L-59 ON THE BULK MODULUS OF THE TRANSITION METALS J. FRIEDEL Physique des Solides, Université de Paris-Sud, 91405 Orsay, France and C. M. SAYERS Physics Department, Imperial College, London SW7 2BZ, U.K. (Re~u le 8 novembre 1977, revise le 6 janvier 1978, accepte le 9 janvier 1978) Résumé. 2014 L’effet des corrélations et de l’ordre magnétique sur le module de rigidité K des métaux 3d est discuté à partir d’un traitement de perturbation du second ordre des corrélations. Pour les éléments au milieu de la série, avec une faible densité d’états n(EF) au niveau de Fermi, l’ordre ferromagnétique, s’il existe, agit de concert avec les corrélations pour réduire K. Les éléments Fe, Co et Ni sont à la fin de la série 3d et ont de fortes valeurs de n(EF) dans l’état non magnétique. Pour ces éléments, l’effet du ferromagnétisme sur K est faible et peut augmenter K. Abstract. 2014 The effect of correlations and ferromagnetic order on the bulk modulus K of the 3d metals is discussed using a second order perturbation treatment of the correlation. For elements in the middle of the series with a low density of states n(EF) at the Fermi level, ferromagnetic order, if possible, acts together with correlation to reduce K. The ferromagnetic elements Fe, Co and Ni lie towards the end of the 3d series and have large values of n(EF) in the non-magnetic state. For these elements the effect of ferromagnetism on K is found to be small and may act to increase K. LE JOURNAL DE PHYSIQUE - LETTRES TOME 39, 15 FEVRIER 1978, Classification Physics Abstracts 62.20 In a previous letter [1] we discussed the effect of d-electron correlation on the atomic volume and bulk modulus of the transition metals, and found that correlations give an increase in atomic volume and a decrease in bulk modulus, the effect being greatest in the middle of the 3d series. The bulk modulus was evaluated at the atomic volume of the uncorre- lated system, and since dKldR is strongly negative in the transition metals, this underestimates the decrease in K due to correlations. At the atomic volume of the correlated system, the bulk modulus is given by the difference between this result and that of [ 1 ] having the following effect. (i) In terms of the bandwidth in the absence of correlations, W = Wo e-qRo, equation (1) may be written as where is the relative change in the Wigner-Seitz radius due to electron correlations. In contrast to the previous result, which gave a relative decrease in K of the same magnitude as the relative increase in the atomic volume, equation (2) predicts an anomaly in K about four times that in the atomic volume, in better agree- ment with the relative magnitudes deduced from a comparison of figures (1) and (2) of [1]. (ii) An expansion of equation (1) to first order in the change 6R in the Wigner-Seitz radius due to the onset of long range ferromagnetic order gives where, for the rectangular density of states, Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyslet:0197800390405900