NATIONAL BUREAU OF STANDARDS REPORT

A REFINEMENT OF THE CRYSTAL STRUCTURE OF Na^O^O

by

B. Dickens,* F. A. Mauer + and W. E. Brown44

* Research Chemist, Dental Research Section, National Bureau of

Standards, Wash ington, D. C. 20234

+Solid State Physicist, Crystallography Section, National Bureau

of Standards, Washington, D. C. 20234

» Research Associate from the American Dental Association in the

Dental Research Section, National Bureau of Standards, Washington,

D. C. 20234

This investigation is part of the dental research program conducted by

the National Bureau of Standards in cooperation with the Council on

Dental Research of the American Dental Association; the National Insti-

tute for Dental Research; the Dental Research Division of the U. S.

Army Medical Research and Development Command; the Dental Sciences

Division of the School of Aerospace Medicine, USAF; and the Veterans

Adm ini stration.

NBS PROJECT

31 1.05-1 1-31 1056 1 December 18, 1969

NBS REPORT

10 128

Progress Report

on

IMPORTANT NOTICE

NATIONAL BUREAU O'

for use within the Governm

and review. For this reaso

whole or in part, Is not a

Bureau of Standards, Was

the Report has been specit

Approved for public release by the

Director of the National Institute of

Standards and Technology (NIST)

on October 9, 201 5.

ogress accounting documents intended

it is subjected to additional evaluation

ature listing of this Report, either in

n the Office of the Director, National

ver, by the Government agency for which

nal copies for its own use.

U.S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS

_|

L_L_L-L 1 1 II I 1 1 l l i l l. 1

A REFINEMENT OF THE CRYSTAL STRUCTURE OF Na 2 C03 ‘H 2 0

by

B. Dickens, F. A. Mauer and W. E. Brown*

Institute for Materials ResearchNational Bureau of Standards

Washington, D. C. 20234

ABSTRACT

The crystal structure of synthetic Na 3 C0 3 *H 20 has been

refined using 1231 unique x-ray diffraction data collected by

the peak height method on a diffractometer. R = 0.034. The

unit cell is a = 6.474(2) , b = 10.724 (3) and _c = 5.259(2) A

with Z = 4 and space group P2 x ab. The calculated density is

-3the same as the observed density, 2.26 g*cm . The structure

contains sheets of C0 32- ions bonded to Na~

r ions and water

molecules roughly halfway between the sheets. Each C0 32 "

bonds edgewise to both Na+

ions. The Na ‘ ions have irregular

but similar coordinations of seven neighbors. Each water

molecule is bonded to both Na^ ions and forms hydrogen bonds

to both neighboring C0 32- layers.

*Director, Research Associate Program of the American Dental

Association at the National Bureau of Standards.

2

1. INTRODUCTION

The crystal structure of Na 2 C0 3 *H 2 0 was determined

except for the hydrogen positions, by Harper [1] in 1936

using qualitative estimates of the x-ray intensities. In

our program of studies on coordination in hydrated carbonates

[2] and phosphates [3], we have refined Harper's structure for

Na 2 C03 ’HgO using new x-ray data. Na 2 C0 3 *H 2 0 is the mineral

thermonatr ite and often occurs with Na 2 C03 *10H 2 0 (natron) and

NasC03 *NaHC03 *2H 2 0 (trona) [4,5,6].

2. DETERMINATION OF THE STRUCTURE

Formula : Na 2 C0 3 *H 2 0. Unit cell : Orthorhombic with _a =

6.474(2) A, b = 10.724(3) A, c = 5.259(2) A at 24°C as calculated

from three pairs of 2 0 values of axial reflections from a

single crystal and observed on a diffractometer. The standard devi-

ations of the cell parameters are in parentheses and are estimates

based on experience with the technique. Cell volume : 365.1 A3.

Wavelength used: 0.710688 A (Mo Ka) . Filter : 0.025 mm Nb.

Space Group ; P2 1 ab. Cell contents in formula Wts: 4. Equivalent

positions ; x, y, z; 1/2+x, -y, -z; 1/2+x, 1/2-y, z;x, 1/2+y , -z. Reciprocal

lattice extinctions: hOi-, h/2n; hkO, k^2n. Observed density :

2.255 g •cm" 3[7]. Calculated density : 2 . 256 g. cm" 3

. Habit ; Frag-

ment from plate. Size of crystal ; —0.35 mm max. ~0.05 mm min.

3

Origin : Evaporation of aqueous solution at 60°C. Linear

absorption coefficient : 4.37 cm-1 . Absorption corrections:

None applied. Maximum error in any intensity from absorption

is ~10%. Number of reflections : 2189 were collected from 2

octants and merged into a unique set of 1231 of which 1132 are

"observed" reflections and 99 are less than 2a above back-

° ~ 1ground and are "unobserved". Maximum sinQ/l for data : 0.904 A

Method used to estimate data : peak height measurement [8] with

a single crystal diffractometer [9] and some peak heights

standardized against 0/20 scans. Scattering factors : Na , C, O,

for neutral atoms given in reference [10]; H from reference [11].

Least-squares refinements : Full-matrix, with E (w||F|-

|

Fj, )

c

minimized. Refinements include unobserved reflections for which the

intensities arecal-cu latedy^more than 2a above background. Least-squares weights ;

1/a 2 normalized so that maximum weight is 1. Definitions : counts

in peak = I = P-(T/2T e ) (B L + B H ) , <5“(I) = (P+(BL + B H ) (T/(2T E ) )

2)^

,

i iF = ( (AF) (LP) (I) )

2, <T (F) = (GT(I) /2) (LP/I) s where P = counts at

the peak position, BL

and B H = background counts at lower and

higher 20 respectively, T = time spent counting peak, T B =

time spent counting background, AF = attenuator factor, LP =

1

Lorentz polarization correction. Rw = ( Z ( w||f0 |

—|

F c |

j )

S /Z ( w |

FQ j

)

2)

R = (E||F 0 |-|f c ||)/S|F0 |. Final R. . : 0.029. Final R : 0.032.

4

Average shift/error for last cycle : 0.015. Thermal parameters;

anisotropic with form exp ( -1/4 ( a_*8 B 1 x h

2 + l>*2B.2 2.k

2 + _c* 2 B33 i 2-f

2a*b*Bi a hk + 2a_*c*B 13 hJ, + 2b*£*B 23 ki) .

The structure was refined isotropically from Harper's

parameters using the X-ray 67 system [12] of computer programs

to R = 0.065; the x parameter of Na(l) was fixed at x = 0.w — —

The structure was refined anisotropically to Rw = 0.044 and

the hydrogens were found unambiguously as the two highest peaks

in the difference synthesis in which the coefficients were

weighed by the least-squares weights. The two next highest

peaks were less than 3/4 as high as the peaks assigned to

hydrogens and were (a) halfway between C and 0(3) in the C0 3

group and (b) 0.7 A from 0(1) of the C0 3 group. The hydrogens

were included with variable positional parameters and fixed

thermal parameters (B H = 1 A 2) in the final refinement to R =

w

0.029. The largest correlation coefficients are ~0.25 be-

tween the scale factor and the B. 1

1

thermal parameters of the

two Na ions and~0.15 between these B^ 1 thermal parameters. Most

correlation coefficients are less than 0.05.

The atomic parameters are given in table 1. The observed

and calculated structure factors are given in table 2. The

hydrogen positions obtained from the weighted difference syn-

thesis and from the refinements differ by ~0.17 A. "Calculated"

hydrogen positions were derived by applying the geometry of free

water (0-H = 0.958 A, Z_H-0-H = 104.5°) with the constraint

that the 0-H...0 angles be as near to linear as possible. These

hydrogen positions differ from the other positions by about

0. 3 A. The three sets of hydrogen positions are compared in

table 3. The distances and angles which involve hydrogen were

obtained using the "calculated" hydrogen positions.

3. DESCRIPTION OF THE STRUCTURE

The structure (fig. 1) contains C0 3 anions whose planes areand

' almost

perpendicular to a_^which form sheets at x:- 0.25 and x=:0.75.

Because the C atoms lie close to the planes of the a_ glides,

they form columns along a_ at y = 0.25, 0.60. Two ad-

jacent C0 3 groups in a column are held together by both

being ionically bonded to four Na ions and hydrogen bonded

by one water molecule. The four Na ions and the water mole-

cule form a pentagon roughly halfway between the C0 3 sheets.

Adjacent C0 3 groups in a given sheet are linked by the Na

ions that lie above and below the sheet.

3.1. The Carbonate Anion and Environment

The dimensions in the C0 3 anion are given in table 4

and the environment is detailed in table 4 and figure 2. The

C0 3 group is nearly trigonal. As can be seen in figures 1

and 2, 0(2) is the only oxygen which is not hydrogen bonded,

being instead ionically bonded to four Na ions. The absence

6

of hydrogen bonding to 0(2) may account for the observation

that the C-0(2) bond is apparently the shortest of the three.

0(1) is coordinated to three Na ions and is the acceptor in

the hydrogen bond 0 ( 1) . . .H ( 1) -0 (4) from the water molecule.

0(3) is bonded strongly to two Na ions and more weakly (2.822 A)

to a third Na(2) . 0(3) is the acceptor in the hydrogen bond

0 ( 3) . . .H ( 2) -0 (4) from the water molecule,planes of the

Since theAC0 3 groups are all essentially perpendicular

to a_, this is expected to be the direction of lowest refractive

index, as was found by Harper [1]. Later workers [13,14]

apparently did not permute the refractive indexes when they

permuted the unit cell axes to fit crystallographic convention.

3.2. The Sodium Environments

The two crystallographically distinct Na ions in the

structure are in general positions. Their environments are

shown in figure 3 and are given in table 5.

Na(l) is bonded ionically to five oxygens from C0 3

groups, and strongly to one water oxygen. Four of the C0 3

oxygens, 0(1), 0(2 '), 0(3), 0(3^, figure 3, define an approxi-

mate square about Na(l), and water oxygen 0(4) forms the apex

of a square pyramid. The fifth carbonate oxygen, 0(2), is

in the same C0 3 group as 0(1); the C0 3 group is therefore

7

coordinated edgewise to Na(l). The position of 0(2) is such

that the coordination about Na(l) cannot be considered octahedral.

The next oxygen in the direction of the octahedral apex is the

water oxygen 0(4'), which is relatively far (3.669 A) from Na(l).

The coordination of Na(2) is similar to that of Na(l).

Na(2) is slightly displaced from the center of an approximate

square of carbonate oxygens, 0(17

), 0(2"), 0(1"), 0(2'"). The

displacement is towards the strongly bonded water molecule

0(4), which is the apex of a square based pyramid (base down in

figure 3). The coordination of Na(2) is completed by 0(4")

o

(2.936 A) which is the remaining apex of an approximate

octahedron, and by 0(3 ') which is in the same C0 3 group as

0(2"). Thus the C0 3 group is coordinated edgewise to Na(2)

also, this time using 0(2) and 0(3) instead of 0(1) and 0(2),

which are used to coordinate to Na(l). This edgewise coordination

is shown in figure 2. The coordination to Na(2) comprises

five carbonate oxygens and two water molecules instead of four

carbonate oxygens and two water molecules as suggested by

Harper [1] and noted by Wells [15].

3.3. The Water Environment

The water environment is given in table 6 and shown in

figure 3. The water molecule is bonded to Na(l) and Na(2)

8

with distances of 2.434 and 2.384 A respectively, and forms

hydrogen bonds to oxygens 0(1) and 0(3) of neighboring C0 3

groups. Na(l), Na(2), 0(1), and 0(3) are arranged approxi-

mately tetrahedrally about the water oxygen. The distortion

of this tetrahedron is considerable as can be seen from the

angles listed in table 6. The closest H. . .Na distance is

H(l)...Na(2) = 2.42 A, which is in the normal range.

The calculated hydrogen positions in table 3 were

obtained using the geometry of free water and imposing the

condition that the 0-H...0 angles both be as linear as possible.

Because H(2)...0(3) is shorter (1.74 A) than H(1)...0(1)

(1.96 A) it is possible that the hydrogen bond 0 (4) -H ( 2) . . . 0 ( 3)

is strictly linear. Assuming the same water geometry, the

hydrogens would then be ^ 0 . 14 A away from the positions given

in table 3 at 0.145, -0.046, 0.182 for H(l) and -0.065, -0.095,

0.102 for H(2). The 0 (4) -H ( 1) . . . 0 ( 1) angle would 'then be 156°,

and the H(1)...0(1) and H(2)...0(3) distances would be 2.01 A

and 1.73 A, respectively. The closest H 0 ..Na distance

would be H(l)...Na(2) = 2.39 A.

9

Acknowledgment.—Collection of the diffractometer data was

made possible through the cooperation of E. C. Prince. The

X-ray 67 system of computing programs (J Q M. Stewart,

University of Maryland, Editor) was used for most calculations.

We thank Joy S. Bowen and Pamela B. Kingsbury for technical

help

.

This investigation was supported in part by research

grant DE-00572-09 to the American Dental Association from

the National Institute of Dental Research and is part of the

dental research program conducted by the National Bureau of

Standards, in cooperation with the Council on Dental Research

of the American Dental Association; the United States Army

Medical Research and Development Command; the Dental Sciences

Division of the School of Aerospace Medicine; USAF; the

National Institute of Dental Research; and the Veterans

Administration

.

10

References

[1] Harper, J. P., Crystal structure of sodium carbonate

monohydrate, Na 2 C0 3*H 2 0, Z. Krist. 9_5, 266-273 (1936).

[2] Dickens, B., and Brown, W. E., The crystal structures of

CaNa ( C0 3 ) 2 • 5H 2 0, synthetic gaylussite, and CaNa 2 ( C0 3 ) 2 • 2H 2 0

,

synthetic pirssonite, Inorg. Chem. 8_, 2093-2103 (1969).

[3] Brown, W. E. , Crystal structure of octacalcium phosphate;

Nature 196 , 1048-1050 (1962) .

[4] Brown, C. J., Peiser, H. S., and Turner-Jones , A., The

crystal structure of sodium sesquicarbonate,Acta. Cryst.

2 , 167-174 (1949)

.

[5] Bacon, G. E., and Curry, N. A., A neutron-diffraction

study of sodium sesquicarbonate, Acta Cryst. 2_, 82-85

(1956)

.

[6] Candlin, R., Thermal changes in the structure of sodium

sesquicarbonate, Acta. Cryst. 9_, 545-554 (1956).

[7] Pabst, A., On the hydrates of sodium carbonate, Amer.

Min. 15, 69-73 (1930) .

[8] Reimann, C. W. , Mighell, A. D., and Mauer, F. A 0 , The

crystal and molecular structure of tetra ispyrazole-

nickel chloride, Ni (C 3 H4 N 2 ) 4 Cl 2 , Acta Cryst. 2_3, 135-

141 (1967)

.

11

[9]

Mauer, F. A., and Koenig, A. L. ,An automatic diffract-

ometer for off-line operation, American Crystallographic

Association, Summer Meeting, Abstract E10, University of

Minnesota, Minneapolis, Minn. Aug. 20-25, (196^.

[10] International Tables for X-ray Crystallography _3, p. 202

(the Kynoch Press, Birmingham, England, 1962).

[11] McWeeney, R., X-ray scattering by aggregates of bonded

atoms. I. analytical approximations in single-atom

scattering, Acta Cryst. 4_, 513-519 (1951).

[12] Chastain, R. V., An algorithm for finding a set of phases

directly from sigma two relationships, In, X-ray 67-Program

System for X-ray Crystallography, Technical Report 67-58,

Ed. J. M. Stewart, pp 71-75, University of Maryland,

College Park, Md. (1967).

[13] Palache, C. , Berman, H. , and Frondel, C. , Thermonatr ite

[Na 2 C03 *H 2 0] , In, The System of Mineralogy of J. D. Dana

and E. S. Dana, 7th ed., _2, p.224 (J. Wiley and Sons,

New York, N.Y. , 1951).

[14] Winchell, A. N c , and Winchell, H. ,The Microscopical

Characters of Artifical Inorganic Solid Substances:

Optical Properties of Artifical Minerals, (Academic

Press, New York, 1964)

.

12

[15] Wells, A. F. , Structural Inorganic Chemistry, 3rd ed.

p. 587 (Oxford University Press, London, 1962).

USCOMM-NBS-DC

Table

1-

Atomic

Parameters

of

Na

2C0

13

oTO

m

v 03CM 00 in b b b b <U

CO >—

'

" * 4JTO 00 00 r- r-~ CM 00 3m o o o b b oo 00 Cu

0 • • • t 9 0 £1 l I 0

0

aj

uy—v ^ s (D

oo OO in CD in b inv—

"

V—X v—

'

—

'

mlLD in in b in in TO

rH CM o i—

1

o CNJ CM c

I l 1 1

CO

TO^—

v

^

x

. ^—

v

^

^

V <U

co CM in in in in in 4-)

0)"—' " v— v—" v—" >—' 0

rHI

m,r- rH CD 00 in CO rH 3i—

1

00 O o o CM CM o1

1 1 I 1 Q)

U3

^-v X s b00 oo in uo b CD •H

CO **—

'

'— • "—" V ' MMCO CO CO 0" CM b o CM

ml oo c- i—

1

CM CTl a> 4-)

c1

1 i—

1

i—

1

CM 11 O (—

1

ro

u 0

*H 44144 c

,—^ ^

^

•H CD

oo OO CD in in CD CD c 6TO N—

•

—

4

Cn CD

TO 'sf o rH CM r" b OO •H Cml LT) i—

1

i—

1

0" CM 11 'sf w •H

• • • • 0 0 0 441

1 i—

1

i—

1

O 11 CM 1

1 44 CD

CO 54

ro

^

^

X -V rH CO

-i 00 00 CD CD CD CD (DH v—

"

N—

"

—

"

' o—

^

G 54

*1

o b in CD 00 CM *H 3m b b in r- b CD 3

to brH rH i

—1 rH i

—1

11 54 CO

0 1

*• ^ s. 54 44rH CM 00 00 CM CM CO 54 CON ' —' v—

'

a) 300 CD in r- cn 00 CD

N cr> 00 CM in CD 00 00 b rH00 O b CM CD CD 54

rH oo CD in b 11 O rO X

• • « • • • • H •HI I C 54 TO

ro 44 o<3s x—

x

^

^

s /«s y—

S

44 3rH rH CM f—

1

11 rH H CO S cW >— >—+

I

CO O CD l—

1

cn CD CD e I 1

>i 00 CM in 00 CD O' <yr 54 rH 3<30 O in 00 00 CO CM ro 3 54

1

—1 o CM rH oo CM o 44 3• 0 0 • 0 • • CO

I CD 44 3CO O 5-1

Cl) 3b CD 44

s „ s 44 1 1 3CM 00 00 00 00 00 c U g

’ *w" >—- >—*•

a> >i 3O rH rH o 00 in 54 0 5-1

XI O LD in rH CM OO CM rO 3O CD rH o O 00 00 a, rH Oro O CM CM CM CM o 3• • • • 0 • • c C H

1 I I 1 •H •H 344 g

to 54

CD 3 3.—

V

54 b rGg rH CM , N. 3 44 E40 — S ' rH CM 00 Cn+J rO rO

s—

'

v—

^

•H C< S S u o O o o m •H *

i i i

14

Table 2

Observed and Calculated Structure

Factors for Na 2 C0 3 *H 2 0

84) 932942 97924) 286

244 2742)) 22842 92

4 >71 1676 29 )0b m in

10 24 2)

0 24 9 274

4 211 1929 26* 7684 200 |'I 7

7 >99 >97

10 147 >91

1) 170 177

>0 209 706

8 1)4 > )4

10 80 79

12 70 72

14 1 4 )

4

14 29 )219 49 4>IT 29 79

8 29 799 TO 68

I 0 14 4 > 4 7

II 4 T 4617 7 T 7 T

9 110 109

10 73 7111 67 7017 ) 7 )0

19 ) 4 47

0 174 187

11 17 * 17

1 61 622 28 27

) 29 294 129 1219 128 1266 18) >877 109 10)9 >94 1919 111 110

10 116 11411 78 28

12 DO 177

I ) l » II

10 29 2911 27 7612 >4 D

) 9 ) 6

92 9924 2616 19

42 4)

1 1 til 1

) 6 ) 6

14 19!>• 10

1) 104 13)14 90 9119 4) 4)

0 279 278

2 498 469

1 4) 4)

2 102 104) 111 1114 88 899 1 > 4 114

12 )0 )11) 97 9714 24 )2

19 »> >7

I* It >1

0 4*9 430

) 74 '# 74 9

•#.9

129 124

II 4) ) 4

19 74 70

a) The columns are k, 10Fo ,10F C . "Unobserved" reflections are marked

by F and F are on an absolute seale,o c

15

Table 3 - The Hydrogen Positions in Na 2 C0 3 *H 2 0

Weighted LeastAtom difference squares Calculated*

synthesis refinements

X X. z X z X -X z

H ( 1) .12i"-

0•1 1

—

1

•1—

I

1—

1

• O•1 .15 .134 -.056 . 190

H ( 2) 000•1 000•

1 1—

1

• 01—

1

•1 CO0•1 .12 -.077 -.089 .084

o

*Assuming the geometry of free water with 0-H = 0.958 A and

AH-O-H = 104. 5°, and making the 0-H. . .0 hydrogen bonds as

linear as possible

16

Atoms

Table 4 - The C0 S Group

o

Distances, A,

or angle, deg.

C,0(1)C , 0 ( 2)

C, 0 ( 3)

0(1) ,0(2)

0(1) ,0(3)

0(2) ,0(3)

1.299(3)1.274(2)1.285(2)2.223(2)2.229(2)2.230 (2)

0(1) , C, 0 (2)

0(1) , C, 0 ( 3)

0(2) , C , 0 ( 3

)

119.6(2)119.2(2)121.2(2)

0(1) , Na ( 1)

0(1) , Na ( 2)

0(1) , Na ( 27

)

0(1) ,0(4)

0(1) , H ( 1)

2.570(2)2.293(2)2.307 (2)

2.907(2)1.96

0(2) , Na ( 1)

0(2) , Na (

1

/

)

0(2) ,Na (2 ')

0(2) ,Na (2)

2.521(2)2.468 (2)

2.508 (2)

2.491(2)

0(3) , Na ( 1)

0(3) ,Na(l')0(3) , Na (2)

0(3) ,0(4)

0(3) , H ( 2)

2.444(2)2.330(2)2.822(2)2.684(2)1.74

In all tables of interatomic distances and angles, the quantities

in parentheses are standard errors in the last significant figure

and were computed from the standard errors in the atomic positional

parameter and in the cell parameter^ The primes refer to atoms in

figure 2.

17

Table 5 - The Sodium Environments

Atoms

Na(l) ,0(1)Na ( 1) ,0(2)Na(l) ,0(3)Na(l) , 0(4)

Na ( 1) ,0(2")Na ( 1) ,0(3')Na ( 1) ,0(4')

Na ( 2 ) ,0(4)Na ( 2 ) , 0 (

1

7

)

Na ( 2 ) ,0(1")Na ( 2 ) , 0 ( 2 "

)

Na ( 2) ,0(2 "')

Na ( 2 ) ,0(4")

Na ( 2 ) , 0 ( 37

)

Distance, A

2.570(2) A

2.521(2)2.444(2)2.434 (2)

2 .468(2)2.330(2)3.669(2)

2.384(2) A

2.293(2)2.307(2)2.508(2)2.491(2)2.936(2)2.822(2)

The primes refer to the atoms in figure 3.

18

Table 6 - The Water Environment

atom

0(4) ,Na ( 1)

0(4) , Na (2)

0(4) , Na (2 ')

0(4) ,0(1)

0(4) ,0(3)

H ( 1) ,0(1)

H ( 2) ,0(3)

Na ( 1) ,0(4) , Na (2)

0(1) ,0(4) , Na ( 1)

0(1) ,0(4) , Na ( 2

)

0(3) ,0(4) , Na ( 1)

0(3) ,0(4) , Na (2)

0(1) ,0(4) ,0(3)0(4) , H ( 1) ,0(1)

0(4) , H ( 2 ) ,0(3)

distance A

or angle, deg.

2.434(2) A

2. 384 (2)

2.936(2)2.907(2)2.684(2)1.961.74

91.15(6)°109.70(7)133.83 (9)

129.28(9)110.29(7)

88 . 12 ( 6 )

168.167.

The prime refers to an atom in figure 3

Figure Legends

Figure 1

Figure 2

Figure 3

I

!

A stereoscopic illustration of Na 2 C0 3 *H 2 0 viewed

along a_. The origin of the unit cell is marked

by the asterisk.

The carbonate group environment in Na 2 C0 3 *H 2 0.

The primes refer to atoms in table 4.

The water and sodium environments in Na2 C0 3 *H 2 0.

The primes refer to atoms in tables 5 and 6.

-{

1

]

J

I)

-

No

1

C\J

o

I

I

I

-

i I i n 1 i i—r i i