Relation between Ga ordering and magnetostriction of Fe-Ga alloys studied by x-ray diffuse scattering

Transmission synchrotron diffraction was employed to characterize the Ga ordering in magnetostrictive ${\text{Fe}}_{100-x}{\text{Ga}}_x$ alloys with Ga concentrations from 0 to $20.3\text{at}\text{.}\mathrm{\%}$. The experiments focused on the development of atomic short-range ordering (SRO) by analysis of the diffuse scattering appearing at superlattice positions of the $\text{D}{0}_3$ ordered alloy structure. No SRO was found for Ga concentrations less than $4\text{at}\text{.}\mathrm{\%}$. Between 13 and $20.3\text{at}\text{.}\mathrm{\%}$, $\text{D}{0}_3$-type SRO clusters are observed whose size increases with Ga concentration for both slow-cooled and quenched samples. Thermal quenching of the samples suppresses the cluster sizes when compared to slow-cooled samples of the same concentration. For quenched samples with large Ga concentration, Ga pairing is evidenced by growing B2-type correlations. At low concentrations, the presence of SRO appears to have little (if any) effect on the enhanced magnetostriction. However, the dramatic suppression of magnetostriction near $\sim 20\text{at}\text{.}\mathrm{\%}$ Ga can be linked rapid growth of SRO just before the onset of long-range chemical order.

Figure 1

Saturated MS for quenched (filled squares) and slow-cooled Fe-Ga (circles) along [100] direction verses Ga concentration. Solid and dashed lines are guide to the eyes for slow-cooled and quenched MS curves, respectively. Different regions of MS behavior (I, II, III, and IV) are described in the text. From Ref. 7.

Figure 2

Metastable phase diagram for Fe-Ga alloys (Ref. 10). Solid lines describe solid-solid phase transformations between the A2, B2, and $\text{D}{0}_3$ ordered alloy phases. The dash-dotted line indicates the ferromagnetic ordering (Curie) temperature.

Figure 3

Crystal structures for (left) A2, (center) B2, and (right) $\text{D}{0}_3$ structures of ${\text{Fe}}_{100-x}{\text{Ga}}_x$ alloys.

Figure 4

(a) Image of x-ray diffuse scattering using Mar 345 image plate from a single crystal of slow-cooled ${\text{Fe}}_{81.7}{\text{Ga}}_{18.3}$ with [011] direction aligned along the incident x-ray beam. Diffuse features are labeled as either originating from SRO or thermal diffuse scattering, as described in the text. Linear scans measured along $\left[0.5LL\right]$ direction are shown in (b) (quenched) and (d) (slow cooled). Linear scans along $\left[H00\right]$ are shown in (c) (quenched) and (e) (slow cooled). Linear scans are measured using a Canberra germanium point detector and indicated as the dashed line in (a). The hatched region is the background.

Figure 5

Intensity of calculated TDS (a) obtained from a phonon model for $\alpha$-Fe (Ref. 17) as compared to the normalized data (background removed) and (b) along $\left[1LL\right]$ direction for quenched ${\text{Fe}}_{82.3}{\text{Ga}}_{17.7}$ in reciprocal space. TDS peaks are indicated by bold arrows while SRO peaks are indicated by ordinary arrows.

Figure 6

Fitting of diffuse-scattering data from (a) quenched and (b) slow-cooled ${\text{Fe}}_{82.3}{\text{Ga}}_{17.7}$ along $\left[0.5LL\right]$. The dots correspond to the raw data with background removed. The hatched regions correspond to the contributions of SRO, TDS, and SE scattering to the total fit (solid line).

Figure 7

Correlation lengths of Ga SRO versus Ga concentration for different heat treatments as determined from the widths of (0.5 0.5 0.5) and (100) SRO peaks cut in different crystallographic directions. Dashed and gray lines stand for slow-cooled (Sc) results while solid and black lines stand for quenched (Qu) results. The three symbols “◼,” “○,” and “△” indicate the three cut directions of (111), (100), and (011), respectively. The shaded vertical rectangles indicate the Ga composition where MS reaches first maximum for both slow-cooled ($\sim 18–18.5\text{at}\text{.}\mathrm{\%}$, lighter gray) and quenched samples ($\sim 19.5–20\text{at}\text{.}\mathrm{\%}$, darker gray).

Figure 8

Positions of (100) peaks (a) along (100) direction and positions of (0.5 0.5 0.5) and (b) peaks along (111) direction as a function of Ga concentration.

Figure 9

(Color online) The normalized intensity along the $\left[HHH\right]$ direction for (a) quenched and (b) slow-cooled samples, respectively, for various Ga concentrations. The black region is background.

Figure 10

Integrated intensity of Ga SRO peaks at (a) (0.5 0.5 0.5) and (b) (100) superlattice positions measured along (111) direction versus Ga concentration for the two different heat treatments.