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Revised Effective Ionic Radii and Systematic Study of Inter Atomic Distances
in Halides and Chalcogenides
Article in Acta crystallographica. Section A, Foundations of crystallography · September 1976
DOI: 10.1107/s0567739476001551
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751
Acta Cryst. (1976). A32, 751
Revised Effective Ionic Radii and Systematic Studies of Interatomie Distances
in Halides and Chaleogenides
BY R. D. SHANNON
Central Research and Development Department, Experimental Station, E. L Du Pont de Nemours
and Company, Wilmington, Delaware 19898, U.S.A.
(Received 30 October 1975; accepted 9 March 1976)
The effective ionic radii of Shannon & Prewitt [Acta Cryst. (1969), B25, 925-945] are revised to include
more unusual oxidation states and coordinations. Revisions are based on new structural data, empirical
bond strength-bond length relationships, and plots of (1) radii vs volume, (2) radii vs coordination
number, and (3) radii vs oxidation state. Factors which affect radii additivity are polyhedral distortion,
partial occupancy of cation sites, covalence, and metallic character. Mean NbS+-O and Mo6+-O
octahedral distances are linearly dependent on distortion. A decrease in cation occupancy increases
mean Li+-O, Na+-O, and Ag+-O distances in a predictable manner. Covalence strongly shortens
Fe2+-X, Co2+-X, Ni2+-X, Mn2+-X, Cu+-X, Ag+-X, and M - H - bonds as the electronegativity of X
or M decreases. Smaller effects are seen for Zn2+-X, Cd2+-X, In3+-X, pb2+-X, and TI+-X. Bonds with
delocalized electrons and therefore metallic character, e.g. Sm-S, V-S, and Re-O, are significantly
shorter than similar bonds with localized electrons.
Introduction
Procedure
A thorough and systematic knowledge of the relative
sizes of ions in halides and chalcogenides is rapidly
being developed by crystal chemists as a result of (1)
extensive synthesis within certain structure types, e.g.
rocksalt, spinel, perovskite and pyrochlore; (2) preparation of new compounds with unusual oxidation states
and coordination numbers; and (3) the abundance of
accurate crystal structure refinements of halides, chalcogenides, and molecular inorganic compounds. A set
of effective ionic radii which showed a number of
systematic trends with valence, electronic spin state,
and coordination was recently developed (Shannon &
Prewitt, 1969, hereafter referred to as SP 69). This work
has since been supplemented and improved by studies
of certain groups of ions: rare earth and actinide ions
(Peterson & Cunningham, 1967, 1968); tetrahedral
oxyanions (K~ilm~in, 1971); tetravalent ions in perovskites (Fukunaga & Fujita, 1973); rare earth ions
(Greis & Petzel, 1974); and tetravalent cations (Knop
& Carlow, 1974).
Further, the relative sizes of certain ions or ion pairs
were studied by Khan & Baur (1972)" N H + ; Ribbe &
Gibbs (1971): O H - ; Wolfe & Newnham (1969):
Bi3+-La 3+; McCarthy (1971): Eu2+-Sr2+; Silva,
McDowell, Keller & Tarrant (1974): No 2+. These
authors' results have been incorporated here into a
comprehensive modification of the Shannon-Prewitt
radii.
In this paper the revised list of effective ionic radii,
along with the relations between radii, coordination
number, and valence is presented. The factors responsible for the deviation of radii sums from additivity
such as polyhedral distortion, partial occupancy of
cation sites, covalence, and metallic behavior (electron
delocalization) will be discussed.
The same basic methods used in SP 69 were employed
in preparing the revised list of effective ionic radii
(Table 1). Some of the same assumptions were made:
(1) Additivity of both cation and anion radii to reproduce interatomic distances is valid if one considers
coordination number (CN), electronic spin, covalency,
repulsive forces, and polyhedral distortion.*
(2) With these limitations, radii are independent of
structure type.
(3) Both cation and anion radii vary with coordination number.
(4) With a constant anion, unit-cell volumes of isostructural series are proportional (but not necessarily
linearly) to the cation volumes.
Other assumptions made in SP 69 have been modified:
(1) The effects of covalency on the shortening of
M - F and M - O bonds are not comparable.
(2) Average interatomic distances in similar polyhedra in one structure are not constant but vary in a
predictable way with the degree of polyhedral distortion (and anion CN). Both of these modified assumptions will be discussed in detail later.
The anion radii used in SP 69 were subtracted from
available average distances. Approximately 900 distances from oxide and fluoride structures were used,
and Table 2 lists their references according to CN and
spin. These references generally cover from 1969 to
1975. The cation radii were derived to a first approximation from these distances, and then adjusted to be
consistent with both the experimental interatomic distances and radii-unit cell volume (r 3 vs V) plots, as in
A C 32A - 1
* Polyhedral
distortion
was not considered
in SP 69.
752
REVISED
EFFECTIVE
IONIC
RADII
IN
SP 69. Although such r a v s V plots are not always
linear (Shannon, 1975), their regular curvilinear nature
still allows prediction of radii. This system is particularly accurate for radii in the middle of a series, and
least reliable for large polarizable cations like Cs +,
Ba z +, and T13 +. Radii-volume plots were used by Knop
& Carlow (1974) and Fukunaga & Fujita (1973) to
derive radii of tetravalent cations. These radii were
used along with experimental interatomic distances in
deriving the final radii. Greis & Petzel (1974) derived
rare earth radii in eight- and nine-coordination using
accurate cell dimensions for rare earth trifluorides and
distances calculated using the structural parameters
of YF3 and LaF3. These radii were used in Table 1
after applying small corrections ( + 0.030 ,~ to lXLa3+,
IXCe3+, 'Xpr3+, and ~XNd3+; +0.025 A to all other
Greis & Petzel ~XRE3+ radii, and 0.015 A to all
HALIDES
AND
CHALCOGENIDES
VI"RE3+ radii) for consistency with experimental interatomic distances and radii-CN plots.
Where structural data were not available or not accurate, plots of (1) radii v s unit cell volumes, (2) radii
v s CN and (3) radii v s oxidation state, or combinations
of these were used to obtain estimated values. Fig. 1
shows examples of radii-valence plots used to provide
consistency between experimental radii and those anticipated from the regular nature of these plots. Cations
whose final radii values were derived from both
estimated values and experimental interatomic distances a r e : V l O s S + ,
VIOs6+,
VIOs
7+,
VlRe4+, VIRES+,
VlRe6+, VIReT+, VIRh4+,
vI1U4+,
VIIUS+,
and
VIIU6+.
Fig. 2(a)-(e) shows plots of radii v s C N . Generally,
it was assumed that radii-CN plots for two different
ions do not cross. Radii for 'VCu+, V'Cu+, IXRb+,
VNi2+, VIIEr3+' vIIyb3+ ' WITb3+ ' X.Nd3+ ' IVCr4+'
Table 1. Effective ionic radii
CR crystal radius, IR effective ionic radius, R from P vs V plots, C calculated, E estimated, ? doubtful, * most reliable, M from
metallic oxides.
ION
EC
CN
AC÷3 6P 6 V l
A G ÷ I 4D10 11
IV
VSQ
~
AGed 60 9
AGe3 60 8
AL*3
2P 6
AM*2 5F 7
AM÷3 5F 6
AM÷~ 5F 5
AS+3 4S 2
AS+$ 3D10
AT÷7 5DIO
AU÷I 5 0 1 0
AUe3 50 8
AU÷5 50 6
d +J 1S 2
8A÷~ 5P 6
BEe2 15 2
Ble3
65 2
vI
Vll
Vlll
IVSO
Vl
IVSQ
Vl
IV
v
Vl
Vll
Vlll
IX
Vl
VIII
Vl
Viii
Vl
lV
vl
Vl
Vl
IVSQ
Vl
Vl
Ill
I¢
Vl
Vl
Vii
Viil
IX
X
Xl
XI!
Ill
IV
l
~
Vl
Vlll
81÷5 5 0 1 0 V l
8K+3 5F 8 Vl
b K ÷ 6 5F 7 V l
VlIl
8 R - I 6P 6 V l
8 R e 3 6P 2 IVSO
8R+5 45 2 I I I P Y
8R÷7 3010 IV
Vl
c e 4 15 2 l l I
IV
VI
CA+2 3P 6 Vl
•
Vll
Vlli
x
~
Xll
CDeZ 6 0 1 0 I V
v
Vl
Vli
Vlll
Xll
CE+3 65 1 V l
Vll
Vlll
IX
II
CE÷4 5P 6 Vl
VIll
II
C F * 3 bD I VI
C F * 6 5F 8 V l
5P
Ck
1.26
.81
1.14
1.16
1.23
1.29
1.36
1.42
.93
1.08
.81
.89
• 53
.62
.675
1.35
1.40
1.65
1.115
1.23
.g9
l.og
.72
.675
.60
.76
1.51
.82
.g9
.71
.15
.25
.41
1.49
1.52
1.56
1.61
1.66
1.71
h75
.30
.41
.59
1.10
1.17
1.31
.go
1.1o
.97
1.07
1.82
.73
.65
.39
.53
.06
.29
.30
1.14
1.20
1.26
1.32
1.37
1.68
.92
1.01
1.09
1.17
1.24
1.45
1.15
1.21
1.283
1.336
1.39
1.48
1.Ol
1.11
1.21
1.28
l.og
.961
*IR*
1.12
R
.67
1.00
C
1.02
1.09
C
1.15
c
1.22
1.28
.79
.94
.67
.75
R
.39
.68
.535
*
1.21
1.26
1.31
.g75 R
1.09
.85
R
.g5
.58
A
. 3 3 5 Re
.46
C*
.62
A
1.37
A
.68
.85
A
.57
.01 *
.11
*
C
.2T
1.35
1.38
C
1.42
"
1.47
1.52
1.57
1.61
C'
.16
.27
*
. 6 5 'C
.96
C
1.03
Re
1.17
R
.76
E
.96
R
.83
R
.93
R
p
l.Vb
.59
.31
.25
.39
A
-.08
.15
P
.16
A
1.oo
1.06
*
1.12
•
1.18
1.23
1.34
.78
.87
.95
1.03
c
¢
1.10
1.31
1.01
R
1.07
E
1.163 R
1.196 R
1.25
1.36
C
.87
R
.97
R
1.07
1.16
.95
R
.821R
ION
EC
CN
C L - I 3P 6 V l
CL+b 35 2 l l l P Y
CL÷7 2P 6 I V
Vl
C~÷3 5F 7 V l
GHe6 5F 6 V l
VIll
CO÷2 3D 7 I V
V
Vl
Vlll
C0÷3 30 6 V l
GO÷4 3D 5 IV
Vl
CR+2.3D 4 VI
SP
HS
L5
HS
kS
HS
HS
L$
HS
CR+3 3D 3 V l
CR÷4 30 2 IV
Vl
Cg÷5 30 1 I V
Vl
VIll
eRe& 3P 6 IV
Vl
c $ + 1 5p 6 V I
Vlll
lx
X
Xl
Xll
CUe1 3010 11
IV
VI
CUe2 30 9 IV
IVSQ
1
CU*3 30 8 Vl
0 +1 15 0 I I
0Y÷2 6 F I O Vl
vI I
Vl I
UYe3 6F 9 Vl
VII
Vlll
IX
E&e3 4 F 1 1 V l
Vl 1
Vl I
IX
EU÷2 4F 7 V l
Vll
VIII
IX
x
EUe3 4F 6 V i
Vll
Vlll
IX
F - 1 2P 6 i l
Ill
IV
Vl
F e7 I S 2 V l
FEe2 30 6 IV
IVSQ
Vl
VIII
FE+3 30 5 I V
v
VI
Vlll
Vl
IV
Vl
IV
V
Vl
GD÷3 ~F ? V l
FEe4
FEe6
FR*I
GAe3
3D 4
30 2
6P 6
3010
kS
HS
H$
LS
HS
HS
H$
LS
HS
HS
CR
1.67
.26
.22
,61
1.11
.99
1.09
.72
.81
.79
.885
1.06
.685
.75
.56
.67
.87
.94
.755
.55
.69
.485
.63
.71
.40
.58
1.81
1.88
1.92
1.95
1.g9
2.02
.60
.76
.91
.71
.71
.79
.87
.68
.04
1.21
1.27
1.33
1.052
1.11
1.167
1,223
1.030
1.085
1.144
1.202
1.31
1.34
1.39
1.44
1.49
1,087
1.15
1.206
1.260
1.145
1 .16
1.17
1,19
.22
.77
.78
.75
.920
1.06
.63
.72
.69
aT05
.92
.725
.39
1.9~
.61
.69
.TbO
1.078
ION
fIR'
1.81
.12
*08
,27
.97
.85
.95
.58
.67
.65
.765
.90
.565
.61
.40
.53
.73
.80
.615
.41
.55
.365
.69
.$7
.26
.44
1,67
1.76
1.78
1.81
1.85
1.88
.46
.60
.77
.57
.57
.65
.73
.56
-.10
1.07
1.13
1.19
.g12
.97
1.027
1.083
.ago
.9~5
1.004
1.062
1.17
1.20
1.25
1.30
1.35
.g6~
1.01
1.066
1.120
1.285
1.30
1.31
1.33
.08
.63
.66
.61
.780
.g2
.49
.58
.55
.665
.78
.585
.25
1.80
.47
.55
.620
.938
P
•
A
R
R
R
C
R
Re
R•
R
E
R
R•
R
R
ER
c
EG
CN
SP
G 0 " 3 4F 7 V l l
VIII
IX
GE÷2 45 2 V I
GE*q 3010 I V
Yi
H e l 1S 0 I
II
H F * 4 "6F16 I V
VI
VII
VIII
HG÷I 6S 1 I l l
VI
HGe2 5010 I |
IV
VI
rill
HOe3 6 F 1 0 VI
VIll
IX
X
I :~ 8. )
v1
2.0.
5S
IIIPY
VI
1 ÷7 4D10 1V
Vl
IN÷3 6 0 1 0 I V
.58
l.Og
.56
.67
.76
Vl
E
E
IR+J
IR*4
IR÷5
K "1
50
50
50
3P
6
5
4
b
*
*
,6o
Vlll
Vl
Vl
Vl
IV
Vl
VII
VIII
x
1.06
.82
.765
.71
1.51
1.52
1.60
1.65
1.69
1.73
1.78
1.172
1.24
1.300
1.356
1.41
1.50
.730
.90
1.06
1.ooi
1.117
1.172
.71
~
Xll
LAe3 4 0 1 0 V l
Vl!
vllI
X
I
R
R
g
R
R
R
xli
IS 2 IV
Vl
VIII
LU*3 4F14 Vl
Vlll
1X
MG+2 2P 6 IV
Ll÷l
il
R
• 860
ll
HN÷2 30 5 I V
V
Vl
R
R
Vll
lll
MN÷3 30 6
~
Vl
A
E
Re
c
*
R
R•
R
R
A
*
R*
R
HN÷6 30 3 l V
Vl
MN÷5 30 2 I V
MNe6 30 l IV
MNe7 3P b I V
Vl
MO+3 40 3 Vl
MO*~ 40 2 Vl
~ o e 5 6D I IV
Vl
MO÷b 4P 6 l v
•
v
VI
Vll
"
:l
2,
) iv
2S
Vl
N
N ÷5 I S 2 I l l
Vl
CR
1,14
1,193
1,247
,87
.530
*670
--,26
-.06
.72
.85
.90
.97
1.11
1.33
*83
1.10
1.16
1.28
1.041
1,155
1.212
1.26
HS
H5
LS
H$
HS
L$
HS
1.03
......
.80
.89
.81
.970
1.04
1.10
.72
.72
.785
.53
.670
.67
.395
.3g
.60
.83
.790
.60
.75
.55
.64
.73
.87
*IR*
1,00
1,053
10107
.73
,390
*530
-,38
-.18
.58
.71
.76
.83
R
R¢
A
•
R•
:
,97
1.19
.69
.96
1.02
1.16
.901
1,015
1.072
1,12
220
.66
*g5
.62
k
R
R
R
,.
.53
.62
8oo.
Re
*g2
.68
E
.625 R
.57
E
1.37
1.38
1.66
1.51
1.55
1.$9
1.66
1.032 R
I.IO
l.lbO R
1.216 R
1.27
1.36
G
.590
.7&
•
.92
C
.8bl R
.977 R
1.032 R
.57
.720
.89
.66
.75
.67
.830
.90
.9b
.58
.58
.665
.3g
.530
.33
.255
.25
.66
.69
.650
.46
.61
.61
.50
.59
.73
1.32
.30
....
.044
.27
-.106
.16
.13
*
G
C
E
Re
C
R
R
Re
R
Re
R
A
RH
R
R
Re
R*
A
A
753
R. D. S H A N N O N
Table 1 (cont.)
EC
ION
NA*I
2P 6 I V
V
VI
VlI
VIII
IX
XIl
NB+J 4 0 2 V l
N 8 , 4 4 0 1 Vl
VIII
N 8 , 5 4P 6 I V
Vl
VII
VIII.
ND+Z 6F 6 VIII
IX
N O + ~ 6F 3 V l
VIII
IX
XlI
N I ÷ 2 3 0 8 IV
IVSQ
v
VI
N I * J 3 0 7 Vl
NI÷4
NO+2
NP÷2
NP*3
NP+6
NP+5
NPeb
NP+7
o -2
OH-I
0S+6
0S+5
0S.0
05"7
0S,8
p .3
p *5
PA+3
PAt4
PA~5
P8+Z
PB*6
p0÷l
PD÷2
PO•J
POe6
P~*3
PO÷4
POeb
30 6
5F16
5F 5
5F 6
5F 3
Vl
VI
VI
VI
V[
Viil
5F 2 VI
5F 1 V I
6P 6 V I
2P b I f
Ill
IV
VI
VIII
11
Ill
IV
Vl
5D 6 VI
5 0 3 Vl
50 2 V
Vl
50 1Vl
5P 6 I V
3S 2 vl
2P 6 I V
v
Vl
5F 2 Vl
6D 1 V l
• viii
bP 6 Vl
VIII
IX
6 5 2 IVPY
VI
VII
VIII
IX
x
XI
XIl
5 0 1 0 IV
V
Vf
VIII
6 0 9 II
4 0 0 IVSO
Vl
60 7 VI
40 6 Vl
6F 4 V l
Viii
IX
65 2 VI
rill
5010 VI
LS
HS
LS
1.13
1.14
1.16
1.26
1.32
1.38
1.53
.86
.82
.93
.62
.78
.83
.88
1.63
1.49
1.123
1.249
1.303
1.61
.69
.63
.77
.830
.70
.74
.62
1.26
1.26
1.13
1.oi
1.12
.89
.86
.85
1.21
1.22
1.26
1.26
1.28
1.18
1.20
1.21
1.23
.770
.715
.63
.685
.665
.53
.58
.31
.43
.52
1.18
1.06
1.15
.92
1.05
1.09
1.12
1.33
1.37
1.63
1.69
1.54
1.59
1.63
.79
.87
.915
1.08
.73
.70
1.oo
.90
.755
1.11
1.233
1.286
1.08
1.22
.81
.99
1.00
1.02
I.IZ
1.18
1.26
1.39
.72
.68
.79
.68
.66
.69
.76
1.29
1.35
.983
1.109
1.163
1.27
.55
.69
.63
.690
.56
.60
.68
1.I
1.10
1.01
.87
.98
.75
.72
.71
1.35
1.36
1.38
1.40
1.62
1.32
1.36
1.35
1.37
.630
.575
.49
.545
.525
.39
.46
.17
.29
.38
1.0¢
.90
1.01
.70
.91
.95
.98
1.19
1.23
1.29
1.35
1.40
1.45
1.49
.65
.73
.775
.96
.59
.66
.86
.76
.615
.97
1.093
1.146
.96
1.08
.07
C
RE
C
C
E
R•
R•
E
R
E
R
R
R
R
A
SP
~o.05~vi
RA*2
R
R*
R
E
CN
PR÷3 CF 2 V l
Viii
IX
PR+4 4F I V I
VlIl
PT+2 5 0 8 IVSQ
VI
PT+4 5D 6 V [
PT+5 5 0 3 V l
P U * 3 5F 5 Vl
P U * 6 5F 6 V I
Vl[l
P 0 + 5 5F 3 v I
6P
RB+L4P
RE*~
RE+5
RE+O
RE*/
50
50
50
5P
RH+3
RH+4
AHe~
RU*3
RU*4
RU*5
RO*/
RU*8
40
4D
40
40
40
40
40
4P
VIII
XlI
6 VI
vll
VIll
IX
X
Xl
xlI
XlV
3 Vl
2 VI
I Vl
b IV
Vl
b Vl
5 VI
6 V[
5 VI
6 VI
3 VI
1 IV
6 IV
+6 3 5
Vl
5 .6 2P 6 IV
vl
5 5 . 2 IVPY
v
vl
$8÷5 4010 Vl
5 C ÷ 3 3P 0 v I
VIII
S E - 2 6P 6 VI
S E * 6 6S 2 v I
S E * 6 3D10 IV
Vl
SI.6 2P 6 IV
vl
$H+2 6F 6 VIl
Vl I I
IX
SN*3 4F 5 v I
Vll
VIII
IX
Ill
SN*4 4010 IV
58+3
E
E
RM
E
E
E
A
*
C
e
g
c
C
C
c
C
C
E
E
R
R
VII
VIII
SR*2 4P 6 V l
VII
VIII
IX
~lI
TA*J
TA*4
TA*5
R
R
k
g
R
R
A
5 0 2 VI
50 1 Vl
5P 6 V l
VII
VIII
T 8 + 3 4F 8 VI
VII
VIII
IX
T 0 . 6 4F 7 Vl
Vill
vIIIV4+, IVpb4+, and XTh4+ obtained from these plots
were used to help determine the values in Table 1. The
first estimate of vIHV4+ was made from distances in
C32H28SsV (Bonamico, Dessy, Fares & Scaramuzza,
19741.
Another method used to estimate radii was based on
the empirical relationship between interatomic distances and bond strengths. Brown & Shannon (1973)
derived these relationships for the cations in the first
three rows of the periodic table from a large number of
experimental interatomic distances. These curves can
be used to calculate hypothetical distances for cations
in any coordination (Brown & Shannon, 19731 Shannon, 19751 Brown, 1975). Examples of cations whose
radii were calculated in this way are: lVMn2+, V[Be2+,
VtB3+ ' wps+, v l S 6 + ' V m M g 2 + ' and VmFe 2+. These are
marked with a C in Table l. In certain cases, these
values were combined with known structural data (see
Table 2) to obtain the radii in Table 1. Although the
A C 32A - I*
CR
ION
eIRt
1.13
1.266
1.319
.99
I.IO
.74
.99
.765
,71
1.14
1.oo
I,IO
.88
.99
1.126
1.179
.85
.96
.60
.80
.625
.57
1.00
.86
.96
.76
.85
.71
1,62
1.86
1.66
1o70
1.75
1.77
1.80
1.83
1.86
1.97
.77
.72
.69
.52
.67
.805
.74
.69
,82
.760
.705
.52
.50
1.48
1.70
1.52
1.56
1.61
1.63
1.66
1.69
1.72
1.83
.63
.58
.55
.38
.53
.665
.60
.55
.68
.620
.565
.38
.36
.51
.26
.43
.90
.96
.90
.76
.885
1.OLO
1.84
.64
.62
.56
.40
.540
1.36
1.41
1.46
1.098
1~16
1.219
1.272
1.38
.69
.37
.12
.29
.76
.80
.76
.60
.765
.870
1.98
.so
.28
.62
.26
.~oo
1.22
1.27
1.32
.958
1.o2
1.079
1.132
1.24
.55
• 830
.09
.95
1.32
1.35
1.40
1.65
1.50
1.58
.86
,82
.78
.83
.88
1.063
1.12
1.180
1.235
.90
1.02
.690
.75
.81
1.18
1.21
1.26
1.31
1.36
1.46
.72
.68
.04
.69
,76
.923
.98
1.040
1.095
.76
.88
R
R
R
R
R
A
R
ER
R
E
1
R
E
RM
E
E
R
RM
RM
ER
A
•
c
A
*
R•
Re
P
A
•
c
*
R*
R
E
R
R
C
R
c
E
E
R
R
R
EC
CN
TC+4 4 0 3 V I
TG*5 40 2 Vl
TC+7 4P 6 I V
Vl
T E - 2 5P b V I
TE+4 55 2 I l l
IV
Vl
TE+b 4 0 1 0 I V
Vl
TH÷6 6P 6 V I
VIII
IX
X
XI
Xll
TI+2 30 2 Vl
T 1 + 3 30 1 VI
r l + ~ 3P 6 I V
v
Vl
VIII
1 L * 1 6S 2 v l
VIII
Xll
T L + 3 5D10 I V
Vl
VIII
TM+2 4 F 1 3 V I
VII
TM+) k F l 2 V I
viii
IX
0 + J 5F 3 V I
O ÷ 4 5F 2 V I
VII
viii
IX
Xll
u +5 5F 1 V l
vii
U +b 6P 6 I 1
IV
Vl
Vll
Vlll
v * 2 30 J V l
v . 3 3 0 2 Vl
v +4 3 0 I v
Vl
VIII
V +5 3P 6 I V
v
Vl
w +~ 50 2 V I
w +5 50 1Vl
w +6 5P 6 IV
v
vl
XE+8 4D10 IV
vl
Y +J 4P 6 v I
VII
Vill
IX
YB+2 4 F 1 4 VI
Vll
VIII
Y8+3 4F13 Vl
Vll
Vlll
IX
I N * 2 3 0 1 0 IV
v
vI
VIII
Z R + ~ 6P 6 I V
V
Vl
Vll
VIII
IX
SP
CR
fiR*
.783
.74
.51
,70
2.07
066
.80
1.11
.57
,7o
1.08
1+19
1.23
1,27
1,32
1,35
1.00
.810
.$6
.65
.745
.88
1.64
1.73
1.84
.89
1.025
1,12
1.17
1.23
1.020
1.13~
1.192
1,165
1.03
1.09
1.14
1.19
1,31
.90
.98
.59
.66
.87
.95
1.00
.93
.780,
.67
.72
.85
.495
.6o
.68
.80
.76
.56
.65
.7~
.54
.62
1.040
1.10
1.159
1.215
1.16
1.22
1.28
1.008
1.065
1.125
1.182
.7~
.82
.880
1.04
.73
.80
.86
.92
.98
1.03
.845
.60
.37
.56
2.21
.52
,68
097
.43
,56
,94
1.05
1.09
1,13
1.18
1.21
.86
.670
.42
.51
.605
.74
1.50
1.59
1,70
,75
,885
.98
1,03
l.Oq
.880
,994
1.052
1,025
.89
.95
1.00
1.05
1,17
.76
.84
.45
.52
.73
;81
.86
.79
.640
.53
.58
.72
.355
.46
.54
.66
.62
.42
.51
.bO
.40
.~8
.900
.96
1.019
1.075
1.02
1.08
1.14
.868
.925
.985
1.042
.0o
.68
.740
.90
.59
.66
.72
.78
.8~
.89
AN
ER
A
e
G
C
RC
•
E
C
C
E
R•
G
C
R•
C
a
R
RE
R
¢
R
R
R
R
E
Re
E
*
E
Re
R*
E
R*
*
RH
R
*
*
Re
R*
R
E
R*
E
R
R
•
*
R*
C
R
C
R•
*
*,
majority of radii were derived from oxides and fluorides,* some were taken from chlorides, bromides,
iodides, and sulfides. For large electropositive cations
with highly ionic bonds, very little covalent shortening
is believed to occur and radii derived from these other
compounds should differ only slightly from those
derived from fluorides and Oxides. Examples are divalent rare earths such as Yb 2+ , Tm 2+, Dy 2+ , Sm 2+, Nd 2+
and the ions Am 2+, Ac 3÷, Np a+, and U 4÷.
Another useful scheme for estimation of radii is the
comparison of unit-cell volumes of compounds containing cations of similar size. McCarthy (1971) prepared a number 6f isotypic Sr 2÷ and Eu 2÷ ternary
oxides and generally found the unit cells of the Sr 2÷
* Because of covalency differences in M - O and M - F bonds,
oxide distances were emphasized. Therefore the radii in Table 1
are m o r e applicable to oxides than fluorides. This subject is
treated further in the discussion Effects of covalence.
754
REVISED
EFFECTIVE
IONIC
Table
RADII
2.
IN
HALIDES
AND
CHALCOGENIDES
Referencesfor Tab& 1
The references here and in T a b l e s 4, 5, 6 and 8 are a b b r e v i a t e d according to Codensfor Periodic Titles ( 1 9 6 6 1 .
AC*3 v|
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71JPGSA
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65 ACCRA
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67 ACCRA
68 N J ~ A
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71 SPNOA
71 AC8C6
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6 8 ACDCA
68 A N N I A
ALeS v |
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7Z J $ S C 8
72 J$SC8
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6 6 JACSA
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72 J|NCA
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73 J I N C 8
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72 INOCA
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6 7 ADCSA
67 INUC6
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68 CJCHA
63 8APCA
6 9 ACSCA
6 9 AC8C6
68 A N N I A
63 CAHIA
7O ACBCA
7 0 ACDCA
6 9 CHOCA
70 ARR|A
30
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393
28B
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7 1 9 AG FE 0 2
2 6 6 SR AG6 0 4
2 6 3 BA AG6 0 4
364
AG2 CR 0 4
64
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1968
8O CA AL 8 0 ~
2 6 1 2 3 0 CA AL6 07
1970
5 4 7 CA12 A L l 4 0 3 3
15 9 0 S CA4 A L 6 o l o ( O H ) 6
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v
131R
)CE4,)
73 JS$C8
CE.4 VIII
8
$3 1~ N 4 1 2 CE F6
JC$1A 1174 2021Ni6
CE u l O 0 3 6 H 2 . 3 0 H 2 o
74 J$TCA
l~
39t CEIS 04)2
F4 ACSAA
2 8 1079 A - CE t A C A C ) 4
C t * 4 XXX
68 JSCSA
90 3 5 8 9 I N H 4 ) 2 H6 ICE NOt2 0 4 2 1 . 1 2 H2 0
C F * 3 VX
F4 J I N C A
36 2 0 2 3 R3 VS V ICF2 15 0 4 ) 3 )
C L * 5 111
T3 NASUA
8
791 8 8 CL 0 3
CL*/ Iv
r z ACDCA
28
039 TMPO CL U4
12 ZK~XA
0~
65 X CC 0 4
6O ACL~A
13
e s 5 N o z CL 0 4 , n CL OA,
Hct
0 4 . N 2 O , C l CL 0 4 . 3 H2 O
s q JPCNA
6)
ZTe H CL O 4 . H 2 0
~8 JRCSA
0 0 8 0 / 5 C6 HD.AG CL 0 4
$7 P l S A A
56
134 N H4 CL 04
ST P l S A A
~6
143 K CL 0 4
6 2 ACCJ~R
15 1 2 0 1 N N4 CL O4
71 J C S I A 1971 1 3 t l c u ) c l o H9 N ) ) 2 COL 0 4 ) 2
7O AC~CA
2 6 1928 Ha . s CL 0 4
11 AC8C6
zt
8 9 8 H CL 0 4 . 2 112 H2 o
13 I C " D A
1 4 1 7 ¢G N I 2 - T R I E N - C U CL 0 4
11A¢DCA
ZT 8 9 8 x CL 0 4 , Z I l l
,2 0
12
7t
62
bQ
13
NRSUA
7 1281CL(*7)
-0
J C S I A 1971 1 8 5 7 C L ( * 7 )
-o
ACCRA
15
I s N3 o CL 0 4 1 - 8 0 C I
ACDCA
25 ~875 N H3 o H CL 0 4
ACSAA
2 7 2 3 0 9 )PaR 1o H 1 4 1 3 C 0 3 (CL 0 4 1 1 0
. o H2 o
73 ACSAA
273523
CU i t 3 H4 N I ) *
(CL O412
CN,~ vi
67 )NUCA
)
)27 R ICE*4)
cu*z I V
69 ZAACA
369
306 C0 V2 U4
C0,2 v
12 ACBCA
2 8 2 8 0 3 C02 PZ 0 7 ALPHA
C0,2 v!
68 ZAACA 3 5 8
125 CO SE 0 6
08 ZKKKA
120
2 9 9 CO GE 0 3
70 CJCHA
48
881 C03 A$2 0 8
70 JCPSA
5 ) 3 2 / 9 BA C0 F4
10 P E P l A
3
| 6 1 C02 SI OA
7 J AC~CA
2 9 2 ) 0 4 CO3 V2 O8
T l HCACA
54 1621 CO3 (O N ) 2 ( S 0 4 | 2 ° 2
H2 0
REF I
C02 $ ! 0 4
72 ACECA
28 2083 COl pz 07
70 INOCA
9
l S I CO ( O N P A ) 3 (CL 0 4 1 2
73 ACBCA
2 9 2 7 4 1 CO S I F 6 . b H2 0
74 A N N I A
59
4 7 5 C02 $ | 0 4
T4 JCHL8
4
55 C | 6 H 1 8 CO 0 6
CO*Z V ) I I
6 6 INOCA
S 1208 (A$(C6 HSIRI2(CO(N O3J~)
co,) Vl
LS.
6 8 CCJDA 1 9 6 8
871 c0 (N 0313
O80JCHA
4 6 3 4 1 2 C03 0 4
6 6 JACSA
8 8 2 9 5 1 C0 (CS H7 O213
74 ACUCA
30
8 2 2 C0 1C5 H7 0 2 3 3
69 JACSA
e l 6 8 0 1 I N H 4 1 6 ( H 4 C02 N 0 1 0 O381
•
, 7 H2 o
74 ZAACA 4 0 8
97 K C02 0 4
C0"4 IV
71ZAACA
306
I 8A2 CO 0 4
73 ZAAOA
398
54 L l 8 G0 0 6
7 4 ZAACA 4 0 8
75 C52 CO 0 3
74 ZAACA 4 0 9
lsz 86 co2 o7
C0.4 v)
HS
6 7 STGBA
3
I 8 3 VS V ( F L U O R I D E S )
14 ZAACA 4 0 8
97 K C02 0 4
CR*2 vl
LS
7L ANCPA
6
411A2
CR 0 6
6 9 ACDGA
25
9 2 5 8 VS o ELECTRONS
CA*3 vl
6 9 MDUUA
4
6 2 | NA3 CR F6
7O INOCA
4• a Z Z 8 HA3 )CR NO 006HOZ4 M 6 3 . 8 , 2 0
1o ACSAA
2
3 6 2 7 ~A2 CA3 0 8
73 NROUA
8
5 9 3 CA CR FS
6 5 ACCRA
19
1 3 1 C R | C ~ H7 0 2 1 3
CR*4 IV
14 ZAACA 4 0 7
129 BA2 CR 0 4
CR*4 Vl
72 NRBUA
?
1 5 7 CR o z
CR*5 Vl
67 SEGOA
3
I A3 v s v ) F L O O R ) D E S )
CR*6 IV
6 8 CJCHA
96
9 3 5 K2 CR2 O7
70 ACGCA
26
2 2 2 CR 0 3
6 9 JC$1A 7 9 8 9 1 8 5 7 ( N H R ) 2 CR 0 4
h 9 ACAC8
2 5 $|16 AG~ CR2 0 7
70 5PHDA
15
5 3 0 K2 CR4 0 1 3
to ANNIA
55
7 8 4 P82 CR2 0 5
7 0 ACSAA
2 4 3 6 2 7 N2 CR3 0 8 0 H
71 $FHCO
15
8 2 0 NA2 CR2 0 7 . 2 H2 0
71SPHCA
15
8 2 6 L I 2 CR2 0 7 . 2 H2 o
73 AC8CA
29
BqO NA2 CR2 0 7 ALPHA
71ACSAA
2S
4 4 RB2 CR2 0 7
7 0 CJCHA
48
5 3 7 8 8 2 CR2 0 7
71ACSAA
2S
35 R82 CRZ 0 7
71JSSC8
3
3 6 4 A02 CR 0 4
72 ACeCA
Z8 2 8 4 5 82 CR 0 4
73 ACSAA
Z7
1 7 7 ZR4 CO H | 6 CCR O ~ ) S . H Z O
73 ACSCA
2 e 21~l R82 CR4 013
•73 6COCA
29 2 9 6 3 NA2 CA 0 4 . 4 H2 0
71JCSIA
letl
1 8 5 7 ( N H R I 2 CR 0 4
73 NRDUA
8
271 K2 CA2 O l
C R * 6 vl
74 AMMIA
59 1 1 0 0 P86 CR CL6 X6 V2
C$*l vlll
0 9 SPHCA
13 9 3 0 CS2 BE F4
CS*l x
6 9 INOCA
8 1 6 6 5 CS4 M03 F I O
6 9 $PHCA
13 9 3 0 C$2 BE F4
cs*l
xl
6 9 INOCA
8 1 6 6 5 C$4 NG3 F I O
C$.1 x11
67 ACCRA
23
8 6 5 C$ U F 6
6 8 ACSAA
2 2 2 7 9 3 CS CO CL3
71AC8CA
27
2~S C$ U6 F 2 5
CU*| II
b 9 ZKKKA
129
2 5 9 CU LA 0 2
70 ZAACA 3 7 9
1 1 3 SR CU2 O2
CU*| Iv
49 ACCRA
2
158
c u CL3
Cu*l vl
70 NRBUA
S 2 0 7 CU TA 0 3
cu*a Iv
57 ACCRA
10
5 5 4 c u CR2 0 4
71ACIEA
1o 4 1 3 SR CU 8 4 , CA CU F4
CU*2 IV $0
O7 ZK~KA
124
9 1 Z N 2 CU 6 8 2 O8
68 ACBCA
24
888 cuz IN2 05
t l ACBGA
27
6 7 7 CU 02 0 4
6 5 JCPSA
4 3 3 9 5 9 CU ( 0 6 H S I C H 3 ) 2 C ) O212
6 6 INOCA
$
5 1 7 CU 1 0 | 0 H9 0 2 1 2
61JCS~*
1967
3 0 9 CU ( 0 4 C l 2 H I 8 )
6 6 PRLAA 2 8 9
161 C14 HLO 0 4 CU
70 ACSCA
26
8 cu o
cu.z v
6 9 ACSAA
23
221CU) W 0 6
~8 C a ) H A
46
9 1 7 CU3 AS2 O8
6 8 JCPSA
40 2 6 1 9 CU NO 0 4
cu*z vI
:I .ACCDA
. . . . . . .|.6. . . |.z.4. .c.u.5
'68
;o
68
68
JCPSA
AC8CA
CJCHA
J&CSA
70 )NOCA
t 3 ACBCA
CU*3 Vl
12 MRBUA
DV*Z v )
UNPUI
DY*2 V l l
UNPUI
OY*Z V I I I
uNPul
or,3 vl
6 3 PHSSA
0Y'3 VII
I t JCNLB
oy.1 viii
I ~ .$$COA
......
ov.J ix
) p o 4 3 2 ~o , 1 4
4 8 2 6 1 9 CU NO 0 4
2 6 10Z0 CU i o ~
~6
60S CU2 P2 O7
90 5621 CU(((C H3)2 N)2 I P l 0 1 2 O111 ; e l 0 4 1 2
9
is| cu )O~FA)3 (eL 04)2
2 9 1 7 4 3 CU V 2 0 b
7
9 1 3 LA GU 0 3
OY 12
Of Ct2*
0Y 8R2
ov eL2
3 K446 0 ¥ 2 o )
|
83 OYITHO)3oH2 0
1 | 7 1 ~ .o.r. ). . . . .FE3
... all
R. D. SHANNON
Table
74 2AACA
ER*3 Vl
7~ ACbCA
ER*3 VII
TO SPHCA
72 JCMLB
ER+~ V I I I
6 8 CHPL8
?0 [NOCA
7O SSCOA
7L ACSAA
403
I
26
484
13
Z
36 ER2 GE2 0 7
1 9 7 ER8 U i T H D ) I O
~4 ZAACA
4O3
2
ER2 S12 OT
10 H ) 1 2
2
4 7 ER ~ 0 4 . ER V 0 4
9 2AO0 ER I C 2 0 4 ) I H C2 0 4 ) . 3 H 2
8 1 7 4 5 ER3 F E 5 0 L 2
28
372 E~ | H U C H2 G 0 O 8 3 . 2 H 2
3 6 2 EK I C 2 H3 S 0 4 ) 3 . 9 H 2
I R3 V$ V IER F31
201
oA+~ I V
16 ACRC~
T5 AC~CA
GA.) V l
14 A T R I A
GD*3 V I I
70 &CBCA
?2 ACSCA
T2 SPHC~
O9 [VNM&
T2 JSSCB
GO*J V I I I
IA SPHCA
l Z SPHCA
74 ZAACA
~ 0 ~ 3 ZX
72 SPHE&
6 9 IVNNA
7~ ZAACA
OE*4 I V
68 ZKKKA
69 $ C I E A
69 Z~KKA
7O JS$CB
Zl sP-c*
70 ACSAA
6 7 ACSAA
7~ NOCNe
I1 " 0 C ~ 6
72 SPHCA
12 ROCk5
GE*4 v i
10 SSCO~
I0 J$$C8
TA ,OCM8
TA AC~CA
12 ANN1&
12 2KKKA
TZ ~OCM8
.,A
I
............
L!
0
EU3 O4
EU F Z ,
EU 8RZ
7~ EU CL2
EU F2
2 1 8 EU2 SI
6,,cc.
EU4 AL2 o g
L 1 2 EU5 8 8
l o g 4 EU3 FE2 GA3 0 1 2
I R3 VS V (EU ~38
2 5 2 7 EU2 I C 3 H2 0 4 1 3 . e H 2
0
20
(cont.)
8 6 9 HG NO 0 4
2049
1745
437
1
| R3 V$ V I H U F J )
2 6 1 3 HOICZ H5 S 0 6 ) 3 . 9 H 2
409
IS
24
24
llbE
BA FE S14 0 1 0
139g
3O6
452
|29&
( N A , K ) 2 FE4 S [ A 2
FE V2 O4
FE2 TI 0 4
FE2 MO 04
0
030.H2
0
V25 R VS A I F E S21
4 3 0 FE AL~ IP O412 IO H J 2 l 0
.2H2 0
tgO ~E S O4
g 9 9 FE3 BE S I 3 0 9 [ F I O H I 2
7 7 5 FE ( N H 4 ) 2 ( $ 0 4 ) 2 , 6 H 2
0
290 LIFE
P O4
4 8 & F~2 SA 0 4
79A GARNE~$
333 FE3 A L 2 S I 3
2 6 6 CALCULATEO
1469
1745
A263
T2S
36A6
832
I
Z469
1745
335
I
6315
3616
239
440
0L2
CA2 FE2 OS
M3 FE5 0 1 2
BA FE2 0 4
BA CA FE4 0 8
CA2 FE2 05
6A FE2 0 4
FE V 0 4
CAZ FEZ O5
~3 FE5 0 1 2
K FE F4
FE v 0 4
B I FE O3
CA2 F E 2 0 S
FE lOS H7 0213
FE I C 7 H5 0 2 1 3
33L ESTIMATED
3 3 1 R3 VS V I P E R O V S K I T E S I
R3 VS V I S ~ Fe O3)
*3
K2 FE 0 4
R3 VS v (K2 FE 0 4 )
6t6 L | 5 GA 0 4
56O S~ OAZ S l Z
08
3O 1364 ItS HAl Ob O&
26
4 8 4 GDZ S I 2 0 7
28
6 0 GO2 NO3 O12
16 7 9 0 G O 2 0 E Z 07
5 1823 G O g . 3 3 S I 6 0 2 6
S 266 0 0 9 . 3 3 $ 1 b 0 2 6
1~
16
4O3
9 2 6 NA GO S ] 0 4
79O ~ 0 2 GE2 O?
A R3 V$ V IO0 F ) |
16
7 9 0 GO2 GEZ QT
5 IR23 GD9.33 S]6 026
4O3
A R3 VS V IO0 F 3 )
t26
165
129
Z
18
24
2A
A02
IOZ
t7
103
299
586
427
612
~a~
1287
12B!
964
I245
244
1560
CO 0E 0 8
AN2 GE 0 4
~N3 FEZ GE3 OAZ
~ 0 2 8 G E| O 0 4 8
~
sm GE o~
NA4 $N2 GE4 0 1 2 I 0 H I 4
NAB SN4 GEIO 0 3 0 (O H I 4
NAZ 0£ O3
K 2 0 E ~ O9
CO GE O3
GE5 0 ( P 0 4 1 6
1 $ 5 7 CA2 GE O4
2
662 . G 2 8 GEtO O48
Ao2 I Z 4 S K 2 0 E 4 0 9
2T 2 1 3 3 OE 02
~1
62 MN2 GE 0 4 OELT&
186
38T Ge I O H I P 04
103 AS60 GES 0 I P 0 4 ) 6
+
13
2 3 5 0 N H~
750 L| |
841LI
1
1015 CEII
794 C i I I
7 2 9 N H4
I 03
O]
03
0314
0314.H2
I 03
ZT~ ~
~
o2
~ ~C$AA
ZJ 3341
I0 ,42
14 AC>AA
2T 3467 . P ~ ( O , 1 8
.F*4 VIII
TJ &CSAA
27 Z * 5 5 NF ( 0 H I 2
.0,1 vl
? l CCJO& | 9 1 |
4 6 6 NO2 F2
2 5 5 6 N H4 I 03
1782 NA I 0 4
308 A I 04
1 8 5 7 II*TI-U
7o~.s.
,'/6
INOCA
~9 ZKKKA
S 04
0
0
97 ~82 IN4 07
2 8 0 SR2 I N Z 0 3
9 7 R82 I N 4 0 7
t437 IN O H S 04.lHZ
3 e 8 CUE I N Z OS
1662 IN 0 0 H
3583 , G 2 NAZ $ ] 6
2667 K~ NG 84
OAR
A966 ~G) P2 0 8
A42 MG 84 0 7
NG3 P2 O8
RG2 P2 07
A l S q . G 2 P2 07
36A ~G2 A$2 OT
1419 , G ,
H4 P O*
o41
S 04*~Z 0
IC~ 0 4 1 4 . , Z
0
012
AC6CA
30 1882 NA I N S l Z 0 6
74 SPHOA
18
7 6 t I N Z GE2 07
Vl
7A J 5 $ C 8
3
1 7 4 SR ZR 0 3
IR+S V I
74 NROUA
9 1177 R3 VS V ICO2 I R 2 071
K*I
IV
68 ZAACA
3SR 2 4 1 K
AG O
RE~ 2
K2 0
K*Z
VI
SA ZAACA 2 6 4
144 K 58 F6
6 8 SPHOA
12 1095 K Y N02 0 8
09 CCJDA
II
6 0 6 K2 ZR2 O5
b 9 ACUGA
2 5 1919 ~ U2 F9
K*L
vii
~e CJCHA
46
9 3 5 ~2 ¢R2 0 7
69 JCSIA 19~9
8 4 q KZ NO 0 4
TA S~COA
S 3 3 8 ~ FE F4
K*I
Vlll
~0 ZKKKA
74
3O6 K H2 P 0 4
62 ZKKKA
|AT
4A1K2
TI6 013
37 ZKKKA
98
2 6 6 K H2 I H 3 O) 85 0 1 0
7A INUCA
7
8 7 3 K H C2 0 4
6 8 CJCHA
46
9 3 5 K2 CR2 O7
70 J C S I A 1 9 7 0 3 0 9 2 K AU I N 0 3 ) 4
6 5 ACCRA
19 6 2 9 K4 H2 12 0 1 0 . 8 H 2 0
K*|
IX
70 ZKKKA
132
27 K A . 6 N A S . 5 CAO.3 A L T . 3
L18*5 032
6 9 ~CBCA
25
6 0 0 K CE F4
6 9 ACSCA
25 1 9 1 9 K U2 F9
K*A
X
73 CJCHA
$1 2 6 1 3 K AL P2 0 7
K +I
XII
6 8 SPHCA
13 4 2 0 K Y ~2 08
? l INOCA
10 1264 K2 P8 CO I N 0 2 1 6
67 I~0CA
5
5 1 4 K2 BA CO I N U 2 8 6
74 IACSA
9 6 6 6 0 6 K2 CA CO I N 0 2 ) 6
75 ACOEA
3A
$ 9 6 K2 8A CU I N 0 2 1 6
57 PASAA
56
643 K CL 0 ~
LA*3 Vl
6 9 ZKKKA
129
2 ~ 9 CU LA 02
T3 NRUUA
8 1 2 6 9 ~ 3 V$ V I ~ E 2 ~ 3 0 A 2 1
LA+3 V I I !
?4 A N N I A
59 1277 LA4 ~G2 T I 3 S [ 4 0 2 2
73 ACRCA
2 9 2 0 7 4 LA2 H03 U I 2
6 8 INOCk
7 2 2 9 5 LA ( C 5 H7 0 2 ) 3 I H Z 0 4 2
74 ZAACA +03
A R3 VS V ( L A F31
7~ SPHCA
L8 67S LA2 SR3 (B 0 3 1 4
LA*3 IX
71NRBUA
6
2 3 LA FE 0 3
?~ Z ~ C A
~O~
A ~ ) VS V ( L ~ ~31
74 A~IA
59 12T7 LA~ NG2 T13 S I 4 0 2 2
LI+A IV
3V ZKKKA
A02 119 L I O HoHZ O
TO 2AACA 3 7 9
| 5 7 L I Z CU 02
70 INOCA
9 1 0 9 6 Y8 L [ F4
71AMNIA
56
18 NA3 AL2 L l 3 F 1 2
71ACSCA
27
0 6 6 L 1 5 OA O4
T3 JSSCB
6
538 L I 3 V O4
73 ACRCA
2 9 2&Z$ L I {N~ HSI 8E F4
T ) ACBCA
2 9 ~ 6 2 8 L [ N H3 0 H $ 04
6~ ACCRA
17 7 8 3 L I 2 C2 0 4
14 ACSCA
30 2 4 h 6 L I Z 8E Sl 0 4
LI+L V|
&8 ACBCA
24
2 2 3 L | 3 AL F6
6 9 2AACA
)TA
3 0 6 L 1 2 ZR O3
70 ZKKKA
132
I 1 8 L I 2 AL2 S [ 3 0 l O
TA ~RRUA
6 ~
U Z ~0 F6
6~ A¢C~A
19 ~ 0 1 L I C6 07 H7
74 A¢IEA
66 819 LI N8 P
0204
68 CZ~YA
66
29O Ll Fe
?l A¢SA6
2~ 3387 LI N ~ O8
73 IJCHA
~Z 26~ LI V OJ
T3 ACBCA
29 2 2 9 4 L I 2 ZR F6
CU+3 V l
7O ZAACA 3T7
70 C~ LU2 O4
?z J*CC*
4
2 ~ ~ u e o~
LU*~ VIA!
74 ZAACA *03
| R3 VS V ( L U F31
LU+3 IX
7~ ZAACA ~ 0 3
A R~ VS v ( L U F31
~G*2 I v
72 AC§C~
28
2 6 7 KZ NGS $ I 1 2 0 3 0
AC~CA
2
~4 ACUC6
30
~0+2 V
6~ ~CSAA
ZZ
&6 , J N N A 1966
UNPU$
UNPU3
NO*2 V l
65 CJCH&
~)
68 UAPCA
11
TO ACeCA
26
,3 7
2 7 5 6 3 V5 V 1~4 . F
H236
0
2S35"HOIN2 014 IH C 0313.2H2
83L IN OIZIHOIN 03)51
19 6 2 9 K4
2 0t0.8H2
59 2 0 3 6 I N H 4 1 Z H ) [ 0 6
409
393
74
T|
73
74
K HO BE F6
H 0 3 FE5 0 1 2
H0 Pb 0 1 4
R3 VS V IHO F 3 I
IR'4
A R3 VS V I E U F 3 |
2 8 2 7 EU2 ( C 3 H2 0 4 ) 3 . 8 H 2
33~7 EU TRISGLYCOLATE
2T
36
2
73 ACBCA
29
H0*J VIII
T~ ACBCA
30
TO SSCOA
8
72 8UFCA
9S
74 ZAACA 4 0 3
HO+3 I x
14 ZAACA 4 0 3
7 4 ACOCA
30
H0+3 X
T4 INOCA
13
75 CJEHA
S3
1.5
Ill
71JCPSA
54
6 6 ACCRA
20
6 6 ACCRA
21
58 ACGRA
9
58 ACCRA
It
4 3 RTCPB
6Z
I+5
Vl
7 t JCPSA
54
1+7
IV
?0 RCBC~
26
2 6 ZEPYA
3g
71 J C S I A A971
I*7
VI
6 5 ACCRA
37 JACSA
IN.3 IV
T4 ZAACA
73 ZAACA
IN*3 VI
74 ZAACA
~ t ACSAA
6 0 ACOCA
70 ACSAA
04
EU4 AL2 0 9
L | EU3 0 4
L I 2 EU5 08
201
8
.......
0
201CI
EU3 O4
It04 EU 12
L I 2 EUS 0 8
7O SUFCA
93
71SPHCA
|5
6 ? ACCRA
22
6 8 GIWYA
68
14 A ~ N [ A
59
FE*2 rill
TA AMMIA
$6
71ZKK~A
134
T3 ACAC8
29
FE+J AV
H$
TO ACECA
26
70 SSCOA
8
?1ACRCA
27
I I MREUA
6
71AESAA
2S
73 ACBCA
29
FE+3 v
TA JS$CB
~
FE*3 vI
H$
TO ACSCA
26
70 SSCOA
6
71SSCOA
9
?L JS$CB
~
TL JPCSA
32
11ACSAA
25
67 ACCRA
23
6 9 CCJO~ 1 9 6 9
FE*) VIII
T3 JSSCB
8
FE*4 Vl
73 JSSCB
8
FE+o I V
z~ JSSCB
0
I R3 VS V (eR F31
I97 ER8 0 I T H D ) I O I 0 N ) 1 2
72 JGHL8
ER.3 IX
5 9 ZKKKA
112
?4 ZAACA 4O3
EU+2 V l
7O ZAACA
374
EU+2 V I I
70 2AACA 3 7 4
6 9 ACRCA
25
7 3 REF 3
EU*2 VIII
UNPUt
EU+2 I x
73 RVCMA
|0
UNPUl
EU+Z x
? l NATMA
S8
EU+3 V l
68 REF 4
7 0 ZAACA
374
73 REF 3
EU÷3 V I I
68 REF 4
13 REF 3
EU+S V I I I
65 JCP$A
48
~ ZAACA 4O3
3 ACSAA
27
EU+3 [ X
74 ZAAC~ 4O3
73 ACSAA
27
71ACSAA
25
F E * Z I V SQ H$
74 AMHIA
59
FE*Z IV
HS
69 $C]EA
L&6
6 9 ZAACA 3 6 9
TI JUPSA
31
12 JUPSA
33
FE*Z VI
LS
69 ACRCA
28
FE+2 V I
HS
&9 NJMMA 1 9 6 9
• 6 JCPSA
~P.~ Iv
TS J 5 5 C 8
NF.~ Vll
R3 VS V |OY F 3 )
2
755
8 A665 E$4 H03 FAO
IZ9
6~ NG S l U3
698P.C,
lI
93,,..
10 J 5 5 C 8
~12 . G 2 e
I0 O48
6 ~ .NL.O 196~
i v 6 . ~ AL 6 o ,
70 BSC++ 1970 + 2 4 3 "G $ 0 4 . . Z 0
71 l c e c l
z?
813 .~
=E o 6
bB &CSAA
22 A466 MG$ P2 08
ro 6 k F A
C~ MO Sl O4
0
AGSCA
ANM|A
ANMIA
CJCNR
10 INOCA
72 C J C H i
7~ ACBCA
NG*Z V I I I
73 AGRC8
MN*Z I V
HS
70 ANNIA
6 9 ZAA¢A
F I AGBCA
6 9 PMSSA
13 ACACB
NN*~ V
HS
6e ANNIA
74 MPMTA
~N*Z VI
LS
0 9 ACBCA
MN*~ Vl
HS
6 9 SGIEA
6 q JCPSA
70 ZKK~A
6 g ANMIA
70 N J ~ I A
6 5 ACCRA
72 A N N I A
6 7 PRLAA
67 HCACA
MN*2 V I I
72 AMNIA
MN*Z V I A l
6 9 ZKKKA
71AMM|A
73 SSCOA
74 JCPS6
NN*J V!
HS
0 7 ACSAA
b 7 ZKKKA
b8 ACSCA
6 9 JCPSA
6 3 PHSSA
6 8 BUFCA
7A JS$C8
7J JSSC8
7~ A N N I A
6 8 ACBCA
* INOCA
4 INOCA
NN*~ IV
7S JSSC8
NN+~ V l
73 JS$CB
6 9 INOCA
6 3 CZYPA
6 7 HCACA
.N*6 IV
12 ACOCA
M~*7 I v
6 8 ACOCA
MO+3 V I
6 9 ACBCA
6 9 INOCA
.0.~ vl
7A MRUUA
MO+~ IV
7 4 INOCA
~O.S Vl
7 t INOCA
~
68 JCPSA
6 8 SPHDA
69 JCS|A
72 ACUCA
6 9 JCPSA
71 SPH~A
?A SPHCA
71JCPSA
73 ACBCA
71JCSIA
NO*6 V
67 CCJOA
08 J C S I A
NO+6 VI
68 JCSIA
70 JSSCB
70 INOCA
r o ACSAA
6 6 ACSAA
TO CCJOA
6~ INOCA
73 ACRCA
74 ACECA
Iv
REF 6
N*5
Ill
REF 6
JO
86
$8
$2
q
SO
29
29
2 4 9 1 M G 2 V2 0 1
| 5 8 3 NG 1 8 6 O f I 0 H I 6 1 * Z H |
1 0 Z 9 MG C OS
11S5 CA L l ~G2 HZ I P 0 4 1 1 6
I S I ~G I O N P ~ 1 3 (CA 0 4 1 2
3 6 1 9 NG Y2 U6
2 6 1 1 M G 3 AS2 0 8
266 CALGULAIIO
NN? S | AS U | 2
Iq~ VZ 0 4
NN CO CA 0 4
MN ¢R2 0 4
GALGULATEO
55 1 4 8 9
369
306
2T 1 0 4 6
J2
Kql
29
266
53
21
28
U
1 8 6 1 M N 2 0 H AS 04
2 6 6 NN2 AS OA OH
9 2 8 R VS 0 £LECTMONS
168
SR6 ~ Z
GE U6
51 4 9 2 8 BA MN F 4
l~Z
INNS
tO N l z $ 1 2 0 8
5 4 | 3 6 2 NN eE2 | P 0 4 l Z I O H I 2 . S H 2 0
113
1MN? ~A|2 IS 0~)1$.18H2
0
19
8 8 ~ MN S O~
ST
6 2 1 M N 2 GE 04
9~
i ~ 5 NN C 03
)020))
MN) 0 8
S?
621MN2
GE O~
229
427
56
791
12
L09
6~ 1899
~ N ) FE2 GE$ 0 1 2
GARNETS
NN3 AL2 GE3 0 1 2
MN U4 0 7
Z&
124
24
50
3
9~
3
MNZ 0 3
NNZ 0 3
jl~ 0 0 H
I N H 4 ) 2 RN F5
f'~Z 03
TO NN 0 8 , PR n N O ) , N u x N O )
LA JCN 03, RN3 04,
L A . 9 S CA.o5 #N 0 3
NA MN? 0 1 2
NGZ ~N e o s
NA4 MN~ TLS OAR
~N I t 7 H5 0 Z 1 3 , 1 1 4 C6 HS CH$
~N IACACi3
ZO?|
428
1233
1066
K.46
339
238
6
16
39
9as
2 4 11A4
13 IRSA
13 1 8 6 4
L3
2 7 5 R3 V$ V IM4 NN O ~ l
8
23k
8
33S
13
39e
SO 2 0 2 3
8 6 NN O3
NIL2 NN NBL2 0 3 8 . S O N 2
NAT H4 MN I I 0 6 I S * I T H 2
NN5 GO, c o 2 MN) 0 5
0
2 ~ 1 0 5 3 AG NN 0 4
25
4 0 0 KJ NO CL~
8 2 6 9 4 K8 NO F6
6
5 5 5 L 1 2 MO F 6
13 2 7 1 5
t0
R3 VS V ¢AE N 0 0 * l
9 2 2 8A2 NO NO 0 6
48
12
1969
28
50
18
15
55
29
1971
2 6 t 9 CU N0 O~
LOgS K Y N 0 2 0 8
8 4 9 K2 1~3 0 4
6 0 GU2 NO) OA2
8 6 N02 NO3 0 1 2
611LI3
FE NO3 0 1 2
8 2 9 K AL N02 0 8 . K FE ROE 0 8
1093 CA N0 0 ~ , SR NO 0 *
2 0 7 4 LA2 NO) O12
1 8 5 7 NO(*63 - O
1967
1968
3 7 4 ~2 NO3 0 1 0
1 3 9 8 KZ X0$ O10
19&8
1
9
24
20
1970
13V8 K2 M03 0ZO
kS& AG6 M010 0 3 3
2 2 2 8 NA3 ICR MO 0 6 0 2 ~ H b I * R H 2
3711Cl
~ 0 0 2 AS O~
2 6 9 8 NO F 6 IGASI
SO NO 0 3 ( H 2 0 ) 2
1603 K
I R 0 O2 C2 O4I H2 0 1 2 O
29
8 6 9 HG NO 0 4
30 11V5 NO 03VHZ O
N-J
NA+I I V
74 ZAACA
REF 2
NA+A
V
68 ACeCA
6 8 SPHOA
6~ ZAACA
NA+I Vl
70 ACSAA
6 5 ACCeA
63
60
58
~6
,ccA,
ZKKRA
ZKKKA
ACCRA
0
2 8 2 8 4 S K2 MN O~
NG3 N 2 , S I 3
N~.8
NITI
N
NHk N O3t~L~ N 0 3 t K N OAt
RAin 0312,TIIN
O314
409
6 9 N A 6 ZN 0 4
NA2 O
2 4 1077 ~A2 S I 2 OS
A2 9 8 7 NA2 ZNZ S l 2
329
110 NA2 HO O2
07
2 4 1287 N&~ SN2 GE4 0 1 2
19
5 6 1 N A C6 0 7 H7
i~
115
111
~
s g ACCRA
1
74 ACRCA
30
78 ACBCA
31
NA*I VII
71 SPHCA
IS
;0 NJNlA
113
T ) ACBCA
29
NA*A V I I I
6 8 AGBGA
24
6 8 SPHOA
A2
71ANMIA
56
NA+I Xll
[ l J$SC8
3
32 ZKKRA
81
Ne.3 vl
7. ACIEA
U6
,8.~ Viii
75 JACSA
9?
NR+~ v l
6 8 JCPSA
*a
70 JS~C~
l
70 JSSC8
1
70 ~ l A
ss
$5 PRVAA
98
71J5$CB
J
71Z*~c~
3co
14 J I N C A
36
It JCSI& lVll
1233
6)0
Z4I
811
I0 H)4
NA o I O . I * . Z , 2 0
NA2 AL2 S I S O [ O * 2 H Z 0
NA CL 0 3
INAsAS RAIN
5 2 6 NA U ACETATE
1872 NA2 u O4
8 9 0 NA2 C O 3 . H Z O
9 2 6 NA GO S l 0 4
I NN7 NAA2 I $ O 4 1 3 . 1 5 N 2 0
RqO NA2 OR2 07 ALPHA
1 7 0 3 NA 8 F4
V8? NA~ Z . Z $12 0 7
18 NA3 AL2 L I 3 FAZ
89 NA|3 N833 094
13S NA A~ S I 0 4
RA9 L I
NU OZ
2713 NBIOPNI~
5048
.19
*S~
90
go3
09
119
1965
AZIO
8 A 2 7 S R 7 . 5 NB2 0 5 . 7 8
~ - , 8 2 OS
NA2 . 8 4 OAA
c a NSZ 0 6
C~2 NEZ 07
N ~ l $ NeS~ O94
~ ~96 0 6
CA2 NB2 U7
8 l ~ NRA7 O * 7
0
756
REVISED
EFFECTIVE
IONIC
RADII
IN
Table 2
70 ACOC&
2b
7 t ACSAA
25
59 IPHCA
4
73 JSSC8
e
66 ACSA6
20
74 8UFC&
97
N8"5 VII
t o JSSC8
1
TL J$$Co
3
? l ACSCA
27
; 5 ACBCA
31
N0,2 VIII
UNPUI
N0+2 i x
v~NPUt.
ND*3
?1 INOCA
1o
74 RRSUA
9
ND*3 V I I I
b9 JCPSA
50
71 JSSC6
3
lO SPHC&
14
?u 4C8CA
26
70 ACSAA
24
71 SPHDA
15
71SPHCA
15
74 MR6UA
9
74 Z4AC4 4O3
14 ACOCA
30
ND+J IX
TO ACSAA
24
71SPHCA
15
73 6C$AA
27
74 ZAAC& 403
73 ACSA&
ZI
73 ~ c s ~
27
74 AHH|A
5q
NO~$ X l l
7Z JSSCO
4
N[*2 Iv
bL J A P [ A
32
65 8SCFA 1965
NZ+2 t v SQ
b6 [NOCA
5
NI+2 v
67 8APCA
15
NI*2 Vl
?* &HNIA
5e
74 ACBCA
30
68 ZAACA 358
67 8APC&
15
70 ACOCA
28
70 ZAACA 3T8
70 JSSC5
2
7 t PHSSA 438
70 REF I
b4 ACCRA
t?
13 ACOCA
29
63 Z K K ~
11o
?4 JCPS&
61
73 JCRL8
3
?3 &C8C6
29
NI*~ vi
LS
?4 ZSAC4
405
71CH0C~
2tZ
NI*3 V]
NS
54 JACS&
76
Nle4 Vl
L$
&? STGBA
~
74 J[NCA
3
No+2 V l
?4 [NOCA
73
NP*J v [
68 J I N C ~ "
3O
NP*~ Vi
6? iNUC4
J
14 CJCH4
52
NPt6 Vl
105
354?
?qb
15~
T2
3
045 $14 NSb O26
LI N03 00
I V . YS) NO O~
8X ~8 O4
N8 P 05
NA3 N8 04
454
89
1610
&?3
N6Z N04 o l t
NAI3 N095 09~
I N H 4 ) 3 NO o [ c 2 0 4 1 3 . H 2
NB2 05
~
o
NO [2
NO e L 2 ,
NO ~R2
922 0A2 NO RO 06
1661 NO AL3 04 012
86
450
518
484
340&
b3&
ggl
129
I
4&8
N02 HO3 012
NO V 04
K NO U2 O8
NO2 T I 2 o?
N04 RE2 Oil
NO2 H 0b
N04 ~3 015
NO P5 014
~3 VS V IN0 F31
ND P3 09
2969
g91
2441
I
2813
29?3
12T7
NO2 {C2 0 4 | $ * I 0 . $ H 2
0
N04 M3 015
NO2 IC3 H2 O 4 ) 3 . 6 H 2 o
R3 V$ v (NO F31
N02 (C3 H2 0 4 1 3 . 6 H 2 o
NO 0~ C O3
N04 HG2 T I 3 $14 022
IL NO A~ o ~
685 NI CR2 04
1085 SPINEL$
1200 N]
[OPN)2
47 N I 2 P2 07
N i 2 $I 04
NI IPV N 0 J 6 (B F 4 i 2
N[ SE 04
H I 2 P2 Q7
R8 NI F3
$R2 N[ TE 06
RO N[ F3
NI (O H)Z
NI2 51 04
1461 N| IC5 H? 0 2 1 2 . 2 H 2 o
2T41Ni
$1F6.6H2 0
291NI
IH c o O ) 2 * Z H 2 O
852 NI C4 0 4 . Z H 2 0
1 8 1 N I IC5 H7 O 2 ) 2 . ( C 2 N 5 0
2304 H I 3 VZ 08
485
1686
|25
47
1464
12g
416
125
H)2
167 ~2 N* NI F6
2163 H0 N[ O3
14q9 N& NI 02
l R3 VS ~61FLOORIOE$1
L561 K2 N]
2233 EIT[NA?EO
823 NP CL3
32? ESTiNATEO
2175 R~ VS v
a3 vs v 186Z s~ NP O6)
OH-I II
71 6~X14
OH-I I[[
~ I 6H~16
oH-I
56 t155 R 0 6 . 6 Feo4 513 012 F 0 H,
R[OH-IIIRIF*Z)~.04
56 I I S 5
~6.6
F E . 4 S13 012 F 0 H.
R(OH-I)=8(F-I|+.04
Iv
OH-I Vl
RIOH-I)IRIF*11*.04
05.4 Vl
6q JC0HA
I T 45q 05 02
?0 ACSAA
24 125 05 02
OS+5 V l
71 ~CSI4 1 9 7 [ 2760 os F5
?4 SSCOA
14 357 R3 V$ V ICU2 O52 071
56 JINCA
2
79 K 05 F6
0S'6 Vl
~ VS V IPE~OVSKI?~Sl
o$+? v l
R3 V$ v IPEROV$~iTE$1
05+6 I v
66 ACSA&
20
395 o$ 04
7 ) ACOCA
29 1703 os o4
65 ~ c c ~
19 157 os o4
7 1 J C S I & 1971 1857 0 5 1 8 . ) - o
P*5
Iv
t z ACaC&
20 z083 co2 P2 07
60 CJCH6
46 6O5 CU2 PZ o?
65 C~¢H4
43 113~ nGz p z o7
60 IN0C~
7 1345 C42 P2 o?
71 8SCF~ I v 7 1 426 ZR P2 o?
?o ~C0CA
26 16Z6 H~ p 0 4 . 1 / Z HZ O
?1 ~C0CA
27 2 9 t N4Z H2 PZ 0 7 . 6 H 2 0
?~ NJNN& [ V ? I
241SR AL3 {P 0412 I0 H ) 5 * H 2 o
69 z x ~ x ~
130
148 K z ~ z I p O4)3
?1AC0C6
27 2124 N43 P 0 4 . 1 2 H 2 o
60 ~C$A6
22 18ZZ NA LR2 P~ 012
b8 2KKKA 127
2 1 A L 3 PZ 0 8 . $ H 2 o
68 ClWYA
68 290 Li FE P 04
lO &C6CA
26 1826 H3 p 04
?2 ANNIA
$?
45 NN,65 FE,35 P O~
tZ AG6GA
Z§ l g ~ $ | q H ~ | ~ M P U4
73 ACS¢A
Z~ 14t LU P O4
I I ACSCA
~ Z~4T CA {H2 p 0 4 ) 2 . H 2 U
?3 AC§¢A
ZZgZ A L P 0 4 . 2 H 2 o
?L ACSAA
25 512 K H5 [P 0412
pe$?OvJ$$CB
1 120 ZNZ P2 07
6T JACSA
09 2268
6? Jac$a
o~ 227o
P*5
Vl
71ZA~C~
380
5[
?2 CCJO& l g T 2
676
7J ACAC3
29 266
~A*~ vl
67 INUCA
3 3Z?
74 CJCH4
52 Z [ 7 5
P~+$ V l
z [ ac8c8
27 731
P~*5 I x
67 JC$1A l g 6 T 1429
PBe~ IV
PY
63 ZXKK~
126 98
PI*2 Vl
C23 H29 US p
CzJ HZ9 05 P
p eL5
ET3 N H IC6 H4 0 2 ) 3 P
C6LCULAtEO
R IP&+41
R3 v$ v
~ P6 O3
K2 PA F7
p$ $1 oJ
1o 4CAC8
PB*2 V I I
9 ZKKK&
4 &CCRA
PB*2 v i i i
t l SPHCA
64 ACGRA
?3 CJCH4
?2 HROUA
p o * z IX
67 ACCRA
73 GJGHA
?~ ZKKKA
?~ CJGHA
P8*Z x
70 ZKKKA
P8.2 Xl[
51 6CCR~
26
HALIDES
501 p e z 03
09
15 728 P8 w 04
17 1539 PB P2 06
51
?o P02 V2 O?
7 1025 BI t l T & N A T E S
22
744 PO F2
51
TO P02 V 2 0 t
139 215 P8 c 03
S2 2 7 0 1 P U V2 06
228 P03 P2 08
1o3 p8 IN 0312
R3 VS v IOA $ 041
70 ZKKKA 132 220 P83 P2 00
71 INOC~
10 1264 K2 P8 CU IN 0 2 1 6
P 6 " 4 IV
72 JCSIA 1972 2448 R3 VS V INA4 P8 041
po** v
7o ZAaC6 375 255 RS2 po 03
PB$4 v I
70 6CAC8
26 501 P02 03
65 JINCA
27 150g PB3 04
74 CJCHA
52 2175 ~3 V5 v
po.~ viii
60 N~ou~
3
153 P8 02
PO*2 I v SQ
67 INOCA
6 730 P0 lob H5 OH3 CHIC 01212
60 J $ [ C A
g
166 po I I C 6 H 5 ) 2 CH C2 0212
po*~ vI
68 NRBUA
3 699 R3 V$ V INZ P02 071
73 INOCA
12 1726 XE PO F I [
6 1 J C $ I A l g 6 1 3?ze K2 po F6
PH*~ vI
PH*$ V I I I
74 2AACA 403
I R3 VS v IPX F31
PH*3 I x
74 ZA4C4 403
I 03 VS V IPH F3i
PO+4 v l
74 OJCHA
52 2175 R3 v$ v
POt4 v i i i
R3 VS v ( F L U g R [ T E I
PR*J V l
t l MRBUA
6 545 R3 V$ v (PR2 N03 0121
P a * 3 VIII
70 SPHCA
1~
28 PR2 U2 09
74 ZAACA 403
I R3 V$ v (PR F 3 |
P 8 . 3 IX
7o SPHCA
15
28 PRZ U2 og
5g ZKKKA 112
362 PR IC2 MS S 0 4 1 3 . g H 2 0
74 ZAAC4 403
I R) v$ v IPR F ) i
e~*4 Vl
72 ACBCA
20 956 OA PR 03
?~ ACBC6
31 971 ~ R t 0Z2
73 JSSC8
U 3 3 1 R IPR941
74 CJCHA
52 2175 R3 VS V
PT*2 I V SQ
72 REF 5
PC3 C0 06
Pt*4 vI
89 JINCA
31 3803 PY 02
R3 v$ v 1N2 p l 2 o71
?4 CJCHA
52 2175 R3 V5 v
Pt*5 Vl
67 STBGA
3
I R3 v$ v (FLUORIDES)
67 J C $ I A 1967 478 XE PT F I I
pu*~ vt
61 [NUCA
3 327 R I P U * J )
75 JINCA
37 743 R (PU~31
PU*4 VI
b7 INUCA
J 32? R IPU*41
73 JS5C6
8 331R (PU*4)
t ~ CJCHA
52 2175 R3 VS v
PU+6 V l
R3 VS v tSA2 SR PU O61
ao+1Vl
lO 244c~
3/5
255 R02 P6 O3
~ o * z ix
74 ACSCA
30 L640 R02 s 04
RS+I x l
7~ ACSCA
30 1640 R02 s o*
RO+I x x i
70 ACSCA
26 1464 R8 N[ F3
?o J$$C6
2 416 R9 N I F3
70 JS$CB
2 562 86 NI F3
R O - I XXV
65 ACC86
19 2O5 ~8 u 02 IN 0312
aE+4 v i
4 CJCH~
RE+5 v |
70 ACSA~
uNPu2
O8 ACSCA
REe6 V l
t 5 JS$C6
1o
3
2175 R t vs v
24 3406 N04 RE2 011
co2 aE2 o?
24 6T4 Re CL5
13
77 BA2 HN RE 05
R3 V$ V IPEROVIRITE$1
R V$ VALENCE
~E*? IV
b8 ACIEA
? 295 RE2 o? IO H212
7 1 J C $ 1 6 1971 1857 R E I * 7 ) - o
70 CJCH6
40 219 IRE2 I N - C 4 H7 02121 (RE 0 4 | 2
kE÷Z v l
68 ACiEA
7 295 RE2 07 {H2 012
l o 4C8CA
RH*~ V l
?3 INOC6
Ru+3 v i
CHALCOGENIDES
(cont.)
120 213 P8 CAZ $ | 3
17 1539 Pe P2 06
132
AND
26 1876 R,2 o )
12 2640 ~N F5
R3 vs v I L 6 Ru 03i
RU*4 V l
?o ac$64
24
l l 6 RU o z
74 4 c o c ,
30 143~ N413-X~ ~U4 0~
7~ CJCH4
5~ 2175 R3 vs v
RU*5 v i
?I J C $ [ A IVTI 2789 RU F$
REF 7
k3 VS V IC02 RU2 o ? )
I ) INOC~
. I Z l / I T X~ RU F I I
R U * t IV
S4 J6CS~
76 3317 ~ RU O4
au+u Iv
67 A~$A6
21
T37 RU 04
S+6 Iv
GO 6C0CA
24 508 C0 3 04.3 H2 U
7o ZKKK&
132
99 PB2 S 05
?0 8UFC6
q3 LgO FE $ 04 ALPHA
?o BUFC4
~3
1e5 FE S 04 0 H
70 6$CFA lg?O 4Z43 n G $ 04 N2 0
71 6C0C6
27 ZTZ N H4 N $ o4
70 NJNIA
113
I NN? NA~2 IS 0 4 ) | 3 . 1 5 H 2
6~ ~CCaA
[9
664 NN $ O4
,i 6c566
~s 3 2 1 3 N A s H 0 5 4 ° 4 N z °
?z 6cuc6
28 864 SN
12 N~IU6
Z36
g5 C4 $ 0 4 . 2 H 2 o
72 6C6C4
26 284S x z s O4
T3 JSTCA
14 499 TL2 $ 04
14 ACUC~
30 g21 C6 $ O4.2N2 o
74 NJHIA
121 208 FE2 IS 0413
S*6 v t
13 ACA¢~
~9 265 ¢4LCU~6tEO
o
$0.J Iv
?o A¢$AA
24
320 38 P 04
$0.5 Vl
?o 4 n n t 4
5s 1480 NN? $8 AS 012
71JCSl&
I V T l 942 AS $8 f 8
1 1 J G S I A 1911 2318 8R2 $83 F16
74 JC$$8
q 345 Na 58 03
s~*J Vl
68 CJCHA
46 | 4 4 6 S C 2 0 J
60 ARKE4
29
)43 scz oJ
U~PU4
5CZ ~ I Z 01
73 5PHCA
17 749 SG2 $12 o?
t 3 INOC~
12 927 SC IC5 H? 0 2 ) 3
73 ACBCA
2V 2615 NA SG 512 06
14 INOCA
13 IS8 SC IC? N5 0 2 ) 3
73 ACSAA
2? 2 8 4 1 S C U H IC3 H2 0 4 1 . 2 H 2 o
69 5PHDA
14
9 NA3 SC 512 O7
sc*J rill
14 INUCA
tO
1 3 t SC H ICY H5 0 2 i 4
T2 ACSA4
25 1337 SG2 (G2 0 6 1 3 . b ~ I 0
74 INOCA
13 1a06 H sc I £ 1 N3 0214
74 :NOCA
13 ] e e o .
sc I c ? . s o z i 4
$E*O I V
be ZAACA 358
125 NN S£ 0 4 , CO $Z 0 4 * N i $ [ 04
b l JGSIA
2]?
968 H2 SE 04
70 ACOCA
26 436 NA2 SE 04
?o ACeCA
26 1451KZ SE 04
t o ZAACA 37V 20~ N I SE 0 4 . 6 H 2 0
?2 4C8CA
28 204~ K~ 5E 04
~9 AC8C4
as
[ 9 C U IN . 3 1 4 S~ 04
?1J$cIA
1971 1857 S e l * 6 1 - o
Sl*4 IV
63 NAT~A
50
9 1 F E 2 $1 04
;~ ZKaK4
137
86 MG2 SI 04
6 I 6CCR4
14 835 NG3 AL2 $13 012
1o ZKKKA 132
I RN5 10 H i 2 S12 00
$8 ACCRA
II
437 CA3 AL2 S i 3 012 I G R O S S U L A R I T ( I
71 4 N N I 6
56
I V 3 CUZ C&Z $13 0 1 0 . 2 N 2 o
?1 5PHEA
15 926 ~A Gb $1 13~
71SPHCA
15 806 V2 5Z OS
71NATWA
58 218 EU2 51 o~
7o P E P l 6
3
l b l C02 $ I 04
70 ACOCA
25
105 043 S [ 4 Nab 026
71 4 c 8 c 4
27
747 CA2 $ i 0 4 . C A CL2
7| AGBCA
27
848 C42 $I 04
71 &NNIA
56 1222 N A . | 6 K . 8 4 CA4 1518 0 2 0 1 F . 8 H 2 0
71ANNIA
56 1155 HGS*b F E . 4 $13 0 1 2 . ~
F 0 N
69 NS4PA
2
31 L ; N $12 0 6 , H A M S I 2 ~6
CA NG $12 06
69 ~S4PA
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95 F E 6 * I H N * I NG*8 C A * I $10
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101 L 1 2 . 4 N A . I H G I Z . 9 5 1 1 5 . 7
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132 288 C&5 $ I 2 0 t
IC 0312
71ACBC&
27 2269 NA2 $ l U J . 6 N 2 0
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14 z o z l 8 e z s i o~
72 4CBC&
28 1899 AL2 BE3 S i 6 018
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30 2434 112 BE 51 Ok.
IX*4 V[
62 NA[WA
49 34S $1 02
69 CJCH6
47 3859 CU $ l F b * 4 N 2 D
?o ACBCA
26 233 SI P2 o?
71ACOCA
27 2133 SI 02
? l ACSCA
27
594 CA3 S 1 1 0 H I 6 . | Z H 2 D . $ 0 4 . C 0 3
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2g 2 7 4 1 N $i F b . b H 2 o
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29 2748 C0 $ 1 F b * b H 2 0
14 CJCHA
52 2115 63 V5 V
SH*2 v l I
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SN*3 V I i i
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15 214 $M2 $12 o?
14 ZNOC4
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70 asses
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52 217~ R3 V$ v
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379
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SR*Z V l l
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28 3668 SRIO IP 0416 I 0 H ) 2
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SR*2 IX
69 4C,C4
to ZKKX4
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72 ACSCA
14 SP,C6
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70 Z&AC4
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73 ACBCA
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74 PRVBA
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be RCBCA
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70 Z K • K •
71 JESTS
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70 INOCA
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13 CJCHA
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73 JSSCB
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73 CJCHA
73 ACBCA
73 ACBCA
73 CJCHA
757
(cont.)
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27
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3
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1
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51
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43
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1
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49
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29
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27
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371
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52
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26
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53
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27
73 ACSAA
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56
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b 9 NOCMB 100 1809 AGE TE 0 2 l 0 H I 4
71 B U F C •
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20
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20
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30
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6 9 ACBCA
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T 17TT YIC6HSCOCHCOCH3J~.H20
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14 ZAACA
IX
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YB*Z V l
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YB*Z V I I
74 ZAACA
71ZAAC•
Y6e¢ v i i i
T l ZAACA
YB,J vl
7u SPHCA
10 •CBCA
70 ZAACA
74 ACBCA
YB'~ Vll
70 SPHCA
~
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O9 INUCA
YBe3 V I I I
T0 INOCA
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Z3
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YB*~ IX
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2658
306
478
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2294
ZR (M AS 0 4 I Z . M Z
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• 2 ZRZ OS
~ • ZR2 P 3 0 l Z
L I Z ZR F6
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243
1944
250
ZRZ (S 0 4 1 4 I H 2 O I B . 6 H 2
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0
0
O
R.M.G.MVC•0FF,CRYSTAL STRUCTURES,WILEY,
N.Y.eI96B
H.BARNIGHAUSEN ET A L . , P R O C . 1 0 7 H R . E .
RES.CONF.CAREEREE,AR|ZII973)P.490
C.BRANOLEeH.STEiNFIN•.PROC.7TH
R.E.
RES.CONF.eCORONAOO,CAL.OCT 2 8 , 1 9 6 §
R.D.SHANNON,U.S.PAT.3&bSIBLtNAYIb.1972
W.H.BAUR,NITROGEN,HANOBOOK OF GEUCHEM.
SPRINGER-VERLAG,N.Y.1974
A.M.SLEIGHTtU.S.PAT.38&9544,NOV
19,1974
H.BARNIGHAUSEN,PERSONAL COMMUNICATION
A.M.SLEIGMTePERSONAL COMMUNICATION
C.C•LVOePERSONAL COMMUNICATION
C . T . P R E M I T T , P E R S O N A L COMMUNICATION
M . H . B A U R , P E R S O N A L COMMUNICATION
REF 7
UNPUI
UNPU2
UNPU3
UNPU4
UNPUS
I R3 VS V { F L U O R I O E S I
IO H ) 2 . 2 H 2
1147 ZN2 PZ 0 7
127 ZN M 0 4
1 2 0 ZNZ P2 0 7
3 0 S b Z N ) V2 OB
1 1 k 7 ZN4 AS2 0 8 IO H I 2 . 2 H Z
2741Zfl
S| Fb.6H2 O
1 5 4 l ZN S 0 3 . 2 I / Z M Z 0
G.
REF S
REF b
432 V P 05
2 6 7 5 V6 0 1 3
3619 NG V2 06
2621V
P O3 ALPHA
2 1 8 4 K3 V OZ C2 O 4 . 3 H Z
1743 GU VZ 0 6
3
25
50
$1
52
29
0
KEF |
REF 4
4 1119 vz 05
8
~O9 Li V2 0 5
30 2 6 4 4 V3 0 7
30 2 4 9 1 H G Z V2 0 T
29
S&7 HG2 V2 0 7
270
9SZ CA VZ 0 6
1 2 0 ZN2 P2 0 7
I 0 0 4 ZNZ V2 0 7
1 1 4 7 ZN~ AS2 0 8
REF 2
REF 3
3~ 16~BN, v 0 3
V*5
Y*~
B23 R l U * 3 !
26
3B I N H k ) 4
Z9 IV 4Z U e L 4
~,,CRCA
28 3609 U 03
KQ| ZN FEZ 0 4
1541ZN
$ 03.2 1/2H2
2 6 5 . ZN 10PMI2
ACACB
ACOCA
• CCRA
ACIEA
ACSAA
ADCSA
• MMIA
ANCPA
AR•EA
BAPCA
BCSJA
8SCFA
OUFCA
CANIA
CCACA
CCJDA
CHOBA
CHOIR
CHPLB
CIMYA
CJCHA
CSCMC
CZYPA
DANK•
HCACA
ICHAA
INOC•
|NOMA
INUC•
iVNMA
J•CSA
JACG•
JACTA
JAPIA
JCNLB
JCOMA
JCPSA
JCSIA
JCSPA
JESUA
JIHCA
JMOSA
JNBAA
J0P~A
JPCHA
JPCS•
JSbCS
JSTCA
JUPSA
HNLHB
H0CMB
HRBUA
MSAPA
NATUA
NATMA
NJMIA
NJMMA
PEPIA
PHSSA
PlS•A
PISUA
PRLAA
PRVAA
PRVBA
p~r~VA
RICPB
RVCMA
SCIEA
5PHCA
SPHOA
SSCO•
STBGA
TPSU•
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UNPUI
ZAAL&
E. BR0~N, PH.0. THESIS, VIRGINIA
POLYTECH.INST.,UNIV.MICROFILNS,TE-49B
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RECL TRAV. C H I N * PAVS-BAS
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SCIENCE
SOVIET PHYS. CRYSTALLOGR.
SOVIET PHYS. OOKL.
SOLID ST•TE CO"MUM.
STRUCT.
AMO BOND.
;RAMS. F A • • O A Y s a c . .
TSCHERMAKS M I N E R . PETROGR. M I T T .
I U , P U B L I S H E 0 REFEREMGE)
Z . •NORG. • L L G . CHEM.
Z•~R• Z. KRISTALLOGR. MINER.
ZEPY• ~ . P . v S .
ZE~BA
. NArURF.
Z S T • I ZM. STRUKT. • H I M ,
758
REVISED EFFECTIVE
I O N I C R A D I I IN H A L I D E S
compounds to be slightly larger than those of the E u 2 +
compounds. This difference was assumed to exist for
all Sr z+ and Eu 2+ coordinations. Because compounds
of Am 2+ and Sr 2+ have similar cell volumes, the radius
of Am 2+ was made equal to that of Sr 2+
Wolfe & Newnham (1969) studied Bi4_xRExTi3012
and concluded that Bi3÷ and La 3+ have nearly equal
radii. From a study of BiTaO4 Sleight & Jones (1975)
have concluded that although Bia + and La 3÷ have essentially equal radii, the size of Bi3÷ depends on the
degree of the 6s 2 lone-pair character. When BiTaO4
transforms from a structure where the lone-pair character is dominant to the LaTaO4 structure, it undergoes
a volume reduction. Table 3 shows a comparison of
isotypic Bia+ and La a+ compounds where the lone-pair
character of Bi3+ is (1) constrained and (2) dominant.
Bi pyrochlores such as Bi2Ru207, Bi2Ir207 and Bi2Pt207
were omitted from the table because no corresponding
La pyrochlore exists, but they have unit-cell volumes
close to those of the Sm or Nd pyrochlores and thus
have smaller volumes than those of La. When Bi3÷ is
forced into high symmetry, a Bi 3+ compound has a
smaller volume than that of La 3+, but when the lonepair character is dominant, the Bi a+ compound is distorted and Bi 3÷ and La a+ compounds have approximately equal volumes. This behavior was also noted
in the highly symmetric garnet structure where the
hypothetical BiaFesOlz was estimated to have cell
dimensions between those of the hypothetical
NdaFesO12 and Pr3FesO12 (Geller, Williams, Espinosa,
Sherwood & Gilleo, 1963). For practical purposes,
Bi a+ is listed as slightly smaller than La 3+ but this
dependence on lone-pair character must be kept in
mind when comparing the volumes of Bi a + and La a+
compounds. Similar behavior may also exist for Pb 2+
and Sr 2+, but this relationship was not investigated.
Table 3. Cell volumes of isotypic Bi 3+ and La 3+
compounds
(a) Lone pair character of Bi a+ constrained
Compound
BiLi(MoO4)2
LaLi(MoOa)z
BiNa(MoO4)z
LaNa(MoO4)2
BiOF
LaOF
Cell volume
314.7
328.7
320-5
332.1
87.6
97.7
Ratio
0.96
110.7
116.8
123.8
126.4
293-0
304.7
0.95
BiOCI
LaOC1
BiOBr
LaOBr
BiPO4
LaPO4
(b) Lone pair character of Bi a +
BizMoO6
LazMoO6
BiFeO3
LaFeO3
Bi2Sn207
La2SnzO7
dominant
268.5 ( × 8)
267.3
62.49 ( x 6)
60.77 ( x 4)
1219.9 ( x 8)
1225.3
AND CHALCOGENIDES
A similar study of relative cell volumes of isotypic
compounds involving the pairs Cu÷-Li +, Ag+-Na +,
TI+-Rb ÷, and pb2+-Sr 2÷ was used to obtain more
reliable estimates of the radii of Cu +, Ag +, TI ÷, and
Pb 2÷ (Shannon & Gumerman, 1975).
The nature of Sn 2÷, NH~-, and H - made it impossible to define their ionic radii. The coordination of
Sn 2÷ by oxygen or fluorine is always extremely irregular,* leading to average distances which depend
on the degree of distortion. Since this distortion varies
widely from one compound to another, it is not meaningful to define an ionic radius.
Khan & Baur (1972) derived an apparent radius of
the NH4+ ion by analyzing the N - O distances in a large
number of ammonium salts. They concluded that
NH + has an octahedral radius of 1.61 A, between that
of Rb ÷ (1.52 A) and Cs ÷ (1.67 A). Alternatively, cell
volumes of NH~ and Rb ÷ fluorides, chlorides,
bromides, iodides and oxides may be compared. This
leads to the conclusion that N H ~ is not significantly
different in size from Rb ÷. No explanation is offered
for this inconsistency and therefore the radius of NH~
is not included.
The radius of the hydride ion, H - , has been the
subject of some controversy. A number of different
radii have been proposed: 2.08 (Pauling, 1960); 1.40
(Gibb, 1962); and 1.53 A (Morris & Reed, 1965). Gibb
studied interatomic distances in many hydrides and
concluded that good agreement between observed and
calculated distances could be obtained using r(V~H -) =
1.40 A if corrected for cation and anion coordination.
The value of r(IVH -) was taken to be 1.22 A.
Morris & Reed (1965) concluded that differences in
observed distances in hydrides were caused by the
large H - polarizability. Because of such wide variations in the apparent H - radius, it was omitted. However, an explanation for the variations based on covalence differences will be discussed later.
* Although cell dimensions of Sn2M207 pyrochlores were
used in SP 69 to derive r(VmSn2+), Stewart, Knop, Meads &
Parker (1973) and Birchall & Sleight (1975) recently found that
the pyrochlore A site in Sn2Ta207 is not fully occupied. Thus,
even this example of apparently regular Sn 2÷ polyhedra is not
valid.
0"97
I
.90
0.90
.80
I
I
I
I
V
0.98
0.96
.70
1-00
.50
1"03
,40
1"00
~---------"~ To "91'
-
I
+2
r
I
I
4"5
+4
+5
OXIDATION STATE
Fig. 1. Effective ionic radius (,~)
vs
I
.+6
+7
oxidation state.
•
R.
D.
SHANNON
Results and discussion
In Table 1 two sets of radii are included. The first is a
set of traditional radii based on r(V'Oz-) = 1.40 A. The
2.oo1---~--~
. . . .
I
r -
I
--
I
I
1
I
1.901
759
other set is based on r(WO z-) = 1.26 and r(V~F-)= 1.19
A,, and corresponds to crystal radii as defined by Fumi
& Tosi (1964). As pointed out in SP 69, crystal radii
differ from traditional radii only by a constant factor
1.70
I
J
. 1.60
1.50
1.40
1.30
,
. . . . .
1.50
Rbd
1.70
,
1.60
Cs -
~iaoi
,
1.40
1.30
1.20
1.10
r
1.00
.90
1.20
.80
~
1.10
Y0
1.00
.60
•
.90
Li +
Ni2-~
.50
80
Be +
.4O
.70
.30
.60
.20
.50~
I
4
I
I
I
I
5
6
7
8
CN
I
I
9
10
ill
12
I
.10
13
2
CN
(a)
I
I
1
•
1.20
(b)
I
.
I
I
.
- ~Bi3+
. . . .
,
1.10
J
1.00
•
j .
I
i
I
I
la3F+~]
~.~TL3÷
1.30
.90
.80
p 3+
.70
.60
.50
A0
.30
_ B
°/ ~
~
3
Go3+
1.10
~_---~-Tb 3+
AI 3+
~Tm
1.00
-
Er
..
~""~'~"Lu-'yb3÷
-.
.90
+
.20
Zi
.10
=
.7
0
CN
I
7
I
8
9
CN
(c)
F i g . 2.
I
6
.
(d)
(a)-(e)
Effective ionic radius ( • )
vs C N
for some common cations.
1
10
!i
]
12
760
REVISED EFFECTIVE
I
I
t
I
I
I O N I C R A D I I IN H A L I D E S
p.4+
VXOs6+, VlRe6+, and V1Os7+. The symbol A means that
Ahrens (1952) ionic radius was used whereas P means
Pauling's (1960) crystal radius was used. The symbol
M means that the radius was derived from a comp o u n d having metallic conductivity. Distances calculated from these radii may be too small for use in
compounds having localized electrons. (See discussion
Bk 4+
Effects of electron delocalization.)
I
I
I
'1
Th 4÷
1.20
i.I0
!.00
~
.90
:Hf4 +
.80
Ti 4+
~/4+
.70
.60
/
.50
.40
.30
y
AND CHALCOGENIDES
Ge4+
Si +
.20
In addition, the sources of the radii are indicated
in Table 2.
Fig. 2(a)-(e) shows that r - C N plots are reasonably
regular. Notable exceptions are IVNa+, VNa+, and
~VK+. It is apparent that N a - O and K - O distances do
not decrease as much as anticipated from the r - C N
curve* when the CN falls below six. Typical distances
and corresponding radii in Table 4 show that N a - O
distances in four-coordination are only slightly less
than in six-coordination. The reduction in interatomic
distances is caused primarily by the decreased repulsive
forces due to fewer ligands according to the expression
of Pauling (1960):
Rc.<c~_[ANacl Bc,c~_]~I('-~)
.10
RNaCl
CN
(e)
Fig. 2. (cont.)
of 0.14 ~ . Although their inclusion in Table 1 may seem
superfluous, it is felt that crystal radii correspond more
closely to the physical size of ions in a solid. They
should be used, for example, in discussions of closest
packing of spheres, structure field maps (Muller &
Roy, 1974), and diffusion in solids (Flygare & Huggins,
1973). Traditional radii have been retained because of
their familiarity to crystal chemists and physicists.
They will probably continue to be used for comparison
of unit-cell volumes and interatomic distances. In the
table, the ion is followed by electron configuration
(EC), coordination number (CN), spin state (SP),
crystal radius (CR), and effective ionic radius (IR),
and in the last column, a symbol indicating the derivation of the radii and their reliability. Those with a
question mark are doubtful because of: uncertainty in
CN, or deviation from radii vs CN, or radii v s valence
plots. Where at least five structural determinations
resulted in radii differing by no more than + 0.01 A,
the values are marked with an asterisk.
When the choice of a radius was influenced by any
of the various correlations described earlier, it is indicated by the following: R - from r 3 vs unit cell volume
plots; C - calculated from bond length-bond strength
equations; E - estimated from one or more plots of r
v s valence, r v s CN, and r vs cell volume. E implies poor
or nonexistent structural data. Radii in this category
include VIFeZ+LS, WMn2+LS, vlcIa+LS, vIV2+,
VINo2+ ' VINia+HS, wit3+, WMo 3+, VITa3+, Wpaa+,
VlTa4+ ' IVpb4+ ' V~IrS+' WOsS+ ' WReS+, WpuS+, WBiS+,
L Acscl BNaCl
where R = i n t e r a t o m i c distance, A = M a d e l u n g constant, B = t h e cation CN and n = Born repulsion coefficient. It appears that this equation is not valid for
four-coordinated Na ÷ or K +.
There are a few small irregularities in r - C N plots
probably caused by poor or insufficient data, e.g.
curves for TI 3+ vs y3+. The differences in slopes of
Ti 4+ VS C r 4+ and V s + vs As 5÷ are probably caused by
Ti4+-O and V5+-O octahedra being generally more
distorted, which leads to greater average interatomic
distances.
It is also interesting to compare distances in square
planar coordination v e r s u s tetrahedral coordination.
Radii of square planar Cu 2÷ and Ag ÷ are equal to or
slightly greater than corresponding tetrahedral radii,
consistent with the trend anticipated from anion
* Extrapolation of the Na curve gives r(~VNa÷)=0-90 A.
\
Ul S b . . . . . .
"
-' .'!ll,
[ \ , %.
i\",
(.9
Z
"'
n,,
.~%
~
........
I- - -t~ --~,,
',
ci
I
I
!
i
7
!I
ii
I",,:,
I
I
I
i
I
_1
I
°
"' s,
.......
~
~
"__'__i
Ti- - Ti ~ I i
',
- ]l , ~
I
Rb R! R2
R,
AVERAGE INTERATOMIC DISTANCE , R
Fig. 3. Typical bond length vs bond strength plot.
R. D. S H A N N O N
repulsion effects. A similar comparison with Fe 2+ and
Ni 2+ cannot be made because of electron distribution
changes from tetrahedral to square planar coordination.
I
i
2.05
,
-v'r NbS+
2.03
2.02
2.01
~¢~)
2.00
1.99
1.97
1.96
1.95
ii
1.94
i
•002
[
i
.004 .006 .008
i
i
I
.010 .012 .014 .016
Fig. 4. Mean NbS+-O b o n d length v s distortion. Vertical bars
represent average e.s.d.'s quoted by the authors. Solid
circles represent m o r e accurate data.
r
2.o0
i
i
"v'r M06 +
1:98
1.97
1.95
1.94
J
1.911
1.90
R (/~,)
2.40
2.37
2.36
2.39
Mean 2-38
2.38
2-37
2"39
2.48
2.44
2.41
2-415
2.45
2-460
2.375
2-406
2.42
r (/~)
Reference
1-02
0.99
1.00
0.99
1.00
60 A C C R A 13
57 A C C R A 10
69 Z A A C A 4 0 9
1.00
1.01
1-02
1.10
1.06
1.04
1.05
1.10
1-09
1.025
1.046
1.05
74
65
70
64
65
67
61
67
63
59
75
A C B C A 30
A C C R A 19
A C S A A 24
A C C R A 17
A C C R A 18
S C I E A 154
A C C R A 14
A C C R A 22
A C C R A 16
A C C R A 12
A C B C A 31
263
462
69
1872
561
1287
672
818
1453
555
182
1233
526
19
Additivity of radii to give mean interatomic distances
is not so important to the synthetic chemist who is
primarily interested in ionic radii for predicting substitution in crystal structures. Crystallographers and
physicists, however, are concerned with comparing
calculated and experimental interatomic distances and
predicting distances, e.g. for distance least-squares
(DLS) structure refinements (Baur, 1972; Tillmanns,
Gebert & Baur, 1973; Dempsey & Strens, 1975). The
effective ionic radii in Table 1 can be used to reproduce
moderately well most average interatomic distances in
oxides and fluorides. However, certain deviations do
occur. Some of these are unexplained but others can
be attributed to (1) polyhedral distortion, (2) covalence,
(3) partial occupancy of cation sites, or (4) electron
delocalization.
R=1.920 + 3 . 7 3 A
1.99
1.93
Compound
(a) lVNa+
Na20
NasP3010
NaOH.H20
Na6ZnO4
Factors affecting mean interatomic distances
1.9e
2.01
Table 4. lnteratomic distances in some compounds
containing tetrahedral and octahedral Na +
(b) VlNa+
Na2WO4
NaC6OTH7
Na4Sn2GeaO12(OH)a
Na2P2OT. 10H20
NaHCO3
Na2B406(OH)2.3H20
Na4P4OI2.4H20
NaAI(SO4)2.12H20
NaB(OH)4.2H20
N a U acetate
CloHI3NsNaO6P.6H20
Mean
R= 1.976 + 6.45 A
2.04
761
~
.002
,
.004
F i g . 5. M e a n
~
,
.006 .O08
M06+-O
v
.010
Z~
bond
,
.012
~
.014
,
.016
.018
l e n g t h vs d i s t o r t i o n .
1. Polyhedral distortion
To see the effects of polyhedral distortion consider
the relationship between bond length (R) and Pauling
bond strength (s) (Brown & Shannon, 1973). The analytical expression S=So(R/Ro) -N, where So is an ideal
bond strength associated with R0, and R0 and N are
fitted parameters, was evaluated for cation-oxygen
pairs for the first three rows of the periodic table. Using
these relationships, the sums of bond strengths about
cations and anions were found to equal the valences
with a mean deviation of about 5 %. Accepting the
approximate validity of Pauling's second rule, p = ~s
where p = valence, it is possible to derive the effects of
distortion of various polyhedra on their mean bond
distances. Fig. 3 shows a typical R-s curve. An undistorted octahedron results in an average bond
strength g and a mean distance/~a. A distorted octahedron with three bonds of length R= and three of
length Rb results in the same average bond strength, g,
but a mean distance Rz >/~1.
762
REVISED
EFFECTIVE
IONIC
RADII
The effects of distortion on m e a n bond lengths in
numerous polyhedra have been determined. Although
distortions in tetrahedra are not as important as in
octahedra, they can contribute to variations in m e a n
tetrahedral distances (Baur, 1974; Hawthorne, 1973).
Strongly distorted octahedra like those containing V 5+,
Cu 2+, and M n 3+ show a significant variation in m e a n
distance with distortion, A* (Brown & Shannon, 1973;
S h a n n o n & Calvo, 1973a; Shannon, G u m e r m a n &
Chenavas, 1975). Octahedra containing Mg 2+, Zn z+,
Co 2+, and Li + are generally less distorted than those
of V 5+, Cu 2+, and M n 3+ and show a less pronounced
dependence on m e a n bond length (Brown & Shannon,
1973).
The effects of distortion on m e a n bond lengths in
N b S + , O and M o 6 + - O octahedra are illustrated in
Figs. 4 and 5. Tables 5 and 6 list the data used to derive
the figures.
Table 7 lists the results of linear regression analyses
of m e a n bond length on distortion for all octahedra
studied. It is clear from Fig. 4 that undistorted N b 5+
octahedra in pyrochlores have a distinctly smaller mean
value than in compounds like NbOPO4, CaNb206, and
NaaNbO4. Most of the accurately refined molybdates
have relatively distorted octahedra. However, certain
ordered perovskites with no octahedral distortion such
as BazCaMoO6 would be expected to have much
smaller m e a n Mo6+-O distances than a typical molyb* Octahedral distortion is defined by A=~Y(R~-R/R) z
where R=average bond length and Rl=an individual bond
length.
IN HALIDES
AND
CHALCOGENIDES
date. In fact, the M o 6 + - O octahedra in Mo2(O2C6C14)6
with a very small distortion have the short mean distance of 1.919 A.
Table 7 also lists the results of regression analyses
for TaS+-O and W 6 + - O octahedra but they are only
approximate because of the scarcity of accurate structural data. Analysis of Ti4+-O octahedra was unsuccessful because of scatter in the data. Distances in
Ba6Ti17040 (Tillmanns & Baur, 1970) and BaTiO3
(Evans, 1951) deviated significantly from a linear
relation.
Relations between m e a n distance and distortion
should be particularly useful to help determine oxidation states in mixed valence compounds with such
combinations as MoS+-Mo 6+, W s + - W 6+, v a + - v 5+,
Nb4+-Nb 5+ and Mn3+-Mn 4+. Such considerations
helped rationalize M n - O distances in NaMnvO12 and
the mineral pinakiolite (Shannon, G u m e r m a n &
Chenavas, 1975).
The radii in Table 1 are generally derived for an
average degree of distortion. Thus, interatomic distances calculated from these radii m a y be inaccurate
if the distortion in a particular c o m p o u n d is much less
or greater than usual. This applies particularly to cations whose polyhedra frequently show a large distortion, e.g. MO 6+, N b s+, V 5+, Ba 2+, and the alkali ions.
2. Effects of partial occupancy of cation sites on mean
cation-anion distances
In compounds with partially occupied sites, abnormally large c a t i o n - a n i o n distances are usually
found, as expected if the anions surrounding unoc-
Table 5. Compar&on of mean octahedral N b s + - O distances with distortion
Only structures with e.s.d.'s for Nb-O distances of < 0.025 ~ were used.
Compound
HgzNb207
Cd2Nb207
NazNb4Ol i
Ba0.27Sr0.75NbzOs.Ts
NalaNbasO94
Ba3Si4Nb6026
Na13Nb3sO94
Nax3Nb35094
Na13NbasO94
NaNbO3
NalaNb35094
Na13Nb35094
Na13Nb35Og4
Na13Nb35094
LiNb308
LiNbO3
Ca2Nb207
Ca2Nb207
SbNbO4
KNbO3
NaaNbO4
CazNb207
Ca2Nb207
Na3NbOa
CaNb206
GaNbOa
/~ (/~)
1.999
1.957
1.977
1.967
1"965
1"989
1"967
1.959
1"964
1.985
1"947
1"991
1"987
1"978
1-993
2"000
1.997
2.005
2.003
2.011
2.013
2.010
.2.015
2.021
2.021
2.031
Distortion
/t = ((AR/R) 2) × 104
0
0
1
6
7
9
11
12
12
16
18
22
22
24
28
31
31
34
37
42
52
53
58
60
76
83
Reference
68 INOCA
7
72 CJCHA
50
70 JSSCB
1
61 JCPSA
48
71 JSSCB
3
70 ACBCA
26
71 JSSCB
3
71 JSSCB
3
71 JSSCB
3
69 ACBCA
25
71 JSSCB
3
71 JSSCB
3
71 JSSCB
3
71 JSSCB
3
71 ACSAA
25
66 JPCSA
27
74 JINCA
36
74 JINCA
36
65 CCJDA
1965
67 ACACA
22
74 BUFCA
97
74 JINCA
36
74 JINCA
36
74 BUFCA
97
70 AMMIA
55
65 ACACA
18
1704
3648
454
5048
89
102
89
89
89
851
89
89
89
89
3337
997
1965
1965
611
639
3
1965
1965
3
90
874
R. D. SHANNON
763
T a b l e 6. Comparison o f mean octahedral M o 6 + - O distances with distortion
Only structures with e.s.d.'s for M o - O distances of < 0.025 A were used.
Compound
Mo2(O2C6C14)6
Mo4On
Mo4On
Mo4On
Mo4On
Mo4Ot~
Mo4On
orthorhombic
monoclinic
monoclinic
orthorhombic
orthorhombic
monoclinic
(ClsHnO2)2MoO2
(NH4)6[M07024].4H20
(NH4)6[MoTOz4]. 4 H 2 0
(NH4)6[M07024].4H20
LiMoO2AsO4
(NH4)6MoaO27.4H20
HgMoO4
(NH4)6[MoTO24]. 4H20
(NH4)6[Mo7024]. 4H20 •
(NH4)6[MoTO24]. 4 H 2 0
MoOa .2H20
MoOa. 2H20
MOO3.2H20
MOO3.2H20
(NHg)5[MoOa)5(PO4) (HPO4)]. 3H20
Naa(CrMo6024H~). 8HzO
(NH4)6MoaO27.4H20
Na3CrMo6Oz4H6.8H20
(NH4)5[(MoO3)5(PO4) ( H P O 4 ) ] . 3 H 2 0
(NH4)dTeMo6024]. Te(OH)6.7HzO
CoMoO4
(NHg)6MoaO27.4H20
MoO3
(NH4)6[Mo7024].4H20
K2{[MoO2(C204) (H20)]20}
(NH4)6MoaO27.4H20
(NH4)s[(MoOz)s(PO4) (HPO4)]. 3H20
Na3CrMo6Oz4H6.8H20
(NH4)5[(MoOa)s(PO4) (HPO4)]. 3HzO
MOO3.H20
(NH4)~[(MoO3)5(PO4) (HPO4)]. 3H20
(NH4)6[ Mo7024]. 4 H 2 0
(NH4)6[Mo7Oz4]. 4 H 2 0
"
R (A)
1"919
1.944
1.946
1.937
1"951
1.911
1.945
1"952
1"962
1"972
1"960
1"967
1"960
1"965
1 "955
1"962
1.974
1.966
] "961
1"957
1"953
1"970
1.976
1.976
1.976
1.974
1.981
1.991
1.972
1.981
1"976
1"976
1"974
1"982
1.986
1 "977
1-984
1 "991
1"991
2"008
Distortion
zi = ((AR/R) z) x 10'
5
9
10
56
67
96
96
99
99
101
104
104
106
111
113
115
118
121
123
126
134
140
141
141
143
145
147
150
151
151
152
152
152
159
163
167
167
186
189
197
Reference
75 J A C S A
97
63 A R K E A
21
63 A R K E A
21
63 A R K E A
21
63 A R K E A
21
63 A R K E A
21
63 A R K E A
21
74 A C B C A
30
75 JCSIA
1975
75 JCSIA
1975
75 J C S I A
1975
70 A C S A A
24
74 A C B C A
30
73 A C B C A
29
75 JCSIA
1975
75 JCSIA
1975
68 J A C S A
90
72 ACBCA
28 .
72 A C B C A
28
72 A C B C A
28
72 A C B C A
28
74 JCSIA
1974
70 I N O C A
9
74 A C B C A
30
70 I N O C A
9
74 JCSIA
1974
74 A C B C A
30
65 A C A C A
19
74 A C B C A
30
63 A R K E A
21
68 J A C S A
90
64 I N O C A
3
74 A C B C A
30
74 J C S I A
1974
70 I N O C A
9
74 J C S I A
1974
74 A C B C A
30
74 J C S I A
1974
75 JCSIA
1975
75 JCSIA
1975
2123
365
365
365
365
365
365
300
505
505
505
' 3711
48
869
505
505
3275
2222
2222
2222
2222
941
2228
48
2228
941 2095
269
48
357
3275
1603
48
941
2228
941
1795
941
505
505
T a b l e 7. Variation o f mean M - O distance and effective ionic radius in octahedral environments as a function o f distortion
Maximum
Correlation G o o d n e s s
Ion
A x 104
N*
Rot
r0:l:
m
coefficient of fit ( x 103)
M o ~+
212
38
1.920
3-73
0.74
67
0.572
3.01
0-63
70
W e+
122
7
1-925
3-30
0.75
19
0"565
3.28
0.66
24
V 5+
576
16
1.887
2.62
0.98
8
N b s÷
83
29
1.976
6.45
0.69
71
0.599
6.83
0.44
99
Ta 5+
79
6
1.984
6.70
0.81
18
0.617
3.79
0-15
46
M n 3+
71
15
1"994
7"08
0-82
30
0-624
6.15
0"54
50
Cu 2+
316
26
2.085
3"99
0"82
77
Mg 2÷
156
28
2.094
8.31
0.72
21
'
0"728
8"86
0"77
• 18
Co 2+
46
15
2"106
7"38
0"42
19
0"734
11 "70
0-70
16
Zn 2 +
71
16
2"099
7"70
0-64
21
0"736
8"20
0.74
16
Li ÷
148
il
2"159
8"42
0"81
30
0"784
9.02
0-79
35
* N = n u m b e r of independent octahedra
t R=Ro+mA.
r = ro+ mzl.
764
R E V I S E D E F F E C T I V E I O N I C R A D I I IN H A L I D E S A N D C H A L C O G E N I D E S
cupied sites relax toward their bonded cation neighbors. Therefore average distances should increase as
the occupancy factor decreases. In general, partial occupancy seems to be more prevalent for cations which
are weakly bonded to oxygen like Cu ÷, Ag ÷, alkali
ions, and large alkaline earths. The most prominent
examples are Li and Na compounds. Table 8 summarizes the existent data on some structures with partial cation occupancy. Fig. 6 shows the dependence of
mean Li-O bond length on the degree of occupancy.
Although the data are not extensive, it is apparent that
mean distance increases as occupancy factor decreases.
Extrapolation of the Li curve in Fig. 6 to zero occupancy, i.e. a tetrahedral Li vacancy, gives 2.10-2.15 A,
which is close to the 2.11 A found for c~-LisGaO4 by
Stewner & Hoppe (1971) and for fl eucryptite by
Tscherry, Schulz & Laves (1972).
Another example of the effects of partial occupancy
can be found in the non-stoichiometric feldspar
Sr0.a4Na0.03vq0.13All.69Si2.2908 reported by Grundy &
Ito (1974). The mean Sr-O distance in this compound
is 0.03 A greater than in the stoichiometric SrA1ESi2Oa
(Chiari, Calleri, Bruno & Ribbe, 1975).
The relation between mean distance and occupancy
probably cannot be quantified precisely because the
relaxation of oxygen ions will depend on the nature
and number of other cation neighbors.
3. Effects of covalence
Changes in interatomic distances due to covalence
effects are anticipated in compounds with (1) anions
less electronegative than fluorine or oxygen, i.e. chlor-
ides, bromides, sulfides, selenides, etc. and (2) tetrahedral oxyanions such as the VO]- and AsO ]- groups.
The effects of covalence show up as a lack of additivity
of the radii and are generally referred to as 'covalent
shortening'.
(a) Halides and chalcogenides. Covalence effects can
be observed by comparing the relative contraction of
cation-anion distances in two different isotypic compounds as the anion becomes less electronegative, e.g.
Fe 2+ in Fe2GeO4 and Fe2GeS4 vs Mg 2+ in Mg2GeO4
and Mg2GeS4. Covalence shortens both Fe-S and
Mg-S bonds relative to Fe-O and Mg-O bonds, but
because of the greater electronegativity of Fe 2+ (1.8)
compared to Mg 2+ (1.2), the Fe-S bonds are shortened
to a greater extent. Thus a 'covalency contraction'
parameter (Shannon & Vincent, 1974) can be defined:
d(Fe-X) a
Ra= d(Mg_X)3
where d ( F e - X ) = m e a n Fe-X distance.
A similar parameter
Rv=
V(Fer, Xn)
V(MgmXn)
compares the volume of an Fe 2+ compound with that
of an isotypic Mg 2+ compound. To see the effects of
covalence on the Fe-X distance relative to the Mg-X
distance, the ratio Rv or Rd may be plotted against the
difference in electronegativity of the Fe-X bond,
AZFe-x. Such schematic Rv-A Z plots are shown in
Fig. 7. The reference ions for Cd 2÷ and In 3+ are Ca 2+
and Sc3+ respectively. Such plots usually show a strong
Table 8. Mean distances in structures with partially occupied cation sites
Compound
(a) IVLi+
Typical
LiAISiO4 (fl eucryptite)
Occupancy
factor
Reference
Table 1
73 AMMIA
72 ZKKKA
68 ZKKKA.
69 ZKKKA
72 ZKKKA
70 ZKKKA
68 ZKKKA
71 ACBCA
72 ZKKKA
58
135
126
130
135
132
127
27
135
681
175
46
420
161
118
327
616
175
59
9
59
25
127
9
27
280
345
280
1503
94
345
1826
LiA1Si206 II (fl spodumene)
0"50
LiA1SiO4 (fl eucryptite)
Li2Al2Si3Olo
LiAISi206 III
~-LisGaO4
LiAISiO4
0-50
0-40
0.33
0.00
0.00
1.97
2.020 (4)
2.025 (7)
2-08 (4)
2-085 (9)
2.056 (2)
2.064 (4)
2.068 (5)
2.11
2.11
1.00
0.91
0.82
0.70
0.50
0"35
0.29
0.25
2.42
2.533 (6)
2.74
2.723 (6)
2.600 (9)
2"839 (I)
2.65
2.88
Table 1
74 AMMIA
74 JSSCB
74 AMMIA
69 ACBCA
68 ZKKKA
74 JSSCB
71 ACBCA
1.00
0"44
0.33
0.22
2.50
2"64
2.75
2.83
Table 1
74 JSSCB
74 JSSCB
72 JSSCB
(b) VINa+
Typical
Na2Fe2AI(PO4)3 (wyllieite)
NaSbO3
Na2Fe2AI(PO4)3 (wyllieite)
NaA1Si3Oa (high albite)
NaAlnOt7 (fl-A1203)
NaSbO3
Na2.58A121.81034 (fl-A1203)
(c) ViAg÷
Typical
AgSbO3
AgSbO3
Agz.4A122034.2.
1"00
1.00
R
345
345
60
R.
z.15 /
,
,
,
i
|
2'10I
2.05~-
IL~
D. S H A N N O N
i
i
VACANCY
IN ,, UsC.-aO
4
AND .8 EUCRYPTITE
e
LiALSi206 T
(~ SPODUMENE)
l
LiAISi04~ ,,~
~LiAISiz06]I[
(~ EUCRYPTITE)
= UzAIzSisO~o
~UAtSi04
2"00i (,8 EUCRYPTITE)
e~TYPICAL
i .95F-Li+-O DISTANCE
I'S°/~-
i
I
t
1.0
.9
.8
.7
I
I
5
I
,
I
.2
I
,
0
OCCUPANCY
Fig. 6. Mean Li÷-O bond length us partial occupancy.
1.20
|
I
I
I
UNFILLED "d" SHELL
2+,Mn2+, C02+,N j2+
1.10
1.00
FI LLED "d" SHELL
Zn2+ Cd2+ in3+
~ - ~
Rv
or
Rd
0.90
0.80
FLUORIDES OXIDES
2.5
CHLORIDES SULFIDES/SELENIDESJ BROMIDES |
/IODIDES
1.5
2.0
1.0
0.5
0.0
L~
Fig. 7. Covalency contraction parameter, Ro or Ra, vs ,dZ for
filled and unfilled d shell cations.
1.30
t
i
i
i
i
,2o-C'-.": ~_~"
eNa-H
LIO
eLi-H
eLiBaH3
1.00
• Mg-H
0.90
Rv
aSi-H
f ~ 0.80
aAt-H
0.70
B-H
o
D P-H
a As-H
0.60
aC-H
O.5C
I
0.,~ l~
,Io
&
oo'
-~.s
N-Ho
-o9
z~x
Fig. 8. Covalency contraction parameter, R, or Rd, vs AX for
hydrides. Solid circles represent ratios of cell volumes of
isotypic compounds. Squares represent ratios of the cubed
M-H distances to the cubed M-F distances.
765
dependence of Rv on ZIZ. For Fe2+-Mg 2+ the Fe 2+
fluoride volumes are ~ 1 1 0 % of the corresponding*
Mg 2+ fluoride volumes whereas the Fe 2÷ sulfide volumes are ~ 9 6 % of the corresponding Mg z+ sulfide
volumes. Plots for the cations with filled 'd' shells show
a markedly smaller dependence on zlg. This appears
to be due to the difference in covalence of hybrid orbitals formed from metal 'd' orbitals vs metal 's-p' orbitals.
These relations show that effective ionic radii derived
primarily from oxides are not strictly applicable to
fluorides - note the change in Rv for Fe 2+, Co 2+, Ni 2+,
and Mn 2+ from fluorides to oxides. This effect is particularly noticeable in R~-ZIX plots for the pairs
Cu+-Li ÷ and Ag+-Na ÷ (Shannon & Gumerman,
1975). The Cu+-Li + and Ag+-Na ÷ plots are very steep,
e.g. the volume of AgF is 120 % of the volume of NaF,
whereas the volume of Ag2Se is only 72 % of the volume
of Na2Se. Although most of this change arises from
covalency, double repulsion effects present in the Li
and Na halides described by Pauling (1960) may also
play a role.
Covalence effects are useful in explaining certain
differences between the effective ionic radii of Table 1
and the ionic radii of Pauling (1927) and Ahrens (1952).
Pauling's radii for Cu ÷ (0.96 A) and Ag ÷ (1.26/~) are
considerably larger than those in Table 1 (0.77 and
1.15 A respectively). Since these radii were derived
from comparison of alkali halide distances, using an
equation relating effective nuclear charge and screening
constants (Pauling, 1927), they are valid in primarily
ionic crystals. The smaller radii in Table 1 are applicable in the more covalent oxides. Extrapolation of R vs
ZIX curves such as in Fig. 7 leads to values of 0.91 /~
and 1.23 A for fluorides, which are close to Pauling's
ionic values.
A final example of covalence effects concerns
M + - H - distances. According to Gibb (1962), the radius of the hydride ion is slightly larger than the radius
of the fluoride ion. To rationalize the behavior of the
hydride ion, the M - H bond has been treated as covalent. Therefore, it is useful to make R~ vs AZ plots similar
to those just discussed for Fe 2+, Cu +, etc. In this case,
the reference ion is F - and volumes of certain hydrides
are compared to those of isotypic fluorides. The results
of this analysis are shown in Fig. 8. The solid circles
represent volume ratios, R~ = V ( M = H , ) / V ( M m F , ) ; open
squares represent ratios of typical distances Rd=
d ( M - H ) 3 / d ( M - F ) 3. In the more ionic hydrides of Cs,
Rb, K, and Na, hydride volumes are considerably
larger than those of the fluorides. For the Li and Mg
compounds, hydride and fluoride volumes are approximately equal, whereas the more covalent hydrides have
increasingly smaller relative volumes than the corresponding fluorides. Fig. 8 partly explains the differences in reported radii. The Morris & Reed (1965)
value of 1.53 A was derived essentially from the large
alkali halides, while Gibb's value of 1.40 A was derived
primarily from hydrides of the more electronegative
766
REVISED EFFECTIVE
I O N I C R A D I I IN H A L I D E S A N D C H A L C O G E N I D E S
metals such as: Sc, Ti, Y, Zr, HI', Nb, Ta, and Th.
Because of this strong dependence of M - H distances
on cation electronegativity, it does not seem very useful
to quote a unique radius for H - .
(b) Tetrahedral oxyanions. Lack of additivity also
appears in most small tetrahedral groups and is particularly noticeable for the ions lVB3+, ~VFe3+, IVGe4+,
tVA:+, IvVS+, IVS6+, XVSe6+, and IVflT+. The deviations in vanadates have been studied in detail (Shannon
& Calvo, 1973b). Assuming that the V-O bond is
strongly covalent, and that relatively electronegative
cations such as Cu 2+, Ni 2+, and Co 2+ tend to remove
electron density from the V-O bond, a V-O bond
length increase in Cu, Ni, and Co vanadates is anticipated. Plots of mean radii (~) vs mean cation electronegativity (:~) show a marked slope with a gradual increase in ~(~vvs+) from vanadates of the alkali and
alkaline earth ions to those of Cu, Ni, and Co. Similar
plots for other ions, ps+, AsS+ (Shannon & Calvo,
1973b), B 3+, Si 4+, Se 6+ (Shannon, 1975), showed the
same behavior. The statistical data on the tetrahedra
of B3+, SIS+, Ge4+, p5+, ASS+, 56+, Se6+, Cr6+, M06+,
W 6+, and C17+ have been summarized by Shannon
(1975). The slopes of the i vs '2 plots were greatest for
V 5+, Se 6+, and C17+, and least for Si4+. Although the
evidence for covalence as the origin of these effects in
the above systems is only indirect, this behavior is
consistent with accepted ideas of 'covalent shortening'
of bonds.
The evidence for covalent shortening of lVFe3+-O
bonds is more direct. Jeitschko, Sleight, McClellan &
Weiher (1976) have found a good correlation between
(1) the Fe M6ssbauer isomer shift and mean Fe-O
distance and (2) ~ and mean Fe-O distance (R). Thus,
in fl-NaFeO2/~= 1.86/~ and 3=0.18 mm s -1 relative
to ~ Fe whereas in Bia(FeO4) (MOO4)2/~ = 1.909 A and
= 0.282 mm s- 1.
4. Effects o f electron delocalization
At a pressure of 6.5 kbar SmS (NaCI structure)
undergoes a semiconductor to metal transition and a
reduction in cell edge from 5.97 to 5.70 A. (Jayaraman,
Narayanamurti, Bucher & Maines, 1970). The reduction in cell volume was attributed to a partial conversion of Sm 2+ to Sm 3+ ; some of the electrons presumably
go into a conduction band.
Electron delocalization effects can also be seen by
comparing the volumes of the conducting V sulfides
VS, VTSs, V3S4 and VsSs with the corresponding Cr
sulfides which have localized 'd' electrons (de Vries &
Jellinek, 1974). The V compounds have volumes ~ 5 %
smaller than the corresponding chromium compounds.
This does not agree with the relative sizes of V and Cr
in oxides and fluorides, e.g. r(WV3+)=0"64 and
r(WCr3+)=0.615 A. For the sulfides, this unit-cell volume anomaly is not simply attributable to metallic vs
semiconducting behavior. While Cr3S4, Cr556, and
Cr7Sa show a positive temperature dependence of resistivity typical of a metal, magnetic susceptibility
measurements indicate Curie-Weiss behavior and
therefore nearly localized electrons (van Bruggen,
1969). This is in contrast to the Pauli paramagnetic
behavior of the corresponding V sulfides (de Vries &
Haas, 1973) characteristic of delocalized electrons.
Thus, in SmS and the sulfides of V metallic character
accompanied by electron delocalization appears to be
associated with reduced bond distances.
A further example of delocalization effects occurs in
the compound NaVS2 (Weigers, van der Meer, van
Heinigen, Kloosterboer & Alberink, 1974). The molecular volume of Pauli paramagnetic NaVS2 1 (67.9 .&3)
is significantly less than that of NaVS2 II (72.7 .&3).
NaVS2 II is characterized by localized electrons (Jellinek, 1975) and its molecular volume is consistent with
that of isotypic NaCrS2 (71.1 N3).
If electron delocalization in oxides results in reduced
metal-oxygen distances and thereby an effective increase in valence, radii derived for the ions Mo 4+,
TC4+, Ru 4+, Rh 4+, W 4+, Re 4+, Os 4+, and Ir s+ from
metallic oxides may not be reliable when applied to
insulating oxides. Thus, radii obtained from distances
in the metallic phases, e.g. RhOz, ReOz, and Cd2IrzO7,
will be smaller than radii obtained from semiconducting or insulating compounds.* When both types of
compounds have been studied, a significant difference
in distances is generally found. The mean octahedral
Re4+-O distance in insulating K4[Re202(C204)4]. 3H20
(Lis, 1975) of 2.021 (10)/~ (r=0.671 A) is greater than
the estimated mean distance in metallic ReO2 of 1-99/~
(r=0.63/k). Knop & Carlow's (1974) value o f r = 0 . 6 6 2
A derived from cell volumes of the insulating Cs2ReF6
phases is consistent with the radius of Re 4+ from
K4[Re202(CEO4)4].3H20. The ReS+-O distance in
Nd4Re2Olt (Wilhelmi, Lagervall & Muller, 1970) of
1"987 (12) ,~ (r=0.607 A) is significantly greater than
the distance in metallic Cd2Re207 (Sleight, 1975) of
1.93 (2)/k (r=0.55 A). The radii of 0"58 A derived from
XeFsRuF6 and 0.60 A from XeFRuF6 (Bartlett, Gennis, Gibler, Morrell & Zalkin, 1973) are greater than
the radius of 0.565 A derived from the r a - V plot for
metallic Cd2Ru207. In contrast, however, the Mo 4+
radius of 0.64 /~ derived from insulating Li2MoF6
(Brunton, 1971) is not greatly different from the radius
of 0.65 A derived from metallic MoO2 (Brandt &
Skapski, 1967).
Although there appears to be ample evidence to
show that M - O bond distances in compounds with
localized electrons are greater than M - O distances in
compounds with delocalized electrons, the data are not
yet sufficient to derive a reliable set of radii for semicon2ucting compounds4containing+Mo4+, Tc 4+ , Ru 4+ ,
Rh , W , Re , Os , and Ir . This will become
possible as additional accurate structure refinements of
fluorides, molecular inorganic compounds, and semiconducting oxides containing these ions become available.
* This assumes that metallic character can be equated with
delocalized electron behavior in these compounds.
R. D. S H A N N O N
I would like to acknowledge the help of F. Jellinek
for providing unpublished data on NaVS2, F. C. Hawthorne for pointing out numerous structures containing
partially occupied cation sites, O. Muller for several
sources of radii of unusual ions, M. Fouassier for unpublished data on K4MO4 compounds, I. D. Brown for
unpublished bond length-bond strength curves, and P. S.
Gumerman for assistance with data collection. Structure data on rare earth halides and an analysis of the
radii of divalent rare earths provided by H. Bg.rnighausen were especially valuable. I am particularly indebted to Ruth Shannon for the tabulation of data and
proof reading. Finally, I would like to thank R. J.
Bouchard, W. H. Baur, and H. B/irnighausen for
critically reviewing the manuscript prior to publication.
References
AHRENS,L. H. (1952). Geochim. Cosmochim. Acta, 2,155-169.
BARTLETT, N., GENNIS, M., GIBLER, D., MORRELL, B. &
ZALKIN, A. (1973). Inorg. Chem. 12, 1717-1721.
BAUR, W. H. (1972). Amer. Min. 57, 709-731.
BAUR, W. H. (1974). Acta Cryst. B30, 1195-1215.
BIRCHALL, T. & SLEIGHT, A. W. (1975). J. SolidState Chem.
13, 118-130.
BONAMICO, M., DESSY, G., FARES, V. & SCARAMUZZA, L.
(1974). J. Chem. Soc. Dalton, pp. 1258-1263.
BRANDT, B. G. & SKAPSKI, A. C. (1967). Acta Chem. Scand.
21, 661-667.
BROWN, I. D. (1975). Private communication.
BROWN, I. D. & SHANNON, R. D. (1973). Acta Cryst. A29,
266-282.
BRUGGEN, C. F. VAN (1969). Ph.D. Thesis, Univ. of Groningen.
BRUNTON, G. (1971). Mater. Res. Bull. 6, 555-560.
CHIARI, G., CALLERI, M., BRUNO, E. &. R1BBE,P. H. (1975).
Amer. Min. 60, 111-119.
Codens for Periodical Titles (1966). Vol. II. ASTM Data
series DS23A, Philadelphia.
DEMPSEY, M. J. & STRENS, R. G. J. (1975). Proc. NATO
Conf. on Petrophysics, Newcastle-upon-Tyne, April
22-26.
EVANS, H. T. JR (1951). Acta Cryst. 4, 377.
FLYGARE, W. H. & HUGGINS, R. A. (1973). J. Phys. Chem.
Solids, 34, 1199-1204.
FUKUNAGA, O. & FUJITA, T. (1973). J. Solid State Chem. 8,
331-338.
FUMI, F. G. & TosI, M. P. (1964). J. Phys. Chem. Solids,
25, 31-43.
GELLER, S., WILLIAMS, H. J., ESPINOSA, G. P., SHERWOOD,
R. C. &; GILLEO, M. A. (1963). Appl. Phys. Lett. 3, 21-22.
GIBB, T. R.. P. (1962). Prog. Inorg. Chem. 3, 315-509.
GREIS, O. & PETZEL,Z. (1974). Z. anorg, allgem. Chem. 403,
1-22.
GRUNDY, H. D. & ITO, J. (1974). Amer. Min. 59, 1319-1326.
HAWTHORNE, F. C. (1973). The Crystal Chemistry of the
Clino-Amphiboles, Ph.D. Thesis, McMaster Univ.
JAYARAMAN, A., NARAYANAMURTI, V., BUCHER, E. &
MAINES, R. G. (1970). Phys. Rev. Lett. 25, 1430-1433.
A C 32A - 2
View publication stats
767
JEITSCHKO, W., SLEIGHT, A. W., MCCLELLAN, W. R. &
WEIHER, J. F. (1976). Acta Cryst. B32, 1163-1170.
JELLINEK, F. (1975). Private communication.
KA,LM~.N, A. (1971). Chem. Commun. pp. 1857-1859.
KHAN, A. A. • BAUR, W. (1972). Acta Cryst. B28, 683-693.
KNOP, O. & CARLOW, J. S. (1974). Canad. J. Chem. 52,
2175-2183.
LIs, T. (1975). Acta Cryst. B31, 1594-1597.
MCCARTHY, G. J. (1971). Mater. Res. Bull. 6, 31-40.
MORRIS, D. F. C. & REED, G. L. (1965). J. Inorg. Nucl.
Chem. 27, 1715-1717.
MULLER, O. & ROY, R. (1974). Crystal Chemistry of NonMetallic Materials. 4. The Major Ternary Structural
Families. New York: Springer-Verlag.
PAULING, L. (1927). J. Amer. Chem. Soc. 49, 765-794.
PAULING, L. (1960). The Nature of the Chemical Bond.
Ithaca: Cornell Univ. Press.
PETERSON, J. R. & CUNNINGHAM,B. B. (1967). Inorg. Nucl.
Chem. Lett. 3, 327-336.
PETERSON, J. R. & CUNNINGHAM, B. B. (1968). J. Inorg.
Nucl. Chem. 30, 1775-1781.
RIBBE, P. & GIBBS, G. V. (1971). Amer. Min. 56, 1155-1173.
SHANNON, R. D. (1975). Proc. NATO Conf. on Petrophysics, Newcastle-upon-Tyne, April 22-26.
SHANNON, R. D. & CALVO, C. (1973a). Acta Cryst. B29,
1338-1345.
St-IANNON, R. D. & CALVO,C. (1973b). J. Solid State Chem.
6, 538-549.
SHANNON, R. D. & GUMERMAN,P. S. (1975). J. Inorg. Nuel.
Chem. 38, 699-703.
SHANNON, R. D., GUMERMAN,P. S. & CHENAVAS,J. (1975).
Amer. Min. 60, 714-716.
SHANNON, R. D. & PREWITT, C. T. (1969). Acta Cryst. B25,
925-945.
SHANNON, R. D. t~ VINCENT, H. (1974). Struct. Bond.
(Berlin), 19, 1-43.
SILVA, R. J., McDOWELL, W. J., KELLER, O. L. & TARRANT,
J. R. (1974). Inorg. Chem. 13, 2233-2237.
SLEIGHT, A. W. (1975). Private communication.
SLEIGHT, A. W. & JONES, G. (1975). Acta Cryst. B31, 27482749.
STEWART, D., KNOP, O., MEADS, R. & PARKER, W. (1973).
Canad. J. Chem. 51, 1041-1049.
STEWNER, F. & HOPPE, R. (1971). Acta Cryst. B27, 616--621.
TILLMANNS, E. & BAUR, W. H. (1970). Acta Cryst. B26,
1645-1654.
TILLMANNS, E., GEBERT, W. & BAUR, W. H. (1973). J. Solid
State Chem. 7, 69-84.
TSCHERRY, V., SCHULZ, H., & LAVES, F. (1972). Z. Kristalloaf. 135, 175-198.
VRIES, A. B. DE t~ HAAS, C. (1973). J. Phys. Chem. Solids,
34, 651-659.
VRIES, A. B. DE & JELLINEK, F. (1974). Rev. Chim. Miner.
11, 624-636.
WEIGERS, G., VAN DER MEER, R., VAN HEININGEN, H.,
KLOOSTERBOER, H. & ALBERINK, A. (1974). Mater. Res.
Bull. 9, 1261-1266.
WILHELMI, K., LAGERVALL,E. t~ MULLER, O. (1970). Acta
Chem. Scand. 24, 3406-3408.
WOLFE, R; W. & NEWNHAM, R. E. (1969). J. Electrochem.
Soc. 116, 832-835.