The true low field Hall coefficient of pure aluminium at low temperatures

Barnard, Robert; Rahiem, A E E Abdel

doi:10.1088/0305-4608/10/12/013

Cited by 15 publications

(9 citation statements)

References 15 publications

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“…In addition to the enhanced values of the Hall coefficient, the RH against T curves of the slow-cooled samples also exhibit peaks below 30 K. This feature conforms to a prediction given by Barnard and Abdel Rahiem (1980), from an analysis of the low-field Hall effect in pure AI and some dilute alloys, that such peaks should normally always be observed in AI alloys, irrespective of the type of impurity, provided R H was less than about -1 x IO-" m3 C -l . The temperature of the peak T,, was shown to be given by the exmession …”

Section: P(k K') Is Proportional To It/p(r) V(r) @(R)lz It Follows supporting

confidence: 88%

“…In the QFM states, the Hall coefficients are characterised by being nearly independent of temperature with values very close to the free-electron value of -3.47 x lo-" m3 C-' appropriate to the three valence Table I electrons of AI (see Barnard and Abdel Rahiem 1980). The failure of Kohler's rule, which would otherwise give the same limiting value of the Hall coefficient RH at zero temperature, is due to the partial clustering mentioned earlier which has occurred in AI-522 PPM Ti (QFM) sending R H to a more negative value as is evident from the slowcooled samples.…”

Section: The Loiv-field Hall Coeflcientmentioning

confidence: 74%

“…These slow-cooled AI-Ti and AI-V alloys are the first examples of Hall coefficients of dilute AI alloys in which R H is less than the free-electron value of -3.5 x lo-" m3 C-'; all other defects so far investigated hold R H at higher values and, in the case of Ge and Cu in AI (Boning et a1 1975, Papastaikoudis et a1 1979, R H is actually positive. The slow-cooled samples both show low-temperature peaks in RH, a rather important feature because the theory given by Barnard and Abdel Rahiem (1980) predicted that such peaks should normally occur in any alloy provided R H was less than about -1 x IO-'' m3 C-I. Their failure to appear in the QFM alloys will be discussed later.…”

Section: The Loiv-field Hall Coeflcientmentioning

confidence: 87%

“…Our discussion of the results will be based on the three-group model of Kesternich (1976) and its development for application to the temperature dependence of the low-field Hall coefficient (Barnard and Abdel Rahiem 1980) and resistivity (Barnard 1980) of pure aluminium.…”

Section: R D Barriardmentioning

confidence: 99%

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Michael's theory of continuous selections. Development and applications

Repovš¹,

Semenov²

1994

Russ. Math. Surv.

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A study has been made of the residual resistivity and magnetoresistivity at 4.2 K, the Hall coefficient between 4.2 and 7 7 K and the deviation from Matthiessen's rule at 7 7 K in AI-210 PPM Ti and AI-522 PPM Ti in both the slow-cooled condition and when quenched from the melt. It is shown that in the slow-cooled state, clustering/precipitation of solute atoms occurs creating electron scattering entities which. while appearing to behave like point defects. nevertheless possess a scattering anisotropy entirely different from conventional point defects. As a result these clusters produce considerably enhanced deviations from Matthiessen's rule, Hall and magnetoresistance coefficients. Values of the anisotropy in the mean free paths are calculated using a three-group model and a simple clustering model is invoked which demonstrates why the scattering becomes more 'interstitial' ill the clustered alloys. This leads to a scattering anisotropy for which the mean free path of electrons in the third zone becomes greater than that for holes in the corners of the second zone.

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Section: P(k K') Is Proportional To It/p(r) V(r) @(R)lz It Follows supporting

confidence: 88%

Section: The Loiv-field Hall Coeflcientmentioning

confidence: 74%

Section: The Loiv-field Hall Coeflcientmentioning

confidence: 87%

Section: R D Barriardmentioning

confidence: 99%

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Michael's theory of continuous selections. Development and applications

Repovš¹,

Semenov²

1994

Russ. Math. Surv.

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“…1. The case of dislocations in Ag is not well explained by the two group expression at low temperatures although it gives excellent agreement a t high temperatures (Goodarz and Barnard [ 171) where the isotropisation of the electron-phonon scattering makes the (pa ) z term of (12) rather large. However it is difficult to escape from the conclusion that the three separate @T versus log Po curves shown in Fig.…”

Section: Deviations From Matthiessen's Rule In Alloysmentioning

confidence: 99%

Some Remarks on Deviations from Matthiessen's Rule in Dilute Alloy Systems

Barnard

1981

Physica Status Solidi (b)

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An examination is made of the main features of deviations from Matthiessen's rule in alloy systems from a general standpoint based on anisotropy in the electron-phonon and electron-impurity scattering. It is shown that in virtually all metals a t low temperatures, a T 3 or near T3 contribution to the electron-phonon inverse relaxation time exists due to the geometry of the Fermi surface or from U processes which produce large angle scattering. As a result, such metals a t low temperatures will possess considerable anisotropy in the electron-phonon mean free paths associated with the transport properties, which arises purely from the geometry of the transitions. It is further shown that the usually small high curvature regions of the Fermi surface which produce the anisotropy, while not making a large contribution to the resistivity of the intrinsically pure metal, however are of paramount importance when impurity scattering dominates and results in near T3 variations of the temperature dependent resistivity, eT. Such variations appear to be obeyed almost universally in alloys for which eo >@In. The role of anisotropy in the mean free paths due to gold and dislocations as scattering centres in the silver system is discussed in connection with their failure to adhere to the universal curve of er versus log co for silver.Es werden die hauptsachlichen Merkmale der Abweichungen von der Matthiessenschen Regel in Legierungssystemen vom allgemeinen Standpunkt aus durchgefuhrt, die auf der Anisotropie der Elektron-Phonon-und Elektron-Storstellen-Streuung beruht. E s wird gezeigt, daS tatsgchlich in allen Metallen bei tiefen Temperaturen ein T3-oder nahezu T3-Beitrag zur inversen ElektronPhonon-Relaxationszeit existiert, der von der Geometrie der Fermiflache oder von U-Prozessen, die GroDwinkelstreuung produzieren, herriihrt. Als Ergebnis besitzen solche Metalle bei tiefen Temperaturen eine betrachtliche Anisotropie in der mit den Transporteigenschaften verbundenen mittleren freien Elektron-Phonon-Weglange, die vollstandig aus der Geometrie der tfbergange herruhrt. Es wird weiter gezeigt, daD die ublichen geringen stark gekrummten Bereiche der FermiflBche, die die Anisotropie hervorrufen, obwohl sie keinen grolen Beitrag zum Widerstand des intrinsisch reinen Metalls liefern, von hochster Wichtigkeit sind, wenn Storstellenstreuung dominiert und sich in der nahezu T3-Anderung des temperaturabhangigen Widerstands, eT LuDert. Solche Anderungen scheinen fast universe11 in Legierungen zu existieren, fur die eo >>@ID gilt.Die Rolle der Anisotropie in den mittleren freien Weglangen infolge von Gold und Versetzungen als Streuzentren im Silbersystem wird in Verbindung mit ihrem Versagen, die universelle Kurve von p r uber log eo fur Silber zu befolgen, diskutiert.

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