Crystal structure reinvestigation and spectroscopic analysis of tricadmium orthophosphate

Cherif, F.-Z.; Taibi, M.; Boukhari, A.; Assani, A.; Saadi, M.; El Ammari, L.

doi:10.1107/S2056989023009775

Crystal structure reinvestigation and spectroscopic analysis of tricadmium orthophosphate

F.-Z. Cherif, M. Taibi, A. Boukhari, A. Assani, M. Saadi and L. El Ammari

The transition-metal orthophosphate, β-Cd₃(PO₄)₂, was synthesized by a solid-state reaction and characterized by single-crystal X-ray diffraction and EDS spectroscopy. It crystallizes in the monoclinic system, space group P2₁/n.

Keywords: crystal structure; cadmium phosphate; orthophosphates; infrared spectroscopy.

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Supporting information

	Crystallographic Information File (CIF) https://doi.org/10.1107/S2056989023009775/oo2001sup1.cif Contains datablock I
	Structure factor file (CIF format) https://doi.org/10.1107/S2056989023009775/oo2001Isup2.hkl Contains datablock I

CCDC reference: 2306650

checkCIF report

Key indicators

Structure: I

Single-crystal X-ray study
T = 296 K
Mean (P-O) = 0.002 Å
R factor = 0.023
wR factor = 0.054
Data-to-parameter ratio = 28.0

checkCIF/PLATON results

No syntax errors found



Alert level A
POWD001_ALERT_1_A _pd_proc_ls_prof_wR_factor (R_wp) and
              _refine_ls_goodness_of_fit_all are missing.
              These should be present for a powder diffraction study.

Alert level C
PLAT042_ALERT_1_C Calc. and Reported MoietyFormula Strings  Differ     Please Check
PLAT241_ALERT_2_C High   'MainMol' Ueq as Compared to Neighbors of         O6 Check
PLAT906_ALERT_3_C Large K Value in the Analysis of Variance ......      2.624 Check
PLAT971_ALERT_2_C Check Calcd Resid. Dens.  0.62Ang From Cd2             1.54 eA-3
PLAT972_ALERT_2_C Check Calcd Resid. Dens.  0.61Ang From Cd3            -1.73 eA-3
PLAT975_ALERT_2_C Check Calcd Resid. Dens.  0.88Ang From O8      .       0.82 eA-3

Alert level G
PLAT004_ALERT_5_G Polymeric Structure Found with Maximum Dimension          3 Info
PLAT045_ALERT_1_G Calculated and Reported Z Differ by a Factor ...      0.333 Check
PLAT794_ALERT_5_G Tentative Bond Valency for Cd1       (II)      .       2.03 Info
PLAT794_ALERT_5_G Tentative Bond Valency for Cd2       (II)      .       2.13 Info
PLAT794_ALERT_5_G Tentative Bond Valency for Cd3       (II)      .       2.16 Info
PLAT794_ALERT_5_G Tentative Bond Valency for Cd4       (II)      .       2.15 Info
PLAT794_ALERT_5_G Tentative Bond Valency for Cd5       (II)      .       2.21 Info
PLAT794_ALERT_5_G Tentative Bond Valency for Cd6       (II)      .       2.16 Info
PLAT794_ALERT_5_G Tentative Bond Valency for Cd7       (II)      .       2.17 Info
PLAT794_ALERT_5_G Tentative Bond Valency for Cd8       (II)      .       2.20 Info
PLAT794_ALERT_5_G Tentative Bond Valency for Cd9       (II)      .       2.12 Info
PLAT899_ALERT_4_G SHELXL2018 is Deprecated and Succeeded by SHELXL     2019/3 Note
PLAT910_ALERT_3_G Missing # of FCF Reflection(s) Below Theta(Min).          1 Note
PLAT933_ALERT_2_G Number of HKL-OMIT Records in Embedded .res File          1 Note

   1 ALERT level A = Most likely a serious problem - resolve or explain
   0 ALERT level B = A potentially serious problem, consider carefully
   6 ALERT level C = Check. Ensure it is not caused by an omission or oversight
  14 ALERT level G = General information/check it is not something unexpected

   3 ALERT type 1 CIF construction/syntax error, inconsistent or missing data
   5 ALERT type 2 Indicator that the structure model may be wrong or deficient
   2 ALERT type 3 Indicator that the structure quality may be low
   1 ALERT type 4 Improvement, methodology, query or suggestion
  10 ALERT type 5 Informative message, check

# start Validation Reply Form
_vrf_POWD001_I
;
PROBLEM: _pd_proc_ls_prof_wR_factor (R_wp) and
RESPONSE: ...
;
# end Validation Reply Form

Reference check results

The following references were not checked in detail as they were not recognized as references to journal articles

Bruker, (2016). APEX3 (Version 5.054), SAINT (Version 6.36A), SADABS; Bruker AXS Inc.: Madison, WI, USA. [software reference?]

Rajasri, S., Krishnakumar, B., Abilio, J. F., Sobral, N., Balachandran, S., Swaminathan, M. & Muthuvel, I. (2019). Materials Today Proceedings, 15, 471--480.

Rong, J., Zhang, T., Qiu, F. & Zhu, Y. (2017). ACS Sustainable Chem. Eng. 5, 4468--4477. https://doi. org/10.1021/acssuschemeng. 8b01469

Stephens, J. S. (1967). Doctor of Philosophy, Thesis, McMaster University, Hamilton, Ontario, (May, 1967).

The following reference may be incorrectly formatted

Sugiyama, K. & Tokonami, M. (1990). Mineralogical Journal 15, 141-146. doi: 10.2465/minerj. 15.141
[Unrecognized journal title.]

All references appear to be cited unambiguously

Computing details top

Tricadmium bis(orthophosphate) top

Crystal data top

Cd₃(PO₄)₂	F(000) = 2856
M_r = 527.14	D_x = 5.165 Mg m⁻³
Monoclinic, P2₁/n	Mo Kα radiation, λ = 0.71073 Å
a = 9.1895 (7) Å	Cell parameters from 9851 reflections
b = 10.3507 (8) Å	θ = 2.2–36.3°
c = 21.6887 (16) Å	µ = 9.81 mm⁻¹
β = 99.644 (3)°	T = 296 K
V = 2033.8 (3) Å³	Parallelepiped, colourless
Z = 12	0.31 × 0.27 × 0.22 mm

Data collection top

Bruker X8 APEX Diffractometer	9851 independent reflections
Radiation source: fine-focus sealed tube	8280 reflections with I > 2σ(I)
Graphite monochromator	R_int = 0.047
φ and ω scans	θ_max = 36.3°, θ_min = 2.2°
Absorption correction: multi-scan (SADABS; Krause et al., 2015)	h = −15→15
T_min = 0.544, T_max = 0.747	k = −17→17
129694 measured reflections	l = −36→36

Refinement top

Refinement on F²	0 restraints
Least-squares matrix: full	Primary atom site location: dual
R[F² > 2σ(F²)] = 0.023	Secondary atom site location: difference Fourier map
wR(F²) = 0.054	w = 1/[σ²(F_o²) + (0.0205P)² + 4.3579P] where P = (F_o² + 2F_c²)/3
S = 1.07	(Δ/σ)_max = 0.004
9851 reflections	Δρ_max = 1.60 e Å⁻³
352 parameters	Δρ_min = −1.74 e Å⁻³

Special details top

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

Refinement. The crystal structure of β-Cd₃(PO₄)₂ was investigated using single-crystal X-ray diffraction data collected at room temperature with a Bruker D8 Venture Super DUO Diffractometer equipped with a PHOTON100 CMOS area-detector and monochromatic MoKα radiation (λ=0.71073 Å). APEX3 (Bruker, APEX3 (Version 5.054), SAINT (Version 6.36A), SADABS. (Bruker, 2016) software was used for data reduction and the absorption correction was performed by multi-scan semi-empirical method using SADABS program (Krause, et al. 2015). The crystal structure was solved using dual space algorithm as implemented in SHELXT program (Sheldrick, 2015a), completed by a Difference Fourier map and refined by least-squares using SHELXL program (Sheldrick 2015b) integrated into the WinGX interface (Farrugia, 2012).

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq
Cd1	0.74691 (2)	0.71080 (2)	0.36476 (2)	0.01178 (3)
Cd2	0.27909 (2)	0.39633 (2)	0.92293 (2)	0.01251 (3)
Cd3	0.60228 (2)	0.39417 (2)	0.58439 (2)	0.01124 (3)
Cd4	0.94569 (2)	0.28838 (2)	0.95686 (2)	0.01149 (3)
Cd5	0.71202 (2)	0.41020 (2)	0.77990 (2)	0.01002 (3)
Cd6	0.05148 (2)	0.60385 (2)	0.74786 (2)	0.01157 (3)
Cd7	0.60491 (2)	0.60229 (2)	0.89221 (2)	0.00988 (3)
Cd8	0.40399 (2)	0.70425 (2)	0.70409 (2)	0.01088 (3)
Cd9	0.93970 (2)	0.59251 (2)	0.56014 (2)	0.01049 (3)
P1	0.69824 (6)	0.43486 (5)	0.43995 (2)	0.00739 (9)
P2	0.95135 (6)	0.36168 (6)	0.67096 (3)	0.00825 (9)
P3	0.69971 (7)	0.64250 (6)	0.66858 (3)	0.00801 (9)
P4	0.35072 (6)	0.42713 (5)	0.77938 (2)	0.00705 (9)
P5	−0.03383 (6)	0.57903 (5)	0.89456 (2)	0.00714 (9)
P6	0.62768 (7)	0.35381 (6)	1.00079 (3)	0.00835 (9)
O1	0.7195 (2)	0.32411 (17)	0.39518 (8)	0.0153 (3)
O2	0.62835 (19)	0.55464 (17)	0.40326 (8)	0.0120 (3)
O3	0.84808 (19)	0.46875 (17)	0.47901 (8)	0.0132 (3)
O4	0.5870 (2)	0.39020 (19)	0.48128 (8)	0.0158 (3)
O5	0.8179 (2)	0.30534 (18)	0.62739 (9)	0.0161 (3)
O6	1.0338 (2)	0.4652 (2)	0.63983 (10)	0.0255 (5)
O7	1.0579 (2)	0.24766 (18)	0.68907 (8)	0.0166 (3)
O8	0.9105 (2)	0.41803 (19)	0.73139 (8)	0.0175 (4)
O9	0.7346 (2)	0.57633 (18)	0.60939 (8)	0.0153 (3)
O10	0.5947 (2)	0.75733 (17)	0.64955 (8)	0.0149 (3)
O11	0.8400 (2)	0.70048 (17)	0.70769 (9)	0.0154 (3)
O12	0.6177 (2)	0.5506 (2)	0.70596 (9)	0.0204 (4)
O13	0.28310 (19)	0.54515 (17)	0.74156 (8)	0.0117 (3)
O14	0.3730 (2)	0.31593 (17)	0.73519 (8)	0.0138 (3)
O15	0.50013 (19)	0.45790 (17)	0.82041 (8)	0.0125 (3)
O16	0.2369 (2)	0.38617 (18)	0.82065 (8)	0.0138 (3)
O17	0.0602 (2)	0.63773 (19)	0.84925 (8)	0.0163 (3)
O18	−0.18533 (19)	0.53473 (17)	0.85947 (8)	0.0128 (3)
O19	−0.0598 (2)	0.68256 (17)	0.94219 (8)	0.0136 (3)
O20	0.05089 (19)	0.46386 (16)	0.92864 (8)	0.0117 (3)
O21	0.4881 (2)	0.30043 (18)	0.95967 (9)	0.0168 (3)
O22	0.6649 (2)	0.49060 (17)	0.98153 (8)	0.0156 (3)
O23	0.7475 (2)	0.25479 (18)	0.99447 (9)	0.0186 (4)
O24	0.6119 (2)	0.36004 (19)	1.07107 (8)	0.0167 (3)

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
Cd1	0.01169 (7)	0.01256 (7)	0.01087 (6)	−0.00280 (6)	0.00125 (5)	0.00014 (5)
Cd2	0.01060 (7)	0.01629 (8)	0.00983 (6)	0.00050 (6)	−0.00060 (5)	−0.00269 (5)
Cd3	0.00935 (7)	0.01100 (7)	0.01280 (7)	−0.00021 (5)	0.00021 (5)	−0.00116 (5)
Cd4	0.01258 (7)	0.01305 (7)	0.00873 (6)	−0.00046 (6)	0.00142 (5)	0.00123 (5)
Cd5	0.01194 (7)	0.00914 (7)	0.00902 (6)	−0.00021 (5)	0.00187 (5)	0.00066 (5)
Cd6	0.00914 (7)	0.01060 (7)	0.01430 (7)	−0.00063 (5)	0.00009 (5)	−0.00122 (5)
Cd7	0.01032 (7)	0.01008 (7)	0.00935 (6)	0.00014 (5)	0.00200 (5)	0.00078 (5)
Cd8	0.01204 (7)	0.01262 (7)	0.00817 (6)	0.00067 (5)	0.00220 (5)	0.00167 (5)
Cd9	0.01215 (7)	0.01086 (7)	0.00841 (6)	0.00036 (5)	0.00158 (5)	0.00089 (5)
P1	0.0078 (2)	0.0074 (2)	0.0064 (2)	−0.00011 (18)	−0.00040 (17)	−0.00001 (17)
P2	0.0080 (2)	0.0090 (2)	0.0074 (2)	0.00023 (18)	0.00032 (17)	−0.00032 (18)
P3	0.0085 (2)	0.0079 (2)	0.0072 (2)	0.00045 (18)	0.00022 (17)	−0.00030 (17)
P4	0.0076 (2)	0.0069 (2)	0.00626 (19)	−0.00028 (18)	0.00013 (17)	−0.00019 (17)
P5	0.0077 (2)	0.0068 (2)	0.0065 (2)	−0.00028 (18)	−0.00001 (17)	−0.00010 (17)
P6	0.0090 (2)	0.0093 (2)	0.0066 (2)	−0.00031 (18)	0.00063 (18)	0.00027 (18)
O1	0.0210 (9)	0.0105 (7)	0.0122 (7)	0.0037 (6)	−0.0040 (6)	−0.0047 (6)
O2	0.0108 (7)	0.0113 (7)	0.0139 (7)	0.0031 (6)	0.0018 (6)	0.0041 (6)
O3	0.0094 (7)	0.0163 (8)	0.0127 (7)	−0.0006 (6)	−0.0016 (6)	−0.0052 (6)
O4	0.0163 (8)	0.0198 (9)	0.0118 (7)	−0.0071 (7)	0.0042 (6)	0.0019 (6)
O5	0.0124 (8)	0.0132 (8)	0.0194 (8)	0.0010 (6)	−0.0070 (6)	−0.0054 (6)
O6	0.0160 (9)	0.0360 (12)	0.0225 (9)	−0.0078 (8)	−0.0023 (7)	0.0188 (9)
O7	0.0176 (9)	0.0154 (8)	0.0157 (8)	0.0064 (7)	−0.0010 (6)	−0.0020 (6)
O8	0.0161 (9)	0.0231 (9)	0.0145 (7)	−0.0024 (7)	0.0060 (6)	−0.0087 (7)
O9	0.0155 (8)	0.0166 (8)	0.0145 (7)	−0.0019 (7)	0.0048 (6)	−0.0060 (6)
O10	0.0162 (8)	0.0117 (8)	0.0157 (7)	0.0051 (6)	−0.0004 (6)	0.0013 (6)
O11	0.0124 (8)	0.0102 (8)	0.0203 (8)	0.0006 (6)	−0.0066 (6)	−0.0037 (6)
O12	0.0143 (9)	0.0254 (10)	0.0212 (9)	−0.0013 (7)	0.0022 (7)	0.0144 (8)
O13	0.0094 (7)	0.0108 (7)	0.0144 (7)	0.0015 (6)	0.0002 (6)	0.0046 (6)
O14	0.0175 (8)	0.0109 (7)	0.0116 (7)	0.0043 (6)	−0.0020 (6)	−0.0042 (6)
O15	0.0095 (7)	0.0145 (8)	0.0122 (7)	0.0004 (6)	−0.0019 (6)	−0.0030 (6)
O16	0.0138 (8)	0.0177 (8)	0.0103 (7)	−0.0043 (6)	0.0034 (6)	0.0015 (6)
O17	0.0179 (9)	0.0194 (9)	0.0122 (7)	−0.0069 (7)	0.0045 (6)	0.0041 (6)
O18	0.0080 (7)	0.0155 (8)	0.0141 (7)	−0.0006 (6)	−0.0004 (6)	−0.0058 (6)
O19	0.0199 (9)	0.0095 (7)	0.0098 (6)	0.0042 (6)	−0.0025 (6)	−0.0026 (6)
O20	0.0115 (7)	0.0093 (7)	0.0141 (7)	0.0022 (6)	0.0015 (6)	0.0029 (6)
O21	0.0134 (8)	0.0153 (8)	0.0185 (8)	−0.0015 (6)	−0.0065 (6)	−0.0026 (7)
O22	0.0207 (9)	0.0112 (8)	0.0133 (7)	−0.0040 (6)	−0.0017 (6)	0.0036 (6)
O23	0.0153 (9)	0.0152 (8)	0.0272 (9)	0.0027 (7)	0.0092 (7)	−0.0004 (7)
O24	0.0165 (9)	0.0258 (10)	0.0080 (6)	0.0053 (7)	0.0030 (6)	0.0029 (6)

Geometric parameters (Å, º) top

Cd1—O2	2.1913 (17)	Cd8—O13	2.2156 (17)
Cd1—O14ⁱ	2.2782 (17)	Cd8—O1ⁱ	2.2783 (17)
Cd1—O17ⁱⁱ	2.3068 (18)	Cd8—O16^xii	2.2973 (18)
Cd1—O24ⁱⁱⁱ	2.3243 (18)	Cd8—O7ⁱⁱⁱ	2.3285 (18)
Cd1—O7^iv	2.338 (2)	Cd8—O10	2.3381 (19)
Cd2—O16	2.1896 (17)	Cd8—O12	2.522 (2)
Cd2—O21	2.1900 (19)	Cd9—O3	2.2248 (17)
Cd2—O20	2.2336 (18)	Cd9—O6	2.2297 (19)
Cd2—O22^v	2.3602 (18)	Cd9—O21ⁱⁱⁱ	2.3135 (19)
Cd2—O1^vi	2.3996 (18)	Cd9—O9	2.3230 (18)
Cd3—O4	2.2176 (17)	Cd9—O3^iv	2.3411 (18)
Cd3—O5	2.2409 (18)	Cd9—O23ⁱⁱⁱ	2.550 (2)
Cd3—O2ⁱ	2.2437 (17)	P1—O3	1.5316 (18)
Cd3—O9	2.2598 (18)	P1—O1	1.5358 (18)
Cd3—O19^vii	2.2818 (18)	P1—O4	1.5388 (18)
Cd4—O23	2.1454 (19)	P1—O2	1.5529 (17)
Cd4—O20^viii	2.1924 (17)	P2—O6	1.533 (2)
Cd4—O4^ix	2.2702 (18)	P2—O5	1.5327 (18)
Cd4—O19^v	2.2836 (17)	P2—O8	1.5376 (18)
Cd4—O10^x	2.2978 (18)	P2—O7	1.5417 (19)
Cd5—O12	2.2292 (18)	P3—O12	1.5283 (19)
Cd5—O18^viii	2.2326 (17)	P3—O9	1.5354 (18)
Cd5—O11^x	2.2486 (18)	P3—O11	1.5409 (18)
Cd5—O8	2.2543 (18)	P3—O10	1.5430 (18)
Cd5—O15	2.3196 (18)	P4—O14	1.5334 (18)
Cd6—O17	2.2150 (18)	P4—O15	1.5391 (18)
Cd6—O11^xi	2.2293 (18)	P4—O13	1.5430 (17)
Cd6—O13	2.2396 (17)	P4—O16	1.5451 (18)
Cd6—O14^xii	2.3131 (18)	P5—O19	1.5348 (18)
Cd6—O8^xi	2.313 (2)	P5—O17	1.5383 (18)
Cd7—O22	2.2441 (17)	P5—O18	1.5404 (18)
Cd7—O15	2.2547 (17)	P5—O20	1.5429 (17)
Cd7—O18^viii	2.2732 (17)	P6—O23	1.527 (2)
Cd7—O5ⁱⁱⁱ	2.2808 (18)	P6—O22	1.5311 (19)
Cd7—O24^v	2.2990 (19)	P6—O21	1.5372 (19)
Cd7—O7ⁱⁱⁱ	2.5935 (19)	P6—O24	1.5566 (18)

O2—Cd1—O14ⁱ	94.64 (7)	O15—Cd7—O7ⁱⁱⁱ	77.53 (6)
O2—Cd1—O17ⁱⁱ	98.73 (7)	O18^viii—Cd7—O7ⁱⁱⁱ	112.89 (6)
O14ⁱ—Cd1—O17ⁱⁱ	73.41 (6)	O5ⁱⁱⁱ—Cd7—O7ⁱⁱⁱ	60.05 (6)
O2—Cd1—O24ⁱⁱⁱ	121.70 (6)	O24^v—Cd7—O7ⁱⁱⁱ	72.69 (6)
O14ⁱ—Cd1—O24ⁱⁱⁱ	141.54 (7)	O13—Cd8—O1ⁱ	92.86 (7)
O17ⁱⁱ—Cd1—O24ⁱⁱⁱ	87.86 (7)	O13—Cd8—O16^xii	113.40 (7)
O2—Cd1—O7^iv	142.93 (6)	O1ⁱ—Cd8—O16^xii	73.32 (6)
O14ⁱ—Cd1—O7^iv	80.58 (7)	O13—Cd8—O7ⁱⁱⁱ	77.26 (6)
O17ⁱⁱ—Cd1—O7^iv	114.60 (7)	O1ⁱ—Cd8—O7ⁱⁱⁱ	158.96 (7)
O24ⁱⁱⁱ—Cd1—O7^iv	77.21 (6)	O16^xii—Cd8—O7ⁱⁱⁱ	93.39 (6)
O16—Cd2—O21	110.02 (7)	O13—Cd8—O10	145.55 (6)
O16—Cd2—O20	93.60 (7)	O1ⁱ—Cd8—O10	81.31 (7)
O21—Cd2—O20	153.63 (7)	O16^xii—Cd8—O10	97.48 (6)
O16—Cd2—O22^v	152.72 (7)	O7ⁱⁱⁱ—Cd8—O10	117.23 (7)
O21—Cd2—O22^v	81.75 (7)	O13—Cd8—O12	87.84 (6)
O20—Cd2—O22^v	82.22 (7)	O1ⁱ—Cd8—O12	101.36 (7)
O16—Cd2—O1^vi	72.91 (6)	O16^xii—Cd8—O12	158.06 (6)
O21—Cd2—O1^vi	79.03 (7)	O7ⁱⁱⁱ—Cd8—O12	96.82 (7)
O20—Cd2—O1^vi	97.73 (7)	O10—Cd8—O12	60.58 (6)
O22^v—Cd2—O1^vi	134.32 (6)	O3—Cd9—O6	108.60 (8)
O4—Cd3—O5	108.31 (7)	O3—Cd9—O21ⁱⁱⁱ	118.11 (7)
O4—Cd3—O2ⁱ	102.91 (7)	O6—Cd9—O21ⁱⁱⁱ	127.43 (7)
O5—Cd3—O2ⁱ	146.53 (7)	O3—Cd9—O9	95.37 (6)
O4—Cd3—O9	101.42 (7)	O6—Cd9—O9	80.79 (7)
O5—Cd3—O9	80.78 (7)	O21ⁱⁱⁱ—Cd9—O9	115.63 (7)
O2ⁱ—Cd3—O9	104.80 (7)	O3—Cd9—O3^iv	77.59 (7)
O4—Cd3—O19^vii	75.41 (6)	O6—Cd9—O3^iv	83.26 (7)
O5—Cd3—O19^vii	79.23 (6)	O21ⁱⁱⁱ—Cd9—O3^iv	84.39 (7)
O2ⁱ—Cd3—O19^vii	97.58 (7)	O9—Cd9—O3^iv	159.49 (7)
O9—Cd3—O19^vii	157.50 (7)	O3—Cd9—O23ⁱⁱⁱ	82.85 (6)
O23—Cd4—O20^viii	133.04 (7)	O6—Cd9—O23ⁱⁱⁱ	153.31 (7)
O23—Cd4—O4^ix	105.57 (7)	O21ⁱⁱⁱ—Cd9—O23ⁱⁱⁱ	59.54 (6)
O20^viii—Cd4—O4^ix	118.55 (7)	O9—Cd9—O23ⁱⁱⁱ	74.04 (6)
O23—Cd4—O19^v	86.54 (7)	O3^iv—Cd9—O23ⁱⁱⁱ	123.24 (6)
O20^viii—Cd4—O19^v	90.31 (7)	O3—P1—O1	108.84 (10)
O4^ix—Cd4—O19^v	74.37 (6)	O3—P1—O4	111.71 (10)
O23—Cd4—O10^x	110.78 (8)	O1—P1—O4	108.13 (11)
O20^viii—Cd4—O10^x	80.80 (6)	O3—P1—O2	110.91 (10)
O4^ix—Cd4—O10^x	96.33 (6)	O1—P1—O2	110.94 (10)
O19^v—Cd4—O10^x	162.23 (7)	O4—P1—O2	106.28 (10)
O12—Cd5—O18^viii	104.06 (7)	O6—P2—O5	113.44 (11)
O12—Cd5—O11^x	130.59 (7)	O6—P2—O8	108.65 (12)
O18^viii—Cd5—O11^x	122.38 (7)	O5—P2—O8	112.67 (11)
O12—Cd5—O8	83.60 (7)	O6—P2—O7	107.92 (12)
O18^viii—Cd5—O8	94.01 (7)	O5—P2—O7	105.92 (10)
O11^x—Cd5—O8	107.18 (7)	O8—P2—O7	107.98 (11)
O12—Cd5—O15	83.32 (7)	O12—P3—O9	110.88 (12)
O18^viii—Cd5—O15	81.78 (6)	O12—P3—O11	113.07 (11)
O11^x—Cd5—O15	87.22 (7)	O9—P3—O11	111.18 (11)
O8—Cd5—O15	164.84 (7)	O12—P3—O10	106.22 (11)
O17—Cd6—O11^xi	101.60 (7)	O9—P3—O10	109.20 (10)
O17—Cd6—O13	103.11 (7)	O11—P3—O10	105.98 (10)
O11^xi—Cd6—O13	150.83 (7)	O14—P4—O15	108.48 (10)
O17—Cd6—O14^xii	74.45 (6)	O14—P4—O13	110.24 (10)
O11^xi—Cd6—O14^xii	81.67 (6)	O15—P4—O13	112.60 (10)
O13—Cd6—O14^xii	90.24 (7)	O14—P4—O16	109.29 (11)
O17—Cd6—O8^xi	102.19 (6)	O15—P4—O16	110.29 (10)
O11^xi—Cd6—O8^xi	83.31 (7)	O13—P4—O16	105.89 (10)
O13—Cd6—O8^xi	106.17 (7)	O19—P5—O17	108.76 (11)
O14^xii—Cd6—O8^xi	163.55 (7)	O19—P5—O18	108.10 (10)
O22—Cd7—O15	105.64 (7)	O17—P5—O18	111.09 (10)
O22—Cd7—O18^viii	90.72 (7)	O19—P5—O20	109.87 (9)
O15—Cd7—O18^viii	82.34 (6)	O17—P5—O20	108.60 (11)
O22—Cd7—O5ⁱⁱⁱ	126.62 (7)	O18—P5—O20	110.39 (10)
O15—Cd7—O5ⁱⁱⁱ	126.31 (7)	O23—P6—O22	113.50 (11)
O18^viii—Cd7—O5ⁱⁱⁱ	85.34 (7)	O23—P6—O21	104.52 (11)
O22—Cd7—O24^v	83.70 (7)	O22—P6—O21	112.15 (10)
O15—Cd7—O24^v	93.27 (7)	O23—P6—O24	107.62 (11)
O18^viii—Cd7—O24^v	171.73 (7)	O22—P6—O24	106.90 (11)
O5ⁱⁱⁱ—Cd7—O24^v	102.88 (7)	O21—P6—O24	112.17 (11)
O22—Cd7—O7ⁱⁱⁱ	156.36 (7)

Symmetry codes: (i) −x+1, −y+1, −z+1; (ii) x+1/2, −y+3/2, z−1/2; (iii) −x+3/2, y+1/2, −z+3/2; (iv) −x+2, −y+1, −z+1; (v) −x+1, −y+1, −z+2; (vi) x−1/2, −y+1/2, z+1/2; (vii) −x+1/2, y−1/2, −z+3/2; (viii) x+1, y, z; (ix) x+1/2, −y+1/2, z+1/2; (x) −x+3/2, y−1/2, −z+3/2; (xi) x−1, y, z; (xii) −x+1/2, y+1/2, −z+3/2.

Infrared bands of β-Cd₃(PO₄)₂ and their assignments top

Band	Assignment
431	PO₄ v2 out of plane bending modes
531	PO₄ v4 out of plane bending modes
544	PO₄ v4 out of plane bending modes
558	PO₄ v4 out of plane bending modes
570	PO₄ v4 out of plane bending modes
597	PO₄ v4 out of plane bending modes
624	PO₄ v4 out of plane bending modes
936	The symmetric P—O stretching corresponds to the fundamental vibrational mode v1
971	The symmetric P—O stretching corresponds to the fundamental vibrational mode v1
1026	The triple-degenerate asymmetric P—O stretching mode corresponds to the v3 fundamental vibrational mode
1051	The triple-degenerate asymmetric P—O stretching mode corresponds to the v3 fundamental vibrational mode

Divalent cation-based orthophosphates [M₃(PO₄)₂] summary crystallographic data (Å, °, Å³) top

Compound	Space group	a	b	c	β	Z	V	Reference
Ca₃(PO₄)₂	P2₁/a	12.89 (6)	27.28 (5)	15.22 (3)	126.2 (9)	24	4317.5	Mathew et al. (1977)
Cd₃(PO₄)₂	P2₁/c	9.22 (4)	10.34 (9)	24.90 (2)	120.7 (1)	12	2030.0	Stephens (1967)
	P2₁/n	9.19 (7)	10.35 (1)	21.69 (9)	99.6 (2)	12	2033.8	Present work
Co₃(PO₄)₂	P2₁/n	5.06 (8)	8.36 (2)	8.79 (4)	121.0 (1)	2	319.4	Anderson et al. (1975)
Cr₃(PO₄)₂	P2₁/n	4.97 (9)	9.50 (3)	6.48 (2)	91.4 (3)	2	305.6	Glaum et al. (2011)
Fe₃(PO₄)₂	P2₁/a	10.44 (3)	4.79 (2)	6.03 (2)	91.0 (5)	2	301.3	Ericsson & Khangi (1988)
	P2₁/n	8.88 (2)	11.17 (3)	6.15 (8)	99.4 (8)	4	601.0	Kostiner & Rea (1974)
Mg₃(PO₄)₂	P2₁/n	7.60 (7)	8.23 (1)	5.08 (1)	94.1 (5)	2	316.6	Nord & Kierkegaard (1968)
	P21/m	7.605 (2)	8.233 (3)	5.080 (1)	94.19 (3)	2	317.2	Baykal et al. (1997)
	P2₁/n	10.25 (9)	4.72 (2)	5.92 (4)	90.9 (1)	2	287.0	Nord & Stefanidis (1983)
Mn₃(PO₄)₂	P2₁/c	8.94 (3)	10.04 (1)	24.12 (8)	120.8 (3)	12	1861.1	Stephens & Calvo (1969)
	P2₁/c	8.80 (4)	11.45 (1)	6.25 (5)	99.0 (2)	4	621.9	Volkova et al. (2016)
	P2₁/c	8.92 (1)	9.15 (9)	8.66 (9)	111.7 (1)	4	657.2	Neher & Salguero (2017)
Ni₃(PO₄)₂	P2₁/n	5.82 (6)	4.69 (2)	10.10 (5)	91.1 (3)	2	276.1	Escobal et al. (2005)
	P2₁/c	8.70 (2)	11.12 (1)	6.11 (2)	100.0 (8)	4	581.7	Nord & Stefanidis (1983)
Pb₃(PO₄)₂	C2/c	13.81 (8)	5.69 (8)	9.43 (3)	102.4 (3)	4	723.5	Brixner et al. (1973)
Sr₃(PO₄)₂	R3m	5.3901 (8)	5.3901 (8)	19.785 (5)		4	497.8	Sugiyama & Tokonami (1990)
Ba₃(PO₄)₂	R3m	5.6038 (7)	5.6038 (7)	21.000 (5)		4	571.1	Sugiyama & Tokonami (1990)
Zn₃(PO₄)₂	P2₁/c	5.07 (2)	8.47 (3)	8.77 (2)	120.5 (5)	2	323.1	Calvo (1963); Stephens & Calvo (1967)
	C2/c	8.14 (7)	5.63 (3)	15.04 (9)	105.1 (8)	4	665.4	Calvo (1965)
	P2_1/n	9.39 (8)	9.17 (1)	8.69 (3)	125.7 (3)	4	607.3	Stephens & Calvo (1969)

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