Frictional forces and resistance to the beginning of plastic deformation in Cu-Al solid solutions

Extension curves have been obtained for Cu-Al solid solutions in the microdeformation range 10^–6-10^–3. It is shown that the dependence of the resistance to microdeformation on the degree of this deformation is described by = ₀ ⁰ + A^1/2, where ₀ ⁰ is the resistance to the beginning of plastic deformation, and A = const. The stresses _F due to frictional forces are determined from the unloading curves. The dependences of ₀ ⁰ and _F on the Al concentration c in the alloy are studied. The ₀ ⁰ = f(c) and F = (c) dependences are analyzed in the light of current ideas regarding the nature of impurity strengthening. The grain size is shown to affect the resistance to microdeformation in Cu-Al alloys.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, Vol. 12, No. 5, pp. 94–103, May, 1969.     

Contribution of quantum corrections and superconducting fluctuations to the magnetic field and temperature dependence of the conductivity in amorphous CuTi and CuZr alloys

We report conductivity measurements on Cu _x Ti_100–x and Cu _x Zr_100–x glasses as a function of magnetic field (0B6T) and temperature (1.5–5. At low temperatures the measured conductivity(T,B)= ₀+(T)+(B,T) is compared quantitatively with the predictions of diagrammatic perturbation theories including quantum interference effects, spin-orbit scattering and electron-electron interaction. We obtain a set of characteristic fields for inelastic and spin orbit scattering from both the magnetic field and the temperature dependence of the measured (T, B). Below about 4K the Coulomb interaction determines (T) in consistence with the Hall effect, whereas quantum interference processes and spin-orbit scattering dominate the magnetic field dependence. In case of Cu _x Zr_100–x , (B, T) can be explained by taking into account superconducting fluctuations (Maki-Thompson and Aslamasov-Larkin parts) in addition. Superconducting fluctuations dominate the temperature dependence as well. For high magnetic fields and lower temperatures (B/T>1T/K) we find discrepancies between experiment and calculations from perturbation theory.     

Observation of variable range hopping at “natural” phonon frequencies

Hill's analysis of hopping conductivity data has been applied to ion-bombarded amorphous-silicon samples. The apparent hopping conductivity parameters derived from a standardT ^–0.25 plot undergo changes by several orders of magnitude when plotted with the exact scaling of the abscissa. A typical example is characterized by a temperature dependence ofdc conductivity according to= ₀ exp (—(T ₀/T) ^m ), withm=0.45,T ₀ =6.410⁴K and ₀=6.610^{1 –1} cm^–1. From ₀ a phonon frequency of about 3–1510¹² s^–1 is derived.     

The metal-semiconductor transition in amorphous Si1−x Cr x films:T 0.19-contribution to the metallic conductivity

A detailed phenomenological re-analysis of previously published conductivity data, (T, x), is presented. It is based on the investigation of differences, (T, x ₁)–(T, x ₂). In this way, the cusp-like low-temperature term is amplified against the other temperature dependent contributions. This term can be described by wherep=0.19±0.03. It is present, if (4.2 K,x) exceeds 260 ^–1 cm^–1, at least up to (4.2 K,x)1350 ^–1 cm^–1 and forT60 K. But it is absent, if (4.2 K,x)180 ^–1 cm^–1. The disappearance of this contribution should be related to the metal-semiconductor transition, taking place atx _c 0.14. On the other hand, the presence of a term proportional toT ^1/2, as predicted by Altshuler and Aronov, seems unlikely.It is argued that the term should be related to the interplay of electron-electron interaction and disorder. The comparison with data from the literature shows that this contribution might also be present in heavily doped crystalline semiconductors.     

Unified fields of analytic space-time-energy

An analytic gravitational fieldZ (Z ^y ) is shown to include electromagnetic phenomena. In an almost flat and almost static complex geometryds ² =zdzdz of four complex variables z=t, x, y, x the field equationsR Rz = –(U U – Z ) imply the conventional equations of motion and the conventional electromagnetic field equations to first order if =(Z ^v) and =(z ) are expressed in terms of the conventional mass density function , the conventional charge density function , and a pressurep as follows: v=const=p/c ²–10^–29 gm/cm³.     

Vacuum Einstein spaces with axial symmetry

Four classes of solutions are found to the equations R=–2_{; ;} and g _;=0 in three-dimensional space with metric gdxdx and signature (+ ––), equivalent to the Einstein equations R_ij=0 in a vacuum for the metric . The metric ds² assumes axial symmetry and symmetry with respect to the reflection .Translated from Izvestiya Uchebnykh Zavedenii, Fizika, No. 9, pp. 43–45, September, 1976.     

Insensitivity of Quantized Hall Conductance to Disorder and Interactions

A two-dimensional quantum Hall system is studied for a wide class of potentials including single-body random potentials and repulsive electron–electron interactions. We assume that there exists a nonzero excitation gap above the ground state(s), and then the conductance is derived from the linear perturbation theory with a sufficiently weak electric field. Under these two assumptions, we prove that the Hall conductance _xy and the diagonal conductance _yy satisfy | _xy+e ² /h|const·L ^–1/2 and | _yy|const·L ^–1/12. Here e ²/h is the universal conductance with the charge –e of the electron and the Planck constant h; is the filling factor of the Landau level; and L is the linear dimension of the system. In the thermodynamic limit, our results show _xy=–e ² /h and _yy=0. The former implies that integral and fractional filling factors with a gap lead to, respectively, integral and fractional quantizations of the Hall conductance.     

Resistance to dislocation motion in copper-based solid solutions with a statistically disordered atomic distribution

The stress _F due to friction forces in copper-based solid solutions was determined. Under the conditions of the procedure used to measure _F, on the basis of the half-wave hysteresis with polycrystalline samples, the value of d: _F = _F0 + K_Fd^–(1/2) where _F0 is the resistance to dislocation motion in an alloy having an infinite grain size, and K_F is a constant. It is shown that _F0 is governed by the interaction of moving dislocations with impurity atoms in the case of a statistically disordered atomic distribution. A study was made of the effects of various factors on _F and of the nature of the changes in _F0 caused by alloying.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No.3, pp. 18–23, March, 1971.     

Interchangeability and bounds on the effective conductivity of the square lattice

The effective conductivity ^* of an infinitely interchangeable two-component random medium is considered. This class of media includes cell materials in the continuum and the bond lattice on ^d , where the cells or bonds are randomly assigned the conductivities ₁ and ₂ ( ₁, ₂ne0) with probabilitiesp ₁ andp ₂=1–p ₁. A rigorous basis for the very old and widely used low volume fraction expansion of ^* is established, by proving that ^* is an analytic function ofp ₂ in a suitable domain containing [0, 1]. In the case of the bond lattice ind=2, rigorous fourth-order upper and lower bounds on ^* valid for allp ₂, ₁, and ₂ are derived. The four perturbation coefficients entering into the bounds are obtained from the first-order volume fraction coefficient using the method of infinite interchangeability.     

The effect of grain size on the deformation resistance of nickel

The effect of the grain sizel of commerical nickel on the lower yield point, _y, and flow stress, _f , has been investigated. From the relationship between _y andl ^–1/2 and between _f andl ^–1/2, and also by extrapolation, the parameters ₁( _i ^f ) and k_y(kf), which occur in Petch's well-known expression, were determined. It was found that the values of these parameters depend on the previous history of the samples. It is suggested that the more marked dependence of the deformation resistance of nickel on grain size arising from certain thermal treatments is due to the segregation of impurities to the grain boundaries. It is shown that this is in accord with the presence of grain-boundary hardening and with its dependence on quenching temperature.     

Correlation inequalities for the truncated two-point function of an Ising ferromagnet

We establish the following new correlation inequalities for the truncated twopoint function of an Ising ferromagnet in a positive external field: _j ; _l ^T _j ; _k ^T _k ; _l ^T , and _j ; _l ^T _{k K j} ; _k ^T _{k l} , whereK is any set of sites which separatesj froml. The inequalities are also valid for the pure phases with zero magnetic field at all temperatures. Above the critical temperature they reduce to known inequalities of Griffiths and Simon, respectively.NSERC Postgraduate Fellow, 1978–1981. Research supported in part by NSF Grant No. PHY-78-25390-A02.     

Unitarity equations and structure of theS-matrix at them-particle threshold in a theory with purem→m interaction

The structure of theS-matrix at them-partical thresholds=(m)² of amm process (m2) inv-dimensional space-time is determined in a theory with a simplified unitarity equation corresponding to a puremm interaction. If (m–1)(v–1) is odd, a two-sheeted, square-root type structure is obtained as in the usual case of two-particle thresholds in dimension 4. The nature of the singularity is more complicated if (m–1)(v–1) is even (e.g.m=3 in dimension 4). Results obtained in this case include an orthogonal decomposition of the scattering functionT with nonholomic eigenvalues of the form [1/2iln+b _i ()]^–1 [where =(m)²–s andb _i is uniform around =0] and a related infinite expansion ofT in powers of ln involving an on-shell irreducible kernelU which is the analogue for (m–1)(v–1) even of Zimmerman'sK-matrix.     

Pauli-Dirac matrix generators of Clifford Algebras

This article presents a Pauli-Dirac matrix approach to Clifford Algebras. It is shown that the algebra C₂ is generated by two Pauli matrices i₂ and i₃; C₃ is generated by the three Pauli matrices ₁, ₂, ₃; C₄ is generated by four Dirac matrices ₀, ₁, ₂, ₃ and C₅ is generated by five Dirac matrices i₀, i₁, i₂, i₃, i₅. The higher dimensional anticommuting matrices which generate arbitrarily high order Clifford algebras are given in closed form. The results obtained with this Clifford algebra approach are compared with the vector product method which was described in a recent article [Found. Phys. 10, 531–553 (1980) by Poole, Farach and Aharonov] and with the Dirac, Rashevskii and Ramakrishnan methods of matrix generation.Supported by the National Science Foundation under Grant ISP-80-11451.     

Ferromagnetic resonance and magnetic crystallographic anisotropy of monocrystalline lithium ferrite films

The crystallographic anisotropy constant K₁ of monociystalline lithium ferrite films was measured by the methods of ferromagnetic resonance and rotational moments. The presence of uniaxial anisotropy in the plane of a film with the constant K_u 10₃ erg · cm^–3 is established experimentally. The nature of the uniaxial anisotropy is explained by the anisotropy of the stresses in the plane of the film, a formula is obtained to compute the angle of deflection of the easy magnetization axis from the crystallographic direction. An estimate is made of the difference in the stresses along the axes (_x–_z) 10¹⁰ dyne · cm^–2.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, Vol. 16, No. 9, pp. 86–89, September, 1973.     

An algebraic approach to quantum field theory and commutation relations for energy momentum in the framework of general relativity

We present a consistent set of commutation relations (C.R.) for a quantum system immersed in a classical gravitational field. The gravity field is described by metric tensorg _ik (x) andg ₀₀(x) with coordinate gaugeg _i0=0. The Hamiltonian of the system is found to be a linear function of [–g ₀₀(x)]^1/2. Its properties we define by C.R. avoiding explicit expression in terms of fields, as well as its splitting into free and interaction parts. In this way a consistent set of C.R., which are equally simple for a flat and curvilinear space, can be established. To stress the main idea of our approach, we consider the simple but still nontrivial example of a scalar electrodynamics immersed in a gravity field. The electromagnetic current operator we define by its C.R. and not explicitly. An interesting feature of this approach is that the Poisson equation follows from the consistency of the C.R. The C.R. for the energy and momentum operators of the system in a gravity field are established which generalize the usual Poincare group generators C.R. For example, we find (i/hc ²)[H _(x) ,H _(x) ]=P _– , whereH _(x) is the Hamiltonian of the system, which is a linear functional of (x)[–g ₀₀(x)]^1/2 andP _s(x) represents the momentum-density operator [averaged with the classical functions(x)].     

On the equivalence of boundary conditions

We show that ifb andb are two boundary conditions (b.c.) for general spin systems on ^d such that the difference in the energies of a spin configuration in ^d is uniformly bounded, |H _,b ()–H _,b()|C < , then any infinite-volume Gibbs states and obtained with these b.c. have the same measure-zero sets. This implies that the decompositions of and into extremal Gibbs states are equivalent (mutually absolutely continuous). In particular, if is extremal,=. Application of this observation yields in an easy way (among other things) (a) the uniqueness of the Gibbs states for one-dimensional systems with forces that are not too long-range; (b) the fact that various b.c. that are natural candidates for producing non-translation-invariant Gibbs states cannot lead to such an extremal Gibbs state in two dimensions.Supported in part by NSF Grant PHY 78–15920 and by the Swiss National Foundation For Scientific Research.     

An investigation of finite-size scaling for systems with long-range interaction: The spherical model

A method is suggested for the derivation of finite-size corrections in the thermodynamic functions of systems with pair interaction potential decaying at large distancesr asr ^{–d –} , whered is the space dimensionality and>0. It allows for a unified treatment of short-range (=2) and long-range (<2) interaction. The asymptotic analysis is illustrated by the mean spherical model of general geometryL ^d–d× ^d subject to periodic boundary conditions. The Fisher-Privman equation of state is generalized to arbitrary real values ofd, 0d. It is shown that the-expansion may be used to study the breakdown of standard finite-size scaling at the borderline dimensionalities.     

Random walks on cubic lattices with bond disorder

We consider diffusive systems with static disorder, such as Lorentz gases, lattice percolation, ants in a labyrinth, termite problems, random resistor networks, etc. In the case of diluted randomness we can apply the methods of kinetic theory to obtain systematic expansions of dc and ac transport properties in powers of the impurity concentrationc. The method is applied to a hopping model on ad-dimensional cubic lattice having two types of bonds with conductivity and ₀=1, with concentrationsc and 1–c, respectively. For the square lattice we explicitly calculate the diffusion coefficientD(c,) as a function ofc, to O(c²) terms included for different ratios of the bond conductivity. The probability of return at long times is given byP ₀(t) [4D(c,)t]^–d/2, which is determined by the diffusion coefficient of the disordered system.     

Energetical structure of muonic molecular ions ddµ and dtµ

The long-lived states lying below then=2 threshold in muonic molecular ions ddµ and dtµ are reviewed. We have considered all the known long-lived states both of normal and anomalous spatial parity, the bound states as well as resonant three-body states of shape and Feshbach types. It is shown that these states could be satisfactorily classified in terms of the Born-Oppenheimer adiabatic theory. We calculate some characteristic properties of the Feshbach resonances, thus obtaining that the life-time of the 3d states is greater than 10^–11 s, and the fusion rate from these states less than 10⁹ s^–1. The geometry of the 4f(J=0,v=0) state shows that it does not obey approximate ungerade symmetry. On the contrary, the low vibrational 3d states are approximately of gerade symmetry, as a result these states decay ejecting dµ atoms in the same proportion as tµ atoms.     

Exact expressions for row correlation functions in the isotropicd=2 ising model

We present exact explicit expressions for the row spin-spin correlation functions _{00 n}0 in the isotropicd= 2 Ising model, in terms of elliptic integrals, forn 5. We also give a general structural formula for _{00 n}0.