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Langbeinites
Class of chemical compounds

Langbeinites are a family of crystalline substances based on the structure of langbeinite with general formula M2M'2(SO4)3, where M is a large univalent cation (such as potassium, rubidium, caesium, or ammonium), and M' is a small divalent cation (for example, magnesium, calcium, manganese, iron, cobalt, nickel, copper, zinc or cadmium). The sulfate group, SO2−4, can be substituted by other tetrahedral anions with a double negative charge such as tetrafluoroberyllate (BeF2−4), selenate (SeO2−4), chromate (CrO2−4), molybdate (MoO2−4), or tungstates. Although monofluorophosphates are predicted, they have not been described. By redistributing charges other anions with the same shape such as phosphate also form langbeinite structures. In these the M' atom must have a greater charge to balance the extra three negative charges.

At higher temperatures the crystal structure is cubic P213. However, the crystal structure may change to lower symmetries at lower temperatures, for example, P21, P1, or P212121. Usually this temperature is well below room temperature, but in a few cases the substance must be heated to acquire the cubic structure.

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Crystal structure

The crystal structures of langbeinites consist of a network of oxygen vertex-connected tetrahedral polyanions (such as sulfate) and distorted metal ion-oxygen octahedra.3 The unit cell contains four formula units. In the cubic form the tetrahedral anions are slightly rotated from the main crystal axes. When cooled, this rotation disappears and the tetrahedra align, resulting in lower energy as well as lower crystal symmetry.

Examples

Sulfates include dithallium dicadmium sulfate,4 dirubidium dicadmium sulfate,5 dipotassium dicadmium sulfate,6 dithallium manganese sulfate,7 and dirubidium dicalcium trisulfate.8

Selenates include diammonium dimanganese selenate.9 A diammonium dicadmium selenate langbeinite could not be crystallised from water, but a trihydrate exists.10

Chromate based langbeinites include dicaesium dimanganese chromate.11

Molybdates include Rb2Co2(MoO4)3.12 Potassium members are absent, as are zinc and copper containing solids, which all crystallize in different forms. Manganese, magnesium, cadmium and some nickel double molybdates exist as langbeinites.13

Double tungstates of the form A2B2(WO4)3 are predicted to exist in the langbeinite form.14

An examples with tetrafluroberyllate is dipotassium dimanganese tetrafluoroberyllate (K2Mn2(BeF4)3).15 Other tetrafluoroberyllates may include: Rb2Mg2(BeF4)3; Tl2Mg2(BeF4)3; Rb2Mn2(BeF4)3; Tl2Mn2(BeF4)3; Rb2Ni2(BeF4)3; Tl2Ni2(BeF4)3; Rb2Zn2(BeF4)3; Tl2Zn2(BeF4)3; Cs2Ca2(BeF4)3; Rb2Ca2(BeF4)3; RbCsMnCd(BeF4)3; Cs2MnCd(BeF4)3; RbCsCd2(BeF4)3; Cs2Cd2(BeF4)3; Tl2Cd2(BeF4)3; (NH4)2Cd2(BeF4)3; KRbMnCd(BeF4)3; K2MnCd(BeF4)3; Rb2MnCd(BeF4)3; Rb2Cd2(BeF4)3; RbCsCo2(BeF4)3; (NH4)2Co2(BeF4)3; K2Co2(BeF4)3; Rb2Co2(BeF4)3; Tl2Co2(BeF4)3; RbCsMn2(BeF4)3; Cs2Mn2(BeF4)3; RbCsZn2(BeF4)3; (NH4)2Mg2(BeF4)3; (NH4)2Mn2(BeF4)3; (NH4)2Ni2(BeF4)3; (NH4)2Zn2(BeF4)3;KRbMg2(BeF4)3; K2Mg2(BeF4)3; KRbMn2(BeF4)3; K2Ni2(BeF4)3; K2Zn2(BeF4)3.16

The phosphate containing langbeinites were found in 1972 with the discovery of KTi2(PO4)3, and since then a few more phosphates that also contain titanium have been found such as Na2FeTi(PO4)3 and Na2CrTi(PO4)3. By substituting metals in A2MTi(PO4)3, A from (K, Rb, Cs), and M from (Cr, Fe, V), other langbeinites are made. The NASICON-type structure competes for these kinds of phosphates, so not all possibilities are langbeinites.17 Other phosphate based substances include K2YTi(PO4)3, K2ErTi(PO4)3, K2YbTi(PO4)3, K2CrTi(PO4)3,18 K2AlSn(PO4)3,19 KRbYbTi(PO4)3.20 Sodium barium diiron tris-(phosphate) (NaBaFe2(PO4)3) is yet another variation with the same structure but differently charged ions.21 Most phosphates of this kind of formula do not form langbeinites, instead crystallise in the NASICON structure with archetype Na3Zr2(PO4)(SiO4)2.22

A langbeinite with arsenate is known to exist by way of K2ScSn(AsO4)3.23

Properties

Physical properties

Langbeinite-family crystals can show ferroelectric or ferroelastic properties.24 Diammonium dicadmium sulfate identified by Jona and Pepinsky25 with a unit cell size of 10.35 Å becomes ferroelectric when the temperature drops below 95 K.26 The phase transition temperature is not fixed, and can vary depending on the crystal or history of temperature change. So for example the phase transition in diammonium dicadmium sulfate can occur between 89 and 95 K.27 Under pressure the highest phase transition temperature increases. ∂T/∂P = 0.0035 degrees/bar. At 824 bars there is a triple point with yet another transition diverging at a slope of ∂T/∂P = 0.103 degrees/bar.28 For dipotassium dimanganese sulfate pressure causes the transition to rise at the rate of 6.86 °C/kbar. The latent heat of the transition is 456 cal/mol.29

Dithallium dicadmium sulfate was shown to be ferroelectric in 1972.30

Dipotassium dicadmium sulfate is thermoluminescent with stronger outputs of light at 350 and 475 K. This light output can be boosted forty times with a trace amount of samarium.31 Dipotassium dimagnesium sulfate doped with dysprosium develops thermoluminescence and mechanoluminescence after being irradiated with gamma rays.32 Since gamma rays occur naturally, this radiation induced thermoluminescence can be used to date evaporites in which langbeinite can be a constituent.33

At higher temperatures the crystals take on cubic form, whereas at the lowest temperatures they can transform to an orthorhombic crystal group. For some types there are two more phases, and as the crystal is cooled it goes from cubic, to monoclinic, to triclinic to orthorhombic. This change to higher symmetry on cooling is very unusual in solids.34 For some langbeinites only the cubic form is known, but that may be because it has not been studied at low enough temperatures yet. Those that have three phase transitions go through these crystallographic point groups: P213 – P21 – P1 – P212121, whereas the single phase change crystals only have P213 – P212121.

K2Cd2(SO4)3 has a transition temperature above room temperature, so that it is ferroelectric in standard conditions. The orthorhombic cell size is a=10.2082 Å, b=10.2837 Å, c=10.1661 Å.35

Where the crystals change phase there is a discontinuity in the heat capacity. The transitions may show thermal hysteresis.36

Different cations can be substituted so that for example K2Cd2(SO4)3 and Tl2Cd2(SO4)3 can form solid solutions for all ratios of thallium and potassium. Properties such as the phase transition temperature and unit cell sizes vary smoothly with the composition.37

Langbeinites containing transition metals can be coloured. For example, cobalt langbeinite shows a broad absorption around 555 nm due to the cobalt 4T1g(F)→4T1g(P) electronic transition.38

The enthalpy of formation (ΔfHm) for solid (NH4)2Cd2(SO4)3 at 298.2 K is −3031.74±0.08 kJ/mol, and for K2Cd2(SO4)3 it is −3305.52±0.17 kJ/mol.39

Sulfates

Properties of langbeinites with sulfate anions
FormulaWeight (g/mol)Comment / SymmetriesTransition temperature (K)DensityCell size (Å)Refractive index
12340
Na2Mg2(SO4)3382.783 phases, 1–2, >325035057541
K2Mg2(SO4)3414.994 phases langbeinite5154.963.82.832429.9211431.53644
Rb2Mg2(SO4)3507.73made3.3674510.0051461.55647
Cs2Mg2(SO4)3602.61no compound48
(NH4)2Mg2(SO4)3372.87Efremovite4924150220512.49529.97953
Tl2Mg2(SO4)3745.56≥3 phase227.854330.855
K2CaMg(SO4)3430.77made2.7235610.1662571.52558
K2Ca2(SO4)3446.544 phases calciolangbeinite5960614572.69 2.6836210.429Å a=10.334 b=10.501 c=10.186Nα=1.522 Nβ=1.526 Nγ=1.527
Rb2Ca2(SO4)3539.282 phases1833.0346310.5687641.52065
Cs2Ca2(SO4)3634.153.417666710.72131.549
Tl2Ca2(SO4)3no compound68
(NH4)2Ca2(SO4)3404.42made1582.2976910.5360701.53271
(NH4)2V2(SO4)3colour clear green722.767310.08974
K2Mn2(SO4)3476.26manganolangbeinite752 phasespale pink761913.027710.01478(orthorhombic)a=10.081, b=10.108, c=10.048 Å791.57680
Rb2Mn2(SO4)3569made813.5468210.2147831.59084
Cs2Mn2(SO4)3663.87predicted85
(NH4)2Mn2(SO4)2434.14made2.728610.190887
Tl2Mn2(SO4)3806.83made5.0158810.2236891.72290
K2Fe2(SO4)3478.07made?130
Rb2Fe2(SO4)3predicted91
Tl2Fe2(SO4)3808.64exists92
(NH4)2Fe2(SO4)393435.95mineral ferroefremovite2.849410.068951.57496
K2Co2(SO4)3484.252 phasesdeep purple1263.280979.9313981.60899
Rb2Co2(SO4)3576.99made3.80710010.02041011.602102
Cs2Co2(SO4)3671.87
(NH4)2Co2(SO4)3442.13made2.941039.997104
Tl2Co2(SO4)3813.82made5.36110510.03121.775
K2Ni2(SO4)3483.77made106 light greenish yellow1073.3691089.84361091.620110
Rb2Ni2(SO4)3576.51made3.9211119.92171121.636113
Cs2Ni2(SO4)3671.39predicted114
(NH4)2Ni2(SO4)3441.65made1151603.021169.904117
Tl2Ni2(SO4)3814.34predicted118
Rb2Cu2(S04)3predicted119
Cs2Cu2(S04)3predict not120
Tl2Cu2(S04)3predicted121
K2Zn2(SO4)3497.14 phases751383.3761229.92471231.592124
Rb2Zn2(S04)3predicted125
Cs2Zn2(S04)3predict not126
Tl2Zn2(S04)3predicted127
K2Cd2(SO4)3591.212 phases4322.615 3.677128a=10.212 b=10.280 c=10.171Nα=1.588 Nγ=1.592
Rb2Cd2(SO4)3683.954 phases661031294.06012913010.38101311321.590133
(NH4)2Cd2(SO4)3549.094 phases953.28813410.3511135
Tl2Cd2(SO4)3921.784 phases921201325.46713610.38411371.730138

Fluoroberyllates

Properties of langbeinites with fluoroberyllate (BeF2−4) anion
FormulaWeight (g/mol)Cell size (Å)VolumeDensityComment
K2Mn2(BeF4)31394 phases transition at 213
K2Mg2(BeF4)31409.875962.81.59
(NH4)2Mg2(BeF4)31419.9681.37
KRbMg2(BeF4)31429.9331.72
Rb2Mg2(BeF4)31439.9711.91
Tl2Mg2(BeF4)31449.9972.85
K2Ni2(BeF4)31459.8881.86
Rb2Ni2(BeF4)31469.9742.19
Tl2Ni2(BeF4)31479.9933.13
K2Co2(BeF4)31489.9639881.82
(NH4)2Co2(BeF4)314910.0521.61
Rb2Co2(BeF4)315010.0612.14
Tl2Co2(BeF4)315110.0783.05
RbCsCo2(BeF4)315210.1152.28
K2Zn2(BeF4)31539.9321.89
(NH4)Zn2(BeF4)315410.0361.67
Rb2Zn2(BeF4)315510.0352.20
Tl2Zn2(BeF4)315610.0603.14
RbCsZn2(BeF4)315710.1022.36
K2Mn2(BeF4)315810.1021.72
KRbMn2(BeF4)315910.1871.82
(NH4)2Mn2(BeF4)316010.2171.50
Rb2Mn2(BeF4)316110.2432.00
Tl2Mn2(BeF4)316210.2552.87
RbCsMn2(BeF4)316310.3272.12
Cs2Mn2(BeF4)316410.3762.26
K2MnCd(BeF4)316510.1331.92
KRbMnCd(BeF4)316610.2202.04
Rb2MnCd(BeF4)316710.1331.92
RbCsMnCd(BeF4)316810.3802.28
Cs2MnCd(BeF4)316910.4512.41
(NH4)2Cd2(BeF4)317010.3421.87
Rb2Cd2(BeF4)317110.3852.32
Tl2Cd2(BeF4)317210.4023.16
RbCsCd2(BeF4)317310.4742.43
Cs2Cd2(BeF4)317410.5582.53
RbCsCdCa(BeF4)317510.5012.15
Rb2Ca2(BeF4)317610.4801.74
RbCsCa2(BeF4)317710.5831.86
Cs2Ca2(BeF4)317810.6721.98
Cs2Mg2(BeF4)3does not exist179

Phosphates

Properties of langbeinites with phosphate (PO2−4) anion
FormulaWeight (g/mol)Cell size (Å)DensityCommentref
LiCs2Y2(PO4)3735.4810.59454.108180
LiRb2Y2(PO4)3non-linear optical181
K2YTi(PO4)3578.2510.10533.192182
K2ErTi(PO4)3584.0310.0943.722183
K2YbTi(PO4)3499.8910.13183.772184
K2CrTi(PO4)3462.989.80013.267185
(NH4)(H3O)TiIIITiIV(PO4)3417.719.9384186
K2Ti2(PO4)3458.849.8688Also K2−x; dark blue187
Rb2Ti2(PO4)3551.589.9115188
Tl2Ti2(PO4)3789.419.9386189
Na2FeTi(PO4)39.837190
Na2CrTi(PO4)39.775191
K2Mn0.5Ti1.5(PO4)39.9033.162dark brown192
K2Co0.5Ti1.5(PO4)39.8443.233dark brown193
Rb4NiTi3(PO4)61113.99÷29.9386194
K2AlTi(PO4)3437.969.76413.125colourless195
K2TiYb(PO4)3196
Li2Zr2(PO4)3481.24197
NaZr2(PO4)3980,7110.20883.06125negative thermal expansion 25-500 °C198
K2(Ce, ..., Lu)Zr(PO4)3594.45...629.310.29668199
Rb2FeZr(PO4)3602.9210.1199200
K2FeZr(PO4)3510.1810.0554dark grey Note Na2FeZr(PO4)3 is not a langbeinite.201202
K2YZr(PO4)3543.2410.3346random Y and Zr203
K2GdZr(PO4)3611.5810.3457random Gd and Zr204
K2YHf(PO4)3630.5110.30753.824205
Li(H2O)2Hf2(PO4)3684.8710.1993206
K2BiHf(PO4)3750.58207
Li(H2O)2Zr2(PO4)3510.3310.2417208
K2AlSn(PO4)3508.789.798209
K2CrSn(PO4)39.8741
K2InSn(PO4)310.0460
K2FeSn(PO4)39.921
K2YbSn(PO4)310.150
K4Al3Ta(PO4)6988.119.7262210
K4Cr3Ta(PO4)61063.169.8315211
K4Fe3Ta(PO4)61074.709.9092212
K4Tb3Ta(PO4)610.3262213
K4Ga3Ta(PO4)6214
K4Gd3Ta(PO4)6215
K4Dy3Ta(PO4)6216
K4Ho3Ta(PO4)6217
K4Er3Ta(PO4)6218
K4Yb3Ta(PO4)6219
Rb4Ga3Ta(PO4)6220
Rb4Gd3Ta(PO4)6221
Rb4Dy3Ta(PO4)6222
Rb4Ho3Ta(PO4)6223
Rb4Er3Ta(PO4)6224
Rb4Yb3Ta(PO4)6225
K4Fe3Nb(PO4)6986.669.9092226
KBaEr2(PO4)3795.857227
RbBaEr2(PO4)3842.227228
CsBaEr2(PO4)3889.665229
(Rb,Cs)2(Pr,Er)Zr(PO4)3230
KCsFeZrP3O12603.9910.103231
CaFe3O(PO4)3508.53232
SrFe3O(PO4)3556.1233
PbFe3O(PO4)3675.6234
KSrFe2(PO4)3523.329.8093.68yellowish235
Pb1.5VIV2(PO4)3697.69.78184.912236
K2TiV(PO4)39.855green237
BaTiV(PO4)39.9223.54at high temperature > 950 °C dark grey238
KBaV2(PO4)39.873greenish yellow239
Ba1.5V2(PO4)39.884grey240
Ba1.5Fe3+2(PO4)3241242602.59
KSrSc2(PO4)3243501.54
Rb0.743K0.845Co0.293Ti1.707(PO4)32449.8527
K2BiZr(PO4)6245663.3210.3036
KBaSc2(PO4)3246503.25
KBaIn2(PO4)3247
KBaRZrP2SiO12248R = La, Nd, Sm, Eu, Gd, Dy, Y
KBaYSnP2SiO12249666.07
KBaFe2(PO4)3250525.039.8732 (at 4 K)
KBaCr2(PO4)3251517.339.7890
Rb2FeTi(PO4)3252511.569.8892Na2FeTi(PO4)3 has NZP structure253
KBaMgTi(PO4)3254485.519.914KSrMgTi crystallises in kosnarite form
KPbMgTi(PO4)3255555.399.8540KSrMgTi in kosnarite form
RbBaMgTi(PO4)39.954531.88CsBa does not form256
RbPbMgTi(PO4)3601.769.9090CsPb does not form257
KSrMgZr(PO4)3479.1610.165258
KPbMgZr(PO4)3598.7410.111259
KBaMgZr(PO4)3528.8710.106260
RbSrMgZr(PO4)3525.5310.218261
RbPbMgZr(PO4)3645.1110.178262
RbBaMgZr(PO4)3575.2410.178263
CsSrMgZr(PO4)3572.9710.561over 1250 °C forms kosnarite phase264
Ba3In4(PO4)610.1129265
Ba3V4(PO4)61185.589.88254.08yellow-green266
KPbCr2(PO4)39.7332267
KPbFe2(PO4)39.8325beige268
K4NiHf3(PO4)6660.192 (half)10.122014.228yellow269
NaBaBi2(PO3)3270

Phosphate silicates

substanceformula weightunit cell edge Ådensitycommentref
K2Sn2(PO4)2SiO4271Stable to 650 °C
K2Zr2(PO4)2SiO4272Stable to 1000 °C
Cs2Zr2(PO4)2SiO4273
CsKZr2(PO4)2SiO4274
KBaZrY(PO4)2SiO4275
KBaZrLa(PO4)2SiO4276
KBaZrNd(PO4)2SiO4277
KBaZrSm(PO4)2SiO4278
KBaZrEu(PO4)2SiO4279

Mixed anion phosphates

substanceformula weightunit cell edge Ådensitycommentref
K2MgTi(SO4)(PO4)2280
K2Fe2(MoO4)(PO4)2281
K2Sc2(MoO4)(PO4)2282
K2Sc2(WO4)(PO4)2283

Vanadates

The orthovanadates have four formula per cell, with a slightly distorted cell that has orthorhombic symmetry.

formula weightcommentCell dimensions ÅVolumedensityrefractive
Formulag/molsymmetriesabcindex
LiBaCr2(VO4)3284593.08Orthorhombic9.9810.529.519984.02
NaBaCr2(VO4)3285609.13Orthorhombic9.9910.529.5310024.09
AgBaCr2(VO4)3286694.00Orthorhombic10.0210.539.5310054.62

Arsenates

substanceformula weightunit cell edge Ådensity
K2ScSn(AsO4)3287658.6210.3927
Zr2NH4(AsO4)3·H2O288632.55810.5323.379

Selenates

Langbeinite structured double selenates are difficult to make, perhaps because selenate ions arranged around the dication leave space for water, so hydrates crystallise from double selenate solutions. For example, when ammonia selenate and cadmium selenate solution is crystallized it forms diammonium dicadmium selenate trihydrate: (NH4)2Cd2(SeO4)3·3H2O and when heated it loses both water and ammonia to form a pyroselenate rather than a langbeinite.289

substanceformula weightunit cell edge Ådensitynote
(NH4)2Mn2(SeO4)3290574.8310.533.26forms continuous series with SO4 too

Molybdates

substanceformula weightunit cell edge Ådensityref
Cs2Cd2(MoO4)3970.511.239291
Rb2Co2(MoO4)3768.7
Cs2Co2(MoO4)3292
Cs2Fe2(MoO4)310.9112293
Cs2Ni2(MoO4)3863.0110.7538294
(H3O)2Mn2(MoO4)3627.7510.8713295
K2Mn2(MoO4)3296

Tungstates

substanceformula weightunit cell edge Ådensity
Rb2Mg2(WO4)3297963.0610.766
Cs2Mg2(WO4)32981057.9310.878

Preparation

Diammonium dicadmium sulfate can be made by evaporating a solution of ammonium sulfate and cadmium sulfate.299 Dithallium dicadmium sulfate can be made by evaporating a water solution at 85 °C.300 Other substances may be formed during crystallisation from water such as Tutton's salts or competing compounds like Rb2Cd3(SO4)4·5H2O.301

Potassium and ammonium nickel langbeinite can be made from nickel sulfate and the other sulfates by evaporating a water solution at 85 °C.302

Dipotassium dizinc sulfate can be formed into large crystals by melting zinc sulfate and potassium sulfate together at 753 K. A crystal can be slowly drawn out of the melt from a rotating crucible at about 1.2 mm every hour.303

Li(H2O)2Hf2(PO4)3 can be made by heating HfCl4, Li2B4O7, H3PO4, water and hydrochloric acid to 180 °C for eight days under pressure.304 Li(H2O)2Hf2(PO4)3 converts to Li2Hf2(PO4)3 on heating to 200 °C.305

The sol-gel method produces a gel from a solution mixture, which is then heated. Rb2FeZr(PO4)3 can be made by mixing solutions of FeCl3, RbCl, ZrOCl2, and dripping in H3PO4. The gel produced was dried out at 95 °C and then baked at various temperatures from 400 to 1100 °C.306

Langbeinites crystals can be made by the Bridgman technique, Czochralski process or flux technique.

A Tutton's salt may be heat treated and dehydrate, e.g. (NH4)2Mn2(SeO4)3 can be made from (NH4)2Mn(SeO4)3·6(H2O) heated to 100 °C, forming (NH4)2(SeO4) as a side product.307 Similarly the ammonium vanadium Tutton's salt, (NH4)2V(SO4)2, heated to 160 °C in a closed tube produces (NH4)2V2(SO4)3. At lower temperatures a hydroxy compound is formed.308

Use

Few uses have been made of these substances. Langbeinite itself can be used as an "organic" fertiliser with potassium, magnesium and sulfur, all needed for plant growth. Electrooptic devices could be made from some of these crystals, particularly those that have cubic transition temperatures as temperatures above room temperature. Research continues into this. Ferroelectric crystals could store information in the location of domain walls.

The phosphate langbeinites are insoluble, stable against heat, and can accommodate a large number of different ions, and have been considered for immobilizing unwanted radioactive waste.309

Zirconium phosphate langbeinites containing rare earth metals have been investigated for use in white LEDs and plasma displays.310 Langbeinites that contain bismuth are photoluminescent.311 In case of iron-containing ones complex magnetic behavior may be found.312

References

  1. Norberg, Stefan T. (2002). "New phosphate langbeinites, K2MTi(PO4)3 (M = Er, Yb or Y), and an alternative description of the langbeinite framework". Acta Crystallographica B. 58 (5): 743–749. Bibcode:2002AcCrB..58..743N. doi:10.1107/S0108768102013782. PMC 2391006. PMID 12324686. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2391006

  2. Norberg, Stefan T. (2002). "New phosphate langbeinites, K2MTi(PO4)3 (M = Er, Yb or Y), and an alternative description of the langbeinite framework". Acta Crystallographica B. 58 (5): 743–749. Bibcode:2002AcCrB..58..743N. doi:10.1107/S0108768102013782. PMC 2391006. PMID 12324686. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2391006

  3. Kumar, Sathasivam Pratheep; Gopal, Buvaneswari (October 2015). "New rare earth langbeinite phosphosilicates KBaREEZrP2SiO12 (REE: La, Nd, Sm, Eu, Gd, Dy) for lanthanide comprising nuclear waste storage". Journal of Alloys and Compounds. 657: 422–429. doi:10.1016/j.jallcom.2015.10.088. /wiki/Doi_(identifier)

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