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Definitions and units 263

Definitions and units

The following glossary is intended as a conveniently accessible source of technical terms used in context with tracks. It is compiled mainly on the basis of the references [1], [2], [3], [4], [5], [6].

[1] D.H. Menzel (editor): "Fundamental Formulas of Physics." Dover Publications, New York, 1960 [2] "Glossary of Terms used in Nuclear Science." British Standards Institution, B.S. 3455, 1962 [3] "The Radiochemical Manual." Amersham, the Radiochemical Centre, 1966 [4] Cohen, E., P. Giacomo: "Symbols, Units, Nomenclature and Fundamental Constants in Physics." International Union of Pure and Applied Physics (IUPAP), Revision 1987,67 pp. (1987). [5] Alan Isaacs (editor): "Concise Dictionary of Physics." Oxford University Press, pp. 1-295, 1985. [6] Hansen, J.W.: "Experimental Investigation of the Suitability of the Track Structure Theory in Describing the Relative Effectiveness of High-LET Irradiation of Physical Detectors." RiSl/l National Laboratory, DK-4000 Roskilde, Denmark; RiSl/l-R-507, (1984).

absorbed dose, absorbed per unit . SI of the element. The de• unit is the Gray (Gy). I Gy = 1 J / fines the chemical properties of the element. kg = 104 erg / g = 6.25-1015 eV/g. atomic radius of , ao = h2 / 4n2 m e2 = actuator, a device for inducing an action. 0.5292-10-8 cm. alpha particle, (a), the nucleus of a 4He con• atomic (W), for a given specimen of an sisting of two and two . element, the mean weight of its atoms, ex• pressed in either units (physical areal of targets, (Ps)' thickness-equivalent scale) or atomic weight units (chemical scale). of targets, Ps ;;; P d, where p is the mass density and d the target thickness, usually given in atomic weight unit (awu), one-twelfth of the mean mg / cm2. mass of the neutral atoms of naturally occurring carbon. areal dose (fluence), number of accumulated (recorded) particle tracks per unit surface area. A vogadro number, N A = 6.0220-1023 / , number of per mole. asp~ct ratio, ratio between length and width of an ion track. bar, unit of . 1 bar = lOS Pa = 750.19 torr. atom, a unit of consisting of a single nu• barn, a unit of cross-section. 1 bam = 10-24 cm. cleus surrounded by one or more orbital elec• (Bq), unit of radioactivity, 1 Bq = trons. The number of corresponds to 1 decay event / s. Official unit before 1986: the number of protons in the nucleus. 1 Curie (Ci) = 3.7-1010 decay events / s. atomic mass (A • u), mass of a measured , . in atomic mass units, where A = atomic mass Bohr magneton, JlB = e h / (4n me c) = number, and u = atomic mass unit. 9.2741 - 10-24 pro Tesla. atomic (A), mass number of a nu• , ao = a / 4 n R~ = 0.529177-10-8 cm. clide, number, number of protons and a = constant, n = 3.1415, R~ = neutrons in the nuclide. A is the nearest integer . to its atomic mass. Bohr velocity, Vo = 2n e 2 / h = a c = atomic mass unit (u), one-twelfth of the mass of a 2.1847-108 cm / s, where e electron charge, 27 = neutral atom of 12C, u = 1.6606-10- kg. h = , a = fine structure con• atomic number (2) of an element, nuclear charge stant, C = velocity of light. number, number of protons in the nucleus of the , k = R / N A = 1.3806-10-23 J 264 Defmitions and units fK = 1.3806.10-16 erg / K. R = molar gas con• number, u = atomic mass unit, NA = Avogadro stant, N A = . number, V rn = molar . Bragg peak: region of maximum energy loss of a density, number - (N), number of atoms per vol• high energy ion traversing matter. ume element, N = P / (A u), where p = mass bremsstrahlung, the electromagnetic radiation re• density, A = atomic mass number, u = atomic sulting from the retardation of charged particles. mass unit. calorie, unit of , 1 calorie = dose, energy -, absorbed energy per unit mass. SI 4.18400 . unit is the Gray (Gy). 1 Gy = 1 J / kg = 104 erg / g = 6.25.1015 eV / g. Radiation en• capacitance, unit of capacitance is the Farad (F). 1 2 ergy deposited in a medium causes bond rupture, Farad = 1 Coulomb / Volt = 1 m- kg-I S4 N. radical formation, and physico- and chemical charge, electric -, given in units of Coulomb (C). changes, which are detectable in different ways. 9 1 C = 1 A s = 3.10 esu. dose equivalent, see Rem. A unit of biologically cross section of a nucleus, atom, or grain for a effective dose, defined as the absorbed dose in rad given radiation, that area perpendicular to the di• multiplied by the quality factor - or relative bi• rection of the radiation attributed geometrically ological effectiveness (RBE) -. For all x rays, for its interaction with the radiation; or, in other y rays, ~- rays and ~+ rays encountered from ra• words, the number of interactions per unit time dioisotopes the RBE is 1. For a-particles and divided by the radiation flux and the number of heavier the RBE can be different from 1, scattering objects present. The cross section of a depending on the ion charge and its velocity. nucleus is roughly of the order of 10-24 cm, of an 16 Dose-response: relation between the deposited en• atom roughly of the order of 10- cm. ergy per volume, in other words the dose, and Coulomb (C), the unit of . The the observed effect, which may for example be charge of 1 Coulomb corresponds to the charge optical absorption, survival of cells, etc .. For of an electrical current of 1 Ampere flowing dur• many physical radiation recorders, irradiated by ing 1 second. 1 C = 1 A s. 1 Coulomb corre• low-LET radiation, the dose-response function is sponds to the charge of 0.62414.1019 electrons. approximately linear at low doses and saturates Coulomb barrier of nuclear reactions, minimum exponentially at high doses and the response is a energy of projectile ions required for inducing single-valued function of dose within a large nuclear reactions. The coulomb barrier corre• range of initial and electron . sponds to a specific energy in the range between dyne, unit of force, 1 dyne = 1 g cm S-2. 1 and 10 MeV/nucleon, depending on the projec• electron, the negatively charged particle which tile/target combination. forms a constituent of all atoms. Electron charge Coulomb explosion, origin of the atomic collision e = - 1.60219.10-19 Coulomb = -4.8032.10-10 cascade.in solids, caused by the passage of a esu. Electron mass me = 9.1095.10-28 g. rapidly moving ion and leading to displaced Classical electron radius r e = e 2 / (me c2 ) = atoms and ultimately to a latent track. 2.8179.10-13 cm. Coulomb per kilogramm (C / kg), "unit" of ab• electron volt (eV), a unit of energy equal to the ki• sorbed dose, defined as total electron charge gen• netic energy acquired by an electron when accel• erated during - preferentially x or y - irradia• erated through a potential difference of 1 volt. 1 tion. Official unit before 1986: 1 Roentgen = eV = 1.602.10-12 erg = 1.602.10-19 Joule. 4 2.58.10- C / kg. One Roentgen produces eV, electron volt. 1 eV = 1.602.10-12 erg. 3.7·1010 ion pairs in air at standard pressure and temperature. element, matter consisting of atoms having the same atomic number Z. Curie (Ci), old unit of activity. One curie corre• sponds to 3.7.1010 nuclear transformations per energy, a measure of a system's ability to do . second. 1 Ci =3.7·1010 Bq. is the energy stored in a body or system as a consequence of its position, shape, De Broglie wavelength of a particle, A = h / p , or state. is energy of motion and where h = Planck constant, and p is the particle is usually defined as the work that will be done momentum. The magnitude of the associated by the body when it is brought to rest. For a wave vector is k == 21t / A = 21t P / h. body of mass m having a speed v, the kinetic delta ray: secondary and higher order electrons gen• energy is m v2/2. The rotational kinetic energy erated by a primary radiation. This term is anal• of a body with an angular velocity 0) is I 0)2/ 2, ogous to the terms alpha-ray and beta-ray. where I is its moment of inertia. density, electron - (Ne)' number of electrons per energy units, 1 erg = I g cm2 S-2. 1 J = 107 erg = volume element, Ne = Z P / (A u), where Z = 0.239 calories. 1 erg = 6.25.1011 eV. 1 eV = nuclear charge number, p = mass density, A = 1.6.10-12 erg. 1 kJ / mole = 1.038.10-2 eV / atomic mass number, u = atomic mass unit. . density, mass - (p), mass per volume element, energy, free -, corresponds to the following two p = Au NA / V rn , where A = atomic mass thermodynamic functions. Gibbs free energy, Definitions and units 265

G=H-TS, is the energy liberated or absorbed in a ture T at which the energy is absorbed, reversible process at constant pressure and con• t1S=t1Q/T. However, all real processes are to a stant temperature (n, H is the enthalpy and S certain extent irreversible changes and in any the entropy of the system. Changes in Gibbs closed system an irreversible change is always free energy, t1G, are useful in indicating the con• accompanied by an increase in entropy. The in• ditions under which a will oc• crease in the entropy of a body during an in• cur. If t1G is positive the reaction will only oc• finitesimal stage of a reversible process is equal cur if energy is supplied to force it away from to the infinitesimal amount of heat absorbed di• the equilibrium position (when t1G=O). If t1G is vided by the absolute temperature of the body. negative the reaction will proceed spontaneously Thus for a reversible process dS=dQ/T. S(n is to equilibrium. Helmholtz free energy, F=U-TS, the integral of dQ/T = cp dT/T from 0 to T, where U is the , is that portion of where dQ = heat increment at temperature T, the energy of a system which is the maximum cp = specific heat at constant pressure. In a wider available energy for doing work. For a reversible sense entropy can be interpreted as a measure of isothermal process, t1F represents the useful a system's disorder; the higher the entropy the work available. greater the disorder. energy, internal ~, U, U=Q+W, where Q and Ware Boltzmann relation of entropy, S = k In W, W = heat and work transferred to the system, respec• probability, k = Boltzmann constant. tively. The relation U=Q+W is referred to as the erg, cgs unit of energy. 1 erg = 1 g cm S-2. first law of thermodynamics. The internal energy 1 erg = 10-7 Joule. of a body is the sum of the potential energy and excitation, The addition of energy to a system, the kinetic energy of its component atoms and transforming it from its to an ex• molecules. It does not include the kinetic and po• cited state. tential energies of the system as a whole nor their nuclear energies or other intra-atomic ener• Faraday constant, F = N A e = 9.6484 0 1Q4 C/mo!. gies. The value of the absolute internal energy of fine structure constant, a = 2It e 2 / (h c) = a system in any particular state cannot be mea• 7.29735 0 10-3 "" 1/137. sured; the significant quantity is the change in Fermi level, in a solid at which the internal energy, t1U. For a closed system (a sys• probability to find an electron is 1/2. At abso• tem that is not being replenished from outside lute zero all electrons would occupy energy its boundaries) the change in internal energy is levels up to the Fermi level and no higher levels equal to the heat absorbed by the system (t1Q) would be occupied. from its surroundings, plus the work done on the system by its surroundings (t1 W ) , fission, a in which a heavy nu• t1U=t1Q+t1W. cleus splits into two (or rarely three) approxi• mately equal parts. The specific energy of fission energy loss (dE / dx), linear energy transfer fragments is of the order of 1 MeV/nucleon. (LEn, or stopping power (S), energy deposited by the incident ion per unit path length of the fluence of particles, areal dose, number of accumu• stopping medium. lated (recorded) particle impacts (tracks) per unit surface area. energy, specific ~, (T,) characteristic energy of a high frequency accelerator, corresponding to iden• flux of particles, number of particles penetrating a tical ion velocities, independent of the nucleon unit surface area per unit time or product of the number. A given ion of nucleon number A will number of particles per unit volume and their average speed. be accelerated to an energy T corresponding to the specific energy T, times the nucleon number gamma radiation, gamma rays, electromagnetic ra• A, T = T, A. Unit of the specific energy is diation emitted by atomic nuclei. MeV/nucleon (MeV/u). , molar ~, R = 8.314 J / (mol K). enthalpy, heat content, H=U+pV, where R = k N A; k = Boltzmann constant, N A = U=internal energy of system, pV=product of Avogadro constant. pressure and volume of the system. For chemical grain, sensitive element, sensitive volume, It is reactions at constant pressure one has t1H = assumed that the medium consists of identical t1U+p t1V. For an exothermic reaction t1H is sensitive "elements", which may be either taken to be negative. atoms, molecules or larger entities embedded in a enthalpy, free~, Gibbs free enthalpy:= Gibbs free more or less passive matrix acting as an energy energy, G=H-TS. transfer medium. Once the sensitive element has entropy, a measure of the (isothermally) unavail• been activated it will in principle stay activated able energy in a thermodynamic system. An in• despite being hit several times. The amount of crease in entropy is accompanied by a decrease in excitation and deposited by energy availability. When a system undergoes a secondary electrons is taken as a measure of the reversible change the entropy S changes by an density of hits in the irradiated medium. amount equal to the energy Q absorbed by the Gray (Gy), unit of absorbed energy dose, 1 Gy = system divided by the thermodynamic tempera- 1 J / kg. Official unit before 1986: 1 rad = 10-2 266 Definitions and units

2 Gy = 10- J / kg = 100 erg / g. MeV, million electron volts = 106 eV. ground state: the lowest-energy state of a system. MeV/nUcleon, MeV/u, unit of specific energy Ts half-life, the time in which an ensemble of excited produced by a specific high frequency accelerator. particles decays to half its initial number. milliatom, one thousandth part of the atomic hit: a quantized interaction which implies that one weight of the element in grams . event under consideration takes place in the sen• millimole, (mM), one thousandth part of a mole. sitive element - grain - of the medium and initiates an effect. The activation may be mole (M), molecular weight of a compound in brought about by a single electron passing grams. through the sensitive element. moment of inertia, (I), I = f dm r2. For a mass point at distance r from the origin I = m r2. hydrogen radius, Bohr radius, ao =0.529177 0 10-8 cm. momentum, quantity of motion equal to the prod• inductance, unit of inductance is the Henry (H). 1 uct of mass and velocity of a particle. Henry = 1 Weber / Ampere = m2 kg S-2 k 2• multi-hit recorder: A track-recording medium in ionization, any process by which ions are formed; which the sensitive grains consist either of sev• in particular, ionization of a gas by the passage eral targets each of which has to be hit once or of fast charged particles. one target which has to be hit several times be• fore the effect is observed. Accordingly, multi• ionization energy, electron , energy hit recorders may either be described as single-hit required for removal of one electron. The hydro• multi-target systems or as multi-hit single target gen ionization energy is 13.6 eV. systems. effect, differences that may be detectable in , one of the particles of which nuclei con• the chemical or physical behavior of two iso• sist; it is of zero charge and slightly heavier than topes or their compounds. a . mn = 1.67495 0 10-24 g. , having the same atomic number Newton, (Nt), unit of force, 1 Nt = 1 kg m S·2. Z but different mass numbers A. nuclear charge number (2), atomic number, num• isotopic abundance, the number of atoms of a par• ber of protons contained within the nucleus. ticular isotope in a mixture of the isotopes of an element, expressed as a fraction of all the atoms nucleon, a particle constituting the atomic nu• of the element. cleus; proton or neutron. (A), Joule, (J), SI unit of energy. 1 J = 1 kg m2 S·2. nucleon number, mass number, number of 1 J = 107 erg. protons and neutrons in an . Josephson frequevcy/voltage ratio, 2 e / h = nucleus, the positively charged central portion of an atom, containing almost the whole mass of 4.83590 1014 Hz V . the atom, but only a minute part of its volume. keY, thousand electron volts = 103 eV. Radius rA '" 1.20 1O· 13 ·A 1/3, where A = atomic LET, linear energy transfer, deposited energy per mass number. unit path length. More or less equivalent to en• nuclide, a species of atom characterized by its mass ergy-loss (dE /dx) and stopping power S. number A, atomic number Z, and nuclear energy linear energy transfer (LET), energy loss state. (dE I dx), or stopping power (S), energy de• Pasqual, (Pa), unit of pressure. 1 Pa = 1 Nt / m2 = posited by the incident ion per unit path length 10-5 bar =0.75.10. 2 torr. of the stopping medium. The LET is roughly pfoportional to Zefr where Zeff is the ef• permeability of vacuum, /l{) = 1 / Eo c2 =4 7t 010.7 rp2, I l fective charge of the penetrating ion and p = H m- = 1.256637 .1O@ H m· . v / c its relative velocity, measured in units of permittivity of vacuum, £0 = 1 / (110 c 2 ) = the . 8.854188 0 10.12 F m-I. Loschmidt constant, no =N A / V m = 2.6868 0 1019 photon, a quantum of electromagnetic radiation, cm·3• possessing the energy hv (h being Planck's con• stant and v the frequency). magnetic flux, unit of the magnetic flux is th~ Weber (Wb). 1 Weber = 1 V s = 1 = m2 kg s• Planck constant (h), h = 6.6262.10.34 J s ki. = 6.6262.10.27 erg s. Frequently used quantity: h / 27t = 1.054590 10-34 J s. magnetic flux quantum,

List of symbols

In the following a list of the most frequently used symbols is given. In order to avoid multiply indexed symbols, the defInitions depend on the context.

A alignment parameter, ment of inertia dius, resistance amplitude, atomic mass I electric current, heat p mass density number flow, intensity, ionization p, charge density a. alpha particle, angle potential Rc condensation rate a distance, size ~ scattering angle Re evaporation rate ao Bohr radius J linear ionization density S,S solubility constant, sorp- B magnetic induction q> scattering angle tion constant, stopping ~ angle, relative velocity j mass flow density, elec- power, surface area vic tric current density cr surface area, cross sec- b distance of closest ap- q> phase tion proach K Kelvin T kinetic energy, tempera- e,c capacitance, concentra- k Boltzmann constant ture, oscillation time in- tion, lithographic con- K elastic compliance, ther- terval trast, velocity of light mal conductivity time cv specific heat k wave number 2 re/).. 't time interval, life time X magnetic susceptibility k wave vector Tc critical temperature D,d diffusion constant, diam- L, I inductance, length Ts specific energy eter, differentiation oper- A, wave length U potential energy, voltage ator M magnetization u atomic mass unit Ll divergence operator M,m mass, molecular weight V potential energy, volume Ii displacement, variation Il chemical potential v track etch rate operator Il v velocity E electric field strength mo rest mass at velocity v = Vo Bohr velocity E energy 0 Vc critical velocity e Euler's number IlB Bohr magneton Vm e electron charge Ms saturation magnetization W atomic weight, cumula- E energy density, dose N,n areal dose, fluence, inte- tive probability EF Fermi energy ger number, number n solid angle F force density, refractive index co angular frequency F particle flux (ions per v frequency COo plasma frequency cm2 and per s) NA Avogadro number w probability 'Y lithographic contrast P,p diffusion permeability, S coherence length g general etch rate, earth impact parameter, linear x x-coordinate gravitational acceleration momentum, nominal 'l' scattering angle, wave 'Y relativistic mass ratio porosity, static pressure, function m/mo , interface energy probability y y-coordinate H strength Peff effective porosity Z nuclear charge number h Planck constant Q,q electric charge, thermal z z-coordinate 11 viscosity constant energy Zeff effective charge number I , mo- R,r ion range in matter, ra- Y' gradient operator Index 269

Index

accelerator 14, 20-41 dtain elastic _ 74-76 application of _s 13 bonding and _ scission 247 plasmon _ 76, 79 classes 21-23, 26 charge cyclotron accelerator 26, 32-34 electrostatic _ 26-28 . effective _ 86, 87 damage (see defect) high frequency _ 28-35 exchange 80, 85-87 De Broglie linear _ 31-32 state 50, 80-87 wavelength 160 parameters 21 chromatography 216-217 defect principles 26 coercivity annealing 100, 108-109 travelling wave _ 29 magnetic _ 234 attraction 104-105 activation (see thermal activation) coherence branched chain of s 221 adhesion, increasing the _ 261 length 201, 211 density 134-135 - alignment parameter 23S phase _ 199-210 diffusion 104-109,220 alpha source 14, 18·20 collision distribution 115 annealing 101, 137·138 atomic _ cascade 94 extended _ 102, 108-110 antiferromagnet 235 central_ 60-64 formation by electrons 116- antireftection treatment 257·260 elastic _ 60-71 125 Arrhenius electronic _ cascade 113-116 formation energy 102-103 plot 100 inelastic _ 60 frozen _ 8, 94, 101 compensation interaction 104-107 aspect ratio 4, 6 line _ 106-108 Becquerel43 point writing 243 temperature 243 linear chain of s 221 Bernoulli linear density of _s 101-102 equation 184 composite material 261 majority _ 106 binary-encounter model 54-60 migration 106-107 bistability, magnetic 238 concentration spike 214-215 minority _ 106 BOOr - point _ 103 step 217-218 radius 80, 83 primary _ 102-103 stripping criterion 85 conductivity radial distribution of _s 122- velocity 88 sensor 165, 196-198 123 Boltzmann cone relaxation 104-109 distribution 231 angle 144-145,257 sink 107-108 factor 100, 129, 130,231, conservation theorems 54-57 thermal_ 97-102 238 contrast trap 220 statistics 98-100 definition 250 definition of used terms 263 box potential 81 variation technique 220, 221 deformation ofparticles Bragg convection observation 196 diffraction 159-160 transport 187 red blood cells 198 peak 22,51 cooperative phenomena 232 deformation ofparticles rule 89 Coulomb counteracting force 191 break-down counter 163 collision 52, 68-71 droplet model 193 bubble explosion 93 equation of motion 191 magnetic _ 240 threshold 22, 42, 45-47 red blood cells 193 bulk properties of solids 230-245 cross-section deformation ofparticles capacity definition of _ 57-59 droplet model 189 magnetic-storage _ 240 energy-loss _ 58-60 observation 188 sensor 208 Curie potential energy 191 capillary depression 189 temperature 233 stages of deformation 190 center·of·mass 65·68, 71 cut-oft' energy 73-79 density 270 Index

effective 251,258 energy transfer 63, 71-72,111 Hagen-Poiseuille depolymerizab 247 in elastic collisions 64 law 184 depth . maximum_64 half-life 17-20 resolutIon 251-252 to electrons 72 harmonic oscillator 75 deIEctIr energy-loss 72-73 heavy-ion track (see track) electronic _ 163-165 and range 92 Helmholtz development of tracks 126-154 basic steps of _ 52 resonator 209 difIhu:tion detector 164 hit 120 phase calculation 159 electronic 52-91 tedness 110 phenomena 158-162 function 51,80,87-89 mUlti_ 173, 174, 175 techniques 158-162 nuclear 52-53,90-91 probability 121-122, 175-180 diffusion observation 50-53, 164 Huygen's cage model oC 142-143 phenomena 49-92 principle 144 constant 143 straggling 90-91 epitaxy hydrodynamic length 191 dynamic _ 212 80 electric analogue 213 liquid-phase _ 241 -etching (see track etching) hysteresis equations 212-213 magnetic _ 234 flux 218, 219 event spike 214 multi-hit _ 175 impact parameter 54, 58, 59, 60, stationary _ 212 71 103 maximum 59, 72-73, 76- through tracks 211-224 self-trapped _ 104 79,88 - transport 141-143, 187 Faraday . implantation dipole rotation 244 ion _ 21, 22, 43, 45,248 interaction 235 feedback loop 233 index oriented _s 261 ferromagnetism 232 dislocation line 105-108 refractive _ 257, 258 Fick's interacCioo displacement energy 94 first law 141-143,212 dipole-dipole _ 235 dhtan.a! second law 212 exchange _ 235, 237 of closest approach 45, 61-62 field emitter pins 261 interface distribution ruter energy 127-130, 188, 190 binomial_ 176 ion track _ 225 Poisson _ 121, 176 interstitial 103-107 fission source 20 aggregation 105 domain (see magnetic domain) flow introduction to ion tracks 1-13 dose alignment of particles 186 ion areal 15, 16,41, 174 confinement of particles 185 energy _ 43-44, 111-118,249 deflection 24-25 cytometry 183-198 energy observation 164 grain _ 120-125 hydrodynamics 184-185 permissible _ 44 focussing 25 in capillaries 184-185 microbeam 42, 255 radial distribution of _ 114- viscous _ 184 116 source 23-24 focussing screen 256 ion track (see track) double formation of ion tracks 93-125 ionization cone 168 Frenkel exposure 166, 254 chamber 164 defect 103 density along track 134 pore 175-182, 225 Fresnel elastic wave 76 irradiaIion 247 formula 258 double 254 eIectroo gap model 135-137 emission from ion path 111- equipment 39-42 prnet parameters 15 113 composition 242 pre-_255 gas 80-84 _ 241-245 magnetic moment of _ 230 source 14 range 113-114 gas . target 39 permeatIon 222-223 technology 14-48 resonance 162 wide-beam _ 41 emitter glossary 263-267 field _ 261 grain 110, 118-125 Josephson effect 199-210 energy boundary 108 delocalization 102 dose 118-119 Kepler domain wall _ 239 growth 131-132 s second law 57 potential _ 236 response 120, 123 knOCk-on frequency 101 specific 28 sensitivity 110 laboratory system 62, 63 thermal excitation 237 size 110, 117 Lagrange growth areas 246-261 multiplicator 99 Index 271

Langevin 158 principle function 232 moment least time 151 LET (see energy·loss) magnetic _ 242 probability lift·ofT technique 248 momentum track_173-182 light angular _56 properties scattering 256 approximation 73-75 bulk 230-245 linear energy transfer (see energy· multilayer track recorder 171 magnetic _ 230-235 loss) multiple ion tracks 211·229 magneto-optic _ 230-245 lithography 3·9 neutron radiation safety 42-48 additive 248 diffraction 162 excitation threshold 45-47 contrast in _ 249 nudear handling of isotopes 43-45 conventional _ 249 activation 47-48 mean-free-path 47-48 ion _ 246, 25t-255 reactor 15 monitors 44-45 projection _ 253 nuclear track (see track) permissible dose 43-44 subtractive _ 248 nucleation (see phase sample activation 22, 23, 45- Lorentz tramformation) 48 force 24, 26 barrier 132 units of dose 43-44 lArentz..l.orenz observation 155·166 I'IKIit3 formula 258 mechanical 166 observation 162 MaW off-line _ 155, 165 radioisotopes 16·20 cone 144-145 on-line _ 155, 163 range magnetic thickness 166 ion _ 92,254 anisotropy 244-245 overkill effect 123 straggling 251 bistability 238 paramagnetism 231 reduced mass 62, 69 bubble 240 particle track (see track) reOectivity domain 236, 238 permeation 223 anti-_ treatment 257-260 domain alignment 244 constant 219 calculation of 257-260 dynamic _ 257- domain size 241 gas _165 stationary _ 259 domain wall energy 239 pIBie domain wall pinning 239, coherence 199-210 relative coordinates 61, 68-70 243 diffraction _ 159 relativistic energies 35·39 materials terminology 235 shift 258 energy-velocity relation 39 moment 230-231 slippage 202-208 fundamental relations 36 resonance frequency 33 stability 29-30 37 magnetization 230 synchronous detection 188 remanence spontaneous _ 233 phase transformation magnetic _ 234 magneto-optics condensation nucleus for replica technique 172, 247 matrix model of _ 235-241 133 resist simulation of _ 236 curved interface 130 characterization 251 materials technology 7, 211·229 density fluctuations 133 negative _ 247, 250 membrane hindered _ 132 positive _ 247,249 permeability 211, 217-224 intemal_ 127 solubility 249-251 technology 224-229 nucleation 126-133 resistance microbeam 4, 14,42, 255 nucleation barrier 132 surface _ 261 scattered ions in _s 173 planar interface 127 resistive pulse technique 183, micromechanics 1 stability condition 127, 130, 187·188 . microparticles in Ooids 131-132 safety (see radiation safety) angular cOnImement 186 vapor pressure 128-130 sample inlet system 40 counting of _ 196 phononsl02 saturation magnetization 233 deformability 183-198 plasmon scattering deformation time 192 excitation 77-79 angle 60, 67, 71 local confinement 186 frequency 79 coherent 257-260 number density 183-198 point defect (see defect) ion _ 173 passage time 197 Poisson light _ 256 sedimentation 185 distribution 121, 176 neutron small angle _ 161 size 183-198 polymerization 247 plate 256 volume 187 pore overlap 170·182,225,226 x ray small angle _ 161 microscopy 155·158 porosity sensitive volume (see grain) optical _ 155-156 effective _ 181, 251 sensitization scanning electron _ 156 nominal 174 track _ 138, 225, 255 transmission electron 157- 272 Index sensor surface _ 256-261 at constant etch rate 144-145 capacitive _ 208 thermal activation 97,100-102 at varying etch rate 147-152 conductivity _ 165,196-198 Arrhenius plot 100 digestion stage 140 single-ion tracks 183-210 barrier 97, 10 1 dissolution stage 140 slope Boltzmann factor 98 in isotropic medium 143-152 of resist 251 thermal annealing 100,101,106, induction time 139-140 small-angle scattering 220 109 main parameters 149 solubility 249 thermal diffusion primary factors 138-140 dynamic _ 95-96 reaction zone 139 sorption constant 219 soaking stage 140 spark counter 165 spike solution 96-97 stationary _ 95 transport processes 139 SSNID (see track) thermal spike track pattern state density 82 evolution of 97 defming parameters 175 Stirling model 94-10:3 regular _ 173 approximation 98 Thomas-Fermi stochastical _ 173-182, 252 Stoke atom model 83-84 three-dimensional overlap equation 185 equation 83-84 181-182 stopping power (see energy-loss) threshold two-dimensional overlap 174- straggling track etch _ 251,255 180 range _ 251 utilization 255 track shape 138, 147-152, 167- 170, 198, 209-210 stripping criterion 85 trad< structure of etched tracks 167-182 annealing 100, 101, 137-138 calculation 143-152 supertluid 49 conicaL 168 basic creation steps cylindrical _ 167 s and ion tracks 199-210 conferences 9 in fibres 169 chemical potential of _s 202 core 93 circulation quantum 205 in spheres 169 creation 14-182 prismatic _ 167 coherence length 201 development 126-154,172, special techniques 168, 171- density 201 247 energy-loss process 207 double s 177-180 172 spherical _ 168 equation of motion 205 etch threshold 135-137 flow through aperture 200 etching (see track etching) two-step procedure 169 Josephson effect 201-204 filter 224-228 track technique nucleation of vortex 206 formation 93-125 parameters of _ 246 phase slip rate 207 grafting 172 triaI-escape frequency 101 phase-velocity relation 204 halo 110-125 undercut in lithography 247 resonator 209 history of _s 8 units single-pore cell 208 introduction to _s 1-13 used_ 263 types of _s 199 journals 9 vacancy 103-105 velocity 204 latent _ observation 157, 160, aggregation 105 vortex creation 200 162, 165 vapor pressure 200-201 multilayer _ recorder 171 of curved interface 130 weak link between _s 199, multiple ion _s 175,211-229 of flat interface 128-130 210 non-overlapping _s 170 virial theorem 85-86 superposition principle 214 observation 155-166 viscosity surface overlapping _s 170 definition 184 smoothness 252 parameters (see track of blood 194 texture 256-261 technique) void susceptibility pattern (see track pattern) network 221 magnetic _ 231 pre-etching of _s 255 probability 173-182 wave suspensions (see microparticles in amplitude 258 fluids) recorder 8-13 response function 134-138 elastic 76 symbols phase 258 list of _ 268 sensitization 137-138 shape (see track shape) wavelength synchrotron accelerator 26, 34-35 single-ion _ 3,167-169,177, De Broglie _ 160 synergism 183-210 weak link shapes 210 magnetic moment _ 232 size observation 166 x ray topography 162 target 39 structure 167-182 theory 120-122 terminology 9 temperature track detector (see track recorder) compensation _ 243 track etching 147, 247 texture Probability and Heat

Fundamentals of Thermostatistics by Friedrich Schlagl

1989. XII, 249 pp. with 52 figs. Hardcover OM 98,- ISBN 3-528-06343-2

Contents: General Statistics: Probability, Information Measures, Generalized Canonical Distributions - Thermodynamics of Equilibria: Thermal States, Statistical Foundations of the Macroscopic Scheme, The Phenomenological Framework, The Low Temperature Regime - Macroscopic Description of Special Systems: Gases and Solutions, Chemical Reactions, The Method of Cycle Processes - Microscopic Description of Special Systems: Thermal Equations of State, Specific Heat, Magnetism - Nonequilibria: Thermal Fluctuations, Nonequilibrium Dynamics, Linear Thermodynamics, A Model of Time Scale Separation.

(.. .) The aim of the author. 'to make things simpler and more transparent in statistical thermodynamics" is fully attained. (. . .) (.. .) This textbook can not be only recommended to graduate students, but also to all those who do research work in physics, physical chemistry, and even in the modelling of technical processes. Prof. Dr. Schirmer, Zeitschrift fUr physikalische Chemie 5/89

Dr. Dr. h. c. Friedrich Schlagl is Professor Emeritus for Theoreti• cal Physics at the Technical University Aachen (Rheinisch• Westfalische Technische Hochschule Aachen), FRG. Vieweg Verlag . Postfach 5829 . 0-6200 Wiesbaden 1 ...... ~eweg Festkorperprobleme Advances in Solid State Physics

Eine Buchreihe mit den Referaten des Fachausschusses Halbleiter der Deutschen Physi• kalischen Gesellschaft. The aim of the "Festkorperprobleme" ist to stimUlate the interest in modern problem in condensed matter physics covering fundamental and applied aspects, to show the state of the art of some examples, and to help the reader to find an approach to those topics and to the original literature.

Festkorperprobleme 29 Advances in Solid State Physics. Plenary Lectures of the Divisions Semiconductor Physics. Thin Films, Dynamics and Statistical Physics, of the German Physical Society (DPG), MU nster, April 3 to 7,1989. 1989. VIII, 345 pp. with 204 figs. Hardcover OM 168,- ISBN 3-528-08035-3 Die FrUhjahrstagung des Arbeitskreises Festkor• perphysik der Deutschen Physikalischen Gesell• schaft fand 1989 in MUnster statt. Der vorliegende Band 29 der Festkbrperprobleme enthalt eine Auswahl von Plenar- und Hauptvortragen dieser lime Konferenz, darunter auch die Vortrage der dies• jahrigen Trager des Walter-SchottkY-Preises zur Theorie quantenmechanisch koharenter dissipati• ver Systeme. Bei den Ubrigen Beitragen stehen Themen aus dem Bereich der Halbleiter- und der Oberflachenphysik im Vordergrund.

Vieweg Verlag . Postfach 5829 . D-6200 Wiesbaden 1 Vleweg