Ionic conduction in space charge regions

The diffusion coefficients of several transition elements (Ti, V, Cr, Mn, Fe, Co, Ni, Cu, and Zn) and a few non-transition elements (Mg, Si, Ga, and Ge) in fcc and liquid Al are critically reviewed and assessed by means of the least-squares method and semi-empirical correlations. Inconsistent experimental data are identified and ruled out. In the case of the elements, for which plentiful experimental data are available in the literature, the least-squares analysis gives rise to the activation energies and pre-exponential factors in an Arrhenius equation. For the elements with limited experimental data or no data at all, the diffusion parameters are estimated from two semi-empirical correlations. In one correlation, the logarithmic pre-exponential factors are plotted against the activation energies for various elements in Al. In the other correlation, the activation energies are shown as a function of valences relative to Al. The diffusion coefficients calculated by using the evaluated diffusion parameters agree reasonably with the reliable experimental data. The proposed semi-empirical correlations are used to predict the diffusion coefficients of a few elements in liquid Al. A satisfactory agreement between the predicted and measured diffusion coefficients is obtained.

Diffusion coefficients of some solutes in fcc and liquid Al: critical evaluation and correlation

Massive charged particles create regions of intense damage (tracks) by passing through bulk samples of insulating materials. These tracks are shown to result from the positively charged region created by ionization. An approximate model of an ``ion explosion spike'' is proposed in which the mutual repulsion of the positive ions ejects them into the surrounding lattice. This model is shown to be generally consistent with a wide range of experimental fact. An additional damage mechanism appears to apply to polymers, in some of which tracks are produced by light projectiles such as α particles. The data here are shown to be consistent with tracks consisting primarily of broken bonds caused by decay of directly excited electrons.

Ion Explosion Spike Mechanism for Formation of Charged-Particle Tracks in Solids

We describe four criteria for the selection of alloying elements capable of producing castable, precipitation-strengthened Al alloys with high-temperature stability and strength: these alloying elements must (i) be capable of forming a suitable strengthening phase, (ii) show low solid solubility in Al, (iii) low diffusivity in Al, and (iv) retain the ability for the alloy to be conventionally solidified. With regard to criterion (i), we consider those systems forming Al3M trialuminide compounds with a cubic L12 crystal structure, which are chemically and structurally analogous to Ni3Al in the Ni-based superalloys. Eight elements, clustered in the same region of the periodic table, fulfill criterion (i): the first Group 3 transition metal (Sc), the three Group 4 transition metals (Ti, Zr, Hf) and the four latest lanthanide elements (Er, Tm, Yb, Lu). Based on a review of the existing literature, these elements are assessed in terms of criteria (ii) and (iii), which satisfy the need for a dispersion...

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Criteria for developing castable, creep-resistant aluminum-based alloys - A review

http://physlab.phys.uoa.gr/org/pdf/tecto91.pdf

Latest aspects of earthquake prediction in Greece based on seismic electric signals, II☆

Two aspects of defect interactions in AgCl and AgBr are discussed. 1 ) The establishment of equilibrium between charged jogs (on surfaccs and dislocations) and point defects produces surface charges. space charge regions, and local changes in electric potential and defect concentration. The locur and environment of the jogs play a large role iri dcterminiilg the nature of the space charge. For the silver halides, implications of these erects to the photographic process are discussed. The available information on the space charges at surfaces and dislocations in both AgBr and AgCl is surveyed ; it is seen that whereas it is energetically cheaper to produce an interstitial Ag ' than a vacancy at a surface jog, the opposite may be true at dislocations. 2) lnternal friction techniques have been used to study the binding of solutes to dislocations. In AgCI, the binding energy is approximately 0.2 eV. After a small perturbation of the Maxwcll atmosphere around the dislocation, the recovery follotvs a 0 ' 3 law ; a simple model yields this dependence, and also the correct activation energy. Similar studies in AgBr. however, have revealed a strange regime in whicli the rate constant for recovery ha:, a negative activation energy, the magnitude and temperature range of the erect depending on concentration of dopant. N o sirnplc explanation is yet available. I . Introduction. T h e interactions of point defects with dislocations and surfaces a r e especially interesting in ionic crystals because these lattice imperfections and discontinuities a r e usually electrically charged. Thus, in addi t ion t o the interaction phenomena observed in metallic crystals, one finds for ionic systenis such effects as space charges and electric fields near surfaces a n d dislocations [I], [2], additional ionic conductivity [3] a n d dilrusion [4] in these space charge regions, the development of ~nacroscopic electric the influence of dislocauon charges o n a variety o f other physical properties [13]. O f these many phenomena, the present paper discusses the current s ta te of knowledge a b o u t only t w o such effects in crystalline silver chloride a n d silver bromide : a) the equilibrium between point defects a n d the jogs on dislocations a n d surfaces, with their accompanying space charges, a n d 6 ) t h e pinning o f dislocations by point defects. a s studied by internal friction techniques. potential dilrercilces upon inhornogeneous plastic deformation L ~ I L ~ J . a en~l;lllcement of. i o n i c 2. Charged surfaccs and dislocations. Electrical d u e to pl.odL,ction ,,(, i n i Li,,f-2ctj by c I l ; ~ r g e ~ on line and surface imperfections arise lnovil le dis~oc.ions 1 ~ 1 . se l l s i l i \\ . i t ) , s u r l , l c e ~ l ~ l l ~ l l e s s bcc:iuse their jogs can create o r annihilate separately to corllpnsil;oll of :if, iidj;lceot i o f l i r s i , j u l i o n j101. 11 11. eacll c o ~ n p o n e n t o f tile n;ltivc tllermal defect pair [I I , a n ofsurf;lcc clli,r,,c sLlhliminatioll (171, ilnd [?I. These Processes, and their compellsatinf >Pace charge region a n d local electric lielci, a re discus.icd by ( * ) Su red I,y N ; l r io r l a l Scicrlcc I c,,,,, darjo,, ((;,.i,,l, M,'liit\\\\orth in ano ther p:ipcr in thcse proceeding5 [14]. No. GI4 35794) . In the silver halides, the native defect is the cat ion Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1973943 Frenkel pair. The halide lattice can be considered to be virtually immobile and perfect, so that the equilibrium of significance to us is that between the jogs and the defects in the cation lattice silver vacancies, interstitial silver ions, and divalent cation impurities. For a pure crystal, the potential difference that is established between the surface and the deep interior is given by [15] Here, GI is the free energy required to create a vacancy from a jog, i. e., to remove a silver ion from an interior lattice site to a negatively charged jog, and is given by where G, is the free energy required to create the vacancy exclusive of configurational contributions and M is the ratio of the number of positively charged jogs to that of negative jogs ; the second term on the right-hand side is only important if the density of jogs is not large compared to the net charge density. Similarly, GI, the free energy required to create an interstitial by the removal of an Ag+ from a positively charged jog to an interstitial site in the interior, is given by The entropic contribution (kTln 2) arises because there are two interstitial sites per lattice point. The importance of G:. and G; is that their difference determines the signs and the magnitudes of the space charge distribution and of (p, : moreover, tlie fractional concentration of the ,;Ih defect at a depth s is given by exp { [Gi q j c p ( s ) ] / l i 7 ' ) , where (1 is the charge on the defect. Thus, i f i t is easier to create vacancies than interstitial silver ions from the jogs (i. e., G: GI < O), then the surface will be positively charged, and the compensating space charge will consist of an excess of vacancies. In such a case, if one adds divalent cation impurity to the crystal, thereby increasing the bulk vacancy concentration. ultimately the charge on the surface or dislocation must go through zero (this is called the isoelectric point) and become negative the space charge now consists of impurity cations and interstitial Ag'. On the other hand, if G:. GI > 0, then the surface is negatively charged, regardless of cation impurity. and there is no isoelectric point ; the space charge layer now will always contain an excess of interstitial silver ions. 0.15 to 0.3 V, this potential difference being accomplished over a depth of the order of 0. I ym. The average electric field in the space charge region is thus of the order of 2 x lo4 V/cm. Since the thickness of a typical grain in a photographic emulsion is only perhaps a few tenths of a micron, it is clear that most of the volume of the grain is in a region of intense field. This field will, for example, quickly extract from the interior of the grain the photohole produced by the primary photon absorption act, thereby decreasing the probability of recombination. In AgBr, the hole mobility at rooin temperature is 1 cmvV/s ; in a field of 2 x 10\" V/cm, the hole w~ll drift across a distance of 0.1 pin in 5 x s. By contrast, in the absence of a field, its diffusion time would be12/(kTLi/e) = 4 x lo-\" s, or ten times longer. This field will also, of course, influence the dynamics of the pl~otoelectron. One reason for the high sensitivity of photographic emulsions is that the majority of surface sites are ineffective as electron traps, so that successive pl~otoelectrol~s ultimately collect at just one or a few sites the so-called tr sensitivity specks )) thereby increasing the el-iiciency for production of the latent image. It is likely that i t is the negative potential at the surface that prevents all but the deepest surface traps from serving as sitcs for the formation of atomic silver. In support of this notion, Fatuzzo and Coppo [I61 Iiave found that Ag metal and AgzS are both at n positive potential when in contact with AgBr ; thus the sulfide sensitivity center and the silver latent image precursor would both provide electrostatic (( windows H in the otherwise repulsive surface layer. Lastly, a negatively charged surface will guarantee an enhanced concentration of interstitial silver ions in the layer just underneath it . This is consistent with the large ionic conductivities found i n small gr:lins of AgBtby Brady and Hamilton [17], and is most surely a n csseniial ingredient i n the eficicnl formation of surface latent image f~-om photoelectrons. 4. J o g equilibria. Although thc sum of G: and GI is required to equal G,, thc fl-cc energy of formation of the Frenkel pair in the bulk, the details as to how this total energy is divided into tlie vacancy and tlie interstitial components depend on thc properties of the jogs themselves, and thcir ambients. Call G I the free energy required to remove a lattice silver ion from the crystal to the vacuum, and G2 the free energ)? required to remove a n interstitial sil\\/er ion from the crystal; G , Gz = G,. Also. call G , the free energy required to remove a n Ag' -. 3. photographic implications. i t seems most from a positively charged jog to the vacuum. Then. likely that these surfilce potent ia l phenomena are of if \\Ye form point defects from such jogs, we must great importance in the functioning of the photogra: phic process [6]. I t will be seen below that the surf:rce Gi = G j G , , is generally negative, relative to the bulk, by about G, = G , Gi , INTERACTIONS OF POINT DEFECTS WITH DISLOCATIONS AND SURFACES C9-249

Interactions of point defects with dislocations and surfaces in silver halide crystals

A new technique for recording heavy primary cosmic radiation and nuclear processes has been developed through decoration of dislocations formed by these processes in large silver chloride single crystals. The crystals are prepared and exposed to cosmic radiation during high altitude balloon flights. The crystals are then treated according to the Haynes-Shockley photoelectric technique which results in silver collecting at the dislocations and thereby decorates the dislocations at room temperature within two hours. Since silver chloride is transparent to visible light, the decorated dislocations are observable with an optical microscope at a magnification of about 150-200. A one-to-one correspondence has been established between tracks in the crystals and those in photographic emulsions accompanying the crystals during balloon flights. Examples of heavy primary cosmic radiation and nuclear processes in crystals are shown.

A New Technique for Recording Heavy Primary Cosmic Radiation and Nuclear Processes in Silver Chloride Single Crystals

Luminescent recombination processes of the self-trapped hole in copper-doped silver chloride

Annealing of silver chloride crystals containing internal print-out

In ionic crystals, jogs on surfaces and dislocations act as sources and sinks for point defects. Establishment of equilibria with the vacancies, solute ions, and interstitials in the interior produces a net charge on the surface or dislocation, surrounded by a compensating space charge region. Within this space charge region, which typically has a thickness of the order of 10nm, there are very large electric fields (up to about 105 V/cm) and very large perturbations of point defect concentrations (by factors of several hundred). Thus, ion diffusivities can be dramatically perturbed. In addition, determination of the electric potential difference across the space charge region allows one to separate the formation enthalpies and entropies of Frenkel and Schottky defects into contributions from each component of the pair. Examples of such studies in the silver and alkali halides will be described.

Lawrence Slifkin

Papers

Interactions of point defects with dislocations and surfaces in silver halide crystals

A New Technique for Recording Heavy Primary Cosmic Radiation and Nuclear Processes in Silver Chloride Single Crystals

Luminescent recombination processes of the self-trapped hole in copper-doped silver chloride

Annealing of silver chloride crystals containing internal print-out

Surface and Dislocation Effects on Diffusion in Ionic Crystals