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4 Mössbauer and Magnetic Study of Neptunyl(+1) Complexes

4 Mössbauer and Magnetic Study of Neptunyl(+1) Complexes

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5.4 MOSSBAUER

AND MAGNETIC STUDY OF NEPTUNYL(ỵ1) COMPLEXES



99



FIGURE 5.6

Plot of x1T and xT–T for

(NH4)[NpO2(O2CH)2] (1). The data

were corrected by subtraction of

$2.8% of ferromagnetic impurity

that can be identified as

[NpO2(O2CH)(H2O)] (3). The peak

at $13 K is due to the residual by

subtraction for correction.

(Reproduced from Ref. 10 with

permission of Transworld

Research Network.)



of a ferromagnetic interaction among the magnetic moments. The magnetization curve measured at 4.5 K is shown in Fig. 5.7.

The magnetization curve does not reach the saturation at 5.5 T, although it seems to be quite close to the saturation. The

magnetization 1.78mB/Np at 5.5 T is much smaller than the theoretical value for free ion 3.20mB/Np.

ossbauer spectra of 1 at 5.3 and 20 K. Although a large magnetic splitting ($500–550 T)

Figure 5.8 shows 237 Np M€

is frequently seen in the spectrum of the pentavalent neptunyl compounds, the obtained spectra do not show a



FIGURE 5.7

Magnetization curve of

(NH4)[NpO2(O2CH)2] (1) at 4.5 K.

No correction was made for the

ferromagnetic impurity.

(Reproduced from Ref. 10 with

permission of Transworld

Research Network.)

100.05

100.00

99.95



Transmittance (%)



99.90

99.85

99.80



20 K



100.05

100.00

99.95

99.90

99.85

99.80

99.75



5.3 K



–150 –100 –50



0



Velocity (mm



50



s–1)



100



FIGURE 5.8

237

€ ssbauer spectra of

Np Mo

(NH4)[NpO2(O2CH)2] (1). The solid

lines represent theoretical fits

obtained by Wickman’s

paramagnetic relaxation model

(see text). (Reproduced from Ref.

10 with permission of Transworld

Research Network.)





5 MOSSBAUER

AND MAGNETIC STUDY OF NEPTUNYL(ỵ1) COMPLEXES



100



ssbauer Parameters of (NH4)[NpO2(O2CH)2] (1)

TABLE 5.1 Mo

T (K)

20

5.3



da (mm sÀ1)



e2qQ (mm sÀ1)



G (mm sÀ1)



t  1012 (s)



Heffb (T)



À16.0(7)

À15.8(7)



110(3)

108(3)



6.3(6)

5.5(5)



11.2(7)

8.0(6)



550

550



a



The isomer shift data are referred to NpAl2.

Fixed value. See text.



b



magnetic splitting, and also their overall shape does not resemble a pure quadrupole pattern (Fig. 5.3). Such shape

can be seen in the simulated spectra for paramagnetic relaxation with the addition of a collinear axial electric

quadrupole interaction. These spectra can be well fitted by Wickman’s paramagnetic relaxation model [21]

described in Section 5.5.1. Because the magnetic hyperfine field Heff and paramagnetic relaxation time t could

not be unequivocally determined from these spectra, the hyperfine field has been fixed at 550 T, which is

frequently observed in other pentavalent neptunyl compounds. The M€

ossbauer parameters are summarized in

Table 5.1. The estimated isomer shift value of À15.8(7) mm sÀ1 clearly indicates that the Np ion in 1 is pentavalent

(see Fig. 5.4) [22].



5.4.2 [NpO2(O2CCH2OH)(H2O)] (2)

Single-crystal X-ray structure determination of 2 has been reported by Grigor’ev et al. previously [23]. As shown in

Fig. 5.9, the crystal structure has revealed that the coordination polyhedron of the Np atom is a pentagonal bipyramid, of

which equatorial plane consists of five O atoms, and that there is only one crystallographic neptunium site in the crystal.





The Np–O bond distances are 1.828(8) and 1.801(9) A for Np-(“yl” O) and 2.420(8)–2.467(8) A for Np-(equatorial O).

One of the oxygen atoms in the equatorial plane also serves one of the “yl” oxygen atom of the adjacent neptunyl cation,

forming a 1D zigzag CCB chain structure extended along crystallographic c axis.

237

Np M€

ossbauer spectra of 2 measured at 5.3 K, 20 K, and 42 K [24] are shown in Fig. 5.10. The solid lines in

Fig. 5.10 show successful result of least-square fitting. The spectra of 2 are also strongly affected by paramagnetic

relaxation effect and can be well fitted by Wickman’s paramagnetic relaxation model similar to 1. The magnetic

ossbauer parameters are summarized in Table 5.2. The

hyperfine field Heff has been fixed at 550 T. The obtained M€

isomer shift value, À19.0(2) mm sÀ1 at 5.3 K, is very close to those of sulfate (NpO2)2SO4 Á 2H2O (À18.9 mm sÀ1)

[25] and mellitate compound Na4(NpO2)2(C12O12) Á 8H2O (À20.4(6) mm sÀ1) [26] measured at 4.2 K. The present

result suggests that the isomer shift value of pentavalent neptunium in NpO7 polyhedron (pentagonal bipyramid) falls

within a limited range around ca. À20 mm sÀ1 with respect to NpAl2. The isomer shift value slightly smaller than 1 is

probably due to the systematic trends of the 237 Np M€

ossbauer isomer shifts for NpOn polyhedra of neptunyl

compounds [22,27]. A correlation is found between the isomer shift and the coordination number; an increase of the

Np coordination number leads to an increase of the isomer shift. To explain this correlation, increase of the covalency

of Np–ligand bonds has been proposed and the proposal has been supported by the theoretical calculation taking

account of relativistic effects [27].



FIGURE 5.9

Crystal structure of

[NpO2(O2CCH2OH)(H2O)] (2). The

dashed lines correspond to

hypothetical H-bonds. Atom

labels were added by the author

of this Chapter. (Reproduced

from Ref. 23 with permission of

Springer.)





5.4 MOSSBAUER

AND MAGNETIC STUDY OF NEPTUNYL(ỵ1) COMPLEXES



101



€ ssbauer Parameters of [NpO2(O2CCH2OH)(H2O)] (2)

TABLE 5.2 Mo

T (K)

42

20

5.3



da (mm sÀ1)



e2qQ (mm sÀ1)



G (mm sÀ1)



t  1012 (s)



Heffb (T)



À18.5(3)

À18.6(1)

À18.86(9)



93(1)

92.4(7)

96.0(8)



6.4(4)

4.5(2)

5.2(2)



2.8(2)

2.8(1)

4.1(1)



550

550

550



a



The isomer shift data are referred to NpAl2.

Fixed value. See text.



b



100.0

99.9

99.8



42 K



99.7



Transmittance (%)



99.6

100.0

99.8

99.6



20 K



99.4

99.2

100.0

99.6

5.3 K



99.2

98.8

98.4

–150



–100



–50



0



Velocity (mm s–1)



50



100



150



FIGURE 5.10

237

€ ssbauer spectra of

Np Mo

[NpO2(O2CCH2OH)(H2O)] (2).

(Reproduced from Ref. 24 with

permission of Springer.)



5.4.3 [NpO2(O2CH)(H2O)] (3)

The compound 3 has an interesting 2D layered structure. As shown in Fig. 5.11, the previously reported crystal structure

of 3 has revealed that compound 3 forms the bumpy cationic 2D sheet extended by the neptunyl monocations (NpO2ỵ)

as a result of CCB, in which the neptunyl cation acts as a bidentate bridging ligand [28]. The 2D sheets are layered with an



intersheet separation of a/2 ¼ 7.06 A (Fig. 5.11a). There are no covalent or coordination bonds between the sheets, but

some hydrogen bonds are present. There is only one crystallographically independent Np site and its coordination





polyhedron is a pentagonal bipyramid with the distances of 1.846(5), 1.850(5) A for Np-(“yl” O) and 2.388(6)–2.544(5) A

for Np-(equatorial O). The neptunyl cations are oriented in roughly two directions with the angle slightly deviating from

90 (ca. 80 ) in the 2D sheet.

Figure 5.12 shows the temperature dependence of the reciprocal magnetic susceptibility x(T)À1 of 3. Above 50 K,

the susceptibility follows the Curie–Weiss law, where the paramagnetic Curie temperature up is 12.7 K, and the effective

magnetic moment is obtained to be 2.8lmB/Np. This value of 2.8lmB/Np is close to 2.71mB/Np in (NpO2)2C2O4 Á 4H2O

[29]. These are, however, smaller than the theoretical values of 3.58mB/Np and 3.63mB/Np for a Np5ỵ(5f2) ion based on

the LS- and the intermediate-coupling models, respectively [30]. This experimental result clearly indicates that this

compound is ferromagnetic below $13 K [9]. The typical magnetization curve at 4.5 K is shown in Fig. 5.13. The initial

magnetization curve shows an S-shaped character and seems to reach the saturation by 5.5 T. The subsequent

magnetization curve is highly different from the initial magnetization curve, showing a hysteresis loop. This is common

in the usual polycrystalline ferromagnet. We obtained a coercive field Hc ¼ 0.10 T and remnant magnetization



102





5 MOSSBAUER

AND MAGNETIC STUDY OF NEPTUNYL(ỵ1) COMPLEXES



FIGURE 5.11

Crystal structure of

[NpO2(O2CH)(H2O)] (3). (a) View

projected along the direction

parallel to the 2D sheet. (b) 2D

cation–cation bond network.

Only neptunyl cations are

illustrated for clarity.



MR ¼ l.00mB/Np, which corresponds to 82% of the averaged powder saturation moment mpowder ¼ l.22mB/Np. This

saturation moment l.22mB/Np obtained for the powdered sample is close to 1.20mB/Np in (NpO2)2C2O4 Á 4H2O [29] but

much smaller than the theoretical values of 3.20mB/Np and 3.24mB/Np based on the LS- and the intermediate-coupling

models, respectively [26]. It is usually recognized as an effect due to the strong magnetocrystalline anisotropy of the

powdered actinide ferromagnets [31,32].

237

Np M€

ossbauer spectra of 3 at 5.3, 20, and 42 K shown in Fig. 5.14 exhibit a well-resolved magnetic hyperfine

splitting at each temperature. The most striking feature is that the spectra are insensitive to the onset of magnetic

ordering. The origin of the magnetic splitting observed for 3 below Tc is clearly from the ferromagnetic ordering, while



FIGURE 5.12

Plot of xÀ1–T and xTT for

[NpO2(O2CH)(H2O)] (3).





5.4 MOSSBAUER

AND MAGNETIC STUDY OF NEPTUNYL(ỵ1) COMPLEXES



103



FIGURE 5.13

Hysteresis loop of

[NpO2(O2CH)(H2O)] (3) at 4.5 K.



that above Tc is a slow paramagnetic relaxation. Because the paramagnetic relaxation spectrum at the slow limit is

ossbauer

identical with a magnetically split spectrum, the spectra above Tc are fitted without relaxation effect. M€

parameters are summarized in Table 5.3. The observed hyperfine field 555.2 T at 5.3 K belongs to the largest class among

Np compounds. On the basis of the relation that magnetic hyperfine field is proportional to the size of magnetic moment

(i.e. Hhf / hJZ i) in a localized electron system [30], the magnetic moment is considered to originate from a large Jz

component. Because no other magnetically split spectrum with different Heff can be observed, only one Jz component is

distributed at least up to 42 K. The estimated isomer shift value of À18.86(9) mm sÀ1 clearly indicates that the Np ion in 3



100.04

100.00



99.96

99.92



Transmittance (%)



42 K



100.00

99.95

99.90

99.85



20 K



99.80

100.00

99.90

99.80



5.3 K

99.70

–200



–150



–100



–50



0



Velocity (mm



50



s –1)



100



150



FIGURE 5.14

237

€ ssbauer spectra of

Np Mo

[NpO2(O2CH)(H2O)] (3).

(Reproduced from Ref. 10 with

permission of Transworld

Research Network.)





5 MOSSBAUER

AND MAGNETIC STUDY OF NEPTUNYL(ỵ1) COMPLEXES



104



ssbauer Parameters of [NpO2(O2CH)(H2O)] (3)

TABLE 5.3 Mo

T (K)

42

20

5.3



da (mm sÀ1)



e2qQ (mm sÀ1)



G (mm sÀ1)



Heff (T)



À18.2(6)

À18.4(2)

À18.9(1)



81(4)

84(1)

88.5(6)



10(2)

9.9(5)

6.1(3)



544(3)

551.0(9)

555.2(5)



a



The isomer shift data are referred to NpAl2.



is pentavalent. The slightly smaller isomer shift value than 1 is attributable to the difference of coordination number in

equatorial plane based on the same reason as 2.

5.4.4 [(NpO2)2((O2C)2C6H4)(H2O)3] Á H2O (4)

This complex was first reported as a hexahydrate (NpO2)2(O2C)2C6H4 Á 6H2O [33], but its correct formula was found to

be tetrahydrate (NpO2)2(O2C)2C6H4 Á 4H2O by the later single-crystal structure determination [34]. The crystal

structure has revealed that the complex 4 forms a 2D cationic square net layer structure similar to 3 (Fig. 5.11b)

constructed by two independent Np sites. Unfortunately, there was no detailed crystal structure data for this complex at

the time of our magnetic study, and hence incorrect molecular weight based on the hexahydrate formula was used for the

calculation of magnetization per Np atom. Therefore, the magnetization values per Np atom may become at most ca. 5%

larger than those described below. On the other hand, it was predicted that two kinds of Np sites exist in the crystal

before the structure determination [11,33].

The xÀ1 versus T and xT versus T plots at 0.01 T in the zero-field-cooled (ZFC) mode are given in Fig. 5.15. The

À1

x –T plot is slightly curved over the wide temperature range (see the inset), but generally obeys the Curie–Weiss law.

The effective magnetic moment meff and the paramagnetic Curie temperature up evaluated for 10–70 K range are 2.54mB/

Np and ỵ7.75 K, respectively. Likewise, meff ẳ 2.29mB/Np and up ẳ ỵ29.8 K were obtained by using the xÀ1 values at the

temperature range between 150 and 300 K having steeper slope. The positive paramagnetic Curie temperatures indicate

the presence of a ferromagnetic interaction among the magnetic moments on the Np atoms. A significant increase of the

xT with decreasing temperature also indicates the presence of ferromagnetic interaction.

The magnetization (M) versus magnetic field (H) curve at 2 K, as shown in Fig. 5.16, is rather unusual. The initial

magnetization curve exhibits a kink around H ¼ $0.4 T. With the increase of applied field from 0 to 0.1 T, the

magnetization rapidly increases to $0.60mB/Np, then the increment ceases (inset). With further increase of the

applied field, the magnetization restarted increasing beyond $0.35 T. The magnetization finally reaches saturation of

$1.23mB/Np at 5.5 T. When the applied field was decreased from 5.5 T, the magnetization traced the initial curve down

to 0.35 T, and the magnetization ceased decreasing, showing a plateau at the applied field between 0.35 and 0 T. The

magnetization curve has a hysteresis loop with a coercive field HC $ 0.076 T and remnant magnetization MR ¼ 0.68mB/

Np, which roughly corresponds to the half of the saturation moment at 2 K. The magnetization curve without hysteresis

at higher applied field (H > 0.75 T) is strongly indicative of a metamagnetic behavior, while the hysteresis loop observed in

the low fields indicates the existence of ferromagnetism. Similar metamagnetic magnetization curve accompanied by a

small hysteresis loop is also reported for a canted antiferromagnet [Fe(Cpà )2][DCNQ] at 1.8 K [35]. This hysteresis loop



FIGURE 5.15

Plot of reciprocal molar

susceptibility xÀ1 and xT versus

temperature for

[(NpO2)2((O2C)2C6H4)(H2O)3] Á H2O

(4). The inset shows xÀ1–T plot in

the temperature range of

2 K T 300 K. (Reproduced from

Ref. 11 with permission of Elsevier.)





5.4 MOSSBAUER

AND MAGNETIC STUDY OF NEPTUNYL(ỵ1) COMPLEXES



105



FIGURE 5.16

Plot of magnetization versus

temperature at 2 K for

[(NpO2)2((O2C)2C6H4)(H2O)3] Á

H2O (4). The inset shows an

expansion of the field range of

À1 T H 1 T. (Reproduced from

Ref. 11 with permission of

Elsevier.)



of this system has been assigned to originate from the so-called weak ferromagnetism. In the present complex, however,

the remnant magnetization corresponding to half of the saturation moment seems to be too large for the weak

ferromagnet; therefore, this is considered to originate from normal ferromagnetic component.

Most plausibly this unique magnetic behavior of the present system is supposed to arise from the existence of two

kinds of Np-(magnetic) sublattices almost in equal amount in this compound; one is ferromagnetic and the other is

metamagnetic. All the magnetic data are interpretable on this basis; a ferromagnetic ordering in one Np sublattice and a

metamagnetic Np sublattice, which switches to a ferromagnetic state induced by the former at higher magnetic field.

Although we cannot completely exclude the possibility that the powder sample may be mere a two-phase mixture, the

fact that the present system exhibits only one magnetic transition at 4.5 K seems in favor of the existence of the two kinds

of sublattice in a single-phase material. If the former is the case, it seems difficult to justify such smooth M–H curves

variation, as shown in Fig. 5.16.

According to the present interpretation, the magnetization curve at 2 K can be analyzed as shown in Fig. 5.17. Filled

circle () data show the ferromagnetic component with hysteresis loop at jHj 0.4 T region. By subtracting this

ferromagnetic contribution from the raw magnetization data shown by open circle (), the metamagnetic component (&)

can be obtained. The two kinds of sublattices are consistent with the presence of two crystallographically independent

Np sites [34].

237

Np M€

ossbauer spectra of 4 measured at 11, 30, and 50 K, shown in Fig. 5.18, exhibit a well-resolved magnetic

hyperfine splitting at each temperature. Only one kind of magnetically split spectrum can be seen, suggesting that the

ossbauer spectroscopy, because their local chemical

two Np sites in 4 could not be distinguished by 237 Np M€

environments are quite similar to each other. Such another example is the malonate tetrahydrate complex

[(NpO2)2(C3H2O4)(H2O)3] Á H2O, of which single-crystal structure determination has revealed the existence of

crystallographically different two Np sites [36,37]. More noteworthy point is that all three well-resolved magnetically

split spectra are measured at the temperatures where 4 is paramagnetic. These spectra are fitted without relaxation

effect, because the observed magnetic hyperfine spectra are caused by slow paramagnetic relaxation. M€

ossbauer

parameters are summarized in Table 5.4. The estimated isomer shift value of ca. À19 mm sÀ1 clearly indicates that the

Np ion in 4 is pentavalent, and its coordination environment is pentagonal bipyramid.



FIGURE 5.17

Magnetization curve at 2 K. Raw

data (). Magnetization curve of

the metamagnetic site (&) and

the ferromagnetic site () under

consideration (see text).

(Reproduced from Ref. 11 with

permission of Elsevier.)





5 MOSSBAUER

AND MAGNETIC STUDY OF NEPTUNYL(ỵ1) COMPLEXES



106



€ ssbauer Parameters of [(NpO2)2((O2C)2C6H4)(H2O)3] Á H2O (4)

TABLE 5.4 Mo

T (K)

50

30

11



da (mm sÀ1)



e2qQ (mm sÀ1)



G (mm sÀ1)



Heff (T)



À19.2(2)

À19.3(1)

À19.07(7)



73(1)

76.7(7)

75.3(5)



4.5(5)

5.1(4)

4.4(2)



488.6(9)

495.0(6)

496.3(4)



a



The isomer shift data are referred to NpAl2.



100.10

100.00



Transmittance (%)



99.90



Para



50 K



99.80

100.05

100.00

99.95



Para



99.90



30 K



99.85

100.00

99.90



Para



99.80



FIGURE 5.18

237

€ ssbauer spectra of

Np Mo

[(NpO2)2((O2C)2C6H4)(H2O)3] Á

H2O (4).



99.70



11 K



99.60

–200



Tc = 4.2 K



–100



0



100



Velocity (mm s–1) (NpAl2)



5.5 DISCUSSION

5.5.1



237



€ ssbauer Relaxation Spectra

Np Mo



It is common for the M€

ossbauer spectra to be insensitive to the onset of magnetic ordering when the paramagnetic

relaxation time is “slow” [38]. The origin of the magnetic splitting observed for 3 below Tc is clearly from the

ferromagnetic ordering, while that observed above Tc is a slow paramagnetic relaxation. The notable feature is that both

the ferro- and the paramagnetic hyperfine splittings exhibit a pure Zeeman pattern that can be interpreted by the same

Hamiltonian for the collinear combined electric and magnetic interactions,

Ã

eQV zz  2

3I z II ỵ 1ị :

(5.1)

H MỵQ ẳ gN mN HI Z ỵ

4I2I 1ị

This is the simplest form for the combined electric and magnetic interactions when both exist, although its complete form

is more complicated [39] as shown in Fig. 5.19. For appearance of this special case, the following three conditions must

hold both in the ferro- and paramagnetic states.

(i) The effective-field approximation is valid (i.e., A? ¼ 0 and A== 6¼ 0, where A are the principal components of the

magnetic hyperfine tensor).

(ii) The quadrupole tensor is axial (i.e., V ZZ 6¼ 0 and h ¼ 0).

(iii) The electric field gradient (EFG) acts in the same direction as the effective hyperfine field (i.e., ~

H==V ZZ or

q ¼ 0 ).



107



5.5 DISCUSSION



z(Vzz)



FIGURE 5.19



H

ϑ



x(Vxx)

ϕ



y(Vyy)



[



H M +Q = H M + H Q = – g N μ N H 0 I z cosϑ + ( I xcosϕ + I ycosϕ ) sinϑ



+



[



eQVzz

3 I 2 – I ( I + 1) +η ( I x2 – I y2 )

4 I ( 2 I – 1) z



]



]



Definition of the two angles q

and w specifying the direction of

Heff with respect to the electrical

field gradient (EFG). The

coordinates x, y, and z are chosen

as the principal axes of the EFG.

Hamiltonian in general form is

written under the figure:

gN ¼ nuclear g-factor,

mN ¼ nuclear magneton,

I ¼ nuclear spin, e ¼ elementary

electric charge, Q ¼ electric

quadrupole moment,

h ¼ (Vxx À Vyy)/Vzz ¼ asymmetry

parameter of the electric field

gradient tensor, Ix, Iy,

Iz ¼ matrices of the angular

momentum operator.



These conditions sometimes hold for a Kramers ion of lanthanide elements with the effective spin Seff ¼ ặ1=2 at low

temperature [21]. However, because the Np5ỵ(5f2) ion is a non-Kramers ion, the condition (i) hardly holds in the

paramagnetic state. Then, one is led to the idea that the ground doublet jJZ ẳ ặ4i has an Ising-type magnetic moment

that is strongly confined along the principal axis of the ligand field, that is, OÀ

ÀNpÀ

ÀO axis, just like a Kramers doublet.

Probably, the quadrupole interaction mainly originates from the linear bond structure rather than the two 5f electrons,

for a large quadrupole interaction is present even in the UO22ỵ complex that has no 5f electrons [40,41].

Before our studies, there have been a few careful studies of magnetic relaxation in 237 Np compound, probably

because the relaxation generally results in the M€

ossbauer spectra exhibiting complex shape that is difficult to be fitted by

Lorentzian lines. Successful interpretation of the observed spectrum can be seen only in a few hexavalent Np compounds

such as NpF6 [42]. For the pentavalent neptunyl compounds, investigation has been restricted to limited cases of very

slow or very fast spin fluctuations, that is, the cases in which the spectrum can be fitted by Lorentzian lines without any

ossbauer

consideration of the relaxation effect [43]. In order to estimate the precise isomer shift values from the 237 Np M€

spectra affected by relaxation effect, a least-squares fitting was required. To fit the relaxation spectra observed for 1 and

2, we adopted the “field up–down” model, the so-called “Wickman’s relaxation model,” illustrated in Fig. 5.20. The

calculated relaxation spectra are illustrated in Fig. 5.21. Wickman’s relaxation model also assumes that all the three

conditions (i)–(iii) are valid. It means that the paramagnetic system in all four complexes 1–4 is quite the same and that

only the difference between the paramagnetic hyperfine splitting of 3 and 4 and the paramagnetic relaxation spectra of 1

and 2 is their relaxation times t. The spectra of 3 (above Tc) and 4 correspond to a static limit of the paramagnetic

relaxation spectra (t > $10À9 s in the present case), while the paramagnetic relaxation spectra of 1 and 2 are due to the

comparable relaxation time to the reciprocal of the magnetic splitting width (t ¼ $10À11–10À12 s). The calculated

ossbauer spectra of 1 and the calculated spectrum (b) to those of 2. Leastspectrum (a) resembles the observed 237 Np M€

squares fittings of the M€

ossbauer spectra of 1 and 2 were carried out by using a software IGOR pro ver. 3.0 [44].

5.5.2 Magnetic Susceptibility and Saturation Moment: Averaged Powder Magnetization

for the Ground jJz ẳ ặ4i Doublet

Because the paramagnetic susceptibilities of 1, 3, and 4 obey the Curie–Weiss law, it can be assumed that only the lowest

level jJZ ẳ ặ4i is populated below room temperature. Some previous works assume this ground doublet, but none of

them assumes the strongly confined Ising-type magnetic moment along the ligand-field principal axis. Such magnetic

moments cannot rotate freely by applied field. If the magnetic moments rotate to order along the applied field in

anisotropic polycrystalline sample, the polycrystalline particles must rotate. However, the particles tightly stuffed into a

quartz ample are unlikely to rotate by applied field of 5.5 T. This was confirmed by the measurement for the

polycrystalline samples fast in STYCAST, indicating no difference in the magnetization curve and magnetic susceptibilities.

Let us derive the expression for the magnetization of such case below.





5 MOSSBAUER

AND MAGNETIC STUDY OF NEPTUNYL(ỵ1) COMPLEXES



108



mI



8



3



11



5



1



7



2



13

10



4

6



15

16



12

9



14



mI



14



5/2

3/2

1/2

+1/2



9



16



6



12



4



10



15

13



2



7



8



+5/2



1



5



11



+3/2



+5/2

+3/2

+1/2

1/2



3



3/2

5/2



Simple relaxation



5/2



+5/2



3/2



+3/2



1/2



+1/2



+1/2



1/2



+3/2



3/2



+5/2



5/2



Jz = +4

H = HM + HQ = –gNμNHIz + HQ



Jz = –4



AzIzJz

FIGURE 5.20

Hyperfine levels for the hyperfine field Hamiltonian of a uniaxial magnetic field with a collinear axial electric

quadrupole interaction.



(i) Free Ion Model [30].

The treatment for the lanthanides series is not generally applicable for the actinides series in interpreting the

magnetic susceptibilities, but it provides a useful starting point in discussing the actinides. When the ligand field

is not too strong, the total angular momentum quantum number J is still a good quantum number. The

magnetization of a free ion with total angular momentum quantum number J is





gJ mB JH 0

;

M ¼ NgJ mB JBJ

kB T



(5.2)



where N is the number of atoms per unit volume, gj is Lande g-factor, H0 is applied field, kB is Boltzmann

constant, and BJ is the Brillouin function,

BJ ðxÞ ẳ











2J ỵ 1

2J ỵ 1

1

1

coth

x coth

x :

2J

2J

2J

2J



(5.3)



According to the high-temperature approximation, the susceptibility x is

xẳ



M

Ng2J m2B JJ ỵ 1ị

;



H0

3kB T



(5.4)



109



5.5 DISCUSSION



τ = 1.0 x 10–8 s



τ = 2.0 x 10–10 s



τ = 5.0 x 10 –11 s



(a)



τ = 1.0 x 10 –11 s



(b)



τ = 3.0 x 10 –12 s



τ = 7.0 x 10 –13 s

FIGURE 5.21



τ = 1.0 x 10 –15 s



–200



–150



–100



–50



0



50



100



150



Velocity (mm s–1)



Calculated paramagnetic

relaxation spectra of Np for

different fluctuation rates. The

hyperfine parameters are

Hhf ¼ 550 T and a collinear

quadrupole interaction

e2qQ ¼ 100 mm sÀ1.



and the paramagnetic effective moment (meff) is obtained as

p

meff ẳ gJ mB JJ ỵ 1ị:



(5.5)



The saturation moment msat is derived as the magnetization per atom at 0 K,

msat ¼



M T¼0

¼ gJ mB J:

N



(5.6)



For an f2 ion with J ¼ 4 and gj ¼ 4/5, meff ¼ 3.58mB/Np and msat ¼ 3.20mB/Np are well known.

(ii) Ising-Type Magnetic Moment.

In case of an Ising-type magnetic moment, the magnetization is given by summation of only J and ỵJ levels. The

Brillouin function becomes hyperbolic tangent (tanh) and then magnetization is given by,





gJ JmB H 0

:

M ¼ NgJ JmB tanh

kB T



(5.7)



According to the high-temperature approximation (tanh x ffi x), the susceptibility is





Ng2J m2B J 2

;

kB T



(5.8)



and the paramagnetic effective moment is obtained as

meff ¼



pffiffiffi

3gJ mB J:



(5.9)



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4 Mössbauer and Magnetic Study of Neptunyl(+1) Complexes

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