 2  Author
 A. R. Allnatt  Requires cookie*   Title
 Statistical Mechanics of Thermotransport of a Heavy Impurity in an Insulating Solid    Abstract
 A kinetic equation is derived for the singlet distribution function for a heavy im purity in a lattice o f lighter atom s in a tem perature gradient. In the one dimensional case the equation can be solved to find formal expressions for the jum p probability and hence the heat o f transport, q*, for a single vacancy jum p o f the im purity. < 7* is the sum o f the enthalpy o f activation, a term involving only averaging in an equilibrium ensem ble, and two nonequilibrium term s in volving tim e correlation functions. The m ost im portant nonequilibrium term concerns the cor relation betw een the force on the im purity and a microscopic heat flux. A plausible extension to three dim ensions is suggested and the relation to earlier isothermal and nonisothermal theories is indicated.   
Reference
 (Z. Naturforsch. 26a, 10 [1971])   
Published
 1971   
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 ZNA197126a0010    Volume
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3  Author
 W. B. Alexander  Requires cookie*   Title
 Electromigration in Single Crystal Cadmium 1*    Abstract
 The results are also expressed in terms of the effective charges for the separate atomic jumps, (1) to a vacancy in the same basal plane and (2) to a vacancy in an adjoining plane. While the parallelism of these findings with those for zinc is apparent, there is one significant difference. In cadmium vacancy creation (and annihilation) tends to alter the caxis dimension preferentially.   
Reference
 (Z. Naturforsch. 26a, 18—20 [1971])   
Published
 1971   
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 ZNA197126a0018    Volume
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4  Author
 D. Heitkamp  Requires cookie*   Title
 On the Interpretation of the Heat of Transport of Substitutional Impurities in Noble Metals    Abstract
 The heats of transport of several substitutional impurities (such as Sb, Sn, In, Ag, Ni and Co) in copper and silver are discussed in terms of atomic quantities. They are considered as consisting of essentially two parts. The first one, the socalled intrinsic heat of transport, can be derived from the electrostatic potential generated by the impurity at the site of a normal lattice atom in excess over the potential of the host lattice. This interpretation is compatible with the thermo dynamic definition of the heat of transport. The calculations were carried out for fee lattices but, in principle, may be easily extended to other alloy structures. The second part, calculated by Gerl, is due to the electronic scattering potential of the impurities. From comparison of theore tical and observed data of heats of transport one finds the agreement to be very good. This is taken to be an indication of the validity of the theoretical models used and of the vacancy mech anism as the dominating mass transport mechanism in these systems, not only in a uniform temperature field but also in a temperature gradient.   
Reference
 (Z. Naturforsch. 26a, 21—31 [1971])   
Published
 1971   
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 ZNA197126a0021    Volume
 26  
5  Author
 P. S. Ho, L. D. Glowinski  Requires cookie*   Title
 Observation of Void Formation Induced by Electromigration in Metallic Films *' *    Abstract
 Observation has been made on void formation induced by electromigration in single crystal and bicrystal (100) Au films and polycrystalline A1 films. In the Au film, voids were observed to be bound by crystal planes with low surface energies, and dislocations appeared to be the preferred sites for void formation. In the A1 film, void formation was observed to begin at grain boundaries or grain boundary junctions. Under our experimental conditions, the formation of voids and hillocks is determined by the local concentration of defects at the grain boundary, but the overall effect is determined by the divergence of the diffusion flux under a temperature gradient.   
Reference
 (Z. Naturforsch. 26a, 32—35 [1971])   
Published
 1971   
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6  Author
 R. E. Hummel, H. M. Breitling  Requires cookie*   Title
 Observations on Electrotransport in Thin Aluminum Films Using Resistance Measurements    Abstract
 Resistance measurements of five different portions of uncoated and partially SiOovercoated aluminum stripes are reported. In specimens of both types the resistance increases at the cathode when the stripe is subjected to high current densities. In partially coated specimens the resistance decreases at the anode whereas it remains constant in the uncoated sample. The difference in behavior at the anode between coated and uncoated specimens is interpreted as being due to dif ferences of ion accumulation: In the uncoated films hillocks are formed whereas in the specimen with partial overcoat the ions accumulate more evenly. Scanningelectron micrographs are shown to support this interpretation.   
Reference
 (Z. Naturforsch. 26a, 36—39 [1971])   
Published
 1971   
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 ZNA197126a0036    Volume
 26  
7  Author
 P. Adam  Requires cookie*   Title
 Electrotransport on Surfaces and Interfaces    Abstract
 A summary of possible mechanisms of surface and interface mass transport in the presence of an electric field and current, and a brief review of experimental data are presented. Emphasis has been given to the relationship between faceting on metal surfaces and a charge carrier flow. A theory for this is presented based on the theory of pure thermal faceting by Mullins 8. The cal culated values of the effective charge show a negative temperature gradient and are close to one for reasonably high temperatures, proving that the “drift term” caused by charge carrier scattering is negligible.   
Reference
 (Z. Naturforsch. 26a, 40—44 [1971])   
Published
 1971   
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 ZNA197126a0040    Volume
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8  Author
  Requires cookie*   Title
 vt    Abstract
 ,v2 grad x2 (1) are the partial molar volumes of compo nents 1 and 2 respectively, Z j, x2 are mole fractions of component 1 and 2, u2 chemical potential of component 2, Q2 * molar heat of transport of components 1 and 2 respectively. Here Q2*, the heat of transport, is the difference between the total enthalpy transported by one mole of moving molecules of type two in the solution and the average enthalpy of one mole of the type two in the same solution. This Q2* is of special interest be cause it will depend strongly on the mechanism of atom transport and any theory on diffusion in li quids must explain its magnitude and sign satis factorily. In the case of a very dilute binary alloy, Eq. (1) can be simplified, d r = d (ln x 2) = d (ln C 2) (2)   
Reference
 (Z. Naturforsch. 26a, 45 [1971])   
Published
 1971   
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9  Author
 P.S B, H.J V T  Requires cookie*   Title
 Thermal Diffusion in Mixtures of Alcohols and Aromatic Hydrocarbons    Abstract
 The thermal diffusion factors observed for these systems vary considerably with concentration, and frequently show a change in sign at some concentration. New data on ethanoltoluene mixtures show that the sign and magnitude of the separation of the components in a thermal gradient are also strongly dependent on the mean temperature of the system. These observations, together with earlier ones on similar systems, can be given a semiquantitative interpretation in terms of a shift in the average degree of association of the alcohol along the temperature gradient.   
Reference
 (Z. Naturforsch. 26a, 48 [1971]; received 6 October 1970)   
Published
 1971   
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 ZNA197126a0048    Volume
 26  
10  Author
  Requires cookie*   Title
 Separative Fluodiffusion    Abstract
 Earlier work on fluodiffusion is discussed. General phenomenological equations for fluodiffusion are given. It is shown that in a Poiseuille flow of a molecular mixture, separational fluodiffusion is expected to be much bigger in the direction of the flow than perpendicular to it. Experiments with liquid lithium are reported. They show a clear isotope effect, but it remains a question whether this effect is due to fluodiffusion or to an interaction of the lithium with the iron in which it was contained.   
Reference
 (Z. Naturforsch. 26a, 52—55 [1971]; received 6 October 1970)   
Published
 1971   
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 ZNA197126a0052    Volume
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11  Author
 D. L., D.N Y, R. N. Je  Requires cookie*   Title
 Atom Transport Under Varying Pressure * *    Abstract
 Study of the effect of hydrostatic pressure on the rate of diffusionlimited processes gives in formation regarding the intrinsic volume changes associated with formation and motion of defects. While there are basic problems associated with interpretation of the motional volume, such effects may be measured directly in some cases and subtracted to give unambiguous results for the defect formation volume. Experimentally, precise measurement of specimen temperature within a highpressure environment poses the most severe practical constraint. Results are given for measurements to pressures of 7 kilobars of ionic conductivity in a series of pure and doped alkali halides: NaCl, KC1, NaBr, and KBr, all of which are predominantly cationic vacancy conductors. The activation volumes are found to be pressure dependent in the intrinsic regions. In all cases the Schottky pair vacancy formation volume is found to be larger than the molar volume, the ratio being largest for NaCl and smallest for KBr. Results are also given for the total activation volume for diffusion of Ti44 in betaTi, a case of "anomalous" bulk diffusion. The tracer penetration plots do not follow a perfect gaussian profile. However, if the penetration plots are fit to a single gaussian, the activation volume derived is consistent with that expected for a vacancy mechansm in bcc metals.   
Reference
 (Z. Naturforsch. 26a, 56—61 [1971]; received 6 October 1970)   
Published
 1971   
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 ZNA197126a0056    Volume
 26  
12  Author
  Requires cookie*   Title
 The Volumes of Formation of Schottky Defects in Ionic Crystals    Abstract
 a n d A. B. L i d i a r d In this paper we calculate the volumes and energies of formation of Schottky defects in the alkali halides NaCl, NaBr, KC1 and KBr. Both the polarisable pointdipole and a simple shell model are evaluated. The calculation uses a generalised and extended MottLittleton approach in conjunction with results derived previously by the lattice statics method of Kanzaki. The polarisable pointdipole model, as might be expected, is bad, but the shell model leads to good values for the Schottky formation energies, which not only compare well with experiment but are insensitive to the size of the region ('region I') around the defect for which the lattice displacements are com puted explicitly (i. e. as distinct from the outer MottLittleton region, 'region II') . The predicted volumes of formation of Schottky defects are less than the molecular volume, i?m , i. e. the volumes of relaxation are negative (NaCl, — 0.69 t;m; NaBr, — 0.73 t>m; KC1, — 0.52 t>m; KBr, —0,51 vm in the static lattice approximation). This is in conflict with the results of experiments on the effect of pressure upon the ionic conductivity of these crystals although some other experimental data are consistent with negative relaxation volumes. The disagreement is briefly discussed and the pos sibility that temperature effects are greater than is implied by the quasiharmonic model is noted as a possible explanation. 1. I n tr o d u c tio n   
Reference
 (Z. Naturforsch. 26a, 62—68 [1971]; received 20 October 1970)   
Published
 1971   
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 ZNA197126a0062    Volume
 26  
13  Author
  Requires cookie*   Title
 Correlation Effects and Activation Energies for Diffusion in Alloys    Abstract
 The problems involved in calculating correlation factors for diffusion in dilute alloys can be contrasted to those arising in concentrated solid solutions. As one moves from the pure element to the dilute alloy to the concentrated alloy, the calculation becomes progressively more difficult. Because of the complex atom configurations which can occur in concentrated alloys, it usually is not possible to calculate correlation factors in these alloys exactly. Several important simplifications are available in nondilute random alloys. A large reduction in complexity can be secured by using a random alloy model where each atom is treated as diffusing in a uniform matrix, with the matrix properties being determined by the composition and jump frequencies in the alloy. Resulting equations in this random alloy model can be expressed directly in terms of the experimentally measurable tracer diffusion coefficients with no unknown vacancy jump frequencies appearing. Also these equations have the advantage of being in simple analytic form and not requiring numerical methods to evaluate the correlation factors. These two features make possible the direct expression of the temperature dependence of the correlation factor in terms of the experimental activation energies. Equations are found for AH/AQ in random binary cubic alloys, where AH is the difference between the activation enthalpies for diffusion of the two species and AQ is the difference between the experimentally measured activation energies of the two species. This ratio is never less than unity and can be much larger than unity. Values are plotted for diamond, bodycentered cubic and facecentered cubic structures. From the magnitude and composition dependence of AH/AQ, it is concluded that the temperature dependence of the correlation factor cannot by itself explain the difference between the activation energies measured from tracer diffusion and from internal friction in the nondilute range.   
Reference
 (Z. Naturforsch. 26a, 69—76 [1971]; received 6 October 1970)   
Published
 1971   
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 ZNA197126a0069    Volume
 26  
14  Author
 R. C. Brown, J. Worster, N. H. March, Sheffield, R. C. Perrin, R. Bullough  Requires cookie*   Title
 Isotope Effects in ClosePacked Metals and in Alkali Halides    Abstract
 An expression was obtained earlier by the authors, on the basis of Vineyard's rate theory, for the sharing of the kinetic energy of a diffusing isotope at the saddlepoint with other host atoms. The theory is expressed in terms of the (imaginary) frequency of the localised vibration in which the diffusing atom at the saddlepoint is coupled to its neighbours. Numerical results are presented for the case of a Cu isotope diffusing by the vacancy mechanism in a pure Cu lattice. The pair potential determined by Englert, Tompe and Bullough, which fits the phonon spectra and the stacking fault energy, has been employed in the calculation. The effects of coupling between the diffusing atom and its immediate neighbours are very small with this potential. The main coupling is found to be to the eight thirdnearest neighbours. Treating the vibrations of these nine atoms, a sharing of kinetic energy is found, which is in quantitative agreement with the experimentally observed isotope effect, assuming a vacancy mechanism for self diffusion. This situation for Cu is in marked contrast to Na, where it was shown in earlier work that the present theory could not explain the observed mass effect, assuming a vacancy mechanism for diffusion. The diffusion of Cs in the CsCl lattice is also discussed using the same theory. Following our earlier work on NaCl, the localized normal mode considered is that in which the Cs isotope at the saddlepoint is at the centre of a square with four Cl nearneighbour ions at the vertices. A formula for the sharing of kinetic energy is derived, and it is pointed out that, as for NaCl, the force con stants can be obtained from the classical approach of Mott and Littleton. An argument is proposed which suggests that, as with NaCl, the sharing of kinetic energy will be small. No experimental data appear as yet to be avaialable for the CsCl structure.   
Reference
 (Z. Naturforsch. 26a, 77 [1971]; received 6 October 1970)   
Published
 1971   
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 ZNA197126a0077    Volume
 26  
15  Author
 A. Lodding, A. Ott  Requires cookie*   Title
 Differential Diffusion of Impurities in Isotopic Lithium Matrices    Abstract
 The diffusion of 22Na and 195Au has been investigated in solid, isotopically pure 8Li and 7Li metal. The Na tracer has been found to diffuse by about 4 % faster in 8Li than in 7Li. For Au the corresponding difference was 4% at the melting point, but as much as about 15% at Tm (°K). A formalism is given for the interpretation of diffusion experiments where the matrix isotope mass is varied. The present results for Na in Li can be plausibly explained in terms of the vacancy mechanism. For Au diffusion in Li, the interpretation appears incompatible with a simple vacancy mechanism, and the anomalous departure from the inverse root mass relationship can be connected with recently detected quantum effects in ®Li —7Li mutual diffusion. I n tr o d u c tio n   
Reference
 (Z. Naturforsch. 26a, 81—84 [1971]; received 6 October 1970)   
Published
 1971   
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 ZNA197126a0081    Volume
 26  
16  Author
 IsotopicM. Ass, D. Ep, J.S M, An, R.M C  Requires cookie*   Title
 SelfDiffusion in Molten Lithium    Abstract
 The liquid state selfdiffusion coefficients of Li6 and Li7 in isotopically enriched Li6 and Li7 metal and in several isotopic alloys have been measured by the nuclear magnetic resonance spin echo, pulsed magnetic gradient technique. At the melting point 180.5 °C, the self diffusion co efficients are measured as Dm8= (6 . 8 + 0.7) *10—5 cm2/sec for Li® in 99% Li6, and Dm7 = (5 . 8 ± 0.6) 105 cm*/sec for Li7 in 99.9% Li7. The ratio of measured values (Dm6/D m7) = 1.18 ± 0.07, which is greater than the square root of the mass ratio, (m7/m6) lj't = 1.08. The isotopic ratio of self diffusion coefficients is observed to be less than the ratio of the mutual diffusion coefficients in almost pure Li6 and almost pure Li7, (ÖMm6/ÖMm7) = 1 .3 5 , and the viscosity ratio, (J?7/??6) = 1.44. The dependence of D upon isotopic alloy concentration appears to be relatively weak and linear in all but the very low concentrations. As a test of the experimental method, D was measured in liquid Na, H20 , and D20 . In liquid sodium at the melting point, D = (3.7 + 0.3) • 10—5 cm2/sec. The Na measurement and the values of D in water are about 5% below other published data, but they are in agreement within experimental uncertainties. Results of this experiment contain syste matic corrections amounting to 15 — 20% caused principally by the finite size of the droplets of the liquid metal samples. The corrections as well as the limitations of the technique in measurement of self diffusion coefficients in metals are discussed. 1. I n tr o d u c tio n   
Reference
 (Z. Naturforsch. 26a, 85—93 [1971]; received 6 October 1970)   
Published
 1971   
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 ZNA197126a0085    Volume
 26  
17  Author
 G. J. Krüger, W. MüllerWarmuth, A. Klemm  Requires cookie*   Title
 Seif Diffusion of Liquid 6Li and 7Li as Measured by Nuclear Magnetic Resonance    Abstract
 The selfdiffusion coefficients of liquid 6Li and 7Li have been measured using NMR spin echo techniques with pulsed gradients. In the experimental procedure, and in the sample preparation, particular attention has been paid to a relative, rather than to an absolute measurement. At 190 °C, the ratio of the selfdiffusion coefficients is found to be Z>6 (x6 = l) / D 7 (x7 = l) = 1 .0 9 ± 0 .0 6 , in agree ment with the square root of the mass ratio (mlme)1,t = 1.08. In an atomic mixture of 80% 6Li and 20% 7Li, D6 (x6 = 0 .8)/D 7 (r6 = 0.8) = 1 .0 3 ± 0 .0 8 has been obtained.   
Reference
 (Z. Naturforsch. 26a, 94 [1971]; received 15 October 1970)   
Published
 1971   
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 ZNA197126a0094    Volume
 26  
18  Author
 C.P F  Requires cookie*   Title
 Anharmonicity in Diffusion * *    Abstract
 It is emphasized that anharmonic effects are important in determining the parameters describing diffusion processes at elevated temperatures in crystals. The relevance of anharmonicity to the reaction rate and the dynamical theories of diffusion, and to models of defect formation and migra tion, is discussed. A comparison is made between the theoretical results and some collected experi mental data pertaiining mainly to ionic crystals. 1. I n tr o d u c tio n   
Reference
 (Z. Naturforsch. 26a, 99 [1971]; received 6 October 1970)   
Published
 1971   
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 ZNA197126a0099    Volume
 26  
20  Author
 O. R.  Requires cookie*   Title
 On the Computation of Lattice Green's Functions by Sine Series Expansions    Abstract
 In stitu te o f Physical Chem istry, Technical U n iversity o f N orway, Trondheim M ahanty has pointed ou t th a t by expanding the im aginary part o f a lattice Green's function in a sine series, direct numerical treatm ent o f the principal value integral which determines the real part o f a Green's function o f real argum ent can be circum vented. H ere M ahanty's result is extended to cover Green's functions o f purely im aginary argum ents. Also, alternative expressions which, in certain cases, sim plify numerical com putations are recorded. W hereas the aforem ention ed formulas are o f quite general valid ity, an included recurrence relation, which links defect induced changes in m om ents o f the frequency distribution w ith the Fourier coefficients, is re stricted to th e case o f a m ass defect in a diagonally cubic lattice. The prospects o f applying M ahanty's m ethod to m oderately com plex polyatom ic crystals are assessed on the basis o f com putations pertaining to alkaline earth fluorides. I t is found, through studying simple point de fects in CaF2, SrF2, and B a F 2, th a t b y truncating the sine series expansions when associated functionals assum e satisfactory values a t functions which are constants on th e set o f phonon frequencies, one obtains sets o f Fourier coefficients containing sufficient inform ation to cover a variety o f defect properties. A lso th e number o f Fourier coefficients is no larger than to preserve a chief merit o f the m ethod, nam ely th e provision o f a convenient w ay o f condensing and storing information. For the ty p e o f lattices considered M ahanty's w ay o f evaluating Fourier coefficients is found to be im practicable. H owever, upon supplem enting the sine series expansion m ethod by an adaptation o f G ilat's extrapolation procedure for frequency spectra, Brillouin zone integra tions involving rapidly varying functions becom e redundant.   
Reference
 (Z. Naturforsch. 26a, 111—123 [1971]; received 6 November 1970)   
Published
 1971   
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