supplementary materials


Acta Cryst. (2013). E69, i3    [ doi:10.1107/S1600536812050969 ]

RbYb(PO3)4

J. Zhu and H. Chen

Abstract top

Rubidium ytterbium(III) tetrakis(polyphosphate), RbYb(PO3)4, was synthesized by solid-state reaction. It adopts structure type IV of the MRE(PO3)4 (M = alkali metal and RE = rare earth metal) family of compounds. The structure is composed of a three-dimensional framework made up from double spiral polyphosphate chains parallel to [10-1] and irregular [YbO8] polyhedra. There are eight PO4 tetrahedra in the repeat unit of the polyphosphate chains. The Rb+ cation is located in channels extending along [100] that are delimited by the three-dimensional framework. It is surrounded by 11 O atoms, defining an irregular polyhedron.

Comment top

Extensive studies on structures and properties of condensed rare earth phosphates have been carried out in the past owing to their potential application in the optics domain (Miyazawa et al., 1979; Malinowski et al., 1989). Furthermore, their chemical and thermal stability ensures the feasibility of possible applications. Numerous rare-earth phosphates with ytterbium, such as YbP3O9 (Hong, 1974), CsYbP2O7 (Jansen et al., 1991), and K2CsYb(PO4)2 (Rghioui et al., 2002) have been synthesized and structurally determined. However, the literature shows that in the polyphosphate family with general formula MRE(PO3)4 (M = monovalent cation, RE = rare earth cation), only a few examples with ytterbium are known [LiYb(PO3)4 (Fang et al., 2008)]. The reason for this situation is probably the difficulty in obtaining crystals of high quality. Accordingly, our research group is paying attention to the preparation of new polyphosphates MYb(PO3)4. We successfully grew single crystals of rubidium ytterbium polyphosphate, RbYb(PO3)4, the structure of which is reported here.

The crystal structure of RbYb(PO3)4 is shown in Figs. 1 and 2. It is isostructural with CsEu(PO3)4 (Zhu et al., 2009) and belongs to type IV of the MRE(PO3)4 (M = alkali metal and RE = rare earth) family of compounds. The structure can be described as a three-dimensional framework made up from polyphosphate double spiral chains extending parallel to [101] and YbO8 polyhedra. The Rb+ cations are located in infinite tunnels along [100] delimited by the three-dimensional framework. As illustrated in Fig. 3, the P atom is four-coordinated, and four crystallographically distinct PO4 tetrahedra form the (PO3)- double spiral chains by corner-sharing. The P–O bond lengths and O—P—O bond angles show normal values for catena-polyphosphates. There are eight PO4 tetrahedra in the repeating unit of the double spiral chain. The YbIII cation is eight-coordinated in form of a distorted polyhedron with Y—O bond lengths ranging from 2.253 (5) to 2.412 (5) Å, which are consistent with those reported previously (Fang et al., 2008). The shortest Yb···Yb contact is 6.3540 (8) Å. The Rb+ cation are located in the intersecting channels and are surrounded by eleven O atoms, with Rb—O bond lengths in the range of 2.915 (5)–3.504 (5) Å. Neighboring two RbO11 polyhedra are connected by corner-sharing.

Related literature top

For background to applications of condensed rare earth phosphates, see: Malinowski (1989); Miyazawa et al. (1979). For the structures of other ytterbium phosphate compounds, see: Rghioui et al. (2002); Fang et al. (2008); Hong (1974); Jansen et al. (1991). For an isotypic structure, see: Zhu et al. (2009).

Experimental top

Single crystals of RbYb(PO3)4 were grown by solid state reactions. All reagents were purchased commercially and used without further purification. The starting materials RbNO3, Yb2O3 and NH4H2PO4 were weighed in the molar ratio of Rb/Yb/P = 7/1/18 and finely ground in an agate mortar to ensure the best homogeneity and reactivity, and were then placed in a corundum crucible and preheated at 373 K for 6 h. Afterwards, the material was reground and heated to 723 K for 36 h and then cooled to 393 K at a rate of 6 K/h and finally air-quenched to room temperature. A few colourless block-shaped crystals were obtained from the reaction product.

Refinement top

EDX spectrometry using a JSM6700F scanning electron microscope confirmed the composition. The remaining maximum and minimum electron densities are located 0.87 Å and 0.81 Å, respectively, from the Rb atom.

Computing details top

Data collection: APEX2 (Bruker, 2008); cell refinement: SAINT (Bruker, 2008); data reduction: SAINT (Bruker, 2008); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: SHELXTL (Sheldrick, 2008) and DIAMOND (Brandenburg, 2006); software used to prepare material for publication: publCIF (Westrip, 2010).

Figures top
[Figure 1] Fig. 1. View of a part of the title structure. Ellipsoids are shown at the 50% probability level. [Symmetry code: (i) -0.5 + x, 0.5 - y, -0.5 + z; (ii) 1.5 - x, 0.5 + y, 1.5 - z; (iv) 1 - x, -y, 2 - z; (x) x, 1 + y, z; (xiii) 1 - x, 1 - y, 2 - z;]
[Figure 2] Fig. 2. The packing of the structure of RbYb(PO3)4, viewed along the a axis. Polyhedra represents PO4 tetrahedra.
[Figure 3] Fig. 3. The polyphosphate double spiral chains
Rubidium ytterbium(III) tetrakis(polyphosphate) top
Crystal data top
RbYb(PO3)4F(000) = 1049
Mr = 574.40Dx = 4.052 Mg m3
Monoclinic, P21/nMo Kα radiation, λ = 0.71073 Å
Hall symbol: -P 2ynCell parameters from 2802 reflections
a = 10.2022 (15) Åθ = 2.4–29.5°
b = 8.7975 (13) ŵ = 15.80 mm1
c = 10.9300 (16) ÅT = 296 K
β = 106.323 (2)°Block, colorless
V = 941.5 (2) Å30.10 × 0.07 × 0.04 mm
Z = 4
Data collection top
Bruker APEXII CCD
diffractometer
2676 independent reflections
Radiation source: fine-focus sealed tube2024 reflections with I > 2σ(I)
Graphite monochromatorRint = 0.143
φ and ω scansθmax = 30.1°, θmin = 2.4°
Absorption correction: multi-scan
(SADABS; Bruker, 2008)
h = 1414
Tmin = 0.725, Tmax = 0.854k = 1212
9912 measured reflectionsl = 1515
Refinement top
Refinement on F20 restraints
Least-squares matrix: fullPrimary atom site location: structure-invariant direct methods
R[F2 > 2σ(F2)] = 0.043Secondary atom site location: difference Fourier map
wR(F2) = 0.078 w = 1/[σ2(Fo2) + (0.016P)2]
where P = (Fo2 + 2Fc2)/3
S = 1.00(Δ/σ)max < 0.001
2676 reflectionsΔρmax = 2.95 e Å3
163 parametersΔρmin = 2.99 e Å3
Crystal data top
RbYb(PO3)4V = 941.5 (2) Å3
Mr = 574.40Z = 4
Monoclinic, P21/nMo Kα radiation
a = 10.2022 (15) ŵ = 15.80 mm1
b = 8.7975 (13) ÅT = 296 K
c = 10.9300 (16) Å0.10 × 0.07 × 0.04 mm
β = 106.323 (2)°
Data collection top
Bruker APEXII CCD
diffractometer
2676 independent reflections
Absorption correction: multi-scan
(SADABS; Bruker, 2008)
2024 reflections with I > 2σ(I)
Tmin = 0.725, Tmax = 0.854Rint = 0.143
9912 measured reflectionsθmax = 30.1°
Refinement top
R[F2 > 2σ(F2)] = 0.043Δρmax = 2.95 e Å3
wR(F2) = 0.078Δρmin = 2.99 e Å3
S = 1.00Absolute structure: ?
2676 reflectionsFlack parameter: ?
163 parametersRogers parameter: ?
0 restraints
Special details top

Geometry. All e.s.d.'s (except the e.s.d. in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell e.s.d.'s are taken into account individually in the estimation of e.s.d.'s in distances, angles and torsion angles; correlations between e.s.d.'s in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell e.s.d.'s is used for estimating e.s.d.'s involving l.s. planes.

Refinement. Refinement of F2 against ALL reflections. The weighted R-factor wR and goodness of fit S are based on F2, conventional R-factors R are based on F, with F set to zero for negative F2. The threshold expression of F2 > σ(F2) is used only for calculating R-factors(gt) etc. and is not relevant to the choice of reflections for refinement. R-factors based on F2 are statistically about twice as large as those based on F, and R- factors based on ALL data will be even larger.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
Yb0.49845 (3)0.22753 (3)0.68227 (3)0.00898 (9)
Rb0.68841 (9)0.06519 (10)0.95773 (7)0.02424 (19)
P10.45844 (18)0.1715 (2)0.63271 (16)0.0088 (3)
P20.85263 (18)0.0916 (2)0.74217 (16)0.0093 (3)
P30.75504 (18)0.0245 (2)1.27947 (15)0.0088 (3)
P40.67393 (18)0.3877 (2)0.97599 (16)0.0091 (3)
O10.4366 (5)0.2434 (6)0.5063 (4)0.0135 (11)
O20.5242 (5)0.2914 (6)0.7444 (5)0.0141 (10)
O30.5348 (5)0.0274 (6)0.6642 (5)0.0144 (10)
O40.8988 (5)0.0414 (6)0.8251 (5)0.0137 (10)
O50.7325 (5)0.1773 (6)0.7555 (5)0.0142 (10)
O60.6458 (5)0.0858 (6)1.2179 (4)0.0112 (10)
O70.6895 (5)0.1572 (6)1.3448 (5)0.0122 (10)
O80.8156 (5)0.3283 (6)1.0176 (5)0.0140 (11)
O90.5637 (5)0.2853 (6)0.9024 (4)0.0118 (10)
O100.6370 (5)0.4504 (6)1.1006 (4)0.0100 (10)
O110.3317 (5)0.4059 (6)0.6976 (4)0.0125 (10)
O120.6715 (5)0.4534 (6)0.9034 (4)0.0134 (10)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Yb0.00774 (14)0.01101 (15)0.00853 (13)0.00035 (12)0.00286 (9)0.00056 (12)
Rb0.0245 (4)0.0340 (5)0.0145 (4)0.0045 (3)0.0060 (3)0.0013 (3)
P10.0063 (8)0.0108 (8)0.0098 (8)0.0007 (6)0.0029 (6)0.0001 (7)
P20.0078 (8)0.0108 (9)0.0089 (8)0.0006 (6)0.0018 (6)0.0012 (6)
P30.0074 (8)0.0117 (9)0.0076 (8)0.0011 (6)0.0024 (7)0.0015 (6)
P40.0076 (8)0.0127 (9)0.0066 (7)0.0003 (6)0.0015 (6)0.0006 (6)
O10.013 (2)0.020 (3)0.009 (2)0.001 (2)0.0051 (18)0.0006 (19)
O20.012 (2)0.018 (3)0.011 (2)0.006 (2)0.0026 (19)0.006 (2)
O30.006 (2)0.016 (3)0.022 (3)0.005 (2)0.005 (2)0.002 (2)
O40.014 (3)0.013 (3)0.014 (2)0.001 (2)0.005 (2)0.002 (2)
O50.006 (2)0.021 (3)0.015 (2)0.002 (2)0.0018 (19)0.005 (2)
O60.010 (2)0.013 (3)0.011 (2)0.0024 (19)0.0025 (19)0.0004 (19)
O70.011 (2)0.012 (3)0.015 (2)0.002 (2)0.006 (2)0.0038 (19)
O80.010 (2)0.020 (3)0.013 (2)0.004 (2)0.0054 (19)0.002 (2)
O90.007 (2)0.015 (2)0.011 (2)0.004 (2)0.0002 (18)0.003 (2)
O100.005 (2)0.019 (3)0.007 (2)0.0004 (19)0.0035 (18)0.0024 (19)
O110.014 (3)0.017 (3)0.010 (2)0.001 (2)0.010 (2)0.001 (2)
O120.019 (3)0.013 (3)0.007 (2)0.002 (2)0.002 (2)0.0045 (19)
Geometric parameters (Å, º) top
Yb—O8i2.253 (5)P2—O41.474 (5)
Yb—O32.291 (5)P2—O51.480 (5)
Yb—O4ii2.300 (5)P2—O12ii1.590 (5)
Yb—O1iii2.339 (5)P2—O2ii1.599 (5)
Yb—O52.337 (5)P2—Rbii3.681 (2)
Yb—O112.355 (5)P3—O11vi1.477 (5)
Yb—O92.364 (5)P3—O61.488 (5)
Yb—O6iv2.412 (5)P3—O10vii1.595 (5)
Yb—P43.5025 (18)P3—O71.609 (5)
Yb—P3iv3.5196 (18)P3—Ybiv3.5196 (18)
Yb—Rb4.0215 (9)P4—O81.483 (5)
Yb—Rbii4.3152 (10)P4—O91.489 (5)
Rb—O42.915 (5)P4—O12x1.604 (5)
Rb—O1v2.962 (5)P4—O101.609 (5)
Rb—O11vi2.970 (5)O1—Ybiii2.339 (5)
Rb—O63.000 (5)O1—Rbix2.962 (5)
Rb—O23.164 (5)O2—P2viii1.599 (5)
Rb—O33.168 (5)O4—Ybviii2.300 (5)
Rb—O53.193 (5)O5—Rbii3.504 (5)
Rb—O7vii3.265 (5)O6—Ybiv2.412 (5)
Rb—O93.326 (5)O7—P1iv1.601 (5)
Rb—O123.463 (5)O7—Rbxi3.265 (5)
Rb—P33.4796 (19)O8—Ybvi2.253 (5)
Rb—O5viii3.504 (5)O10—P3xi1.595 (5)
P1—O31.477 (5)O11—P3i1.477 (5)
P1—O11.479 (5)O11—Rbi2.970 (5)
P1—O7iv1.601 (5)O12—P2viii1.590 (5)
P1—O21.610 (5)O12—P4xii1.604 (5)
P1—Rbix3.695 (2)
O8i—Yb—O380.51 (18)O6—Rb—P325.18 (10)
O8i—Yb—O4ii116.63 (18)O2—Rb—P3143.14 (10)
O3—Yb—O4ii140.91 (18)O3—Rb—P3154.20 (11)
O8i—Yb—O1iii71.65 (18)O5—Rb—P3121.50 (10)
O3—Yb—O1iii83.67 (18)O7vii—Rb—P364.64 (9)
O4ii—Yb—O1iii70.81 (17)O9—Rb—P385.96 (9)
O8i—Yb—O5140.30 (18)O12—Rb—P3112.54 (9)
O3—Yb—O570.73 (18)O4—Rb—O5viii51.42 (13)
O4ii—Yb—O575.36 (18)O1v—Rb—O5viii53.59 (12)
O1iii—Yb—O578.36 (18)O11vi—Rb—O5viii138.09 (13)
O8i—Yb—O1175.48 (18)O6—Rb—O5viii135.50 (13)
O3—Yb—O11142.76 (18)O2—Rb—O5viii43.63 (12)
O4ii—Yb—O1176.06 (17)O3—Rb—O5viii62.28 (13)
O1iii—Yb—O11114.32 (16)O5—Rb—O5viii82.41 (2)
O5—Yb—O11142.25 (18)O7vii—Rb—O5viii80.78 (12)
O8i—Yb—O9142.46 (17)O9—Rb—O5viii128.79 (12)
O3—Yb—O9107.00 (18)O12—Rb—O5viii42.07 (12)
O4ii—Yb—O981.08 (17)P3—Rb—O5viii143.41 (9)
O1iii—Yb—O9144.61 (17)O3—P1—O1121.0 (3)
O5—Yb—O973.97 (17)O3—P1—O7iv110.8 (3)
O11—Yb—O977.69 (17)O1—P1—O7iv106.0 (3)
O8i—Yb—O6iv77.00 (17)O3—P1—O2107.8 (3)
O3—Yb—O6iv70.55 (17)O1—P1—O2110.4 (3)
O4ii—Yb—O6iv144.63 (17)O7iv—P1—O298.3 (3)
O1iii—Yb—O6iv142.15 (17)O3—P1—Rbix157.9 (2)
O5—Yb—O6iv116.22 (17)O1—P1—Rbix49.7 (2)
O11—Yb—O6iv76.54 (17)O7iv—P1—Rbix62.01 (18)
O9—Yb—O6iv71.55 (16)O2—P1—Rbix94.2 (2)
O8i—Yb—P4156.26 (13)O3—P1—Rb54.7 (2)
O3—Yb—P4114.82 (13)O1—P1—Rb150.9 (2)
O4ii—Yb—P463.63 (12)O7iv—P1—Rb101.48 (18)
O1iii—Yb—P4125.81 (12)O2—P1—Rb55.5 (2)
O5—Yb—P463.41 (13)Rbix—P1—Rb144.73 (6)
O11—Yb—P481.96 (12)O4—P2—O5118.2 (3)
O9—Yb—P419.19 (12)O4—P2—O12ii110.5 (3)
O6iv—Yb—P490.74 (11)O5—P2—O12ii109.0 (3)
O8i—Yb—P3iv59.09 (13)O4—P2—O2ii110.3 (3)
O3—Yb—P3iv62.33 (13)O5—P2—O2ii108.4 (3)
O4ii—Yb—P3iv156.75 (13)O12ii—P2—O2ii98.6 (3)
O1iii—Yb—P3iv122.81 (12)O4—P2—Rb53.8 (2)
O5—Yb—P3iv123.65 (14)O5—P2—Rb64.7 (2)
O11—Yb—P3iv80.89 (13)O12ii—P2—Rb126.9 (2)
O9—Yb—P3iv91.18 (12)O2ii—P2—Rb134.3 (2)
O6iv—Yb—P3iv19.64 (11)O4—P2—Rbii168.4 (2)
P4—Yb—P3iv110.36 (4)O5—P2—Rbii71.5 (2)
O8i—Yb—Rb125.11 (14)O12ii—P2—Rbii69.6 (2)
O3—Yb—Rb51.84 (13)O2ii—P2—Rbii58.8 (2)
O4ii—Yb—Rb117.65 (12)Rb—P2—Rbii136.06 (6)
O1iii—Yb—Rb120.11 (13)O11vi—P3—O6116.9 (3)
O5—Yb—Rb52.52 (13)O11vi—P3—O10vii107.9 (3)
O11—Yb—Rb125.40 (11)O6—P3—O10vii111.2 (3)
O9—Yb—Rb55.76 (13)O11vi—P3—O7109.0 (3)
O6iv—Yb—Rb63.71 (11)O6—P3—O7108.8 (3)
P4—Yb—Rb63.69 (3)O10vii—P3—O7102.0 (3)
P3iv—Yb—Rb73.93 (3)O11vi—P3—Rb57.8 (2)
O8i—Yb—Rbii109.77 (13)O6—P3—Rb59.07 (19)
O3—Yb—Rbii103.25 (13)O10vii—P3—Rb129.2 (2)
O4ii—Yb—Rbii39.06 (13)O7—P3—Rb128.73 (19)
O1iii—Yb—Rbii40.64 (12)O11vi—P3—Ybiv149.9 (2)
O5—Yb—Rbii54.17 (13)O6—P3—Ybiv33.00 (19)
O11—Yb—Rbii111.43 (12)O10vii—P3—Ybiv90.31 (19)
O9—Yb—Rbii104.20 (12)O7—P3—Ybiv89.63 (19)
O6iv—Yb—Rbii170.36 (11)Rb—P3—Ybiv92.05 (4)
P4—Yb—Rbii85.20 (3)O8—P4—O9118.4 (3)
P3iv—Yb—Rbii161.86 (3)O8—P4—O12x109.7 (3)
Rb—Yb—Rbii106.683 (15)O9—P4—O12x110.8 (3)
O4—Rb—O1v54.42 (14)O8—P4—O10107.5 (3)
O4—Rb—O11vi99.00 (14)O9—P4—O10110.1 (3)
O1v—Rb—O11vi85.77 (14)O12x—P4—O1098.4 (3)
O4—Rb—O6142.98 (13)O8—P4—Yb110.0 (2)
O1v—Rb—O698.05 (13)O9—P4—Yb31.48 (19)
O11vi—Rb—O650.08 (14)O12x—P4—Yb87.94 (19)
O4—Rb—O289.44 (14)O10—P4—Yb137.13 (18)
O1v—Rb—O291.34 (13)O8—P4—Rb67.5 (2)
O11vi—Rb—O2167.11 (13)O9—P4—Rb53.3 (2)
O6—Rb—O2118.21 (14)O12x—P4—Rb147.1 (2)
O4—Rb—O373.31 (13)O10—P4—Rb113.9 (2)
O1v—Rb—O3113.31 (13)Yb—P4—Rb64.49 (3)
O11vi—Rb—O3145.61 (14)P1—O1—Ybiii142.4 (3)
O6—Rb—O3143.52 (13)P1—O1—Rbix107.9 (2)
O2—Rb—O346.43 (13)Ybiii—O1—Rbix108.41 (17)
O4—Rb—O548.79 (13)P2viii—O2—P1129.8 (3)
O1v—Rb—O5102.94 (13)P2viii—O2—Rb95.6 (2)
O11vi—Rb—O599.53 (14)P1—O2—Rb99.7 (2)
O6—Rb—O5141.49 (14)P1—O3—Yb140.6 (3)
O2—Rb—O593.36 (13)P1—O3—Rb102.9 (3)
O3—Rb—O549.81 (13)Yb—O3—Rb93.51 (16)
O4—Rb—O7vii100.66 (14)P2—O4—Ybviii138.6 (3)
O1v—Rb—O7vii46.25 (13)P2—O4—Rb102.2 (2)
O11vi—Rb—O7vii76.57 (13)Ybviii—O4—Rb111.14 (19)
O6—Rb—O7vii57.20 (13)P2—O5—Yb149.0 (3)
O2—Rb—O7vii92.37 (13)P2—O5—Rb90.6 (2)
O3—Rb—O7vii137.41 (14)Yb—O5—Rb91.97 (16)
O5—Rb—O7vii148.80 (13)P2—O5—Rbii84.9 (2)
O4—Rb—O998.07 (14)Yb—O5—Rbii93.09 (16)
O1v—Rb—O9145.46 (13)Rb—O5—Rbii174.93 (17)
O11vi—Rb—O977.95 (13)P3—O6—Ybiv127.4 (3)
O6—Rb—O994.50 (13)P3—O6—Rb95.7 (2)
O2—Rb—O9110.67 (12)Ybiv—O6—Rb136.85 (19)
O3—Rb—O970.33 (13)P1iv—O7—P3130.7 (3)
O5—Rb—O951.39 (12)P1iv—O7—Rbxi92.3 (2)
O7vii—Rb—O9150.34 (12)P3—O7—Rbxi135.0 (2)
O4—Rb—O1289.65 (13)P4—O8—Ybvi147.0 (3)
O1v—Rb—O1257.93 (13)P4—O9—Yb129.3 (3)
O11vi—Rb—O12127.26 (12)P4—O9—Rb105.7 (2)
O6—Rb—O1295.14 (13)Yb—O9—Rb88.25 (15)
O2—Rb—O1242.48 (12)P3xi—O10—P4124.3 (3)
O3—Rb—O1286.74 (13)P3i—O11—Yb146.7 (3)
O5—Rb—O12123.37 (12)P3i—O11—Rbi97.3 (2)
O7vii—Rb—O1250.74 (12)Yb—O11—Rbi115.97 (17)
O9—Rb—O12152.28 (12)P2viii—O12—P4xii133.6 (3)
O4—Rb—P3121.61 (10)P2viii—O12—Rb84.9 (2)
O1v—Rb—P391.92 (10)P4xii—O12—Rb141.4 (2)
O11vi—Rb—P324.90 (10)
Symmetry codes: (i) x1/2, y+1/2, z1/2; (ii) x+3/2, y+1/2, z+3/2; (iii) x+1, y, z+1; (iv) x+1, y, z+2; (v) x+1/2, y1/2, z+1/2; (vi) x+1/2, y+1/2, z+1/2; (vii) x+3/2, y1/2, z+5/2; (viii) x+3/2, y1/2, z+3/2; (ix) x1/2, y1/2, z1/2; (x) x, y+1, z; (xi) x+3/2, y+1/2, z+5/2; (xii) x, y1, z.
Acknowledgements top

This investigation was supported by the National Natural Science Foundation of China (No. 20901066), the Natural Science Foundation of Yunnan Province (No. 2012FB122), the training program for young academic and technical leaders in Yunnan Province, the training program for young teachers in Yunnan University, and the program for innovative research teams (in science and technology) of the University of Yunnan Province.

references
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