Lead(II) iodide

Last updated
Lead(II) iodide
Lead-diiodide-3D-polyhedra.png
Lead iodide.jpg
Names
Other names
Plumbous iodide
Identifiers
3D model (JSmol)
ChemSpider
ECHA InfoCard 100.030.220 OOjs UI icon edit-ltr-progressive.svg
EC Number
  • 233-256-9
PubChem CID
UNII
UN number 2291 3077
  • InChI=1S/2HI.Pb/h2*1H;/q;;+2/p-2 Yes check.svgY
    Key: RQQRAHKHDFPBMC-UHFFFAOYSA-L Yes check.svgY
  • InChI=1/2HI.Pb/h2*1H;/q;;+2/p-2
    Key: RQQRAHKHDFPBMC-NUQVWONBAP
  • I[Pb]I
Properties
PbI
2
Molar mass 461.01 g/mol
Appearancebright yellow powder
Odor odorless
Density 6.16 g/cm3 [1]
Melting point 410 °C (770 °F; 683 K) [1]
Boiling point 872 °C (1,602 °F; 1,145 K) decomp. [1]
  • 0.44 g/L (0 °C)
  • 0.76 g/L (20 °C) [1] [2]
  • 4.1 g/L (100 °C) [3] [4]
4.41×10−9 (20 °C)
Solubility
Band gap 2.34 eV (direct) [6] [7]
−126.5·10−6 cm3/mol [8]
Structure [9]
Hexagonal hP6
P63mc, No. 186
a = 0.4556 nm, b = 0.4556 nm, c = 1.3973 nm
α = 90°, β = 90°, γ = 120°°
2
octahedral
Thermochemistry [10]
77.4 J/(mol·K)
Std molar
entropy (S⦵298)
174.9 J/(mol·K)
-175.5 kJ/mol
-173.6 kJ/mol
Hazards
GHS labelling:
GHS-pictogram-exclam.svg GHS-pictogram-silhouette.svg GHS-pictogram-pollu.svg
Danger
H302, H332, H360, H373, H410
P201, P202, P260, P261, P264, P270, P271, P273, P281, P301+P312, P304+P312, P304+P340, P308+P313, P312, P314, P330, P391, P405, P501
NFPA 704 (fire diamond)
NFPA 704.svgHealth 3: Short exposure could cause serious temporary or residual injury. E.g. chlorine gasFlammability 0: Will not burn. E.g. waterInstability 0: Normally stable, even under fire exposure conditions, and is not reactive with water. E.g. liquid nitrogenSpecial hazards (white): no code
3
0
0
Flash point Non-flammable
Related compounds
Other anions
Other cations
Tin(II) iodide
Related compounds
Except where otherwise noted, data are given for materials in their standard state (at 25 °C [77 °F], 100 kPa).
X mark.svgN  verify  (what is  Yes check.svgYX mark.svgN ?)

Lead(II) iodide (or lead iodide) is a chemical compound with the formula PbI
2. At room temperature, it is a bright yellow odorless crystalline solid, that becomes orange and red when heated. [11] It was formerly called plumbous iodide.

Contents

The compound currently has a few specialized applications, such as the manufacture of solar cells, [12] X-rays and gamma-ray detectors. [13] Its preparation is an entertaining and popular demonstration in chemistry education, to teach topics such as precipitation reactions and stoichiometry. [14] It is decomposed by light at temperatures above 125 °C (257 °F), and this effect has been used in a patented photographic process. [4] [15]

Lead iodide was formerly employed as a yellow pigment in some paints, with the name iodide yellow. However, that use has been largely discontinued due to its toxicity and poor stability. [16]

Preparation

PbI
2 is commonly synthesized via a precipitation reaction between potassium iodide KI and lead(II) nitrate Pb(NO
3)2 in water solution:

Pb(NO3)2 + 2 KI → PbI2 + 2 KNO3

While the potassium nitrate KNO
3 is soluble, the lead iodide PbI
2 is nearly insoluble at room temperature, and thus precipitates out. [17]

Other soluble compounds containing lead(II) and iodide can be used instead, for example lead(II) acetate [12] and sodium iodide.

The compound can also be synthesized by reacting iodine vapor with molten lead between 500 and 700 °C. [18]

A thin film of PbI
2 can also be prepared by depositing a film of lead sulfide PbS and exposing it to iodine vapor, by the reaction

PbS + I2 → PbI2 + S

The sulfur is then washed with dimethyl sulfoxide. [19]

Crystallization

Lead iodide prepared from cold solutions usually consists of many small hexagonal platelets, giving the yellow precipitate a silky appearance. Larger crystals can be obtained by exploiting the fact that solubility of lead iodide in water (like those of lead chloride and lead bromide) increases dramatically with temperature. The compound is colorless when dissolved in hot water, but crystallizes on cooling as thin but visibly larger bright yellow flakes, that settle slowly through the liquid — a visual effect often described as "golden rain". [20] Larger crystals can be obtained by autoclaving the PbI
2 with water under pressure at 200 °C. [21]

Even larger crystals can be obtained by slowing down the common reaction. A simple setup is to submerge two beakers containing the concentrated reactants in a larger container of water, taking care to avoid currents. As the two substances diffuse through the water and meet, they slowly react and deposit the iodide in the space between the beakers. [22]

Another similar method is to react the two substances in a gel medium, that slows down the diffusion and supports the growing crystal away from the container's walls. Patel and Rao have used this method to grow crystals up to 30 mm in diameter and 2 mm thick. [23]

The reaction can be slowed also by separating the two reagents with a permeable membrane. This approach, with a cellulose membrane, was used in September 1988 to study the growth of PbI
2 crystals in zero gravity, in an experiment flown on the Space Shuttle Discovery. [24]

PbI
2 can also be crystallized from powder by sublimation at 390 °C, in near vacuum [25] or in a current of argon with some hydrogen. [26]

Large high-purity crystals can be obtained by zone melting or by the Bridgman–Stockbarger technique. [18] [25] These processes can remove various impurities from commercial PbI
2. [27]

Applications

Lead iodide is a precursor material in the fabrication of highly efficient Perovskite solar cell. Typically, a solution of PbI
2 in an inorganic solvent, such as dimethylformamide or dimethylsulfoxide, is applied over a titanium dioxide layer by spin coating. The layer is then treated with a solution of methylammonium iodide CH
3NH
3I and annealed, turning it into the double salt methylammonium lead iodide CH
3NH
3PbI
3, with a perovskite structure. The reaction changes the film's color from yellow to light brown. [12]

PbI
2 is also used as a high-energy photon detector for gamma-rays and X-rays, due to its wide band gap which ensures low noise operation. [4] [13] [25]

Lead iodide was formerly used as a paint pigment under the name "iodine yellow". It was described by Prosper Mérimée (1830) as "not yet much known in commerce, is as bright as orpiment or chromate of lead. It is thought to be more permanent; but time only can prove its pretension to so essential a quality. It is prepared by precipitating a solution of acetate or nitrate of lead, with potassium iodide: the nitrate produces a more brilliant yellow color." [16] However, due to the toxicity and instability of the compound it is no longer used as such. [16] It may still be used in art for bronzing and in gold-like mosaic tiles. [4]

Stability

Common material characterization techniques such as electron microscopy can damage samples of lead (II) iodide. [28] Thin films of lead (II) iodide are unstable in ambient air. [29] Ambient air oxygen oxidizes iodide into elemental iodine:

2 PbI2 + O2 → 2 PbO + 2 I2↑

Toxicity

Lead iodide is very toxic to human health. Ingestion will cause many acute and chronic consequences characteristic of lead poisoning. [30] Lead iodide has been found to be a carcinogen in animals suggesting the same may hold true in humans. [31] Lead iodide is an inhalation hazard, and appropriate respirators should be used when handling powders of lead iodide.

Structure

The structure of PbI
2, as determined by X-ray powder diffraction, is primarily hexagonal close-packed system with alternating between layers of lead atoms and iodide atoms, with largely ionic bonding. Weak van der Waals interactions have been observed between lead–iodide layers. [13] The most common stacking forms are 2H and 4H. The 4H polymorph is most common in samples grown from the melt, by precipitation, or by sublimation, whereas the 2H polymorph is usually formed by sol-gel synthesis. [9] The solid can also take an R6 rhombohedral structure. [32]

See also

Related Research Articles

<span class="mw-page-title-main">Iodine</span> Chemical element, symbol I and atomic number 53

Iodine is a chemical element; it has symbol I and atomic number 53. The heaviest of the stable halogens, it exists at standard conditions as a semi-lustrous, non-metallic solid that melts to form a deep violet liquid at 114 °C (237 °F), and boils to a violet gas at 184 °C (363 °F). The element was discovered by the French chemist Bernard Courtois in 1811 and was named two years later by Joseph Louis Gay-Lussac, after the Ancient Greek Ιώδης 'violet-coloured'.

<span class="mw-page-title-main">Silver iodide</span> Chemical compound

Silver iodide is an inorganic compound with the formula AgI. The compound is a bright yellow solid, but samples almost always contain impurities of metallic silver that give a gray coloration. The silver contamination arises because some samples of AgI can be highly photosensitive. This property is exploited in silver-based photography. Silver iodide is also used as an antiseptic and in cloud seeding.

An iodide ion is the ion I−. Compounds with iodine in formal oxidation state −1 are called iodides. In everyday life, iodide is most commonly encountered as a component of iodized salt, which many governments mandate. Worldwide, iodine deficiency affects two billion people and is the leading preventable cause of intellectual disability.

<span class="mw-page-title-main">Caesium iodide</span> Chemical compound

Caesium iodide or cesium iodide is the ionic compound of caesium and iodine. It is often used as the input phosphor of an X-ray image intensifier tube found in fluoroscopy equipment. Caesium iodide photocathodes are highly efficient at extreme ultraviolet wavelengths.

<span class="mw-page-title-main">Sodium iodide</span> Chemical compound

Sodium iodide (chemical formula NaI) is an ionic compound formed from the chemical reaction of sodium metal and iodine. Under standard conditions, it is a white, water-soluble solid comprising a 1:1 mix of sodium cations (Na+) and iodide anions (I−) in a crystal lattice. It is used mainly as a nutritional supplement and in organic chemistry. It is produced industrially as the salt formed when acidic iodides react with sodium hydroxide. It is a chaotropic salt.

<span class="mw-page-title-main">Iodic acid</span> Chemical compound (HIO3)

Iodic acid is a white water-soluble solid with the chemical formula HIO3. Its robustness contrasts with the instability of chloric acid and bromic acid. Iodic acid features iodine in the oxidation state +5 and is one of the most stable oxo-acids of the halogens. When heated, samples dehydrate to give iodine pentoxide. On further heating, the iodine pentoxide further decomposes, giving a mix of iodine, oxygen and lower oxides of iodine.

<span class="mw-page-title-main">Copper(I) iodide</span> Chemical compound

Copper(I) iodide is the inorganic compound with the formula CuI. It is also known as cuprous iodide. It is useful in a variety of applications ranging from organic synthesis to cloud seeding.

<span class="mw-page-title-main">Titanium tetraiodide</span> Chemical compound

Titanium tetraiodide is an inorganic compound with the formula TiI4. It is a black volatile solid, first reported by Rudolph Weber in 1863. It is an intermediate in the van Arkel–de Boer process for the purification of titanium.

<span class="mw-page-title-main">Mercury(II) iodide</span> Chemical compound

Mercury(II) iodide is a chemical compound with the molecular formula HgI2. It is typically produced synthetically but can also be found in nature as the extremely rare mineral coccinite. Unlike the related mercury(II) chloride it is hardly soluble in water (<100 ppm).

<span class="mw-page-title-main">Thallium(I) iodide</span> Chemical compound

Thallium(I) iodide is a chemical compound with the formula TlI. It is unusual in being one of the few water-insoluble metal iodides, along with AgI, CuI, SnI2, SnI4, PbI2 and HgI2.

<span class="mw-page-title-main">Strontium iodide</span> Chemical compound

Strontium iodide (SrI2) is a salt of strontium and iodine. It is an ionic, water-soluble, and deliquescent compound that can be used in medicine as a substitute for potassium iodide . It is also used as a scintillation gamma radiation detector, typically doped with europium, due to its optical clarity, relatively high density, high effective atomic number (Z=48), and high scintillation light yield. In recent years, europium-doped strontium iodide (SrI2:Eu2+) has emerged as a promising scintillation material for gamma-ray spectroscopy with extremely high light yield and proportional response, exceeding that of the widely used high performance commercial scintillator LaBr3:Ce3+. Large diameter SrI2 crystals can be grown reliably using vertical Bridgman technique and are being commercialized by several companies.

Organoiodine chemistry is the study of the synthesis and properties of organoiodine compounds, or organoiodides, organic compounds that contain one or more carbon–iodine bonds. They occur widely in organic chemistry, but are relatively rare in nature. The thyroxine hormones are organoiodine compounds that are required for health and the reason for government-mandated iodization of salt.

<span class="mw-page-title-main">Californium compounds</span>

Few compounds of californium have been made and studied. The only californium ion that is stable in aqueous solutions is the californium(III) cation. The other two oxidation states are IV (strong oxidizing agents) and II (strong reducing agents). The element forms a water-soluble chloride, nitrate, perchlorate, and sulfate and is precipitated as a fluoride, oxalate or hydroxide. If problems of availability of the element could be overcome, then CfBr2 and CfI2 would likely be stable.

<span class="mw-page-title-main">Methylammonium lead halide</span>

Methylammonium lead halides (MALHs) are solid compounds with perovskite structure and a chemical formula of [CH3NH3]+Pb2+(X−)3, where X = Cl, Br or I. They have potential applications in solar cells, lasers, light-emitting diodes, photodetectors, radiation detectors, scintillator, magneto-optical data storage and hydrogen production.

<span class="mw-page-title-main">Golden rain demonstration</span>

Golden rain demonstration is made by combining two colorless solutions, potassium iodide solution and Lead(II) nitrate solution at room temperature to form yellow precipitate. During the chemical reaction, golden particles gently drop from the top of Erlenmeyer flask to the bottom, similar to watching the rain through a window. The golden rain chemical reaction demonstrates the formation of a solid precipitate. The golden rain experiment involves two soluble ionic compounds, potassium iodide (KI) and lead(II) nitrate (Pb(NO3)2). They are initially dissolved in separate water solutions, which are each colorless. When mixed, as the lead from one solution and the iodide from the other combine to form lead(II) iodide (PbI2), which is insoluble at low temperature and has a bright golden-yellow color. Although this is a reaction solely of the dissociated ions in solution, it is sometimes referred to as a double displacement reaction:

Iron(III) iodide is an inorganic compound with the chemical formula FeI3. It is a thermodynamically unstable compound that is difficult to prepare. Nevertheless, iron(III) iodide has been synthesised in small quantities in the absence of air and water.

<span class="mw-page-title-main">Praseodymium(III) iodide</span> Chemical compound

Praseodymium(III) iodide is an inorganic salt, consisting of the rare-earth metal praseodymium and iodine, with the chemical formula PrI3. It forms green crystals. It is soluble in water.

<span class="mw-page-title-main">Praseodymium diiodide</span> Chemical compound

Praseodymium diiodide is a chemical compound with the empirical formula of PrI2, consisting of praseodymium and iodine. It is an electride, with the ionic formula of Pr3+(I−)2e−, and therefore not a true praseodymium(II) compound.

<span class="mw-page-title-main">Lanthanum(III) iodide</span> Chemical compound

Lanthanum(III) iodide is an inorganic compound containing lanthanum and iodine with the chemical formula LaI
3.

Lutetium compounds are compounds formed by the lanthanide metal lutetium (Lu). In these compounds, lutetium generally exhibits the +3 oxidation state, such as LuCl3, Lu2O3 and Lu2(SO4)3. Aqueous solutions of most lutetium salts are colorless and form white crystalline solids upon drying, with the common exception of the iodide. The soluble salts, such as nitrate, sulfate and acetate form hydrates upon crystallization. The oxide, hydroxide, fluoride, carbonate, phosphate and oxalate are insoluble in water.

References

  1. 1 2 3 4 5 Haynes (2016), p. 4.69.
  2. ↑ Clever, H. L.; Johnston, F. J. (1980). "The Solubility of Some Sparingly Soluble Lead Salts: An Evaluation of the Solubility in Water and Aqueous Electrolyte Solution" (PDF). J. Phys. Chem. Ref. Data (NIST data review). 9 (3): 751–784. Bibcode:1980JPCRD...9..751C. doi:10.1063/1.555628. Archived from the original (PDF) on 2014-02-11. Retrieved 2017-07-13.
  3. ↑ Haynes (2016), p. 5.171.
  4. 1 2 3 4 Patnaik, P. (2002). Handbook of Inorganic Chemicals. McGraw-Hill. ISBN   978-0070494398.
  5. ↑ West, Philip W.; Carlton, Jack K. (1952). "The extraction of lead iodide by methyl iso-propyl ketone". Analytica Chimica Acta. 6: 406–411. doi:10.1016/S0003-2670(00)86967-6.
  6. ↑ Ahuja, R.; Arwin, H.; Ferreira Da Silva, A.; Persson, C.; Osorio-Guillén, J. M.; Souza De Almeida, J.; Moyses Araujo, C.; Veje, E.; Veissid, N.; An, C. Y.; Pepe, I.; Johansson, B. (2002). "Electronic and optical properties of lead iodide". Journal of Applied Physics. 92 (12): 7219–7224. Bibcode:2002JAP....92.7219A. doi:10.1063/1.1523145. hdl: 10495/11556 . S2CID   29398039.
  7. ↑ Zhong, Mianzeng; Zhang, Shuai; Huang, Le; You, Jingbi; Wei, Zhongming; Liu, Xinfeng; Li, Jingbo (2017). "Large-scale 2D PbI2 monolayers: experimental realization and their indirect band-gap related properties". Nanoscale. 9 (11): 3736–3741. doi:10.1039/c6nr07924e. PMID   28102404.
  8. ↑ Haynes (2016), p. 4.128.
  9. 1 2 Brixner, L.H.; Chen, H.-Y.; Foris, C.M. (1981). "X-ray study of the PbCl2−xIx and PbBr2−xIx systems". Journal of Solid State Chemistry. 40 (3): 336–343. Bibcode:1981JSSCh..40..336B. doi:10.1016/0022-4596(81)90400-X.
  10. ↑ Haynes (2016), p. 5.24.
  11. ↑ "Sigma-Aldrich catalog: Lead(II) iodide 99%". www.sigmaaldrich.com. Retrieved 2016-04-29.
  12. 1 2 3 Dhiaputra, I.; Permana, B.; Maulana, Y.; Dwi Inayatie, Y.; Purba, Y. R.; Bahtiar, A. (2016). Composition and crystal structure of perovskite films attained from electrodes of used car battery. The 2nd Padjadjaran International Physics Symposium 2015 (PIPS-2015). Vol. 1712. Jatinangor, Indonesia. doi: 10.1063/1.4941896 .
  13. 1 2 3 Shah, K. S.; Olschner, F.; Moy, L. P.; Bennett, P.; Misra, M.; Zhang, J.; Squillante, M. R.; Lund, J. C. (1996). "Lead iodide x-ray detection systems". Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment. Proceedings of the 9th International Workshop on Room Temperature Semiconductor X- and γ-Ray Detectors, Associated Electronics and Applications. 380 (1–2): 266–270. Bibcode:1996NIMPA.380..266S. doi:10.1016/S0168-9002(96)00346-4.
  14. ↑ Anthony, Seth (2014). I. Cognitive and instructional factors relating to students' development of personal models of chemical systems in the general chemistry laboratory. [...] (Thesis). Colorado State University. hdl:10217/82503.
  15. ↑ US 3764368,Jacobs, J.&Corrigan, R.,"Lead iodide film",published 9 October 1973
  16. 1 2 3 Eastaugh, N.; Walsh, V.; Chaplin, T.; Siddall, R. (2004). The Pigment Compendium: a Dictionary of Historical Pigments. Butterworth-Heinemann. ISBN   978-0750657495.
  17. ↑ Ahmad, S.; Prakash, G. V. (2012). "Fabrication of excitonic luminescent inorganic‑organic hybrid nano and microcrystals". International Conference on Fibre Optics and Photonics. OSA: MPo.40. doi:10.1364/photonics.2012.mpo.40.
  18. 1 2 Matuchova, M.; Zdansky, K.; Zavadil, J.; Danilewsky, A.; Riesz, F.; Hassan, M.A.S.; Alexiew, D.; Kral, R. (2009). "Study of the influence of the rare-earth elements on the properties of lead iodide". Journal of Crystal Growth. 311 (14): 3557–3562. Bibcode:2009JCrGr.311.3557M. doi:10.1016/j.jcrysgro.2009.04.043.
  19. ↑ Chaudhuri, T.K.; Acharya, H.N. (1982). "Preparation of lead iodide films by iodination of chemically deposited lead sulphide films". Materials Research Bulletin. 17 (3): 279–286. doi:10.1016/0025-5408(82)90074-5.
  20. ↑ Fleming, Declan (6 January 2015). "Golden rain". Education in Chemistry . 52 (1): 10.
  21. ↑ Zhu, Xinghua; Wangyang, Peihua; Sun, Hui; Yang, Dingyu; Gao, Xiuying; Tian, Haibo (2016). "Facile growth and characterization of freestanding single crystal PbI2 film". Materials Letters. 180: 59–62. doi:10.1016/j.matlet.2016.05.101.
  22. ↑ Fernelius, W. Conard; Detling, Kenneth D. (1934). "Preparation of crystals of sparingly soluble salts". Journal of Chemical Education. 11 (3): 176. Bibcode:1934JChEd..11..176F. doi:10.1021/ed011p176..
  23. ↑ Patel, A.R.; Rao, A. Venkateswara (1980). "An improved design to grow larger and more perfect single crystals in gels". Journal of Crystal Growth. 49 (3): 589–590. Bibcode:1980JCrGr..49..589P. doi:10.1016/0022-0248(80)90134-7.
  24. ↑ Scaife, C. W. J.; Cavoli, S. R.; Blanton, T. N.; Morse, M. D.; Sever, B. R.; Willis, W. S.; Suib, S. L. (1990). "Synthesis and characterization of lead(II) iodide grown in space". Chemistry of Materials. 2 (6): 777–780. doi:10.1021/cm00012a034.
  25. 1 2 3 Fornaro, L.; Saucedo, E.; Mussio, L.; Yerman, L.; Ma, X.; Burger, A. (2001). "Lead iodide film deposition and characterization". Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment. 458 (1–2): 406–412. Bibcode:2001NIMPA.458..406F. doi:10.1016/S0168-9002(00)00933-5.
  26. ↑ Liu, X.; Ha, S. T.; Zhang, Qing; de la Mata, M.; Magen, C.; Arbiol, J.; Sum, T. C.; Xiong, Q. (2015). "Whispering Gallery Mode Lasing from Hexagonal Shaped Layered Lead Iodide Crystals". ACS Nano. 9 (1): 687–695. doi:10.1021/nn5061207. hdl: 10220/38493 . PMID   25562110.
  27. ↑ Tonn, J.; Matuchova, M.; Danilewsky, A. N.; Cröll, A. (2015). "Removal of oxidic impurities for the growth of high purity lead iodide single crystals". Journal of Crystal Growth. 416: 82–89. Bibcode:2015JCrGr.416...82T. doi:10.1016/j.jcrysgro.2015.01.024.
  28. ↑ Forty, A. J. (August 1960). "Observations of the decomposition of crystals of lead iodide in the electron microscope". Philosophical Magazine. 5 (56): 787–797. Bibcode:1960PMag....5..787F. doi:10.1080/14786436008241217.
  29. ↑ Popov, Georgi; Mattinen, Miika; Hatanpää, Timo; Vehkamäki, Marko; Kemell, Marianna; Mizohata, Kenichiro; Räisänen, Jyrki; Ritala, Mikko; Leskelä, Markku (2019-02-12). "Atomic Layer Deposition of PbI2 Thin Films". Chemistry of Materials. 31 (3): 1101–1109. doi: 10.1021/acs.chemmater.8b04969 .
  30. ↑ Flora, G.; Gupta, D.; Tiwari, A. (2012). "Toxicity of lead: a review with recent updates". Interdisciplinary Toxicology. 5 (2): 47–58. doi:10.2478/v10102-012-0009-2. PMC   3485653 . PMID   23118587.
  31. ↑ "Haz-Map Category Details". hazmap.nlm.nih.gov. Retrieved 2016-04-29.
  32. ↑ Sears, W. M.; Klein, M. L.; Morrison, J. A. (1979). "Polytypism and the vibrational properties of I2". Physical Review B. 19 (4): 2305–2313. Bibcode:1979PhRvB..19.2305S. doi:10.1103/PhysRevB.19.2305. hdl: 11375/12129 .

Cited sources

This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.