proportion to the field. Debye and Giauque proposed this in 1926. Giauque and Duncan MacDougall carried it out in 1933, reaching about 0.25 K.

Light diffracted by ultrasound (1932)

A sound wave of wavelength \(\Lambda\) in a liquid makes a periodic variation of density and refractive index. Debye and Sears, and independently René Lucas and Pierre Biquard, observed that light crossing it is diffracted into orders at angles \(\sin\theta_m=m\lambda/\Lambda\). The effect underlies acousto-optic modulators and allows sound speeds to be measured optically.

Light scattering and polymers

For the general reader. During the Second World War the United States needed synthetic rubber, and chemists needed a quick way to measure how large their long-chain molecules were. At Cornell Debye showed that the brightness of light scattered by a polymer solution measures the polymer’s molecular weight, and that the way the scattering changes with angle measures the polymer’s size. Light scattering became a standard method of polymer and protein science.

Debye’s paper Light scattering in solutions appeared in the Journal of Applied Physics in 1944, extending ideas of Marian Smoluchowski and Einstein, who had explained scattering by density and concentration fluctuations.

Fluctuation theory

A small volume of solution scatters light in proportion to the mean square fluctuation of its refractive index. In a dilute solution these come from concentration fluctuations, and thermodynamics fixes their size through the osmotic pressure \(\Pi\): \(\langle\delta c^2\rangle\propto k_BTc\,/\,(\partial\Pi/\partial c)\). With \(\Pi/c=RT\big(\frac1M+A_2c+\cdots\big)\), the scattering gives the molecular weight \(M\) and the second virial coefficient \(A_2\).

For a flexible chain with Gaussian statistics, Debye (1947) computed the full form factor by applying the orientational average of Lesson 06 to every pair of segments:

Plotting \(Kc/R_\theta\) against both \(c\) and \(\sin^2(\theta/2)\) and extrapolating to zero in both (the Zimm plot, 1948) gives \(M\), \(A_2\) and \(R_g\) from one set of measurements.

Leipzig, Berlin and the Nazi state, 1927–1940

In 1927 Debye became professor of experimental physics and director of the Physical Institute at Leipzig. That autumn Werner Heisenberg took the chair of theoretical physics, and the two made Leipzig a leading centre for molecular physics and quantum theory. Debye’s group used X-ray and electron diffraction by gases to measure molecular structure and studied dipole moments and ultrasonics.

The Kaiser Wilhelm Institute for Physics

In late 1933 Max Planck, as president of the Kaiser Wilhelm Society, offered Debye the directorship of a new Kaiser Wilhelm Institute for Physics in Berlin-Dahlem, financed largely by the Rockefeller Foundation. Debye accepted, also becoming professor at the University of Berlin, and took up the post in 1935. He kept his Dutch nationality, with written assurance from the German education ministry that he would not be required to become a German citizen. The institute’s new building opened in 1937. In 1936 he received the Nobel Prize in Chemistry “for his contributions to our knowledge of molecular structure”, through his work on dipole moments and on the diffraction of X-rays and electrons in gases. From 1937 to 1939 he was chairman of the German Physical Society, and in April 1937 he joined the German Academy for Aviation Research.

Lise Meitner, July 1938

After the annexation of Austria in March 1938, the Austrian physicist Lise Meitner, of Jewish origin and working at the Kaiser Wilhelm Institute for Chemistry, lost the protection of her foreign citizenship and was forbidden to emigrate. Debye joined Dutch colleagues, Dirk Coster of Groningen and Adriaan Fokker, in arranging her escape. Coster came to Berlin on 11 July, and on 13 July Meitner crossed into the Netherlands with him. Historians agree that Debye took a real risk in this.

The letter of 9 December 1938

Five months later, a month after the November pogrom, Debye as chairman signed a circular to the German members of the German Physical Society. It stated that, under the circumstances, the membership of German Jews as defined by the Nuremberg Laws could no longer be maintained, and asked those affected to notify the society of their resignation. The letter was drafted under pressure from the regime, and Debye’s motives have been debated ever since: whether he acted to protect the society from worse interference, from opportunism, or from indifference. The historian Jurrie Reiding reports that seven Jewish members resigned in response.

Departure

After the war began in September 1939, the Army Ordnance Office took over the Kaiser Wilhelm Institute for Physics for its uranium project. According to Debye’s own account, Ernst Telschow of the Kaiser Wilhelm Society told him that he could no longer enter the laboratory unless he became a German citizen. He refused. He was granted leave, telling the German authorities that his directorship was only suspended, and he kept open the possibility of return. He left Germany in mid-January 1940, sailed from Genoa on 23 January and reached New York on 1 February to give the Baker Lectures at Cornell University. His wife followed in January 1941; his daughter remained in Germany. In the autumn of 1940 the FBI investigated him, prompted in part by information from Einstein.

Cornell, the controversy and legacy, 1940–1966

Cornell appointed Debye professor of chemistry and chair of its chemistry department in 1940, and he remained in Ithaca for the rest of his life. During the war he worked on polymers for the American synthetic rubber programme, which led to the light-scattering methods of Lesson 10. He became a United States citizen in 1946, stepped down as chair in 1952 and remained active in research as an emeritus professor. He enjoyed trout fishing and his garden. His honours included the Rumford Medal (1930), the Lorentz Medal (1935), the Franklin Medal (1937), the Max Planck Medal (1950), the Priestley Medal (1963) and the National Medal of Science (1965). He suffered a heart attack in April 1966 and died after a second one on 2 November 1966 in Ithaca, aged 82.

The controversy, 2006–2008

In January 2006 the Dutch weekly Vrij Nederland published extracts from Einstein in Nederland, a book by the journalist Sybe Rispens, which presented Debye as having actively collaborated in the purge of Jewish scientists, with the 1938 letter as central evidence. Events moved quickly.

• February 2006. After the Netherlands Institute for War Documentation (NIOD) confirmed that the letter was authentic, Utrecht University removed Debye’s name from its Debye Institute, and Maastricht University withdrew from the Debye Prize.
• May–June 2006. Martinus Veltman, the Nobel laureate who had written the book’s foreword, withdrew it and asked Utrecht to reverse its decision. Cornell’s chemistry department, after its own review, reported that it had found no evidence that Debye was a Nazi sympathizer, collaborator or antisemite, and kept his name on its professorship.
• November 2007. The NIOD report by the historian Martijn Eickhoff, commissioned by the Dutch education ministry, described Debye as an opportunist who kept his options open in Germany and the Netherlands, including contacts with German authorities as late as 1941, and noted his concern for his daughter in Germany. It found no evidence of Nazi party membership or antisemitism.
• January 2008. A committee chaired by Jan Terlouw found no evidence of bad faith, concluded that Debye had been neither a resistance hero nor a collaborator, and called the 1938 letter a dark episode. It recommended restoring his name. Utrecht accepted and restored the Debye Institute. Maastricht did not resume its role in the prize, which the Hustinx Foundation continued to award; the city kept its Debye street names.

In 2010 Jurrie Reiding, using Debye’s American papers and FBI records, proposed that Debye may have passed information to Paul Rosbaud, a Berlin science editor who was a British intelligence source. Reiding presented this as a hypothesis, not a proven fact. The science writer Philip Ball disputed it; his book Serving the Reich (2013) examines Debye’s case alongside those of Planck and Heisenberg. The documented record supports neither the picture of an active Nazi collaborator nor that of a secret resister.

Legacy

• Solids: the Debye model and temperature, the \(T^3\) law, the Debye–Waller factor and phonon counting.
• Molecules: dipole moments and the debye unit, dielectric relaxation, the Debye scattering equation.
• Crystallography: the Debye–Scherrer powder method, the most widely used diffraction technique in materials science.
• Solutions and plasmas: the Debye length and Debye–Hückel theory.
• Polymers and colloids: light scattering, the Debye function and molecular-weight measurement.
• Students and collaborators: Paul Scherrer, Erich Hückel, Hertha Sponer, Lars Onsager and many Cornell chemists.

Connections

People linked to Peter Debye across this collection. A name without a link has no page here yet. See Peter Debye in the network of all 337 lives →

Teachers and advisors

• Arnold Sommerfeld 1908

Students

• Hertha Sponer
• Paul Scherrer 1916

Influenced by

• Paul Langevin
• Svante Arrhenius
• Wilhelm Wien

Influenced

• Ivar Waller

Colleagues and collaborators

• Albert Einstein
• Arthur Compton 1923
• Erwin Schrödinger 1925
• Lise Meitner 1938
• Max Born
• Max Planck
• Max von Laue 1935-1939
• Werner Heisenberg 1927-1935
• Wolfgang Pauli
• Dirk Coster 1938
• Erich Hückel 1923
• Francis Sears 1932
• Lars Onsager

Rivals

• Arthur Compton 1923
• William Giauque 1926

Friends

• Paul Rosbaud

Also mentioned in this life

• Ludwig Boltzmann
• Charles-Augustin de Coulomb
• Joseph Fourier
• Benjamin Franklin
• Hendrik Antoon Lorentz
• James Clerk Maxwell
• Siméon Denis Poisson
• Joseph Priestley
• Lord Rayleigh
• Count Rumford
• Theodore von Kármán

Fields

• theoretical physics 11 lives
• physical chemistry 9 lives
• solid-state physics 6 lives

On CoursesHub

• Physical Chemistry

Sources and further reading

Biography

1. Peter Debye, Wikipedia; Peter Debye, German Wikipedia (for family details).
2. Peter Debye, Biographical and Nobel Prize in Chemistry 1936, NobelPrize.org.
3. J. W. Williams, Peter Joseph Wilhelm Debye, 1884–1966, Biographical Memoirs of the National Academy of Sciences (1975).
4. J. Reiding, Peter Debye: Nazi collaborator or secret opponent?, Ambix 57 (2010) 275–300.
5. M. Eickhoff, In the Name of Science? P. J. W. Debye and his Career in Nazi Germany, NIOD / Aksant, 2008.
6. S. I. Rispens, Einstein in Nederland, Ambo, 2006.
7. P. Ball, Serving the Reich: The Struggle for the Soul of Physics under Hitler, Bodley Head, 2013.
8. R. L. Sime, Lise Meitner: A Life in Physics, University of California Press, 1996 (for the escape of July 1938).

Physics and chemistry

1. P. Debye, Der Lichtdruck auf Kugeln von beliebigem Material, Ann. Phys. 30 (1909) (doctoral thesis).
2. P. Debye, Der Wahrscheinlichkeitsbegriff in der Theorie der Strahlung, Ann. Phys. 33 (1910).
3. P. Debye, Zur Theorie der spezifischen Wärmen, Ann. Phys. 39 (1912) 789–839.
4. P. Debye, Einige Resultate einer kinetischen Theorie der Isolatoren, Phys. Z. 13 (1912) 97–100; Polar Molecules, Chemical Catalog Co., 1929.
5. P. Debye, Interferenz von Röntgenstrahlen und Wärmebewegung, Ann. Phys. 43 (1914); I. Waller, Z. Phys. 17 (1923).
6. P. Debye, Zerstreuung von Röntgenstrahlen, Ann. Phys. 46 (1915) 809–823.
7. P. Debye and P. Scherrer, Interferenzen an regellos orientierten Teilchen im Röntgenlicht, Phys. Z. 17 (1916) 277–283.
8. P. Debye and E. Hückel, Zur Theorie der Elektrolyte, Phys. Z. 24 (1923) 185–206.
9. P. Debye, Zerstreuung von Röntgenstrahlen und Quantentheorie, Phys. Z. 24 (1923) 161–166.
10. P. Debye, Einige Bemerkungen zur Magnetisierung bei tiefer Temperatur, Ann. Phys. 81 (1926); W. F. Giauque and D. P. MacDougall, Phys. Rev. 43 (1933).
11. P. Debye and F. W. Sears, On the scattering of light by supersonic waves, Proc. Natl. Acad. Sci. USA 18 (1932) 409–414.
12. P. Debye, Light scattering in solutions, J. Appl. Phys. 15 (1944) 338; Molecular-weight determination by light scattering, J. Phys. Colloid Chem. 51 (1947) 18–32.
13. N. W. Ashcroft and N. D. Mermin, Solid State Physics, Holt, Rinehart and Winston, 1976 (chapters 22–23 on the Debye model and Debye–Waller factor).