HREM examination of [101] screw dislocations in Ni3Al

Abstract

The dissociation of [101] screw dislocations in Ni³Al has been examined using high-resolution electron microscopy. [101] superdislocations are found to be dissociated into (a/2)[101] superpartial dislocations on the (010) cube cross-slip plane. These superpartials in turn dissociate into complex stacking faults on the (111) or (111) which are bounded by Shockley partials in agreement with theoretical predictions. The degree of antiphase boundary spreading on (010) was found to increase with deformation temperature while the superpartial core dissociations remain unchanged.     

Algebraic Functions

Let A be an algebra. We say that the functions f ₁, . . . , f _m : A ⁿ ?? A are algebraic on A provided there is a finite system of term-equalities ${{\bigwedge t_{k}(\overline{x}, \overline{z}) = s_{k}(\overline{x}, \overline{z})}}$ satisfying that for each ${{\overline{a} \in A^{n}}}$ , the m-tuple ${{(f_{1}(\overline{a}), \ldots , f_{m}(\overline{a}))}}$ is the unique solution in A ^m to the system ${{\bigwedge t_{k}(\overline{a}, \overline{z}) = s_{k}(\overline{a}, \overline{z})}}$ . In this work we present a collection of general tools for the study of algebraic functions, and apply them to obtain characterizations for algebraic functions on distributive lattices, Stone algebras, finite abelian groups and vector spaces, among other well known algebraic structures.     

Dislocations in indented Ga0·7 Al0·3As

Abstract

Transmission electron microscope observations have been made of dislocations in Ga_0·7Al_0·3As after indentation of (001) surfaces at room temperature. Using two-beam imaging, in bright-field and weak-beam imaging, dissociated dislocations with extended stacking faults were observed both in the [110] and [110] directions. This is different from GaAs in which dissociated dislocations are seen in only one of these directions. These results are compared with published work on indented GaAs and considered in the light of possible mechanisms.     

Resolution of Algebraic Systems of Equations in the Variety of Cyclic Post Algebras

There is a constructive method to define a structure of simple k-cyclic Post algebra of order p, L _p,k , on a given finite field F(p ^k ), and conversely. There exists an interpretation ??₁ of the variety ${\mathcal{V}(L_{p,k})}$ generated by L _p,k into the variety ${\mathcal{V}(F(p^k))}$ generated by F(p ^k ) and an interpretation ??₂ of ${\mathcal{V}(F(p^k))}$ into ${\mathcal{V}(L_{p,k})}$ such that ??₂??₁(B) =  B for every ${B \in \mathcal{V}(L_{p,k})}$ and ??₁??₂(R) =  R for every ${R \in \mathcal{V}(F(p^k))}$ . In this paper we show how we can solve an algebraic system of equations over an arbitrary cyclic Post algebra of order p, p prime, using the above interpretation, Gröbner bases and algorithms programmed in Maple.     

Cathodoluminescence-mode imaging of dislocations in zinc oxide

Abstract

The cathodoluminescence mode in the scanning electron microscope has been used to image bands of dislocations in zinc oxide. It has been shown that dislocations lying on pyramidal, {1012}, planes are generated beneath indentations on {0001} surfaces. Basal plane dislocations lying parallel to the surface are also observed. Indentations on {1100} prismatic surfaces result in slip on {0001} and {0110} planes.     

Characterisation of magnesium oxide and its interface with α-Mg in Mg–Al-based alloys

Magnesium oxide (MgO) films and particles have been collected by pressurised filtration of a Mg-8.6wt%Al-0.67wt%Zn (AZ91D) alloy melt. The morphology of the oxides and their interfaces with the α-Mg phase were investigated by high-resolution transmission electron microscopy. It was found that the oxide films consisted of large numbers of sub-micrometre-sized MgO particles, and that melt shearing can effectively break up the oxide films and disperse the oxide particles. For the first time, orientation relationships (ORs) of OR I: [1?1?1]_MgO～2° from (0?0?0?1)_α-Mg and (0?1?1)_MgO?//[2?1?1?0)_α-Mg; and OR II: (1?1?1)_MgO//(1?1?0?1)_α-Mg and [0?1?1]_MgO//[1?2?1?1]_α-Mg, were observed between the MgO particles and the α-Mg matrix. The calculated Bramfitt planar disregistries were 5.5% and 2.5% for the two ORs, respectively, indicating good lattice matching between MgO and α-Mg at the interface. With the evidence of grain refinement effect observed in the sheared AZ91D magnesium alloy, the possibility of MgO particles to act as potent nucleants for heterogeneous nucleation of α-Mg grains is discussed in terms of the crystallographic criterion.     

Inversion domain boundary in a ZnO film

Transmission electron microscopy has been used to investigate the (1100) and (1103) inversion domain boundaries in a ZnO film prepared by molecular beam epitaxy. The inversion domain was revealed by dark-field images and confirmed by convergent-beam electron diffraction. Interacting with a (0002) stacking fault, the inversion domain boundary in the (1100) plane alters its orientation from the [0001] direction and climbs on the (1103) plane to release the strain energy. These features are characterized and analysed by high-resolution electron microscopy and the geometric phase method. The findings are significant for understanding the formation and propagation of inverse domain boundaries in epitaxial ZnO films.     

Propositional Reasoning that Tracks Probabilistic Reasoning

This paper concerns the extent to which uncertain propositional reasoning can track probabilistic reasoning, and addresses kinematic problems that extend the familiar Lottery paradox. An acceptance rule assigns to each Bayesian credal state p a propositional belief revision method ${\sf B}_{p}$ , which specifies an initial belief state ${\sf B}_{p}(\top)$ that is revised to the new propositional belief state ${\sf B}(E)$ upon receipt of information E. An acceptance rule tracks Bayesian conditioning when ${\sf B}_{p}(E) = {\sf B}_{p|_{E}}(\top)$ , for every E such that p(E)?>?0; namely, when acceptance by propositional belief revision equals Bayesian conditioning followed by acceptance. Standard proposals for uncertain acceptance and belief revision do not track Bayesian conditioning. The ??Lockean?? rule that accepts propositions above a probability threshold is subject to the familiar lottery paradox (Kyburg 1961), and we show that it is also subject to new and more stubborn paradoxes when the tracking property is taken into account. Moreover, we show that the familiar AGM approach to belief revision (Harper, Synthese 30(1?C2):221?C262, 1975; Alchourrón et al., J Symb Log 50:510?C530, 1985) cannot be realized in a sensible way by any uncertain acceptance rule that tracks Bayesian conditioning. Finally, we present a plausible, alternative approach that tracks Bayesian conditioning and avoids all of the paradoxes. It combines an odds-based acceptance rule proposed originally by Levi (1996) with a non-AGM belief revision method proposed originally by Shoham (1987).     

Bohrification of operator algebras and quantum logic

Following Birkhoff and von Neumann, quantum logic has traditionally been based on the lattice of closed linear subspaces of some Hilbert space, or, more generally, on the lattice of projections in a von Neumann algebra A. Unfortunately, the logical interpretation of these lattices is impaired by their nondistributivity and by various other problems. We show that a possible resolution of these difficulties, suggested by the ideas of Bohr, emerges if instead of single projections one considers elementary propositions to be families of projections indexed by a partially ordered set ${\mathcal{C}(A)}$ of appropriate commutative subalgebras of A. In fact, to achieve both maximal generality and ease of use within topos theory, we assume that A is a so-called Rickart C*-algebra and that ${\mathcal{C}(A)}$ consists of all unital commutative Rickart C*-subalgebras of A. Such families of projections form a Heyting algebra in a natural way, so that the associated propositional logic is intuitionistic: distributivity is recovered at the expense of the law of the excluded middle. Subsequently, generalizing an earlier computation for n × n matrices, we prove that the Heyting algebra thus associated to A arises as a basis for the internal Gelfand spectrum (in the sense of Banaschewski?CMulvey) of the ??Bohrification?? ${\underline A}$ of A, which is a commutative Rickart C*-algebra in the topos of functors from ${\mathcal{C}A}$ to the category of sets. We explain the relationship of this construction to partial Boolean algebras and Bruns?CLakser completions. Finally, we establish a connection between probability measures on the lattice of projections on a Hilbert space H and probability valuations on the internal Gelfand spectrum of ${\underline A}$ for A?=?B(H).     

X-ray study of phason strain in Al-based quasicrystals

Abstract

X-ray powder diffraction spectra have been measured for melt-spun Al-Si–Mn, Al-Cu–Fe and Al-Li–Cu and Bridgman-grown Al-Li-Cu quasicrystals to investigate the phason strain frozen during the solidification process. For the melt-spun samples, most of the peaks have a shoulder or a tail which is attributed to the anisotropic linear phason strain. The peak shapes for the three melt-spun samples are essentially the same, which indicate that the same type of linear phason is quenched in these samples. In contrast, symmetric peak shapes without shoulders nor tails are seen for the Bridgman-grown Al-Li–Cu, indicating that it contains little linear phason strain.

Our findings are discussed with respect to the three linear phason models which can be derived by degradation of the symmetry from ideal icosahedral group m35 to its maximal subgroups 3m, m3 and 5m. Of these three, the model for 3m reproduces best the observed shapes and widths of the peaks.     

Analytic Calculi for Circular Concepts by Finite Revision

The paper introduces Hilbert– and Gentzen-style calculi which correspond to systems ${\mathsf{C}_{n}}$ from Gupta and Belnap [3]. Systems ${\mathsf{C}_{n}}$ were shown to be sound and complete with respect to the semantics of finite revision. Here, it is shown that Gentzen-style systems ${\mathsf{GC}_{n}}$ admit a syntactic proof of cut elimination. As a consequence, it follows that they are consistent.     

Precipitate characteristics and selected area diffraction patterns of the β′ and Q′ precipitates in Al–Mg–Si–Cu alloys

In this study, the precipitate characteristics and selected area diffraction patterns (SADP) of the β?′ and Q?′ precipitates formed at the over-aged state of Al–Mg–Si–Cu alloys are systematically investigated by means of high-resolution transmission electron microscopy and transition matrix. The β?′ precipitates have two cross-sections, rectangle-shaped and round-shaped aligned with [0?0?1]_Al direction, but only rectangle-shaped cross-section exists for Q?′ precipitates. And, both of them have 12 variants and orientations with Al matrix. However, there are only three different zone axes, [0?0?0?1]_β?′, [1?4?5?0]_β?′, and [5?4?1?0]_β?′ for β?′ precipitates, and [0?0?0?1]_Q?′, [1?4?5?0]_Q?′, and [3?2 1?0]_Q?′ for Q?′ precipitates, parallel to the [0?0?1]_Al direction when they are precipitated from the Al matrix, respectively. Then, a new [0?0?1]_Al SADP model, which superposes diffraction patterns of the β?′ and Q?′ precipitates, is established. Furthermore, some “cross-shaped” diffraction streaks appeared at over-aged state can be explained reasonably by this model, which is good in agreement with the experimental data.     

Finite axiomatization for some intermediate logics

LetN. be the set of all natural numbers (except zero), and letD _n ^* = {k ∈N ∶k|n} ∪ {0} wherek¦n if and only ifn=k.x f or somex∈N. Then, an ordered setD _n ^* = 〈D _n ^* , ? _n , wherex? _ny iffx¦y for anyx, y∈D _n ^* , can easily be seen to be a pseudo-boolean algebra. In [5], V.A. Jankov has proved that the class of algebras {D _n ^* ∶n∈B}, whereB =,{k ∈N∶ ? \(\mathop \exists \limits_{n \in N} \) (n > 1 ≧n ² k)is finitely axiomatizable. The present paper aims at showing that the class of all algebras {D _n ^* ∶n∈B} is also finitely axiomatizable. First, we prove that an intermediate logic defined as follows: $$LD = Cn(INT \cup \{ p_3 \vee [p_3 \to (p_1 \to p_2 ) \vee (p_2 \to p_1 )]\} )$$ finitely approximatizable. Then, defining, after Kripke, a model as a non-empty ordered setH = 〈K, ?〉, and making use of the set of formulas true in this model, we show that any finite strongly compact pseudo-boolean algebra ? is identical with. the set of formulas true in the Kripke modelH _B = 〈P(?), ?〉 (whereP(?) stands for the family of all prime filters in the algebra ?). Furthermore, the concept of a structure of divisors is defined, and the structure is shown to beH D _n ^* = 〈P (D _n ^* ), ?〉for anyn∈N. Finally, it is proved that for any strongly compact pseudo-boolean algebraU satisfying the axiomp ₃∨ [p ₃→(p₁→p₂)∨(p₂→p₁)] there is a structure of divisorsD _* ⁿ such that it is possible to define a strong homomorphism froomiH D _n ^* ontoH D _U . Exploiting, among others, this property, it turns out to be relatively easy to show that \(LD = \mathop \cap \limits_{n \in N} E(\mathfrak{D}_n^* )\) .     

Dependence and Independence

We introduce an atomic formula ${\vec{y} \bot_{\vec{x}}\vec{z}}$ intuitively saying that the variables ${\vec{y}}$ are independent from the variables ${\vec{z}}$ if the variables ${\vec{x}}$ are kept constant. We contrast this with dependence logic ${\mathcal{D}}$ based on the atomic formula = ${(\vec{x}, \vec{y})}$ , actually equivalent to ${\vec{y} \bot_{\vec{x}}\vec{y}}$ , saying that the variables ${\vec{y}}$ are totally determined by the variables ${\vec{x}}$ . We show that ${\vec{y} \bot_{\vec{x}}\vec{z}}$ gives rise to a natural logic capable of formalizing basic intuitions about independence and dependence. We show that ${\vec{y} \bot_{\vec{x}}\vec{z}}$ can be used to give partially ordered quantifiers and IF-logic an alternative interpretation without some of the shortcomings related to so called signaling that interpretations using = ${(\vec{x}, \vec{y})}$ have.     

Book reviews and books received

Counselling as a Career Ross, R, 1997 Oxford: Baldrick Press ISBN 0-9530477-0-9 £9-95

Which Psychotherapy?: Leading Exponents Explain their Differences Feltham, C. (Ed.), 1997 London: Sage ISBN 0-8039-7479-5 £12.95

An Introduction to Existential Psychotherapy Cohn, H. W., 1997 London: Sage ISBN 0-7619-5-109 £11.99

Therapeutic Work with Children and Young People Copley, B. & Forryan, B., 1997 London: Cassell ISBN 0-304-70010-X (hb); 0-304-70011-8 (pb) £16.99

Counselling in Terminal Care and Bereavement Parkes, C. M., Relf, M. & Couldrick, A., 1996 Leicester: British Psychological Society ISBN 1-85433-178-7 £14.99

The Gains of Listening Feltham, C., 1997 Buckingham: Open University Press ISBN 0-335-19280-7 £18.99     

Sequent Calculi for Semi-De Morgan and De Morgan Algebras

A contraction-free and cut-free sequent calculus \(\mathsf {G3SDM}\) for semi-De Morgan algebras, and a structural-rule-free and single-succedent sequent calculus \(\mathsf {G3DM}\) for De Morgan algebras are developed. The cut rule is admissible in both sequent calculi. Both calculi enjoy the decidability and Craig interpolation. The sequent calculi are applied to prove some embedding theorems: \(\mathsf {G3DM}\) is embedded into \(\mathsf {G3SDM}\) via Gödel–Gentzen translation. \(\mathsf {G3DM}\) is embedded into a sequent calculus for classical propositional logic. \(\mathsf {G3SDM}\) is embedded into the sequent calculus \(\mathsf {G3ip}\) for intuitionistic propositional logic.     

Book reviews and books received

Paradox and Passion in Psychotherapy van Deurzen, E., 1998 Chichester: Wiley Isbn 0-471-97390-4 £14.95

Witness and Vision of the Therapists Feltham, C. (Ed.), 1998 London: Sage ISBN 0-7619-5158-X £13.99

Are You Sitting Uncomfortably?: Windy Dryden Live and Uncut Dryden, W., 1998 Ross-on-Wye: PCCS Books ISBN 1-898059-18-7 £10.50 (discounts for buying direct)

The Integrative Power of Cognitive Therapy Alford, B.A. & Beck, A.T., 1997 New York: Guilford Press ISBN 1-57230-171-6 £11.95

Psychotherapy Counselling and Mental Health Care: Assessment for Brief or Longer-Term Treatment Burton, M., 1998 Chichester: Wiley ISBN 0-471-98228-8 £17.99

Career Counselling: a Narrative Approach Cochran, L., 1997 London: Sage ISBN 0-7619-0442-5 £14.99

Telling Tales: Perspectives on Guidance and Counselling in Learning Edwards, R., Harrison, R. & Tait, A.I. (Eds), 1998 London: Routledge ISBN 0-415-19443-1 £14.99

Taking Issue: Debates in Guidance and Counselling in Learning Crawford, M., Edwards, R. & Kydd, L. (Eds), 1998 London: Routledge ISBN 0-415-19667-1 £14.99     

Book reviews

One Thousand Roads to Mecca. Michael Wolfe (Ed.), 1997. New York, Grove Press. 620 pp., hb. $32.50, ISBN 0 8021 1611 6

Early Mamluk Syrian Historiography: Al‐Yunini's Dhayl Mir'at al‐zaman. Li Guo, 1998. Leiden, E.J. Brill. 2 vols, 241 pp. and xv + 338 pp. Arabic, hb. n.p., ISBN 90 04 11028 3 and 90 04 11029 1

Defenders of Reason in Islam: Mu'tazilism from medieval school to modern symbol. Richard C. Martin & Mark R. Woodward with Dwi S. Atmaja, 1997. Oxford, Oneworld Publications. xv+ 251 pp., pb. £14.99/$22.95, ISBN 1 85168 147 7

Rethinking Tradition in Modern Islamic Thought. Daniel Brown, 1996. Cambridge Middle East Studies 5. Cambridge, Cambridge University Press. x+ 185 pp., hb. n.p., ISBN 0 521 57077 8

Ebu's su'ud, the Islamic Legal Tradition. Colin Imber, 1997. Edinburgh, Edinburgh University Press. 288 pp., hb. £40.00, ISBN 07486 0767 6

Islam and the West: the making of an Image. Norman Daniel, 1997 (1993). Oxford, Oneworld. 467 pp., pb. $25.95/£16.99, ISBN I 85168 129 8

Exegesis as Polemical Discourse: Ibn Hazm on Jewish and Christian Scriptures. Theodore Pulcini, 1998. Atlanta, GA, Scholars Press. 216 pp., hb. $44.95, ISBN 0 7885 0396 0; pb. $19.95, ISBN 0 7885 0395 2

Christians and Jews under Islam. Youssef Courbage & Philippe Fargues, trans. Judy Mabro, 1997. London and New York, I.B. Tauris. xii + 242 pp., hb. £39.50, ISBN 1 86064 013 3

The Construction of Nationhood: ethnicity, religion and nationhood. Adrian Hastings, 1997. Cambridge, Cambridge University Press. 235 pp., pb. £12.95, ISBN 0 521 62544 0

Muslim Identity and Balkan State. Hugh Poulton & Suha Taji‐Farouki (Eds), 1997. London, Hurst & Co.. 250 pp., hb. n.p., ISBN 1 85065 276 7; pb. n.p., ISBN 1 85065 348 8

Turkish and Other Muslim Minorities of Bulgaria. Ali Eminov, 1997. London, Hurst & Co.. 218 pp., hb. £25, ISBN 1 85065 319 4

Al‐yahūd fi misr min al‐fath al‐'uthmani hatta awa'il al‐qarn al‐tas’ ‘ashar. [History of the Jewish Community in Egypt from the Ottoman Invasion to the. Beginning of the Nineteenth Century] (Arabic). Mohsen Shouman, 1996. Cairo, privately printed (available from the author, Department of History, College of. Arts, University of Zaqaziq, Egypt). 492 pp., n.p., no ISBN

The Society of the Muslim Brothers in Egypt: the rise of an Islamic mass movement 1928–1942. Brynjar Lia, 1998. Reading, Ithaca. 272 pp., hb, £30.00, ISBN 0 86372 220 2

African Islam and Islam in Africa: encounters between Sufis and Islamists. David Westerlund & Eva Evers Rosander (Eds), 1997. London, Hurst & Co.. 347 pp., hb. £40, ISBN 85065 282 1; pb. £15.95, ISBN 1 85065 281 3

Transforming Female Identities: women's organizational forms in West Africa/Transformation des identités feminines: formes d'organisations feminines en Afrique de l'Ouest. Eva Evers Rosander (Ed.), 1997. Uppsala, Nordiska Afrikainstitutet 243 pp., pb. £18.95, ISBN 91 7106 403 6

The Pure and the Powerful. Nadia Abu‐Zahra, 1977. Reading, Ithaca, NY. xx+ 320 pp., hb. £35.00, ISBN 0 86372 179 6