Effect of magnetism and atomic order on static atomic displacements in the Invar alloy Fe-27 at.% Pt

Fe-27 at.% Pt was aged at 1123 K and quenched to room temperature (RT) to set up a state of thermal equilibrium. The local atomic arrangement was studied by diffuse x-ray scattering above (at 427 K) and below (at RT) the Curie temperature as well as at RT under a saturating magnetic field. The separated short-range order scattering remained unchanged for all three states, with maxima at 100 positions. Effective pair interaction parameters determined by the inverse Monte Carlo method gave an order-disorder transition temperature of about 1088 K, close to direct experimental findings. The species-dependent static atomic displacements for the first two shells show large differences, with a strong increase in magnitude from the state at 427 K over RT to the state under saturating magnetic field. This outcome is in agreement with an increase in atomic volume of Fe with increasing local magnetic moment. Electronic-structure calculations closely reproduce the values for the static atomic displacements in the ferromagnetic state, and predict their dependence on the atomic configuration. They also reveal a strong dependence of the magnetic exchange interactions in Fe-Pt on the atomic configuration state and lattice parameter. In particular, the increase of the Curie temperature in a random state relative to that in the ordered one is demonstrated to be related to the corresponding change of the magnetic exchange interactions due to the different local atomic chemical environment. There exists a similar strong concentration dependence of the chemical interactions as in the case of magnetic exchange interactions. Theoretical effective interactions for Fe-27 at.% Pt alloy are in good agreement with experimental results, and they also reproduce well the ${\mathrm{L}1}_2$-A1 transition temperature.

Figure 1

Macroscopic length change $\mathrm{\Delta }l/l$ of Fe-27.1 at.% Pt around the Curie temperature.

Figure 2

As-measured diffuse scattering of Fe-27.1 at.% Pt at RT in Lu. The hatched areas around Bragg reflections present the regions that were not employed in data evaluation due to strong thermal diffuse scattering.

Figure 3

Short-range order scattering $I_{\mathrm{SRO}}$ of Fe-27.1 at.% Pt at room temperature, at 427 K, and at RT under saturating magnetic field. The as-separated and as-fitted intensities are shown.

Figure 4

Size-effect scattering $\mathbf{h}·{\mathbf{Q}}^{\mathrm{FeFe}}$ and $\mathbf{h}·{\mathbf{Q}}^{\mathrm{PtPt}}$ of Fe-27.1 at.% Pt at RT under saturating magnetic field. The fitted scattering is shown.

Figure 5

Species-dependent static atomic displacements of Fe-Fe and Pt-Pt pairs in radial approximation. The values in radial direction ${\langle r\rangle }_{lmn}^{\mu \mu }$ are shown in units of the lattice parameter.

Figure 6

Fe-Fe magnetic exchange interaction $J_{\mathrm{xc}}$ at the first coordination shell in Fe-Pt alloys as a function of concentration. All the results but those shown by diamonds are obtained at a fixed lattice constant of 3.75 Å. The results shown by diamonds are obtained at the experimental room-temperature lattice constants. The large up triangle shows the result of the scalar relativistic calculations of the ${\mathrm{L}1}_2$ ordered ${\mathrm{Fe}}_3\mathrm{Pt}$. Only the results shown by squares are obtained in the FM state, all the others in the DLM state. Small down triangles show the results of the fully relativistic calculations, which include spin-orbit coupling.

Figure 7

Fe-Fe magnetic exchange interactions at the first two coordination shells in random Fe-25 at.% Pt as function of the lattice constant in the DLM state.

Figure 8

Fe-Fe magnetic exchange interactions in the DLM state in random Fe-25 at.% Pt, obtained in the scalar (SR) and fully relativistic (FR) calculations and in ${\mathrm{L}1}_2$ ordered ${\mathrm{Fe}}_3\mathrm{Pt}$ for the same lattice constant of 3.75 Å.

Figure 9

Effective pair chemical interactions (chemical part from SGPM calculations) at the first coordination shell in random Fe-Pt alloys as function of Pt concentration.

Figure 10

Effective three-site $V_t^{\left(3\right)}$ and four-site $V_q^{\left(4\right)}$ chemical interactions in random Fe-Pt alloys as function of Pt concentration. Filled symbols show the interactions in the FM state, while the corresponding open symbols show the interactions in the DLM state.

Figure 11

Total and chemical ECI parameters $V_{lmn}^{\left(2\right)}$ in random Fe-27 at.% Pt. The chemical interactions are calculated in the DLM state at a lattice constant of 3.79 Å.