(1976). a32, 751 revised effective ionic radii and...

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

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) prepar- ation 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)" NH+; 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 respon- sible 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.

Procedure

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 iso- structural 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 approxim- ation 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

* P o l y h e d r a l d i s t o r t i o n w a s n o t c o n s i d e r e d i n S P 6 9 .

A C 32A - 1

752 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 I N H A L I D E S A N D C H A L C O G E N I D E S

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

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 + , V I O s 6 + , V I O s 7 + , VlRe4+, VIRES+, VlRe6+, VIReT+, VIRh 4+, v I 1 U 4 + , V I I U S + , a n d V I I U 6 + .

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, metallic oxides.

ION EC CN 5P Ck *IR* ION EC CN SP CR f I R ' ION EG CN SP CR *IR*

AC÷3 6P 6 Vl 1 . 2 6 1 . 1 2 R AG÷I 4D10 11 .81 . 6 7

IV 1 . 1 4 1 . 0 0 C

~ VSQ 1.16 1 . 0 2 1 . 2 3 1 . 0 9 C

v I 1 . 2 9 1 . 1 5 c V l l 1 . 3 6 1 . 2 2 V l l l 1 . 4 2 1 . 2 8

AGed 60 9 IVSO . 9 3 . 7 9 Vl 1 . 0 8 . 9 4

AGe3 60 8 IVSQ . 8 1 . 6 7 V l . 8 9 . 7 5 R

AL*3 2P 6 IV • 53 . 3 9 v . 6 2 . 6 8 Vl . 6 7 5 . 5 3 5 *

AM*2 5F 7 V l l 1 . 3 5 1 .21 Vlll 1.40 1.26 IX 1.65 1.31

AM÷3 5F 6 Vl 1.115 . g 7 5 R V I I I 1 . 2 3 1 . 0 9

AM÷~ 5F 5 Vl . g 9 . 8 5 R V i i i l . o g . g 5

AS+3 4S 2 Vl . 7 2 . 5 8 A AS+$ 3D10 lV . 6 7 5 . 3 3 5 Re

v l . 6 0 . 4 6 C* AT÷7 5DIO V l . 7 6 . 6 2 A AU÷I 5010 V l 1.51 1 . 3 7 A AUe3 50 8 IVSQ . 8 2 . 6 8

V l . g 9 . 8 5 A AU÷5 50 6 Vl . 7 1 . 5 7 d +J 1S 2 I l l .15 .01 *

I¢ . 2 5 .11 * Vl . 41 . 2 T C

8A÷~ 5P 6 V l 1 . 4 9 1 . 3 5 V i i 1 . 5 2 1 . 3 8 C Viil 1 . 5 6 1 . 4 2 " IX 1 . 6 1 1 . 4 7 X 1 . 6 6 1 . 5 2 Xl 1 . 7 1 1 . 5 7 XI! h75 1 . 6 1 C'

BEe2 15 2 I l l . 3 0 . 1 6 IV . 4 1 . 2 7 *

~ l . 5 9 . 6 5 'C B l e 3 65 2 1 . 1 0 . 9 6 C

Vl 1 . 1 7 1 . 0 3 Re V l l l 1 .31 1 . 1 7 R

81÷5 5010 V l . g o . 7 6 E 8K+3 5F 8 Vl 1 . 1 o . 9 6 R bK÷6 5F 7 V l . 9 7 . 8 3 R

V l I l 1.07 . 9 3 R 8 R - I 6P 6 V l 1 . 8 2 l . V b p 8R e3 6P 2 IVSO . 7 3 . 5 9 8R+5 45 2 I I I P Y . 6 5 . 3 1 8R÷7 3010 IV . 3 9 . 2 5

V l . 5 3 . 3 9 A c e4 15 2 l l I . 0 6 - . 0 8

IV . 2 9 . 1 5 P VI . 3 0 . 1 6 A

CA+2 3P 6 Vl 1.14 1 . o o • V l l 1 . 2 0 1 . 0 6 *

V l l i 1 . 2 6 1 . 1 2 •

~ x 1 . 3 2 1 . 1 8 1 . 3 7 1 . 2 3 1 . 6 8 1 . 3 4 X l l

CDeZ 6010 IV . 9 2 . 7 8 v 1 . 0 1 . 8 7 V l 1 . 0 9 . 9 5 V l i 1 . 1 7 1 . 0 3 c V l l l 1 . 2 4 1 . 1 0 ¢ X l l 1 . 4 5 1.31

CE+3 65 1 V l 1 . 1 5 1 . 0 1 R V l l 1 . 2 1 1 . 0 7 E V l l l 1 . 2 8 3 1 . 1 6 3 R IX 1 . 3 3 6 1 . 1 9 6 R

1 . 3 9 1 . 2 5 I I 1 . 4 8 1 . 3 6 C

CE÷4 5P 6 Vl 1 . O l . 8 7 R V I l l 1 .11 . 9 7 R

1 . 2 1 1 . 0 7 I I 1 . 2 8 1.16

CF*3 bD I VI l . o g . 9 5 R CF*6 5F 8 V l . 9 6 1 . 8 2 1 R

C L - I 3P 6 V l 1 . 6 7 1 . 8 1 P CL+b 35 2 l l l P Y . 2 6 . 1 2 CL÷7 2P 6 IV . 2 2 *08 •

Vl , 6 1 , 2 7 A C~÷3 5F 7 V l 1.11 . 9 7 R GHe6 5F 6 V l . 9 9 . 8 5 R

V I l l 1.09 . 9 5 R CO÷2 3D 7 I V HS . 7 2 . 5 8

V . 8 1 . 6 7 C Vl L5 . 7 9 . 6 5 R

HS . 8 8 5 . 7 6 5 Re V l l l 1.06 . 9 0

C0÷3 30 6 V l kS . 6 8 5 . 5 6 5 R• HS . 7 5 .61

GO÷4 3D 5 IV . 5 6 . 4 0 V l HS . 6 7 . 5 3 R

CR+2.3D 4 VI L$ . 8 7 . 7 3 E HS . 9 4 . 8 0 R

CR+3 3D 3 V l . 7 5 5 . 6 1 5 R• CR÷4 30 2 IV . 5 5 .41

Vl . 6 9 . 5 5 R Cg÷5 30 1 IV . 4 8 5 . 3 6 5 R

V l . 6 3 . 6 9 ER V I l l . 7 1 . $ 7

eRe& 3P 6 IV .40 . 2 6 Vl . 5 8 . 4 4 c

c$+1 5p 6 V I 1 . 8 1 1 , 6 7 V l l l 1 . 8 8 1.76 l x 1 . 9 2 1 . 7 8 X 1 . 9 5 1 .81 Xl 1 . g 9 1 . 8 5 X l l 2 . 0 2 1 . 8 8

CUe1 3010 11 . 6 0 . 4 6 IV . 7 6 . 6 0 E V I . 9 1 . 7 7 E

CUe2 30 9 IV .71 . 5 7 IVSQ .71 . 5 7 *

. 7 9 . 6 5 * 1 . 8 7 . 7 3

CU*3 30 8 Vl kS . 6 8 .56 0 +1 15 0 I I . 0 4 - .10 0Y÷2 6F IO Vl 1 .21 1 . 0 7

v I I 1 . 2 7 1 . 1 3 Vl I 1 . 3 3 1 . 1 9

UYe3 6F 9 Vl 1 .052 . g 1 2 R V I I 1 .11 . 9 7 V l l l 1 . 1 6 7 1 .027 R IX 1 , 2 2 3 1 . 0 8 3 g

E&e3 4 F 1 1 V l 1 . 0 3 0 . a g o R V l 1 1 . 0 8 5 . 9 ~ 5 Vl I 1 . 1 4 4 1 . 0 0 4 R IX 1 .202 1 .062 R

EU÷2 4F 7 V l 1 . 3 1 1 . 1 7 V l l 1 . 3 4 1 . 2 0 V I I I 1 . 3 9 1 . 2 5 IX 1 . 4 4 1 . 3 0 x 1 . 4 9 1 . 3 5

EUe3 4F 6 V i 1 , 087 . g 6 ~ R Vll 1.15 1.01 V l l l 1 . 2 0 6 1.066 R IX 1 . 2 6 0 1 . 1 2 0 R

F - 1 2P 6 i l 1 . 1 4 5 1 .285 I l l 1 . 1 6 1 . 3 0 IV 1 . 1 7 1 . 3 1 Vl 1,19 1.33

F e7 IS 2 V l . 2 2 . 0 8 A FEe2 30 6 IV HS . 7 7 . 6 3

IVSQ H$ . 7 8 . 6 6 Vl LS . 7 5 .61 E

HS . 9 2 0 . 7 8 0 Re V I I I HS 1 . 0 6 . g 2 c

FE+3 30 5 I V H$ . 6 3 . 4 9 * v . 7 2 . 5 8 VI LS . 6 9 . 5 5 R

HS aT05 . 6 6 5 R• V l l l HS . 9 2 . 7 8

FEe4 3D 4 V l . 7 2 5 . 5 8 5 R FEe6 30 2 IV . 3 9 .25 R F R * I 6P 6 V l 1 . 9 ~ 1 . 8 0 A GAe3 3010 IV .61 . 4 7 *

V . 6 9 . 5 5 Vl .TbO . 6 2 0 R*

GD÷3 ~F ? V l 1 . 0 7 8 .938 R

G0"3 4F 7 V l l 1 , 1 4 1 , 0 0 V I I I 1 , 1 9 3 1 , 0 5 3 R IX 1 ,247 10107 R¢

GE÷2 45 2 V I , 8 7 . 7 3 A GE*q 3010 IV . 5 3 0 , 3 9 0 •

Y i *670 *530 R• H e l 1S 0 I - - , 26 - , 3 8

I I - . 0 6 - . 1 8 HF*4 "6F16 IV . 7 2 . 5 8 :

VI . 8 5 . 7 1 V I I . 9 0 . 7 6 V I I I . 9 7 . 8 3

HG÷I 6S 1 I l l 1 . 1 1 , 97 VI 1 . 3 3 1 . 1 9

HGe2 5010 I | *83 . 6 9 IV 1 . 1 0 . 9 6 V I 1 . 1 6 1 . 0 2 r i l l 1 . 2 8 1 . 1 6 k

HOe3 6F10 VI 1 .041 .901 R V I l l 1 ,155 1 , 0 1 5 R IX 1 .212 1 .072 R X 1 . 2 6 1 , 1 2

I :~ 8. ) v1 2.0. 220 , . 5S I I I P Y . 5 8 . 6 6

VI l . O g *g5 1 ÷7 4D10 1V . 5 6 . 6 2

Vl . 6 7 . 53 IN÷3 6010 IV . 7 6 . 6 2

Vl , 6 o 8 o o . V l l l 1 . 0 6 *g2 Re

IR+J 50 6 Vl . 8 2 . 6 8 E IR*4 50 5 Vl . 7 6 5 . 6 2 5 R IR÷5 50 4 Vl . 7 1 . 5 7 E K "1 3P b IV 1 . 5 1 1 . 3 7

V l 1 . 5 2 1 . 3 8 V I I 1 . 6 0 1 . 6 6 V I I I 1 . 6 5 1.51

~ x 1 . 6 9 1 . 5 5 1 . 7 3 1 . $ 9

X l l 1 . 7 8 1 . 6 6 LAe3 4010 V l 1 . 172 1 . 0 3 2 R

V l ! 1 . 2 4 I . IO vllI 1 . 3 0 0 l . l b O R

I X 1 .356 1 . 2 1 6 R 1.41 1 . 2 7

x l i 1 . 5 0 1 . 3 6 G L l ÷ l IS 2 IV . 7 3 0 . 5 9 0

Vl . 9 0 . 7& • V I I I 1 . 0 6 . 9 2 C

LU*3 4F14 Vl 1.ooi . 8 b l R V l l l 1.117 . 9 7 7 R 1X 1 .172 1 .032 R

MG+2 2P 6 IV . 71 . 5 7

i l . . . . . . • 860 . 720 *

l l 1.03 . 8 9 G HN÷2 30 5 IV HS . 8 0 . 6 6

V H5 . 8 9 . 7 5 C V l LS . 8 1 . 6 7 E

H$ . 9 7 0 . 8 3 0 Re V l l HS 1 . 0 4 . 9 0 C

~ l l l 1 . 1 0 . 9 b R MN÷3 30 6 . 7 2 . 5 8

Vl L$ . 7 2 . 5 8 R HS . 7 8 5 . 6 6 5 Re

HN÷6 30 3 l V . 5 3 . 3 g R V l . 6 7 0 . 5 3 0 Re

MN÷5 30 2 IV . 6 7 . 3 3 R MNe6 30 l IV . 3 9 5 . 2 5 5 MNe7 3P b IV .3g .25

Vl . 6 0 . 6 6 A MO+3 40 3 Vl . 8 3 . 6 9 MO*~ 40 2 Vl . 7 9 0 . 6 5 0 RH ~oe5 6D I IV . 6 0 . 4 6 R

Vl .75 .61 R MO÷b 4P 6 l v . 5 5 .61 Re • v . 64 . 5 0

V I . 7 3 . 5 9 R* V l l . 8 7 . 7 3

" : l 2, ) iv 1.32 . . . . N 2S V l . 3 0 . 1 6 A N ÷5 IS 2 I l l . 0 4 4 - . 106

Vl . 2 7 . 1 3 A

* most reliable, M from

R. D. S H A N N O N 753

NA* I 2P 6 IV 1 .13 . 99 V 1 .14 1 .00 VI 1 .16 1 .02 V l I 1 . 26 I . I Z V I I I 1 . 3 2 1 . 1 8 IX 1 .38 1 .26 C X I l 1 .53 1 .39

NB+J 40 2 V l . 86 . 72 N8 ,4 40 1 Vl . 82 . 68 RE

VIII . 93 . 79 N8 ,5 4P 6 IV . 62 . 68 C

Vl . 78 . 66 VII . 8 3 . 69 C V I I I . . 88 . 76

ND+Z 6F 6 VIII 1 .63 1 .29 IX 1 .49 1 . 3 5

NO+~ 6F 3 V l 1 . 123 . 983 R VI I I 1.249 1.109 R* IX 1 .303 1 .163 R XlI 1 .61 1 .27 E

N I÷2 30 8 IV . 69 . 55 IVSQ .63 . 69 v . 77 . 63 E VI . 830 . 690 R•

NI *J 30 7 Vl LS . 70 . 56 R• HS . 74 . 60 E

N I÷4 30 6 V l LS . 62 . 68 R NO+2 5F16 VI 1.26 1 . I E NP÷2 5F 5 VI 1 .26 1 .10 NP*3 5F 6 VI 1 .13 1 .01 R NP+6 5F 3 V [ 1.o i . 87 R

Viil 1 .12 . 98 R NP+5 5F 2 VI . 89 . 75 NPeb 5F 1VI . 86 . 72 R NP+7 6P 6 VI . 85 . 71 A o - 2 2P b I f 1 . 21 1 .35

I l l 1 .22 1 .36 IV 1 .26 1 .38 VI 1 .26 1 .40 V I I I 1 .28 1 .62

OH- I 11 1 . 1 8 1 .32 I l l 1 . 2 0 1 . 3 6 IV 1 .21 1 .35 E V l 1 . 23 1 .37 E

0S+6 5D 6 VI . 770 . 630 RM 0S+5 50 3 Vl . 715 . 575 E 0S.0 50 2 V . 63 . 49

V l . 685 . 545 E 05 "7 50 1Vl . 665 . 525 E 0S ,8 5P 6 IV . 53 . 39 p . 3 3S 2 vl . 58 . 46 A p *5 2P 6 IV . 31 . 17 *

v . 43 . 29 V l . 52 . 3 8 C

PA+3 5F 2 Vl 1 .18 1 .0¢ e PA t4 6D 1Vl 1 .06 . 90 g

• v i i i 1 .15 1 .01 PA~5 bP 6 Vl . 92 . 70

V I I I 1 . 0 5 . 9 1 IX 1.09 .95

P8+Z 65 2 IVPY 1 .12 . 98 c VI 1 .33 1 .19 VII 1 .37 1 .23 C V I I I 1 .63 1 .29 C IX 1 .69 1 .35 c x 1 .54 1 .40 C XI 1 .59 1 .45 C XI l 1 . 63 1 .49

PB*6 5010 IV . 79 . 65 E V . 87 . 73 E Vf . 915 . 775 R V I I I 1 .08 . 96 R

p 0 ÷ l 6 0 9 II . 7 3 . 5 9 PD÷2 40 0 IVSO .70 . 66

V l 1 . o o . 86 PO•J 60 7 V I . 90 . 7 6 POe6 40 6 V l . 7 5 5 . 615 R P~*3 6F 4 V l 1 . 1 1 . 97 R

V i i i 1 .233 1.093 k IX 1 . 2 8 6 1 .146 g

PO÷4 65 2 V I 1 . 0 8 . 96 R r i l l 1 .22 1 .08 R

POeb 5 0 1 0 VI . 8 1 . 07 A

Table 1 (cont.)

ION EC CN SP CR eIRt

PR÷3 CF 2 V l 1 . 13 . 99 R V i i i 1 . 266 1 .126 R IX 1 .319 1 .179 R

PR+4 4F I VI . 99 . 85 R V l I l I . IO .96 R

PT+2 50 8 IVSQ .74 . 60 V I . 99 . 80 A

PT+4 5D 6 V [ . 765 . 625 R PT+5 50 3 V l , 71 . 57 ER PU*3 5F 5 Vl 1 . 1 4 1 . 0 0 PU*6 5F 6 VI 1 . o o . 86 R

V l [ l I , IO . 96 P0+5 5F 3 v I . 88 . 76 E ~ o . 0 5 ~ v i .85 .71 1 RA*2 6P V I I I 1 , 62 1 .48

X l I 1 .86 1 .70 R RB+L4P 6 VI 1 .66 1 .52

vll 1o70 1 .56 V I l l 1 .75 1 .61 IX 1 .77 1 .63 E X 1 .80 1 .66 X l 1 . 83 1 .69 x l I 1 .86 1 .72 X lV 1 .97 1 .83

RE*~ 50 3 V l . 77 . 63 RM RE+5 50 2 V I . 72 . 58 E RE+O 50 I V l . 69 . 55 E RE* / 5P b IV . 52 . 38

V l . 67 . 53 RH+3 40 b Vl . 805 . 665 R RH+4 4D 5 V I . 74 . 60 RM AHe~ 40 6 V[ . 69 .55 RU*3 40 5 VI , 82 . 68 RU*4 40 6 VI . 760 . 620 RM RU*5 40 3 V I . 705 . 565 ER RO* / 40 1 IV . 52 . 38 RU*8 4P 6 IV . 50 . 36

+6 35 V l . 51 . 37 A 5 .6 2P 6 IV . 26 . 12 •

v l . 43 . 29 c 58+3 55 .2 IVPY . 90 . 76

v . 96 . 80 v l . 90 . 76 A

$8÷5 4010 V l . 76 . 60 * 5C÷3 3P 0 v I . 885 . 765 R•

V I I I 1.OLO .870 Re SE-2 6P 6 VI 1 .84 1 .98 P SE*6 6S 2 v I . 64 . so A SE*6 3D10 IV . 62 . 28 •

Vl . 56 . 6 2 c SI.6 2P 6 IV . 40 . 26 *

vl . 540 . ~oo R* $H+2 6F 6 VIl 1 .36 1 .22

V l I I 1 .41 1 .27 IX 1 . 4 6 1 .32

SN*3 4F 5 v I 1 .098 . 958 R V l l 1~16 1 . o 2 E V I I I 1.219 1.079 R IX 1 .272 1 .132 R I l l 1 .38 1 .24 C

SN*4 4010 IV . 69 . 55 R

• 830 . 690 V I I . 09 . 75 V I I I . 95 . 81 c

SR*2 4P 6 V l 1 . 32 1 .18 V I I 1.35 1.21 V I I I 1 .40 1 .26 IX 1 . 6 5 1 .31

~ l I 1.50 1 .36 1 .58 1.46

TA*J 50 2 VI . 86 . 72 E TA*4 50 1 V l , 82 . 68 E TA*5 5P 6 V l . 78 . 04

V I I . 83 . 6 9 V I I I . 88 , 76

1.063 . 923 R T8+3 4F 8 VI VI I 1.12 . 98 V I I I 1 . 1 8 0 1 . 0 4 0 IX 1 .235 1.095 R

T0 .6 4F 7 Vl . 90 . 76 R Vill 1 . 0 2 . 88

ION EC CN SP CR fiR*

TC+4 40 3 V I . 783 . 845 AN TG*5 40 2 V l . 74 . 60 ER TC+7 4P 6 IV . 51 . 37

V l , 70 . 56 A TE-2 5P b V I 2 . 07 2 .21 e TE+4 55 2 I l l 066 . 5 2

IV . 80 , 68 V l 1.11 097

TE+b 4010 IV . 57 . 43 G V l , 7o , 56

TH÷6 6P 6 V I 1 . 08 , 94 C V I I I 1+19 1 .05 RC IX 1 .23 1 .09 • X 1 ,27 1,13 E XI 1 , 32 1 .18 C X l l 1 , 3 5 1 .21 C

T I+2 30 2 V l 1 . 0 0 . 86 E T1+3 30 1 VI . 810 . 670 R• r l + ~ 3P 6 IV . $6 . 42 G

v . 6 5 . 51 C V l . 745 . 605 R• VI I I . 88 . 74 C

1L *1 6S 2 v l 1 . 64 1 .50 a V I I I 1 .73 1 . 5 9 R Xll 1 .84 1 ,70 RE

TL+3 5D10 IV . 89 , 75 V l 1 . 0 2 5 , 885 R V I I I 1,12 . 98 ¢

TM+2 4F13 VI 1 . 17 1 ,03 V I I 1 . 23 l .Oq

TM+) kF l2 V I 1 . 020 . 880 R v i i i 1.13~ ,994 R IX 1 .192 1 .052 R

0 +J 5F 3 V I 1 , 165 1 ,025 R O ÷4 5F 2 V I 1 . 03 . 89

V I I 1 .09 . 95 E v i i i 1 . 1 4 1 . 0 0 Re IX 1.19 1 .05 X l l 1 ,31 1,17 E

u +5 5F 1V l . 90 . 76 v i i . 9 8 . 8 4

U +b 6P 6 I1 . 59 .45 IV . 66 . 52 V l . 87 . 73 * V l l . 95 ; 81 E V l l l 1 . 0 0 . 8 6

v *2 30 J V l . 93 . 79 v . 3 30 2 Vl . 780 , . 640 Re v +4 30 I v . 67 . 53

V l . 72 . 58 R* V I I I . 85 . 72 E

V +5 3P 6 IV . 495 . 355 R* v . 6o . 46 * V l . 68 . 54

w +~ 50 2 VI . 80 . 66 RH w +5 50 1 V l . 76 . 6 2 R w +6 5P 6 IV . 56 . 42 *

v . 65 .51 vl . 7~ .bO *

XE+8 4D10 IV .54 .40 v l . 62 . ~8

Y +J 4P 6 v I 1 . 040 . 900 Re V I I 1 . 1 0 . 9 6 V i l l 1 . 1 5 9 1 . 0 1 9 R* IX 1 .215 1 .075 R

YB+2 4F14 VI 1 .16 1 .02 V l l 1 .22 1 .08 E V I I I 1 .28 1 . 1 4

Y8+3 4F13 V l 1 . 008 . 8 6 8 R* V l l 1 . 0 6 5 . 925 E V l l l 1.125 . 985 R IX 1.182 1.042 R

IN *2 3010 IV . 7~ .0o • v . 82 . 68 * v I . 880 . 7 4 0 R* VI I I 1.04 .90 C

ZR+~ 6P 6 IV . 73 . 59 R V . 80 . 66 C Vl . 86 . 72 R• V l l . 92 . 78 * V I I I . 98 . 8~ *, IX 1 .03 . 8 9

vIIIV4+, IVpb4+, and XTh 4+ 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 Shan- non, 19751 Brown, 1975). Examples of cations whose radii were calculated in this way are: lVMn2+, V[Be 2+, 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

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) pre- pared 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 more applicable to oxides than fluorides. This subject is treated further in the discussion Effects of covalence.

A C 32A - I*

754 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 I N H A L I D E S A N D C H A L C O G E N I D E S

Table 2. References for 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 | 68 J |NCA 30 823 8C CL3

AG, I I1 Tl |NOCA |o 719 AG FE 02 TZ ZAACA 393 266 SR AG6 04 7J IENBA 28B 263 BA AG6 04

AG* I | v 7L JSSC8 3 364 AG2 CR 04

AG, I l v so 42 JACS& 64 3S4 AG3 kS 04 69 ACSAA 23 2261AG2 s O3

AG* I v 1o J$$C8 L 484 AG6 NOlO 0 )3

AG* I V l " - 32 ZKKKA 82 16 ! AG2 $04 . 7 J&CSA 69 222 AG3 P04 11JSS08 3 364 AG2 CR O4 69 ACAC8 25 $116 AG2 CR2 07 lO JS$C8 | 484 R02 NO o~

AG, I V lX 7o JSSC8 1 484 AG6 NOlO 03 ) 69 ACACB 25 $116 AG2 CDZ 07

AG~I V lX | 65 ACCRA 19 180 AG7 N Of|

AG*2 [VS0 71JPGSA 32 543 AG F2

AGe2 V I 71JPCSA 32 54 ) AG F2

AO*3 l v so 65 ACCRA 19 180 AG7 N 011

AL ,3 | v 67 ACCRA 23 7S~ NA T | 2 AL5 012 68 N J ~ A 1968 8O CA AL 80~ 7O ACaCA 26 1230 CA AL6 07 70 NJRNA 1970 547 CA12 AL l4 033 7L SPHDA 15 90S CA4 AL6 o l o (OH)6 71 SPNOA | 5 995 CA AL4 07 71 AC8C6 27 1826 8ETA-AL2 03 12 J$$C8 6 60 AG &L | I 017

AL ,3 v 68 ACDCA 24 1518 )NGeFE( AL3 $1 8 oq 68 ANNIA 53 1096 ALZ P04 )0H I3

ALeS v | 7 1 A N N I A 56 18 HA3 AL2 L I3 F IZ 7Z J$SC8 • 11 NO AL O3 72 J$SC8 4 :60 AG ALL | 017 58 ACCRA 5 684 NG RL2 04 72 ACGCA 28 ~899 AL2 883 $ |6 018 66 JACSA 88 ,~95 | AL (ACAC)3 73 &CSC8 ~ .~92 ALP 04 .2 N2 0 67 ERKKA 125 ~423 C5 BE4 B I | 2 -X | ALA 028 H2

~ 4 &C8CA 3O 131; NA AL ) (P 0 * )Z IO H I4 4 ZKKKA 139 129 AL (o H I3

An*2 v l l 72 J |NCA 34 3427 AM 12

AR*2 V I I I r3 J |NCA 35 ~8~ &N 082

AN*Z IX ) 73 J INC8 35 683 AH CLZ

AM* ) v i i i 72 INOCA 11 2233 AN2 (S 0413 .8H2 0

A ~ , 4 v t 67 ADCSA 71 228 8A AN O3 67 INUC6 3 327 R 188*41

AS*5 IV 69 ZKKKA L30 211 2N2 CU A$2 08 68 CJCHA 46 9L? CU3 AS2 08 63 8APCA 11 3 6 1 N G 2 AS2 07 69 ACSCA 25 |54A CA H AS 04 .2 H2 0 69 AC8C6 25 2658 ZA )H kS 04 )2 H2 o 68 ANNIA 5 ) 18~| NN2 o H 6S 04 63 CAHIA 7 Sb l CA CU AS 04 0 H 7O ACBCA 26 1884 HA2 H AS 0~ .7 HZ o 70 ACDCA 26 ~574 NA2 H &$ 04 .7 H2 o 69 CHOCA 268 L694 BA N |2 AS2 08 70 ARR|A 55 2023 NN9 (0 H |9 (H2 O)2

IAS O3) )AS 0412 70 AODCA 26 1889 |N H* I2 , AS 04 70 ACSAA 24 3711L l HO 02 AS O4 70 ]NOCA 9 2259 CA2 AS O4 CL 6S A¢CRA 18 777 CU3 AS O4 |O ~33 70 CJCHA 48 8q0 NG2 AS2 07 7O ( JCNA 48 881 CO) ASZ O8 1 | CJCMA 49 t 0 3 6 CA) RS2 08 70 AR~qlA ~ 1489 NNT $8 AS 012 71ACDCA Z7 2124 HA) AS 04 .12 H20 73 80806 29 2 6 1 1 M G ) AS2 08 81RNHIA 4b 1077 EA2 8 AS 04 (OH)k 73 CJCHA ~1 2082 NA4 .AS2 OT 66 268C6 347 133 CA ~ AS O4 ~2 0 66 ZAAC4 347 |4O SR H 68 O4 H2 U 1 | AHRI8 56 I14T ZN4 A$2 06 )OH)2 . lH2 o 7O 40806 26 4O3 C6 H RS o4 70 Z~KKA 132 332 E03 A$2 08 73 ACSCA 29 1 4 1 L U AS O4 7 ) AC8C6 Ze ZTZ | ~H4 HZ AS O4

AS*S v | 7L eaCH8 49 2519 CL FZ AS F6 73 J$SC8 6 80 H 8 8 . $ AS) 0 | 6 7O CJCN6 48 3 | 24 C08 AS3 u l 6 T ) &C&C8 29 266 CALCULATED 74 INOC4 13 780 XE AS F | I oAEZ AS F9 74 ACDC6 3O 250 ~ AS F6

b9 JC$16 1969 1936 X AU F4 7O ZARCA 3 /S 43 L I 3 AU 03oK AU O I ,RB AU 02 TO JC$1A 1970 3092 A AU (N03 )4

AU ,5 V l 74 INUCA IS 775 XEZ AU F IT

• * 3 I I I 68 NJnNA 1961 80 C6 AL 8 04 70 8CDCA 26 e 0 6 82 O) t 71SPHCA IS 802 K 682 8 03 F2 11 6C8C8 21 672 Z~ 84 o l Io ,cDc, 26.89 • 8 ~2o3

I ACSC& 27 904 L l ) FO ZX=KA 132 241 CA 83 O5 )OH)

JCPSA 60 | 8 9 9 x 84 07 t 4 XRDU8 v L66L ~o RL~ 18 g314

8 * 3 I v 61 AODCA 24 869 02 U3 I I 6d ACSG4 ~4 | 70J NAB F4 69 CJCNS 47 2S79 m 8 F4 I I ACOC& ~ t bT7 CU 62 04 ; | A t ,CA Z l |Z0Z N N4 8 F4 ;U Z~KA | JZ 241 CA 8~ O50 H ~3 ACC84 16 1133 NA 8 l u H )4 .Z .Z 74 JCPSA 60 18V9 #N U4 07 1 | AXN14 $6 15~3 NG 1~60T )0 ~161 , z Hz o 73 6HX16 88 9O9 C8 8 $1 U4 o H Tl 6C8CA 2 t 672 Z~ S~ U7

8 * 3 v l T) ACAC8 29 266 CALCULDTEO

8 6 . Z V l lO Z~8~A 13 ! 161 863 vz O8 t ) /EN8& 28~ 263 8A AOb 04

8Ae4 v i i ; | ACSCA ~7 1263 8A FE2 O4 T$ AC~C~ 29 200~ 8A2 11 O4

1 6 * g v i i i 58 ZXK~A 11o 231 cu lu~8~2FIC O O H16 .4 NZ 0 • 9 JCP$& Sl 4928 8A 70 JCPS& s ) ) 2 ; 9 8A CU F4

7L JCPSA 71ANNIA 7 l ZAACA 13 ACSCA

DA*¢ I x T l ZAACA 13 ACSAA 73 ACSAA

8Ae2 x 1o ZKKKA 70 AC8CA 67 BUFCA

8A*~ x l 71 AGDCA

BA*2 X l l 70 ACDCA 72 CSCNC 71NRSUA 69 CN0CA ~5 AC~CA

88*~ 111 69 ACOCA oo AC8CA

8E*Z xv bZ SPHCA 08 ACSCA 60 ACDCA 69 AC~CA 71SFNCA 72 SPHCA 72 AC8CA 73 ACBC~ $9 ACCRA 67 ZKKKA T4 ACDC6

74 "DCDCA 7~ ANMIA

8 [ *S V 69 35C0A 7O ACSAA

81 "3 V l TO ACSAA ~1JFCSA

BI * ) V I I I 72 NABUA

BI *~ v |

6 K ' 4 v l 6T |NUCA

88 *~ i v SQ 69 JCS |A

8R .5 I l l 69 ACAC8 67 ACSAA

8 R . 7 I v 71JC$1A

C.4 III 65 ACCAA 7L JNSAA 73 ANNIA 67 PDLAA 75 AC8CA

CA*2 V | 68 NJNAA 69 ACSCA $7 JCPSA 65 ACCRA

CA*2 V l l T l CJCHA 71AE80A 73 NR8UA 69 ACSCA

CA*Z V I I I 68 INOCA 14 CJCNA

CA-Z IX • 7 | JNDAA

69 ACSC4 CA*Z x

69 ACSCA CA*2 x [ I

69 AC8C6 74 AXNIA

74 JACSA C0 .2 IV

~9 ACCRA 1 1 Z 4 A C A

co *z v 69 CJCHA 70 ZXK~A

C0*Z vx 09 CJCHA ro ZRKK& 66 SPHOA 67 HCACA 14 JCSIA 74 ACSC&

C0 .2 V I I 74 4CS6&

7~ JCS lA co *z v l x x .

AC8CA t 4 J C S I ~

CE*3 vlll 74 ZADC6 74 JCS I6

CE*3 IX 67 SPH~A T4 ZADCA

cE*3 x 6O ANNIA

CE ,4 v l 72 ACOCA 73 JS$C8

CE .4 V I I I

JC$1A 74 J$TCA F4 ACSAA

C t *4 XXX 68 JSCSA

CF*3 VX F4 J INCA

CL*5 111 T3 NASUA

CL* / I v r z ACDCA 12 ZK~XA 6O ACL~A

sq JPCNA ~8 JRCSA $7 P lSAA ST P lSAA 62 ACCJ~R 71 JCS IA 7O AC~CA 11 AC8C6

55 1093 BAN 04 56 758 8A C OS

306 I 8A2 CO 04 29 2009 8A2 T l 04

386 t BA2 CO O4 27 1695 8A TE ($2 03 )2 ,2 HZ O 21 1653 BATE (52 03 )2 .3 H2 0

131 let 8A3 IV 04 )2 26 105 8A3 $14 N86 026 90 24 8A pz 06

27 1263 BA FEZ 04

26 t 02 8A5 TA4 015 l I BA T I6 013 6 725 8A CA FE4 08

2680 1694 BA N I2 AS2 08 )I .596 K2 BA CU (N O216

25 1647 SR 8E3 04 20 295 CA t2 8E17 O29

6 733 NA BE p 04 24 672 LA2 BE2 0S 24 807 CS BE F3 25 1647 SA 8E3 04 IS 999 FE3 8E $13 09 (F IOH)2 16 1021 8E2 S l U4 28 1899 AL2 BE3 S l6 0 re

229 2976 NA3 8E 7H I0 F45 IZ 634 BE ACETATE

128 423 cs 8E4 8112 -X ) AL4 028 H2 )0 396 NA6 ($116 AL2 t8E (OH)2 O391

1 , 5 H2 0 30 2434 L I2 BE I 04 59 1267 CA 882 P2 08

7 1797 812 N 06 24 386 ~ (2 03 ALPHA

2 " 384 812 03 ALPHA 32 1315 81FE 03

7 102581T ITANAYES

R3 VS V (8A2 LA BI 061

3 327 A (8K .41

196e 1936 K aR F4

25 621SN (GR 0313oqH2 o 21 2634 HG OR 03

1971 1857 0R( *71 -O

18 689 CA C O3 75A 27 CA C 03

58 1oa9 NO c 03 • z t 25 NN C 03 31 890 NA2 C 03 .H2 o

1968 80 CA AL 8 04 25 1933 CA NA (H I p 02 ) ) 26 563 CA (o H I2 18 689 CA C o )

49 1o36 CA3 aSZ 08 27 2311 CA2 AL FE 05

8 593 CA C~ FS 28 1534 CAIO |p 04 )6 IO H I2

1345 CA2 P2 07 5 I155 GALe NG2 H2 (p O4"114

75 27 CA C o ) 25 1534 CA|O )p 04 )6 (O H )2

25 955 CA 82 04 I l l

25 965 CA 82 04 I v 89 41 CA AL3 (0 H )6

IP 03 1O t / 2 IO H1112112 96 6606 X2 CA CU IN 02 )6

12 l o49 CO IN2 04 382 2To 82 C0Z o~

47 3409 co | pz 07 132 132 C03 AS| 08

47 3409 CO2 P2 07 13Z 332 C03 AS2 08 11 11 co w 04 SO 2023 C0Z HN3 08

1974 614 C0 C4 H6 06 JO 188o C02 G4 H12 012

2#A 119 0o D ie H2 c o 0 )2 .3 l l Z HZ 0 C0 DeC H2 c o u ) z . 3 Ha O

197~ t qZz co c~ H50S

98 903 CO2 NSZ 07 25 1806 00 (N 03 )2 .4 D2 u

1976 676 CO C4 H6 06

403 I R) v$ v ICE F31 1974 1165 C41 H24 CE F I2 N De 84

l Z 214 CE e s t O5 403 I R3 V$ V ICE F$ )

45 I CE~ ME ME2 712 514 022

28 956 8R CE o ) v 131R )CE4 , )

8 $3 1~ N412 CE F6 1174 2021N i6 CE u lO 036 H2 .30H2 o

l~ 39 t CEIS 04 )2 28 1079 A - CE tACAC)4

90 3589 INH4 )2 H6 ICE NOt2 0421 .12 H2 0

36 2023 R3 VS V ICF2 15 04 )3 )

8 791 88 CL 03

28 039 TMPO CL U4 0~ 65 X CC 04 13 e s 5 N oz CL 04 ,n CL OA,

Hc t 04 .N2 O ,C l CL 04 .3 H2 O 6 ) ZTe H CL O4 .H20 00 8 0 / 5 C6 HD.AG CL 04 56 134 N H4 CL 04 ~6 143 K CL 04 15 1 2 0 1 N N4 CL O4

1971 1 3 t l cu ) c l o H9 N ) )2 COL 04 )2 26 1928 Ha . s CL 04 z t 898 H CL 04 .2 112 H2 o

13 IC"DA 1 417 ¢G N I2 -TR IEN-CU CL 04 11A¢DCA ZT 898 x CL 04 ,Z I l l , 2 0

12 NRSUA 7 1 2 8 1 C L ( * 7 ) - 0 7 t JCS IA 1971 1857 CL ( *7 ) - o 62 ACCRA 15 I s N3 o CL 04 1 -80 CI bQ ACDCA 25 ~875 N H3 o H CL 04 13 ACSAA 27 2309 )PaR 1o H1413 C 03 (CL 04110

. 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 IV 69 ZAACA 369 306 C0 V2 U4

C0 ,2 v 12 ACBCA 28 2803 C02 PZ 07 ALPHA

C0 ,2 v ! 68 ZAACA 358 125 CO SE 06 08 ZKKKA 120 299 CO GE 03 70 CJCHA 48 881 C03 A$2 08 70 JCPSA 5 ) 32 /9 BA C0 F4 10 PEP lA 3 | 61 C02 SI OA 7J AC~CA 29 2 )04 CO3 V2 O8 T l HCACA 54 1621 CO3 (O N )2 (S 04 |2 °2 H2 0

REF I C02 $ ! 04 72 ACECA 28 2083 COl pz 07 70 INOCA 9 lS I CO (ONPA)3 (CL 0412 73 ACBCA 29 2741 CO SI F6 .b H2 0 74 ANNIA 59 475 C02 $ | 04 T4 JCHL8 4 55 C|6 H18 CO 06

CO*Z V ) I I 66 INOCA S 1208 (A$ (C6 HS IR I2 (CO(N O3J~)

co , ) V l LS . 68 CCJDA 1968 871 c0 (N 0313 O80JCHA 46 3412 C03 04 66 JACSA 88 2951 C0 (CS H7 O213 74 ACUCA 30 822 C0 1C5 H7 0233 69 JACSA el 6801 IN H416 (H4 C02 N010 O381

• , 7 H2 o 74 ZAACA 408 97 K C02 04

C0 "4 IV 71ZAACA 306 I 8A2 CO 04 73 ZAAOA 398 54 L l 8 G0 06 74 ZAACA 408 75 C52 CO 03 74 ZAACA 409 l s z 86 co2 o7

C0 .4 v ) HS 67 STGBA 3 I 83 VS V (FLUORIDES) 14 ZAACA 408 97 K C02 04

CR*2 v l LS 7L ANCPA 6 411A2 CR 06 69 ACDGA 25 925 8 VS o ELECTRONS

CA*3 v l 69 MDUUA 4 62 | NA3 CR F6 7O INOCA 4 • aZZ8 HA3 )CR NO 006HOZ4 M63 .8 , 2 0 1o ACSAA 2 3627 ~A2 CA3 08 73 NROUA 8 593 CA CR FS 65 ACCRA 19 131CR |C~ H7 0213

CR*4 IV 14 ZAACA 407 129 BA2 CR 04

CR*4 V l 72 NRBUA ? 157 CR oz

CR*5 V l 67 SEGOA 3 I A3 vs v )FLOOR)DES)

CR*6 IV 68 CJCHA 96 935 K2 CR2 O7 70 ACGCA 26 222 CR 03 69 JC$1A 7989 1857 (NHR)2 CR 04 h9 ACAC8 25 $|16 AG~ CR2 07 70 5PHDA 15 530 K2 CR4 013 t o ANNIA 55 784 P82 CR2 05 70 ACSAA 24 3627 N2 CR3 08 0 H 71 $FHCO 15 820 NA2 CR2 07 .2 H2 0 71SPHCA 15 826 L I2 CR2 07 .2 H2 o 73 AC8CA 29 BqO NA2 CR2 07 ALPHA 71ACSAA 2S 44 RB2 CR2 07 70 CJCHA 48 537 882 CR2 07 71ACSAA 2S 35 R82 CRZ 07 71JSSC8 3 364 A02 CR 04 72 ACeCA Z8 2845 82 CR 04 73 ACSAA Z7 177 ZR4 CO H |6 CCR O~)S .HZ O 73 ACSCA 2e 21~l R82 CR4 013

• 73 6COCA 29 2963 NA2 CA 04 .4 H2 0 71JCS IA l e t l 1857 (NHRI2 CR 04 73 NRDUA 8 271 K2 CA2 O l

CR*6 vl 74 AMMIA 59 1100 P86 CR CL6 X6 V2

C$* l v l l l 09 SPHCA 13 930 CS2 BE F4

CS* l x 69 INOCA 8 1665 CS4 M03 F IO 69 $PHCA 13 930 C$2 BE F4

cs * l x l 69 INOCA 8 1665 C$4 NG3 F IO

C$ .1 x11 67 ACCRA 23 865 C$ U F6 68 ACSAA 22 2793 CS CO CL3 71AC8CA 27 2~S C$ U6 F25

CU* | I I b9 ZKKKA 129 259 CU LA 02 70 ZAACA 379 113 SR CU2 O2

CU* | I v

49 ACCRA 2 158 cu CL3 Cu* l v l

70 NRBUA S 207 CU TA 03 cu *a I v

57 ACCRA 10 554 cu CR2 04 71ACIEA 1o 413 SR CU 84 , CA CU F4

CU*2 IV $0 O7 ZK~KA 124 91ZN2 CU 682 O8 68 ACBCA 24 888 cuz IN2 05 t l ACBGA 27 677 CU 02 04 65 JCPSA 43 3959 CU (06 HSIC H3 )2 C ) O212 66 INOCA $ 517 CU 10 |0 H9 0212 6 1 J C S ~ * 1967 309 CU ( 04 Cl2 H I 8 ) 66 PRLAA 289 161 C14 HLO 04 CU 70 ACSCA 26 8 cu o

cu . z v 69 ACSAA 23 221CU) W 06 ~8 Ca)HA 46 917 CU3 AS2 O8 68 JCPSA 40 2619 CU NO 04

cu *z v I

: I . . . . . . . . . . . . . . . . . . ACCDA | 6 | z4 cu5 )p o432 ~o , 14 ' 68 JCPSA 48 2619 CU NO 04 ;o AC8CA 26 10Z0 CU i o~ 68 CJCHA ~6 60S CU2 P2 O7 68 J&CSA 90 5621 CU( ( (C H3 )2 N )2 -

IP l 012 O111 ; e l 0412 70 )NOCA 9 i s | cu )O~FA)3 ( eL 04 )2 t 3 ACBCA 29 1743 CU V20b

CU*3 V l 12 MRBUA 7 913 LA GU 03

DV*Z v ) UNPUI OY 12

DY*2 V l l UNPUI Of C t2 * 0Y 8R2

OY*Z VI I I uNPu l ov eL2

o r , 3 v l 63 PHSSA 3 K446 0¥2 o )

0Y '3 V I I I t JCNLB | 83 OYITHO)3oH2 0

oy .1 v i i i

I~ $$COA . . . . . . . 1 | 7 1 ~ . . . . . . . . . . . o r ) FE3 a l l o v . J i x

R. D . S H A N N O N 755

T a b l e 2 (cont.)

74 2AACA 403 I R3 VS V |OY F3 ) ER*3 V l

7~ ACbCA 26 484 ER2 S12 OT ER*3 V I I

TO SPHCA 13 36 ER2 GE2 07 72 JCMLB Z 197 ER8 U iTHD) IO 10 H )12

ER+~ V I I I 68 CHPL8 2 47 ER ~ 04 . ER V 04 ?0 [NOCA 9 2AO0 ER IC2 04 ) IH C2 04 ) . 3H2 0 7O SSCOA 8 1745 ER3 FE50L2 7L ACSAA 28 372 E~ |H U C H2 G 0 O83 .2H2 0 ~4 ZAACA 4O3 I R3 VS V (eR F31 72 JGHL8 2 I97 ER8 0 ITHD) IO I 0 N)12

ER.3 IX 59 ZKKKA 112 362 EK IC2 H3 S 04 )3 .9H2 0 ?4 ZAACA 4O3 I R3 V$ V IER F31

EU+2 V l 7O ZAACA 374 201 L ! EU3 O4

EU+2 V I I 70 2AACA 374 201C I EU3 O4 69 ACRCA 25 It04 EU 12 73 REF 3 L I2 EUS 08

EU*2 V I I I UNPUt EU FZ , EU 8RZ

EU+2 I x 73 RVCMA |0 7~ EU CL2

UNPUl EU F2 EU+Z x

? l NATMA S8 218 EU2 SI 04 EU+3 V l

68 REF 4 EU4 AL2 09 70 ZAACA 374 201 L | EU3 04 73 REF 3 L I2 EU5 08

EU÷3 VI I 68 REF 4 EU4 AL2 og 13 REF 3 L12 EU5 88

EU+S V I I I 65 JCP$A 48 l og4 EU3 FE2 GA3 012 ~ ZAACA 4O3 I R3 VS V (EU ~38

3 ACSAA 27 2527 EU2 IC3 H2 0413 .eH2 0 EU+3 [X

74 ZAAC~ 4O3 A R3 VS V IEU F3 | 73 ACSAA 27 2827 EU2 (C3 H2 04 )3 .8H2 0 71ACSAA 25 33~7 EU TRISGLYCOLATE

FE*Z IV SQ H$ 74 AMHIA 59 l l bE BA FE S14 010

FE*Z IV HS 69 $C]EA L&6 139g (NA ,K )2 FE4 S [A2 030 .H2 0 69 ZAACA 369 3O6 FE V2 O4 TI JUPSA 31 452 FE2 TI 04 12 JUPSA 33 | 29& FE2 MO 04

FE*Z VI LS 69 ACRCA 28 V25 R VS A IFE S21

FE+2 V I HS &9 NJMMA 1969 430 FE AL~ IP O412 IO HJ2 l 0 H236

. 2H2 0 7O SUFCA 93 tgO ~E S O4 71SPHCA |5 g99 FE3 BE S I3 09 [F IO H I2 6? ACCRA 22 775 FE (NH4)2 ($ 04 )2 ,6H2 0 68 GIWYA 68 290 L IFE P O4 14 A~N[A 59 48& F~2 SA 04

FE*2 r i l l TA AMMIA $6 79A GARNE~$ 71ZKK~A 134 333 FE3 AL2 S I3 0L2 T3 ACAC8 29 266 CALCULATEO

FE+J AV H$ TO ACECA 26 1469 CA2 FE2 OS 70 SSCOA 8 1745 M3 FE5 012 ?1ACRCA 27 A263 BA FE2 04 I I MREUA 6 T2S BA CA FE4 08 71AESAA 2S 36A6 CA2 FE2 05 73 ACBCA 29 832 6A FE2 04

FE+3 v TA JS$CB ~ I FE V 04

FE*3 v I H$ TO ACSCA 26 Z469 CAZ FEZ O5 70 SSCOA 6 1745 ~3 FE5 012 71SSCOA 9 335 K FE F4 ?L JS$CB ~ I FE v 04 TL JPCSA 32 6315 BI FE O3 11ACSAA 25 3616 CA2 FE20S 67 ACCRA 23 239 FE lOS H7 0213 69 CCJO~ 1969 440 FE IC7 H5 0213

FE* ) V I I I T3 JSSCB 8 33L ESTIMATED

FE*4 V l 73 JSSCB 8 331 R3 VS V IPEROVSKITESI

R3 VS V IS~ Fe O3) FE+o IV

z~ JSSCB 8 *3 K2 FE 04 R3 VS v (K2 FE 04 )

oA+~ IV 16 ACRC~ 2T 6t6 L |5 GA 04 T5 AC~CA 36 56O S~ OAZ S lZ 08

GA.) Vl 14 ATRIA 3O 1364 ItS HAl Ob O&

GD*3 V I I 70 &CBCA 26 484 GDZ S I2 07 ?2 ACSCA 28 60 GO2 NO3 O12 T2 SPHC~ 16 790 GO20EZ 07 O9 [VNM& 5 1823 GOg.33 S I6 026 T2 JSSCB S 266 009 .33 $1b 026

GO*J V I I I IA SPHCA 1~ 926 NA GO S] 04 l Z SPHCA 16 79O ~02 GE2 O? 74 ZAACA 4O3 A R3 V$ V IO0 F ) |

~0~3 ZX 72 SPHE& 16 790 GO2 GEZ QT 69 IVNNA 5 IR23 GD9.33 S ]6 026 7~ ZAACA 4O3 A R3 VS V IO0 F3)

OE*4 IV 68 ZKKKA t26 299 CO 0E 08 69 $CIEA 165 586 AN2 GE 04 69 Z~KKA 129 427 ~N3 FEZ GE3 OAZ 7O JS$CB Z 612 ~028 GE|O 048 Zl sP -c * 18 ~a~ ~ sm GE o~ 70 ACSAA 24 1287 NA4 $N2 GE4 012 I0 H I4 67 ACSAA 2A 12B! NAB SN4 GEIO 030 (O H I4 7~ NOCNe A02 964 NAZ 0£ O3 I1 " 0C~6 IOZ I 245 K20E~ O9 72 SPHCA t7 244 CO GE O3 12 ROCk5 103 1560 GE5 0 (P 0416

GE*4 v i 10 SSCO~ 1 $57 CA2 GE O4 I0 J$$C8 2 662 .G28 GEtO O48 TA ,OCM8 Ao2 IZ4S K20E4 09 TA AC~CA 2T 2133 OE 02 12 ANN1& ~1 62 MN2 GE 04 OELT& 12 2KKKA 186 38T Ge IO HI P 04 TZ ~OCM8 103 AS60 GES 0 I P 04 )6

. , A I . . . . . . . + ,3 7 • 6 JCPSA 2 ZT~ ~

~P .~ I v TS J55C8 13 275 63 V5 V 1~4 .F o41

NF .~ V l l . . . . . . . . . . . . ~ o2 ~ ~C$AA ZJ 3341 I 0 , 42 S 04 *~Z 0 14 AC>AA 2T 3467 . P ~ (O ,18 IC~ 0414 . ,Z 0

.F *4 V I I I TJ &CSAA 27 Z *55 NF (0 H I2 S 04

. 0 , 1 v l ? l CCJO& | 91 | 466 NO2 F2

73 ACBCA 29 869 HG NO 04 H0*J V I I I

T~ ACBCA 30 2049 K HO BE F6 TO SSCOA 8 1745 H03 FE5 012 72 8UFCA 9S 437 H0 Pb 014 74 ZAACA 403 1 R3 VS V IHO F3 I

HO+3 I x 14 ZAACA 403 | R3 V$ V IHU FJ ) 74 ACOCA 30 2613 HOICZ H5 S 06 )3 .9H2 0

H0+3 X T4 INOCA 13 2S35 "HOIN2 014 IH C 0313 .2H2 0 75 CJEHA S3 83L IN O IZ IHOIN 03 )51

1 .5 I l l 71JCPSA 54 2350 N H~ I 03 66 ACCRA 20 750 L | | O] 66 ACCRA 21 841L I 1 03 58 ACGRA 9 1015 CE I I 0314 58 ACCRA I t 794 C i I I 0314 .H2 0 43 RTCPB 6Z 729 N H4 I 03

I+5 V l 7 t JCPSA 54 2 5 5 6 N H4 I 03

1+7 IV ?0 RCBC~ 26 1782 NA I 04 26 ZEPYA 3g 308 A I 04 71 JCS IA A971 1857 II*TI-U

I * 7 V I 6,,cc. 20 7o~ .s . ,'/6 65 ACCRA 19 629 K4 2 0 t0 .8H2 0 37 JACSA 59 2036 IN H41Z H ) [ 06

IN .3 IV T4 ZAACA 409 97 ~82 IN4 07 73 ZAACA 393 280 SR2 INZ 03

IN *3 VI 74 ZAACA 409 97 R82 IN4 07 ~ t ACSAA IS t 437 IN O H S 04 . lHZ 012 60 ACOCA 24 3e8 CUE INZ OS 70 ACSAA 24 1662 IN 0 0 H

AC6CA 30 1882 NA IN S lZ 06 74 SPHOA 18 76 t INZ GE2 07

IR ' 4 V l 7A J5$C8 3 174 SR ZR 03

IR+S VI 74 NROUA 9 1177 R3 VS V ICO2 IR2 071

K* I IV 68 ZAACA 3SR 241K AG O

RE~ 2 K2 0 K*Z VI

SA ZAACA 264 144 K 58 F6 68 SPHOA 12 1095 K Y N02 08 09 CCJDA I I 606 K2 ZR2 O5 b9 ACUGA 25 1919 ~ U2 F9

K*L v i i ~e CJCHA 46 935 ~2 ¢R2 07 69 JCSIA 19~9 84q KZ NO 04 TA S~COA S 338 ~ FE F4

K* I V l l l ~0 ZKKKA 74 3O6 K H2 P 04 62 ZKKKA |AT 4A1K2 T I6 013 37 ZKKKA 98 266 K H2 IH3 O) 85 010 7A INUCA 7 873 K H C2 04 68 CJCHA 46 935 K2 CR2 O7 70 JCS IA 1970 3092 K AU IN 03 )4 65 ACCRA 19 629 K4 H2 12 010 .8H20

K* | IX 70 ZKKKA 132 27 KA .6 NAS .5 CAO.3 ALT .3

L18 *5 032 69 ~CBCA 25 600 K CE F4 69 ACSCA 25 1919 K U2 F9

K*A X 73 CJCHA $1 2613 K AL P2 07

K+I XI I 68 SPHCA 13 420 K Y ~2 08 ? l INOCA 10 1264 K2 P8 CO IN 0216 67 I~0CA 5 514 K2 BA CO IN U286 74 IACSA 96 6606 K2 CA CO IN 02 )6 75 ACOEA 3A $96 K2 8A CU IN 0216 57 PASAA 56 643 K CL 0~

LA*3 V l 69 ZKKKA 129 2~9 CU LA 02 T3 NRUUA 8 1269 ~3 V$ V I~E2 ~30A21

LA+3 V I I ! ?4 ANNIA 59 1277 LA4 ~G2 T I3 S [4 022 73 ACRCA 29 2074 LA2 H03 U I2 68 INOCk 7 2295 LA (C5 H7 02 )3 IHZ 042 74 ZAACA +03 A R3 VS V (LA F31 7~ SPHCA L8 67S LA2 SR3 (B 0 3 1 4

LA*3 IX 71NRBUA 6 23 LA FE 03 ?~ Z~CA ~O~ A ~ ) VS V (L~ ~31 74 A~ IA 59 12T7 LA~ NG2 T13 S I4 022

L I+A IV 3V ZKKKA A02 119 L I O HoHZ O TO 2AACA 379 | 5 7 L IZ CU 02 70 INOCA 9 1096 Y8 L [ F4 71AMNIA 56 18 NA3 AL2 L l 3 F12 71ACSCA 27 066 L15 OA O4 T3 JSSCB 6 538 L I 3 V O4 73 ACRCA 29 2&Z$ L I {N~ HSI 8E F4 T) ACBCA 29 ~628 L [ N H3 0 H $ 04 6~ ACCRA 17 783 L I2 C2 04 14 ACSCA 30 24h6 L IZ 8E Sl 04

LI+L V| &8 ACBCA 24 223 L |3 AL F6 69 2AACA )TA 306 L12 ZR O3 70 ZKKKA 132 I 18 L I2 AL2 S [30 lO TA ~RRUA 6 ~ UZ ~0 F6 6~ A¢C~A 19 ~01LI 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 2294 L I2 ZR F6

CU+3 V l 7O ZAACA 3T7 70 C~ LU2 O4 ?z J *CC* 4 2~ ~u e o~

LU*~ V IA ! 74 ZAACA *03 | R3 VS V (LU F31

LU+3 IX 7~ ZAACA ~03 A R~ VS v (LU F31

~G*2 I v 72 AC§C~ 28 267 KZ NGS $ I12 030

AC~CA 2 3583 ,G2 NAZ $ ]6 OAR ~4 ACUC6 30 2667 K~ NG 84

~0+2 V 6~ ~CSAA ZZ A966 ~G) P2 08 &6 , JNNA 1966 A42 MG 84 07

UNPU$ NG3 P2 O8 UNPU3 RG2 P2 07

NO*2 V l 65 CJCH& ~ ) A lSq .G2 P2 07 68 UAPCA 11 36A ~G2 A$2 OT TO ACeCA 26 1419 ,G , H4 P O*

INOCA 8 A665 E$4 H03 FAO ~9 ZKKKA IZ9 6~ NG Sl U3 6 9 8 P . C , l I 9 3 , , . . 10 J55C8 ~12 .G2e I0 O48 6 ~ .NL.O 196~ i v 6 . ~ AL 6 o , 70 BSC++ 1970 +243 "G $ 04 . .Z 0 71 l c ec l z? 813 . ~ =E o6 bB &CSAA 22 A466 MG$ P2 08 ro 6kF A C~ MO Sl O4

74 AGSCA JO 2491MG2 V2 01 T | ANM|A 86 | 583 NG 186 O f I 0 H I61 *ZH | U 73 ANMIA $8 10Z9 MG C OS 74 CJCNR $2 11S5 CALl ~G2 HZ IP 04116 10 INOCA q IS I ~G IONP~13 (CA 0412 72 CJCH i SO 3619 NG Y2 U6 7~ ACBCA 29 2611MG3 AS2 08

NG*Z V I I I 73 AGRC8 29 266 CALGULAI IO

MN*Z IV HS 70 ANNIA 55 1489 NN? S | AS U|2 69 ZAA¢A 369 306 Iq~ VZ 04 FI AGBCA 2T 1046 NN CO CA 04 69 PMSSA J2 Kq l MN ¢R2 04 13 ACACB 29 266 GALGULATEO

NN*~ V HS 6e ANNIA 53 1861MN2 0 H AS 04 74 MPMTA 21 266 NN2 AS OA OH

~N*Z VI LS 09 ACBCA 28 928 R VS 0 £LECTMONS

MN*~ Vl HS 69 SGIEA 168 SR6 ~Z GE U6 6q JCPSA 51 4928 BA MN F4 70 ZKK~A l ~Z INNS tO Nlz $12 08 6g ANMIA 54 | 362 NN eE2 |P 04 lZ IOH I2 .SH20 70 NJ~ IA 113 1MN? ~A |2 IS 0~ )1$ .18H2 0 65 ACCRA 19 88~ MN S O~ 72 ANNIA ST 621MN2 GE 04 67 PRLAA 9~ i ~5 NN C 03 67 HCACA )020 ) ) MN) 08

MN*2 V I I 72 AMNIA S? 621MN2 GE O~

MN*Z V IA l 69 ZKKKA 229 427 ~N) FE2 GE$ 012 71AMM|A 56 791 GARNETS 73 SSCOA 12 L09 NN3 AL2 GE3 012 74 JCPS6 6~ 1899 MN U4 07

NN*J V ! HS 07 ACSAA Z& ZO?| MNZ 03 b7 ZKKKA 124 428 NNZ 03 b8 ACSCA 24 1233 j l~ 0 0 H 69 JCPSA 50 1066 IN H4 )2 RN F5 63 PHSSA 3 K .46 f '~Z 03 68 BUFCA 9~ 339 TO NN 08 , PR nN O) , Nu xN O) 7A JS$C8 3 238 LA JCN 03, RN3 04,

LA .9S CA.o5 #N 03 7J JSSC8 6 16 NA MN? 012 7~ ANNIA 39 9as NGZ ~N eos 68 ACBCA 24 11A4 NA4 MN~ TLS OAR

~ * INOCA 13 IRSA ~N I t 7 H5 0Z13 ,114 C6 HS CH$ 4 INOCA 13 1864 ~N IACACi3

NN*~ IV 7S JSSC8 L3 275 R3 V$ V IM4 NN O~ l

NN+~ Vl 73 JS$CB 8 23k 86 NN O3 69 INOCA 8 33S NIL2 NN NBL2 038 .SON2 0 63 CZYPA 13 39e NAT H4 MN I I 06 IS * ITH2 0 67 HCACA SO 2023 NN5 GO, co2 MN) 05

.N *6 IV 12 ACOCA 28 284S K2 MN O~

M~*7 I v 68 ACOCA 2~ 1053 AG NN 04

MO+3 VI 69 ACBCA 25 400 KJ NO CL~ 69 INOCA 8 2 6 9 4 K8 NO F6

. 0 . ~ v l 7A MRUUA 6 555 L12 MO F6

MO+~ IV 74 INOCA 13 2715 R3 VS V ¢AE N00* l

~O.S V l 7 t INOCA t0 922 8A2 NO NO 06

68 JCPSA 48 26 t9 CU N0 O~ 68 SPHDA 12 LOgS K Y N02 08 69 JCS |A 1969 849 K2 1~3 04 72 ACUCA 28 60 GU2 NO) OA2 69 JCPSA 50 86 N02 NO3 012 71 SPH~A 18 611L I3 FE NO3 012 ?A SPHCA 15 829 K AL N02 08 . K FE ROE 08 71JCPSA 55 1093 CA N0 0~ , SR NO 0 * 73 ACBCA 29 2074 LA2 NO) O12 7 1 J C S I A 1971 1857 NO(*63 -O

NO*6 V 67 CCJOA 1967 374 ~2 NO3 010 08 JCSIA 1968 1398 KZ X0$ O10

NO+6 VI 68 JCSIA 19&8 13V8 K2 M03 0ZO 70 JSSCB 1 kS& AG6 M010 033 70 INOCA 9 2228 NA3 ICR MO 06 02~ Hb I *RH2 0 ro ACSAA 24 3711C l ~0 02 AS O~ 66 ACSAA 20 2698 NO F6 IGASI TO CCJOA 1970 SO NO 03 (H2 0 )2

6~ INOCA 1603 K IR0 O2 C2 O4I H2 012 O 73 ACRCA 29 869 HG NO 04 74 ACECA 30 11V5 NO 03VHZ O

N -J I v REF 6 NG3 N2 ,S I3 N~ .8 N IT I N

N*5 I l l REF 6 NHk N O3t~L~ N 03 tK N OAt

RA in 0312 ,T I IN O314 NA+I IV

74 ZAACA 409 69 NA6 ZN 04 REF 2 NA2 O

NA+A V 68 ACeCA 24 1077 ~A2 S I2 OS 68 SPHOA A2 987 NA2 ZNZ S l2 07 6~ ZAACA 329 110 NA2 HO O2

NA+I V l 70 ACSAA 24 1287 N&~ SN2 GE4 012 I 0 H )4 65 ACCeA 19 5 6 1 N A C6 07 H7 63 , c c A , i ~ 1233 NA o I O . I * . Z , 2 0 60 ZKKRA 115 6 )0 NA2 AL2 S IS O[O*2HZ 0 58 ZKKKA 111 Z4 I NA CL 03 ~6 ACCRA ~ 811 INAsAS RA IN

sg ACCRA 1 526 NA U ACETATE 74 ACRCA 30 1872 NA2 u O4 78 ACBCA 31 890 NA2 C O3.HZ O

NA* I V I I 71 SPHCA IS 926 NA GO Sl 04 ;0 NJN lA 113 I NN7 NAA2 I$ O413 .15N20 T ) ACBCA 29 RqO NA2 OR2 07 ALPHA

NA*A V I I I 68 AGBGA 24 1703 NA 8 F4 68 SPHOA A2 V8? NA~ Z .Z $12 07 71ANMIA 56 18 NA3 AL2 L I3 FAZ

NA+I Xl l [ l J$SC8 3 89 NA |3 N833 094 32 ZKKRA 81 13S NA A~ SI 04

Ne .3 v l 7 . ACIEA U6 RA9 L I NU OZ

, 8 .~ V i i i 75 JACSA 9? 2713 NB IOPNI~

NR+~ v l 68 JCPSA *a 5048 8A27 SR7 .5 NB2 05 .78 70 JS~C~ l .19 ~ - , 82 OS 70 JSSC8 1 *S~ NA2 . 84 OAA 70 ~ lA ss 90 ca NSZ 06 $5 PRVAA 98 go3 C~2 NEZ 07 71J5$CB J 09 N~ l$ NeS~ O94 71Z*~c~ 3co 119 ~ ~96 06 14 J INCA 36 1965 CA2 NB2 U7 I t JCSI& lV l l AZIO 8 l~ NRA7 O*7

756 REVISED EFFECTIVE IONIC RADII I N H A L I D E S A N D C H A L C O G E N I D E S

Table 2 (cont.)

70 ACOC& 2b 105 045 $14 NSb O26 7 t ACSAA 25 354? LI N03 00 59 IPHCA 4 ?qb I V . YS) NO O~ 73 JSSC8 e 15~ 8X ~8 O4 66 ACSA6 20 T2 N8 P 05 74 8UFC& 97 3 NA3 N8 04

N8"5 V I I t o JSSC8 1 454 N6Z N04 o l t TL J$$Co 3 89 NAI3 N095 09~ ? l ACSCA 27 1610 INH4)3 NO o [ c2 0413 .H2 o ;5 ACBCA 31 &?3 NB2 05

N0 ,2 V I I I UNPUI NO [2

N0+2 i x v~NPUt. NO eL2 , NO ~R2

ND*3 ?1 INOCA 1o 922 0A2 NO RO 06 74 RRSUA 9 1661 NO AL3 04 012

ND*3 V I I I b9 JCPSA 50 86 N02 HO3 012 71 JSSC6 3 450 NO V 04 lO SPHC& 14 518 K NO U2 O8 ?u 4C8CA 26 484 NO2 T I2 o? 70 ACSAA 24 340& N04 RE2 Oil 71 SPHDA 15 b3& NO2 H 0b 71SPHCA 15 g g l N04 ~3 015 74 MR6UA 9 129 NO P5 014 74 Z4AC4 4O3 I ~3 VS V IN0 F31 14 ACOCA 30 4&8 ND P3 09

ND+J IX TO ACSAA 24 2969 NO2 {C2 0 4 | $ * I 0 . $ H 2 0 71SPHCA 15 g91 N04 M3 015 73 6C$AA 27 2441 NO2 IC3 H2 O4 )3 .6H2 o 74 ZAAC& 403 I R3 V$ v (NO F31 73 ACSA& Z I 2813 N02 (C3 H2 0413 .6H2 o 73 ~cs~ 27 29?3 NO 0~ C O3 74 AHH|A 5q 12T7 N04 HG2 T I 3 $14 022

NO~$ X l l 7Z JSSCO 4 IL NO A~ o ~

N [ * 2 I v bL JAP[A 32 685 NI CR2 04 65 8SCFA 1965 1085 SPINEL$

NZ+2 t v SQ b6 [NOCA 5 1200 N] [OPN)2

N I + 2 v 67 8APCA 15 47 N I2 P2 07

N I * 2 V l ?* &HNIA 5e 485 N i2 $I 04 74 ACBCA 30 1686 NI IPV N 0J6 (B F 4 i 2 68 ZAACA 358 | 25 N[ SE 04 67 8APC& 15 47 HI2 P2 Q7 70 ACOCA 28 1464 R8 NI F3 70 ZAACA 3T8 12g $R2 N[ TE 06 70 JSSC5 2 416 RO N[ F3 7 t PHSSA 438 125 NI (O H)Z 70 REF I NI2 51 04 b4 ACCRA t? 1461 N| IC5 H? 0212.2H2 o 13 ACOCA 29 2 T 4 1 N i $ 1 F 6 . 6 H 2 0 63 Z K K ~ 11o 2 9 1 N I IH c o O)2*ZH2 O ?4 JCPS& 61 852 NI C4 0 4 . Z H 2 0 73 JCRL8 3 181NI IC5 H7 O 2 ) 2 . ( C 2 N 5 0 H)2 ?3 &C8C6 29 2304 H I 3 VZ 08

N I * ~ v i LS ?4 ZSAC4 405 167 ~2 N* NI F6 71CH0C~ 2tZ 2163 H0 N[ O3

NI*3 V] NS 54 JACS& 76 14q9 N& NI 02

N l e 4 V l L$ &? STGBA ~ l R3 VS ~61FLOORIOE$1 74 J[NCA 3 L561 K2 N]

No+2 V l ?4 [NOCA 73 2233 EIT[NA?EO

NP*J v [ 68 J INC~" 3O 823 NP CL3

NP*~ V i 6? iNUC4 J 32? ESTiNATEO 14 CJCH4 52 2175 R~ VS v

NPt6 V l a3 vs v 186Z s~ NP O6)

OH- I I I 71 6~X14 56 t155 R06.6 Feo4 513 012 F 0 H,

R [ O H - I I I R I F * Z ) ~ . 0 4 OH- I I [ [

~ I 6H~16 56 I I S 5 ~ 6 . 6 FE.4 S13 012 F 0 H. R ( O H - I ) = 8 ( F - I | + . 0 4

o H - I I v

OH- I V l R I O H - I ) I R I F * 1 1 * . 0 4

0 5 . 4 V l 6q JC0HA IT 45q 05 02 ?0 ACSAA 24 125 05 02

OS+5 V l 71 ~CSI4 197[ 2760 os F5 ?4 SSCOA 14 357 R3 V$ V ICU2 O52 071 56 JINCA 2 79 K 05 F6

0 S ' 6 V l ~ VS V IPE~OVSKI?~Sl

o$+? v l R3 V$ v IPEROV$~iTE$1

05+6 Iv 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 I v t z ACaC& 20 z083 co2 P2 07 60 CJCH6 46 6O5 CU2 PZ o? 65 C~¢H4 43 113~ nGz pz o7 60 IN0C~ 7 1345 C42 P2 o? 71 8SCF~ Iv71 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 07.6H2 0 ?~ NJNN& [ V ? I 241SR AL3 {P 0412 I0 H)5*H2 o 69 zx~x~ 130 148 K z ~ z I p O4)3 ?1AC0C6 27 2124 N43 P 04.12H2 o 60 ~C$A6 22 18ZZ NA LR2 P~ 012 b8 2KKKA 127 2 1 A L 3 PZ 08.$H2 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 04 .2H2 o ?L ACSAA 25 512 K H5 [P 0412

pe$?OvJ$$CB 1 120 ZNZ P2 07

6T JACSA 09 2268 C23 H29 US p 6? Jac$a o~ 227o CzJ HZ9 05 P

P*5 Vl 71ZA~C~ 380 5 [ p eL5 ?2 CCJO& lgT2 676 ET3 N H IC6 H4 02)3 P 7J ACAC3 29 266 C6LCULAtEO

~A*~ v l 67 INUCA 3 3Z? R IP&+41 74 CJCH4 52 Z [75 R3 v$ v

P~+$ V l z [ ac8c8 27 731 ~ P6 O3

P~*5 I x 67 JC$1A l g 6 T 1429 K2 PA F7

PBe~ IV PY 63 ZXKK~ 126 98 p$ $1 oJ

P I * 2 V l

1o 4CAC8 26 501 pez 03 PB*2 V I I

~ 9 ZKKK& 120 213 P8 CAZ $ | 3 09 4 &CCRA 17 1539 Pe P2 06

PB*2 v i i i t l SPHCA 15 728 P8 w 04 64 ACGRA 17 1539 PB P2 06 ?3 CJCH4 51 ?o P02 V2 O? ?2 HROUA 7 1025 BI t l T&NATES

p o * z IX 67 ACCRA 22 744 PO F2 73 GJGHA 51 TO P02 V 2 0 t ?~ ZKKKA 139 215 P8 c 03 ?~ CJGHA S2 2 7 0 1 P U V2 06

P8*Z x 70 ZKKKA 132 228 P03 P2 08

P8 .2 X l [ 51 6CCR~ 1o 1o3 p8 IN 0312

R3 VS v IOA $ 041 70 ZKKKA 132 220 P83 P2 00 71 INOC~ 10 1264 K2 P8 CU IN 0216

P6"4 IV 72 JCSIA 1972 2448 R3 VS V INA4 P8 041

p o * * 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

p o . ~ v i i i 60 N~ou~ 3 153 P8 02

PO*2 I v SQ 67 INOCA 6 730 P0 lob H5 OH3 CHIC 01212 60 J$ [CA g 166 po I I C 6 H5)2 CH C2 0212

po*~ v I 68 NRBUA 3 699 R3 V$ V INZ P02 071 73 INOCA 12 1726 XE PO F I [ 6 1 J C $ I A lg61 3?ze K2 po F6

PH*~ v I 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 (FLUgR[TE I PR*J V l

t l MRBUA 6 545 R3 V$ v (PR2 N03 0121 Pa*3 VIII

70 SPHCA 1~ 28 PR2 U2 09 74 ZAACA 403 I R3 V$ v (PR F3|

P8 .3 IX 7o SPHCA 15 28 PRZ U2 og 5g ZKKKA 112 362 PR IC2 MS S 0413 .gH2 0 74 ZAAC4 403 I R) v$ v IPR F ) i

e~*4 V l - 72 ACBCA 20 956 OA PR 03 ?~ ACBC6 31 971 ~Rt 0Z2 73 JSSC8 U 3 3 1 R IPR941 74 CJCHA 52 2175 R3 VS V

PT*2 IV SQ 72 REF 5 PC3 C0 06

P t * 4 v I 89 JINCA 31 3803 PY 02

R3 v$ v 1N2 p l 2 o71 ?4 CJCHA 52 2175 R3 V5 v

P t * 5 V l 67 STBGA 3 I R3 v$ v (FLUORIDES) 67 JC$IA 1967 478 XE PT F I I

p u * ~ v t 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 3 3 1 R (PU*4) t~ CJCHA 52 2175 R3 VS v

PU+6 V l R3 VS v tSA2 SR PU O61

a o + 1 V l 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 xx i 70 ACSCA 26 1464 R8 N[ F3 ?o J$$C6 2 416 R9 NI F3 70 JS$CB 2 562 86 NI F3

RO-I XXV 65 ACC86 19 2O5 ~8 u 02 IN 0312

aE+4 v i

4 CJCH~ 3 2175 Rt vs v RE+5 v |

70 ACSA~ 24 3406 N04 RE2 011 uNPu2 co2 aE2 o?

O8 ACSCA 24 6T4 Re CL5 REe6 V l

t5 JS$C6 13 77 BA2 HN RE 05 R3 V$ 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 IN-C4 H7 02121 (RE 0 4 | 2

kE÷Z v l 68 ACiEA 7 295 RE2 07 {H2 012

l o 4C8CA 26 1876 R,2 o ) RH*~ V l

?3 INOC6 12 2640 ~N F5 Ru+3 v i

R3 vs v IL6 Ru 03i RU*4 V l

?o ac$64 24 l l 6 RU oz 74 4 c o c , 30 143~ N413-X~ ~U4 0~ 7~ CJCH4 5~ 2175 R3 vs v

RU*5 v i ?I JC$[A IVTI 2789 RU F$

REF 7 k3 VS V IC02 RU2 o?) I ) INOC~ . IZ l / I T X~ RU F I I

RU*t IV S4 J6CS~ 76 3317 ~ RU O4

au+u I v 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 o 6~ ~CCaA [9 664 NN $ O4 ,i 6c566 ~s 3213NAsH054 °4Nz° ?z 6cuc6 28 864 SN 12 N~IU6 Z36 g5 C4 $ 04 .2H2 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

$ 0 . J I v ?o A¢$AA 24 320 38 P 04

$ 0 . 5 V l ?o 4 n n t 4 5s 1480 NN? $8 AS 012 7 1 J C S l & IVTl 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 V l 68 CJCHA 46 |446 S C 2 0 J 60 ARKE4 29 )43 scz oJ

U~PU4 5CZ ~ I Z 01 73 5PHCA 17 749 SG2 $12 o? t3 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 041 .2H2 o 69 5PHDA 14 9 NA3 SC 512 O7

s c * J r i l l 14 INUCA tO 13 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 IV be ZAACA 358 125 NN S£ 0 4 , CO $Z 04* 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~ NI SE 04 .6H2 0 ?2 4C8CA 28 204~ K~ 5E 04 ~9 AC8C4 as [ 9 C U IN . 3 1 4 S~ 04 ? 1 J $ c I A 1971 1857 S e l * 6 1 - o

S l * 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 I I 437 CA3 AL2 S i 3 012 IGROSSULARIT( I 71 4NNI6 56 IV3 CUZ C&Z $13 010 .2N2 o ?1 5PHEA 15 926 ~A Gb $1 13~ 71SPHCA 15 806 V2 5Z OS 71NATWA 58 218 EU2 51 o~ 7o PEPl6 3 l b l C02 $ I 04 70 ACOCA 25 105 043 S [4 Nab 026 71 4c8c4 27 747 CA2 $ i 04 .CA CL2 7| AGBCA 27 848 C42 $I 04 71 &NNIA 56 1222 N A . | 6 K . 8 4 CA4 1518 0201F .8H2 0 7 1 A N N I A 56 1155 HGS*b FE.4 $13 0 1 2 . ~ F 0 N 69 NS4PA 2 31 L ; N $12 06 ,HA M S I2 ~6

CA NG $12 06 69 ~S4PA 2 95 F E 6 * I H N * I NG*8 C A * I $10

0 2 2 . ! I O H I I . 4 F . 5 6g NSAPA 2 101 L 1 2 . 4 N A . I H G I Z . 9 5 1 1 5 . 7

A L * | 0 4 3 . 4 F4o$ I O H I . 3 7o 2KKK4 132 288 C&5 $ I 2 0 t IC 0312 71ACBC& 27 2269 NA2 $ l UJ .6N2 0 ?z SPHC4 14 z o z l 8ez s i o~ 72 4CBC& 28 1899 AL2 BE3 S i 6 018 ; 4 ACOCA 30 2434 112 BE 51 Ok.

IX*4 V[ 62 NA[WA 49 34S $1 02 69 CJCH6 47 3859 CU $ l Fb*4N2 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 73 4CBCA 2g 2 7 4 1 N $i Fb .bH2 o 73 ACSCA 29 2748 C0 $ 1 F b * b H 2 0 14 CJCHA 52 2115 63 V5 V

SH*2 v l I UNPUl SN 12

SH*2 V i i i UNPUI SN 8R2, SN F2

SH*Z i x vUNPUI. IN CL2, SH 8R2

5M.3 71SPHCA IS 924 NA SN GE 04

$N.3 V l l 70 SPHC& 15 214 SH2 SI2 07 14 SPHCA 1o 575 K2 SN F5

SN*3 V I i i 74 ZAAGA 403 ! R3 V$ V ($N FJ I 74 4CaCA 30 Z?Sl SN P5 014

S~*3 i x 69 ACAC8 25 6 2 | SN ISR 0313 .eH2 0 ?o SPHC4 15 214 $M2 $12 o? 14 ZNOC4 13 2eO N H4 SN IS 0412°4H2 0 7G ZAACA 403 I R3 VS V |SN F3|

SHe3 X l l 72 JSSC8 4 l [ SN 41 03

SH*~ I V ?~ 6C8C6 31 511 K4 SN 04 72 JC$IA 1972 2448 R3 V$ V iNA4 SN 041 7J 4C4CB 29 2bb C4LGUL4TEO

SN*~ V 70 6HHI4 ~5 367 SN t4Z O? 70 asses 2 410 x2 SN 03

SN*4 v I 69 ZAACA 3be 248 L18 IN 06 70 4C$44 24 128? NA4 $N2 GE4 012 IO N)2 74 CJCHA 52 217~ R3 V$ v

$N.4 V l I I 6 t JC$14 1967 1949 SN IN 0 3 ) 4

5R*Z V l 70 244C4 379 I f3 ~ c u z 02 72 ZAAC& 393 266 SR 4Gb 04

SR*Z V l l 72 6CBCA 28 3668 SRIO IP 0416 I0 H )2

SR*2 v i i i ;: . . . . . . . . . . . . . . ~ o,

JCPSA 55 1093 SR H 04 , SR M o~ 7 1 A K M I A $b ?58 $~ c 03 71ACSCA 27 2429 SR IN C o 012 .2H2 0 74 SPHCA 18 ~75 L42 $R3 04 012

SR*2 IX 69 4C,C4 2~ 16~7 s~ 8E~ 04 to ZKKX4 lJl 455 SR ¢ O3 ?2 ACBC4 28 b?9 IR I I 0312.HZ o 72 ACSCA 28 3668 SR5 Ip 0413 0 H 14 SP,C6 18 675 C6a 5 ~ 64 012

s~*~ x ?o AHNIA 55 1911SR CA 014 020 10 H I b . SH2 o 74 SPHC4 18 b75 LA2 ~3 84 012

5~.2 Ill 70 Z&AC4 378 129 SR2 NI IE 06 ? l JS~CO 3 [74 SR I~ 03 I 1 N J H H A 19?1 2 4 1 S R AL3 IP 04 )2 IO H I S . H 2 0

TA*S vl 7 1 A N N | A 55 307 SN T62 07 70 JSSC8 L 454 C4 TA4 o11 71JSSC8 J 145 CA2 o$ ?o ACOCA 26 102 865 t&4 015 b? ACGR& 23 93q v TA 04

t * * ~ v i i ?o J$$C8 I 4~4 CA TA4 O i l ?i JSSC~ 3 i~s v4a os

1 4 . ~ V I I I 5 ~ DANKA 90 T 8 1 T A 8 04

r s * J ~ V l 6U ZAACA 383 14S 182 03

tO$J VIII ?o 5$C06 8 1?45 T03 ~E3 o12 ~4 266C6 403 Z R3 V$ V 178 F31

t 0 * ~ I x ; 4 ZAAGA 403 I R3 V5 V IT8 F3)

TO*4 V l

R. D. SHANNON 757

Table 2 (cont.)

72 ACBCA 28 956 B& TO O) TC*~ V I

67 STBGA 3 I R3 VS V IFLUORIOES) IC÷7 IV

6g MILER 8 381 TO2 07 71ZRACA 3B0 146 TCZ 07

7E*4 IV b9 ACBCA 25 ISSL H3 FE2 TE4 012 CL 7 l ACBGA 27 602 T l TE3 08 , SN TE3 O8~ TE 02~

HF TE3 0B , ZR TE$ 06 71ACBCA 27 60B U 7E~ O9

7E÷4 Vl 61ZKKKA ~18 34S 7E 02 71ACBCA 27 602 M TE3 oe 71ACBCA Z? 60B U TE3 09

TE ,6 IV 11JCS IA Iq71 | 8S7 TE (÷61 -O

TE~6 VI 69 ZENBA 24 64? L I6 TE 08 7O MRBUA 5 19q RG3 TE O6 b9 ACSAA 2~ 3082 NA2 K4 TE2 08 IO H )2 [H2 0 )14 64 INOCA b3~ • TE 0 I 0 H IS .H2 0 64 NATMA $ l 5SZ • 7E O O H 66 ACSAA 20 2138 K4 TEE O6 10 H )4 *H2 0 I o H•;MA ~7 ~ HG~ TE O6 ?0 ZAACA 378 129 SR2 NI TE Ob 70 ACSAA 24 3178 75 l 0 H I6 66 ACSAA 20 153S TE F6 7L ACBCA Z7 815 ~G3 TE 06 65 ZAACA 334 223 • TE 02 {0 H I3 68 CHDBA 267 1433 CUE TE Ob b9 NOCMB 100 1809 AGE TE 02 l 0 H I4 71 BUFC• 94 172 TE (0 H )6 73 ACBCA 29 &43 TEE 05 13 ACBCA 29 956 HZ TEZ 06 73 ACSAA 27 B§ TE IO N )6 74 ACdCA 30 1813 HZ TE 04 14 ACBCA 30 207S IN H4 )6 ITE M0b 024 ) TE {OHI6

7H2 0 THe4 V |

74 CJCHA 52 217S R3 VS V TH*~ V I i i

7 l ACBEA 2? eL~ K5 TH F9 1 l ACBGA 27 2290 •7 TH6 F31 7~ ICHAA B 27 ] K TM P3 010

?H*4 IX B8 CCJOA 1968 990 (N H4 |4 TH F8 69 ACBCA 2S 1958 IN H4 )4 TH F8 bB CCACA 40 147 • THZ P3 O12 . lO ICHAA 4 STZ N• TN2 {P 0 4 | 3 71ACBCA 27 1823 R6 TH3 F13 73 ACBCA 29 2976 NA3 BE 7H I0 F4S 70 ACBCA 26 1185 K NA TH Fb 71ACBCA 27 22Tq IN H413 TH FT

7H '4 X 75 ACBCA 2g Z687 TH IN 03 )4 ( (CA H533 P 0 )2

7H,4 X l 66 ACCRA 20 B42 TH IN O3 )4 .5H2 0 66 ACCRA 20 83b TH IN 03 )~ .BH2 0

7He4 X l l 6S ACCRA 18 698 ~G TH IN 031b . BH2 O

TI*~ Vl 73 JSSC8 6 213 T [4 07 b3 PHRVA 130 2Z30 712 03 74 J$SC8 9 235 712 03 74 ACBCA 30 662 CS T I tS 04 )2 .12H20

T1÷4 IV 73 ACbCA 29 2009 BA2 T[ 04 6L •CCRA 14 875 8A2 TI 04 1 1 J C S I A 1971 1657 T [ I * 41 -0 74 ZAACA 408 60 RB2 TI 03

T I * k V 68 ACBCA 24 132T YZ TI O5

71 ,4 V I 70 2KKKA 131 276 Y2 T I2 07 71ACBCA 27 6 )S NZ H6 T l P6 11JSSCB 3 340 T I~ 07 70 ACACB Z6 ~36 eA TI O)" ~4 •CCRA IT 240 CO TI 03 71 ~cps, B~ 32~ , , o2 72 CSCMC 8A T Ib O13 72 ZKKKA 136 273 T[ 02 7~ ZKKKA 139 103 K T IP 05 72 INOCA 11 2989 ITi O(CB H7 021212 T4 ICHAA 11 243 (NHA)2 TI O (C20~e lE .HZ O 74 ACBCA 30 2894 8A T IZ O5 T4 CJCHA 52 21TS R3 VS V

T I *4 V I I I 66 JC$1A 196B 1496 T[ {N 0314

7L ' 1V l R3 VS V INF )

T L * t VI I I 75 •CBC• 31 365 TL N 03

7L÷3 IV 71ZAACA 381 IZ9 LI5 TL 04 73 ZAACA 396 IT3 SR4 TL2 O7 74 ZAACA 403 19T BA2 7L20S

7L *~ V l 68 ZKKKA 12& 143 TL2 03 74 ZAACA 409 l g7 BA2 TL20S 75 ZAACA A IZ S7 R8 71 F4

TLeJ V l l l 72 ZAACA 393 223 TL F )

TH,Z V l UNPU l TH IZ

TM*Z V I I UNPUI TM CLZ,TM BR2

TM*J V l a3 PHSSA 3 K4Ab TM2 03

TM*J r i l l 70 SSGO& 8 174S TN3 FES O12 Tk Z•ACA 4O) I k~ vS v ITM F~)

TM*3 IX 74 1ARIA 403 I K ) vS V ITM F31

U*~ V l OB J INC• 3O B23 R lU *3 !

U *4 V l ?3 JSSCB B 331 R3 VS V o7 ,NUt , , 3 . R ,u .4 ,

CJCHA SZ 21 /S R3 V$ V u *~ V i i i

70 ACBIA 26 3B IN Hk )4 U FB T ) ACUCA Z9 IV4Z U eL4

u , k I x b? ACBCA 23 | 9 1 9 K U2 F9 6q •GBCA 2S 2163 K2 u P6 TZ ATRIA Z7 245 C~ U6 EZ~ I$ ACBC& 29 4&O CS U2 F9 Tk ACBC• ) u l e66 B - NH4 u FB

u.S v l 6T ACCR~ Z~ B65 tS U F8

A~ BUFC~ 6B 21k U CR OT BUFC• vO 2BT U FE U4

U*3 V I I T$ SPNCA 1 | ~23 U2 RO 08

U ,6 v l oE &CBCA 2 " q67 CU u 04 =e ACBC~ ZS /OT SR u o * , 8~ u O4, CA2 U O~,

$~Z u US, CA3 U OB,SR~ U O6

J0~0A 23 477 CO u

; I . . . . . . I . . . . . . . . . . . . INU~A 4SB u 03

I t J INCA 33 2867 CR2 U 06 72 ACBCA 28 3~89 U O2 I 0 H I2 13 ACBCA 29 7 U E8

U~6 V I I ?2 ACBCA 28 3609 U 03

U*6 V I I i 09 ACBCA 25 787 CA U 04 65 ACCRA 19 205 RB U 02 IN 03 )3

V *Z Vl UNPU3 V F2

V* ) VI 70 PRVBA 2 3771 V2 03 7J JESTS 6 419 V4 O7 69 ACECA 25 1334 V IC3 H7 02 )J b9 ZAACA 369 306 N VZ 04 74 MRBUA 9 1091 IV0 .99 CRO.01 IZ 03 70 JPCSA 3 1 Z ~ 6 9 V2 O3

V*4 V b5 ACGRA 19 432 L I V2 05 b l JCPSA SS 53 V O I tS H7 0212 73 ACBCA 29 269 CA V3 0T 73 ACBCA 2g 1335 CA V4 09

V *4 V i 72 JSSC8 5 446 CU V 03 T5 JSSC~ A 419 vk a t 72 PRVBA 5 2361V OZ CR 74 ACBCA S0 26~4 V3 07 71ACSAA 25 2675 Vb 013 70 ACSAA Z4 4~0 V02 74 PRVBA I0 49o VO2

V*5 IV be RCBCA 24 292 Y V 04 6O CHPLB 2 47 ER V 04 67 ACSAA 2L 590 MN2 VZ 07 70 ZK•K • 1 3 l 161 5&3 IV O412 71 JESTS 3 4~a NO V 04 71ACBCA 2~ 2124 NA3 V 04 .12H20 70 INOCA 2259 CA2 V O4 CL 1L CJCHA 4V 1629 MG3 V2 08 73 ACBCA 29 2304 C03 VZ 0e , N i3 vz 08 72 JSSCB 4 29 FE v 04 13 CJCHA 51 100¢ ZN2 VZ 07 71CJCHA A9 30S6 ZN3 V20B 73 JSSCB 6 $38 L13 v O4 12 CJCHA 50 3964 CU3 vz 08 73 CJCHA $1 70 PB2 VZ O7 73 ACBCA 29 14 ! Y V 04 73 ACBCA 29 133B CUB VZ O10 73 CJCHA $1 265 L i V 03 ~, ,CRCA 3~ 16~BN, v 0 3

4 NJMMA Z I0 CAS IV 0413 0 H V*5 V

SO ACSAA 4 1119 vz 05 71RVCMA 8 ~O9 Li V2 05 74 ACBCA 30 2644 V3 07 74 ACBCA 30 2491HGZ V2 0T 73 ACECA 29 S&7 HG2 V2 07 TO CMOCA 270 9SZ CA VZ 06

V *5 V i 73 JSSCB 3 432 V P 05 11ACSAA 25 2675 V6 013 ZZ CJCHA 50 3619 NG V2 06 73 CJCHA $1 2621V P O3 ALPHA T~ CJCMA 52 2184 K3 V OZ C2 O4.3HZ 0 73 ACBCA 29 1743 GU VZ 06

M*3 Vl bT STBGA 3 I R3 VS V {FLUORIOESI

M+6 IV b9 ACBCA 25 | 704 K2 H 04 ~1SPHOA 13 b56 N02 M 06 TI SPHCA 13 92B PB M Ok 72 ACBCA 28 3174 SN w O4 71JCPSA 55 IO93 SR M O4,BA M Ok

ACBCA 30 1872 N •Z "M 04 T~ ACBCA ~O l e t 8 • LZ IM O~33

W*6 V T4 ACBCA 3O Z3e7 CA3 M O~ CLZ

M.6 Vl 69 SPHCA 13 933 HG H 04 b9 SSCOA 7 1797 612 M O& 70 SPHCA 14 B18 K NO (M 04 )2 10 SPHCA 14 $15 L i 2 FE MZ OB 70 SPHCA 15 28 PRZ MZ 09 T0 ACBCA 26 1020 CU M O4 70 JSSCB 2 Z /8 LIFE (H O4)2 66 ACSAA Z0 269B H Fb IGAS) 72 ZENSA 27 ZO3 SN M 04 TI SPHCA 13 991 N~4 M3 013 74 JSSC8 10 3 FEE N 0b 74 •CBCA 30 2069 6A M 04

XE,~ IV 71JCPSA $2 8 |2 XE 0~ 71JCS IA l g71 1837 XE{+8 ) -O

xE*e V l 6~ INOC, 3 1~12 NA4 XE 06 .B .2 0 6h INOCA 3 1417 N•4 XE 06 .BHZ 0

K4 XE 06 .0HZ 0 V , 3 V l

6T ACCR~ ZZ 3Sk YZ BE O4 . . . . . . . . . . . . . ~R TZs~ % 67 SPHCA 11 ~83 A Y 69 ACBCA 2S 2140 Y2 03 7 1 s p . c • 1~ Bo6Yz Sl OB ~k JCS lA 197k 229 C6& H I2 [ 3 N12 06 Y

Y*3 V l i 6B INOCA T 17TT YIC6HSCOCHCOCH3J~.H20

Y*3 V l l i 6~ AC~CA 24 Z92 ~ V O~ 57 AECRA 10 Z39 Y3 FE5 012 o8 EPHOR 12 1095 • Y NOZ 0E 69 SPHCA 13 420 • Y ~2 U8 , O ~ R ~ , , l , l . S Y Z . 2 0 T ~T MICRA Z3 939 Y 7A 0~ 14 ZAACA ~03 I R ) VS v I v F~)

Y*~ IX S9 Z•KKA | | Z 3bZ Y IC2 HS S 0k l 3 . 9HZ O 1 , ZAACA 40~ I R3 VS V IY P~ |

YB*Z V l 11Z •ACA 3B6 22 | YB BR2, Y8 12

YB*Z V I I 74 ZAACA 4O3 4~ Y8 eL2 71ZAAC• JSb 221YB 8R2

Y6e¢ v i i i T l ZAACA JB6 ZZ l YB FZ

YB ,J v l 7u SPHCA 14 85A YBZ SI O5 10 •CBCA 26 4B~ YBZ S12 O7 70 ZAACA J77 T0 C• v~Z 0~ , SR YBZ O4 74 ACBCA 30 18S7 Y6 P3 09

YB '~ V l l 70 SPHCA I~ B3~ YB2 S l 05 ~ INOCA B ZZ VB I t 5 MT O I l 3 I~Z OI O9 INUCA 8 29 VB ICE HT OZ l J IHZ 03 1 /Z C6

YBe3 V I I I T0 INOCA 9 109b YU L I Fk ~o $SCOA 8 174~ YBJ FE3 01Z

ZAACA ko3 v . V lYE FS! YB*~ IX

I k ZA~CA ~OS I M3 vS v lYE FSI ZN,Z i v

~a SP.0A IZ eeT N •Z ZNZ S lZ O7 6V ACBCA 23 IZ3 ) ZN 0

b9 PHSSA 32 KQ| ZN FEZ 04 73 ACSAA 27 1541ZN $ 03 .2 1 /2H2 0 bA INOCA 3 265 . ZN 10PMI2

ZN*Z V 70 JSSCB 1 120 ZN2 P2 07 73 CJCHA 51 I 004 ZNZ V2 07 7 l AMNIA 56 1147 ZN~ AS2 08 IO H )2 .2H2 0

ZN*Z V l b5 CJEHA 43 1147 ZN2 PZ 07 68 SPNCA 13 127 ZN M 04 70 JSSCB 1 120 ZNZ P2 07 71CJCHA 49 30Sb ZN) V2 OB 71AHMIA 56 11k7 ZN4 AS2 08 IO H I2 .2HZ 0 73 ACUCA 29 2741Z f l S | Fb .6H2 O 73 ACSAA 27 154 l ZN S 03 .2 I / ZMZ 0

ZR*4 IV 75 JSSCB 13 ZTB R3 VS V IM~ ZR OAI

ZR*4 V b9 CCJOA 1969 727 K2 ZR 03 70 JSSCe 2 410 KZ ZR 03

ZR*4 v l 69 ACBCA Z5 2658 ZR (M AS 04 IZ .MZ 0 b9 ZAACA 371 306 L12 ZR 03 70 JSSC8 L 478 •2 ZRZ OS eO ACS• • ~2 I a2Z ~ • ZR2 P30 lZ ; 3 ACBCA Z9 2294 L IZ ZR F6 71ACBCA 2T 1944 RBS ZRA FZ I 14 CJCHA 52 2175 R3 VSV

ZR*4 VII 6e ACBCA Z5 21e4 NAZ ZR F6 70 AGBCA 26 417 IN H413 ZR F t 70 JACTA 53 12b ZR OZ 73 ACSAA 27 177 ZR4 I0 N l6 (CR 04 IS .HE 0 73 ACSAA Z7 Z614 ZR (0 H IZ S O4,.MZ 0 11ACBCA 27 1944 Re5 ZR4 F21

ZR*4 v i i i • b9 ACBCA E3 1558 ZRZ (S 0414 IH2 O IB .6H2 0 b9 ACBCA 2S IB66 ZR2 iS 0414 (HE O IB .EHZ O b9 ACBCA ZS IS tZ ERE IS 0414 .§HE 0 71ACBCA 2T 63B NZ H6 ZR F6 71AMMIA 56 Tee ZR SI Ok b3 INOCA 2 243 ZR (ACA¢ I4 ?L ACBC& 27 1944 RE5 ZR4 F21 bJ INOCA 2 250 NA4 ZR ICE 04 )6 *3H2 0

KEF | G. E . BR0~N, PH .0 . THESIS , V IRGIN IA POLYTECH.INST.,UNIV.MICROFILNS,TE-49B

REF 2 R .M .G .MVC•0FF ,CRYSTAL STRUCTURES,WILEY, N .Y .e I96B

REF 3 H.BARNIGHAUSEN ET AL . ,PROC.107H R .E . RES .CONF.CAREEREE,AR |Z I I 973 )P .490

REF 4 C .BRANOLEeH.STE iNF IN• .PROC.7TH R .E . RES.CONF.eCORONAOO,CAL.OCT 28 ,196§

REF S R .D .SHANNON,U .S .PAT .3&bS IBL tNAY Ib .1972 REF b W.H.BAUR,NITROGEN,HANOBOOK OF GEUCHEM.

SPRINGER-VERLAG,N .Y .1974 REF 7 A .M .SLE IGHT tU .S .PAT .38&9544 ,NOV 19 ,1974 UNPUI H.BARNIGHAUSEN,PERSONAL COMMUNICATION UNPU2 A.M.SLEIGMTePERSONAL COMMUNICATION UNPU3 C.C•LVOePERSONAL COMMUNICATION UNPU4 C .T .PREMITT ,PERSONAL COMMUNICATION UNPUS M.H.BAUR,PERSONAL COMMUNICATION

ACACB ACTA tRYST . SECT. A ACOCA ACTA CRYST. SECT. B • CCRA ACIA CRYST. ACIEA ANGEM. CHEH. INT . EO. ACSAA ACTA CHEM. SCAND. ADCSA AOV. CHEM. SER. • MMIA AM. MINER. ANCPA ANNLS CNIH . AR•EA ARK. KEM] BAPCA BULL. ACAO. POL. SC I . SER. SC I . CH IH . BCSJA BULL . CHEN. SOC. JAPAN 8SCFA BULL. SOC. C . IM . FR. OUFCA BULL. BOG. FR. H INER. CMISTALLOGR. CANIA CAN. MINERALOGIST CCACA CROAT. CHEM. ACTA CCJDA CHEM. COMMUN. CHOBA C. R . HEBD. SEAN. ACAO. SC I . SEA. B CHOIR C . R. HEBO. BEAN. ACAO. SC I . SERe C CHPLB CHEM. PHYS. LETT . CIMYA C•RNEGIE iNST. MASH. YEARBOOK CJCHA CAN. J . CHEN. CSCMC CRYST. STRUCT. COMM. CZYPA CZECH. J . PHYS. DANK• 00RL . AKAD. NAU• , SSSR HCACA HELV. CMIM. ACTA ICHAA INORG. CH IN . AGTA INOC• INORG. CHEM. |NOMA RUSS. J . INORG. CHEM. INUC• INORG. NUCL. CHEM. LETT* iVNMA IZV . A •AD . NAUK SSSR, NEORD. CHEH. J•CSA J . AH. CHEM. SOC. JACG• J . APPL. CRYSIALLOGR. JACTA J . AM. CERAN. SOC. JAP IA J . APPL. PHYS. JCNLB J* CRYST. MOLEC. STRUCT. JCOMA J . L,'SS-¢OHMON METALS JCPSA J . CHEM. PHYS. JCS IA J . CMEM Sac . LON0. 10ALTOM) JCSPA J * CHEM. SOC. LONO* (PC•K IN I | ! JESUA J . ELECTROCHEN. SOC. J IHCA J . INORG. NUCL. CHEM. JMOSA J . MOLEC. SPECTROSC, JNBAA J . RES. NAT. SUB. STAND. SECT. A J0P~A J . P~YS. IFR . | JPCHA J . PHYS. CHEM. JPCS• J . PHYS CHEM. SOLIOS JSbCS J . SOLID STATE CHEM. JSTCA J . STRUCT. CHEM. JUPSA J . PHI'Be SOC* JAPAN HNLHB MINERALOG. M•G. H0CMB MH* CHEM. HRBUA MATER. RES. BULL . MSAPA H IM . $0C. AMER. SPEC. PAPER NATUA NATUREILONO. NATMA NATURMISSENSCHAFTEN NJMIA NEUES JS . H INER. ASH. NJMMA NEUES JB . MINER. NH. PEPIA PHYS. E•RTH PLANET. INTERIORS PHSSA PHYS. STATUS SOLIDI P lS •A PRUC. IN01 •N ACAD. $C I . A PISUA PROC. IND IAN ACA0. S¢ I . 8 PRLAA PROC. R. SOC. SERIES A PRVAA PHYS. REV, SECT. • PRVBA PHTS. REV. SECT. 8 p~r~VA PNTS. Rev . RICPB RECL TRAV. CHIN* PAVS-BAS RVCMA REVUE CHIN . MINER* CPR.) SCIEA SCIENCE 5PHCA SOVIET PHYS. CRYSTALLOGR. SPHOA SOVIET PHYS. OOKL. SSCO• SOLID ST•TE CO"MUM. STBGA STRUCT. AMO BOND. TPSU• ;RAMS. FA••OAY sac . . MP~[& TSCHERMAKS MINER. PETROGR. M ITT . UNPUI IU ,PUBL ISHE0 REFEREMGE) ZAAL& Z . •NORG. •LLG . CHEM. Z•~R• Z. KRISTALLOGR. MINER. ZEPY• ~ . P . vS . ZE~BA . NArURF. ZST• I ZM. STRUKT. •H IM ,

758 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 AND C H A L C O G E N 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 Bi 3÷ and La 3+ have nearly equal radii. From a study of BiTaO4 Sleight & Jones (1975) have concluded that although Bi a + and La 3 ÷ have essentially equal radii, the size of Bi 3÷ 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 Bi a+ and La a+ compounds where the lone-pair character of Bi 3+ 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 Bi 3 ÷ is forced into high symmetry, a Bi 3+ compound has a smaller volume than that of La 3+, but when the lone- pair 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 Cell volume Ratio BiLi(MoO4)2 314.7 0.96 LaLi(MoOa)z 328.7 BiNa(MoO4)z 320-5 0"97 LaNa(MoO4)2 332.1 BiOF 87.6 0.90 LaOF 97.7 BiOCI 110.7 0.95 LaOC1 116.8 BiOBr 123.8 0.98 LaOBr 126.4 BiPO4 293-0 0.96 LaPO4 304.7

(b) Lone pair character of Bi a + dominant BizMoO6 268.5 ( × 8) 1-00 LazMoO6 267.3 BiFeO3 62.49 ( x 6) 1"03 LaFeO3 60.77 ( x 4) Bi2Sn207 1219.9 ( x 8) 1"00 La2SnzO7 1225.3

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 impos- sible to define their ionic radii. The coordination of Sn 2÷ by oxygen or fluorine is always extremely ir- regular,* leading to average distances which depend on the degree of distortion. Since this distortion varies widely from one compound to another, it is not mean- ingful 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 NH~ 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. How- ever, 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.

. 9 0 I I I I I

.80 V

. 7 0 ~- - - - - - - - - "~ To "91'

. 5 0 -

, 4 0 I r I I I + 2 4"5 + 4 + 5 . + 6 + 7

OXIDATION STATE

Fig. 1. Effective ionic radius (,~) v s oxidation state.

• R . D . S H A N N O N 7 5 9

Results and discussion

In Table 1 two sets of radii are included. The first is a set of traditional radii based on r(V'O z-) = 1.40 A. The

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

2.oo1--- 1.901

~iao i 1 . 7 0

. 1 . 6 0

1.50

1.40

1.30

1.20

1.10

1.00

.90

8 0

.70

.60

.50~

1.20

1.10

~ - - ~ . . . . r - I I - - I I 1 I I

Cs -

Rbd

J • L i +

I I I I I I I ill 4 5 6 7 8 9 10 12 13

CN

(a)

1.70

1.60

1.50

1.40

1.30

1.20

1.10 r

1.00

.90

.80

Y0

.60

.50

.4O

.30

.20

I .10 2

, , , . . . . .

~ Ni2-~

Be +

CN

( b )

1.00

.90

.80

.70

.60

.50

A0

.30

.20

.10

0

I I 1 I I I

• . .

. . . . - ~ B i 3 + ,

• j . ~ . ~ T L 3 ÷

°/ ~ Go3+

~ AI 3+

_ B 3 +

CN

(c) (d) F i g . 2. (a)-(e) Effective ionic radius ( • ) vs C N for some common cations.

J I i I I la3F+ ~]

1.30

p 3+

1.10 ~_---~-T b 3+ -

~Tm Er ..

1.00 ~""~'~"Lu-'yb3÷ - .

.90

Zi = .

.7 I I I 1 ] 6 7 8 9 10 !i 12

CN

760 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 AND C H A L C O G E N I D E S

1.20

i . I0

!.00

.90

.80

.70

.60

.50

.40

.30

.20

.10

I I t I I I I I

/ Ge4+

y Si +

~ p.4+ Bk 4+

:Hf4 +

Ti 4+ ~ / 4 +

CN

(e)

Fig. 2. (cont.)

'1 Th 4÷

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 deriva- tion 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 vs 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 vs valence, r vs 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+, VITa 3+, Wpaa+, VlTa4+ ' IVpb4+ ' V~IrS+ ' WOsS+ ' WReS+, WpuS+, WBiS+,

VXOs6+, VlRe6+, and V1Os 7+. 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 compound having metallic conductivity. Distances calculated from these radii may be too small for use in compounds having localized electrons. (See discussion E f f e c t s o f e l e c t r o n d e l o c a l i z a t i o n . )

In addition, the sources of the radii are indicated in Table 2.

Fig. 2(a)-(e) shows that r -CN plots are reasonably regular. Notable exceptions are IVNa+, VNa+, and ~VK+. It is apparent that Na-O and K-O distances do not decrease as much as anticipated from the r -CN curve* when the CN falls below six. Typical distances and corresponding radii in Table 4 show that Na-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('-~) RNaCl L Acscl BNaCl

where R=intera tomic distance, A=Made lung 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 -CN plots probably caused by poor or insufficient data, e .g . curves for TI 3+ vs y3+. The differences in slopes of Ti 4+ VS Cr 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 " ' ~ . . . . . . . . I - - - t~ --~,, n, ,

I ! ~ ', c i I i ~ ', 7 ! i I " , , : , I i ° . . . . . . . " _ _ ' _ _ i " ' s, T - - T ~ I - ] , ~ i i i l

I I I I

i I _1 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 761

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.

2.05

2.04

2.03

2.02

2.01 ~¢~)

2.00

1.99

1.9e

1.97

1.96

1.95

1.94

i I ,

-v'r NbS+

R= 1.976 + 6.45 A

i i i [ i i i I • 002 .004 .006 .008 .010 .012 .014 .016

Fig. 4. Mean NbS+-O bond length v s distortion. Vertical bars represent average e.s.d.'s quoted by the authors. Solid circles represent more accurate data.

r i i

2.01 "v ' r M 0 6 +

2.o0

1.99

1:98

1.97

1 . 9 5

1 . 9 4

1.93 J

R=1.920 + 3 .73 A

1.911 1.90 ~ , ~ , v , ~ ,

.002 .004 .006 .O08 .010 .012 .014 .016 .018 Z~

F i g . 5. M e a n M 0 6 + - O b o n d l e n g t h vs d i s t o r t i o n .

Table 4. lnteratomic distances in some compounds containing tetrahedral and octahedral Na +

R (/~,) r (/~) Reference C o m p o u n d

(a) lVNa+ Na20 2.40 1-02 NasP3010 2.37 0.99 60 A C C R A 13 263 N a O H . H 2 0 2.36 1.00 57 A C C R A 10 462 Na6ZnO4 2.39 0.99 69 ZAACA409 69

Mean 2-38 1.00 (b) VlNa+ Na2WO4 2.38 1.00 74 A C B C A 30 1872 NaC6OTH7 2-37 1.01 65 A C C R A 19 561 Na4Sn2GeaO12(OH)a 2"39 1-02 70 ACSAA 24 1287 Na2P2OT. 10H20 2.48 1.10 64 A C C R A 17 672 NaHCO3 2.44 1.06 65 A C C R A 18 818 Na2B406(OH)2.3H20 2.41 1.04 67 SCIEA 154 1453 Na4P4OI2.4H20 2-415 1.05 61 A C C R A 14 555 NaAI(SO4)2.12H20 2.45 1.10 67 A C C R A 22 182 NaB(OH)4 .2H20 2-460 1-09 63 A C C R A 16 1233 NaU acetate 2.375 1.025 59 A C C R A 12 526 CloHI3NsNaO6P.6H20 2-406 1.046 75 A C B C A 31 19

Mean 2.42 1.05

Factors affecting mean interatomic distances

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 sub- stitution 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.

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 an- alytical 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 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

The effects of distortion on mean bond lengths in numerous polyhedra have been determined. Al though distortions in tetrahedra are not as important as in octahedra, they can contribute to variations in mean tetrahedral distances (Baur, 1974; Hawthorne, 1973). Strongly distorted octahedra like those containing V 5 +, Cu 2+, and Mn 3+ show a significant variation in mean distance with distortion, A* (Brown & Shannon, 1973; Shannon & Calvo, 1973a; Shannon, Gumerman & Chenavas, 1975). Octahedra containing Mg 2+, Zn z+, Co 2+, and Li + are generally less distorted than those of V 5+, Cu 2+, and Mn 3+ and show a less pronounced dependence on mean bond length (Brown & Shannon, 1973).

The effects of distortion on mean bond lengths in NbS+,O and Mo6+-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 mean bond length on distortion for all octahedra studied. It is clear from Fig. 4 that undistorted Nb 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 mean 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.

date. In fact, the Mo6+-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 W6+-O octahedra but they are only approximate because of the scarcity of accurate structural data. Analysis of Ti4+-O octahedra was unsuc- cessful because of scatter in the data. Distances in Ba6Ti17040 (Til lmanns & Baur, 1970) and BaTiO3 (Evans, 1951) deviated significantly from a linear relation.

Relations between mean distance and distortion should be particularly useful to help determine oxidation states in mixed valence compounds with such combinat ions as MoS+-Mo 6+, Ws+-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, Gumerman & Chenavas, 1975).

The radii in Table 1 are generally derived for an average degree of distortion. Thus, interatomic distances calculated from these radii may be inaccurate if the distortion in a part icular compound is much less or greater than usual. This applies particularly to cations whose polyhedra frequently show a large distortion, e.g. MO 6+, Nb 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, ab- normal ly large ca t ion-anion distances are usually found, as expected if the anions surrounding unoc-

Table 5. Compar&on of mean octahedral Nb s +-O distances with distortion

Only structures with e.s.d.'s for Nb-O distances of < 0.025 ~ were used.

Distortion Compound /~ (/~) /t = ((AR/R) 2) × 104 Reference HgzNb207 1.999 0 68 INOCA 7 1704 Cd2Nb207 1.957 0 72 CJCHA 50 3648 NazNb4Ol i 1.977 1 70 JSSCB 1 454 Ba0.27Sr0.75NbzOs.Ts 1.967 6 61 JCPSA 48 5048 NalaNbasO94 1"965 7 71 JSSCB 3 89 Ba3Si4Nb6026 1"989 9 70 ACBCA 26 102 Na13Nb3sO94 1"967 11 71 JSSCB 3 89 Nax3Nb35094 1.959 12 71 JSSCB 3 89 Na13NbasO94 1"964 12 71 JSSCB 3 89 NaNbO3 1.985 16 69 ACBCA 25 851 NalaNb35094 1"947 18 71 JSSCB 3 89 Na13Nb35094 1"991 22 71 JSSCB 3 89 Na13Nb35Og4 1"987 22 71 JSSCB 3 89 Na13Nb35094 1"978 24 71 JSSCB 3 89 LiNb308 1-993 28 71 ACSAA 25 3337 LiNbO3 2"000 31 66 JPCSA 27 997 Ca2Nb207 1.997 31 74 JINCA 36 1965 Ca2Nb207 2.005 34 74 JINCA 36 1965 SbNbO4 2.003 37 65 CCJDA 1965 611 KNbO3 2.011 42 67 ACACA 22 639 NaaNbO4 2.013 52 74 BUFCA 97 3 CazNb207 2.010 53 74 JINCA 36 1965 Ca2Nb207 .2.015 58 74 JINCA 36 1965 Na3NbOa 2.021 60 74 BUFCA 97 3 CaNb206 2.021 76 70 AMMIA 55 90 GaNbOa 2.031 83 65 ACACA 18 874

R . D . S H A N N O N 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.

Distor t ion C o m p o u n d R (A) zi = ((AR/R) z) x 10' Reference Mo2(O2C6C14)6 1"919 5 75 JACSA 97 2123 Mo4On or thorhombic 1.944 9 63 A R K E A 21 365 Mo4On monocl inic 1.946 10 63 A R K E A 21 365 Mo4On monocl inic 1.937 56 63 A R K E A 21 365 Mo4On or thorhombic 1"951 67 63 A R K E A 21 365 Mo4Ot~ or thorhombic 1.911 96 63 A R K E A 21 365 Mo4On monocl inic 1.945 96 63 A R K E A 21 365 (ClsHnO2)2MoO2 1 "952 99 74 A C B C A 30 300 (NH4)6[M07024]. 4H20 1"962 99 75 JCSIA 1975 505 (NH4)6[MoTOz4]. 4H20 1"972 101 75 JCSIA 1975 505 (NH4)6[M07024]. 4H20 1 "960 104 75 JCSIA 1975 505 LiMoO2AsO4 1"967 104 70 A C S A A 24 ' 3711 (NH4)6MoaO27.4H20 1"960 106 74 A C B C A 30 48 HgMoO4 1"965 111 73 A C B C A 29 869 (NH4)6[MoTO24]. 4H20 1 "955 113 75 JCSIA 1975 505 (NH4)6[Mo7024]. 4H20 • 1"962 115 75 JCSIA 1975 505 (NH4)6[MoTO24]. 4H20 1.974 118 68 JACSA 90 3275 MoOa .2H20 1.966 121 72 ACBCA 28 . 2222 MoOa. 2H20 ] "961 123 72 ACBCA 28 2222 MOO3.2H20 1"957 126 72 A C B C A 28 2222 MOO3.2H20 " 1"953 134 72 A C B C A 28 2222 (NHg)5[MoOa)5(PO4) (HPO4)]. 3H20 1"970 140 74 JCSIA 1974 941 Naa(CrMo6024H~). 8HzO 1.976 141 70 I N O C A 9 2228 (NH4)6MoaO27.4H20 1.976 141 74 A C B C A 30 48 Na3CrMo6Oz4H6.8H20 1.976 143 70 I N O C A 9 2228 (NH4)5[(MoO3)5(PO4) (HPO4)] .3H20 1.974 145 74 JCSIA 1974 941 - (NH4)dTeMo6024]. Te(OH)6.7HzO 1.981 147 74 ACBCA 30 2095 CoMoO4 1.991 150 65 A C A C A 19 269 (NHg)6MoaO27.4H20 1.972 151 74 ACBCA 30 48 MoO3 1.981 151 63 A R K E A 21 357 (NH4)6[Mo7024]. 4H20 1"976 152 68 JACSA 90 3275 K2{[MoO2(C204) (H20)]20} 1"976 152 64 I N O C A 3 1603 (NH4)6MoaO27.4H20 1 "974 152 74 A C B C A 30 48 (NH4)s[(MoOz)s(PO4) (HPO4)]. 3H20 1"982 159 74 JCSIA 1974 941 Na3CrMo6Oz4H6.8H20 1.986 163 70 I N O C A 9 2228 (NH4)5[(MoOa)s(PO4) (HPO4)]. 3HzO 1 "977 167 74 JCSIA 1974 941 MOO3. H20 1-984 167 74 ACBCA 30 1795 (NH4)~[(MoO3)5(PO4) (HPO4)]. 3H20 1 "991 186 74 JCSIA 1974 941 (NH4)6[ Mo7024]. 4H20 1 "991 189 75 JCSIA 1975 505 (NH4)6[Mo7Oz4]. 4H20 2"008 197 75 JCSIA 1975 505

T a b l e 7. Variation o f mean M - O distance and effective ionic radius in octahedral environments as a function Maximum

Ion A x 104

o f distortion Correlation Goodness

N* Rot r0:l: m coefficient Mo ~+ 212 38 1.920 3-73 0.74

0.572 3.01 0-63 W e+ 122 7 1-925 3-30 0.75

0"565 3.28 0.66 V 5 + 576 16 1.887 2.62 0.98 Nb s÷ 83 29 1.976 6.45 0.69

0.599 6.83 0.44 Ta 5+ 79 6 1.984 6.70 0.81

0.617 3.79 0-15 Mn 3+ 71 15 1"994 7"08 0-82

0-624 6.15 0"54 Cu 2+ 316 26 2.085 3"99 0"82 Mg 2 ÷ 156 28 2.094 8.31 0.72

' 0"728 8"86 0"77 Co 2+ 46 15 2"106 7"38 0"42

0"734 11 "70 0-70 Zn 2 + 71 16 2"099 7"70 0-64

0"736 8"20 0.74 Li ÷ 148 i l 2"159 8"42 0"81

0"784 9.02 0-79 * N = number of independent octahedra t R=Ro+mA.

r = ro + mzl.

of fit ( x 103)

67 70 19 24

8 71 99 18 46 30 50 77 21

• 18 19 16 21 16 30 35

764 REVISED E F F E C T I V E IONIC R A D I I IN HALIDES AND 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 sum- marizes 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 o f 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(Fe-X)=mean Fe-X distance. A similar parameter

V(Fer, Xn) Rv=

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 Sc 3 + respectively. Such plots usually show a strong

Table 8. Mean distances in structures with partially occupied cation sites

Occupancy Compound factor R (a) IVLi+ Typical 1 "00 1.97 LiAISiO4 (fl eucryptite) 1.00 2.020 (4)

2.025 (7) LiA1Si206 II (fl spodumene) 0"50 2-08 (4)

2-085 (9) LiA1SiO4 (fl eucryptite) 0-50 2.056 (2) Li2Al2Si3Olo 0-40 2.064 (4) LiAISi206 III 0.33 2.068 (5) ~-LisGaO4 0.00 2.11 LiAISiO4 0.00 2.11

(b) VINa+ Typical 1.00 2.42 Na2Fe2AI(PO4)3 (wyllieite) 0.91 2.533 (6) NaSbO3 0.82 2.74 Na2Fe2AI(PO4)3 (wyllieite) 0.70 2.723 (6) NaA1Si3Oa (high albite) 0.50 2.600 (9) NaAlnOt7 (fl-A1203) 0"35 2"839 (I) NaSbO3 0.29 2.65 Na2.58A121.81034 (fl-A1203) 0.25 2.88

(c) ViAg÷ Typical 1.00 2.50 AgSbO3 0"44 2"64 AgSbO3 0.33 2.75 Agz.4A122034.2. 0.22 2.83

Reference

Table 1 73 AMMIA 58 681 72 ZKKKA 135 175 68 ZKKKA. 126 46 69 ZKKKA 130 420 72 ZKKKA 135 161 70 ZKKKA 132 118 68 ZKKKA 127 327 71 ACBCA 27 616 72 ZKKKA 135 175

Table 1 74 AMMIA 74 JSSCB 74 AMMIA 69 ACBCA 68 ZKKKA 74 JSSCB 71 ACBCA

59 9

59 25

127 9

27

Table 1 74 JSSCB 74 JSSCB 72 JSSCB

280 345 280

1503 94

345 1826

345 345 60

R. D. S H A N N O N 765

z.15 / , , ,

|

2'10 I 2.05~-

~ U A t S i 0 4 2"00 i (,8 EUCRYPTITE)

e~TYPICAL i .95 F-Li+-O DISTANCE

I'S°/~- i I t 1.0 .9 .8 .7

LiALSi206 T (~ SPODUMENE) l

LiAISi04~ , ,~ ~LiAISiz06]I[ (~ EUCRYPTITE) = UzAIzSisO~o

i IL~ i i VACANCY

IN ,, UsC.-aO 4 AND .8 EUCRYPTITE e

I I I I I

5 , . 2 , 0 OCCUPANCY

Fig. 6. Mean Li÷-O bond length us partial occupancy.

1.20

1.10

1.00

Rv o r

Rd

0.90

0.80

2.5

| I I I

UNFILLED "d" SHELL 2+, Mn2+, C02+, N j2+

FI LLED "d" SHELL ~ - ~ Zn2+ Cd2+ in 3+

CHLORIDES SULFIDES/SELENIDES- FLUORIDES OXIDES J BROMIDES | / IODIDES

2.0 1.5 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 . 3 0 t i i i i

,2o-C'-." : ~_~" eNa-H

LIO

e L i - H 1.00 eLiBaH3

• Mg-H

0.90 Rv aSi-H f ~ 0.80

a A t - H

0.70 B-H D P-H o a As-H

0.60 aC-H

O.5C

I N -Ho 0.,~ l~ ,Io & oo' -~.s -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.

dependence of Rv on ZIZ. For Fe2+-Mg 2+ the Fe 2+ fluoride volumes are ~110% 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(MmF,) ; 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 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

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+, IVGe 4+, 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 Si 4+. 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 f l-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 conver- sion 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 re- sistivity 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 (Jel- linek, 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+, TC 4+, 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 .662 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, Gen- nis, Gibler, Morrell & Zalkin, 1973) are greater than the radius of 0.565 A derived from the ra-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 semi- con2ucting 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 767

I would like to acknowledge the help of F. Jellinek for providing unpublished data on NaVS2, F. C. Haw- thorne 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. Struc- ture data on rare earth halides and an analysis of the radii of divalent rare earths provided by H. Bg.rnig- hausen were especially valuable. I am particularly in- debted 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.

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A C 32A - 2

(1976). a32, 751 revised effective ionic radii and...

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