DOCSLIB.ORG

Physical Origins of Anelasticity and Attenuation in Rock I

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Physical Origins of Anelasticity and Attenuation in Rock I 2.17 Properties of Rocks and Minerals – Physical Origins of Anelasticity and Attenuation in Rock I. Jackson, Australian National University, Canberra, ACT, Australia ª 2007 Elsevier B.V. All rights reserved. 2.17.1 Introduction 496 2.17.2 Theoretical Background 496 2.17.2.1 Phenomenological Description of Viscoelasticity 496 2.17.2.2 Intragranular Processes of Viscoelastic Relaxation 499 2.17.2.2.1 Stress-induced rearrangement of point defects 499 2.17.2.2.2 Stress-induced motion of dislocations 500 2.17.2.3 Intergranular Relaxation Processes 505 2.17.2.3.1 Effects of elastic and thermoelastic heterogeneity in polycrystals and composites 505 2.17.2.3.2 Grain-boundary sliding 506 2.17.2.4 Relaxation Mechanisms Associated with Phase Transformations 508 2.17.2.4.1 Stress-induced variation of the proportions of coexisting phases 508 2.17.2.4.2 Stress-induced migration of transformational twin boundaries 509 2.17.2.5 Anelastic Relaxation Associated with Stress-Induced Fluid Flow 509 2.17.3 Insights from Laboratory Studies of Geological Materials 512 2.17.3.1 Dislocation Relaxation 512 2.17.3.1.1 Linearity and recoverability 512 2.17.3.1.2 Laboratory measurements on single crystals and coarse-grained rocks 512 2.17.3.2 Stress-Induced Migration of Transformational Twin Boundaries in Ferroelastic Perovskites 513 2.17.3.3 Grain-Boundary Relaxation Processes 513 2.17.3.3.1 Grain-boundary migration in b.c.c. and f.c.c. Fe? 513 2.17.3.3.2 Grain-boundary sliding 514 2.17.3.4 Viscoelastic Relaxation in Cracked and Water-Saturated Crystalline Rocks 516 2.17.4 Geophysical Implications 517 2.17.4.1 Dislocation Relaxation 517 2.17.4.1.1 Vibrating string model 517 2.17.4.1.2 Kink model 518 2.17.4.2 Grain-Boundary Processes 519 2.17.4.3 The Role of Water in Seismic Wave Dispersion and Attenuation 519 2.17.4.4 Bulk Attenuation in the Earth’s Mantle 520 2.17.4.5 Migration of Transformational Twin Boundaries as a Relaxation Mechanism in the Lower Mantle? 520 2.17.4.6 Solid-State Viscoelastic Relaxation in the Earth’s Inner Core 521 2.17.5 Summary and Outlook 521 References 522 Nomenclature d grain size; characteristic separation of a spacing between adjacent Peierls vacancy sources valleys f frequency; the reciprocal of du/dx ¼ ad period of kink potential measured tan (Figure 4(c)) parallel to dislocation line g dimensionless multiplier of Tm/T in b Burgers vector exponent for thermal activation of relaxation time 493 494 Physical Origins of Anelasticity and Attenuation in Rock h separation of closely spaced disloca- EP activation energy describing position tions in subgrain wall (period) of dissipation peak hj jth coefficient in Fourier series repre- Eup binding energy of dislocation to pin- senting grain-boundary topography ning point k Boltzmann constant G shear modulus ml effective mass per unit length of Gm free energy of kink migration dislocation GHS mean of the Hashin–Shtrikmann n exponent in term tn representing bounds on the shear modulus of a transient creep in the Andrade model polycrystalline aggregate p internal variable providing link between GR relaxed value of shear modulus (ane- stress and anelastic strain lastic relaxation only) pL(L) distribution of dislocation segment GRS Reuss average of single-crystal elastic lengths constants for shear ps small fluctuation in pressure P GU unrelaxed shear modulus p0 stress-dependent equilibrium value Hint kink interaction energy s Laplace transform variable; distance Hk formation energy for a single geome- measured along dislocation line; trical kink exponent describing grain-size sensi- Hkp kink-pair formation energy À1 tivity of Q Hm enthalpy of kink migration t time Hmc activation enthalpy for multicomponent u displacement of dislocation segment, diffusion or position of grain boundary, in J(t) creep function à y-direction J1 real part of J à u0 x-independent amplitude of u; position J2 negative imaginary part of J of straight dislocation segment under JU unrelaxed compliance ("/) static stress Jà dynamic compliance um maximum displacement for newly Kf bulk modulus of fluid formed kink pair Km bulk modulus of melt wk width of a single geometrical kink Ks bulk modulus of solid matrix x coordinate measuring distance parallel K bulk modulus of composite of coexist- to dislocation line or grain boundary ing phases x1 unstable equilibrium spacing of kinks L length of dislocation segment between of opposite sign adjacent pinning points y coordinate measuring distance per- Lc critical dislocation segment length for pendicular to dislocation line dislocation multiplication A measure of anisotropy or inter-phase L subgrain diameter variability in elastic moduli or thermal N number of terms retained in Fourier expansivity involved in thermoelastic series representing grain-boundary relaxation strength topography B dislocation drag coefficient Nv number of dislocation segments of COH concentration of hydroxyl ions given length L per unit volume D diffusivity (either of matter or heat) P of internal variable p D() normalised distribution of anelastic QÀ1 inverse quality factor (¼ tan), a mea- relaxation times sure of strain energy dissipation À1 Db grain-boundary diffusivity QD height of the Debye dissipation peak of Dk kink diffusivity the standard anelastic solid Dmc multicomponent diffusivity R radius of curvature of dislocation E activation energy for relaxation time bowed out under applied stress; Ed elastic strain energy per unit length of gas constant; radius of grain-edge dislocation or line tension tubule Physical Origins of Anelasticity and Attenuation in Rock 495 Sm entropy of kink migration Poisson’s ratio T absolute temperature k0 attempt frequency of dislocation Tm melting temperature vibration To oscillation period (¼ 2/!) crystal density À þ U equilibrium distance for grain-bound- k , k densities of kinks of opposite sign ary sliding (number per unit length of dislocation U(u) Peierls potential line) À þ X chemical composition k0 , k0 as above, under conditions of zero Y Youngs modulus stress eq negative of exponent describing fre- k equilibrium kink density: number of quency dependence of QÀ1 kinks per unit length of dislocation line b aspect ratio of grain-boundary region stress, usually shear stress (¼ /d) n normal stress e aspect ratio (minimum/maximum P Peierls stress dimension) of ellipsoidal inclusion t tectonic shear stress t aspect ratio of grain-edge tubule up unpinning shear stress (¼ 2R/d) 0 amplitude of sinusoidally time-varying coefficient of term tn representing stress transient creep in the Andrade model relaxation time multiplicative constant of order unity A anelastic relaxation time s multiplicative constant d duration of transient diffusional creep phase lag between stress and strain; dr timescale for draining of cylindrical width of grain-boundary region (<<d) laboratory specimen G anelastic relaxation of the shear e relaxation time for elastically accom- modulus modated grain-boundary sliding J anelastic relaxation of the compliance M Maxwell (viscous) relaxation time P width in pressure of binary loop s,t relaxation time for melt squirt between T0 width of melting interval grain-edge tubules Ts pressure-induced perturbation to soli- s,e relaxation time for melt squirt between dus and liquidus temperatures ellipsoidal inclusions pressure-induced perturbation in melt melt fraction; the angle betweeen a fraction dislocation segment and its Peierls " strain valley "a anelastic strain ! angular frequency "e elastic strain !0 (angular) resonance frequency of dis- "m maximum anelastic strain due to location segment migration of geometrical kinks on a À Gamma function dislocation segment Á anelastic relaxation strength "0 amplitude of sinusoidally time-varying à dislocation density, that is, dislocation strain length per unit volume ¼ NvL viscosity or effective viscosity Ãm density of mobile dislocations 1 viscosity of dashpot in parallel with molecular volume of diffusing species spring in the anelastic element of the (/)0 fractional density contrast between Burgers model coexisting polymorphs b grain-boundary viscosity (/)a fractional change in density resulting f fluid viscosity from small change in proportions of m melt viscosity coexisting phases; anelastic volu- wavelength of periodic grain-boundary metric strain topography or of seismic wave (/)e fractional change in density caused by k kink mobility (¼ Dk/kT) pressure ps 496 Physical Origins of Anelasticity and Attenuation in Rock 2.17.1 Introduction Departures from elastic behavior have long been studied in metals. Notable early successes came from The Earth and its constituent materials are subjected the application of resonance (pendulum) methods at to naturally applied stresses that vary widely in inten- fixed frequencies near 1 Hz that revealed low- sity and timescale. At sufficiently high temperatures, temperature dissipation peaks attributable to various nonelastic behavior will be encountered – even at the types of point-defect relaxation (e.g., Zener, 1952; low stress amplitudes of seismic wave propagation, Nowick and Berry, 1972). Until recently most of the tidal forcing, and glacial loading (Figure 1). For har- available information concerning elastic wave speeds in monic loading, nonelastic behavior is manifest in a geological materials and their variations with pressure phase lag between stress and strain giving rise to strain and temperature came from ultrasonic and opto-acous- energy dissipation and associated frequency depen- tic techniques at frequencies at least six orders of dence (dispersion) of the relevant modulus or wave magnitude higher than those of teleseismic waves speed. In the case of glacial loading, the transient creep (Figure 1). However, there is growing recognition of of mantle material of sufficiently low viscosity allows the need for a thorough understanding of viscoelastic time-dependent relaxation of the stresses imposed by behavior in minerals and rocks at low strains and seis- the growth and decay of ice sheets with consequent mic frequencies.
Load more

Recommended publications
  • Stress Relaxation of Glass Using a Parallel Plate Viscometer Guy-Marie Vallet Clemson University, [email protected]
    Clemson University TigerPrints All Theses Theses 8-2011 Stress relaxation of glass using a parallel plate viscometer Guy-marie Vallet Clemson University, [email protected] Follow this and additional works at: https://tigerprints.clemson.edu/all_theses Part of the Materials Science and Engineering Commons Recommended Citation Vallet, Guy-marie, "Stress relaxation of glass using a parallel plate viscometer" (2011). All Theses. 1158. https://tigerprints.clemson.edu/all_theses/1158 This Thesis is brought to you for free and open access by the Theses at TigerPrints. It has been accepted for inclusion in All Theses by an authorized administrator of TigerPrints. For more information, please contact [email protected]. TITLE PAGE STRESS RELAXATION OF GLASS USING A PARALLEL PLATE VISCOMETER A Thesis Presented to The Graduate School of Clemson University In Partial Fulfillment of the Requirements for the Degree of Master of Science Materials Science and Engineering By Guy-Marie Vallet August 2011 Accepted by: Dr. Vincent Blouin, Committee Chair Dr. Jean-Louis Bobet Dr. Evelyne Fargin Dr. Paul Joseph Dr. Véronique Jubera Dr. Igor Luzinov Dr. Kathleen Richardson ABSTRACT Currently, grinding and polishing is the traditional method for manufacturing optical glass lenses. However, for a few years now, precision glass molding has gained importance for its flexibility in manufacturing aspheric lenses. With this new method, glass viscoelasticity and more specifically stress relaxation are important phenomena in the glass transition region to control the molding process and to predict the final lens shape. The goal of this research is to extract stress relaxation parameters in shear of Pyrex® glass by using a Parallel Plate Viscometer (PPV).
    [Show full text]
  • 1 Revision 1 Single-Crystal Elastic Properties of Minerals and Related
    Revision 1 Single-Crystal Elastic Properties of Minerals and Related Materials with Cubic Symmetry Thomas S. Duffy Department of Geosciences Princeton University Abstract The single-crystal elastic moduli of minerals and related materials with cubic symmetry have been collected and evaluated. The compiled dataset covers measurements made over an approximately seventy year period and consists of 206 compositions. More than 80% of the database is comprised of silicates, oxides, and halides, and approximately 90% of the entries correspond to one of six crystal structures (garnet, rocksalt, spinel, perovskite, sphalerite, and fluorite). Primary data recorded are the composition of each material, its crystal structure, density, and the three independent nonzero adiabatic elastic moduli (C11, C12, and C44). From these, a variety of additional elastic and acoustic properties are calculated and compiled, including polycrystalline aggregate elastic properties, sound velocities, and anisotropy factors. The database is used to evaluate trends in cubic mineral elasticity through consideration of normalized elastic moduli (Blackman diagrams) and the Cauchy pressure. The elastic anisotropy and auxetic behavior of these materials are also examined. Compilations of single-crystal elastic moduli provide a useful tool for investigation structure-property relationships of minerals. 1 Introduction The elastic moduli are among the most fundamental and important properties of minerals (Anderson et al. 1968). They are central to understanding mechanical behavior and have applications across many disciplines of the geosciences. They control the stress-strain relationship under elastic loading and are relevant to understanding strength, hardness, brittle/ductile behavior, damage tolerance, and mechanical stability. Elastic moduli govern the propagation of elastic waves and hence are essential to the interpretation of seismic data, including seismic anisotropy in the crust and mantle (Bass et al.
    [Show full text]
  • Entropy Principle and Recent Results in Non-Equilibrium Theories
    Entropy 2014, 16, 1756-1807; doi:10.3390/e16031756 OPEN ACCESS entropy ISSN 1099-4300 www.mdpi.com/journal/entropy Article Entropy Principle and Recent Results in Non-Equilibrium Theories Vito Antonio Cimmelli 1;*, David Jou 2, Tommaso Ruggeri 3 and Péter Ván 4;5;6 1 Department of Mathematics, Computer Science and Economics, University of Basilicata, Potenza 85100, Italy 2 Departament de Física, Universitat Autònoma de Barcelona, Bellaterra, and Institut d’Estudis Catalans, Barcelona, Catalonia 08193, Spain; E-Mail: [email protected] 3 Department of Mathematics and Research Center of Applied Mathematics, University of Bologna, Bologna 40123, Italy; E-Mail: [email protected] 4 Department of Theoretical Physics, Wigner Research Centre for Physics, Institute for Particle and Nuclear Physics, Budapest 1121, Hungary; E-Mail: [email protected] 5 Department of Energy Engineering, BME, Budapest 1111, Hungary 6 Montavid Thermodynamic Research Group, Budapest 1112 , Hungary * Author to whom correspondence should be addressed; E-Mail: [email protected]; Tel.: +39-097-120-5885; Fax: +39-097-120-5896. Received: 30 December 2013; in revised form: 27 January 2014 / Accepted: 7 March 2014 / Published: 24 March 2014 Abstract: We present the state of the art on the modern mathematical methods of exploiting the entropy principle in thermomechanics of continuous media. A survey of recent results and conceptual discussions of this topic in some well-known non-equilibrium theories (Classical irreversible thermodynamics CIT, Rational thermodynamics RT, Thermodynamics of irreversible processes TIP, Extended irreversible thermodynamics EIT, Rational Extended thermodynamics RET) is also summarized. Keywords: continuum thermodynamics; entropy principle; rational thermodynamics; classical irreversible thermodynamics; extended irreversible thermodynamics; rational extended thermodynamics; exploitation of second law PACS Classification: 03.50.-z, 05.70.Ln, 05.70.Ce Entropy 2014, 16 1757 1.
    [Show full text]
  • An Ultrasonic Study on Anelasticity in Metals
    AN ULTRASONIC STUDY ON ANELASTICITY IN METALS J. P. Fulton, S. Nath, and B. Wincheski Analytical Services and Materials, Inc. 107 Research Drive Hampton, VA 23666 M. Namkung Mail Stop 231 NASA, Langley Research Center Hampton, VA 23681 INTRODUCTION Ultrasonic waves are highly sensitive to microstructural variations in materials and have been used extensively to investigate anharmonic effects in various metals and alloys[1-3]. A major focus of these studies is on the higher order elastic constants and their relation to the microstructure of the material. Ultrasonic techniques have also proven quite useful for char­ acterizing the stress state of a material [4-6]. Recently, while using the magnetoacoustic (MAC) method to investigate the residual stress in various steel samples, a time dependent change in the results was observed. It became apparent that the measurements were exhibit­ ing anelastic effects due to some intrinsic properties of the samples. Anelasticity is a phenomena that can occur whenever there is a rapid change in the exter­ nal stress applied to a crystalline solid. The change in stress will cause the induced strain to adopt a new equilibrium position. If the changes in the resulting strain does not take place instantaneously, the material is said to exhibit anelastic behavior. Investigations into anelas­ tic relaxation in crystalline solids have been carried out for many years and provide impor­ tant information relating to the microstructure of the material [7-13]. The time dependence of our MAC test results led us to propose a new approach for studying the causes of anelasticity in metals. Typical studies on anelasticity use strain gauges to monitor the recovery process.
    [Show full text]
  • The Mechanics of Ice
    COLD REGIONS SCIENCE AND ENGINEERING Monograph ll-C2b THE MECHANICS OF ICE John W. Glen December 1975 GB 2401 CORPS OF ENGINEERS, U.S. ARMY .U58m COLD REGIONS RESEARCH AND ENGINEERING LABORATORY no.ll-C2b HANOVER, NEW HAMPSHIRE 1975 Approved for public release; distribution unlimited. 5 fl rolomis The findings in this report are not to be construed as an official Department of the Army position unless so designated by other authorized docume* s. 0 Unclassified BUREAU OF RECLAMATION pENVER UBRARY C/ 92099625 ^ Y REPORT DOCUMENTATION PAGE ...............Q ? n Q 9 f i ? 5 1. REPORT NUMBER 2. GOVT ACCESSION NO. 3. RECIPt_______________ - ..------------ Monograph II-C2b -> 5. TYPE OF REPORT ft PERIOD COVERED 4. TITLE (end Subtitle) j m MECHANICS OF ICE 6. PERFORMING ORG. REPORT NUMBER 8. CONTRACT OR GRANT NUMBER*» 7. AUTHORf» European Research Office r J.W. Glen ,r Contract DAJA37-68-C*0208 £ ■ '« • ' 1 "• - TO. PROGRAM ELEMENT, PROJECT, TASK 9. PERFORMING ORGANIZATION NAME AND ADDRESS AREA ft WORK UNIT NJUMBERS Dr. John W. Glen Department of Physics ^ DA Project 1T062112A130 University of Birmingham ( ^ Task 01 ____ Birmingham. England ____; '____ ; _______ — 11. CONTROLLING OFFICE NAME AND ADDRESS 12. REPORT DATE Office, Chief of Engineers ^ December 1975 u 13. n u m b er o f p a g e s ' Washington, D.C. 47 14. MONITORING AGENCY NAME ft ADDRESS*?/ different from Controlling Office) 15. SECURITY CLASS, (of thie report) UvS ^Army Cold Regions Research and Engineering Laboratory-^ Unclassified Hanover, New Hampshire 03755 15«. DECLASSIFICATION/ DOWNGRADING SCHEDULE 16. DISTRIBUTION STATEMENT (of thla Report) Approved for public release; distribution unlimited.
    [Show full text]
  • The Anelasticity of the Mantle*
    CORE Metadata, citation and similar papers at core.ac.uk ProvidedGeophys. by Caltech i. AuthorsR. astr. - Main Soc. (1967) 14, 135-164. The Anelasticity of the Mantle* Don L. Anderson Summary The attenuation of seismic waves provides the most direct data regarding the non-elastic properties of the Earth. Recent experimental results from body waves, surface waves and free oscillations provide estimates of the anelasticity in various regions of the Earth. Results to date show that the upper mantle is more attenuating than the lower mantle, the maximum attenuation is in the vicinity of the low-velocity zone, a rapid increase in attenuation occurs in the vicinity of the C-region of the mantle and com­ pressional waves are less attenuated than shear waves. A frequency dependence of Q has not yet been discovered. Most laboratory measurements of attenuation have been performed at ultrasonic frequencies on pure specimens of metals, glasses, plastics and ceramics. A general feature of laboratory measurements is an exponential increase of attenuation with temperature on which are superimposed peaks which can be attributed to dislocation or other defect phenomena. Measurements on natural rocks at atmospheric pressure can be attributed to the presence of cracks. The intrinsic attenuation of rocks as a function of temperature and pressure is not known. However, on other materials grain boundary phenomena dominate at high temperature. This can be attributed to increased grain boundary mobility at high temperatures. High pressure would be expected to decrease this mobility. If attenuation in the mantle is due to an activated process it is probably controlled by the diffusion rate of defects at grain boundaries.
    [Show full text]
  • Anelasticity and Attenuation Part 1: Generalities Attenuation a Range Of
    Anelasticity and Attenuation Part 1: Generalities SIO 227C Bernard Minster April 2004 1 2 Attenuation A range of rheologies . Energy is lost to heat . Elasticity . Not explained by theory of elasticity . Inelasticity . Many mechanisms, most of which operate at . Plasticity the microscopic level . Viscosity . “slight” departure from elastic behavior . Viscoelasticity . Rheology based on simple considerations of . Visco-plasticity near-equilibrium thermodynamics. Elasto-plasticity . As much as possible, stick to linear theory . Anelasticity 3 4 1 Elasticity Viscosity . Linear elasticity (Green) . Linear viscosity Stress Stress . Hooke’s law σ = Kε σ = κε˙ . Nonlinear elasticity . Nonlinear viscosity Strain . Example. Strain rate σ = F(ε) σ ∝ε˙1 / N Stress Stress . Fully reversible deformation: . For instance, for water ice,N=3 Loading and unloading paths . Perhaps for the mantle as well are the same . Large stress leads to low effective . Equilibrium reached instantly Strain viscosity Strain rate . Deformation nonrecoverable 5 6 Plasticity Inelasticity . Instantaneous plasticity Stress . Nonlinear, . Rigid-plastic nonrecoverable . Time-dependent Strain . (example: material Stress Stress failure) . Elasto-plasticity Strain Strain rate 7 8 2 Anelasticity postulates Some Comments 1. For every stress there is a unique . Anelasticity is just like elasticity, plus the equilibrium value of strain and vice time dependence postulate versa . There can be an elastic component of the deformation in addition to the time-dependent 2. The equilibrium response is achieved component only after the passage of sufficient . Recovery is also time dependent time . Linearity is taken in the mathematical sense: 3. The stress-strain relationship is linear σ(αε1 + βε2) = ασ(ε1) + βσ(ε2) 9 10 Comparison of Rheologies Thermodynamic Substance Unique equilibrium Instan- Linear .
    [Show full text]
  • Boltzmann Equation 1
    Contents 5 The Boltzmann Equation 1 5.1 References . 1 5.2 Equilibrium, Nonequilibrium and Local Equilibrium . 2 5.3 Boltzmann Transport Theory . 4 5.3.1 Derivation of the Boltzmann equation . 4 5.3.2 Collisionless Boltzmann equation . 5 5.3.3 Collisional invariants . 7 5.3.4 Scattering processes . 7 5.3.5 Detailed balance . 9 5.3.6 Kinematics and cross section . 10 5.3.7 H-theorem . 11 5.4 Weakly Inhomogeneous Gas . 13 5.5 Relaxation Time Approximation . 15 5.5.1 Approximation of collision integral . 15 5.5.2 Computation of the scattering time . 15 5.5.3 Thermal conductivity . 16 5.5.4 Viscosity . 18 5.5.5 Oscillating external force . 20 5.5.6 Quick and Dirty Treatment of Transport . 21 5.5.7 Thermal diffusivity, kinematic viscosity, and Prandtl number . 22 5.6 Diffusion and the Lorentz model . 23 i ii CONTENTS 5.6.1 Failure of the relaxation time approximation . 23 5.6.2 Modified Boltzmann equation and its solution . 24 5.7 Linearized Boltzmann Equation . 26 5.7.1 Linearizing the collision integral . 26 5.7.2 Linear algebraic properties of L^ ............................. 27 5.7.3 Steady state solution to the linearized Boltzmann equation . 28 5.7.4 Variational approach . 29 5.8 The Equations of Hydrodynamics . 32 5.9 Nonequilibrium Quantum Transport . 33 5.9.1 Boltzmann equation for quantum systems . 33 5.9.2 The Heat Equation . 37 5.9.3 Calculation of Transport Coefficients . 38 5.9.4 Onsager Relations . 39 5.10 Appendix : Boltzmann Equation and Collisional Invariants .
    [Show full text]
  • Effects of Glass Transition and Structural Relaxation on Crystal
    Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 31 August 2020 doi:10.20944/preprints202008.0719.v1 Effects of Glass Transition and Structural Relaxation on Crystal Nucleation: Theoretical Description and Model Analysis J¨urnW. P. Schmelzer(1;∗), Timur V. Tropin(2), Vladimir M. Fokin(3), Alexander S. Abyzov(4), and Edgar D. Zanotto(3) (1) Institut f¨urPhysik der Universit¨atRostock, Albert-Einstein-Strasse 23-25, 18059 Rostock, Germany (2) Frank Laboratory of Neutron Physics, Joint Institute for Nuclear Research, ul. Joliot-Curie 6, 141980 Dubna, Russia (3) Vitreous Materials Laboratory, Department of Materials Engineering, Federal University of S~aoCarlos, UFSCar 13565-905, S~aoCarlos-SP, Brazil (4) National Science Center Kharkov Institute of Physics and Technology, 61108 Kharkov, Ukraine Submitted to Entropy, August 27, 2020 Keywords: Nucleation, crystal growth, general theory of phase transitions, glasses, glass transition PACS numbers: 64.60.Bd General theory of phase transitions 64.60.Q- Nucleation 81.10.Aj Theory and models of crystal growth 64.70.kj Glasses 64.70.Q- Theory and modeling of the glass transition; 65.40.gd Entropy * Corresponding author: Dr. J¨urnW. P. Schmelzer Phone: +49 381 498 6889, Fax: +49 381 498 6882 Email: [email protected] 1 © 2020 by the author(s). Distributed under a Creative Commons CC BY license. Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 31 August 2020 doi:10.20944/preprints202008.0719.v1 Abstract In the application of classical nucleation theory (CNT) and all other theoretical models of crystallization of liquids and glasses it is always assumed that nucleation proceeds only after the supercooled liquid or the glass have completed structural relaxation processes towards the metastable equilibrium state.
    [Show full text]
  • Anelastic Behavior of Small Dimensioned Aluminum
    metals Article Anelastic Behavior of Small Dimensioned Aluminum Enrico Gianfranco Campari 1 , Stefano Amadori 1, Ennio Bonetti 1, Raffaele Berti 1 and Roberto Montanari 2,* 1 Department of Physics and Astronomy, Bologna University, Viale Berti Pichat 6/2, I-40127 Bologna, Italy; [email protected] (E.G.C.); [email protected] (S.A.); [email protected] (E.B.); raff[email protected] (R.B.) 2 Department of Industrial Engineering, Rome University “Tor Vergata”, Via del Politecnico, 1-00133 Roma, Italy * Correspondence: [email protected]; Tel.: +39-0672597182 Received: 18 March 2019; Accepted: 9 May 2019; Published: 11 May 2019 Abstract: In the present research, results are presented regarding the anelasticity of 99.999% pure aluminum thin films, either deposited on silica substrates or as free-standing sheets obtained by cold rolling. Mechanical Spectroscopy (MS) tests, namely measurements of dynamic modulus and damping vs. temperature, were performed using a vibrating reed analyzer under vacuum. The damping vs. temperature curves of deposited films exhibit two peaks which tend to merge into a single peak as the specimen thickness increases above 0.2 µm. The thermally activated anelastic relaxation processes observed on free-standing films are strongly dependent on film thickness, and below a critical value of about 20 µm two anelastic relaxation peaks can be observed; both their activation energy and relaxation strength are affected by film thickness. These results, together with those observed on bulk specimens, are indicative of specific dislocation and grain boundary dynamics, constrained by the critical values of the ratio of film thickness to grain size.
    [Show full text]
  • Relaxation Processes in Glass and Polymers Lecture 2
    MITT Ulrich Fotheringham: Relaxation Processes in Glass and Polymers, Lecture 2 Relaxation Processes in Glass and Polymers Lecture 2: Phenomenology of viscoelasticity & glass transition Dr. Ulrich Fotheringham Research and Technology Development SCHOTT AG MITT Ulrich Fotheringham: Relaxation Processes in Glass and Polymers, Lecture 2 In the following, examples from the progress of relaxation research in glass will be shown in order to illustrate what relaxation is about. It is neither a comprehensive picture of the history of relaxation research nor a balanced assessment of the contributions of all individuals involved. To illustrate glass properties, references will be made to different companies. These references have been picked arbitrarily for educational reasons, copyright issues etc., not to provide a balanced view of the achievements of different companies. Despite its careful preparation, the manuscript may contain errors. Dr. Ulrich Fotheringham MITT Ulrich Fotheringham: Relaxation Processes in Glass and Polymers, Lecture 2 Observation 1a (before 1912!): Glass, if heated to high temperatures and cooled down rapidly, shows birefringence like Calcite: (calcite birefringence picture from Carl Zeiss AG, information on polarisation microscopy) In contrast to the permanent birefrigence of Calcite, the birefringence in glass is stress-induced. Otto Schott found that it will relax if the sample is held for 24h at a minimum temperature which depends on the composition: crown flint (historic example: (historic example: window glass) lead
    [Show full text]
  • Inference of Thermodynamic State in the Asthenosphere from Anelastic Properties, with Applications to North American Upper Mantle
    EarthArXiv Cover Page 2020-12-11 Inference of thermodynamic state in the asthenosphere from anelastic properties, with applications to North American upper mantle Christopher Havlin University of Illinois at Urbana-Champaign, havlin!illinois"ed$ Ben&amin Holtzman (amont-Doherty Earth *bservatory, Col$mbia University, benh!l#eo.col$mbia"ed$ Emily Hopper (amont-Doherty Earth *bservatory, Col$mbia University +his man$s ript is a non-peer revie,e# pre-print" It has been s$bmitte# for p$bli ation in Physics of the Earth and Planetary Interiors an# is c$rrently in revie," As s$ h, the content of the present man$s ript may change until the final version is p$blishe#, at whi h point a )*I lin. will dire t you to the final p$blishe# version" 1 Inference of thermodynamic state in the asthenosphere 2 from anelastic properties, with applications to North 3 American upper mantle 4 Christopher Havlin, Benjamin K. Holtzman*, Emily Hopper 5 Abstract 6 Inference of thermodynamic state and full-spectrum mechanical behavior of the litho- 7 sphere and asthenosphere is a central problem in geophysics, implicating our understand- 8 ing of the convection patterns, transient responses and chemical composition of the planet. 9 Anelasticity is responsible for significant relaxation of stress associated with seismic wave 10 propagation in the asthenosphere, while irreversible transient creep may be important in the 11 lithosphere. This paper focuses on the processes that may act at the time scales of seismic 12 wave propagation, and current questions in the effort to determine the dependence of these 13 effects on thermodynamic state.
    [Show full text]