Neutron and X-ray Diffraction Studies of Sonne NiAs-type Structures,
The binar y compound s of Cr, Mn, Fe , Co, and Ni with As, Sb, S, Se , and Te hav e at least two propertie s tha t ar e commo n to the m all. First , eac h compound contains a magneti c ion or a cation with partiall y filled 3d-shells. Second, they crystalliz e in NiAs-typ e structure , or a structur e relate d to this by some distortio n of it. As shown in Figur e 22, normall y ther e ar e four ions pe r unit cell: two cations at 0 0 0, 0 0 1/2, and two inetalloi d ions o r anions at 1/3 2/ 3 1/4; 2/ 3 1/3 3/4 . The four interstice s a r e at l/s 2/ 3 5/8 ; l/s 2/ 3 7/8 ; 2/ 3 l/s l/S ; 2/ 3 l/s 3/8 . The structur e is characterize d by eac h catio n having six anions at its nearest neighbors at a distanc e of {y ao + "jj CQ} '' , two cation s a s next-nearest neighbors at a distanc e of Co/2, and six cation s a s third-nearest neighbors at a distanc e of ao, wher e ao and Cg ar e the lattic e parameters of th e unit cell. Eac h anion is surrounde d by six cations, the anions formin g alternat e layers be - twee n cations along the C0-axis.
T h e composition s of thes e compound s var y betwee n typica l ioni c compound s an d thos e tha t ar e practicall y alloys, an d ma y b e expresse d a s Mj_xX , MX , o r MJ^JJXQ , wher e M stand s fo r a n electropositiv e element, a n d X a n electronegative . Fo r Mj.j^-X composition , a n exces s of anion s ca n result fro m vacancie s a t th e catio n site s i n th e crysta l lattic e rathe r tha n fro m solubilit y of anions, because , althoug h th e atomi c radii of metalloi d atoms , a s give n i n Tabl e II, ar e generall y comparabl e t o thos e of meta l atoms , th e siz e of th e anio n is muc h large r tha n th e cation . Fo r Mj+^X coin - position , o n th e othe r hand , a n exces s of cation s ha s bee n considere d to b e d u e t o th e presenc e of interstitia l ions . Whil e th e tetrahedra l interstice s mentione d abov e ar e no t larg e enoug h t o accomnaodat e ions, eac h pai r ma y com.bin e t o forn n a larg e hol e a t 1/3 2/ 3 3/ 4 an d 2/ 3 l/ s l/4 , whic h ca n accomiTiodat e cation s an d thu s accoun t fo r th e presenc e of interstitials (Goodenough).
T h e cation s occupying regula r octahedra l site s favor axia l rati o (co/ag) to be greate r tha n 1.63 (an idea l valu e for hexagona l close d packe d structure), but an interstitia l cation favors it to be less tha n 1.63. This suggests tha t th e magnitud e of the axia l rati o ma y serv e a s an indicato r of th e numbe r of interstitia l cation s tha t ar e present.^ ^ Neutro n diffrac - tion studie s of som e antiferromagneti c NiAs-typ e structure s show tha t axia l ratio s differ markedl y depending upon the directio n of alignmen t of magneti c moments in the structures. Fo r example , results^' * of neutro n diffraction studie s of two representativ e compounds, FeS and CrSb , show tha t both compound s crystalliz e in NiAs-typ e structur e and both ar e antiferromagneti c at roo m temperature . Th e magneti c cation s in eac h com - pound fori n a simpl e hexagona l structur e with CQ/B.Q - 1.67 for FeS , and 1.33 for CrSb . The magneti c moments of F e ions ar e aligned in the x- y plane , i.e. , perpendicula r to the Co-axis of the hexagona l unit cell. The alignmen t is ferromagneti c in any (OOi) plane , but directe d oppositel y in the adjacent (OOi) planes. In contrast , the magneti c moments of Cr ions ar e aligned paralle l to th e Co-axis, i.e. , perpendicula r to the x- y plane , with th e direc - tion s of moments alternatel y pointed up^ward and downwar d at distanc e Co/2 along the axis. That the antiferromagnetic alignment of magnetic moinents affects the lattice parameters, and consequently the axial ratio, can be seen from the neutron and the X-ray diffraction patterns taken below and above the Neel temperature . When an Eintiferromagnetic substance is heated through the transformation temperatur e between the antiferromagnetic and the paramagnetic states, the nature of the accompanying deformation in the unit cell is such that (l) the elongation takes place in the direction of the alignment of the magnetic moments, and the process is reverse d when the structur e is cooled belo-w the Neel temperature ; and (2) the alignment and disalignment of magnetic moments, and the crystal structur e deformation, take place siiTiultaneously. The alignment of magnetic moments in an antiferromagnetic substance may or may not be collinear with the crystal axes, but it is apparent that it does affect the lattice parameters of the unit cell.
By comparing the axial ratios of some kno^wn antiferromagnetic NiAs-type structure s with those of FeS and CrSb, one may divide them empirically with respec t to their magnetic axes as follows:
It must be added her e that it is intended to present an explanation for the directional alignment of magnetic moments and the deformation of the crystal structur e of NiAs-type antiferromagnetic substances separately, taking into consideration the composition, types of ions and bonding, and the role of interstitials and vacancies.
Reference: A SEMINAR ON GROUPS V AND VI ANIONS
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