Langbeinites

Langbeinites are a family of crystalline substances based on the structure of langbeinite with basic formula M2M'2(SO4)3. M is a large univalent cation such as potassium, rubidium, cesium, or ammonium). 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−), or molybdate (MO4). Although tungstates and monofluorophosphates are predicted, they have not been described.

At higher temperatures the crystal structure is cubic P213.[1] However the crystal structure may change at lower temperatures, for example P21 P1 P212121.[1] Usually this temperature is well below room temperature, but in a few cases the substance must be heated to have the cubic structure.

Crystal structure

The crystal structure of langbeinites is formed by a skeleton of tetrahedron shaped anions (such as the sulfate) held together by the other ions. In the cubic form the tetrahedron anions have slightly random orientations. If cooled the randomness ceases and the ions adopt more coherent orientations with lower energy, changing the crystal to a lower symmetry.

Examples

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

Selenates include diammonium dimanganese selenate.[1]

Chromate based langbeinites include dicesium 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.[7]

Double tungstates of the form A2B2(WO4)3 are predicted to exist in the langbeinite form.[8]

Examples with tetrafluroberyllate include dipotassium dimanganese tetrafluoroberyllate K2Mn2(BeF4)3,[4]

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[9]

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[10] Rb2YbTi(PO4)3.[11] Sodium barium diiron tris-(phosphate) NaBaFe2(PO4)3 is yet another variation with the same structure but differently charged ions.[12] 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.[13]

Properties

Physical properties

Lanbeinite crystals can show ferroelectric or ferroelastic properties.[1] Diammonium dicadmium sulfate identified by Jona and Pepinsky[14] with a unit cell size of 10.35 Å becomes ferroelectric when the temperature drops below 95K.[15] 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.[16] 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.[17] 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.[18]

Dithallium dicadmium sulfate was shown to be ferroelectric in 1972.[19]

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.[20] Dipotassium dimagnesium sulfate doped with dysprosium develops thermoluminescence and mechanoluminescence after being irradiated with gamma rays.[21] Since gamma rays occur naturally, this radiation induced thermoluminescence can be used to date evaporites in which langbeinite can be a constituent.[22]

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.[23] 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.[24]

Where the crystals change phase there is a discontinuity in the heat capacity. The transitions may show thermal hysteresis.[25]

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.[26]

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.[27]

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.[28]

Sulfates

formula weight comment transition temperature K density cell size refractive
elements formula g/mol symmetries 1 2 3[29] Å index
KMg K2Mg2(SO4)3 414.99 4 phases 51 54.9 63.8 2.832[30] 9.9211[31] 1.536[32]
RbMg Rb2Mg2(SO4)3 507.73 made 3.367[33] 10.0051[33] 1.556[33]
CsMg Cs2Mg2(SO4)3 602.61 no compound[8]
(NH4)Mg (NH4)2Mg2(SO4)3 372.87 241[34] 220[34] 2.49[35] 9.979[35]
TlMg Tl2Mg2(SO4)3 745.56 ≥3 phase 227.8[34] 330.8[34]
KCaMg K2CaMg(SO4)3 430.77 made 2.723[36] 10.1662[36] 1.525[36]
KCa K2Ca2(SO4)3 446.54 4 phases 457 2.69 2.683[37] 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[38] 10.5687[38] 1.520[38]
CsCa Cs2Ca2(SO4)3 634.15 3.417[39][40] 10.7213 1.549
TlCa no compound[8]
(NH4)Ca (NH4)2Ca2(SO4)3 404.42 made 158 2.297[41] 10.5360[41] 1.532[41]
NH4V (NH4)2V2(SO4)3 colour clear green[42] 2.76[43] 10.089[42]
KMn manganolangbeinite[44] K2Mn2(SO4)3 476.26 2 phases
pale pink[45]		 191 3.02[31] 10.014[31]
(orthorhombic)
a=10.081, b=10.108, c=10.048 Å[46]		 1.576[45]
RbMn[47] Rb2Mn2(SO4)3 569 made 3.546[48] 10.2147[48] 1.590[48]
CsMn Cs2Mn2(SO4)3 663.87 predicted[8]
(NH4)Mn (NH4)2Mn2(SO4)3 434.14 made 2.72[35] 10.1908[49]
TlMn Tl2Mn2(SO4)3 806.83 made 5.015[50] 10.2236[50] 1.722[50]
KFe K2Fe2(SO4)3 478.07 made ?130
RbFe predicted[8]
TlFe 808.64 exists[8]
NH4Fe (NH4)2Fe2(SO4)3[42] 435.95 exits 2.84[35] 10.068[35]
KCo K2Co2(SO4)3 484.25 2 phases
deep purple		 126 3.280[30] 9.9313[31] 1.608[51]
RbCo Rb2Co2(SO4)3 576.99 made 3.807[52] 10.0204[52] 1.602[52]
CsCo 671.87
(NH4)Co (NH4)2Co2(SO4)3 442.13 made 2.94[35] 9.997[35]
TlCo Tl2Co2(SO4)3 813.82 made 5.361[53] 10.0312 1.775
KNi K2Ni2(SO4)3 483.77 made[54] light greenish yellow[55] 3.369[30] 9.8436[55] 1.620[55]
RbNi Rb2Ni2(SO4)3 576.51 made 3.921[56] 9.9217[56] 1.636[56]
CsNi 671.39 predicted[8]
(NH4)Ni (NH4)2Ni2(SO4)3 441.65 made[54] 160 3.02[35] 9.904[35]
TlNi Tl2Ni2(SO4)3 814.34 predicted[8]
RbCu predicted[8]
CsCu predict not[8]
TlCu predicted[8]
KZn K2Zn2(SO4)3 497.1 4 phases 75 138 3.376[30] 9.9247[57] 1.592[57]
RbZn predicted[8]
CsZn predict not[8]
TlZn predicted[8]
KCd K2Cd2(SO4)3 591.21 2 phases 432 2.615 3.677[58] 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[31][59] 10.3810[31][59] 1.590[59]
(NH4)Cd (NH4)2Cd2(SO4)3 549.09 4 phases 95 3.288[31] 10.3511[31]
TlCd Tl2Cd2(SO4)3 921.78 4 phases 92 120 132 5.467[31] 10.3841[31] 1.730[60]

Fluoroberyllates

comment transition cell size refractive
elements formula symmetries 1 2 3 density Å index
KMnBe K2Mn2(BeF4)3 4 phases 213[4]

Phosphates

substance formula weight unit cell edge Å density
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[61] 417.71
K2AlSn(PO4)3 508.78 9.798[10]
K2YHf(PO4)3[62] 630.51 10.3075 3.824
Li(H2O)2Hf2(PO4)3[63] 684.87 10.1993
Li(H2O)2Zr2(PO4)3[64] 510.33 10.2417
Li2Zr2(PO4)3[64] 481.24
K2(Ce,...,Lu)Zr(PO4)3[65] 594.45...629.3 10.29668
Rb2FeZr(PO4)3[66] 602.92 10.1199
K4(Al,Cr,Fe)3(NbTa)1(PO4)6 ?[67]
K2AlTi(PO4)3[68] 437.96 9.7641
KBaEr2(PO4)3[69] 795.857
RbBaEr2(PO4)3[69] 842.227
CsBaEr2(PO4)3[69] 889.665
(Rb,Cs)2(Pr,Er)Zr(PO4)3[69]
KCsFeZrP3O12 603.99 10.103[70]
CaFe3O(PO4)3[71] 508.53
SrFe3O(PO4)3[71] 556.1
PbFe3O(PO4)3[71] 675.6
Pb1.5VIV2O(PO4)3 697.6 9.7818 4.912[72]
Ba1.5Fe3+2(PO4)3[73] 602.59
KSrSc2(PO4)3[74] 501.54
Rb0.743K0.845Co0.293Ti1.707(PO4)3[75]

Molybdates

substance formula weight unit cell edge Å density
Cs2Cd2(MoO4)3[76] 970.5 11.239
Rb2Co2(MoO4)3 768.7

Preparation

Diammonium dicadmium sulfate can be made by evaporating a solution of ammonium sulfate and cadmium sulfate.[16] Dithallium dicadmium sulfate can be made by evaporating a water solution at 85 °C.[19] Other substances may be formed during crystallisation from water such as Tutton's salts or competing compounds like Rb2Cd3(SO4)4·5H2O.[77]

Potassium and ammonium nickel langbeinite can be made from nickel sulfate and the other sulfates by evaporating a water solution at 85 °C.[54]

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.[46]

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.[63] Li(H2O)2Hf2(PO4)3 converts to Li2Hf2(PO4)3 on heating to 200 °C.[64]

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.[66]

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.[78] 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.[42]

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.[67]

References

  1. ↑ 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 1.10 1.11 1.12 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. doi:10.1107/S0108768102013782. PMC 2391006. PMID 12324686.
  2. ↑ Guelylah, A.; G. Madariaga; W. Morgenroth; M. I. Aroyo; T. Breczewski; E. H. Bocanegra (2000). "X-ray structure determination of the monoclinic (121 K) and orthorhombic (85 K) phases of langbeinite-type dithallium dicadmium sulfate". Acta Crystallographica Section B Structural Science 56 (6): 921–935. doi:10.1107/S0108768100009514.
  3. ↑ Guelylah, Abderrahim; Gotzon Madariaga (2003). "Dirubidium dicadmium sulfate at 293 K". Acta Crystallographica Section C Crystal Structure Communications 59 (5): i32–i34. doi:10.1107/S0108270103007479.
  4. ↑ 4.0 4.1 4.2 Guelylah, A.; M. I. Aroyo; J. M. Pérez-Mato (1996). "Microscopic distortion and order parameter in langbeinite K2Cd2(SO4)3". Phase Transitions 59 (1–3): 155–179. doi:10.1080/01411599608220042.
  5. ↑ Zemann, Anna; J. Zemann (1957). "Die Kristallstruktur von Langbeinit, K2Mg2(SO4)3". Acta Crystallographica 10 (6): 409–413. doi:10.1107/S0365110X57001346.
  6. ↑ Boujelben, Mohamed; Mohamed Toumi; Tahar Mhiri (2007). "Langbeinite-type Rb2Ca2(SO4)3". Acta Crystallographica Section E Structure Reports Online 63 (7): i157–i157. doi:10.1107/S1600536807027043.
  7. ↑ Солодовникова, С.Ф.; Солодовникова, В.А. (1997). "Новый тип строения в морфотропном ряду A+2M+2(MoO4)3: кристаллическая структура Rb2Cu2(MoO4)3". ЖУРНАЛ структур. химии (in Russian) 38 (5): 914–921.
  8. ↑ 8.0 8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8 8.9 8.10 8.11 8.12 8.13 Kiselyova, Nadezhda (September 1997). "Property Predictions for Multicomponent Compounds". Russian Academy of Sciences. Retrieved 6 July 2013.
  9. ↑ Pies, W.; A. Weiss (1973). "Key Elements: F, Cl, Br, I". Landolt-Börnstein - Group III Condensed Matter 7a. pp. 91–103. doi:10.1007/10201462_9. ISBN 3-540-06166-5. |chapter= ignored (help)
  10. ↑ 10.0 10.1 Li, Hai-Yan; Dan Zhao (2011). "A new langbeinite-type phosphate: K2AlSn(PO4)3". Acta Crystallographica Section E Structure Reports Online 67 (10): i56–i56. doi:10.1107/S1600536811037263. PMID 22058680.
  11. ↑ Gustafsson, Joacim C. M.; Stefan T. Norberg; Göran Svensson (2006). "The langbeinite type Rb2TiY(PO4)3". Acta Crystallographica Section E Structure Reports Online 62 (7): i160–i162. doi:10.1107/S1600536806021635.
  12. ↑ Hidouri, Mourad; Hasna Jerbi; Mongi Ben Amara (2008). "The iron phosphate NaBaFe2(PO4)3". Acta Crystallographica Section E Structure Reports Online 64 (8): i51–i51. doi:10.1107/S1600536808023040. PMID 21202994.
  13. ↑ Harrison, William T. A. (2010). "K2ScSn(AsO4)3: an arsenate-containing langbeinite". Acta Crystallographica Section C Crystal Structure Communications 66 (7): i82–i84. doi:10.1107/S0108270110021670.
  14. ↑ Jona, F.; R. Pepinsky (1956). "Ferroelectricity in the Langbeinite System". Physical Review 103 (4): 1126–1126. Bibcode:1956PhRv..103.1126J. doi:10.1103/PhysRev.103.1126.
  15. ↑ McDowell, C.A.; P. Raghunathan; R. Srinivasan (1975). "Proton N.M.R. study of the dynamics of the ammonium ion in ferroelectric langbeinite, (NH4)2Cd2(SO4)3". Molecular Physics 29 (3): 815–824. Bibcode:1975MolPh..29..815M. doi:10.1080/00268977500100721.
  16. ↑ 16.0 16.1 Moriyoshi, C.; E. Magome and K. Itoh (28 March 2007). "Structural Study of Langbeinite-type (NH4)2Cd(SO4)3) Crystal in the High Temperature Phase". IMF-11. Retrieved 24 June 2013.
  17. ↑ Glogarová, M.; C. Frenzel; E. Hegenbarth (1972). "The Behaviour of (NH4)2Cd2(SO4)3 under Pressure". Physica Status Solidi (b) 53 (1): 369–372. Bibcode:1972PSSBR..53..369G. doi:10.1002/pssb.2220530139.
  18. ↑ Hikita, Tomoyuki; Makoto Kitabatake; Takuro Ikeda (1979). "Hydrostatic Pressure Effect on the Phase Transition of K2Mn2(SO4)3". Journal of the Physical Society of Japan 46 (2): 695–696. Bibcode:1979JPSJ...46..695H. doi:10.1143/JPSJ.46.695.
  19. ↑ 19.0 19.1 B̌rzina, B.; M. Glogarová (1972). "New ferroelectric langbeinite Tl2Cd2(SO4)3". Physica Status Solidi (a) 11 (1): K39–K42. Bibcode:1972PSSAR..11...39. doi:10.1002/pssa.2210110149.
  20. ↑ Deshmukh, B. T.; S. V. Bodade; S. V. Moharil (1986). "Thermoluminescence of K2Cd2(SO4)3". Physica status solidi (a) 98 (1): 239–246. Bibcode:1986PSSAR..98..239D. doi:10.1002/pssa.2210980127.
  21. ↑ Panigrahi, A. K.; Dhoble, S. J.; Kher, R. S.; Moharil, S. V. (2003). "Thermo and mechanoluminescence of Dy3+ activated K2Mg2(SO4)3 phosphor". Physica status solidi (a) 198 (2): 322–328. Bibcode:2003PSSAR.198..322P. doi:10.1002/pssa.200306605.
  22. ↑ Léost, I.; Féraud, G.; Blanc-Valleron, M. M.; Rouchy, J. M. (2001). "First absolute dating of Miocene Langbeinite evaporites by 40Ar/39Ar laser step-heating: [K2Mg2(SO4)3] Stebnyk Mine (Carpathian Foredeep Basin)". Geophysical Research Letters 28 (23): 4347–4350. Bibcode:2001GeoRL..28.4347L. doi:10.1029/2001GL013477.
  23. ↑ Franke, V.; E. Hegenbarth; B. Březina (1975). "Specific heat measurement on Tl2Cd2(SO4)3". Physica Status Solidi (a) 28 (1): K77–K80. Bibcode:1975PSSAR..28...77F. doi:10.1002/pssa.2210280165.
  24. ↑ Abrahams, S. C.; J. L. Bernstein (1977). "Piezoelectric langbeinite-type K2Cd2(SO4)3: Room temperature crystal structure and ferroelastic transformation". The Journal of Chemical Physics 67 (5): 2146. Bibcode:1977JChPh..67.2146A. doi:10.1063/1.435101.
  25. ↑ Cao, Hongjie; N. Kent Dalley; Juliana Boerio-Goates (1993). "Calorimetric and structural studies of langbeinite-type Tl2Cd2(SO4)3". Ferroelectrics 146 (1): 45–56. doi:10.1080/00150199308008525.
  26. ↑ Sutera, A.; K. Nassau; S. C. Abrahams (1981). "Phase-transition variation with composition in solid solutions of K2Cd2(SO4)3 with Tl2Cd2(SO4)3". Journal of Applied Crystallography 14 (5): 297–299. doi:10.1107/S0021889881009412.
  27. ↑ Percival, M. J. L. (1990). "Optical Absorption Spectroscopy of Doped Materials: The P213-P212121 Phase Transition in K2(Cd0.98Co0.02)2(SO4)3". Mineralogical Magazine 54 (377): 525–535. doi:10.1180/minmag.1990.054.377.01.
  28. ↑ Zhou, Ya-Ping; Zhang Rui; Wan Hong-Wen; Zhan Zheng-Kun; Xu Ming-Fei (March 2001). "Thermochemical Studies on the Langbeinite-Type Double Sulfate Salts，(NH4)2Cd2(SO4)3 and K2Cd2(SO4)3". Acta Physic0-Chimica Sinica (in Chinese) 17 (3): 247. doi:10.3866/PKU.WHXB20010312 (inactive 2015-01-24).
  29. ↑ Boerio-Goates, Juliana; JohanneI. Artman; BrianF. Woodfield (1990). "Heat capacity studies of phase transitions in langbeinites II. K2Mg2(SO4)3". Physics and Chemistry of Minerals 17 (2): 173. Bibcode:1990PCM....17..173B. doi:10.1007/BF00199670.
  30. ↑ 30.0 30.1 30.2 30.3 Speer, D.; E. Salje (1986). "Phase transitions in langbeinites I: Crystal chemistry and structures of K-double sulfates of the langbeinite type M2++K2(SO4)3, M++=Mg, Ni, Co, Zn, Ca". Physics and Chemistry of Minerals 13 (1): 17–24. Bibcode:1986PCM....13...17S. doi:10.1007/BF00307309.
  31. ↑ 31.0 31.1 31.2 31.3 31.4 31.5 31.6 31.7 31.8 31.9 Burkov, V. I.; Z. B. Perekalina (2001). "Gyrotropy of Cubic Langbeinite Crystals". Inorganic Materials 37 (3): 203–212. doi:10.1023/A:1004165926149.
  32. ↑ Swanson, H. E.; H. F. McMurdie; M. C. Morris; E. H. Evans (September 1970). "Standard X-ray Diffraction Powder Patterns". National Bureau of Standards Monograph 25 Section 6. National Bureau of Standards. p. 40. Retrieved 5 July 2013.
  33. ↑ 33.0 33.1 33.2 Swanson, H. E.; McMurdie, H. F.; Morris, M. C. & Evans, E. H.. (September 1969). Standard X-ray Diffraction Powder Patterns: Section 7. Data for 81 Substances. Washington D.C: UNT Digital Library. p. 50. Retrieved July 4, 2013.
  34. ↑ 34.0 34.1 34.2 34.3 Kahrizi, Mojtaba; M.O. Steinitz (1988). "Phase transitions and thermal expansion in langbeinite type compounds". Solid State Communications 66 (4): 375–378. Bibcode:1988SSCom..66..375K. doi:10.1016/0038-1098(88)90860-5.
  35. ↑ 35.0 35.1 35.2 35.3 35.4 35.5 35.6 35.7 35.8 AtomWork materials database at NIMS
  36. ↑ 36.0 36.1 36.2 Swanson, H. E.; McMurdie, H. F.; Morris, M. C. & Evans, E. H.. (September 1969). Standard X-ray Diffraction Powder Patterns: Section 7. Data for 81 Substances. Washington D.C: UNT Digital Library. p. 37. Retrieved July 4, 2013.
  37. ↑ Swanson, H. E.; McMurdie, H. F.; Morris, M. C. & Evans, E. H.. (September 1969). Standard X-ray Diffraction Powder Patterns: Section 7. Data for 81 Substances. Washington D.C: UNT Digital Library. p. 39. Retrieved July 4, 2013.
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  39. ↑ Swanson, H. E.; McMurdie, H. F.; Morris, M. C. & Evans, E. H.. (September 1969). Standard X-ray Diffraction Powder Patterns: Section 7. Data for 81 Substances. Washington D.C: UNT Digital Library. p. 12. Retrieved June 17, 2013.
  40. ↑ Gattow, G.; J. Zemann (1958). "Über Doppelsulfate vom Langbeinit-Typ, A2+B22+(SO4)3". Zeitschrift für anorganische und allgemeine Chemie 293 (5–6): 233–240. doi:10.1002/zaac.19582930502.
  41. ↑ 41.0 41.1 41.2 Swanson, H. E.; H. F. McMurdie; M. C. Morris; E. H. Evans (September 1970). "Standard X-ray Diffraction Powder Patterns". National Bureau of Standards Monograph 25 Section 8. National Bureau of Standards. p. 7. Retrieved 5 July 2013.
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  49. ↑ Hikita, T. (2005). "(NH4)2SO4 family ... K3BiCl6·2KCl·KH3F4". Inorganic Substances other than Oxides 36B2: 1–3. doi:10.1007/10552342_84. ISBN 9783540313533. |chapter= ignored (help)
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  51. ↑ Swanson, H. E.; H. F. McMurdie; M. C. Morris; E. H. Evans (September 1970). "Standard X-ray Diffraction Powder Patterns". National Bureau of Standards Monograph 25 Section 6. National Bureau of Standards. p. 35. Retrieved 5 July 2013.
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  54. ↑ 54.0 54.1 54.2 Jayakumar, V. S.; I. Hubert Joe; G. Aruldhas (1995). "IR and single crystal Raman spectra of langbeinities M2 Ni2(SO4)3 (M = NH4, K)". Ferroelectrics 165 (1): 307–318. doi:10.1080/00150199508228311.
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  56. ↑ 56.0 56.1 56.2 Swanson, H. E.; H. F. McMurdie; M. C. Morris; E. H. Evans (September 1970). "Standard X-ray Diffraction Powder Patterns". National Bureau of Standards Monograph 25 Section 8. National Bureau of Standards. p. 72. Retrieved 5 July 2013.
  57. ↑ 57.0 57.1 Swanson, H. E.; H. F. McMurdie; M. C. Morris; E. H. Evans (September 1970). "Standard X-ray Diffraction Powder Patterns". National Bureau of Standards Monograph 25 Section 6. National Bureau of Standards. p. 54. Retrieved 5 July 2013.
  58. ↑ Swanson, H. E.; McMurdie, H. F.; Morris, M. C. & Evans, E. H.. (September 1969). Standard X-ray Diffraction Powder Patterns: Section 7. Data for 81 Substances. Washington D.C: UNT Digital Library. p. 34. Retrieved July 4, 2013.
  59. ↑ 59.0 59.1 59.2 Swanson, H. E.; McMurdie, H. F.; Morris, M. C. & Evans, E. H.. (September 1969). Standard X-ray Diffraction Powder Patterns: Section 7. Data for 81 Substances. Washington D.C: UNT Digital Library. p. 45. Retrieved July 4, 2013.
  60. ↑ Swanson, H. E.; H. F. McMurdie; M. C. Morris; E. H. Evans (September 1970). "Standard X-ray Diffraction Powder Patterns". National Bureau of Standards Monograph 25 Section 8. National Bureau of Standards. p. 83. Retrieved 5 July 2013.
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