CRYSTAL STRUCTURE OF MAGNESIUM-VERMICULITE

A. McL. M.q.rurBsoN axn G. F. W,lr-ren' Dittision of Ind'ustriol

C hemis tr y, C ommonweotth S cienilrtc and' I nd.ustrial Res earch

Or ganiz ation, M elb o ur ne, A us tr alia.

Assrn,{cr

A single-crystal r-ray analysis of Mg-vermiculite has located the interlamellar water

molecules and exchangeable cations in definite positions with respect to the adjacent

molecules tend to form hydration shelis. The importance of the hydration behaviour of

the cations rather than direct electrostatic interaction between cations and silicate layer

surfaces in iocating the cations is emphasized.

A regular distortion of the surface oxygen network of the siiicate layers from the ideal

hexagonal form is reveaied by the difiraction data.

Vermiculite must be regarded as a true clay mineral since it is formed

in the clay fractions of certain soils (walker, 1950o). The characteristic

properties of this mineral, such as high cation exchange capacity (Walker,

1O[], tO+O; Barshad, 1948), the ability to form complexes with organic

substances (Walker, 19506; Barshad, 1952) and a variable interlamellar

distance depending on the exchangeable cation present and the humidity

of the sample (Barshad, 1949; Milne and Walker, 1950; Walker, 1951),

bear a striking resemblance to those of montmorillonite. This similarity,

moreover, extends to their structures which, in so far as they are known'

consist of complex silicate layers interleaved with layers of water mole-

cules carrying exchangeable cations.The detailed structure analysis of montmorillonite has been prevented

mainly by the small grain size of the particles, and the configuration

of the interlamellar water molecules and exchangeable cations in this

mineral is not well understood. Mg-vermiculite, on the other hand, is

structure of the silicate lavers and of the relationships between adjacent

231

232 A. MCL. MATHIESON AND G. F. WALKER

silicate layers have appeared which are not in accord with previous views.Earlier workers on the crystal structure of vermiculite (Gruner, 1934,

1939; Hendricks and Jefferson, 1938o) were in general agreement regard-ing the structure of the silicate layers and their relative disposition whenviewed along the D axis, but neither obtained experimental evidence ofthe structure of the interlamellar water layers. Hendricks and Jefferson(19380) proposed a hypothetical structure for the interlameilar waterwhich was based partly on Bernal and Fowler's (1933) concept of thetetrahedral charge distribution of a water molecule in liquid water.Neither Gruner nor Hendricks and Jefferson were aware, at the time oftheir work, of the high cation exchange capacity of vermiculite, andmore complete information on the dehydration characteristics of themineral has since become available.

ExpnnruBr.trAr,

The vermiculite used came from Kenya and was obtained through thecourtesy of Mr. G. E. Howling of the rmperial rnstitute, London. Thesample has a cation exchange capacity of 130 milliequivalents per 100grams, all the exchange positions being occupied by Mg2+ ions. Thechemical analysis (Table 1) shows no alkalis, indicating that no inter-leaved layers of mica are present. small sections, free from cracks, werecut from cleavage flakes and gently pressed flat to minimize any distor-tion arising from the cutting operation. The approximate dimensions ofthe crystals used in obtaining the diffraction data were 0.5 X0.2 X0.2 mm.

Rotation fi lms indicated that, for the three 9.18 A a*es disposed at

Taerr 1. Csnurcar O" "trii;iTonuura

or Knxva Vnnurcur.mr

sio2Al203FezO:MsoCaONurOKzOHrO

wt.7o34.041 J . J /

8 . 0 12 2 . 5 80.000.000.00

19.93

99.93Mg2+o::

1(Mg: mFe+30 raAlo ro) (Alr zesiz zz) Oro(OH)2. 4.32 lF'zO

[CrD4Or0(OH)2]-o st ft.32H2O. 0.32 Mgz+l+o.er

Or

CRYSTAL STRUCTURE OF MAGNESIUM-VERMICU LITE

120o with respect to each other in the cleavage plane, the sharp 3n-layer line spectra coincide in position and intensity, but that markeddifferences occur in the intensity distribution of the (3iz * 1)-layer spec-tra. Oscil lation fi lms disclosed only one axis with equivalence of bothsharp and diffuse *n- and -n-layer spectra. The crystal system istherefore monoclinic. Moving films of the zero, first, second and thirdIayers about the D-axis were recorded on an equiinclination Weissenberggoniometer (Mathieson, 1951). The cell constants obtained are in goodagreement with those of Gruner (1934), but difier from those of Hen-dricks and Jefferson (1938a) in the selection of the B-angle.

a

be

BSpace Group

5 . 39 . 2

28.57-28.7797"09',

Cc or C21c

s . 3 3 Ae . 1 8 A

28 .90 A97"Cc

Hendricks and

Jefferson

5 . 3 39 . 1 8

28 .8593'15',

Cn or C2fn*

Mathieson and

Walker

* Reported as Cc or C2/c.

Comparison oI the h)l a\d h3l moving-film photographs shows that,for B:97", the unit cell corresponding to the sharp fr:32 spectra iscentered on the C Iace and contains one sil icate Iayer (c:14.45 A).Inclusion of the diffuse kI3n spectra requires a doubling of the c axis

Frc. 1. (a) Electron-density distribution on (010) for Mg-vermiculite. Contours foroctahedral (C) atoms at intervals of 4e.A-,, for tetrahedral (D) atoms and oxygens2e' A-2, for HzO and exchangeable Mg2+ at 1e.A-2. The dotted line represents the le'A-'Ievel. Distances parallel to the s-axis are indicated at the right-hand side of the diagram.

@

-@

A. MCL. MATHIESON AND G. F. WALKER

D -

c -

Frc. 1. (b) The corresponding crystal structure of Mg-vermiculite projected on (010).P, Q, R and. Z refer to silicate half-layers; Q' and R', sheets of water molecules; C, (Mg, Fe,Al) octahedrally-coordinated atoms; D, (A1, Si) tetrahedrally-coordinated atoms; 01,oxygens and hydroxyls at z:0.037; Ozt, Oza, 03, oxygens at z:0.I14; HzO, interlamellarwater moleculesl Mg2+, interlamellar cations. An area, (a/2)XGl4), of the unit cellselected by Hendricks and Jefferson (1938a) is indicated by the broken lines.

234

III

R

Il

r@

tI

M g "

H.o

CRYSTALS:TRUCTUREOFMAGNESIUM-VERMICULITE 235

(i.e., c:28.90 A). The general reflexions, hhl, occur only for hlk:2n.The space group for the structure, based on this value of B, is Cc orC2/c. I f the value 0:93.5 ' is used, the k:3ra spectra are accounted forby a cell centered on all faces and containing two silicate layers. The cor-rect space group for this unit cell is either Cn or CZf n, not Cc or C2f cas reported by Hendricks and Jefferson (1938o). The relation of theirunit cell to the one selected in the present study is shown in Fig. 16.

Intensity data for the 001, h)l and h3l, rcflexions were recorded on theWeissenberg goniometer using filtered Mo radiation. For each set ofreflexions, two packs, each of four films interleaved with tin-foil to in-crease the inter-film ratio, were exposed for 100 and 5 hours respectively.Intensity estimations were made by comparison with a set of standardsobtained by timed exposures of a selected individual reflexion oscillatedover a small angular range. For the difiuse reflexions, a crystal waschosen which gave some indication of diffraction maxima rather than thevery diffuse streaks produced by most specimens. Filtered Cu radiationwas uti l ised to provide adequate resolution of the peaks. The distributionol the 021reflexions was measured by means of a Leeds-Northrop record-ing microphotometer and corrected for film background (Fig. 2).

| 2 3 4 5 6 7 A 9 tO l l 12 13 14 ls

0.aL +

Frc. 2. Photometer curve oI the 02tr diffuse reflexions, corrected for film background.The calculated values for the mean-positional arrangement of structures q and r are super-imposed for comparison,

236 A. MCL. MATHIESON AND G. F. WALKER

The F2 values of the 001, h\l and h3l reflexions were obtained aftercorrection for polarization and Lorentz factors by graphical means(Kaan and Cole, 1949). The structure amplitudes were later placed onan approximately absolute scale by correlation with the caiculatedvalues. For the calculation of structure amplitudes, the scattering factorsfor Mgz+ and Sia+ (fnternationale Tabellen, 1935) were loaded by therespective isomorphous replacements indicated by the formula based ona chemical analysis of the sample (Table 1). The temperature factor,B:1.2 X 10-16 cm.2, was determined by p lot t ing loe > j Fc j /> I Fo Iagainst sin2 d in six equal ranges of sin2 d from 0.0 to 0.6 (Wilson, 1942).Fourier summations were carried out on three-figure Beevers-Lipsonstrips, the a and c axes being subdivided into 30 and 120 parts respec-tively. The electron-density map was drawn from ccintour values de-rived from interpolated sections.

Because of the frequent association of chlorite and vermiculite asmixed-layer structures, it was necessary to be certain that the specimenunder investigation contained no interleaved chloritic material, althoughprevious examination of the total sample had indicated its purity. 'Ihe

crystal from which the h)l and. h3l, data had been obtained was thereforeconverted to Li-vermiculite, and the 001 reflexions rephotographed. Aprolonged exposure showed the characteistic 12.2 A basal reflexion ofLi-vermiculite with a regular series of higher orders (Milne and Waiker,loc. cit.). No sign oI a 14 A reflexion, such as would be produced by thepresence of chlorite, could be found. On this basis, it is estimated that thespecimen contained less than 0.5 per cent of chlorite layers.

Srnucrunr Alrer-ysrs

Initial attempts at a unidimensional synthesis of this vermiculite werereported by Milne and Walker (1951), and an interim statement ofresults in the present investigation was made in 1952 (Mathieson andWalker).

l. Electron-density distribution normal to (00 1)

For the preliminary synthesis, the signs of the 001 structure amplitudesof Mg-vermiculite recorded up to the 62nd order were computed fromthe contributions of the atoms of the sil icate layer alone. Omission ofthe water molecules and exchangeable cations from the calculationsensured that no assumptions would be involved in their location. Apartfrom the distribution corresponding to the silicate layer, the synthesisdisclosed two additional peaks, one at z:O.214 and a smaller one atz :0 .250 .

A unidimensional synthesis of the same crystal after conversion to

CRYS:TAL S:IRUCTUREOF MAGNESIUM.TTERMICULITE 237

Sr-vermiculite reproduced the electron-density curve of the Mg-vermicu-

iite except for the peak at z:0.25, rvhich was substantially increased in

size. The exchangeable cations are therefore located midway between

the sil icate layers. The water molecules are arranged on either side of

the central cations in sheets which l ie at a distance of 2.83 A from the

surface oxygens of the adjacent sil icate Iayers.Recalculation of the structure amplitudes, taking into account the

contributions of the water molecules and exchangeable cations, gave

reliabil ity factors,

2 F o - F c t*: - t*rof 0.14 and,0.22 for Mg- and Sr-vermiculite respectively (Table 2).

2. Project'ion along the b-oxi.s

Since the approximate configuration of the sil icate layer is known,

this portion of the structure can be disposed in the unit cell by considera-

tion of the structure amplitudes for the reflexions 20,12 to 204 (see

Table 2) . With the approximate f parameters derived by this means and

taking the a parameters from the l ine synthesis, a preliminary set of

structure amplitudes for the Z0l reflexions was calculated- Again the

contributions of the water molecules and exchangeable cations were

omitted initially so that no assumptions would be involved in their

location. The resultant electron-density contour map provided more

accurate parameters for the atoms of the sil icate layer, and located the

water molecules at r :0 .142, z :0.213 and the exchangeable cat ions at

r:0.0, z:0.250. Recalculation of the structure amplitudes for all con-

stituents of the unit cell necessitated changes in sign for a few minor terms

only, and a subsequent synthesis produced the electron-density distribu-

tion shown in Fig. 1o. The corresponding diagram of the crystal structure

is given in Fig. 10. The final reliabil i ty factor for h\l reflexions was 0.15'

3. The Crystal Structure in Three Dimensions

Initially, deductions arising from the sharp fr:32 spectra wil l be con-

sidered and the results referred to a sub-cell containing a single silicate

laye r ( c :14 .45 A ) .From the equivalence of the [010], [310] and [310] axes, it is evident

that the projections of the crystal structure along [310] and [310] wil l be

identical with that along [010] (Fig. 1b). The three projections can

therefore be combined to give the complete structure if the coordination

values of the atoms are also taken into account. The crystal structure

of half a sii icate layer (e.g., Q, Fig. 16) viewed normal to (001) is shown

238 A. MCL. MATHIESON AND G. F. WALKER

Tael-n 2' CoupamsoN or Oesnnvnn aNo C,{r,culernn Srnucrunc Auprrrunrs r,or (o) Sr-vanlrrcu-r,rrE AND (6) Mg-venurcurrro. NorB rrlAr F(201):Ft13, t,l2): Srrcnr Drr.nnnENcES rN rHE

Cer,curerno Var,uas lon Tnrso Snrs or, RrllrxroNs Ann Duo ro AppnoxruarrclNsrN THE AroMrc Pene,ltntrns eNn SclttnnrNc FAcroRS

00200400600800 ,1000,t200, 1400 ,1600 ,1800,20o0,22oo,24o0,2600,2800,300o,3200,3400,3600,3800,4000,4200,44

29878

-93

1683362 l

-t74- 7 6

422469

150418885879544

-30- 9

- t J

76

0020040060080 0 , 1 000,1200, 1400, 160 0 , 1 800,2000,2200,2400,2600,2800,30o0,3200,3400,3600, 3g00,40oo,4200,4400,4600,4800,5000, 5200,5400, 5600,5800,60oo,62

28262

1 1 02t134260

105

86l o /

8412 l428368

to76T

<2038

<22+l39

<24<24<25

( /

39<26<26< 2 7

30539

-72z t J

J T J

- 6 7-79-95

1241619 l

t2 l34

11069

108612

-19- 1 1

5933

- 7- 1 1

207633o

o

23

20, 582 0 , 5 620,5420,5220, 5020,4920,4620,4420,4220,4020,3920,3620,3420,3220,3O20,292 0 , 2 620,2420,2220,2O20,1820,1620,1420, t220,lo2082062042022002022042062082 0 , \ 020,1220,T420,T62 0 , L 820,n20,22

< 2 5<24< 2 3< 2 2< 2 2< 2 1<20

3732

< 1 9< 1 8

681001051 6t67 6

10579J I

6337

173263105178116304205136t6

1+732

100r4758+ t

15223629463

o2 l2061

-12

1428391 a

- 9

7092

1226

-20

3 187

109-.),/-48

z 3

l / J

25787

18981

3002 1 212720

l / J

J I

72I / J

4l-40

16320328137

20,5620,5820,6020,62

40,5240,5040,4840,4640,4440,4240,4040,3840,3640,3440,3240,3040,2840,2640,24u\ ),)40,204 0 , 1 840,16+o,7440,1240,104084064.0440240040240440640840, 1040,T2Ln 7-tr

40,T640,18

< 2 3<24< 2 5< 2 7

< 2 6< 2 6

294623

<24< 2 3

466335

<20< 2 0< 1 9

5252292946

150t62t44

< 1 61 663

l o /

5811087

127225ro /

< 1 658

127196

- 1 8- 8

. )J

4538

- 9

27445918

08

42354226

t42t43152- 8

-33

8113+94

- 1 2 6_69

122223178

- J U

I J

13220677

\a)

21934455

18563

< 2 020966

15052546576946410

<26/ 4 1

6l

- t . t

51

1 1

CRVSTAL STRUCTURE OF MAGNESIUM.V ERMICA LITE 239

Trl.ts 2-(continued)

(b )

00r \

F"b" ] F".h

I I n* 1n""" F,a* F"ou.

1n tl

20,2620,2820,3420,3220,5420,3620,3820,4)n 4t.

20,T420,4620,420,5420,5220,54

< 1 616

10589

< t 752

< 1 83773

26<20

474737

<22

1

3010098a A

- J U

- I I

7025J I

1 1543628

7

40,2040,22+o,2440,2640,284t0,3040,3240,7440,3640,38N , NLi 4r.N , M40,4640,4840,50

< 1 829

< 1 8J Z

581 l

<20<20

o.J

8181

<22<23<23

40<24

-23

96 lJ I

261 8I J

6866768

- 51 1

321 7

F*,".

47<30<30<30<30<30

h3l 1 F"a". F"ot"

40,5240,5440,5640,5840,60

60,4260,4060,3860 ,3660,3460,3260,3060, 28ff i ,2660,2460,22ff i ,2o60, 1860,1660,1460,1260, 10

<25/ a <

<2623

<27

80,2080, 1880 ,1680, 1480,r280, 1080880680480280080280480680880, 1080,T2go,T480,1680,1-880,2080,2280,'4

<23<23<22<22<22

4279J /

< 2 t<21

63

322616

<2048

<20<20< 2 1

J I

6358

t2,0812 ,o ,Tn72,0,r212,0,1412,o,1612 ,0 , 18

13,461 1 L L

13,421 3 , 4 013 ,381 1 1 6

13,3413,3213 ,3013,28r J , z o13,2473,2213,201 3 , 1 813,161 1 1 L

13,1213, 10138136t34l J z

47/ 1 1

2 l28684626r7488898I J

<2362

209204t394549

17 r12032

206

531 13023o /

551 a

-28. A

9796) 7

238

27rt96l . ) , /

-4040

1807449

r69

5t94

- 9- 2

307042204

5474J I

-32) 7

5 1L9

- 6

25660A J

n A

- 1 88

2922

30t2

-10

19n a

5127

- 5

7 755

- 2- J t

14

<23<23<22<22< 2 1<,20

207650

< 1 9< 1 9

5081oo

< 1 8

< 1 7

2+t4IL

1 110

240 A. MCL. MATHIESON AND G. F. WALKER

Trnr-n 2-(continu,ed)

60860660460260060260460660860,T060,1260,1460,T660,1-g60,2Affi,22()A,2460,2660,2860,30ffi,3260,3460,3660,3860,4060 4'

f f i rM60,4660,4360,5060,5260,54

80, 3280,3080, 2g80,2680,2480,22

4560J . )

/ 1 a

35a 1

1+196J J

20< 1 8

7666

< 1 950

< 1 9868 130

< 2 0306055

< 2 1< 2 1< 2 2< 2 2< 2 3<2+<24<25<26

< 2 7<26<25<25<24<24

3556J O

104362

1+29 1+J

- 1 8

2 l9054

- 1 1- J /

1 )

94

34- 9

5267

7- 1 5

7

t 430

101 1

3430271 1

80,2680,2880,3080,8280,3490,3680,3880,4080,4280,!m80,4680,48

10 ,0 ,14l0,o, l210,0 , 1010,0910,0610,0410,0210,0010,0210, 0410,0610,0810,0,T010,0,1210 ,0,1410 ,0 ,m10,0,1810,0,2010,0,2210,o,2410 ,0,2610,0,2810 ,0 ,3010 ,0 ,32

12,06

Fot"

< 2 2<22<22<22<23<23<23<24<2+<25<25<26

<264726

<25<24<24<23<23<23<22<22<22

3642

<23<23<24

3626

<25< 2 5<26<26<27

<30

F,"u.

1 a

318I J

1 a

0- 7- 7

7?,,

19T J

2 l3724I J

t40

l 66o

0- 8

1028+31 55

1 8+l32

- 7-2 r

019f . l

19

130r32134,rJo13813 ,101 3 , 1 213,1413,1613 ,1813,2013,2213,2473,2613,2813,3013,3213,34l J , J O

13,3813,re13,4213,4413,4613,48

) ,*r

) n*, It3l.

33,401 t ? q

33,3633 ,3433,3233 ,3033,2833,2633,247 \ ) )

3 3 , 2 Q3 3 , 1 83 3 , 1 6

Fa^. F"alc,

1 813021029882

r8792

25917 l24

-45-58

1098930

-19

o

1239269

- 8

392813

36t2

- 3. A

2 l9 l7860

-16

75I I J

119t9

<20111234J I J

l 4 l

174I l J

227179

? )

4945/ o

952 l

<23<24101r t263

<25<26

2930

<28

<28<27< 2 7<26

237868J I

<241 2

t J z

I J O

<23

CRYSTA L STRU CTU RE OT' M AGN ES I U M -V ERM I CU LIT E 24r

T rr;,x, 2 - (c o nt i, n ae d')

D .F2 calc.

100

33 , t+3 3 , t 233 ,10338336334332330332JJ4

336J J 6

33,m1r 1 -

33,T433,T633,T833,m

"7 , t

33,2433,1633,2833,80s3,8233,3433,3633,3833 ,m33,4233,4433,46

( 1 ? ?

s3 ,3053 ,2853,2653,24q l t t

53 ,2053 ,185 3 , 1 653 ,14( ? 1 t

53, 10

70<22

9013965

<22107207J l . )

17582

<22J 6

tr684

-2362

<23130t t762

<24366878LJ

<25<26<26<27<27

55J+

<26<25<25

43o /

<2440

<24109135

827

60Is450

- 8

104140304140t02- 5

53t43594

-88

24135I2279

- 1 5

I L

899924

-30

0l o

33

58a 1

23- 1 5

133972n l

-35- 4

ro2133

53 ,30s3,32JJ , ,i+

53,36

53,4053,42

73,2073 ,1973 , t673 , t+73 ,1273 , r0738736734732730732734i J o

/ J 6

73,m1\ T,

/ J , r +73,T673,1873 ,n73,2273, '473 ,%73,2873 ,m73,3273,94

021022o2302+025026027028o2902 ,10i ) 1 1

02 , t202 ,1302,14n t 1 (

< A

7r1,-25

56- o l

- 1 1-81

+31030o /

- 1 5

29-31

31J I

451

oo18I9

45a

810

M46

<28<29<29<30<30

29t23

o

4l70

- 9- 2 5- t 9

4558

t . )

12679, J

1

o

503820

-35

<28<27<26

/ o

7634

<25<25

45

56<25<25<25

\ I I

7862

<25<25<26

o4

56<26<27<28

3434

<30<32

- 44l72681827+57255

- 2- 1 3- t 2

36291 1

- 6

22308

- 5

2 l4756

<28<28<27<27<26

53

936934932930932934vJt)

242 A. MCL. MATHIESON AND G. F. WALKER

Tl^nr-n 2-(continued)

538536534532s30532534536s38J J , I U\ ? ] t -

53 ,14[53,ms3 ,1853,20

s3,2453,2653,2-8

93893,mo l T t

93,1493,1693 ,18-93,no? te

93,t4

<25<25<25<25<25

39<26<27<28

52<24

43143r+249

<2443436858

<24<25

961 1 150

<26< 2 7

J I

2740

1341303+

- 4

585370l64

o+t021 1 4

- 213

31_T12- 3

725J I

1210

in Fig. 3a. On the basis of the diffraction data considered so far, thearrangement of the water molecule sites and the exchangeable cationsites (my mz, ms) can be represented diagrammatically by the view(normal to (001) and projected on the base of the cell) of the layerp'R'(Fig.3D). The chemical data indicate that the water molecule andexchangeable cation sites are approximately two-thirds and one-ninthfilled respectively. Calculation of the h3l, strtctwe amplitudes for thisstructure gives satisfactory agreement with the observed values (Table 2)establishing its essential correctness (R:0.17). Table 3 l ists the atomiccoordinates; the alternative sets of values (o) and (6), given for the rand y coordinates of the water molecule sites, wil l be discussed at alater stage.

The structure of the silicate layer which emerges is very similar tothat put forward by previous workers, although greater detail is revealedthan has hitherto been obtained for layer silicate structures, largelybecause of increased precision of intensity estimation combined with re-finement by successive Fourier syntheses. The bond lengths are as

CRYSTAL STRUCTURE OF MAGNESIUM-VERMICULITE 2+3

b)a)

@

a\

i )

Fro.3. (a) Section of the crystal structure of Mg-vermiculite from z:0.0 to 0.114(i.e. half-layer Q) projected on the base of the cell normal to (001). (b) Section of the crys-

tal structure from z:0.213 to 0.287. i.e.. sites of the water molecules in sheets O' and R'and sites of exchangeable Mg2+ cations.

fo l iows: C*-Ot ,2.06 Fr ; O*-Or, 1.69 A; ancL D-Oze, D-Or" , p-Ou

1.624 each (probable error, +0.02 A) . The oxygen atom Or is l inkedtetrahedrally with one D (or hydrogen) and three C atoms, the angleCOD being 109o, whereas O2a, Ory and Oa are each linked to two Datoms with a DOD angle of I42o. If r(Sia+) is taken as 0.41 A, th.rtr(Or) is |.28 L and, r(O2, OB) , 121 A. llfte relationship between ionic radiusand coordination number (Wells, 1950, p. 71) gives the ratio of two- to

* For convenience, C will be used to represent the (Mg, Fe, Al) atoms in octahedralpositions at the centre of the silicate layer; and D, the (Si, AI) tetrahedrally-coordinatedatoms near the surface. The key to the oxygen atoms is given in Figs. 1b and 3a.

o C: (M9,F",A|)

Oolo p = (si,Al)

O Q,,

M g'*H,O(a)H,O (R')

244 A. MCL. MATHIESON AND G. F. WALKER

four-coordinated radii as 12/4)t:0.92 and, the observed ratio, 0.95, istherefore of the correct order.

The contour map clearly indicates a distortion in the surface oxygensheet of the sil icate layer. The hexagon of oxygen atoms XIzXtYtXttYtl(Fig. 3a) is not regular but consists of two interpenetrating isoscelestriangles of oxygens XX'X" and YY'Y" with sides 4.35 and 4.84 Arespectiveiy. The corresponding distance in a regular hexagon would be4.59 A. The distortion is accounted for by a rotation through 5$o of thetriad of oxygens above each D a.tom. Since the change from the idealhexagonal to the distorted configuration wouid involve differences inD-O bond lengths of less than 0.01 A, it is improbable that the distor-tion arises from inabil ity to accommodate a regular hexagonal oxygennetwork in the cross-sect ional area of the uni t ce l l ( i .e . ,9.18X5.33 A).The distortion is more readily explained on the basis of electrostaticforces within the sil icate layer, if i t is assumed that a residual negativecharge on each surface oxygen interacts with a residual positive chargeon the octahedral C atom lying below and to one side (viewed normal to(001)). The electrostatic forces thus invoked are correctly disposed toproduce a torque in the required direction (Fig. 3o), the angular move-ment being limited by the over-riding factor of the D-O distance.

At this juncture, it is appropriate to consider the approximate spatialrelationships of the interlamellar water and exchangeable cation sites toan adjacent sil icate layer. It wil l be assumed for the moment that thewater molecules all l ie at the centre of the peak of the electron-densitydistribution (Fig. 1o), although the possibil i ty that this is merely a meanposition wil l be suggested later. The sites for the water molecules l iedirectly over C atoms and those for the exchangeable cations over Datoms (or hydroxyls) of the sil icate layer. This latter observation indi-cates an important point with regard to the relationship of adjacent sil i-cate layers, namely the coll inearity of (i) atoms 01 and D (or f1) of thehalf-layer 0, (i i) the exchangeabie cation site, and (i i i) atoms D (or H)and Or of the halflayer R (Fig. 1D).

The structure of complete sil icate layers and the method of stackingof the Iayers can be deduced from a consideration of the ft*.32 spectra.The water molecules and exchangeable cations were omitted from thecalculations since they can only have a minor influence on the structureampiitudes. The 021 reflexions were employed in testing the various pos-sible structures.

In discussing the sil icate layers, it is convenient to focus attention onthe site at the centre of the distorted hexagon of surface oxygen atoms.Let this site be S(Z) where Z refers to the half-layer P, Q, R or ?. Thenthe half-layers P and Q combine to form a single layer and ,S(Q) can beassociated with S(P1), S(P2) or S(Pr) (Fig.3o). These three possible

s-------------+

+

s )

I',)

r)Frc. 4. Schematic presentation of the possible stacking sequences inMg-vermiculite.

0) (q) and (r) /[-type silicate layer displaced with respect to an M-type layer by O, bl3

and Zbl3 respectively. (s) Z-type layers displaced by b/3 (ot 2b/3). (t) Positional mean of

structures q and r.

layer structures correspond to the L, M and 1[ types of layers referred

to by Brindley, Oughton and Robinson (1950) in their study of the

chlorites. The three types of silicate layer have individual symmetry

C2/mand are indistinguishable until the 6 axis of the crystal is defined

by the mutual relations of the stacked layers. When a second complete

silicate layer RT is added, there are twelve possible ways of grouping

P, Q, R and ?. The existence of a glideoperation c reduces the possibil i-

t ies to four, i l lustrated diagrammatically in Fig. 4 P, Q, z and s' As Hen-

dricks and Jefferson (1938o) have shown) none of these arrangements

yields structure amplitudes in agreement with the observed intensity

distribution. However, structures q and r give some measure of agree-

ment for reflections 021 where l:2n, and a structure with the unit RI

Iocated at the centre of the projection area (Fig. a l) gives a very close

agreement with the observed distribution of intensities for the 021

spectra. Table 2 lists the amplitudes calculated for this arrangement,

and Fig. 2 shows the F2 values superimposed on the photometer curve.

The solution obtained in this way is completely contrary to all the

evidence of the sub-cell analysis, according to which the site S(R) should

CRYSTAL STRUCTURE OF MAGNESIUM-V ERMICULITE a t <

\

Sr--------------{

246 A. MCL. MATHIESON AND G. F. WALKER

lie over the site S(Q) or displaced therefrom by +b/6 in this projection(i.e., S'or S", Fig. a). Furthermore, a unique structure for vermiculitewould be implied by structure I and therefore no explanation for theoccurrence of the diffuse spectra would be possible. The deductions fromboth the sharp and diffuse spectra can be reconciled only if it is assumedthat structures g and r are equally probable and that structure p doesnot occur. In other words, the stacking of the silicate layers in vermicu-lite corresponds to M-type iayers aiternating with V-type layers. TheIayers, however, can only be arranged so that site S(R) is not in line withsite S(Q) nor S(P) with S(7). The resultant crystal structure can berepresented for the purposes of calculation by the average structure I(Fig. a). The mutual relationships of the surface oxygens of the silicatehalf-layers Q and R are illustrated in Fig. 5.

3.t:3

BlsoB:.8:BoB R

O Oa o

i i ii i li i i

3.3:3 a3.3::

.iii .-o o.]oo T a

a)

Fro. 5. Plan and elevation of thg relationship between the surface oxygen network ofhalfJayers Q and R. ?:ttrr, r:n2, ms are sites for exchangeable cations as deduced from the sub-cell analysis, and are defined by their relationship to the halfJayer Q. Projections arenormal to (001).

4. Location oJ the Si,tes oJ the Water Molecules

In the 6-axis projection (Fig. 1o), the contours of the water moieculestend to be drawn out parallel to the a axis and there is evidence of a tailin the negative *-direction. As a result, the peak height is lower thanwould be expected lor 2.16 water molecules (Table 1).

At first sight, the shape of the water peak might seem to be due to highthermal energy in the water molecules, producing movement mainlyparallel to (001) because of restrictions imposed by the environment.

O O

b)( = n ' r , 9 e ;

\ io {

---l|

t,'s:

(P'i\ l. - -Y ,+

CRYSTAL STRUCTU RE OF MAGN ESIU M-VERMICULITE 247

o

L

. M9r.. o(alO H,o(Q)

i..: H.O (R )o o )

Frc.6. (a) Diagram of the reiation of the distorted water network Q'to the surface

oxygen network of the halfJayer Q. Cation sites za1, m4 n s are also shown. This diagram

illustrates the tendency of each water molecule to approach more closely to its associated

surface oxygen. (b), (c) , (d) The three ways of combining two sheets of water sites, the rela-

tive shifts being b/3, 2b/3 and 0 respectively. (d) is excluded by the data. The sites nzr

and mz with suitable undistorted octahedral environment for the Mg2+ cations are shown.

This explanation, however, does not account for the "tail" on the watermolecule peak and, in order to do so, it must be assumed that the asym-metric electron-density distribution corresponds to regular displacementsof the water molecules from the mean position (Table 3, column (a)). Inthis event, one would expect such displacements to be reiated to theadjacent oxygen network and, in a triad of water molecules (HrO(l),HzO(2), HzO(3), Fig. 6o) over a surface oxygen hexagon, each memberof the triad would be displaced equaily towards or away from its relatedoxygen, i.e., the triad would expand or contract. If i t expands, theremust be concomitant rotations of unexpanded triads in opposite direc-tions around ?mr and m2 (Fig. 6a), and the corresponding electron-densitydistribution viewed along the 6-axis would develop a tail in the negativer-direction such as is indicated in the contour map (Fig. 1a)*. The dis-tortion of the water sheet produced in this way results in a closer ap-proach of each water molecule to its related oxygen atom. The relevantatomic parameters are l isted in column (D), Table 3.

Since each water sheet is located by its relation to the adjacent silicatelayer surface, a complete water layer (consisting of two sheets of watermolecules) can only be formed by superimposing the water sheets in thetwo ways permitted by the stacking of the silicate layers. These twoarrangements correspond to relative shifts of b/3 and 2b/3, and are illus-trated in Fig. 6 b and c respectively. Inspection shows that the two ar-rangements are equivaient and, in both, the relative displacements ofthe water molecules maintain normal H2O-H2O approach distances be-

x The displacement of the rn'ater molecules from their ideal hexagonal positions cannot

be determined accurately from the shape of the electron-density distribution but is prob-

ably of the order of 0.2 A.

c )

A. MCL. MATHIESON AND G, F, WALKER

Testa 3. Arourc P.rlnnunrrns lon Mc-vnnurculrrn

L

COtOtOrUD

OztOrnOt

HrO site (1)

site (2)

site (3)

Iv_tg, srte ,firsite m.zsite mz

0000 .3580 .3580 .3580.3970.397o . r470.r470 434

(o) (b)0.142 0.1600.142 0.160o - t42 0 .105

0. 5000.5000. 500

00 .3330.66700.3330.66700.333o.4040.9290.167

(a) (b)

0 - 0 . 0 1 9

0 . 3 3 3 0 . 3 5 20.667 0 .667

00 . 3 3 3o.667

0000 .0370 .0370 .0370.0960.0960 . 1 1 40 . 1 1 40 . 1 1 4

0.2130.2r3o.213

0 .2500.2500 .250

tween the sheets. The method of stacking the water sheets illustrated inFig. 6 d is excluded, since it could only exist if structure f (FiS.4) werepermissible. The nonoccurrence of structure I is perhaps connected withthe fact that such a water-layer arrangement would involve very closeapproach of the water molecules between the sheets.

5. The Structure of the Interl,amellar Region

From the previous sections, it is evident that the arrangement of thesites of the interiamellar cations and water molecules closely resemblesthat of the octahedral C atoms and 01 atoms, respectively, of the silicatelayers although, in the former, the water sites are displaced somewhatfrom the regular octahedral arrangement. According to the chemicaldata, however, only a proportion of the interlamellar water and cationsites are occupied at one time.

Since each water site is equivalent with respect to the associatedoxygen of the siiicate layer surface, any grouping of the water moleculeswill be due to the influence of the cations. The importance of the cationsin this respect is suggested by the variation of the interlamellar spac-ing produced when other cations are substituted for the Mg (Milne andWalker, 1950). A certain amount of evidence has been adduced by othersto show that Me ions tend to attract octahedral hvdration shells in

CRYST:AL STRUCTURE OF MAGNESIUM-V ERMICULITE 249

water solution (e.g. Bernal and Fowler, 1933), and such octahedralgrouping is known to occur in crystal hydrates such as magnesiumchlorate hexahydrate (West, 1935). It is reasonable to suppose, therefore,that there will be a tendency for the exchangeable Mg ions in vermiculiteto form hydration shells.

Examination of the two equivalent water-layer structures in Fig. 6 6and c reveals that in each case only one of the three m cation sites pro-vides und,istorted. octahedral coordination for a cation (m1 in Fig. 6 b orm2inFig.6 c). The Mgr+-HrO distance of 2.06 A involved, moreover,is in agreement with that observed in magnesium benzene sulphonatehexahydrate (Broomhead and Nicol, 1948) which is the most accuratevalue available. All other sites have an asymmetric environment of watermolecules, consisting of an unexpanded triad in one sheet and an ex-panded triad in the other. Equal Mg2+-HzO distances at these sitescould only be maintained by displacing the cations 0.06 A from thecentral plane, which is beyond the limit of error of measurement from thecontour map (Fig. 1o). The resultant equil ibrium Mg,+-HrO distance,moreover, would be 2.20 A.It is almost certainly true, therefore, that thecations will occupy rnror rnz sites depending on the stacking of the adja-cent silicate layers.

The degree of ordering of the water molecules and cations within theavailable sites can now be considered further. The possibility of orderwithin an 'ind'itidual, water-cati,on layer is not excluded by the diffractiondata since mutual ordering of these layers would be necessary for theirstructure to be revealed by the data. A case for the existence of long-range order of this nature, not directly deducible from the diffractionevidence, has been convincingly put forward in recent studies of hol-landite (Bystrcim, 1951) and psilomelane (Wadsley, 1952). So far, wehave shown that the exchangeable cations in vermiculite lie in a planemidway between adjacent silicate layers, and that their lateral disposi-tion is related to the adjacent water sheets. There are, however, onlyenough cations to fill one in three of the available m1 (or mq) sites.

If it is assumed that the cations, due to mutual repulsion effects, tendto distribute themselves uniformly throughout the available sites, ahexagonal distribution of the type shown in Fig. 7 is obtained. Six watermolecules can be arranged around and in contact with a Mg ion at a usite, a triad in the upper and a triad in the lower sheet, forming thesingle hydration shell already postulated. In the lower sheet, additionalwaters can be added in groups of three around unoccupied sites a or a.,.The water molecule sites around zir in this sheet will be closer to thecations than those around z, so that the former sites will be preferredif it is assumed that the tendency of the cations to form single hydration

250 A, MCL. MATHIESON AND G. F. WALKER

o

Io

dI

O

o

o

Mg''

Hp (to* ot

Hp ( .**r

, o ' - - - O - .

.,e-rq t,

A l

i iYl-_ry" I- /

t-o- - - -a'

^ ' - - o -

...e'-'9. 't.

A ' ' AY 'Y

a....6r"' /

' o r - - ' - /

to- -- .- -o' ,' ...*'.o.

+ ?'i\ l*-ol

t to

- - - t /

I

Frc. i. Diagram r,n"L,""o.ii:?,H:.},i?;,ii:iffi:ffi1]", region. Sites z, z,2,,

shells indicates a similar although less-marked tendency to form second

shells.* In the upper sheet, sites around r will be preferred to those around

?, since the former are in this case closer to the cations. Such an arrange-

ment allows each Mg ion to have around it an almost complete double

shell of water molecules, and the linking-up of these double shells pro-

duces layers in which two out of every three water sites are occupied.

In this arrangement of the water layers, there are holes corresponding to

triads of vacant water sites, each triad being equidistant from three cat-

ions with their associated double hydration shells. These sites may tend

to be vacant (at normal temperature and pressure) because a water

molecule in such a site would be in the third hydration shells ol lwo

cations and hence less stable than those associated with a single cation.

The types of bonding operating within the interlamellar region can

now be considered with the aid of measurements taken from the contour

map (Fig. 1o). If each water molecule (e.g.HzO(-4), Fig- 8) is attached

to its related oxygen by means of a hydrogen bond (HzO-O, 2.84 L),

the second hydrogen can be directed towards another water molecule(HrO(B)) in the same sheet, so that the H-O-H angle is 104fo in

agreement with the spectroscopically measured value (Darling and

* Support for the assumption is provided by evidence of the occurrence of Mg2+.12HzO

groups in salt solutions (Sidgwick, 1950, p. 237), and by the high energy of hydration of

Mg cations.

,o- -_ - -o\

CRYSTAL STRUCTURE OF MAGNESIUM-VERMICULITE 251

\ it. j

Frc. 8. Suggested system of weak hydrogen bonding illustrated for a single water sheetassuming all water molecule sites filled. oxygens of water molecules represented by fullcircles, packing radius (Rees, 1949) to scale; hydrogens.linked to silicate surface oxygensnot shown; hydrogens in the plane of the water sheet represented by broken semi-circleslnegative poles represented by black triangles and rectangles, triangles indicate greaterdisplacement of charge from the piane of the sheet than rectangles.

Dennison, 1940). The second hydrogen lies in the plane of the watersheet but the two negative poles of the water molecule are slightly dis-placed therefrom, one directed towards the Mg ion site and the other point-ing in the general direction of a third water molecule site (HrO(C)).

Since the intermolecular distances within a water sheet are either3.06 A or 3.40 A, it is clear that normal hydrogen bonding does notoperate at these points, and that the interactions are of a less specificnature. They may be regarded as weah hydrogen bonds and, as a conse-quence, a rigid application of tetrahedral linkages need not apply. Inthe vicinity of a cation site, the observed intermolecular distance withina water sheet of 3.06 A is greater than the value calculated for a per-fectly regular octahedron of waters around a Mg ion (vi2.2.92 A;. fnetriads of water molecules associated with a cation are expanded slightlyin the plane of the sheets so as to allow each water to approach its associ-ated oxygen. As a consequence, the cations sink slightly into the watertriads in both sheets and the intersheet distance of the water moleculesis reduced to 2.88 A so as to preserve the Mg-H2O distance of 2.06 A.The intersheet distance of 2.88 A is uniform throughout the water

H,O(A) Hp(a)

H,o(c)

252 A. MCL. MATHIESON AND G. F. WALKER

layers, which provides a possible further reason for the occurrence of

triads of vacant water sites associated with the unoccupied a and w

cation sites where the binding effect of the cations is absent. The ob-

served intermolecular distance in an expanded triad of waters, viz.

3.40 A, is consistent with the model if packing radii are assumed (Rees,

re4e).The idealised arrangement proposed above (Fig. 7) gives two out of

three water sites occupied, which is approximately the required ratio,

and the ratio of exchangeable cations to waters in the network is one in

twelve which is close to the value indicated by the chemical formula

(1:13.5). This model may therefore be closely approximated in the Mg-

vermiculite under examination. A highly-ordered arrangement of the

interlameilar region is not inconsistent with the observed ease of cation

replacement (Milne and Walker, 1950), since normal diffusion processes

can be expected to operate through vacant a sites and "interstitial" posi-

tions ? and w, with concomitant adjustments in the water network. It is

evident that the interlamellar region must be regarded as a dynamic sys-

tem in which constant rearrangement and adjustment is taking place.

DrscussroN

Detailed analysis has revealed a distortion in the surface oxygen net-

work of the silicate layer in vermiculite. The explanation advanced is

based on residual electrostatic forces acting between the central octa-

hedrally-coordinated atoms and the surface oxygens of the silicate layers.

Evidence for the existence of a distortion of the silicate layer in muscovite

has been noted prev,iously by Hendricks and Jefferson (1939), although

in this case the data did not allow the nature of the distortion to be

defined.'slight departures from regularity are therefore possible in sili-

cate layers of this type.The solution advanced for the stacking of the silicate layers, if valid,

would impose certain limitations on similar minerals, and may therefore

be applicable to the stacking sequences in talc and pyrophyiiite' No

satisfactory explanation for the \kt, h!3n spectra has so far been deduced

for these minerals. The observed structure amplitudes of the02l reflexions

in vermiculite have been shown to correspond closely to the values

calculated not for g or r (Fig. 4) separately, but for the positional mean

of these two possible arrangements. It is necessary to point out, however,

that the results of the interpretation here placed on the diffuse reflexions

cannot be reconciled with the theoretical treatment of disorder for cobalt

in the region a-] (Wilson, !949, p. 70), which is analogous to the present

case and predicts the almost complete disappearance of the diffuse re-

gions. The discrepancy may arise from the failure of the theoretical

CRYSTAL STRUCTURE OF MAGNESIAM-V ERMICULITE 253

treatment to take into account the apparent increase in symmetry of thestructure in the region a-f.

The main interest attached to the structure analysis lies in the lightwhich it throws on the organization of the interlamellar region. Thewater-cation network consists of two sheets of distorted hexagonally-linked water molecule sites with the cations occupying definite positionsin the midway plane. Although the chemical data require that only one-third of cation sites (zz1 or rm2), and two-thirds of water sites should be oc-cupied, it has been shown that a random filling of the available sites is nota necessary consequence of the data and, in the vermiculite underexamination, a highly-ordered arrangement of the water molecules andcations is probable. In vermiculites which carry a higher population of

exchangeable cations (Barshad, 1950, 1952), the idealised structurewould be realised to a lesser extent, since u, a and w sites would be

expected to be partly occupied by cations and the distribution of the

water molecules in the available sites would be altered accordingly.Nevertheless, grouping of the water molecules around the cations and a

tendency towards a uniform distribution of the cations are to be ex-

pected in all similar minerals if the assumptions made above are valid.ft has usually been assumed, in considering the interaction of ex-

changeable cations with the planar surfaces of layer silicates, that the

former are located by reactive spots of negative charge on the silicate

layer surfaces arising from individual isomorphous substitutions. The

present structure analysis has located the interlamellar Mg2+ ions in a

plane midway between silicate layers. In this plane, the potential energy

due to electrostatic forces can be shown by calculation to be efiectivelyuniform, if the high frequency of isomorphous substitution is taken into

account.* The distribution of the cations in the midway plane is therefore

not related to any directiae efiect of the electrostatic forces. The impor-

tance of the hydration behaviour of the cations in this respect is attested

by the relationship between the cations and the water molecules as

revealed by the difiraction data, and also by the observed spontaneousrehydration of partially-dehydrated Mg-vermiculite ( Walker, 1949). In

the interlamellar region, the water molecules within a sheet are linked

by weak hydrogen bonds and the individual water sheets are held to-gether by the cations. The hydrogen bonds binding the water molecules

to the oxygen atoms of the silicate surfaces are probably stabilised to

some extent by the electrostatic forces acting through the water mole-cules. We may conclude that, in Mg-vermiculite,trthe Iocation of the

* In vermiculite, which is a trioctahedral mineral, the substitution of about one in

three tetrahedral and about one in five octahedral atoms gives rise to negative and positive

charges respectively. The result is a net negative charge acting at the silicate layer surfaces.

254 A, IICL, MATHIESON AND G, F. VI.ALKER

water molecule sites is determined by the surface configuration of thesilicate layers, and that the mutual relationship of the water sheets in asingle water-cation layer is determined by the requirement for octahe-dral coordination of the water molecules around the cations. The unim-portance of direct electrostatic interaction between the cations and sur-face oxygens is consistent with the conclusion of Guggenheim andMcGlashan (1951) that the influence of next-nearest neighbours is en-tirely negligible. Their result, however, does not invaiidate the proposedtendency to the formation of second hydration shells around the inter-lamellar cations in Mg-vermiculite, since each water molecule is equiva-lent in position with respect to the adjacent silicate layer surface anddipole interaction between water molecules can therefore exert a sig-nificant influence.

The structure derived for the interlamellar region in Mg-vermiculite,even in its less specific form, excludes the hypothetical water-layerstructure proposed by Hendricks and Jefierson (1938b) for vermiculite,and later modifications made to take account of the exchangeable cations(e.g. Hendricks, Nelson and Alexander, 1940). Furthermore, the struc-ture observed does not appear to have been considered in any of themodels proposed for the water-cation network of layer silicate minerals.

AcrwowrooGMENT

The authors gratefully acknowledge helpful crit icism by Dr. A. L. G.Rees, particularly with regard to the nature of the forces operating withinthe crystal lattice.

RrrnnnNcrs

BrnsnAo, I. (1948), Am. Mineral.,33, 655.Bansv.ll, I. (1949), Am. Mineral.,34,675.Bansnen, I. (1950), Am. Mineral,.,35,225.Brnsnao, I. (1952), Proc. Soil. Sci. Soc. Am., 16, 176.BrRNAr, J. D., axo Fowr,nn, R. H. (1933), J. Chem. Phys., 1,515.Bmnnr.rv, G. W. (1951), Chap. VI in X-nry IonNrlrcarrox eno Srnucrunrs ol Cr,ev

MrNrt,l.rs, edit. G. W. Brindley, Min. Soc., Lonilon.BnrNnr.nv, G. W., Oucnror, B. M., aNo RonrnsoN, K. (1950), Acta Cryst.,3, 408.Bvsrnciu, A., exn A. M. (1951), Acta Cryst.,4,469.Danr,rNo, B. T., auo DnNNrsoN, D. M. (1940), Phys. Rn.,57, t28.GntrNen, J. W. (1934), Am. Mineral., 19, 557.Gnutnn, J. W. (1939), Am. Mineral.,24, 428.GuGcnxunru, E. A., lNn McGr.asnax, M. L. (1951), Trans. Far.Soc.,47,929.Ifrxontcrs, S. B., eun JelrnnsoN, M. F. (1938a), Am. Mineral.,23r 85l.Hnxontcrs, S. 8., aNn Jrlrrnsox, M. F. (1938b), Am. Mineral.,23r 863.IfrrnRrcrs, S.8., alto Jnlrenson, M. F. (1939), Am. Mi.neral,.,24r729.Hnnonrcrs, S. B., NnlsoN, R. A., ewo Ar-rxeNonr, L. T. (1940), J. Am. Chem. Soc.,62,

1457.

CRYSTAL STRUCTUREOF MAGNESIT]M.VERMICALITE 255

INrnp1q.trroNAl-r Tanrr-r.rN zun Bnsrruv uNG voN Knrsrer.r,srnurrunnN (1935), Berlin :

Borntraeger.KreN, G., rNn Corn, W. F. (1949), Acla Cryst.,2,38.MnrnrnsoN, A. McL. (1951), J. Scimt. Instr.,28, ltz.Mrrurrsox, A. McL., AND WAT,KER, G. F. (1952), Clay Mi,ns. Bull. l' (8),272.

Mrr.rw, A. A.,.lNn WAnnn, G. F. (1950), Trans. Fourth Int. Cong. Soil' Sci'.,2,62.MrlNn, A. A., eNo Wlr,rnt, G. F. (1951), Clay Mi.ns. Bull., | (6),17l.Rens, A. L. G. (1948), J. Chem. Phys., 16,995.Smcwrcr, N. V. (1950), Tne Crrurcer. Er.BMsNrs AND THErR Coupounns: Or/ord.WAnsr-Ev, A. D. (1952), Natwe, l7O,973.Wa.r-ren, G. F. (1947), Clay Mins. Bxtll., | (l), 5.Warxon, G. F. (1949), Natwe, 163,726.War.xrn, G. F. (1950o), Mineral. Mag.,29,72.W.al.r<nn, G. F. (1950b), Natwe, 166,695.W,tt-Kln, G. F. (1951), Chap. VII inlx-nav Iorrurtc.qlron eNr Srnucrunes ol Cr..a.v

Mrurnnr,s, edit. G. W. Brindley, Min. Soc., London.Wrsr, C. D. (1935), Z. Krist. ,9l, 480.Wnrr-s, A. F. (1950), Srnucrun.qr, INoncllrrc CunMEtnY, 2nd ed., OrJoril'Wnsorv, A.J.C. (1942), Nature, 150, 152.Wrr-som, A. J. C. (1949). X-nev Oprrcs, Lond,on.

Manuscript receioed Feb. 18, 1953.