Rhombohedral magnetostriction in dilute iron (Co) alloys

Iron is a well-utilized material in structural and magnetic applications. This does not mean, however, that it is well understood, especially in the field of magnetostriction. In particular, the rhombohedral magnetostriction of iron, λ111 , is anomalous in two respects: it is negative in sign, in disagreement with the prediction of first principles theory, and its magnitude decreases with increasing temperature much too rapidly to be explained by a power law dependence on magnetization. These behaviors could arise from the location of the Fermi level, which leaves a small region of the majority 3d t2g states unfilled, possibly favoring small internal displacements that split these states. If this view is correct, adding small amounts of Co to Fe fills some of these states, and the value of λ111 should increase toward a positive value, as predicted for perfect bcc Fe. We have measured the magnetostriction coefficients (λ111 and λ100) of pure Fe, Fe97Co3, and Fe94Co6 single crystals from 77 K to 450 K. Resonant ultrasound spectroscopy has been used to check for anomalies in the associated elastic constants, c 44 and c′. The additional electrons provided by the cobalt atoms indeed produced positive contributions to bothmagnetostriction constants, λ111 and λ100, exhibiting an increase of 2.8 × 10−6 per at. % Co for λ111 and 3.8 × 10−6 per at. % Co for λ100

Tetragonal magnetostriction and magnetoelastic coupling in Fe-Al, Fe-Ga, Fe-Ge, Fe-Si, Fe-Ga-Al, and Fe-Ga-Ge alloys

This paper presents a comparative study on the tetragonal magnetostriction constant,λγ,2, [ = (3/2)λ100] and magnetoelastic coupling, b1, of binary Fe100-xZx (0 \u3c x \u3c 35, Z = Al, Ga, Ge, and Si) and ternary Fe-Ga-Al and Fe-Ga-Ge alloys. The quantities are corrected for magnetostrains due to sample geometry (the magnetostrictive form effect). Recently published elastic constant data along with magnetization measurements at both room temperature and 77 K make these corrections possible. The form effect correction lowers the magnetostriction by ∼10 ppm for high-modulus alloys and by as much as 30 ppm for low-modulus alloys. The elastic constants are also used to determine the values of the magnetoelastic coupling constant, b1. With the new magnetostriction data on the Fe-Al-Ga alloy, it is possible to show how the double peak magnetostriction feature of the binary Fe-Ga alloy flows into the single peak binary Fe-Al alloy. The corrected magnetostriction and magnetoelastic coupling data for the various alloys are also compared using the electron-per-atom ratio, e/a, as the common variable. The Hume-Rothery rules link thee/a ratio to the regions of phase stability, which appear to be intimately related to the magnetostriction versus the solute concentration curve in these alloys. Using e/a as the abscissa tends to align the peaks in the magnetostriction and magnetoelastic coupling for the Fe-Ga, Fe-Ge, Fe-Al, Fe-Ga-Al, and Fe-Ga-Ge alloys, but not for the Fe-Si alloys for which the larger atomic size difference may play a greater role in phase stabilization. Corrections for the form effect are also presented for the rhombohedral magnetostriction,λɛ,2, and the magnetoelastic coupling, b2, of Fe100-xGax (0 \u3c x \u3c 35) alloys

The Good, the Bad, and the Rare: Memory for Partners in Social Interactions

For cooperation to evolve via direct reciprocity, individuals must track their partners' behavior to avoid exploitation. With increasing size of the interaction group, however, memory becomes error prone. To decrease memory effort, people could categorize partners into types, distinguishing cooperators and cheaters. We explored two ways in which people might preferentially track one partner type: remember cheaters or remember the rare type in the population. We assigned participants to one of three interaction groups which differed in the proportion of computer partners' types (defectors rare, equal proportion, or cooperators rare). We extended research on both hypotheses in two ways. First, participants experienced their partners repeatedly by interacting in Prisoner's Dilemma games. Second, we tested categorization of partners as cooperators or defectors in memory tests after a short and long retention interval (10 min and 1 week). Participants remembered rare partner types better than they remembered common ones at both retention intervals. We propose that the flexibility of responding to the environment suggests an ecologically rational memory strategy in social interactions