# The invar problem - solved

Saunders, G.A. (1993) The invar problem - solved. Accademia Peloritana dei Pericolanti, Classe di Scienze FF. MM. NN., LXXI. pp. 29-52.

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## Abstract

Despite intensive efforts the microscopic origin of the Invar effects and their relationship to magnetoelasticity in ferromagnetic and antiferromagnetic alloys has long remained an issue of controversial debate. However a fundamental understanding of the long-standing Invar problem has recently been achieved. Total-energy band calculations, using a fixed-spin-moment procedure, have confirmed that two different states of iron are involved: a low-spin (LS) solution centred at low volume and high-spin (HS) solution at high volume. For ferromagnetic Invar alloys the ground-state is defined at low temperature by the HS solution and high temperatures by the LS solution. A crossover accounts for the behaviour of the thermal and elsatic properties, which are determined at low temperature by the HS state and at high temperature by the LS state. Since the LS state has a smaller volume there is a pause in volume as Invar is warmed up through the crossover temperature, causing a pause in the thermal expansion while the thermal population of the low volume LS state increases. Measurements of the temperature dependences of the hydrostatic pressure derivatives of the velocities of ultrasonic waves propagated in signle crystals of the Invar $Fe_7_2Pt_2_8$ have shown that the negative thermal expansion in the ferromagnetic phase of these alloys is directly associated with longitudinal ultrasonic waves propagated along the [100] and [110] directions in $Fe_7_2Pt_2_8$ decrease strongly with pressure; thus $( \partial \ C_1_1/ \partial \ P)_P_=_0, ( \partial \ C_L/ \partial \ P)_P_=_0$ and $( \partial \ B^S/ \partial \ P)_P_=_0$ are negative due to the magnetoelastic interaction. This alloy ahows the extraordinary property of becoming easier to compress as pressure is increased. The negative signs of $( \partial \ C_1_1/ \partial \ P)_P_=_0$ and $( \partial \ C_L/ \partial \ P)_P_=_0$ give rise to negative values for all the longitudinal and quasilongitudinal acoustic mode Grunesien parameters in the ferromagnetic phase, accounting for the behaviour of the thermal expansion which is negative in the temperature range between about 260K and the Curie temperature. The source of the Invar behaviour is longitudinal acoustic mode softening, a lattice dynamical mechanism in accord with the HS-LS theory.

Item Type: Article M.U.S. - Miscellanea > Atti Accademia Peloritana > Classe di Scienze Fisiche, Matematiche e Naturali > 1993M.U.S. - Miscellanea > Atti Accademia Peloritana > Classe di Scienze Medico-Biologiche > 1993M.U.S. - Miscellanea > Atti Accademia Peloritana > Classe di Scienze Giuridiche, Economiche e Politiche > 1993M.U.S. - Miscellanea > Atti Accademia Peloritana > Classe di Lettere, Filosofia e belle Arti > 1993 Dr A F 20 Sep 2012 11:41 20 Sep 2012 11:41 http://cab.unime.it/mus/id/eprint/706