Handbuch der Physik Encyclopedia of Physics – serie

191 Apart from numerous difficulties arising from the high pressure technique as such, there is a natural limitation to the possibility of applying a hydrostatic pressure, since liquids under pressure will solidify above a certain pressure limit. 8 2 Up to pressures of 3 X 10 kg.jm. at room temperature, a liquid like isopentane can be used. For higher pressures helium gas may be used, perhaps to about 9 2 10 kg.jm. , but BRIDGMAN already encountered enormous leakage difficulties 7 when using this gas at 7.10 kg.jm.2 at 90° K. A solution has been found by applying mechanical pressure for the range 8 9 2 between 3 X 10 and 10 kg.jm. , by using silver chloride as transmittant. In this case, however, one has to apply unknown corrections for shearing stress and deformation of the sample, a problem which BRIDGMAN solved experimentally by a determination of the resistivity in the pressure region between 2 and 8 2 5 X 10 kg.jm. , by the hydrostatic and by the mechanical pressure method as well, and applying the correction factor thus determined to the results obtained at higher pressures. Though this method seems to be right in good approximation, the data for the highest pressures are to be considered as less accurate.

Ziff. 13. 41 Wir wollen das Problem folgendermaBen formulieren: Gegeben sei eine be- liebige physikalische Eigenschaft eines Kristalls beliebiger Symmetrie. Welche Bedingungen zwingt die Symmetrie des Korpers der betreffenden physikalischen Eigenschaft auf? Man braucht sich dabei keineswegs auf die Kristallsymmetrien zu beschranken. Die Unter- suchungen konnen leicht_auf Korper ausgedehnt werden, die durch irgendeine andere Gruppe von orthogonalen Transformationen in sich iibergefiihrt werden, die die Transformationen dieser Gruppe also als Symmetrieoperationen besitzen. Fiir uns ist nur der Fall der Zylinder- symmetrie (Gruppe Coo) und der Isotropie (Gruppe Roo) wichtig. Beide lassen sich im An- schlul3 an die Symmetrieelemente der Kristalle leicht behandeln. Spezielle* Falle dieses Problems sind schon zahlreich gelost worden, s. z. B. [1], [2]. Der Losungsweg war umstandlich und miihsam, Fehler stellten sich mit- unter ein und blieben lange Zeit unentdeckt. Erst in den letzten Jahren wurde das Problem auf verschiedenen Wegen systematisch angegriffen [3], [4], auf- bauend auf einer Arbeit von HERMANN [5], die zunachst anscheinend unbeachtet geblieben war.Einige der Verfahren, die bisher entwickelt wurden, und ihre Anwendungsmoglichkeiten sollen hier zusamtnengestellt werden. Andere werden nur kurz arlgedeutet, bei diesen muB auf die Originalliteratur verwiesen werden. Physikalische Einwirkungen auf einen Kristallkorper rufen bestimmte Effekte hervor. Die Einwirkung !l kann allgemein durch ein Feld beschrieben werden (Temperatur, elektrisches Feld, mechanische Spannung oder Verzerrung usw.), auch bei dem Effekt ~ ist dies oft moglich, s. Tabelle 4a. Bei hinreichend Tabelle 4a.

71 For a given value of I the field is independent of the geometrical composition of the coil inside the winding space. The actual number of turns and the cross­ section of the conductors is entirely determined by the impedance of the power supply to which the magnet should be adapted. In the case of low impedance (high current and low voltage) few turns of thick metal should be used. In the case of high impedance (low current and high voltage) many turns of thin material are needed. High impedance coils are made of square wire or flat strip wound into layers or "pancakes" 1. A nice system for low impedance coils was deve­ loped by BITTER. The turns of his magnets consist of flat copper discs separated by thin insulating sheets and joined together at their edges. In this type of coil the current density is higher near the axis than at the exterior, resulting into a higher value for G (see above). For the details of the construction we refer to the original papers 2, 3. If the power is dissipated at a low voltage the cooling may be achieved with the help of water. Distilled water should be preferred over mains' water in order to prevent the magnet from corrosion. In the case of a high voltage coil some non-inflammable organic fluid should be used. A low viscosity and a large specific heat are advantageous.

v. Formation of negative ions by processes other than attachment in the gaseous phase at low X/po 17. Introduction. As early as 1912, J. J. THOMSON [32J in his first mass spectro­ graph observed negative ions of 0-, Cl-, H- and what he believed to be N-. He at first ascribed these to possible dissociation of polar gaseous compounds by electron impact but control studies using ionization at low energies in glow discharges indicated that this was not the origin. O. W. RICHARDSON [33J in his book on emission of electricity from hot bodies reported negative ions to come from hot salts. From there on many experimental studies over the years indicated that negative ions could be formed by various processes. By the middle nineteen hundred and thirties the data fairly clearly identified several processes as being active and MASSEY and SMITH [34J developed the theory underlying some of them. More data are summarized in MASSEY'S excellent little monograph on Negative Ions and in )L\SSEY and BURHOP'S recent book [35]. Since that period, stimulated by various investigations and certain industrial problems, very careful studies of the appearance of such ions by mass spectrograph have been carried out in the laboratory of K. G. EMELEUS in Belfast by SLOANE and his co-workers [3J that haw clarified the questions and indicated what ions have been observed and something of the processes at work.

Sect. 1. 247 We have already stated that the subject of ionic conductivity can be properly regarded as one part of the wider study of imperfections, and it is on account of the coherence and unity of this wider subject that ionic conductors acquire their interest [4J. Thus the ideas of mobile interstitial atoms and vacant lattice sites are relevant to a wide range of phenomena; for example diffusion in solidsl, chemical reactions between two solids and between asolid and agas (e. g. tarnish- 3 ing reactions) 2, and annealing of radiation damage . There are, of course, imper- fections such as dislocations whose properties cannot be studied to any great extent through ionic conductivity measurements. However the existence of charges on the ions and the absence of electronic conduction enables the pro- perties and concentration of the simple localised lattice defects to be studied with greater certainty and more directness than is possible in, say, metals. This is true of the original development of the theory of lattice defects by FRENKEL [2J, SCHOTTKY [3J, [5J and WAGNER [5J, and is also true at the present time. Two examples may be mentioned.Firstly the diffusion of impurity atoms in met als may sometimes involve the formation of relatively stable pairs formed from an impurity atom and a vacan- cy [6]. In NaCl (an ionic conductor), such pairs are readily formed between a 2 Na+ vacancy and a substitutionally dissolved multivalent impurity ion, e. g.

Sect. 23. 325 transitions have been drawn for which L1~=0 (n-components). Moreover it is assumed that the hfs splitting of the 3 s 2 Pal, level is negligibly small compared with that of the 3 s 25,/, level. BACK and GOUDSMIT succeeded in resolving the structure of the components of the Bi I line A 4722 A. In each transition they found 10 components, so that in this case 21 + 1 = 10, and the nuclear spin of 209 Bi becomes 1 = 9/ , Later on their results for a group of components were 2 reproduced and published by ZEEMAN, BACK and GOUDSMITI. There are only a few examples where the influence of a magnetic field on the hfs of spectral lines has been shown experimentally in weak, intermediate and strong fields. One of them is the beautiful experiment by JACKSON and 2 KUHN on the Zeeman effect of the hfs of the Na D line A 5890 A. These authors used an atomic beam light source and photographed the lines in absorption.They showed that for the components of this line there was a real Zeeman effect in magnetic fields up to a magnetic field strength of about 1600 oersted, whereas there is a transition to the Back Goudsmit effect in stronger fields, the latter being completed at a field strength of about 3000 oersted. VI. The use of the Zeeman effect in the analysis of atomic spectra.

107 In this way the absolute values of the structure factors may be found, not the phases (6. 8). The problem to find these phases is the phase problem. The present article will treat the following topics. At first the description of the ideal crystal will be given in Chap. B. The underlying principles of this description are the concepts of reciprocal lattice, FOURIER synthesis and sym­ metry. The evaluation of the intensity will then follow in Chap. C and D. Chap. E is concerned with the phase problem and related topics. Though this article treats the analysis of crystal structures, the fundamental concepts for other structures will here be found too. But these topics, and the experimental methods, will l find their place elsewhere . B. Description of the crystalline state. I. Lattice theory. a) The direct lattice. 8. Introduction. In Sect. 3, a description of the ideal crystal was given: The space, occupied by a crystal, is divided into congruent parallelepipeds, each with the same orientation. This parallelepiped is defined by the three basic vectors, a, band c, drawn from an origin 0 (Fig. 2), and is called the primitive cell. This cell is filled with atoms (or ions), and the same configuration of atoms is repeated in space. It has been aptly called a three-dimensional wallpaper, as on a wallpaper the same pattern is repeated again and again.

243 number n and orbital angular momentum 1, but also a total angular momentum 1 f = 1 ± !. This modification lead to striking successes for the model. Almost without exception, the ground state spins of odd nuclei were found to be cor­ rectly predicted. Furthermore several other features of nuclei such as the occur­ rence of isomeric states and the values of magnetic dipole moments were explained, at least qualitatively. However the model completely failed to explain the large values of observed electric quadrupole moments and certain regularities in nuclear spectra, especially of rare earth nuclei. 4. 1950-1953. The emphatic success of the shell-model modified by a spin­ orbit force gave the necessary confidence and incentive to physicists to apply the model in detail to individual nuclei. Guided by parallel calculations in atomic spectroscopy, considerable effort was devoted to computing spectra of levels of nuclear systems with the so-called "Intermediate Coupling Model" in which the independent particle motion is considered to be perturbed by central particle­ particle interactions and spin-orbit forces. Computational labour restricts such calculations to nuclei near closed shells, say within four particles or holes of closed shells. This explains why only light nuclei (A < 20) and isolated groups of nuclei higher in the Periodic Table were thus treated. Usually such calculations were rewarded by agreement with experiment especially those for light nuclei 2 and 20S nuclei near the double closed shell at Pb 3.

45 downwards because (j on the average increases with height; but this conclusion does not follow from (18.3) when the dependency of Kc upon ~o is taken into consideration. s 2 ERTELl and PRIESTLEY and SWINBANK have shown that the upward eddy­ flux of sensible heat must be larger than indicated by (18.3), because this formula does not account for the fact that rising eddies are systematically warmer than sinking eddies because of the effect of buoyancy. The reader is referred to the reviews by SUTTON [22], [23] and PRIESTLEY and SHEP­ PARD [15) for further details concerning eddy-flux of heat and turbulent diffusion. 19. RICHARDSON'S criterion. The right-hand side of (15.10) represents the rate of production of eddy energy. The last term represents energy loss by dissipation; in order that the eddy energy shall be maintained, it is therefore necessary that P div V" - (! V" v" . grad. v > O.

39 2 2 Here B = hJ8:!t Ib and A = hJ8:!t Ia where Ia and Ib are the moments of inertia parallel and perpendicular respectively to the symmetry axis. ~ V I(J + 1) is 2n the total angular momentum of the molecule and K ~ its projection on the 2n symmetry axis. If the molecule possesses a permanent electric dipole moment it can absorb a quantum of microwave energy hv and make a transition to a higher rotational' state governed by the selection rules L1 I = + 1, L1 K = O. The pure rotational absorption frequency is then given by v=2BI (1. 2) where I is the angular momentum quantum number for the upper state of the transition. If an isotopic substitution is made for an atom lying along the sym- metry axis of the molecule, thus changing its moment of inertia and hence its B value, the rotational absorption frequency will shift. The program of mass determination from microwave spectra is to correlate this frequency shift with the change in mass of the substituted isotope. These shifts can range from a few Mc to several thousands of Mc for a change of one mass unit, being larger generally for the lighter atoms.Typical isotopic shifts in the middle mass region (A =60 to 130) are 100 Mc per mass unit. As mentioned above, frequency shifts in the 24000 Mc region can be measured to at least an accuracy of 0.