Damped response of an axially excited rotating liquid bridge in zero-gravity

Summary The response of a solidly rotating finite liquid bridge due to axial excitation exhibits for frictionless liquid at the resonances singularities. For the experimenter in a spacelabmission the actual resonance amplitude is of quite some importance. For this reason damping, that has to be measured in ground tests, has been introduced into the results of the response.Notation a radius of the liquid bridge - h length of the liquid bridge - I ₀,I ₁ modified Besselfunctions - J ₀,J ₁ Besselfunctions - r, ,z polar coordinates - t time - excitation amplitude - elliptic case - hyperbolic case - abbreviation - damping factor of liquid - (z, t) free surface displacement - =² – ² surface tension - surface tension - liquid density - ₀ rotational speed of liquid bridge - forcing frequency of axial excitation - natural frequency of liquid bridge With 2 Figures     

On the torsional waves in an elastic bar with long-range cohesive forces

Summary With reference to some of the results obtained in [1], the equation of motion and the equations of nonlocal stress components in the form of Kroener-Eringen are transformed into the Fourier space. A lengthy calculation using a separable form of the nonlocal elastic moduli leads to the governing equation of the problem with two types of solutions. In each case the nonlocal phase velocity and, respectively, the nonlocal group velocity of the very short waves turn out to be by about 36% less than the velocities of their classical counterparts.Notation a atomic spacing - c ₂ classical speed of shear waves - c _2nonloc nonlocal speed of shear waves - c _a2nonloc,c _b2nonloc nonlocal speeds in rods - k wave number - r radius vector - R radius of the bar - v hoop displacement - Fourier transform ofv - V volume of the rod - z axial coordinate - delta sequence - , Lamé's constants - , nonlocal moduli - transform of - A wave length - * mass density - frequency     

Effect of cold rolling on the superconducting and electronic properties of two amorphous alloys; Nb50Zr35Si15 and Nb70Zr15Si15

The effect of cold rolling on the superconducting properties was examined for amorphous Nb₅₀Zr₃₅Si₁₅ and Nb₇₀Zr₁₅Si₁₅ superconductors. Cold rolling to 10 to 20% reduction in thickness results in a rise of superconducting transition temperature (T _c) and a decrease in transition width (T _c), upper critical field gradient near , critical current density [J _c(H)] and normal electrical resistivity (_n). Changes of about 7% forT _c 33% for T _c, 12% for and 70% forJ _c(H) are found. The rise ofT _c upon cold rolling was considered to originate from the increase in the electron-phonon coupling constant () due to an increase in the electronic density of states at the Fermi level [N(E _f)] and a decrease in the phonon frequency (), while the decreases in T_c,J _c(H) and _n were attributed to the decrease in fluxoid pinning force due to an increase in homogeneity in the amorphous structure. From the results described above, the following two conclusions were derived: (a) cold rolling causes changes in electronic and phonon-states in the quenched amorphous phase, and (b) deformation upon cold rolling occurs not only in the coarse deformation bands observable by optical microscopy, but also on a much finer scale comparable to the coherence length (7.7 nm).     

The Validity of Using the Microscopic Hyperbolic Heat Conduction Model Under a Harmonic Fluctuating Boundary Heating Source

The validity of using the microscopic hyperbolic heat conduction model under a harmonic fluctuating boundary heating source is investigated. It is found that using the microscopic hyperbolic heat conduction model is essential when . The phase shift between the electron-gas and solid-lattice temperatures is found to be . This phase shift reaches a fixed value of 1.5708 rad at very large values of . It is found that the use of the microscopic hyperbolic heat conduction model is essential when ¯>1×10⁹ rads^–1 for most metallic layers independent of their thickness.     

Die Entwicklung von Längswirbeln in zeitlich anwachsenden Grenzschichten an konkaven Wänden

Zusammenfassung Messungen des Anwachsens von Längswirbeln in zeitlich anwachsenden Grenzschichten an konkav gekrümmten Wänden (Görtler-Taylor-Wirbel) ergaben drei deutlich getrennte Bereiche: Es traten zunächst Wirbel mit der Wellenläge 0,9 auf (=Grenzschichtdicke, =Höhe einer Zelle, die zwei gegensinnig drehende Wirbel enthält). Je nach Größe der mit der Verdrängungsdicke ₁ der Grenzschicht gebildeten Reynolds-Zahl erschienen dann kurze Zeit später Wirbel mit 2,5, wenn war. Im Bereiche dagegen traten stattdessen bei den hier durchgeführten Versuchen immer Wirbel mit der Wellenlänge 6,5 auf. Bei werden die ersten Tollmien-Schlichting-Wellen mit der Wellenlänge _TS 6· angefacht. In ihren wandnahen Bereichen der Wellentäler könnten sich dann die oben genannten Längswirbel der Wellenlänge 6,5· ausbilden, die die zwei-in eine dreidimensionale Störung allseits gleicher Größenordnung verwandeln können.

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The development of longitudinal vortices in boundary layers growing with time along concave walls

Summary Measurements of the growth of longitudinal vortices in boundary layers growing with time along concave walls (Görtler-Taylor vortices) rendered three distinctly separated regions. First, vortices with a wave-length 0.9 appeared (-boundary layer thicness, =height of a cell containing two counterrotating vortices). Then, depending on the Reynolds number R _{a 1}/v ₁=displacement thickness), vortices with 2.5 appeared shortly afterwards, provided . In the region , however, the wave-length was 6.5. For the first Tollmien-Schlichting waves with _TS 6 were excited. In the wave-throughs close to the wall the abovementioned longitudinal vortices with wave length 6.5 may then be formed. This might transform the two-dimensional into a three-dimensional flow of equal order of magnitude in all directions.

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Zeichenerklärungen R _a Innenradius - Re _a Reynolds-Zahl gebildet mit dem InnenradiusR _a - Reynolds-Zahl gebildet mit der Verdrängungsdicke ₁ - kritische Taylor-Zahl - h Standhöhe der Flüssigkeit im Zylinder - t Zeit - z Anzahl - Steigungswinkel der Geraden - Grenzschichtdicke - ₁ Verdrängungsdicke - Wellenlänge (enthält ein gegensinnig rotierendes Längswirbelpaar) - v kinematische Zähigkeit - Winkelgeschwindigkeit Indizes K Knickpunkt der Geradensteigung - L unterhalb des Knickpunktes der Geradensteigung - TS Tollmien-Schlichting - e Einsatz der Wirbelentstehung     

Solidification and interfacial structure of in situ Al-4.5Cu/TiB2 composite

In situ particle reinforced Al-4.5Cu/TiB₂ composite was fabricated with TiO₂, H₃BO₃, Na₃AlF₆ powders and Al-4.5Cu alloy by reaction in melt. The composite can be directly casted into moulds to make composite parts. TiB₂ particles distribute uniformly in the matrix. The average size of TiB₂ particles is 0.93 m. At the atomic scale, TiB₂ is hexagonal, and exhibits hexagon or quadrilateral shape. The orientation relationships exist in the interfaces between TiB₂ particle and -Al, and between the reinforced small Al₂Cu phase and -Al in the composite. They are . TiB₂ particle is nucleation site for -Al matrix growth in the composite. The interface between TiB₂ particles and the matrix is clean and well bonded. No reaction product has been found through HREM observation. This is beneficial to the strength of the composite. The as-cast Al-4.5Cu/TiB₂ composite exhibits mechanical excellent properties: the tensile strength is 416.7 MPa, the yield strength is 316.9 MPa, and the elongation is 3.3 pct.     

Stresses in a cylindrical shell supported by a core of a different material

Summary The stress problem of a thin cylindrical shell supported by an elastic core of a different material and subjected to arbitrary loading on its curved surface is considered. The problem is solved by applying the three-dimensional theory of elasticity to the core and using membrane or bending solutions for the shell. Equilibrium and compatibility equations are satisfied at the junction of the shell and the core. It is pointed out that the procedure can easily be extended to the case of a hollow core with or without another shell of another material in it. Numerical results are presented to illustrate the effectiveness of even a weak core in reducing the shell stresses.

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Zusammenfassung Gegenstand der Untersuchung ist eine dünne Kreiszylinderschale, die durch einen elastischen Kern aus einem anderen Werkstoff gestützt ist und eine beliebige Belastung trägt. Die Lösung verbindet die strenge, dreidimensionale Theorie des zylindrischen Kerns mit der Membran- oder Biegetheorie der Schale. An der Grenze zwischen beiden Teilen müssen die Verschiebungen und gewisse Spannungskomponenten stetig übergehen. Es wird darauf hingewiesen, daß die Lösung leicht auf den Fall ausgedehnt werden kann, daß der Kern ein Hohlzylinder ist, der möglicherweise auf der Innenseite mit einer zweiten Zylinderschale verbunden ist. Zahlenergebnisse zeigen, daß selbst ein verhältnismäsig nachgiebiger Kern einen großen (und günstigen) Einfluß auf die Spannungen in der Schale ausübt.

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Principal Symbols a Radius of the middle surface of the shell - t Thickness of the shell - =1–t/2a - u _c,v _c,w _c Displacements respectively in the axial, circumferential and radial directions of a point in the core - X(x), (), (r/a) 3×3 square matrices - ,m Parameters - l Length of the cylinder - c A vector containing constantsc ₁,c ₂ andc ₃ - =r/a - =m+4(1–v _e) - E _c,v _e Elastic constants for the core material - Stresses at a point in the core - D _c - A vector containing _rx , _r and _r - (r/a) A 3×3 matrix - Displacements at the surfacer=a of the core - A vector containing - Amplitudes of displacements - A vector containing - =(x, ,a) - _ij Constants - A A square matrix containing constants _ij - Stress resultants in the shell as defined in reference [3] - p _x,p ,P _r Components of applied loading per unit area of shell's middle surface - () - ()· - u, v, w Displacements of a point on the middle surface of the shell - E _s,v _s Elastic constants for the shell material - D _s - K - k - p _xmn,p _mn,p _rmn Amplitudes of loadsp _x,p , p_r - u _mn, v_mn,w _mn Amplitudes of displacementsu, v, With 1 Figure     

Reference Viscosities of H<Subscript>2</Subscript>, CH<Subscript>4</Subscript>, Ar,and Xe at Low Densities

The zero-density viscosity of hydrogen, methane, and argon was determined in the temperature range from 200 to 400 K, with standard uncertainties of 0.084% for hydrogen and argon and 0.096% for methane. These uncertainties are dominated by the uncertainty of helium’s viscosity , which we estimate to be 0.080% from the difference between ab initio and measured values at 298.15 K. For xenon, measurements ranged between 200 and 300 K and the zero-density viscosity was determined with an uncertainty of 0.11%. The data imply that xenon’s viscosity virial coefficient is positive over this temperature range, in contrast with the predictions of corresponding-states models. Furthermore, the xenon data are inconsistent with Curtiss’ prediction that bound pairs cause an anomalous viscosity decrease at low reduced temperatures. At 298.15 K. the ratios , and were determined with a relative uncertainty of less than 0.024% by measuring the flow rate of these gases through a quartz capillary while simultaneously measuring the pressures at the ends of the capillary. Between 200 and 400 K, a two-capillary viscometer was used to determine with an uncertainty of 0.024% for H₂ and Ar, 0.053% for CH₄, and 0.077% for Xe. From was computed using the values of calculated ab initio. Finally, the thermal conductivity of Xe and Ar was computed from and values of the Prandtl number that were computed from interatomic potentials. These results may help to improve correlations for the transport properties of these gases and assist efforts to develop ab initio two- and three-body intermolecular potentials for these gases. Reference viscosities for seven gases at 100 kPa are provided for gas metering applications.     

Hydrogen reduction of Cu-Mn-Fe-O spinel solid solutions

The crystal-chemical transformations accompanying the hydrogen reduction of Cu_xMn₁ - xFe₂O₄ (x = 0.2, 0.5, 0.8) solid solutions are investigated, and general equations describing these processes over the entire composition range (0 x 1) are derived. The results on the character of the processes involved differ radically from earlier findings. The equilibrium oxygen pressure is evaluated for the low-oxygen phase boundary of the spinel solid solutions throughout their stability region. For solid solutions, which are of practical interest, the data are well represented by the equation , which is of importance in controlled synthesis of single-phase materials in this system.Translated from Neorganicheskie Materialy, Vol. 41, No. 3, 2005, pp. 332–338.Original Russian Text Copyright © 2005 by E. Zinovik, M. Zinovik.This revised version was published online in April 2005 with a corrected cover date.This revised version was published online in April 2005 with a corrected cover date.     

Turbidity Data of Weightless SF<Subscript>6</Subscript> Near its Liquid–Gas Critical Point

Light transmission measurements performed in SF₆ close to its liquid–gas critical point are used to obtain turbidity data in the reduced temperature range (T is temperature, T _c is the critical temperature). Automatic experiments (ALICE 2 facility) were made at a near critical density, i.e., , in the one-phase homogeneous region, under the microgravity environment of the Mir Space Station ( is the average density, ρ _c is the critical density). The turbidity data analysis verifies the theoretical crossover formulations for the isothermal compressibility and the correlation length ξ. These latter formulations are also used to analyze very near T _c thermal diffusivity data obtained under microgravity conditions by Wilkinson et al. (Phys. Rev. E 57 436, 1998).     

Decreasing of the initial shear modulus with increasing axial strain explained by means of a plastic-hypoelastic model

Summary The purpose of this work is to examine in detail the possibility to explain the decreasing of the initial shear modulus with increasing axial strain, observed first by Feigen, by means of the plastic-hypoelastic stress-strain relation suggested by Lehmann and by the author of the present paper.Notations _ij components of the infinitesimal strain tensor dilatation - strain deviator - _ij components of the stress tensor - spherical part of the stress tensor - stress deviator - ²= _{ij ij} second invariant of the stress deviator - = ₃₃ axial strain - e= ₁₃ shear component of the strain tensor - =2 ₁₃ shear strain - = ₃₃ axial stress - s= ₁₃ shear stress - T _ij components of Cauchy's stress tensor - F _ij components of the deformation gradient - L _ij components of the velocity gradient (Eulerian coordinates) - components of the rate of deformation tensor - components of the spin tensor - components of the rate of deformations deviator - components of Cauchy's stress deviator - T=T ₃₃ axial Cauchy's stress With 7 Figures     

Viscous response of an anchored spinning liquid column to various axial excitations

Summary For a solidly rotating viscous cylindrical liquid column of finite length the response to axial synchronous, counter- and one-sided excitation is determined for anchored contact lines at the disc-rim. For a rotating column additional responses of inertial waves (hyperbolic range) appear for < 2 ₀, while in the elliptic range < 2 ₀ the sloshing response occurs. The various responses for the free surface displacement have been numerically evaluated. Only in the one-sided exitation case all resonance peaks appear, while for synchronous excitation only the odd resonances and for counter-excitation only the even resonance peaks occur.Notation a radius of column - h length of liquid bridge - I _n modified Bessel function - p liquid pressure - r, ,z cylindrical polar coordinates - t time - u, v, w velocity distribution - Weber number - z ₀ excitation amplitude - liquid density - surface tension - surface tension parameter - Ohnesorge number - liquid surface displacement - kinematic viscosity - ₀ rotational speed - dimensionless rotational speed - forcing frequency - dimensionless forcing frequency - dimensionless forcing frequency for non-viscous liquid - a= root of bi-cubic Eq.(33) - root of bi-cubic Eq.(33)     

Stabilitätsuntersuchungen in einem 90°-Rechteck-Krümmer

Zusammenfassung Ein 90°-Krümmer mit rechteckigem Querschnitt wird von Wasser stationär durchströmt. Die Strömung am Krümmerangang ist bei Re _h =2,3·10⁴ noch laminar. Längs der konkaven und der konvexen Wand des Krümmers wird beobachtet, welche Veränderung die Strömung erfährt.An der konvexen Wand bleibt die laminare Struktur der Strömung erhalten. An der konkaven Wand dagegen treten nach einer Anlaufstrecke Goertler-Wirbel auf, deren Wellenlänge in Abhängigkeit einer Reynolds-Zahl ausgewertet wird. Weiter stromabwärts vergrößern sich bei zunächst geordneter Strömung die Wirbel, bis durch sie schließlich der laminare in den turbulenten Strömungszustand übergeführt wird.Mit einer optischen Meßmethode, dem Lichtschnittverfahren, wird an der konkaven Wand die Struktur der wandnahen Strömung (Goertler-Wirbel) verdeutlicht.

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Stability of flow through a 90° bend with rectangular cross-section

Summary Stationary flow of water through a 90° bend with rectangular cross-section is considered. At Re _h =2.3·10⁴ the flow at the entrance of the bend is still laminary. Observations on the change of the flow along the convex and concave wall of the bend are made.Laminary structure of the flow along the convex wall is preserved. Along the concave wall, however, Goertler-vortices appear whose wave-length is calculated as a function of the Reynolds number. Further downstream the vortices increase in a still ordered stream until they finally transform the laminary flow into, a turbulent one.Along the concave wall an optical method, confining illumination to a narrow sheet, is used to exhibit the structure of the flow close to the wall (Goertler-vortex).

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Bezeichnungen d Durchmesser - hydraulischer Durchmesser - F Querschnittsfläche - u Geschwindigkeit der Anströmung - U benetzter Umfang - Reynolds-Zahl für Rohrströmung und Kugelumströmung - Reynolds-Zahl für Kanalströmung - Grenzschichtdicke - Wellenlänge - kinematische Zähigkeit - Spaltbreite - Reynolds-Zahl für Strömung längs konkaver Wände (R ₁=Krümmungsradius) - Taylor-Zahl - modifizierte Taylor-Zahl (nachGoertler) Mit 14 Abbildungen     

Thermal expansion of molybdenum in the range 1500–2800 K by a transient interferometric technique

The linear thermal expansion of molybdenum has been measured in the temperature range 1500–2800 K by means of a transient (subsecond) interferometric technique. The molybdenum selected for these measurements was the Standard Reference Material SRM 781 (a high-temperature enthalpy and heat capacity standard). The results are expressed by the relation where T is in K and l ₀ is the specimen length at 20°C. The maximum error in the reported values of thermal expansion is estimated to be about 1% at 2000 K and not more than 2% at 2800 K.Paper presented at the Ninth Symposium on Thermophysical Properties, June 24–27, 1985, Boulder, Colorado, U.S.A.     

Nonlinear liquid oscillations in spherical systems under zero-gravity

Summary Nonlinear free oscillations of the interface of a concentric frictionless immiscible liquid system in a spherical container are investigated in a zero-gravity environment. The natural frequencies are determined for the axisymmetric and asymmetric oscillations of the interfacial surface with the diameter ratio and density ratio as parameters. It was found that for small outer- to inner liquid density ratio the oscillations exhibit softening, while for large density ratios it renders hardening oscillation. The asymmetric oscillations exhibit in the softening range softer and in the hardening range harder liquid oscillations. For a liquid layer around a rigid center sphere the oscillations of the free liquid surface yields softening behavior, where for thinner layers the softening effect is more pronounced.Nomenclature a radius of spherical container, or radius of rigid center sphere - b radius of undisturbed interfacial surface, or radius of undisturbed free liquid surface - k=a/b diameter ratio - pressure - pressure (dimensionless) - , , spherical coordinates - dimensionless radius - R _i main radii of curvaturei=1, 2 time - dimensionless time - v _i liquid velocity (j=1 spherical layer region,j=2 inner liquid sphere region) - V volume of the liquid - Y _nm tesseral surface harmonics - _i density of liquids - velocity potential - dimensionless velocity potential - interfacial surface- or free surface elevation - dimensionless interfacial surface- or free surface elevation - ₀ maximum elevation - circular frequency - circular frequency - _n0 axisymmetric natural frequency - _n1 asymmetric natural frequencym=1 - _nm ⁽⁰⁾ natural frequency of linearized liquid system - mean curvature - _nm Kronecker symbol With 10 Figures     

The laminar stagnation-point flow against a solidifying moving shell

Summary This paper considers the two-dimensional laminar stagnation-point flow due to a jet impinging onto a solidifying moving boundary. The flow is of interest in connection with the horizontal belt strip casting process. An exact solution to the Navier-Stokes equations is found that is shown to depend on a single ordinary differential equation. The solution is useful in the study of morphological and hydrodynamic instabilities within the impingement region. Solutions for the steady-state shape of the initial stages as well as the asymptotic behavior of the solidifying interface are also discussed in a perturbative manner.Nomenclature A suction velocity in boundary layer variables - a jet width [m] - c specific heat of the solid metal [J/m³K] - h Newtonian heat transfer coefficient [W/m²K] - k velocity gradient in units ofU/a - m dS ^*/dX ^* local inclination of the solidifying phase - S ^* (L)/L average slope of the solidifying phase - S ^* local thickness of the solidified phase [m] - S, S local thickness of the solidified phase in units ofL and , resp. - T absolute temperature [K] - T _f fusion temperature of metal [K] - T ₀ temperature of cooling water [K] - U jet velocity [m/s] - V belt velocity [m/s] - +i complex velocity potential in units ofUa - x coordinate tangential to the solidifying interface in units ofa - X ^* coordinate tangential to the belt [m] - X, X coordinates tangential to the belt in units ofL and , resp. - y coordinate orthogonal to the solidifying interface in units ofa - Y ^* coordinate orthogonal to the belt [m] - Y, Y coordinates orthogonal to the belt in units ofL and , resp. - z x+iy complex coordinates in units ofa - unit vector along the belt - unit vector orthogonal to the belt - local unit normal vector to the solidifying interface - h _f latent heat of fusion of metal [J/m³] - thermal diffusivity of solid metal [m²/s] - belt velocity in units ofU - { _n }, { _n } asymptotic sequences of the outer and inner expansion, resp. - m suction velocity outer variables - velocity potential in units ofUa - jet inclination relative to the local solidifying interface - coordinate orthogonal to the solidifying interface in units of - x c thermal conductivity of solid metal [W/mK] - displacement thickness in units of - v kimematic viscosity of liquid metal [m ²/s] - arctan (dS ^*/dX ^*) local angle of inclination of the solidifying interface - =(T–T ₀)/(T _f –T ₀) dimensionless temperature - perturbation parameter - coordinate tangential to the solidifying interface in units ofa/k - stream function in units ofUa - magnified stream function valid within the boundary layer - solidification constant Dimensionless parameter P _eL VS ^* (L)/ Peclet number - Q h/(cV) Heat flux number - R Ua/v Reynolds number - St Stefan number     

Frequency-Dependent Bulk Viscosity in One- And Two-Component Near-Critical Fluids

We assume isomorphism between near-critical fluids and Ising spin systems to calculate the critical anomaly of transport coefficients. As an example we present a very simple and general expression for the frequency-dependent bulk viscosity *() in one- and two-component fluids near the critical point. It reads is a universal complex function, c is the zero-frequency sound velocity, c _c is its critical value, and is the order parameter relaxation rate. We also examine macroscopic adiabatic relaxations of pressure, temperature, and density after stepwise changes of pressure or density. Such measurements give information on the time correlation function of the diagonal part of the stress, which relaxes anomalously slowly near the critical point.     

Angular dependence of the critical magnetic field in granular superconducting films

The critical magnetic fieldH _c () of granular Al films has been measured as a function of the angle between the field direction and the plane of the film at temperatures nearT _c0 .The film thicknessd is smaller than the temperature-dependent coherence length (T), the bulk electron mean free path1 is smaller than the BCS coherence length ₀, and 1 d. The experimental data onH _c () are well fitted by the Tinkham formula. However, the observed values ofH _c/H _care not always consistent with and increase with1/d. This fact suggests that the boundary scattering of electrons at the film surface enhancesH _c () and that the enhancement ofH _cis larger than that ofH _c.On leave from Department of Physics, Faculty of Science, Kyushu University, Fukuoka, Japan.     

Die Herleitung von Schalengleichungen über ein erweitertes Variationsprinzip bei Berücksichtigung der Querschubverzerrungen

Ohne ZusammenfassungBezeichnungen L Bezugsgrößen für dimensionslose Koordinaten - L charakteristische Schalenabmessung - t Schalendicke - Schalenparameter - körperfeste, krummlinige, dimensionslose Koordinaten der Schalenmittelfläche - Dimensionslose Koordinate in Richtung der Schalennormalen - i, j,...=1,2,3 Indizierung des dreidimensionalen Euklidischen Raumes - ,,...=1,2 Indizierung des zweidimensionalen Riemannschen Raumes - (...), Partielle Differentiation nach der Koordinate - (...), Kovariante Differentiation für Tensorkomponenten des zweidimensionalen Raumes nach der Koordinate - (...)| Kovariante Differentiation für Tensorkomponenten des dreidimensionalen Raumes nach der Koordinate - Variationssymbol - a ,a ₃ Basisvektoren der Schalenmittelfläche - V Verschiebungsvektor - U ,U ₃ Verschiebungskomponenten des Schalenraumes - v ,w,w ,W Verschiebungskomponenten der Schalenmittelfläche - Verhältnis der Metriktensoren des Schalenraumes und der Schalenmittelfläche - _ik Verzerrungstensor des Raumes - _{(, )}, Symmetrische Verzerrungstensoren der Schalenmittelfläche - _{[, ]} Antimetrischer Term des Verzerrungsmaßes - ^, Spannungstensor - n ,m ,q Tensorkomponenten der Schnittgrößenvektoren - p ,p,c Tensorielle Lastkomponenten     

Thermodynamic properties of iron doped beta″-alumina by e.m.f. measurements with beta-alumina electrolytes

Thermodynamic studies of the non-stoichiometric iron doped beta-alumina (ID) phase were carried out by electrochemical measurements coupled with coulometric titration using the cell Na_liq/Li-alumina/ID. Hot pressing and glass sealing techniques were developed and employed to obtain a suitable and stable Li-alumina/ID interface. The equilibrium e.m.f. of the cell was determined as a function of sodium concentration over the temperature range 444 to 523 K. The range of sodium concentrations over which the ID phase is stable was also determined. The relative partial molar thermodynamic quantities of sodium, , , and in ID alumina as a function of sodium concentration were obtained from cell e.m.f. data.