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The Bain path of paramagnetic Fe-Cr based alloys
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10.1063/1.3603024
/content/aip/journal/jap/110/1/10.1063/1.3603024
http://aip.metastore.ingenta.com/content/aip/journal/jap/110/1/10.1063/1.3603024

Figures

Image of FIG. 1.
FIG. 1.

Schematic plot of the bcc-fcc Bain transformation path. The black circles mark the body centered tetragonal (bct) unit cell. The bcc lattice corresponds to (c/a)bcc = 1 and the fcc lattice to (c/a)fcc = .

Image of FIG. 2.
FIG. 2.

(Color online) Total energy contours (in mRy) for (a) Fe0.9Cr0.1 (FeCr), (b) Fe0.85Cr0.15 (FeCr-Cr), (c) Fe0.85Cr0.15 (FeCr-Cr), (d) Fe0.85Cr0.1Mn0.05 (FeCr-Mn), (e) Fe0.85Cr0.1Co0.05 (FeCr-Co), and (f) Fe0.85Cr0.1Ni0.05 (FeCr-Ni) alloys as a function of the tetragonal lattice ratio (c/a) and the Wigner-Seitz radius (w). For each alloy, the energies are plotted relative to the minimum of the corresponding bcc (c/a = (c/a)bcc) total energy.

Image of FIG. 3.
FIG. 3.

Calculated total energy differences between the fcc and bcc phases of the paramagnetic Fe0.85Cr0.1 M 0.05 (M = Cr, Mn, Fe, Co, Ni) alloys. The inset shows the fcc-bcc energy differences for hypothetical non-magnetic 3d transition metals as a function of d-occupation calculated at the experimental equilibrium volume using the linear muffin-tin orbitals method (adopted from Ref. 42).

Image of FIG. 4.
FIG. 4.

(Color online) Density of states for Fe-Cr-M (M = Cr, Mn, Ni, Co) random alloys calculated for bcc (solid lines with symbols) and fcc (dotted lines with symbols) phases. The figure shows the effect of alloying on the density of states around the Fermi level (energy reference level). For all compositions, the bcc density of states at the Fermi level is smaller than the fcc density of state.

Image of FIG. 5.
FIG. 5.

(Color online) Theoretical energy differences between the bct and bcc phases of the paramagnetic Fe0.85Cr0.10 M 0.05 (M = Cr, Mn, Fe, Co, Ni) random alloys plotted relative to that of Fe0.90Cr0.10 as a function of transition metal M possessing increasing d-occupation number going from left (Cr) to right (Ni) and for different c/a ratios (distortions).

Image of FIG. 6.
FIG. 6.

(Color online) Theoretical energy differences between the bct and fcc phases of the paramagnetic Fe0.85Cr0.10 M 0.05 (M = Cr, Mn, Fe, Co, Ni) random alloys plotted relative to that of Fe0.90Cr0.10 as a function of transition metal M possessing increasing d-occupation number going from left (Cr) to right (Ni) and for different c/a ratios (distortions).

Image of FIG. 7.
FIG. 7.

(Color online) Local magnetic moments on Fe atoms (in units of μ B) in (a) Fe0.9Cr0.1 (FeCr), (b) Fe0.85Cr0.15 (FeCr-Cr), (c) Fe0.80Cr0.20 (FeCr-Cr-Cr), (d) Fe0.85Cr0.1Mn0.05 (FeCr-Mn), (e) Fe0.85Cr0.1Co0.05 (FeCr-Co), and (f) Fe0.85Cr0.1Ni0.05 (FeCr-Ni) alloys shown as a function of the tetragonal ratio (c/a) and the Wigner-Seitz radius (w). For all compositions, the local magnetic moments have larger values for the bcc phase (c/a = 1) as compared to the fcc phase (c/a = ).

Image of FIG. 8.
FIG. 8.

(Color online) Local magnetic moments on (a) Co and (b) Mn atoms (in units of μ B) in Fe0.85Cr0.1Co0.05 and Fe0.85Cr0.1Mn0.05 alloys, respectively, shown as a function of the tetragonal ratio (c/a) and the Wigner-Seitz radius (w). For the Fe0.85Cr0.1Co0.05, the local magnetic moments vanish for c/a 1.3 at large volumes (w ≈ 2.75 Bohr) and for c/a 1.1 at small volumes (w ≈ 2.60 Bohr). For Fe0.85Cr0.1Mn0.05, the local magnetic moments show weak c/a dependence.

Tables

Generic image for table
Table I.

Calculated equilibrium Wigner-Seitz radii and total energies for fcc and bcc Fe-Cr-M (M = Cr, Mn, Ni, and Co) alloys. The total energies corresponding approximately to the saddle points between the two cubic phases are shown in the last column.

Generic image for table
Table II.

Theoretical local magnetic moments (in units of μ B) on Fe, Mn, and Co atoms in the paramagnetic Fe-Cr-M (M = Cr, Mn, Co, Ni) alloys for fcc and bcc phases calculated at the equilibrium volume.

Generic image for table
Table III.

Theoretical total energy, magnetic entropy, and free energy differences between fcc and bcc phases of paramagnetic Fe-Cr-M (M = Cr, Mn, Co, Ni) alloys (in units of mRy) calculated at T = 1400 K.

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/content/aip/journal/jap/110/1/10.1063/1.3603024
2011-07-07
2014-04-16
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: The Bain path of paramagnetic Fe-Cr based alloys
http://aip.metastore.ingenta.com/content/aip/journal/jap/110/1/10.1063/1.3603024
10.1063/1.3603024
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