Elongation and compression of Fe-Fe atomic pairs in Fe-Ni invar alloys: Microscopic observations of the magnetovolume effect in ferromagnetic Fe-Ni fcc-based alloys

The atomic scale origin of the invar effect and the large magnetovolume effect in Fe-Ni alloys is revisited by investigating the Ni-content dependence of bulk modulus <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:msub><a:mi>B</a:mi><a:mn>0</a:mn></a:msub></a:math> of Fe-Fe, Fe-Ni, and Ni-Ni atomic pairs using reverse Monte Carlo modeling with a dataset of extended x-ray absorption fine structure and powder x-ray diffraction under high pressure. To this end, the results of the <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:msub><b:mi>Fe</b:mi><b:mn>65</b:mn></b:msub><b:msub><b:mi>Ni</b:mi><b:mn>35</b:mn></b:msub></b:mrow></b:math> invar alloy were compared with those of Ni-rich ferromagnetic <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:msub><c:mi>Fe</c:mi><c:mn>55</c:mn></c:msub><c:msub><c:mi>Ni</c:mi><c:mn>45</c:mn></c:msub></c:mrow></c:math> and <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mrow><d:msub><d:mi>Fe</d:mi><d:mn>20</d:mn></d:msub><d:msub><d:mi>Ni</d:mi><d:mn>80</d:mn></d:msub></d:mrow></d:math> alloys. The elongation of Fe-Fe pairs compared to the bond lengths of Fe-Ni and Ni-Ni pairs is commonly observed in the ferromagnetic states of all Fe-Ni alloys. The <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:msub><e:mi>B</e:mi><e:mn>0</e:mn></e:msub></e:math> value of each atomic pair is comparable to the value of bulk <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:msub><f:mi>B</f:mi><f:mn>0</f:mn></f:msub></f:math> when the ferromagnetic phase is stable under high pressure, while the rapid shrinkage of the elongating Fe-Fe pairs results in a smaller value of <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"><g:msub><g:mi>B</g:mi><g:mn>0</g:mn></g:msub></g:math> at the destabilized ferromagnetic region. Therefore, the magnetovolume effect in Fe-Ni alloys is interpreted as a result of the elongating Fe-Fe pairs and their population in the alloy. The elongation and subsequent shrinkage of Fe-Fe pairs at the destabilization of the ferromagnetic order plays a crucial role for initiating the invar effect.