Magnetostriction volume

Notice here the uniaxial deformation, X 0, independent of the direction of the magnetisation, and the contribution to the volume magnetostriction, X 2, which does depend on the magnetisation direction. 

Fig. 73. Volume magnetostriction isotherms of Lao 6Yo.07Cao.33MnO- at selected temperatures. After Ibarra et...

Figure 15. Temperature variation of the maximum volume magnetostriction in Ndo.5SrojMn03 at 13.7T (from Mahendiian et al.21).

High-temperature slope of the thermal expansion (a, in K 1), total spontaneous volume magnetostriction at 4.2 K (us) and relative contributions to s of the 3d and 4f sublattices ( sd and usf) in various R2Fe)4B compounds. (After Buschow and Grossinger 1987.)... 

Fig. 34. Spontaneous volume magnetostriction as a function of temperature in various R2Fe14B compounds. The corresponding Curie temperatures are indicated by arrows. (After Buschow and...

The onset of ferromagnetism in this system has usually been interpreted in terms of an environmental model. Fe atoms which occupy Al sites are surrounded by 8 Fe nearest neighbours and it is suggested that the percolation of such atoms (with pFc = 2.2pB) on Al sites eventually gives rise to ferromagnetism. The critical concentration does not appear to be significantly different for the two conditions. The forced volume magnetostriction peaks at 4 X 10 9 Oe-1 at 70% Fe for... 

The magnetic phase diagram for the Co system is shown in fig. 25 and table 13 lists the important properties. The ferromagnetic alloys are regarded as itinerant because of the linearity of the Arrott plots over a wide range of temperature and also of the Mathon plots of M02 as a function of x (Hilscher and Kirchmayr 1975). Calculations of the density of states (Terao and Shimizu 1983) show that the itinerant-electron model gives a volume magnetostriction consistent with the experimental value (Muraoka et al. 1980, 1983). 

The results obtained for the compounds of the series Rj Fe 4C confirmed the results on the isotypic R2Fej4B compounds, showing that the spontaneous volume magnetostriction extends to temperatures substantially above in this type of ternary compounds. This observation lends credence to the view that the local iron moments in iron-based metallic materials do not disappear above (Holden et al. 1984),... 

Fig. 11. Shear modulus of Invar (Fe-36Ni), comparing pulse-echo and resonance results. The anomalous (positive-slope) behavior of this alloy is related to its large, positive volume magnetostriction. It can be explained by invoking Heisenberg-exchange-energy terms.

The exchange interactions are isotropic to first order. They describe a coupling between the magnetic moments and dominate the magnetic ordering in the materials. The variation of these interactions with the interatomic distance is the reason for a spontaneous deformation (i.e., the volume magnetostriction). 

Fig. 40. Scaling of the volume magnetostriction of (a) CeCug, and (b) mixed-phase CeCu Sij with H T + 0)] at different temperatures (Zieglow-ski et al. 1986). H is the applied magnetic field and 0 a characteristic temperature chosen to make all the isotherms coincide as well as possible. Large differences between superconducting and non-superconducting CeCujSij are found.

Fig. 4.3-33 (a) Schematic diagram of invar-type thermal-expansion anomaly. The dashed curve indicates thermal expansion for hypothetical paramagnetic state. The difference between the two curves corresponds to the spontaneous volume magnetostriction, ah. (b) Temperature dependence of the spontaneous magnetization... 

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