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Lattice Dynamics of Transition Metals; Dynamique de Reseau des Metaux de Transition

Abstract

The frequency versus wave-vector v(q) dispersion relations for the normal modes of vibration of several body-centred cubic transition metal, crystals have been measured recently at room temperature. The dispersion curves for niobium, measured by Nakagawa and Woods, displayed some very unusual features, and the results could only be fitted by means of a Born-von Karman model if interactions out to very distant neighbours (beyond eighth) were included. Subsequent measurements on tantalum by Woods showed very similar results. This is not surprising since niobium and tantalum are in column V of the periodic table and many of their electronic properties are similar. Measurements of the dispersion curves of molybdenum by Woods and Chen and of tungsten by Chen and Brockhouse showed that although these metals, which are in column VI of the periodic table, had dispersion relations which were similar to each other, these dispersion relations were very different from those of the column V metals, niobium and tantalum. The gross features of the v(q) for molybdenum and tungsten were very nearly describable by a third neighbour axially-symmetric Born-von Karman force model, although several important features were not reproduced by this model. One of these features is a striking anomaly in  More>>
Authors:
Woods, A. D.B. [1] 
  1. Chalk River Nuclear Laboratories, Chalk River, ON (Canada)
Publication Date:
Apr 15, 1965
Product Type:
Conference
Report Number:
IAEA-SM-58/3
Resource Relation:
Conference: Symposium on Inelastic Scattering of Neutrons, Bombay (India), 15-19 Dec 1964; Other Information: 17 refs., 4 figs., 1 tab.; Related Information: In: Inelastic Scattering of Neutrons. Vol. I. Proceedings of the Symposium on Inelastic Scattering of Neutrons| 476 p.
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; AXIAL SYMMETRY; BCC LATTICES; DISPERSION RELATIONS; FERMI LEVEL; INTERACTIONS; LATTICE VIBRATIONS; MATHEMATICAL MODELS; MOLYBDENUM; NIOBIUM; PERIODIC SYSTEM; TANTALUM; TEMPERATURE RANGE 0273-0400 K; TUNGSTEN
OSTI ID:
22141792
Research Organizations:
International Atomic Energy Agency, Vienna (Austria)
Country of Origin:
IAEA
Language:
English
Other Identifying Numbers:
Other: ISSN 0074-1884; TRN: XA13M3358096393
Submitting Site:
INIS
Size:
page(s) 87-94
Announcement Date:
Oct 24, 2013

Citation Formats

Woods, A. D.B. Lattice Dynamics of Transition Metals; Dynamique de Reseau des Metaux de Transition. IAEA: N. p., 1965. Web.
Woods, A. D.B. Lattice Dynamics of Transition Metals; Dynamique de Reseau des Metaux de Transition. IAEA.
Woods, A. D.B. 1965. "Lattice Dynamics of Transition Metals; Dynamique de Reseau des Metaux de Transition." IAEA.
@misc{etde_22141792,
title = {Lattice Dynamics of Transition Metals; Dynamique de Reseau des Metaux de Transition}
author = {Woods, A. D.B.}
abstractNote = {The frequency versus wave-vector v(q) dispersion relations for the normal modes of vibration of several body-centred cubic transition metal, crystals have been measured recently at room temperature. The dispersion curves for niobium, measured by Nakagawa and Woods, displayed some very unusual features, and the results could only be fitted by means of a Born-von Karman model if interactions out to very distant neighbours (beyond eighth) were included. Subsequent measurements on tantalum by Woods showed very similar results. This is not surprising since niobium and tantalum are in column V of the periodic table and many of their electronic properties are similar. Measurements of the dispersion curves of molybdenum by Woods and Chen and of tungsten by Chen and Brockhouse showed that although these metals, which are in column VI of the periodic table, had dispersion relations which were similar to each other, these dispersion relations were very different from those of the column V metals, niobium and tantalum. The gross features of the v(q) for molybdenum and tungsten were very nearly describable by a third neighbour axially-symmetric Born-von Karman force model, although several important features were not reproduced by this model. One of these features is a striking anomaly in the [{zeta}{zeta}{zeta}] longitudinal (L) branch for molybdenum where the frequency changes from v = 6.3 x 10{sup 12} c/s at {zeta} = 0.92 to v= 5.5 x 10{sup 12} c/s at {zeta} = 1.0. If this and other observed features are Kohn anomalies, their positions are consistent with the dimensions of the Fermi suriace of the column V metals proposed by Lomer. Thus it is suggested that the striking differences between the dispersion relation for niobium and that for molybdenum (metals which are believed to have quite similar band structures) reflect differences in the Fermi energies and hence the Fermi surfaces for these materials. (author) [French] Les relations de dispersion v(q) (frequence- vecteur d'onde) pour les modes de vibration normaux de plusieurs cristaux de metaux de transition-a structure cubique centree ont fait recemment l'objet de mesures a la temperature ambiante. Les courbes de dispersion relatives au niobium, etablies par Nakagawa et Woods, presentent des particularites tres exceptionnelles et on n'a pu faire concorder les resultats obtenus avec la theorie a l'aide d'un modele Born et von Karman qu'en tenant compte des interactions englobant des voisins tres eloignes (au-dela du huitieme). En procedant ulterieurement a des mesures sur le tantale, Woods a obtenu des resultats tres semblables, ce qui n'est guere surprenant puisque le niobium et le tantale figurent dans la colonne V du tableau de la classification periodique et qu'ils possedent des proprietes electroniques analogues sous de nombreux rapports. Les courbes de dispersion etablies par Woods et Chen pour le molybdene et par Chen et Brockhouse pour le tungstene ont montre que si ces deux metaux qui figurent dans la colonne VI du tableau ont des relations de dispersion semblables l'une a l'autre, ces relations different sensiblement de celles des metaux de la colonne V, niobium et tantale. Les caracteristiques generales de la relation v(q) pour le molybdene et le tungstene peuvent etre decrites avec une grande precision au moyen d'un modele Born et von Karman de forces tenant compte d'une structure a symetrie axiale englobant le troisieme voisin, bien que plusieurs caracteristiques importantes ne soient pas reproduites par ce modele. Pour le molybdene, une de ces caracteristiques est une anomalie frappante de la branche (L) longitudinale [{zeta}{zeta}{zeta}] ou la frequence passe de v 6.3 x 10{sup 12} c/s pour {zeta} = 0.92 to v= 5.5 x 10{sup 12} c/s pour {zeta} = 1.0. Si cette caracteristique et d'autres, qui ont aussi ete observees, sont des anomalies de Kohn, leurs positions sont compatibles avec les dimensions de la surface de Fermi des metaux de la colonne V, proposees par Lomer. On peut donc supposer que les differences nettes entre relations de dispersion pour le niobium et pour le molybdene (metaux dont on admet qu'ils ont des structures de bandes tres semblables) correspondent a des differences dans les energies de Fermi et, partant, dans les isurfaces de Fermi de ces matieres. (author) [Spanish] La relacion de dispersion frecuencia/vector de onda v(q), correspondiente a los modos normales de vibracion de varios cristales cubicos de metales de transicion centrados en el cuerpo, se ha medido recientemente a temperatura ambiente. Las curvas de dispersion del niobio, medidas por Nakagawa y Woods, presentaban algunas particularidades verdaderamente insolitas, y los resultados solo podian ajustarse por medio de un modelo de Born-von Karman si se incluian las interacciones que alcancen hasta atomos vecinos muy distantes (mas alla del octavo). Las mediciones ulteriores realizadas en el tantalo por Woods dieron resultados analogos. Ello no es sorprendente, puesto que el niobio y el tantalo figuran en la columna V de la clasificacion periodica y muchas de sus propiedades electronicas son analogas. Las mediciones de las curvas de dispersion del molibdeno, efectuadas por Woods y Chen, y del volframio, por Chen y Brockhouse, mostraron que si bien estos metales, que figuran en la columna VI de la clasificacion periodica, presentan relaciones de dispersion comparables, estas difieren considerablemente de las correspondientes a metales de la columna V como el niobio y el tantalo. Las caracteristicas generales de v(q) correspondientes al molibdeno y al volframio se pudieron describir adecuadamente por medio de un modelo de fuerzas axialmente simetrico de Born-von Karman que alcanza hasta el tercer atomo vecino, aunque dicho modelo no refleja algunas particularidades importantes. Una de estas es una sorprendente anomalia en la rama longitudinal (L) [{zeta}{zeta}{zeta}] del molibdeno, en que la frecuencia varia de v = 6.3 x 10{sup 12} c/s para {zeta} = 0.92 to v= 5.5 x 10{sup 12} c/s para {zeta} = 1.0. Si estas y otras particularidades observadas son anomalias de Kohn, sus posiciones son compatibles con las dimensiones de la superficie de Fermi propuesta por Lomer para los metales de la columna V. Se formula la hipotesis de que las sorprendentes diferencias existentes entre la relacion de dispersion del niobio y la del molibdeno (metales que, segun se cree, poseen estructuras de banda muy semejantes) reflejan diferencias en las energias de Fermi y, por tanto, en las superficies de Fermi de estos materiales. (author) [Russian] Dispersionnoe sootnoshenie chastota/volnovoj vektor v(q) dlja obychnyh vidov kolebanij nekotoryh ob{sup e}mno-centrirovannyh kubicheskih kristallov perehodnyh metallov bylo nedavno izmereno pri komnatnoj temperature. Krivye dispersii dlja niobija, izmerennye Nakagovoj i Vudsom, projavili nekotorye ochen' neobychnye cherty, i rezul'taty mozhno bylo privesti v sootvetstvie tol'ko s pomoshh'ju modeli Born fon Karmana, esli vkljuchit' vzaimodejstvija s ochen' otdalennymi chlenami rjada dal'she vos'mogo. Posledujushhie izmerenija Vudsom tantala dali ochen' pohozhie rezul'taty. Jeto ne udivitel'no, poskol'ku niobij i tantal nahodjatsja v V gruppe periodicheskoj tablicy i mnogie iz ih jelektronnyh svojstv odinakovy. Izmerenija krivyh dispersij molibdena Vudsom i Chenom i vol'frama Chenom i Brok- hauzom pokazali, chto, hotja u jetih metallov, kotorye nahodjatsja v gruppe VI periodicheskoj tablicy, dispersionnye sootnoshenija javljajutsja analogichnymi, jeti dispersionnye sootnoshenija sil'no otlichajutsja ot dispersionnyh sootnoshenij dlja niobija i tantala, nahodjashhihsja v gruppe V. Osnovnye cherty u(q) dlja molibdena i vol'frama ochen' blizko opisyvajutsja tret'im chlenom rjada simmetrichnoj po osjam silovoj modeli Born-fon Karmana, hotja nekotorye vazhnye cherty ne vosproizvodjatsja jetoj model'ju. Odnoj iz takih chert javljaetsja razitel'naja anomalija v prodol'noj [{zeta}{zeta}{zeta}] vetvi (L) dlja molibdena, gde chastota izmenjaetsja ot v = 6.3 x 10{sup 12} c/s pri {zeta} = 0.92 to v= 5.5 x 10{sup 12} c/s pri {zeta} = 1.0. Esli jeta i drugie otmechennye cherty predstavljajut soboj anomalii Kona, to ih polozhenie sovmestimo s razmerami poverhnosti Fermi dlja metallov gruppy V, predlozhennymi Lomerom. Takim obrazom, predpolagaetsja, chto razitel'nye razlichija mezhdu dispersionnym sootnosheniem dlja niobija i dispersionnym sootnosheniem dlja molibdena (metally, kotorye, kak predpolagajut, imejut sovershenno odinakovye polosnye struktury) otrazhajut razlichija v velichine jenergii Fermi i sledovatel'no v velichine poverhnostej Fermi dlja jetih materialov. (author)}
place = {IAEA}
year = {1965}
month = {Apr}
}