Commentary on ‘The scattering of α and β particles by matter and the structure of the atom’ by E. Rutherford (Philosophical Magazine 21 (1911) 669–688)

To mark the 100th anniversary of the publication of Lord Rutherford's paper in Philosophical Magazine on the nuclear model of the atom, we review his ground-breaking work and outline subsequent developments.     

Edmund Stoner and white dwarf stars

The discovery of a limiting mass for white dwarf stars is today usually attributed to Subramanian Chandrasekhar. However, it would seem that an article by Edmund Stoner, which appeared in the Philosophical Magazine in 1930, was the first publication to give a convincing demonstration of the existence of a limiting mass for white dwarfs. We examine here why it is that the contributions of Stoner and others towards this discovery have been largely forgotten.     

Laplace and the era of differential equations

Between about 1790 and 1850 French mathematicians dominated not only mathematics, but also all other sciences. The belief that a particular physical phenomenon has to correspond to a single differential equation originates from the enormous influence Laplace and his contemporary compatriots had in all European learned circles. It will be shown that at the beginning of the nineteenth century Newton's “fluxionary calculus” finally gave way to a French-type notation of handling differential equations. A heated dispute in the Philosophical Magazine between Challis, Airy and Stokes, all three of them famous Cambridge professors of mathematics, then serves to illustrate the era of differential equations. A remark about Schrödinger and his equation for the hydrogen atom finally will lead back to present times.     

Arthur Cayley and the ‘Gruppen Pest’

The original contributions of Arthur Cayley to the Philosophical Magazine on group theory and his ‘trees’ are revisited and to some extend reinterpreted. Both topics were and are of enormous importance not only in physics (group theory, graph theory), but also in quite a few other disciplines as diverse as information technology or, for example, linguistics (trees, graph theory). In order to show that these two topics originally arose from interests in the theory of permutations also Cayley’s ‘Mousetrap’ game is briefly mentioned.     

Measure for measure

The present system of measures for length, weight and capacity (volume) originates from scientific ideas expressed during the French Revolution in 1789. The history of a compatible unit of length, however, turns out to be less of a scientific but rather of a political character. Here reports to the Philosophical Magazine made in the first quarter of the nineteenth century are used to trace the cultural split between meters and inches, and between kilograms and pounds, that can be experienced in many parts of the world.     

Suppression of charge ordering and thermal hysteresis of electronic transport and magnetisation in La0.5Ca0.5Mn1−xNixO3

A series of polycrystalline La_0.5Ca_0.5Mn_1?xNi_xO₃ (x = 0.00, 0.025, 0.050, 0.075, 0.100 and 0.125) was synthesised using solid state reaction. Measurements in a cooling and warming cycle between 300 and 80 K were carried out to study the Ni-doping effects on the electrical resistivity, thermopower and magnetisation of single-phase La_0.5Ca_0.5Mn_1?xNi_xO₃. Partial substitution of Ni for Mn leads to the suppression of charge ordering state, the evidence of which is shown by the dramatic decrease in electrical resistivity and thermal hysteresis width in electrical resistivity, thermopower and magnetisation. However, the magnitude of both electrical resistivity and thermopower increases with increasing Ni content. This can be attributed to an increase in the Mn⁴⁺ concentration, which favours the antiferromagnetic state and leads to a gradual disappearance of ferromagnetic double exchange interaction. Besides, the metal–nonmetal transition temperature decreases with increasing Ni content until x = 0.075, which might arise from increased electron–phonon coupling due to less ordered spins at temperatures above ferromagnetic transition. For samples with x greater than 0.075, no metal–nonmetal transition is observed due to the suppression of double exchange mechanism.     

The Philosophical Magazine and the Periodic Table of Elements

The history of the Periodic Table of Elements covers almost 300 years: from the discovery of phosphorus in 1669 to that of Lawrencium in 1961. Before that period, only elements such as copper, silver, gold, mercury, lead and of course carbon were known, which already had accompanied the history of mankind for millennia. The first “wave” of discoveries of new metals occurred at the close of the eighteenth and the beginning of the nineteenth centuries and was almost entirely based on “wet chemistry”. Because this period, in which no physics-related techniques of identification were available, seems to be now so remote, it is worthwhile to recall these discoveries in the context and style of their time by making use of the Philosophical Magazine archives.     

Dielectric and magnetic permittivities of three new ceramic tungstates MPr2W2O10 (M = Cd,Co, Mn)

Broadband dielectric spectroscopy measurements revealed an anomalously large relative permittivity value (ε _r?=?884) for MnPr₂W₂O₁₀, a smaller value (ε _r?=?156) for CoPr₂W₂O₁₀ and the smallest value (ε _r?=?22) for CdPr₂W₂O₁₀ at low frequency (ν?=?0.1?Hz) and above room temperature in the insulating and paramagnetic state. Below 273?K, the relative permittivity (ε _r?～?24) did not depend significantly on frequency for all the tungstates under study. Electrical resistivity, thermoelectric power, electron paramagnetic resonance, magnetic susceptibility and magnetization provided experimental evidence that the studies tungstates were paramagnetic insulators with low n-type conduction. Only in the case of MnPr₂W₂O₁₀ was a ferrimagnetic order below 45?K observed. These effects are discussed within the framework of Maxwell–Wagner polarization, chemical covalent bonds and porosity mechanism.     

BaTiO3–ferrite composites with magnetocapacitance and hard/soft magnetic properties

BaTiO₃–ferrite multiphase composites were prepared starting from di-phase mixtures of α-Fe₂O₃ and BaTiO₃ powders. During the sintering step, the formation of small amounts of secondary phases with multifunctional character as BaFe₁₂O₁₉ or Ba₁₂Ti₂₈Fe₁₅O₈₄ was promoted. The resulting multiphase ceramic compounds show interesting dielectric, magnetic and small magnetocapacitance effect at low temperature. The coexistence of different magnetic phases with contrasting coercivities (hard/soft) was detected by the presence of ‘wasp-waisted’ M(H) hysteresis loops and first-order reversal curve analysis. The present approach demonstrates that active materials can be realised by controlling in situ reactions at the interfaces in ferroelectric–magnetic oxide composites.     

Magnetic octopole contributions to the ‘pseudo-contact’ chemical shift

Magnetic multipole contributions to the neighbour-anisotropy or ‘pseudo-contact’ shift are examined theoretically. Truncation of the multipolar expansion of the nuclear magnetic shielding at the dipolar terms is shown to be satisfactory for shift reagents relying on paramagnetic anisotropy in metal ions. However, this procedure is unreliable for benzene and macrocyclic shift reagents such as porphyrins. For molecules of this type, the ratio of the octopolar to the dipolar shielding is in the order of a ²/R ² where a is the ‘ molecular radius ’ and R the distance between the centre of the ring system and the nucleus of interest.     

Single crystal growth and superconductivity of Ca(Fe1−x Co x )2As2

We report the single crystal growth of Ca(Fe_1?x Co _x )₂As₂ (0?≤?x?≤?0.082) from Sn flux. The temperature–composition phase diagram is mapped out based on the magnetic susceptibility and electrical transport measurements. The phase diagram of Ca(Fe_1?x Co _x )₂As₂ is qualitatively different from those of Sr and Ba; this could be due to both the charge doping and structural tuning effects associated with Co substitution.     

Natural J coupling (NJC) analysis of the electron lone pair effect on NMR couplings: 2. The anomeric effects on 1 J (C,H) couplings and its dependence on solvent

The electronic origin of the influence of the anomeric effect (negative hyperconjugative interaction, NHI) on the Fermi contact (FC) term of ¹ J(C, H) couplings has been studied from a theoretical point of view at the DFT-B3LYP level. The HN=CH₂, molecule was chosen as the primary model compound, in which both FC ¹ J(C, H) couplings were decomposed into bond contributions with the natural J coupling dissection approach (NJC). Differences between the ¹ J (C, H)^FC couplings for C——H bonds in synperiplanar and antiperiplanar orientations with respect to the nitrogen non-bonding electron pair closely follow the experimental trend. They are made up chiefly of three NJC contributions: ‘bond’, ‘direct lone pair’ and the ‘carbon-core orbitals’. The NHI influence on these terms was studied by applying the natural bond orbital (NBO) deletion procedure to the charge transfer interaction into the antiperiplanar (C——H) antibond (n(N)→(C——H)?) prior to the NJC dissection calculation. The dielectric solvation effect on both the total FC terms and the respective NJC contributions was estimated by carrying out the calculations using the polarization continuum model. Inhibition of the anomeric effect is evident when the solvent polarity is increased. NHI saturates rapidly with increasing solvent dielectric. Specific solute-solvent interaction effects on ¹ J(C, H) couplings were estimated by evaluating molecular complex models of the form CH₂=HN…S (S = H₂O and DMSO).     

A cellular ligand-field model for ‘l-l’ spectral intensities

A model for the calculation of the intensity distribution in ligand-field ‘l-l’ spectra is presented. The approach builds upon the eigenvectors of prior ligand-field analysis and incorporates the superposition of contributions associated with individual metal-ligand interactions in a complete complex. Local transition moments are parameterized by quantities {t _λ} which bear some resemblance to the {e _λ} of the cellular model of the ligand field itself. Equivalence between matrix elements of the electric-dipole operators acting within mixed-parity, local orbitals and of even-parity, effective transition-moment operators acting within pure l orbitals is exploited to construct a scheme that allows the computation of ‘l-l’ spectral intensities sequentially upon ligand-field diagonalization and within a similar basis of atomic eigenfunctions.     

A cellular ligand-field model for l-l spectral intensities

The intensity distributions in the ‘d-d’ spectra of three planar CuCl^2- ₄ chromophores are reproduced quantitatively within the theoretical model described in the preceding paper. Intensity for these species, namely bis(1-methyl-4-oxo-3,3-diphenylhexyldimethylammonium)tetrachlorocopper(II), bis(2-iminol-1-methy-4-imidazolidinium)tetrachlorocopper(II) and bis(N-methylphenylethylammonium)-tetrachlorocopper(II), is deemed to arise dynamically via the bending vibrations. Fair reproduction of experimental absorbances is achieved using the b _2u mode alone, this being known to be the softest vibration in these systems. The roles of spin-orbit coupling and small departures from D _4h symmetry are discussed. Nearly perfect reproduction of experiment is obtained with addition of small contributions from the e_u bend. The intensity distribution in the ‘d-d’ spectrum of the pseudo-tetrahedral chromophore, bis(N-benzylpiper-azinium)tetrachlorocopper(II), is reproduced quantitatively within the ‘static’ model described in part I of this series. Comparisons between the parameter values obtained from the ‘static’ analysis with those from the ‘dynamic’ analysis for the planar chromophores suggest that dynamic modelling with both b _2u and e_u modes is the more physically persuasive. The efficacy of the model in part IV is critically reviewed in this first application.     

Mn site substitution of La0.67Ca0.33MnO3 with closed shell ions: Effect on magnetic transition temperature

Mn site is substituted with closed shell ions (Al, Ga, Ti, Zr and a certain combination of Zr and Al) and also with Fe and Ru ions carrying the magnetic moment (S=5/2 and 2 respectively) at a fixed concentration of 5 at %. Substitution did not change either the crystal symmetry or the oxygen stoichiometry. All substituents were found to suppress both the metal-insulator and ferromagnetic transition temperatures (T _p(ρ) and T _C, respectively) to varied extents. Two main contributions identified for the suppression are the lattice disorder arising due to difference in the ionic radii between the substituent (r _M) and the Mn³⁺ ion (r _Mn ³⁺) and in the case of the substituents carrying a magnetic moment, the type of magnetic coupling between the substituent and that of the neighboring Mn ion.     

退火对Mn和N共掺杂的Zn0.88Mn0.12O:N薄膜特性的影响

以NH₃为掺N源,采用电子束反应蒸发技术生长了Mn和N共掺杂的Zn_1-xMn_xO:N薄膜,生长温度为300℃,然后在O₂气氛中400℃退火0.5 h.X射线衍射测量表明,Zn_0.88Mn_0.12O(Mn掺杂)薄膜或Zn_0.88Mn_0.12O:N(Mn和N共掺杂)薄膜仍具有单一晶相纤锌矿结构,未检测到杂质相 关键词： ZnO薄膜 Mn和N共掺杂 电学特性 磁特性     

Physical cluster mechanics: Statistical thermodynamics and nucleation theory for monatomic systems

We extend previous computations of mechanical stability of atomic microclusters to the realm of statistical thermodynamics, obtaining thermodynamic functions for small, solid-like Van der Waals clusters of less than some 100 atoms possessing non-crystalline structures of ‘polytetrahedral’ type. These are shown to be almost invariably at a thermodynamic advantage over alternative lattice structures of the same number of atoms, at least for the Lennard-Jones potential in the harmonic-oscillator/rigid-rotor approximation. The dependence of thermodynamic functions upon cluster size appears to be essentially monotonic in the number of internal degrees of freedom; although there are certain exceptional structures, particularly with icosahedral symmetry, there proves to be little evidence for the occurrence of ‘magic numbers’ for stability at any temperature and within the size-range considered. Particular attention is given to the heat capacity of model systems in relation to their vibrational spectra. The Debye T ³ law appears reasonably well obeyed at low temperatures with no evidence for the existence of either ‘soft modes’ or distinct surface contributions.

The results for the free energy of formation of minimal clusters ΔG _f are then applied to the computation of nucleation rates in terms of the Becker-Döring-Volmer-Zeldovitch quasi-equilibrium theory. Gibbsian behaviour in the form of a maximum in the curve of ΔG _f versus size is observed with a critical nuclear size at realistic temperatures and pressures of the order of that predicted by macroscopic liquid-drop theories. These figures and those derived for nucleation rate and critical supersaturation appear remarkably insensitive to the details of the model used, in particular to the distinction between ‘microcrystalline’ and ‘amorphous’ atomistic models.

The general status of atomistic nucleation theory is critically examined in the light of these and similar results.     

A partitioned density functional theory of freezing: application to soft spheres

A non-perturbative density functional theory (DFT) for inhomogeneous fluids is developed by partitioning the functional into short range (‘entropic’) and long range (‘energetic’) contributions. The short range part is treated using standard weighted density functional techniques and the long range contribution is evaluated exactly. This method, which is a generalization of a method due to Likos, C., and Senatore, G., 1995, J. Phys.: Condens. Matter, 7, 6797, does not require the use of a reference system. Results are presented for the calculation of the crystal-/fluid phase coexistence for systems interacting with inverse-power potentials of the form r ^-n , where n = 4, 6 and 12. These results show that this non-perturbative DFT is capable of predicting the freezing of long range inverse power systems (n = 4, 6) into a body-centredcubic lattice. Improvements over earlier methods also are noted in the current results for the solid structure as measured by the Lindemann ratio.     

Studies on differential cross-sections of e–N2 scattering

The differential cross-sections (DCS) of the low-energy electron–N ₂ scattering are studied using the vibrational close-coupling (VCC) method and vibrational scattering potentials which include static, exchange and polarization contributions. The polarization is obtained based on the ‘better than adiabatic dipole’ (BTAD) and the ‘distributed spherical Gaussian’ (DSG) respectively. The converged (0 → 0, 0 → 1, 0 → 2, 0 → 3) DCS are obtained with the impact energies being the resonance's first two elastic scattering peaks?–?approximately 1.90 eV and 2.10 eV. Calculations from both polarization potentials agree with experimental results.