Langbeinites

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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, SO42−, can be substituted by other tetrahedral anions with a double negative charge such as tetrafluoroberyllate BeF42−, selenate (SeO42−), chromate (CrO42−), molybdate (MO4), 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.[1] However, the crystal structure may change to lower symmetries at lower temperatures, for example, P21, P1, or P212121.[1] Usually this temperature is well below room temperature, but in a few cases the substance must be heated to acquire the cubic structure.

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.[2] 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,[3] Dirubidium dicadmium sulfate[4] dipotassium dicadmium sulfate,[5] dithallium manganese sulfate.[6] dirubidium dicalcium trisulfate.[7]

Selenates include diammonium dimanganese selenate.[1] A diammonium dicadmium selenate langbeinite could not be crystallised from water, but a trihydrate exists.[8]

Chromate based langbeinites include dicaesium dimanganese chromate.[1]

Molybdates include Rb2Co2(MoO4)3.[1] Potassium members are absent, as are zinc and copper containing solids, which all crystallize in different forms. Manganese, magenesium, cadmium and some nickel double molydates exist as langbeinites.[9]

Double tungstates of the form A2B2(WO4)3 are predicted to exist in the langbeinite form.[10]

Examples with tetrafluroberyllate include dipotassium dimanganese tetrafluoroberyllate K2Mn2(BeF4)3,[11]

Other tetrafluoroberyllates may include Rb2Mg2(BeF4)3 Tl2Mg2(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 K2Mn2(BeF4)3 K2Ni2(BeF4)3 K2Zn2(BeF4)3[12]

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), Na2CrTi(PO4)3. By substituting metals in A2MTi(PO4)3, A from K, Rb, Cs, and M from Cr, Fe or V other langbeinites are made. The NASICON-type structure competes for these kinds of phosphates, so not all possibilities are langbeinites.[1] Other phosphate based substances include K2YTi(PO4)3 K2ErTi(PO4)3 K2YbTi(PO4)3, K2CrTi(PO4)3[1] K2AlSn(PO4)3[13] Rb2YbTi(PO4)3.[14] Sodium barium diiron tris-(phosphate) NaBaFe2(PO4)3 is yet another variation with the same structure but differently charged ions.[15] Most phosphates of this kind of formula do not form langbeinites, instead crystallise in the NASICON structure with archetype Na3Zr2(PO4)(SiO4)2.[1]

A langbeinite with arsenate is known to exist by way of K2ScSn(AsO4)3.[16]

Properties

Physical properties

Lanbeinite crystals can show ferroelectric or ferroelastic properties.[1] Diammonium dicadmium sulfate identified by Jona and Pepinsky[17] with a unit cell size of 10.35 Å becomes ferroelectric when the temperature drops below 95K.[18] 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.[19] 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.[20] 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.[21]

Dithallium dicadmium sulfate was shown to be ferroelectric in 1972.[22]

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.[23] Dipotassium dimagnesium sulfate doped with dysprosium develops thermoluminescence and mechanoluminescence after being irradiated with gamma rays.[24] Since gamma rays occur naturally, this radiation induced thermoluminescence can be used to date evaporites in which langbeinite can be a constituent.[25]

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.[26] 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.[27]

Where the crystals change phase there is a discontinuity in the heat capacity. The transitions may show thermal hysteresis.[28]

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.[29]

Langeinites 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.[30]

The enthalpy of formation (ΔfHm) for solid (NH4)2Cd2(SO4)3 at 298.2K is −3031.74±0.08 kJ/mol, and for K2Cd2(SO4)3 it is －3305.52±0.17 kJ/mol.[31]

Sulfates

formula weight comment transition temperature K density cell size refractive
elements formula g/mol symmetries 1 2 3[32] Å index
KMg K2Mg2(SO4)3 414.99 4 phases 51 54.9 63.8 2.832[33] 9.9211[34] 1.536[35]
RbMg Rb2Mg2(SO4)3 507.73 made 3.367[36] 10.0051[36] 1.556[36]
CsMg Cs2Mg2(SO4)3 602.61 no compound[10]
(NH4)Mg (NH4)2Mg2(SO4)3 372.87 241[37] 220[37] 2.49[38] 9.979[38]
TlMg Tl2Mg2(SO4)3 745.56 ≥3 phase 227.8[37] 330.8[37]
KCaMg K2CaMg(SO4)3 430.77 made 2.723[39] 10.1662[39] 1.525[39]
KCa calcilangbeinite[40] K2Ca2(SO4)3 446.54 4 phases 457 2.69 2.683[41] 10.429Å a=10.334 b=10.501 c=10.186 Nα=1.522 Nβ=1.526 Nγ=1.527
RbCa Rb2Ca2(SO4)3 539.28 2 phases 183 3.034[42] 10.5687[42] 1.520[42]
CsCa Cs2Ca2(SO4)3 634.15 3.417[43][44] 10.7213 1.549
TlCa no compound[10]
(NH4)Ca (NH4)2Ca2(SO4)3 404.42 made 158 2.297[45] 10.5360[45] 1.532[45]
NH4V (NH4)2V2(SO4)3 colour clear green[46] 2.76[47] 10.089[46]
KMn manganolangbeinite[48] K2Mn2(SO4)3 476.26 2 phases
pale pink[49]		 191 3.02[34] 10.014[34]
(orthorhombic)
a=10.081, b=10.108, c=10.048 Å[50]		 1.576[49]
RbMn[51] Rb2Mn2(SO4)3 569 made 3.546[52] 10.2147[52] 1.590[52]
CsMn Cs2Mn2(SO4)3 663.87 predicted[10]
(NH4)Mn (NH4)2Mn2(SO4)3 434.14 made 2.72[38] 10.1908[53]
TlMn Tl2Mn2(SO4)3 806.83 made 5.015[54] 10.2236[54] 1.722[54]
KFe K2Fe2(SO4)3 478.07 made ?130
RbFe predicted[10]
TlFe 808.64 exists[10]
NH4Fe (NH4)2Fe2(SO4)3[46] 435.95 exits 2.84[38] 10.068[38]
KCo K2Co2(SO4)3 484.25 2 phases
deep purple		 126 3.280[33] 9.9313[34] 1.608[55]
RbCo Rb2Co2(SO4)3 576.99 made 3.807[56] 10.0204[56] 1.602[56]
CsCo 671.87
(NH4)Co (NH4)2Co2(SO4)3 442.13 made 2.94[38] 9.997[38]
TlCo Tl2Co2(SO4)3 813.82 made 5.361[57] 10.0312 1.775
KNi K2Ni2(SO4)3 483.77 made[58] light greenish yellow[59] 3.369[33] 9.8436[59] 1.620[59]
RbNi Rb2Ni2(SO4)3 576.51 made 3.921[60] 9.9217[60] 1.636[60]
CsNi 671.39 predicted[10]
(NH4)Ni (NH4)2Ni2(SO4)3 441.65 made[58] 160 3.02[38] 9.904[38]
TlNi Tl2Ni2(SO4)3 814.34 predicted[10]
RbCu predicted[10]
CsCu predict not[10]
TlCu predicted[10]
KZn K2Zn2(SO4)3 497.1 4 phases 75 138 3.376[33] 9.9247[61] 1.592[61]
RbZn predicted[10]
CsZn predict not[10]
TlZn predicted[10]
KCd K2Cd2(SO4)3 591.21 2 phases 432 2.615 3.677[62] a=10.212 b=10.280 c=10.171 Nα=1.588 Nγ=1.592
RbCd Rb2Cd2(SO4)3 683.95 4 phases 66 103 129 4.060[34][63] 10.3810[34][63] 1.590[63]
(NH4)Cd (NH4)2Cd2(SO4)3 549.09 4 phases 95 3.288[34] 10.3511[34]
TlCd Tl2Cd2(SO4)3 921.78 4 phases 92 120 132 5.467[34] 10.3841[34] 1.730[64]

Fluoroberyllates

elements formula formula weight cell Å volume density comment
KMnBe K2Mn2(BeF4)3[11] 4 phases transition at 213
KMg[65] K2Mg2(BeF4)3 9.875 962.8 1.59
(NH4)Mg (NH4)2Mg2(BeF4)3[65] 9.968 1.37
KRbMg KRbMg2(BeF4)3[65] 9.933 1.72
RbMg Rb2Mg2(BeF4)3[65] 9.971 1.91
TlMg Tl2Mg2(BeF4)3[65] 9.997 2.85 (CsMg does not exist)[65]
KNi K2Ni2(BeF4)3[65] 9.888 1.86
RbNi Rb2Ni2(BeF4)3[65] 9.974 2.19
TlNi Tl2Ni2(BeF4)3[65] 9.993 3.13
KCo K2Co2(BeF4)3[65] 9.963 988 1.82
(NH4)Co (NH4)2Co2(BeF4)3[65] 10.052 1.61
RbCo Rb2Co2(BeF4)3[65] 10.061 2.14
TlCo Tl2Co2(BeF4)3[65] 10.078 3.05
RbCsCo RbCsCo2(BeF4)3[65] 10.115 2.28
KZn K2Zn2(BeF4)3[65] 9.932 1.89
(NH4)Zn (NH4)Zn2(BeF4)3[65] 10.036 1.67
RbZn Rb2Zn2(BeF4)3[65] 10.035 2.20
TlZn Tl2Zn2(BeF4)3[65] 10.060 3.14
RbCsZn RbCsZn2(BeF4)3[65] 10.102 2.36
KMn K2Mn2(BeF4)3[65] 10.102 1.72
KRbMn KRbMn2(BeF4)3[65] 10.187 1.82
(NH4)Mn (NH4)2Mn2(BeF4)3[65] 10.217 1.50
RbMn Rb2Mn2(BeF4)3[65] 10.243 2.00
TlMn Tl2Mn2(BeF4)3[65] 10.255 2.87
RbCsMn RbCs2Mn2(BeF4)3[65] 10.327 2.12
CsMn Cs2Mn2(BeF4)3[65] 10.376 2.26
KMnCd K2MnCd(BeF4)3[65] 10.133 1.92
KRbMnCd KRbMnCd(BeF4)3[65] 10.220 2.04
RbMnCd Rb2MnCd(BeF4)3[65] 10.133 1.92
RbCsMnCd RbCsMnCd(BeF4)3[65] 10.380 2.28
CsMnCd Cs2MnCd(BeF4)3[65] 10.451 2.41
(NH4)Cd (NH4)2Cd2(BeF4)3[65] 10.342 1.87
RbCd Rb2Cd2(BeF4)3[65] 10.385 2.32
TlCd Tl2Cd2(BeF4)3[65] 10.402 3.16
RbCsCd RbCs2Cd2(BeF4)3[65] 10.474 2.43
CsCd Cs2Cd2(BeF4)3[65] 10.558 2.53
RbCsCdCa RbCs2CdCa(BeF4)3[65] 10.501 2.15
RbCa Rb2Ca2(BeF4)3[65] 10.480 1.74
RbCsCa RbCsCa2(BeF4)3[65] 10.583 1.86
CsCa Cs2Ca2(BeF4)3[65] 10.672 1.98

Phosphates

substance formula weight unit cell edge Å density comment
K2YTi(PO4)3[1] 578.25 10.1053 3.192
K2ErTi(PO4)3[1] 584.03 10.094 3.722
K2YbTi(PO4)3[1] 499.89 10.1318 3.772
K2CrTi(PO4)3[1] 462.98 9.8001 3.267
(NH4)(H3O)TiIIITiIV(PO4)3[66] 417.71 9.9384
K2Ti2(PO3)3[67] 458.84 9.8688 Also K2-x; dark blue
Rb2Ti2(PO3)3[67] 551.58 9.9115
Tl2Ti2(PO3)3[67] 789.41 9.9386
Na2FeTi(PO3)3[68] 9.837
Na2CrTi(PO3)3[68] 9.775
K2Mn0.5Ti1.5(PO3)3[69] 9.903 3.162 dark brown
K2Co0.5Ti1.5(PO3)3[69] 9.844 3.233 dark brown
Rb4NiTi3(PO4)6[70] 1113.99÷2 9.9386
K2AlTi(PO4)3[71] 437.96 9.7641 3.125 colourless
Li2Zr2(PO4)3[72] 481.24
K2(Ce,...,Lu)Zr(PO4)3[73] 594.45...629.3 10.29668
Rb2FeZr(PO4)3[74] 602.92 10.1199
K2FeZr(PO3)3[75] 510.18 10.0554 dark grey Note Na2FeZr(PO3)3 is not a langbeinite.[76]
K2YZr(PO3)3[77] 543.24 10.3346 random Y and Zr
K2GdZr(PO3)3[77] 611.58 10.3457 random Gd and Zr
K2YHf(PO4)3[78] 630.51 10.3075 3.824
Li(H2O)2Hf2(PO4)3[79] 684.87 10.1993
K2BiHf(PO4)3[80] 750.58
Li(H2O)2Zr2(PO4)3[72] 510.33 10.2417
K2AlSn(PO4)3 508.78 9.798[13]
K4Al3Ta(PO4)6[81] 988.11 9.7262
K4Cr3Ta(PO4)6[81] 1063.16 9.8315
K4Fe3Ta(PO4)6[81] 1074.70 9.9092
K4Fe3Nb(PO4)6[81] 986.66 9.9092
KBaEr2(PO4)3[82] 795.857
RbBaEr2(PO4)3[82] 842.227
CsBaEr2(PO4)3[82] 889.665
(Rb,Cs)2(Pr,Er)Zr(PO4)3[82]
KCsFeZrP3O12 603.99 10.103[83]
CaFe3O(PO4)3[84] 508.53
SrFe3O(PO4)3[84] 556.1
PbFe3O(PO4)3[84] 675.6
KSrFe2(PO4)3[85] 523.32 9.809 3.68 yellowish
Pb1.5VIV2(PO4)3 697.6 9.7818 4.912[86]
K2TiV(PO4)[87] 9.855 green
BaTiV(PO4)[87] 9.922 3.54 at high temperature >950 °C dark grey
KBaV2(PO4)[87] 9.873 greenish yellow
Ba1.5V2(PO4)[87] 9.884 grey
Ba1.5Fe3+2(PO4)3[88] 602.59
KSrSc2(PO4)3[89] 501.54
Rb0.743K0.845Co0.293Ti1.707(PO4)3[90] 9.8527
K2BiZr(PO3)6[91] 663.32 10.3036
KBaSc2(PO3)3[92] 503.25
KBaRZrP2SiO12 R=La, Nd, Sm, Eu, Gd, Dy, Y[2]
KBaYSnP2SiO12[2] 666.07
KBaFe2(PO3)3[93] 9.8732 (at 4K)
KBaCr2(PO3)3[94] 9.7890
Rb2FeTi(PO3)3[95] 9.8892 Na2FeTi(PO3)3 has NZP structure[76]

Vanadates

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

formula weight comment Cell dimensions Å Volume density refractive
Formula g/mol symmetries a b c index
LiBaCr2(VO4)3[96] 593.08 Orthorhombic 9.98 10.52 9.51 998 4.02
NaBaCr2(VO4)3[96] 609.13 Orthorhombic 9.99 10.52 9.53 1002 4.09
AgBaCr2(VO4)3[96] 694.00 Orthorhombic 10.02 10.53 9.53 1005 4.62

Arsenates

substance formula weight unit cell edge Å density
K2ScSn(AsO4)3[97] 658.62 10.3927
Zr2NH4(AsO4)3.H2O[98] 632.558 10.532 3.379

Selenates

substance formula weight unit cell edge Å density note
(NH4)2Mn2(SeO4)3[99] 574.83 10.53 3.26 forms continuous series with SO4 too

Molybdates

substance formula weight unit cell edge Å density
Cs2Cd2(MoO4)3[100] 970.5 11.239
Rb2Co2(MoO4)3 768.7
Cs2Ni2(MoO4)3[101] 863.01 10.7538
(H3O)2Mn2(MoO4)3[102] 627.75 1.08713

Tungstates

substance formula weight unit cell edge Å density
Rb2Mg2(WO4)3[103] 963.06 10.766
Cs2Mg2(WO4)3[103] 1057.93 10.878

Preparation

Diammonium dicadmium sulfate can be made by evaporating a solution of ammonium sulfate and cadmium sulfate.[19] Dithallium dicadmium sulfate can be made by evaporating a water solution at 85 °C.[22] Other substances may be formed during crystallisation from water such as Tutton's salts or competing compounds like Rb2Cd3(SO4)4·5H2O.[104]

Potassium and ammonium nickel langbeinite can be made from nickel sulfate and the other sulfates by evaporating a water solution at 85 °C.[58]

Dipotassium dizinc sulfate can be formed into large crystals by melting zinc sulfate and potassium sulfate together at 753K. A crystal can be slowly drawn out of the melt from a rotating crucible at about 1.2 mm every hour.[105]

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.[79] Li(H2O)2Hf2(PO4)3 converts to Li2Hf2(PO4)3 on heating to 200 °C.[72]

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.[74]

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.[106] Similarly the ammonium vandadium 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.[46]

Use

Few uses have been made of these substances. Lanbeinite 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.[107]

Rare earth containing zirconium phosphate langeinites have been investigated for use in white LEDs and plasma displays.[91] Langbeinites that contain bismuth are photoluminescent.[91]

References

  1. ↑ 1.00 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.10 1.11 1.12 Lua error in package.lua at line 80: module 'strict' not found.
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  40. ↑ Lua error in package.lua at line 80: module 'strict' not found.
  41. ↑ Lua error in package.lua at line 80: module 'strict' not found.
  42. ↑ 42.0 42.1 42.2 Lua error in package.lua at line 80: module 'strict' not found.
  43. ↑ Lua error in package.lua at line 80: module 'strict' not found.
  44. ↑ Lua error in package.lua at line 80: module 'strict' not found.
  45. ↑ 45.0 45.1 45.2 Lua error in package.lua at line 80: module 'strict' not found.
  46. ↑ 46.0 46.1 46.2 46.3 Lua error in package.lua at line 80: module 'strict' not found.
  47. ↑ NIMS search result
  48. ↑ Bellanca, A. (1947). Sulla simmetria della manganolangbeinite/ Atti Accad. Nazi. Lincei Rend. Classe Sci. Fis. Mat. Nat. 2, 451–455.
  49. ↑ 49.0 49.1 Lua error in package.lua at line 80: module 'strict' not found.
  50. ↑ Lua error in package.lua at line 80: module 'strict' not found.
  51. ↑ Lua error in package.lua at line 80: module 'strict' not found.
  52. ↑ 52.0 52.1 52.2 Lua error in package.lua at line 80: module 'strict' not found.
  53. ↑ Lua error in package.lua at line 80: module 'strict' not found.
  54. ↑ 54.0 54.1 54.2 Lua error in package.lua at line 80: module 'strict' not found.
  55. ↑ Lua error in package.lua at line 80: module 'strict' not found.
  56. ↑ 56.0 56.1 56.2 Lua error in package.lua at line 80: module 'strict' not found.
  57. ↑ Lua error in package.lua at line 80: module 'strict' not found.
  58. ↑ 58.0 58.1 58.2 Lua error in package.lua at line 80: module 'strict' not found.
  59. ↑ 59.0 59.1 59.2 Lua error in package.lua at line 80: module 'strict' not found.
  60. ↑ 60.0 60.1 60.2 Lua error in package.lua at line 80: module 'strict' not found.
  61. ↑ 61.0 61.1 Lua error in package.lua at line 80: module 'strict' not found.
  62. ↑ Lua error in package.lua at line 80: module 'strict' not found.
  63. ↑ 63.0 63.1 63.2 Lua error in package.lua at line 80: module 'strict' not found.
  64. ↑ Lua error in package.lua at line 80: module 'strict' not found.
  65. ↑ 65.00 65.01 65.02 65.03 65.04 65.05 65.06 65.07 65.08 65.09 65.10 65.11 65.12 65.13 65.14 65.15 65.16 65.17 65.18 65.19 65.20 65.21 65.22 65.23 65.24 65.25 65.26 65.27 65.28 65.29 65.30 65.31 65.32 65.33 65.34 65.35 65.36 65.37 65.38 65.39 Lua error in package.lua at line 80: module 'strict' not found.
  66. ↑ Lua error in package.lua at line 80: module 'strict' not found.
  67. ↑ 67.0 67.1 67.2 Lua error in package.lua at line 80: module 'strict' not found.
  68. ↑ 68.0 68.1 Lua error in package.lua at line 80: module 'strict' not found.
  69. ↑ 69.0 69.1 Lua error in package.lua at line 80: module 'strict' not found.
  70. ↑ Lua error in package.lua at line 80: module 'strict' not found.
  71. ↑ Lua error in package.lua at line 80: module 'strict' not found.
  72. ↑ 72.0 72.1 72.2 Lua error in package.lua at line 80: module 'strict' not found.
  73. ↑ Lua error in package.lua at line 80: module 'strict' not found.
  74. ↑ 74.0 74.1 Lua error in package.lua at line 80: module 'strict' not found.
  75. ↑ Lua error in package.lua at line 80: module 'strict' not found.
  76. ↑ 76.0 76.1 Lua error in package.lua at line 80: module 'strict' not found.
  77. ↑ 77.0 77.1 Lua error in package.lua at line 80: module 'strict' not found.
  78. ↑ Lua error in package.lua at line 80: module 'strict' not found.
  79. ↑ 79.0 79.1 Lua error in package.lua at line 80: module 'strict' not found.
  80. ↑ Lua error in package.lua at line 80: module 'strict' not found.
  81. ↑ 81.0 81.1 81.2 81.3 Lua error in package.lua at line 80: module 'strict' not found.
  82. ↑ 82.0 82.1 82.2 82.3 Lua error in package.lua at line 80: module 'strict' not found.
  83. ↑ Lua error in package.lua at line 80: module 'strict' not found.
  84. ↑ 84.0 84.1 84.2 Lua error in package.lua at line 80: module 'strict' not found.
  85. ↑ Lua error in package.lua at line 80: module 'strict' not found.
  86. ↑ Lua error in package.lua at line 80: module 'strict' not found.
  87. ↑ 87.0 87.1 87.2 87.3 Lua error in package.lua at line 80: module 'strict' not found.
  88. ↑ Lua error in package.lua at line 80: module 'strict' not found.
  89. ↑ Lua error in package.lua at line 80: module 'strict' not found.
  90. ↑ Lua error in package.lua at line 80: module 'strict' not found.
  91. ↑ 91.0 91.1 91.2 Lua error in package.lua at line 80: module 'strict' not found.
  92. ↑ Lua error in package.lua at line 80: module 'strict' not found.
  93. ↑ Lua error in package.lua at line 80: module 'strict' not found.
  94. ↑ Lua error in package.lua at line 80: module 'strict' not found.
  95. ↑ Lua error in package.lua at line 80: module 'strict' not found.
  96. ↑ 96.0 96.1 96.2 Lua error in package.lua at line 80: module 'strict' not found.
  97. ↑ Lua error in package.lua at line 80: module 'strict' not found.
  98. ↑ Lua error in package.lua at line 80: module 'strict' not found.
  99. ↑ Lua error in package.lua at line 80: module 'strict' not found.
  100. ↑ Lua error in package.lua at line 80: module 'strict' not found.
  101. ↑ Lua error in package.lua at line 80: module 'strict' not found.
  102. ↑ Lua error in package.lua at line 80: module 'strict' not found.
  103. ↑ 103.0 103.1 Lua error in package.lua at line 80: module 'strict' not found.
  104. ↑ Lua error in package.lua at line 80: module 'strict' not found.
  105. ↑ Lua error in package.lua at line 80: module 'strict' not found.
  106. ↑ Lua error in package.lua at line 80: module 'strict' not found.
  107. ↑ Lua error in package.lua at line 80: module 'strict' not found.
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