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| {{Atomic radius}}
| | I'm a 40 years old and work at the high school ([http://www.ehow.com/search.html?s=Integrated+International Integrated International] Studies).<br>In my free time I'm trying to teach myself Arabic. I have been there and look forward to go there anytime soon. I like to read, preferably on my kindle. I really love to watch Modern Family and Sons of Anarchy as well as documentaries about anything [http://Www.Thefreedictionary.com/scientific scientific]. I love Computer programming.<br><br>My blog post; FIFA coin generator ([http://Www.glucosoralfsc.com/component/k2/item/7-18-puntos/7-18-puntos?limitstart=0%FFlesbian+cams%FFexternal+nofollow%FFWholesale+Forum%FFexternal+nofollow%FFfacebook+campaign+landing%FF%FFThe+Sims+4 Get the facts]) |
| '''Ionic radius''', ''r''<sub>ion</sub>, is the radius of an atom's [[ion]]. Although neither atoms nor ions have sharp boundaries, they are sometimes treated as if they were hard spheres with radii such that the sum of ionic radii of the cation and anion gives the distance between the ions in a [[crystal lattice]]. Ionic radii are typically given in units of either [[picometer]]s (pm) or [[Angstrom (unit)|Angstroms]] (Å), with 1 Å = 100 pm. Typical values range from 30 pm (0.3 Å) to over 200 pm (2 Å). | |
| | |
| == Trends in ionic radii ==
| |
| {| class="wikitable" width=290px style="float:right;margin-left:0.5em;"
| |
| |-
| |
| ! align=left|X<sup>−</sup>
| |
| ! NaX
| |
| ! [[silver halide|AgX]]
| |
| |-
| |
| | F
| |
| | 464
| |
| | 492
| |
| |-
| |
| | Cl
| |
| | 564
| |
| | 555
| |
| |-
| |
| | Br
| |
| | 598
| |
| | 577
| |
| |-
| |
| | colspan=3 |<small>Unit cell parameters (in [[picometre|pm]], equal to two M–X bond lengths) for sodium and silver halides. All compounds crystallize in the [[Cubic crystal system#Rock-salt structure|NaCl structure]].</small>
| |
| |}
| |
| [[File:Atomic & ionic radii.svg|thumb|right|300 px|Relative sizes of atoms and ions. The neutral atoms are colored gray, cations <span style="color:red">red</span>, and anions <span style="color:blue">blue</span>.]]
| |
| Ions may be larger or smaller than the neutral atom, depending on the ion's charge. When an atom loses an electron to form a cation, the lost electron no longer contributes to [[Shielding effect|shielding]] the other electrons from the charge of the nucleus; consequently, the other electrons are more strongly attracted to the nucleus, and the radius of the atom gets smaller. Similarly, when an electron is added to an atom, forming an anion, the added electron shields the other electrons from the nucleus, with the result that the size of the atom increases.
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| | |
| The ionic radius is not a fixed property of a given ion, but varies with [[coordination number]], [[spin states (d electrons)|spin state]] and other parameters. Nevertheless, ionic radius values are sufficiently [[Transferability|transferable]] to allow [[Period (periodic table)|periodic trends]] to be recognized. As with other types of [[atomic radius]], ionic radii increase on descending a [[Periodic table group|group]]. Ionic size (for the same ion) also increases with increasing coordination number, and an ion in a [[spin states (d electrons)|high-spin]] state will be larger than the same ion in a [[low-spin]] state. In general, ionic radius decreases with increasing positive charge and increases with increasing negative charge.
| |
| | |
| An "anomalous" ionic radius in a crystal is often a sign of significant [[Covalent bond|covalent]] character in the bonding. No bond is ''completely'' ionic, and some supposedly "ionic" compounds, especially of the [[transition metal]]s, are particularly covalent in character. This is illustrated by the [[unit cell]] parameters for [[sodium]] and [[silver halide]]s in the table. On the basis of the fluorides, one would say that Ag<sup>+</sup> is larger than Na<sup>+</sup>, but on the basis of the [[chloride]]s and [[bromide]]s the opposite appears to be true.<ref>On the basis of conventional ionic radii, Ag<sup>+</sup> (129 pm) is indeed larger than Na<sup>+</sup> (116 pm)</ref> This is because the greater covalent character of the bonds in AgCl and AgBr reduces the bond length and hence the apparent ionic radius of Ag<sup>+</sup>, an effect which is not present in the halides of the more [[electronegativity|electropositive]] sodium, nor in [[silver fluoride]] in which the fluoride ion is relatively [[Polarizability|unpolarizable]].
| |
| | |
| == Determination of ionic radii ==
| |
| The distance between two ions in an ionic crystal can be determined by [[X-ray crystallography]], which gives the lengths of the sides of the [[unit cell]] of a crystal. For example, the length of each edge of the unit cell of [[sodium chloride]] is found to be 564.02 pm. Each edge of the unit cell of sodium chloride may be considered to have the atoms arranged as Na<sup>+</sup>∙∙∙Cl<sup>−</sup>∙∙∙Na<sup>+</sup>, so the edge is twice the Na-Cl separation. Therefore, the distance between the Na<sup>+</sup> and Cl<sup>−</sup> ions is half of 564.02 pm, which is 282.01 pm. However, although X-ray crystallography gives the distance between ions, it doesn't indicate where the boundary is between those ions, so it doesn't directly give ionic radii.
| |
| | |
| [[File:LiI unit cell, front.png|thumb|Front view of the unit cell of a LiI crystal, using Shannon's crystal data (Li<sup>+</sup> = 90 pm; I<sup>−</sup> = 206 pm). The iodide ions nearly touch (but don't quite), indicating that Landé's assumption is fairly good.]]
| |
| [[Alfred Landé|Landé]]<ref>{{cite journal|last=Landé|first=A.|title=Über die Größe der Atome|journal=Zeitschrift für Physik|year=1920|volume=1|issue=3|pages=191–197|doi=10.1007/BF01329165|url=http://springerlink.com/content/j862631p43032333/|accessdate=1 June 2011|bibcode = 1920ZPhy....1..191L }}</ref> estimated ionic radii by considering crystals in which the anion and cation have a large difference in size, such as LiI. The lithium ions are so much smaller than the iodide ions that the lithium fits into holes within the crystal lattice, allowing the iodide ions to touch. That is, the distance between two neighboring iodides in the crystal is assumed to be twice the radius of the iodide ion, which was deduced to be 214 pm. This value can be used to determine other radii. For example, the inter-ionic distance in RbI is 356 pm, giving 142 pm for the ionic radius of Rb<sup>+</sup>. In this way values for the radii of 8 ions were determined.
| |
| | |
| Wasastjerna estimated ionic radii by considering the relative volumes of ions as determined from electrical polarizability as determined by measurements of refractive index.<ref>{{cite journal|last=Wasastjerna|first=J. A.|title=On the radii of ions|journal=Comm. Phys.-Math., Soc. Sci. Fenn.|year=1923|volume=1|issue=38|pages=1–25}}</ref> These results were extended by [[Victor Goldschmidt]].<ref>{{cite book|last=Goldschmidt|first=V. M.|title=Geochemische Verteilungsgesetze der Elemente|year=1926|publisher=Skrifter Norske Videnskaps—Akad. Oslo, (I) Mat. Natur.}} This is an 8 volume set of books by Goldschmidt.</ref> Both Wasastjerna and Goldschmidt used a value of 132 pm for the O<sup>2−</sup> ion.
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| | |
| Pauling used [[effective nuclear charge]] to proportion the distance between ions into anionic and a cationic radii.<ref name="NOTCB">[[Linus Pauling|Pauling, L.]] (1960). ''The Nature of the Chemical Bond'' (3rd Edn.). [[Ithaca, NY]]: Cornell University Press.</ref> His data gives the O<sup>2−</sup> ion a radius of 140 pm.
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| | |
| A major review of crystallographic data led to the publication of revised ionic radii by Shannon.<ref name="Shannon">{{cite journal|doi=10.1107/S0567739476001551|title=Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides|author=R. D. Shannon|journal=Acta Cryst|volume=A32|year=1976|pages=751–767|bibcode = 1976AcCrA..32..751S }}</ref> Shannon gives different radii for different coordination numbers, and for high and low spin states of the ions. To be consistent with Pauling's radii, Shannon has used a value of ''r''<sub>ion</sub>(O<sup>2−</sup>) = 140 pm; data using that value are referred to as "effective" ionic radii. However, Shannon also includes data based on ''r''<sub>ion</sub>(O<sup>2−</sup>) = 126 pm; data using that value are referred to as "Crystal" ionic radii. Shannon states that "it is felt that crystal radii correspond more closely to the physical size of ions in a solid."<ref name=Shannon /> The two sets of data are listed in the two tables below.
| |
| | |
| {|class="wikitable sortable" cellpadding="1"
| |
| |+<u>''Crystal''</u> ionic radii in [[picometer|pm]] of elements in function of ionic charge and spin (''ls'' = low spin, ''hs''= high spin). <br /> Ions are 6-coordinate unless indicated differently in parentheses (e.g. '''146 (4)''' for 4-coordinate N<sup>3–</sup>).<ref name = "Shannon"/>
| |
| |-
| |
| !Number
| |
| !Name
| |
| !Symbol
| |
| !'''3–'''
| |
| !'''2–'''
| |
| !'''1–'''
| |
| !'''1+'''
| |
| !'''2+'''
| |
| !'''3+'''
| |
| !'''4+'''
| |
| !'''5+'''
| |
| !'''6+'''
| |
| !'''7+'''
| |
| !'''8+'''
| |
| |-
| |
| |3
| |
| |[[Lithium]]
| |
| |Li
| |
| | || || ||90|| || || || || || ||
| |
| |-
| |
| |4
| |
| |[[Beryllium]]
| |
| |Be
| |
| |||||||||59||||||||||||
| |
| |-
| |
| |5
| |
| |[[Boron]]
| |
| |B
| |
| |||||||||||41||||||||||
| |
| |-
| |
| |6
| |
| |[[Carbon]]
| |
| |C
| |
| ||||||||||||||30||||||||
| |
| |-
| |
| |7
| |
| |[[Nitrogen]]
| |
| |N
| |
| ||132 (4)||||||||||30||||27||||||
| |
| |-
| |
| |8
| |
| |[[Oxygen]]
| |
| |O
| |
| |||126||||||||||||||||||
| |
| |-
| |
| |9
| |
| |[[Fluorine]]
| |
| |F
| |
| |||||119|||||||||||||||22||
| |
| |-
| |
| |11
| |
| |[[Sodium]]
| |
| |Na
| |
| | || || ||116|| || || || || || ||
| |
| |-
| |
| |12
| |
| |[[Magnesium]]
| |
| |Mg
| |
| | || || || ||86|| || || || || ||
| |
| |-
| |
| |13
| |
| |[[Aluminum]]
| |
| |Al
| |
| ||||||||||||67.5|||||||||||
| |
| |-
| |
| |14
| |
| |[[Silicon]]
| |
| |Si
| |
| ||||||||||||||54|||||||||
| |
| |-
| |
| |15
| |
| |[[Phosphorus]]
| |
| |P
| |
| ||||||||||||58 <!-- As per Shannon's paper, it's the +3 form not the phosphide anion. -->||||52|||||||
| |
| |-
| |
| | 16
| |
| |[[Sulfur]]
| |
| |S
| |
| |||170|||||||||||51||||43|||||
| |
| |-
| |
| | 17
| |
| |[[Chlorine]]
| |
| |Cl
| |
| |||||167|||||||||||26 (3py)|||||41||
| |
| |-
| |
| | 19
| |
| |[[Potassium]]
| |
| |K
| |
| |||||||152|||||||||||||||
| |
| |-
| |
| | 20
| |
| |[[Calcium]]
| |
| |Ca
| |
| |||||||||114|||||||||||||
| |
| |-
| |
| | 21
| |
| |[[Scandium]]
| |
| |Sc
| |
| |||||||||||88.5|||||||||||
| |
| |-
| |
| | 22
| |
| |[[Titanium]]
| |
| |Ti
| |
| |||||||||100||81||74.5|||||||||
| |
| |-
| |
| | 23
| |
| |[[Vanadium]]
| |
| |V
| |
| |||||||||93||78||72||68|||||||
| |
| |-
| |
| | 24
| |
| |[[Chromium]] ls
| |
| |Cr
| |
| |||||||||87||75.5||69||63||58|||||
| |
| |-
| |
| | 24
| |
| |[[Chromium]] hs
| |
| |Cr
| |
| |||||||||94|||||||||||||
| |
| |-
| |
| | 25
| |
| |[[Manganese]] ls
| |
| |Mn
| |
| |||||||||81||72||67||47 (4)||39.5 (4)||60||
| |
| |-
| |
| | 25
| |
| |[[Manganese]] hs
| |
| |Mn
| |
| |||||||||97||78.5||||||||||
| |
| |-
| |
| | 26
| |
| |[[Iron]] ls
| |
| |Fe
| |
| |||||||||75||69||72.5||||39 (4)||||
| |
| |-
| |
| | 26
| |
| |[[Iron]] hs
| |
| |Fe
| |
| |||||||||92||78.5||||||||||
| |
| |-
| |
| | 27
| |
| |[[Cobalt]] ls
| |
| |Co
| |
| |||||||||79||68.5||||||||||
| |
| |-
| |
| | 27
| |
| |[[Cobalt]] hs
| |
| |Co
| |
| |||||||||88.5||75||67||||||||
| |
| |-
| |
| | 28
| |
| |[[Nickel]] ls
| |
| |Ni
| |
| |||||||||83||70||62 ''ls''||||||||
| |
| |-
| |
| | 28
| |
| |[[Nickel]] hs
| |
| |Ni
| |
| |||||||||||74||||||||||
| |
| |-
| |
| | 29
| |
| |[[Copper]]
| |
| |Cu
| |
| |||||||91||87||68 ''ls''||||||||||
| |
| |-
| |
| | 30
| |
| |[[Zinc]]
| |
| |Zn
| |
| |||||||||88|||||||||||||
| |
| |-
| |
| | 31
| |
| |[[Gallium]]
| |
| |Ga
| |
| |||||||||||76|||||||||||
| |
| |-
| |
| | 32
| |
| |[[Germanium]]
| |
| |Ge
| |
| |||||||||87||||67|||||||||
| |
| |-
| |
| | 33
| |
| |[[Arsenic]]
| |
| |As
| |
| |||||||||||72||||60|||||||
| |
| |-
| |
| |34
| |
| |[[Selenium]]
| |
| |Se
| |
| |||184|||||||||||64||||56||||
| |
| |-
| |
| | 35
| |
| |[[Bromine]]
| |
| |Br
| |
| |||||182|||||||73 (4sq)||||45 (3py)||||53||
| |
| |-
| |
| | 37
| |
| |[[Rubidium]]
| |
| |Rb
| |
| |||||||166|||||||||||||||
| |
| |-
| |
| | 38
| |
| |[[Strontium]]
| |
| |Sr
| |
| |||||||||132|||||||||||||
| |
| |-
| |
| | 39
| |
| |[[Yttrium]]
| |
| |Y
| |
| |||||||||||104|||||||||||
| |
| |-
| |
| | 40
| |
| |[[Zirconium]]
| |
| |Zr
| |
| |||||||||||||86|||||||||
| |
| |-
| |
| | 41
| |
| |[[Niobium]]
| |
| |Nb
| |
| |||||||||||86||82||78|||||||
| |
| |-
| |
| | 42
| |
| |[[Molybdenum]]
| |
| |Mo
| |
| |||||||||||83||79||75||73|||||
| |
| |-
| |
| | 43
| |
| |[[Technetium]]
| |
| |Tc
| |
| |||||||||||||78.5||74||||70|||
| |
| |-
| |
| | 44
| |
| |[[Ruthenium]]
| |
| |Ru
| |
| |||||||||||82||76||70.5||||52 (4)||50 (4)
| |
| |-
| |
| |45
| |
| |[[Rhodium]]
| |
| | Rh
| |
| |||||||||||80.5||74||69||||||
| |
| |-
| |
| | 46
| |
| | [[Palladium]]
| |
| | Pd
| |
| |||||||73 (2)||100||90||75.5||||||||
| |
| |-
| |
| | 47
| |
| | [[Silver]]
| |
| | Ag
| |
| |||||||129||108||89||||||||||
| |
| |-
| |
| | 48
| |
| | [[Cadmium]]
| |
| | Cd
| |
| ||||||||||109||||||||||||
| |
| |-
| |
| | 49
| |
| | [[Indium]]
| |
| | In
| |
| ||||||||||||94||||||||||
| |
| |-
| |
| | 50
| |
| | [[Tin]]
| |
| | Sn
| |
| ||||||||||||||83||||||||
| |
| |-
| |
| | 51
| |
| | [[Antimony]]
| |
| | Sb
| |
| ||||||||||||90||||74||||||
| |
| |-
| |
| | 52
| |
| | [[Tellurium]]
| |
| | Te
| |
| |||207|||||||||||111||||70||||
| |
| |-
| |
| | 53
| |
| | [[Iodine]]
| |
| | I
| |
| |||||206|||||||||||109||||67||
| |
| |-
| |
| | 54
| |
| | [[Xenon]]
| |
| | Xe
| |
| ||||||||||||||||||||||62
| |
| |-
| |
| | 55
| |
| | [[Caesium]]
| |
| | Cs
| |
| |||||||181|||||||||||||||
| |
| |-
| |
| | 56
| |
| | [[Barium]]
| |
| | Ba
| |
| |||||||||149|||||||||||||
| |
| |-
| |
| | 57
| |
| | [[Lanthanum]]
| |
| | La
| |
| |||||||||||117.2|||||||||||
| |
| |-
| |
| | 58
| |
| | [[Cerium]]
| |
| | Ce
| |
| |||||||||||115||101|||||||||
| |
| |-
| |
| | 59
| |
| | [[Praseodymium]]
| |
| | Pr
| |
| |||||||||||113||99|||||||||
| |
| |-
| |
| | 60
| |
| | [[Neodymium]]
| |
| | Nd
| |
| |||||||||143 (8)||112.3|||||||||||
| |
| |-
| |
| | 61
| |
| | [[Promethium]]
| |
| | Pm
| |
| |||||||||||111|||||||||||
| |
| |-
| |
| | 62
| |
| | [[Samarium]]
| |
| | Sm
| |
| |||||||||136 (7)||109.8|||||||||||
| |
| |-
| |
| | 63
| |
| | [[Europium]]
| |
| | Eu
| |
| |||||||||131||108.7|||||||||||
| |
| |-
| |
| | 64
| |
| | [[Gadolinium]]
| |
| | Gd
| |
| |||||||||||107.8|||||||||||
| |
| |-
| |
| | 65
| |
| | [[Terbium]]
| |
| | Tb
| |
| |||||||||||106.3||90|||||||||
| |
| |-
| |
| | 66
| |
| | [[Dysprosium]]
| |
| | Dy
| |
| |||||||||121||105.2|||||||||||
| |
| |-
| |
| | 67
| |
| | [[Holmium]]
| |
| | Ho
| |
| |||||||||||104.1|||||||||||
| |
| |-
| |
| | 68
| |
| | [[Erbium]]
| |
| | Er
| |
| |||||||||||103|||||||||||
| |
| |-
| |
| | 69
| |
| | [[Thulium]]
| |
| | Tm
| |
| |||||||||117||102|||||||||||
| |
| |-
| |
| | 70
| |
| | [[Ytterbium]]
| |
| | Yb
| |
| |||||||||116||100.8|||||||||||
| |
| |-
| |
| | 71
| |
| | [[Lutetium]]
| |
| | Lu
| |
| |||||||||||100.1|||||||||||
| |
| |-
| |
| | 72
| |
| | [[Hafnium]]
| |
| | Hf
| |
| |||||||||||||85|||||||||
| |
| |-
| |
| | 73
| |
| | [[Tantalum]]
| |
| | Ta
| |
| |||||||||||86||82||78|||||||
| |
| |-
| |
| | 74
| |
| | [[Tungsten]]
| |
| | W
| |
| |||||||||||||80||76||74|||||
| |
| |-
| |
| | 75
| |
| | [[Rhenium]]
| |
| | Re
| |
| |||||||||||||77||72||69||67|||
| |
| |-
| |
| | 76
| |
| | [[Osmium]]
| |
| |Os
| |
| |||||||||||||77||71.5||68.5||66.5||53 (4)
| |
| |-
| |
| | 77
| |
| | [[Iridium]]
| |
| | Ir
| |
| |||||||||||82||76.5||71|||||||
| |
| |-
| |
| | 78
| |
| | [[Platinum]]
| |
| | Pt
| |
| |||||||||94||||76.5||71|||||||
| |
| |-
| |
| | 79
| |
| | [[Gold]]
| |
| | Au
| |
| |||||||151||||99||||71|||||||
| |
| |-
| |
| | 80
| |
| | [[Mercury (element)|Mercury]]
| |
| | Hg
| |
| |||||||133||116|||||||||||||
| |
| |-
| |
| | 81
| |
| | [[Thallium]]
| |
| | Tl
| |
| |||||||164||||102.5|||||||||||
| |
| |-
| |
| | 82
| |
| | [[Lead]]
| |
| | Pb
| |
| |||||||||133||||91.5|||||||||
| |
| |-
| |
| | 83
| |
| | [[Bismuth]]
| |
| | Bi
| |
| |||||||||||117||||90|||||||
| |
| |-
| |
| | 84
| |
| | [[Polonium]]
| |
| | Po
| |
| |||||||||||||108||||81|||||
| |
| |-
| |
| | 85
| |
| | [[Astatine]]
| |
| | At
| |
| |||||||||||||||||||76|||
| |
| |-
| |
| | 87
| |
| | [[Francium]]
| |
| | Fr
| |
| |||||||194|||||||||||||||
| |
| |-
| |
| | 88
| |
| | [[Radium]]
| |
| | Ra
| |
| |||||||||162 (8)|||||||||||||
| |
| |-
| |
| | 89
| |
| |[[Actinium]]
| |
| | Ac
| |
| |||||||||||126|||||||||||
| |
| |-
| |
| | 90
| |
| | [[Thorium]]
| |
| | Th
| |
| |||||||||||||108|||||||||
| |
| |-
| |
| | 91
| |
| | [[Protactinium]]
| |
| | Pa
| |
| |||||||||||116||104||92|||||||
| |
| |-
| |
| | 92
| |
| | [[Uranium]]
| |
| | U
| |
| |||||||||||116.5||103||90||87|||||
| |
| |-
| |
| | 93
| |
| | [[Neptunium]]
| |
| | Np
| |
| |||||||||124||115||101||89||86||85|||
| |
| |-
| |
| | 94
| |
| | [[Plutonium]]
| |
| | Pu
| |
| |||||||||||114||100||88||85|||||
| |
| |-
| |
| | 95
| |
| | [[Americium]]
| |
| | Am
| |
| |||||||||140 (8)||111.5||99|||||||||
| |
| |-
| |
| | 96
| |
| | [[Curium]]
| |
| | Cm
| |
| |||||||||||111||99|||||||||
| |
| |-
| |
| | 97
| |
| | [[Berkelium]]
| |
| | Bk
| |
| |||||||||||110||97|||||||||
| |
| |-
| |
| | 98
| |
| | [[Californium]]
| |
| | Cf
| |
| |||||||||||109||96.1|||||||||
| |
| |-
| |
| | 99
| |
| | [[Einsteinium]]
| |
| | Es
| |
| |||||||||||92.8<ref name="Identification">R. G. Haire, R. D. Baybarz: "Identification and Analysis of Einsteinium Sesquioxide by Electron Diffraction", in: ''[[Journal of Inorganic and Nuclear Chemistry]]'', '''1973''', ''35'' (2), S. 489–496; {{DOI|10.1016/0022-1902(73)80561-5}}.</ref>|||||||||||
| |
| |}
| |
| | |
| {|class="wikitable sortable" cellpadding="1"
| |
| |+<u>''Effective''</u> ionic radii in [[picometer|pm]] of elements in function of ionic charge and spin (''ls'' = low spin, ''hs''= high spin). <br /> Ions are 6-coordinate unless indicated differently in parentheses (e.g. '''146 (4)''' for 4-coordinate N<sup>3–</sup>).<ref name = "Shannon"/>
| |
| |-
| |
| !Number
| |
| !Name
| |
| !Symbol
| |
| !'''3–'''
| |
| !'''2–'''
| |
| !'''1–'''
| |
| !'''1+'''
| |
| !'''2+'''
| |
| !'''3+'''
| |
| !'''4+'''
| |
| !'''5+'''
| |
| !'''6+'''
| |
| !'''7+'''
| |
| !'''8+'''
| |
| |-
| |
| |3
| |
| |[[Lithium]]
| |
| |Li
| |
| |||||||76||||||||||||||
| |
| |-
| |
| |4
| |
| |[[Beryllium]]
| |
| |Be
| |
| |||||||||45||||||||||||
| |
| |-
| |
| |5
| |
| |[[Boron]]
| |
| |B
| |
| |||||||||||27||||||||||
| |
| |-
| |
| |6
| |
| |[[Carbon]]
| |
| |C
| |
| |
| |
| ||||||||||||16||||||||
| |
| |-
| |
| |7
| |
| |[[Nitrogen]]
| |
| |N
| |
| ||146 (4)||||||||||16||||13||||||
| |
| |-
| |
| |8
| |
| |[[Oxygen]]
| |
| |O
| |
| |||140||||||||||||||||||
| |
| |-
| |
| |9
| |
| |[[Fluorine]]
| |
| |F
| |
| |||||133|||||||||||||||8||
| |
| |-
| |
| |11
| |
| |[[Sodium]]
| |
| |Na
| |
| ||||||||102|||||||||||||||
| |
| |-
| |
| |12
| |
| |[[Magnesium]]
| |
| |Mg
| |
| ||||||||||72|||||||||||||
| |
| |-
| |
| |13
| |
| |[[Aluminum]]
| |
| |Al
| |
| ||||||||||||53.5|||||||||||
| |
| |-
| |
| |14
| |
| |[[Silicon]]
| |
| |Si
| |
| ||||||||||||||40|||||||||
| |
| |-
| |
| |15
| |
| |[[Phosphorus]]
| |
| |P
| |
| ||||||||||||44 <!-- As per Shannon's paper, it's the +3 form not the phosphide anion. -->||||38|||||||
| |
| |-
| |
| | 16
| |
| |[[Sulfur]]
| |
| |S
| |
| |||184|||||||||||37||||29|||||
| |
| |-
| |
| | 17
| |
| |[[Chlorine]]
| |
| |Cl
| |
| |||||181|||||||||||12 (3py)|||||27||
| |
| |-
| |
| | 19
| |
| |[[Potassium]]
| |
| |K
| |
| |||||||138|||||||||||||||
| |
| |-
| |
| | 20
| |
| |[[Calcium]]
| |
| |Ca
| |
| |||||||||100|||||||||||||
| |
| |-
| |
| | 21
| |
| |[[Scandium]]
| |
| |Sc
| |
| |||||||||||74.5|||||||||||
| |
| |-
| |
| | 22
| |
| |[[Titanium]]
| |
| |Ti
| |
| |||||||||86||67||60.5|||||||||
| |
| |-
| |
| | 23
| |
| |[[Vanadium]]
| |
| |V
| |
| |||||||||79||64||58||54|||||||
| |
| |-
| |
| | 24
| |
| |[[Chromium]] ls
| |
| |Cr
| |
| |||||||||73||61.5||55||49||44|||||
| |
| |-
| |
| | 24
| |
| |[[Chromium]] hs
| |
| |Cr
| |
| |||||||||80|||||||||||||
| |
| |-
| |
| | 25
| |
| |[[Manganese]] ls
| |
| |Mn
| |
| |||||||||67||58||53||33 (4)||25.5 (4)||46||
| |
| |-
| |
| | 25
| |
| |[[Manganese]] hs
| |
| |Mn
| |
| |||||||||83||64.5||||||||||
| |
| |-
| |
| | 26
| |
| |[[Iron]] ls
| |
| |Fe
| |
| |||||||||61||55||58.5||||25 (4)||||
| |
| |-
| |
| | 26
| |
| |[[Iron]] hs
| |
| |Fe
| |
| |||||||||78||64.5||||||||||
| |
| |-
| |
| | 27
| |
| |[[Cobalt]] ls
| |
| |Co
| |
| |||||||||65||54.5||||||||||
| |
| |-
| |
| | 27
| |
| |[[Cobalt]] hs
| |
| |Co
| |
| |||||||||74.5||61||53 ''hs''||||||||
| |
| |-
| |
| | 28
| |
| |[[Nickel]] ls
| |
| |Ni
| |
| |||||||||69||56||48 ''ls''||||||||
| |
| |-
| |
| | 28
| |
| |[[Nickel]] hs
| |
| |Ni
| |
| |||||||||||60||||||||||
| |
| |-
| |
| | 29
| |
| |[[Copper]]
| |
| |Cu
| |
| |||||||77||73||54 ''ls''||||||||||
| |
| |-
| |
| | 30
| |
| |[[Zinc]]
| |
| |Zn
| |
| |||||||||74|||||||||||||
| |
| |-
| |
| | 31
| |
| |[[Gallium]]
| |
| |Ga
| |
| |||||||||||62|||||||||||
| |
| |-
| |
| | 32
| |
| |[[Germanium]]
| |
| |Ge
| |
| |||||||||73||||53|||||||||
| |
| |-
| |
| | 33
| |
| |[[Arsenic]]
| |
| |As
| |
| |||||||||||58||||46|||||||
| |
| |-
| |
| |34
| |
| |[[Selenium]]
| |
| |Se
| |
| |||198|||||||||||50||||42||||
| |
| |-
| |
| | 35
| |
| |[[Bromine]]
| |
| |Br
| |
| |||||196|||||||59 (4sq)||||31 (3py)||||39||
| |
| |-
| |
| | 37
| |
| |[[Rubidium]]
| |
| |Rb
| |
| |||||||152|||||||||||||||
| |
| |-
| |
| | 38
| |
| |[[Strontium]]
| |
| |Sr
| |
| |||||||||118|||||||||||||
| |
| |-
| |
| | 39
| |
| |[[Yttrium]]
| |
| |Y
| |
| |||||||||||90|||||||||||
| |
| |-
| |
| | 40
| |
| |[[Zirconium]]
| |
| |Zr
| |
| |||||||||||||72|||||||||
| |
| |-
| |
| | 41
| |
| |[[Niobium]]
| |
| |Nb
| |
| |||||||||||72||68||64|||||||
| |
| |-
| |
| | 42
| |
| |[[Molybdenum]]
| |
| |Mo
| |
| |||||||||||69||65||61||59|||||
| |
| |-
| |
| | 43
| |
| |[[Technetium]]
| |
| |Tc
| |
| |||||||||||||64.5||60||||56|||
| |
| |-
| |
| | 44
| |
| |[[Ruthenium]]
| |
| |Ru
| |
| |||||||||||68||62||56.5||||38 (4)||36 (4)
| |
| |-
| |
| |45
| |
| |[[Rhodium]]
| |
| | Rh
| |
| |||||||||||66.5||60||55||||||
| |
| |-
| |
| | 46
| |
| | [[Palladium]]
| |
| | Pd
| |
| |||||||59 (2)||86||76||61.5||||||||
| |
| |-
| |
| | 47
| |
| | [[Silver]]
| |
| | Ag
| |
| |||||||115||94||75||||||||||
| |
| |-
| |
| | 48
| |
| | [[Cadmium]]
| |
| | Cd
| |
| ||||||||||95||||||||||||
| |
| |-
| |
| | 49
| |
| | [[Indium]]
| |
| | In
| |
| ||||||||||||80||||||||||
| |
| |-
| |
| | 50
| |
| | [[Tin]]
| |
| | Sn
| |
| ||||||||||||||69||||||||
| |
| |-
| |
| | 51
| |
| | [[Antimony]]
| |
| | Sb
| |
| ||||||||||||76||||60||||||
| |
| |-
| |
| | 52
| |
| | [[Tellurium]]
| |
| | Te
| |
| |||221|||||||||||97||||56||||
| |
| |-
| |
| | 53
| |
| | [[Iodine]]
| |
| | I
| |
| |||||220|||||||||||95||||53||
| |
| |-
| |
| | 54
| |
| | [[Xenon]]
| |
| | Xe
| |
| ||||||||||||||||||||||48
| |
| |-
| |
| | 55
| |
| | [[Caesium]]
| |
| | Cs
| |
| |||||||167|||||||||||||||
| |
| |-
| |
| | 56
| |
| | [[Barium]]
| |
| | Ba
| |
| |||||||||135|||||||||||||
| |
| |-
| |
| | 57
| |
| | [[Lanthanum]]
| |
| | La
| |
| |||||||||||103.2|||||||||||
| |
| |-
| |
| | 58
| |
| | [[Cerium]]
| |
| | Ce
| |
| |||||||||||101||87|||||||||
| |
| |-
| |
| | 59
| |
| | [[Praseodymium]]
| |
| | Pr
| |
| |||||||||||99||85|||||||||
| |
| |-
| |
| | 60
| |
| | [[Neodymium]]
| |
| | Nd
| |
| |||||||||129 (8)||98.3|||||||||||
| |
| |-
| |
| | 61
| |
| | [[Promethium]]
| |
| | Pm
| |
| |||||||||||97|||||||||||
| |
| |-
| |
| | 62
| |
| | [[Samarium]]
| |
| | Sm
| |
| |||||||||122 (8)||95.8|||||||||||
| |
| |-
| |
| | 63
| |
| | [[Europium]]
| |
| | Eu
| |
| |||||||||117||94.7|||||||||||
| |
| |-
| |
| | 64
| |
| | [[Gadolinium]]
| |
| | Gd
| |
| |||||||||||93.5|||||||||||
| |
| |-
| |
| | 65
| |
| | [[Terbium]]
| |
| | Tb
| |
| |||||||||||92.3||76|||||||||
| |
| |-
| |
| | 66
| |
| | [[Dysprosium]]
| |
| | Dy
| |
| |||||||||107||91.2|||||||||||
| |
| |-
| |
| | 67
| |
| | [[Holmium]]
| |
| | Ho
| |
| |||||||||||90.1|||||||||||
| |
| |-
| |
| | 68
| |
| | [[Erbium]]
| |
| | Er
| |
| |||||||||||89|||||||||||
| |
| |-
| |
| | 69
| |
| | [[Thulium]]
| |
| | Tm
| |
| |||||||||103||88|||||||||||
| |
| |-
| |
| | 70
| |
| | [[Ytterbium]]
| |
| | Yb
| |
| |||||||||102||86.8|||||||||||
| |
| |-
| |
| | 71
| |
| | [[Lutetium]]
| |
| | Lu
| |
| |||||||||||86.1|||||||||||
| |
| |-
| |
| | 72
| |
| | [[Hafnium]]
| |
| | Hf
| |
| |||||||||||||71|||||||||
| |
| |-
| |
| | 73
| |
| | [[Tantalum]]
| |
| | Ta
| |
| |||||||||||72||68||64|||||||
| |
| |-
| |
| | 74
| |
| | [[Tungsten]]
| |
| | W
| |
| |||||||||||||66||62||60|||||
| |
| |-
| |
| | 75
| |
| | [[Rhenium]]
| |
| | Re
| |
| |||||||||||||63||58||55||53|||
| |
| |-
| |
| | 76
| |
| | [[Osmium]]
| |
| |Os
| |
| |||||||||||||63||57.5||54.5||52.5||39 (4)
| |
| |-
| |
| | 77
| |
| | [[Iridium]]
| |
| | Ir
| |
| |||||||||||68||62.5||57|||||||
| |
| |-
| |
| | 78
| |
| | [[Platinum]]
| |
| | Pt
| |
| |||||||||80||||62.5||57|||||||
| |
| |-
| |
| | 79
| |
| | [[Gold]]
| |
| | Au
| |
| |||||||137||||85||||57|||||||
| |
| |-
| |
| | 80
| |
| | [[Mercury (element)|Mercury]]
| |
| | Hg
| |
| |||||||119||102|||||||||||||
| |
| |-
| |
| | 81
| |
| | [[Thallium]]
| |
| | Tl
| |
| |||||||150||||88.5|||||||||||
| |
| |-
| |
| | 82
| |
| | [[Lead]]
| |
| | Pb
| |
| |||||||||119||||77.5|||||||||
| |
| |-
| |
| | 83
| |
| | [[Bismuth]]
| |
| | Bi
| |
| |||||||||||103||||76 |||||||
| |
| |-
| |
| | 84
| |
| | [[Polonium]]
| |
| | Po
| |
| |||||||||||||94||||67|||||
| |
| |-
| |
| | 85
| |
| | [[Astatine]]
| |
| | At
| |
| |||||||||||||||||||62|||
| |
| |-
| |
| | 87
| |
| | [[Francium]]
| |
| | Fr
| |
| |||||||180|||||||||||||||
| |
| |-
| |
| | 88
| |
| | [[Radium]]
| |
| | Ra
| |
| |||||||||148 (8)|||||||||||||
| |
| |-
| |
| | 89
| |
| |[[Actinium]]
| |
| | Ac
| |
| |||||||||||112|||||||||||
| |
| |-
| |
| | 90
| |
| | [[Thorium]]
| |
| | Th
| |
| |||||||||||||94|||||||||
| |
| |-
| |
| | 91
| |
| | [[Protactinium]]
| |
| | Pa
| |
| |||||||||||104||90||78|||||||
| |
| |-
| |
| | 92
| |
| | [[Uranium]]
| |
| | U
| |
| |||||||||||102.5||89||76||73|||||
| |
| |-
| |
| | 93
| |
| | [[Neptunium]]
| |
| | Np
| |
| |||||||||110||101||87||75||72||71|||
| |
| |-
| |
| | 94
| |
| | [[Plutonium]]
| |
| | Pu
| |
| |||||||||||100||86||74||71|||||
| |
| |-
| |
| | 95
| |
| | [[Americium]]
| |
| | Am
| |
| |||||||||126 (8)||97.5||85|||||||||
| |
| |-
| |
| | 96
| |
| | [[Curium]]
| |
| | Cm
| |
| |||||||||||97||85|||||||||
| |
| |-
| |
| | 97
| |
| | [[Berkelium]]
| |
| | Bk
| |
| |||||||||||96||83|||||||||
| |
| |-
| |
| | 98
| |
| | [[Californium]]
| |
| | Cf
| |
| |||||||||||95||82.1|||||||||
| |
| |-
| |
| | 99
| |
| | [[Einsteinium]]
| |
| | Es
| |
| |||||||||||83.5<ref name="Identification"/>|||||||||||
| |
| |}
| |
| | |
| ==The Soft-sphere Model==
| |
| {|class="wikitable" cellpadding="1" style="float: right;"
| |
| |+Soft-sphere ionic radii (in pm) of some ions
| |
| |-
| |
| !Cation, ''M''
| |
| !''R''<sub>M</sub>
| |
| !Anion, ''X''
| |
| !''R''<sub>X</sub>
| |
| |-
| |
| ! Li<sup>+</sup>
| |
| | 109.4
| |
| ! Cl<sup>-</sup>
| |
| | 218.1
| |
| |-
| |
| ! Na<sup>+</sup>
| |
| | 149.7
| |
| ! Br<sup>-</sup>
| |
| | 237.2
| |
| |}For many compounds, the model of ions as hard spheres does not reproduce the distance between ions, <math>{d_{mx}}</math>, to the accuracy with which it can be measured in crystals. One approach to improving the calculated accuracy is to model ions as "soft spheres" that overlap in the crystal. Because the ions overlap, their separation in the crystal will be less than the sum of their soft-sphere radii.<ref>{{cite journal|last=Lang|first=Peter F.|coauthors=Smith, Barry C.|title=Ionic radii for Group 1 and Group 2 halide, hydride, fluoride, oxide, sulfide, selenide and telluride crystals|journal=Dalton Transactions|year=2010 |volume=39 |issue=33 |pages=7786–7791|doi = 10.1039/C0DT00401D|pmid=20664858}}</ref>
| |
| The relation between soft-sphere ionic radii, <math>{r_m}</math> and <math>{r_x}</math>, and <math>{d_{mx}}</math>, is given by
| |
| | |
| <math>{d_{mx}}^k = {r_m}^k + {r_x}^k</math>,
| |
| | |
| where <math>k</math> is an exponent that varies with the type of crystal structure. In the hard-sphere model, <math>k</math> would be 1, giving <math>{d_{mx}} = {r_m} + {r_x}</math>. In the soft-sphere model, <math>k</math> has a value between 1 and 2. For example, for crystals of group 1 halides with the [[Cubic crystal system#Rock-salt structure|sodium chloride structure]], a value of 1.6667 gives good agreement with experiment. Some soft-sphere ionic radii are in the table. These radii are larger than the crystal radii given above (Li<sup>+</sup>, 90 pm; Cl<sup>-</sup>, 167 pm).
| |
| {|class="wikitable" cellpadding="1" style="text-align: center; float: right;"
| |
| |+Comparison between observed and calculated ion separations (in pm)
| |
| |-
| |
| ! MX
| |
| ! Observed
| |
| ! Soft-sphere model
| |
| |-
| |
| ! LiCl
| |
| | 257.0
| |
| | 257.2
| |
| |-
| |
| ! LiBr
| |
| | 275.1
| |
| | 274.4
| |
| |-
| |
| ! NaCl
| |
| | 282.0
| |
| | 281.9
| |
| |-
| |
| ! NaBr
| |
| | 298.7
| |
| | 298.2
| |
| |}
| |
| Inter-ionic separations calculated with these radii give remarkably good agreement with experimental values. Some data are given in the table. Curiously, no theoretical justification for the equation containing <math>k</math> has been given.
| |
| | |
| == Non-spherical Ions ==
| |
| The concept of ionic radii is based on the assumption of a spherical ion shape. However, from a [[group theory|group-theoretical]] point of view the assumption is only justified for ions that reside on high-symmetry [[crystal lattice]] sites like Na and Cl in [[halite]] or Zn and S in [[sphalerite]]. A clear distinction can be made, when the [[point symmetry group]] of the respective lattice site is considered,<ref name= Bethe1929>{{cite journal|author = H. Bethe|title = Termaufspaltung in Kristallen|journal = Ann. Physik|volume = 3|issue = 2|pages = 133–208|year = 1929|doi = 10.1002/andp.19293950202|bibcode = 1929AnP...395..133B }}</ref> which are the [[Point_groups_in_three_dimensions#The_seven_remaining_point_groups|cubic groups]] O<sub>h</sub> and T<sub>d</sub> in NaCl and ZnS. For ions on lower-symmetry sites significant deviations of their [[electron density]] from a spherical shape may occur. This holds in particular for ions on lattice sites of polar symmetry, which are the [[crystallographic point groups]] C<sub>1</sub>, C<sub>1h</sub>, C<sub>n</sub> or C<sub>nv</sub>, n = 2, 3, 4 or 6.<ref name= ZPB1995b>{{cite journal|author = M. Birkholz|url=http://www.mariobirkholz.de/ZPB1995b.pdf|title = Crystal-field induced dipoles in heteropolar crystals – II. Physical significance]|journal = Z. Phys. B|volume = 96|pages = 333–340|year = 1995|doi = 10.1007/BF01313055|bibcode = 1995ZPhyB..96..333B }}</ref> A thorough analysis of the bonding geometry was recently carried out for [[pyrite| pyrite-type]] disulfides, where monovalent [[sulfur]] ions reside on C<sub>3</sub> lattice sites. It was found that the sulfur ions have to be modeled by [[thermal ellipsoid]]s with different radii in direction of the symmetry axis and perpendicular to it.<ref name= pssb2008>{{cite journal|author = M. Birkholz, R. Rudert|title = Interatomic distances in pyrite-structure disulfides – a case for ellipsoidal modelling of sulphur ions|url=http://www.mariobirkholz.de/pssb2008.pdf|journal = phys. stat. sol. (b)|volume = 245|pages = 1858–1864|year = 2008|doi = 10.1002/pssb.200879532|bibcode = 2008PSSBR.245.1858B }}</ref> Remarkably, it turned out in this case that it is not the ionic radius, but the ionic volume that remains constant in different crystalline compounds.
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| ==See also==
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| *[[Atomic radii of the elements (data page)|Atomic radii of the elements]]
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| *[[Covalent radius]]
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| *[[Ionic potential]]
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| *[[Ionic radius ratio]]
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| *[[Pauling's rules]]
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| | |
| ==References==
| |
| {{reflist|2}}
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| | |
| [[Category:Properties of chemical elements]]
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