Theoretical studies of the local structures and EPR parameters for Cu²⁺ center in Cd₂(NH₄)₂(SO₄)₃ single crystal
The electron paramagnetic resonance (EPR) parameters (g factors gi and the hyperfine structure constants Ai, i = x, y, z) are interpreted by using the perturbation formulae for a 3d⁹ ion in rhombically (D₂h) elongated octahedra. In the calculated formulae, the crystal field parameters are set up fro...
Saved in:
| Published in: | Condensed Matter Physics |
|---|---|
| Date: | 2015 |
| Main Authors: | , , , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут фізики конденсованих систем НАН України
2015
|
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/155276 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Theoretical studies of the local structures and EPR parameters for Cu²⁺ center in Cd₂(NH₂)₂(SO₄)₃ single crystal / Ch.-Y. Li, L.-B. Chen, J.-J. Mao, X.-M. Zheng // Condensed Matter Physics. — 2015. — Т. 18, № 4. — С. 43701: 1–5. — Бібліогр.: 29 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859628086390161408 |
|---|---|
| author | Li, Ch.-Y. Chen, L.-B. Mao, J.-J. Zheng, X.-M. |
| author_facet | Li, Ch.-Y. Chen, L.-B. Mao, J.-J. Zheng, X.-M. |
| citation_txt | Theoretical studies of the local structures and EPR parameters for Cu²⁺ center in Cd₂(NH₂)₂(SO₄)₃ single crystal / Ch.-Y. Li, L.-B. Chen, J.-J. Mao, X.-M. Zheng // Condensed Matter Physics. — 2015. — Т. 18, № 4. — С. 43701: 1–5. — Бібліогр.: 29 назв. — англ. |
| collection | DSpace DC |
| container_title | Condensed Matter Physics |
| description | The electron paramagnetic resonance (EPR) parameters (g factors gi and the hyperfine structure constants Ai, i = x, y, z) are interpreted by using the perturbation formulae for a 3d⁹ ion in rhombically (D₂h) elongated octahedra. In the calculated formulae, the crystal field parameters are set up from the superposition model, and the contribution to the EPR parameters from the admixture of d-orbitals in the ground state wave function of the Cu²⁺ ion was taken into account. Based on the calculation, local structural parameters of the impurity Cu²⁺ center in Cd₂(NH₄)₂(SO₄)₃ (CAS) crystal were obtained (i.e., Rx ≈ 2.05 Å, Ry ≈ 1.91Å, Rz ≈ 2.32 Å). The theoretical EPR parameters based on the above Cu²⁺-O²⁻ bond lengths in CAS crystal show a good agreement with the observed values. The results are discussed.
Параметри електронного парамагнiтного резонансу (ЕПР) (g -фактори gi
i константи надтонкої структури
Ai
, i = x, y, z) iнтерпретуються за допомогою формули збурень для iона 3d⁹
у ромбiчно (D₂h) видовженому восьмиграннику. У формулах параметри кристалiчного поля встановлюються згiдно суперпозицiйної
моделi, де враховується внесок у параметри ЕПР вiд домiшування d-орбiталей в основному станi хвильової функцiї Cu²⁺. На основi обчислень отримано локальнi структурнi параметри домiшки центру Cu²⁺ у
кристалi Cd₂(NH₄)₂(SO₄)₃ (CAS) (тобто, Rx ≈ 2.05 A, ˚ Ry ≈ 1.91 A, ˚ Rz ≈ 2.32 A). ˚ Теоретичнi параметри ЕПР,
що базуються на вищезгаданих довжинах Cu²⁺–O
²⁻ зв’язку у CAS кристалi, демонструють хороше узгодження з спостережуваними значеннями. Результати дослiджень обговорюються.
|
| first_indexed | 2025-11-29T13:28:53Z |
| format | Article |
| fulltext |
Condensed Matter Physics, 2015, Vol. 18, No 4, 43701: 1–5
DOI: 10.5488/CMP.18.43701
http://www.icmp.lviv.ua/journal
Theoretical studies of the local structures and EPR
parameters for Cu
2+
center in Cd2(NH4)2(SO4)3
single crystal
Ch.-Y. Li∗, L.-B. Chen, J.-J. Mao, X.-M. Zheng
School of Physics and Electronic Information, Shangrao Normal University, Shangrao Jiangxi 334000, P. R. China
Received March 24, 2015, in final form July 10, 2015
The electron paramagnetic resonance (EPR) parameters (g factors gi and the hyperfine structure constants Ai ,
i = x, y, z) are interpreted by using the perturbation formulae for a 3d9 ion in rhombically (D2h) elongatedoctahedra. In the calculated formulae, the crystal field parameters are set up from the superposition model,
and the contribution to the EPR parameters from the admixture of d -orbitals in the ground state wave function
of the Cu2+ ion was taken into account. Based on the calculation, local structural parameters of the impurity
Cu2+ center in Cd2(NH4)2(SO4)3 (CAS) crystal were obtained (i.e., Rx ≈ 2.05 Å, Ry ≈ 1.91 Å, Rz ≈ 2.32 Å). The
theoretical EPR parameters based on the above Cu2+–O2− bond lengths in CAS crystal show a good agreement
with the observed values. The results are discussed.
Key words: defect structure, electron paramagnetic resonance, cadmium ammonium sulphate crystal,
Cu
2+
doping
PACS: 76.30.Fc, 75.10.Dg, 71.70.ch
1. Introduction
Single crystal Cd2(NH4)2(SO4)3 (CAS) has attracted interest of researchers due to the unique dielectric
[1], phase transition [2], optical [3], birefringent and electrooptical properties [4]. The above properties
may be closely related to the local structures, chemical bonding and electronic states of the doped ions in
the hosts. Electron paramagnetic resonance (EPR) has long been considered as one of themost useful tools
for the experimental study of chemical bonding. The EPR method provides a detailed description of the
ground state of paramagnetic ions and enables one to explain the nature of crystal field and its symmetry
produced by ligands around the metal ion [5–7]. Among these transition metal ions, Cu
2+
ions with 3d 9
configuration are widely used as paramagnetic probes as they represent a relatively simple one-hole
magnetic system which can be used to obtain information regarding the electron wave function when
there is a ligand field of low symmetry. Thus, EPR spectra of Cu
2+
ion in different diamagnetic host lattices
have been studied bymanyworkers to get some data on the structure, dynamics and environment of host
lattices [8–12]. For example, the EPR experiments were carried out for Cu
2+
doped in CAS single crystal,
and the EPR parameters (anisotropic g factors gi and the hyperfine structure constants Ai , i = x, y, z)
were also measured for rhombic Cu
2+
center [13]. However, no satisfactory interpretation to the above
experimental results has been made so far, and the data on the defect structures of Cu
2+
center have not
been obtained yet.
Considering that (i) the data on local structures and electronic states for Cu
2+
in the CAS single crystal
would be helpful in understanding the microscopic mechanisms of EPR behaviors of this material con-
taining Cu
2+
dopants and (ii) the anisotropic g factors for a d 9
ion in crystals are sensitive to its immediate
environment (and hence to defect structure of d 9
impurity center). Thus, further investigations on EPR
parameters and the defect structures for the Cu
2+
center are of fundamental and practical significance.
∗
E-mail: cyli1962@126.com
© Ch.-Y. Li, L.-B. Chen, J.-J. Mao, X.-M. Zheng, 2015 43701-1
http://dx.doi.org/10.5488/CMP.18.43701
http://www.icmp.lviv.ua/journal
Ch.-Y. Li et al.
In this paper, we have carried out local structure calculations for a paramagnetic Cu
2+
center in CAS and
have interpreted the EPR parameters in this system. The theoretical results are in good agreement with
the experimental values. The Cu
2+
–O
2−
bond lengths are obtained as follows: Rx ≈ 2.05 Å, Ry ≈ 1.91 Å,
Rz ≈ 2.32 Å.
2. Calculation
In the lattice of CAS crystal, each Cd
2+
is surrounded by six oxygen atoms which form a slightly dis-
torted octahedron [13]. When Cu
2+
is doped in CAS crystal, it enters the lattice at Cd
2+
site. For a 3d 9
(Cu
2+
) ion in an octahedral complex with a rhombic elongation it would give gz > gx , g y > 2 [12, 14, 15].
Experimental results of EPR parameters in reference [9] agree with this relation. That is to say, the studied
Cu(H2O)
2+
6 clusters in CAS crystal are in rhombically elongated octahedra. However, the host Cd(H2O)
2+
6
clusters in CAS crystal are under rhombically compressed octahedra similar to many other tutton [16].
A Jahn-Teller ion is due to Cu
2+
. When it occupies a cubic or trigonal octahedral site, the ground state
is doublet
2E . The degeneracy of 2E state should be removed by Jahn-Teller effect, which makes these
octahedral CuL6 clusters become rhombic. Thus, the change of compressed Cd(H2O)2+
6 octahedra in the
host crystals to elongated Cu(H2O)2+
6 octahedra in the impurity centers due to Jahn-Teller effect for Cu
2+
doped CAS crystal becomes understandable.
The local structures of the impurity Cu
2+
center in CAS single crystal under rhombic symmetry are
described by the metal-ligand distance Ri (i = x, y, z). Then, from the superposition model [17] and local
geometrical relationship of the impurity Cu
2+
center, the rhombic field parameters Ds , D t , Dξ and Dη
can be expressed as follows:
Ds = 4
7
A2(R0)
[(
R0
Rx
)t2
+
(
R0
Ry
)t2
−2
(
R0
Rz
)t2
]
,
D t = 8
21
A4(R0)
[(
R0
Rx
)t4
+
(
R0
Ry
)t4
−2
(
R0
Rz
)t4
]
,
Dξ = 2
7
A2(R0)
[(
R0
Rx
)t2
−
(
R0
Ry
)t2
]
,
Dη = 10
21
A4(R0)
[(
R0
Rx
)t4
−
(
R0
Ry
)t4
]
. (1)
Here, t2 ≈ 3 and t4 ≈ 5 are the power-law exponents due to the dominant ionic nature of the bonds
[9, 12, 18–20]. A2(R0), and A4(R0) are intrinsic parameters with the reference distance R0 [taken as R0 =
R = (Rx +Ry +Rz )/3]. The ratio A2(R0)/A4(R0) was found to be in the range 9−12 as per several studies
of optical and EPR spectra using superposition model for 3d n
ions in crystals [12, 19–22]. Here, we take
A2(R0)/A4(R0) = 12. Therefore, axial and perpendicular anisotropies ∆g [= gz − (gx + g y )/2] and δg [=
g y −gx ] of EPR g factors are correlated to the rhombic field parameters and hence to the local structures
of the systems studied.
For a 3d 9
(Cu
2+
) ion under rhombically elongated octahedra, its lower orbital doublet
2Eg would be
separated into two singlets
2 A1g (θ) and 2 A1g (ε). Meanwhile, the higher cubic orbital triplet 2T2g would
be split into three singlets
2B1g (ζ), 2B2g (η) and 2B3g (ξ) [9]. Since the states 2 A1g (θ) and 2 A1g (ε) belong
to the same representation of rhombic symmetry group, the ground state will be neither
2 A1g (θ) nor
2 A1g (ε) but an admixture of both [8, 22], i.e.,
Φ= N
[
α|dx2−y2 +β|d3z2−r 2
]
, (2)
where N is the probability of finding electron in the metal d -orbital, the characteristic of covalency of
the system. α and β are the mixing coefficients due to the rhombic field components and satisfy the
normalization relation:
α2 +β2 = 1. (3)
43701-2
Cu2+ center in Cd2(NH4)2(SO4)3 single crystal
From perturbation theory, the high-order perturbation formulae of EPR parameters (g factors gx , g y ,
gz and hyperfine structure constants Ax , Ay , Az ) for 3d 9
ions in rhombic symmetry can be expressed
as [14, 22]:
gx = gs +
2kζ
(
α+ p
3β
)
E4
− 2αkζ2
(
α+ p
3β
)
E2E4
+ kζ2
(
α2 −3β2
)
E3E4
−2α2gsζ
2
E 2
2
− gsζ
2
(
α− p
3β
)2
2E 2
3
+ 2αkζ2
(
α− p
3β
)2
E2E3
,
g y = gs +
2kζ
(
α− p
3β
)
E3
− 2αkζ2
(
α− p
3β
)
E2E3
+ kζ2
(
α2 −3β2
)
E3E4
−2α2gsζ
2
E 2
2
− gsζ
2
(
α+ p
3β
)2
2E 2
4
+ 2αkζ2
(
α+ p
3β
)2
E2E4
, (4)
gz = gs + 8α2kζ
E2
− 2αkζ2
(
α− p
3β
)
E2E3
− 2αkζ2
(
α+ p
3β
)
E2E4
− gsζ
2
(
α− p
3β
)
2E 2
3
− gsζ
2
(
α+ p
3β
)2
2E 2
4
− kζ2
(
α−3β2
)
E3E4
,
Ax = P0
[
−κ+ 2N 2
7
−κ′+ (
gx − gs
)− 3
14
(
g y − gs
)]
,
Ay = P0
[
−κ+ 2N 2
7
+κ′+ (
g y − gs
)− 3
14
(
gx − gs
)]
, (5)
Az = P0
[
−κ− 4N 2
7
+ (
gz − gs
)+ 3
14
(
gx + g y −2gs
)]
.
Here, gs (≈ 2.0023) is the spin-only value. k (≈ N ) is the orbital reduction factor. P0 (≈ 172×10−4
cm
−1
[23, 24]) is the dipolar hyperfine interaction parameter. The spin-orbit coupling coefficient for CAS:Cu
2+
is acquired as the free-ion value ζ0 (≈ 829 cm−1
[25]) multiplying N . κ and κ′
are the isotropic and
anisotropic core polarization constants, respectively. The denominators Ei (i = 1− 4) can be obtained
from the energy matrices for a 3d 9
ion under rhombic symmetry in terms of the cubic field parameter
Dq and the rhombic field parameters Ds , D t , Dξ and Dη:
E1 = 4Ds +5D t ,
E2 = 10Dq ,
E3 = 10Dq +3Ds −5D t −3Dξ+4Dη , (6)
E4 = 10Dq +3Ds −5D t +3Dξ−4Dη .
According to optical spectral studies for Cu
2+
in oxides with similar [CuO6]10−
cluster [26, 27], the
cubic field parameter Dq (≈ 1050 cm−1
) and the orbital reduction factor k (≈ 0.84) can be obtained.
From the core polarization constant κ (≈ 0.2− 0.6 [8, 9, 20, 24]) for Cu2+
in many crystals with similar
[CuO6]10−
clusters, one can estimate κ (≈ 0.34) for the system studied here. In view of the anisotropic
contributions to hyperfine structure constants from Cu
2+ 3d–3s (4s) orbital admixtures, the anisotropic
core polarization constants are taken as κ′
(≈ 0.021).
Then, for the impurity Cu
2+
in CAS single crystal, we take the Cu
2+
–O
2−
bond lengths:
Rx ≈ 2.05 Å, Ry ≈ 1.91 Å and Rx ≈ 2.32 Å. (7)
Substituting the above values into the matrix formulae in equation (1), and using the ground state
wave function as follows:
Φ= 0.85
[
0.995|dx2−y2 +0.0999|d3z2−r 2
]
(8)
the calculated results (Cal
b
.) of EPR parameters are shown in table 1. For comparison, the results (Cal
a
.)
based on the omission of admixture
2 A1g (θ) and 2 A1g (ε) states (i.e., taking α= 1, β= 0) are also listed in
table 1.
43701-3
Ch.-Y. Li et al.
Table 1. The calculated and experimental anisotropic g factors and hyperfine structure constants (in
10−4
cm
−1
) for Cu
2+
in Cd2(NH4)2(SO4)3 single crystal.
gx g y gz Ax Ay Az
Cal
a
. 2.078 2.047 2.431 −33.5 −32.0 −103.8
Cal
b
. 2.145 2.096 2.412 −19.7 −13.1 −101.9
Expt.[9] 2.144 2.094 2.415 18.7 15.9 97.1
a
Calculations based on the perturbation formulae but with the omission of admixture
2 A1g (θ) and
2A1g (ε) states (i.e., taking α = 1, β = 0).
b
Calculations based on the perturbation formulae and considering the admixture of
2 A1g (θ) and 2 A1g (ε)
states.
3. Discussion
From table 1, it can be seen that the calculated EPR parameters are in good agreement with the ex-
perimental data. Thus, the obtained Cu
2+
–O
2−
bond lengths and admixture coefficients of d -orbitals for
the impurity Cu
2+
ion in CAS single crystal are reasonable.
1. From table 1, one can find that the calculated EPR parameters by using the perturbation formulae
and considering the admixture of the ground states
2 A1g (θ) and 2 A1g (ε) are in good agreement with the
experimental data and the results are better than those obtained using the above formulas while neglect-
ing the admixture of the d -orbitals (i.e., α= 1, β= 0). Moreover, it is noted that the mixing coefficient α
(≈ 0.980) is very close to that (α ≈ 0.977−0.996 [8, 14, 22]) based on the analysis of EPR parameters for
similar rhombic Cu
2+
centers in many crystals.
2. From table 1, one can see that the absolute values of the calculated hyperfine structure constants Ai
are in good agreement with the experimental findings, but the signs of all of them are negative. Actually,
the signs of hyperfine structure constants are very difficult to ascertain. Thus, many experiments give
them as absolute ones [8, 24, 28, 29]. However, negative signs of constants Ai for 3d n
ions inmany crystals
were proposed [20–23]. Thus, the negative signs of hyperfine structure constants obtained in this work
can be regarded as reasonable.
4. Conclusion
The EPR parameters and the local structures of rhombic Cu
2+
center in the CAS crystal are theo-
retically investigated from perturbation formulae for a 3d 9
ion in rhombically elongated octahedra.
The theoretical results based on the above perturbation formulae and considering the admixture of the
ground states
2 A1g (θ) and 2 A1g (ε) are in good agreement with the experimental data. The ligand octa-
hedra around Cu
2+
are found to suffer a relative elongation along the C4 axis due to Jahn-Teller effect,
which may entirely depress the original compressed Cd(H2O)2+
6 octahedra in the host crystals.
Acknowledgements
This work was financially supported by Chinese Natural Science Foundation (grants 11365017,
11465015).
43701-4
Cu2+ center in Cd2(NH4)2(SO4)3 single crystal
References
1. Glogarová M., Fousek J., Phys. Status Solidi A, 1973, 15, 579; doi:10.1002/pssa.2210150227.
2. Kreske S., Devarajan V., J. Phys. C: Solid State Phys., 1982, 15, 7333; doi:10.1088/0022-3719/15/36/015.
3. Satyanarayana N., Radhakrishna S., Solid State Commun., 1985, 54, 891; doi:10.1016/0038-1098(85)91164-0.
4. Konak C., Fousek J., Ivanov N.R., Ferroelectrics, 1973, 6, 235; doi:10.1080/00150197408243973.
5. Kripal R., Misra M.G., Dwivedi P., Appl. Magn. Reson., 2012, 42, 251; doi:10.1007/s00723-011-0286-5.
6. Swalen J.D., Johnson B., Gladney H.M., J. Chem. Phys., 1970, 52, 4078; doi:10.1063/1.1673613.
7. Bozkurt E., Karabulut B., Kartal İ., Spectrochim. Acta A, 2009, 73, 163; doi:10.1016/j.saa.2009.02.015.
8. Kartal İ., Karabulut B., Köksal F., İçbudak H., Z. Naturforsch. A, 2000, 55, 887; doi:10.1515/zna-2000-11-1208.
9. Kuang M.Q., Wu S.Y., Zhang H.M., Optik, 2012, 123, 1601; doi:10.1016/j.ijleo.2011.08.032.
10. Aramburu J.A., Moreno M., J. Chem. Phys., 1985, 83, 6071; doi:10.1063/1.449597.
11. Abragam A., Bleaney B., Electron Paramagnetic Resonance of Transition Ions, Oxford University Press, London,
1970.
12. Zhang H.M., Wu S.Y., Kuang M.Q., Zhang Z.H., J. Phys. Chem. Solids, 2012, 73, 846; doi:10.1016/j.jpcs.2012.02.021.
13. Yerima J.B., Dikko A.B., De D.K., The IJES, 2014, 3, No. 7, 48.
14. Zhang D.T., He L., Yang W.Q., Zheng W.C., Physica B, 2010, 405, 3642; doi:10.1016/j.physb.2010.05.057.
15. Dong H.N., Wu S.Y., Li P., Phys. Status Solidi B, 2004, 241, 1935; doi:10.1002/pssb.200402033.
16. Petrashen V.E., Yablokov Yu.V., Davidovich R.L., Phys. Status Solidi B, 1980, 101, 117; doi:0.1002/pssb.2221010112.
17. Newman D.J., Ng B., Rep. Prog. Phys., 1989, 52, 699; doi:10.1088/0034-4885/52/6/002.
18. Wei W.H., Wu S.Y., Dong H.N., Z. Naturforsch. A, 2005, 60, 541; doi:10.1515/zna-2005-0713.
19. Rudowicz C., Yang Z.Y., Yueng Y.Y., Qin J., J. Phys. Chem. Solids, 2003, 64, 1419; doi:10.1016/S0022-3697(03)00190-2.
20. Zhang H.M., Wan X., Zhang Z.M., Z. Naturforsch. A, 2012, 67, 407; doi:10.5560/zna.2012-0030.
21. Dong H.N., Wu S.Y., Liu X.R., Chen W.D., Z. Naturforsch. A, 2005, 60, 373; doi:10.1515/zna-2005-0509.
22. Zhang H.M., Xiao W.B., Wan X., Radiat. Eff. Defects Solids, 2014, 169, 603; doi:10.1080/10420150.2014.913590.
23. Dong H.N., Wu S.Y., Li P., Phys. Status Solidi B, 2004, 241, 1935; doi:10.1002/pssb.200402033.
24. McGarvey B.R., J. Chem. Phys., 1967, 71, 51; doi:10.1021/j100860a007.
25. Griffith J.S., The Theory of Transition-Metal Ions, Cambridge University Press, London, 1964.
26. Chakravarty A.S., Introduction to the Magnetic Properties of Solids, Wiley Interscience Publication, New York,
1980.
27. Jorgensen C.K., Absorption Spectra and Chemical Bonding in Complexes, 2nd Edn., Pergamon Press, Oxford,
1964.
28. Kripal R., Singh D.K., Spectrochim. Acta A, 2007, 67, 815; doi:10.1016/j.saa.2006.08.038.
29. Kalfaoglu E., Karabulut B., Chem. Phys. Lett., 2011, 505, 154; doi:10.1016/j.cplett.2011.02.038.
Теоретичнi дослiдження локальних структур та параметрiв
електронного парамагнiтного резонансу для центру Cu
2+
в монокристалi Cd2(NH4)2(SO4)3
Ч.-I. Лi, Л.Б. Чен, Дж.-Дж.Мао, Кс.-M. Женг
Школа фiзики i електронної iнформацiї, Нормальний унiверситет Шанграо,Шанграо Цзянсi, КНР
Параметри електронного парамагнiтного резонансу (ЕПР) (g -фактори gi i константи надтонкої структури
Ai , i = x, y, z) iнтерпретуються за допомогою формули збурень для iона 3d9 у ромбiчно (D2h) видовжено-му восьмиграннику. У формулах параметри кристалiчного поля встановлюються згiдно суперпозицiйної
моделi, де враховується внесок у параметри ЕПР вiд домiшування d -орбiталей в основному станi хвильо-
вої функцiї Cu2+. На основi обчислень отримано локальнi структурнi параметри домiшки центру Cu2+ у
кристалi Cd2(NH4)2(SO4)3 (CAS) (тобто, Rx ≈ 2.05 Å, Ry ≈ 1.91 Å, Rz ≈ 2.32 Å). Теоретичнi параметри ЕПР,
що базуються на вищезгаданих довжинах Cu2+–O2− зв’язку у CAS кристалi, демонструють хороше узго-
дження з спостережуваними значеннями. Результати дослiджень обговорюються.
Ключовi слова: дефектна структура, електронний парамагнiтний резонанс, кристал кадмiй амонiєвого
сульфату, легування Cu
2+
43701-5
http://dx.doi.org/10.1002/pssa.2210150227
http://dx.doi.org/10.1088/0022-3719/15/36/015
http://dx.doi.org/10.1016/0038-1098(85)91164-0
http://dx.doi.org/10.1080/00150197408243973
http://dx.doi.org/10.1007/s00723-011-0286-5
http://dx.doi.org/10.1063/1.1673613
http://dx.doi.org/10.1016/j.saa.2009.02.015
http://dx.doi.org/10.1515/zna-2000-11-1208
http://dx.doi.org/10.1016/j.ijleo.2011.08.032
http://dx.doi.org/10.1063/1.449597
http://dx.doi.org/10.1016/j.jpcs.2012.02.021
http://dx.doi.org/10.1016/j.physb.2010.05.057
http://dx.doi.org/10.1002/pssb.200402033
http://dx.doi.org/0.1002/pssb.2221010112
http://dx.doi.org/10.1088/0034-4885/52/6/002
http://dx.doi.org/10.1515/zna-2005-0713
http://dx.doi.org/10.1016/S0022-3697(03)00190-2
http://dx.doi.org/10.5560/zna.2012-0030
http://dx.doi.org/10.1515/zna-2005-0509
http://dx.doi.org/10.1080/10420150.2014.913590
http://dx.doi.org/10.1002/pssb.200402033
http://dx.doi.org/10.1021/j100860a007
http://dx.doi.org/10.1016/j.saa.2006.08.038
http://dx.doi.org/10.1016/j.cplett.2011.02.038
Introduction
Calculation
Discussion
Conclusion
|
| id | nasplib_isofts_kiev_ua-123456789-155276 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1607-324X |
| language | English |
| last_indexed | 2025-11-29T13:28:53Z |
| publishDate | 2015 |
| publisher | Інститут фізики конденсованих систем НАН України |
| record_format | dspace |
| spelling | Li, Ch.-Y. Chen, L.-B. Mao, J.-J. Zheng, X.-M. 2019-06-16T15:22:02Z 2019-06-16T15:22:02Z 2015 Theoretical studies of the local structures and EPR parameters for Cu²⁺ center in Cd₂(NH₂)₂(SO₄)₃ single crystal / Ch.-Y. Li, L.-B. Chen, J.-J. Mao, X.-M. Zheng // Condensed Matter Physics. — 2015. — Т. 18, № 4. — С. 43701: 1–5. — Бібліогр.: 29 назв. — англ. 1607-324X DOI:10.5488/CMP.18.43701 arXiv:1512.07796 PACS: 76.30.Fc, 75.10.Dg, 71.70.ch https://nasplib.isofts.kiev.ua/handle/123456789/155276 The electron paramagnetic resonance (EPR) parameters (g factors gi and the hyperfine structure constants Ai, i = x, y, z) are interpreted by using the perturbation formulae for a 3d⁹ ion in rhombically (D₂h) elongated octahedra. In the calculated formulae, the crystal field parameters are set up from the superposition model, and the contribution to the EPR parameters from the admixture of d-orbitals in the ground state wave function of the Cu²⁺ ion was taken into account. Based on the calculation, local structural parameters of the impurity Cu²⁺ center in Cd₂(NH₄)₂(SO₄)₃ (CAS) crystal were obtained (i.e., Rx ≈ 2.05 Å, Ry ≈ 1.91Å, Rz ≈ 2.32 Å). The theoretical EPR parameters based on the above Cu²⁺-O²⁻ bond lengths in CAS crystal show a good agreement with the observed values. The results are discussed. Параметри електронного парамагнiтного резонансу (ЕПР) (g -фактори gi i константи надтонкої структури Ai , i = x, y, z) iнтерпретуються за допомогою формули збурень для iона 3d⁹ у ромбiчно (D₂h) видовженому восьмиграннику. У формулах параметри кристалiчного поля встановлюються згiдно суперпозицiйної моделi, де враховується внесок у параметри ЕПР вiд домiшування d-орбiталей в основному станi хвильової функцiї Cu²⁺. На основi обчислень отримано локальнi структурнi параметри домiшки центру Cu²⁺ у кристалi Cd₂(NH₄)₂(SO₄)₃ (CAS) (тобто, Rx ≈ 2.05 A, ˚ Ry ≈ 1.91 A, ˚ Rz ≈ 2.32 A). ˚ Теоретичнi параметри ЕПР, що базуються на вищезгаданих довжинах Cu²⁺–O ²⁻ зв’язку у CAS кристалi, демонструють хороше узгодження з спостережуваними значеннями. Результати дослiджень обговорюються. This work was financially supported by Chinese Natural Science Foundation (grants 11365017, 11465015). en Інститут фізики конденсованих систем НАН України Condensed Matter Physics Theoretical studies of the local structures and EPR parameters for Cu²⁺ center in Cd₂(NH₄)₂(SO₄)₃ single crystal Теоретичнi дослiдження локальних структур та параметрiв електронного парамагнiтного резонансу для центру Cu²⁺ в монокристалi Cd₂(NH₄)₂(SO₄)₃ Article published earlier |
| spellingShingle | Theoretical studies of the local structures and EPR parameters for Cu²⁺ center in Cd₂(NH₄)₂(SO₄)₃ single crystal Li, Ch.-Y. Chen, L.-B. Mao, J.-J. Zheng, X.-M. |
| title | Theoretical studies of the local structures and EPR parameters for Cu²⁺ center in Cd₂(NH₄)₂(SO₄)₃ single crystal |
| title_alt | Теоретичнi дослiдження локальних структур та параметрiв електронного парамагнiтного резонансу для центру Cu²⁺ в монокристалi Cd₂(NH₄)₂(SO₄)₃ |
| title_full | Theoretical studies of the local structures and EPR parameters for Cu²⁺ center in Cd₂(NH₄)₂(SO₄)₃ single crystal |
| title_fullStr | Theoretical studies of the local structures and EPR parameters for Cu²⁺ center in Cd₂(NH₄)₂(SO₄)₃ single crystal |
| title_full_unstemmed | Theoretical studies of the local structures and EPR parameters for Cu²⁺ center in Cd₂(NH₄)₂(SO₄)₃ single crystal |
| title_short | Theoretical studies of the local structures and EPR parameters for Cu²⁺ center in Cd₂(NH₄)₂(SO₄)₃ single crystal |
| title_sort | theoretical studies of the local structures and epr parameters for cu²⁺ center in cd₂(nh₄)₂(so₄)₃ single crystal |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/155276 |
| work_keys_str_mv | AT lichy theoreticalstudiesofthelocalstructuresandeprparametersforcu2centerincd2nh42so43singlecrystal AT chenlb theoreticalstudiesofthelocalstructuresandeprparametersforcu2centerincd2nh42so43singlecrystal AT maojj theoreticalstudiesofthelocalstructuresandeprparametersforcu2centerincd2nh42so43singlecrystal AT zhengxm theoreticalstudiesofthelocalstructuresandeprparametersforcu2centerincd2nh42so43singlecrystal AT lichy teoretičnidoslidžennâlokalʹnihstrukturtaparametrivelektronnogoparamagnitnogorezonansudlâcentrucu2vmonokristalicd2nh42so43 AT chenlb teoretičnidoslidžennâlokalʹnihstrukturtaparametrivelektronnogoparamagnitnogorezonansudlâcentrucu2vmonokristalicd2nh42so43 AT maojj teoretičnidoslidžennâlokalʹnihstrukturtaparametrivelektronnogoparamagnitnogorezonansudlâcentrucu2vmonokristalicd2nh42so43 AT zhengxm teoretičnidoslidžennâlokalʹnihstrukturtaparametrivelektronnogoparamagnitnogorezonansudlâcentrucu2vmonokristalicd2nh42so43 |