NATIONAL BUREAU OF STANDARDS REPORT

NBS PROJECT NBS REPORT

311.05-11-3110561 April 28, 1971 10 579

Progress Report

on A REFINEMENT OF THE CRYSTAL STRUCTURE

OF CaHP0

4

(SYNTHETIC MONETITE)

by

B. Dickens, J. S. Bowen* and W. E. Brown**

Institute for Materials Research

National Bureau of Standards

Washington, D. C. 20234

* Research Associate, American Dental Association

Research Unit at the National Bureau of Standards,

Washington, D. C. 20234.

** Director, American Dental Association Research

Unit at the National Bureau of Standards,

Washington, D. C. 20234.

This investigation was supported in part by Research Grant

D E — 0057 2 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 American Dental Association; the United

States Medical Research and Development Command; the Dentai

Sciences Division of the School of Aerospace Medicine, USAF;

the National Institute of Dental Research and the Veterans

Administration.

IMPORTANT NOTICE NATIONAL BUREAU OF STA

for use within the Government. E and review. For this reason, the whole or in part, is not authoriz Bureau of Standards, Washington

the Report has been specitically p

Approved for public release by the

Director of the National Institute of

Standards and Technology (NIST)

on October 9, 2015.

; accounting documents intended

ubjected to additional evaluation

listing of this Report, either in Office of the Director, National

the Government agency for which

pies for its own use. <NBS>

U.S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS
*
Abstract

CaHP0 4 , synthetic monetite, crystallizes in the triclinic unit cell a. = 6.910(1) a, b = 6.627 (2) a, _c = 6.998(2) a, a = 96.34(2) °, 3 = 10 3 . 82 (2 ) °

, y = 88.33 (2) °

at 25°C with cell contents of 4[CaHP0 4 ] . The structure

has been refined in space-group Pi by the method of least

squares to = 0.032, R = 0.031 using 3738 observed reflections

measured on a diffractometer. Corrections were made for

anomalous dispersion, absorption and isotropic secondary

extinction.

The structure may be considered to consist of CaHP0 4

three types of

chains bonded together by Ca...O bonds and^ hydrogen bonds,

type of

One/ hydrogen bond, O (1) -H (1) . . . 0 (5) , is normal but is at

the short end of the normal range with 0(1). ..0(5) = 2.565 (1) A; one, 0 (7 ) -H (2 )

. . . 0 (7 ')

, is very short with

0(7).. .0(7') = 2.458(2) A and is

and

across a nominal center of symmetry; /one, 0 (6 ) -H ( 3 ) . . . 0 (8)

where 0(6)... 0(8) = 2.669(1) ^

i

s in the normal range but is

presumed to be statistically disordered, with hydrogen

covalently bonded to half of the 0(6) atoms on average. The

P-0 distances support the choice of these hydrogen positions.

The calculated position of H(3) suggests that it is coordinated

to the 0(6,8) edge of the adjacent P(2)0 4 group. The two

possible sites for H(3) are then 1.45 & apart and simultaneous

occupation of these two sites is improbable. The strong
hydrogen bonding may distort CaHP0 4 from the orthorhombic

CaS0 4 structure to triclinic. Ca(l) is coordinated to

seven oxygens in an approximate pentagonal bipyramid with

Ca(l)...0 distances ranging from 2.2951(9) ? to 2.763(1)

ft. Ca(2) is coordinated to eight oxygens with Ca(2)...0

distances ranging from 2.379(1) A to 2.5718(9) A, which

all indicate strong Ca...O bonding. The Ca coordinations

in several calcium phosphates and related compounds are

compared

.
Introduction

The general features of the crystal structure of CaHP04

were determined by MacLennan and Beevers (1955) , who refined

the structure to R = 0.20 using hkO, hO £ and 0k£ photographic

data. They gave no positions for the hydrogen atoms because

they considered the structural details to be obscured by the

large standard deviations (> 0.05 A) associated with the interatomic distances.

The structure was refined to R = 0.15 by Jones and

Cruickshank (1961) using 790 reflections collected and measured

by MacLennan and Beevers but uncorrected for high absorption.

Possible positions for the hydrogen atoms given by Jones and

Cruickshank were based on the P-0 and 0...0 distances they

obtained. Curry, Denne and Jones (1968) measured 381 reflections

at room temperature

from a large single crystal of CaHP04 /using neutron diffraction

and refined the occupational parameters of possible hydrogen sites

while keeping the parameters of the heavier atoms fixed at the

fairly imprecise and ambiguous values obtained in the X-ray

refinements reported earlier by Jones and Cruickshank. On the

basis of these results, hydrogens were assigned to the 0(1) atoms

and to half of the 0(6) and 0(7) atoms in the structure. This

work has been continued by Denne and Jones (1969).
The heat capacity versus temperature curve of CaHP0 4 has

been observed (Egan and Wakefield, 1964) to contain an abnormality

(a broad hump beginning at 223°K with a maximum at 273 °K).

Although neither the

line width nor the second moment changed significantly in NMR

results obtained by Jones and Cruickshank on a sample of CaHP0 4

cooled from room temperature to liquid-nitrogen temperature,

hydrogen-motion remains a plausible explanation for

the anomaly in the heat capacity curve fcr CaHP04

. It is not

yet known whether the anomaly arises from rapid hydrogen motion

or from an order-disorder process. As a precursor to work

at two or more temperatures on the crystal structure of CaHP0 4

using neutron diffraction and to intended spectral investigations,

we have refined the crystal structure using new X-ray data collected from a single crystal. The precision of the structural

features has been greatly improved and these features are now

more consistent with the chemical aspects of the structure. The

hydrogen atoms have been located approximately. The bonding scheme

given by Jones and Cruickshank and Curry, Denne and Jones is

confirmed

.

Data collection and structure refinement

The crystal used in the collection of X-ray data was

colorless and approximately rhombic in shape with an edge of about

0.15 mm and a volume of 0.004 mm3

. It was taken from a sample

of CaHP04 grown by cyclic dilution and concentration of the

supernatant aqueous solution over a mixture of CaHP0 4 and

Ca5 (P0 4 ) 3 0H in the lower chamber of a Soxhlet apparatus. It was

attached to the goniometer head in our usual way (Dickens and

Bowen, 1971a)

.

2
formula (ideal) : CaHPO^

cell: triclinic

= 6.910 (1) k at 25°C

b = 6.627 (2)

£ = 6.998(2)

a = 96.34(2)

P = 103.82 (2)

Y = 88.33 (2\

volume = 39CK27 A

0

space-group Pi assumed; cell contents 4[CaHP0 4 ] calculated density 2.933 g-cm“ 3

; observed density 2.929 g-cm

-3

(de Schulten, 1901)

.

The X-ray data were measured using the general procedure given

in Dickens and Bowen (1971b). 0-20 scans were done at 1 °/min for

20, and the backgrounds were counted for 10 sec each. 8849 reflections were collected from two hemispheres of the reciprocal lattice;

hk£ and hk i pairs were merged into a unique set of 3861 reflections,

of which 3738 were "observed" and 123 were "unobserved". After

correction for absorption, symmetrically equivalent F^^'s agreed

within 2% on average. Unobserved reflections were those less than

2a(l) above background. The intensities were corrected for absorption as described in Dickens and Bowen (1971a and 1971b). p(Mo)

was taken to be 21.3 cm” 1

. The maximum and minimum transmission

factors were 0.796 and 0.701, respectively. 20 for the highly

oriented graphite monochromator crystal was 12.32°.

The structure as given by Jones and Cruickshank was refined

isotropically using the program RFlNE (written by L. W. Finger

of the Carnegie Institute of Washington) to Rw = 0.086, R = 0.089 in two cycles (average shift/error for second cycle = 0.91)

and then to Rw = 0.035, R = 0.032 in two cycles of anisotropic

refinement. The scattering factors were those of the neutral

atoms and were taken from Cromer and Mann (1968)

.

3
The hydrogen atoms were found in a difference electron-density

synthesis as peaks of 0.75, 0.77 and 0.34 electrons

AT

3 for the

hydrogens H(l), H(2) and H(3) on 0(1), 0(7) and 0(6), respectively.

H(3) is a hydrogen atom disordered over two widely separated

sites, while H(2) is either in a centered hydrogen bond or in

two sites which are very close to each other. The background

in the map was 0.50 electrons • A” 3

; steric considerations were

UC3)

used to find the "half" hydrogen atom ion 0(6). The structure

was refined for (i) two more cycles with these hydrogens included

with fixed isotropic thermal parameters of 1 and with H(2)

fixed at the origin, (ii) two cycles in which the isotropic

extinction parameter, r_ in the notation of Zachariasen (196 7) , was also varied, and (iii) three cycles in which allowance was

also made for the anomalous scattering of Ca and P. The values

for f

' and f" were taken from Cromer (1965) . In these last three cycles, Rw decreased from 0.035 to 0.032,

R changed from 0.032 to 0.031, and the extinction parameter changed

from 0.0021(6) cm to 0.000009(6) cm. It appears that there is a

high correlation between the corrections for secondary extinction

and anomalous dispersion. The largest correlation coefficient

was 0.46 between the extinction and scale parameters. The next

largest was 0.40 between x and _z of 0(8). The position of H(3)

was not well defined in any of the refinements. It wandered from

1.24 A to 1.58 A from 0(6), with 0 (6) -H. . . 0 (8) angles of about

150-160°. From the P-0 bond lengths observed here (see later)

and from the findings of Curry, Denne and Jones, H(3) is believed

to be covalently bonded to 0(6)

.

4
The structural parameters obtained in the refinements which

included corrections for extinction and anomalous dispersion are

given in table 1. In general, the precision is improved by a

factor of 15 to 20 over the previous determinations. The

structural details in the P04 groups are more consistent with

the observed chemistry and hence are also considered to be more

accurate than earlier values. The observed and calculated structure factors are given in table 2. Three sets of hydrogen positions from (i) the Fourier difference synthesis, (ii) the leastsquares refinements and (iii) calculations to idealize the

HP04

2 - geometry (see later) are given in table 3. The calculated

hydrogen positions were used in the calculation of interatomic

distances mentioned in table 4.

Description of the structure

The structure of CaHP04 (Fig. 1) contains, parallel to [010],

distorted versions of the Ca-X04 chains found in several other

calcium phosphates and related compounds, e. .c[. , Ca (H 2 P04 ) 2 *H 2 0

(Dickens and Bowen, 1971b; Jones and Cruickshank, 1961; MacLennan

and Beevers, 1956); CaHP04 *2H 2 0 (Curry and Jones, 1970; Jones

and Smith, 1962; Beevers, 1958); CaS0 4 *2H2 0 (Atoji and Rundle,

1958) and CaS0 4 (Hohne, 1962; Cheng and Zussmann, 1963) . In

CaHP0 4 , one set of chains consists of the Ca(l) and P(2)0 4 ions.

5
and the other set consists of the Ca(2) and P(1)0 4 ions. The

usual chain linkage of two X0 4 edges to each Ca ion has been

reduced to one P0 4 edge and a P0 4 apex in CaHP04 .

The Ca ion environment

The details of the environments of the two crystallographically

different Ca ions in the structure are given in Table 4 and

Figs. 2a and 2b. Ca(l) is coordinated (Fig. 2a) to seven oxygens,

six [ 0 (4, 8, 1, 2 , 2 ', 6 ) ] with Ca...O distances in the range 2.295 A

to 2.450 A, which denote strong Ca...O bonding, and one [0(7)]

at 2.763 A, which is at the upper end of the normal range. The

0(6,7) P0 4 edge and the P0 4 apexes 0(2), 0(8) and 0(4) are

arranged in an approximately planar pentagon; 0(1) and 0(2 f

) are the apexes of an approximately pentagonal bipyramid. This

type of coordination is common in calcium phosphates. As is the

case in other compounds where CarX0 4 chains are found, the P(2)0 4

edge [0(6,7)] coordination to Ca(l) in the Ca(l)-P(2)0 4 chain

involves the longest Ca...O distances, which is in accord with

Pauling's rule (Pauling, 1960) concerning repulsion between

(in this case) Ca and P. Only the apex 0(8) of the opposite

P (2 )

0

4 edge 0(5,8) is coordinated to Ca(l) and is involved

in the second shortest Ca 0 bond. The Ca(l)...P(2)

distances along the direction of the Ca(l)-p(2)0 4 chain are

3.2380(4) a for edge coordination of the P(2)0 4 group to Ca(l)

and 3.4496(4) A for apex coordination, which shows that, as

judged from the Ca...P distances in this and other calcium

phosphates, the Ca(i)...p(2) repulsion is normal in both cases.

6
Ca(2) is coordinated (Fig. 2b) to eight oxygens [0(3, 5, 4, 3',

8,7,6, 2)] with Ca...O distances in the range 2.379 & to 2.572 l.

All these bonds are strong. In the Ca(2) coordination geometry,

0(8), 0(6), 0(5), 0(7), and 0(3 ') lie in an approximate pentagon.

0(3) lies at one apex of an approximate pentagonal bipyramid, and

the center of the 0(2,4) edge of the P(1)0 4 group lies at the

remaining apex position. The chain involving Ca(2) includes the

P(1)0 4 group coordinated in a manner very similar to the coordination of the P(2)0 4 group to Ca(l)

.

Both chain directions are

vertical in Figures 2a and 2b. The Ca(2)...P(l) distances for

the 0(2,4) edge and the 0(3) apex coordination in the Ca(2)-P(l)0 4

chain are 3.1005(4) A and 3.5750(4) l, respectively. (Figures

2c to 2e are mentioned in the Discussion, where the calcium

coordinations in CaHP04 and several related compounds are compared.)

The P0 A groups and their environments

The details of the two unique P0 4 groups and their environments

are given in Table 4 and Figures 3a and 3b. In the P(1)0 4 group

(Fig. 3a), the 0(2,4) edge is the only edge coordinated to Ca.

The 0 (2 ) -P ( 1) -0 (4) angle is less than the tetrahedral angle, in

accord with Pauling's rule. The two other O-P-O angles in the

P(1)0 4 group which are less also than the tetrahedral angle

involve oxygens 0(1) which is covalently bonded to hydrogen.

Such P-0 bonds may be expected to contain less double bond

character than P-0 bonds where the oxygen is "terminal" and

O-P-O angles with one or both oxygens of this type are expected

to be less than tetrahedral (Cruickshank, 1961) . Similar angles

have been observed in the recent refinements of Ca (H 2 P0 4 ) s *H2 0

/Dickens and Bowen, 1971b) and CaP0~F-2H o 0

£(Perloff, 1971). The 0 (1) -P (1) -0 (3; angle in CaHP0 4 is, however,

not less than this, tetrahedral angle, although 0(1) is involved

in the angle.

7
The P ( 1

) — O distances (table 5) overwhelmingly point to

0(1) as being covalently bonded to hydrogen. (P(l)-0(2) is the

second longest, 1.5397 A, of the P(l)-0 bonds; this apparent

lengthening compared to P(l)-0(3) and P(l)-0(4) is probably due

to the influence of the three Ca ions bonded to 0(2) .) 0(1) is

the donor in the hydrogen bond of H(l) to 0(5); the 0(1)... 0(5)

distance, 2.565 A, is very short, and the H(l)...0(5) distance,

1.59 A, indicates that there is a strong hydrogen bond between

these two atoms. (Distances and angles involving hydrogen atoms

were obtained using the calculated hydrogen positions.)

In the P(2)0 4 group (Fig. 3b), P(2)-0(6) and P(2)-0(7) are

the longest P-0 distances and are about equal with an average

value of 1.547 A. This value is close to being halfway (1.554 A)

between (i) the average (1.516 A) of the P(l)-0(3) and P(l)-0(4)

distances, which are the P(l)-0 distances least disturbed by cationic

and hydrogen bonding, and (ii) the P(l)-0(1) distance of 1.5925 A,

where the extension is due mainly to the presence of a covalently

bonded hydrogen. Thus the P(2)-0 distances support the assignment

of half a covalently bonded hydrogen on average to each 0(6) and 0(7)

0(5) has the next longest P-0 distance after 0(6) and 0(7).

Although 0(5) is bonded only to one Ca ion, where 0(6) and 0(7)

and 0(8) are all bonded to two, it is the acceptor in the strong

"normal" hydrogen bond involving H(l) on 0(1), which probably

serves to lengthen the P(2)-0(5) bond. The shortest P(2)...0

distance is P-0 (8), which is the acceptor in the hydrogen bond

involving the statistically affected hydrogen H(3) covalently

bonded to 0(6).

8
Because on average 0(8) enters into only half a hydrogen bond,

P(2)...0(8) is not expected to be as long as P(2)...0(5) (the

effect of the two Ca ions bonded to 0(8) and one Ca ion to

0(5) is expected to be subordinate to the effect of hydrogen

bonds). Thus, the observed P(2)...0 distances are compatible

with the environments of the oxygen atoms.

The hydrogen positions

The four hydrogens in the unit cell of CaHP0 4 have an

unusual distribution over the hydrogen bonding sites. The

shortest interphosphate 0....0 distance, 2.458(2) A, is

between the centrosymmetrically related atoms 0(7) and 0(7 ') . Only one of the four hydrogen atoms, H(2), can be placed in

this hydrogen bond, and is either on the center of symmetry or

disordered about that center. The next shortest interphosphate

0....0 distance, 2.565(1) A, is between 0(1) and 0(5). Two

hydrogens, H(l) and H(l / ), in general positions, can be

accommodated in hydrogen bonds of this type. The fourth

hydrogen, H(3), seems to occupy a hydrogen bonding position

where 0(6)... 0(8') = between 0(6) and 0(8 / ),£2.669 l . This hydrogen can fill only one

half of the two available sites and must, therefore, be disordered

When an idealized position is generated for H(3) according to

the rationale given below, H(3) occupies a site (see Fig. 3b)

where it also appears to form a very weak bond between 0(6)

and 0(6 7 ), which have a separation of 3.144(2) A. in this

bond, the disorder would be with respect to a center of

the hydrogen bond.

symmetry analogous to that in^H(2)/v Full occupancy of the H(3)

sites would bring pairs of hydrogen atoms improbably close

9

together, i.e., about 1.45 A. Thus, it would appear that - all the H ( 3) sites could not be filled even if hydrogen

atoms were available.

Because hydrogen positions are imprecisely located by

X-ray methods, probable positions of the hydrogen atoms in

CaHP0 4 were calculated assuming the 0-H distance to be 1.00 A and the P-O-H angle to be 109.5° . The hydrogens were assumed

to lie in the same plane as the heavy atoms in the system

P-O-H... 0. This will give the shortest possible H...0 distance,

which in general is a realistic approximation. H(3), however,

forms a hydrogen bond between two oxygen atoms in the Ca(2)

coordination (see Fig. 3b) and its position may lie out of the

P(2), 0(6), 0(8) plane because of repulsion by Ca. The

positions of H(3) given in Table 3 lie -0.06 A, -0.20 A

o and 0 A (assumed), respectively, out of this plane; Ca(2)

o lies 1.592 A from the same plane. The Ca(2)...H(3) distance

is 2.52 A for the calculated hydrogen position. Because H(3)

is poorly defined in the X-ray refinements, clarification of

the effect of Ca(2) on the position of H(3) will have to be

made from a neutron diffraction study of CaHP0 4

.

9a
Discussion

The distance 0(7)... 0(7') in the hydrogen bond 0 ( 7 ) -H (2) . . . 0 (7 )

is 2.458(2) A, which implies a very strong hydrogen bond. An

extensive study at different temperatures of the hydrogen

bonds in CaHP04 by neutron diffraction and spectroscopic

methods appears warranted. Whether or not this hydrogen bond

and indeed the whole structure is truly or cnly nominally

centrsymmetric is not yet known, although Denne and Jones (1969)

give a personal communication from W. G. Perdok ftiat a very

weak piezo-electric effect has been found in CaHP0 4 . In the

opinion of the^authors, the Ft* factor reported here is close to or

at the limit of the data and testing the centrosymmetry of the

whole structure by refining in space-group PI and subsequently

applying the ratio test (Hamilton, 1965) would not be worthwhile. The distance 0(7)... 0(7 ) reported here is comparable

with the 0...0 separations of 2.459(9) A in potassium

hydrogen malonate, K00C-CH.,-C00H (Sime and Speakman, 1970),

2.40 A in potassium hydrogen chloromaleate, K00C-CH — CC1 G00H

(Ellison and Levy, 1965), 2.437(4) A in potassium hydrogen

o maleate, K00C-CH = CH-OOCH (Darlow and Cochran, 1961), and 2.49(2) A

in HCo0 s (Hamilton and Ibers, 1963) where centered hydrogen bonds

are probable in all cases.

In the 0 (6) -H (3) 0(8) hydrogen bond in CaHP0 4 , the observed

0(6)... 0(8) distance of 2.669(2) A is close to halfway between

the 0(7)... OH 7) distance of 2.458 A observed here for a very

10
strong hydrogen bond and the usual non-hydrogen bonded 0...0

o closest inter-ionic approach of —2.76 A, and is, therefore,

reasonable for a hydrogen bond in which half the hydrogens are

statistically absent. This bond is in the edge of the Ca coordination and hence is probably a relatively unfavorable place

for a hydrogen atom. Further, the calculated hydrogen position

for H(3) (see Fig. 3b) is such that both 0(8') and 0(6') in

the adjacent P(2)0 4 group may be considered to be acceptors of

the hydrogen bond. Thus, the two possible sites for H(3) are

o only 1.45 A apart, and it is improbable that both sites would

rms

be occupied simultaneously. The maximum^/amplitudes of apparent

vibration for 0(6) and 0(8) are 0.175 A in each case. In our

experience more typical values in the absence of positional

° disorder are —0.10 A. The maximum amplitude of 0(8) is more

or less along the 0(6)... 0(8 ') vector; that for 0(6) is roughly

perpendicular to this vector (see Fig. 3b). 0(6) and 0(8'),

therefore, seem to be exhibiting positional disorder depending

on the occupancy of the H(3) site, as would be expected because

the average 0(6)... 0(8 ') separation of 2.669 A is too small to

be realistic in those cases where there is no H(3) between 0(6)

and 0(8 ' )

.

The 0(6)...0(8 / ) separations with and without H(3) intervening can be estimated. When the H(3) site is occupied, 0(8')

is expected to be —(0.175 - 0.100) = -0.075 A nearer 0(6) than the

observed average separation (2.669 A) of 0(6) and 0(8 ). Similarly,

0(6) may be expected to move toward the continuation of the P('2)...0(8)

vector. By Pythagoras' rule, the 0(6)... 0(8) separation when the

hydrogen bond is occupied will be approximately [ (2.66 9 - 0.07 5) 2 - (0.075) 2

] = 2.593 A, which indicates a strong hydrogen bond.

11
When the H(3) site is unoccupied, the 0(6). ..0(8) separation will

1 be —[ (2.669 1 0.075) 2 + (0.075) 2

] 2 = 2.745 A, which is comparable

with the closest 0...0 non-bonded contact distance of —2.76 A usually observed. That 0(6)... 0(8) are undergoing positional

disorder is corroborated by the apparent thermal motion of Ca(2) # which is bonded to both 0(6) and 0(8), and which has apparent

thermal amplitudes of 0.138 A and 0.132 A toward 0(6) and 0(8),

respectively.

The positional disorder of 0(6) inferred above from the

thermal parameters indicates that, as expected, 0(6) approaches

Ca(l) more closely when there is no H(3) attached and vice versa . Ca(l)...0(6) is a short bond for an oxygen covalently bonded to

later in the

hydrogen ( see /Discussion) . The apparent thermal parameters in

h.

the remainder of the P(2)04 group suggest that this whole group

undergoes some displacement depending on the occupancy of the

hydrogen sites.

The distance of 1.45 A between the occupied and unoccupied

sites for H(3) is probably too large for a rapid interchange of

occupancy to take place. Further, if rapid interchange were takingplace, the apparent thermal parameters of 0(6) and 0(8) might be

expected to be more isotropic since, because of their greater

mass and their fairly rigid attachment to the P0 4 group, they

would be expected to move more slowly than H(3). Indeed, because

of the changing tt character of the P(2)-0(6) bond depending

on whether or not H(3) is covalently bonded to 0(6), the

greatest apparent thermal motion of 0(6) under these circumstances

might be expected to be along tie P(2)-0(6) bond. Actually 0(6)

has essentially its smallest amplitude of apparent thermal

motion (0.087 A) along this direction. Thus, H(3) seems to be

12
relatively firmly attached to 0(6), and probably forms a hydrogen bond which is abnormal only in its statistical disorder.

The relationship of CaHP0 4 to some other calcium phosphates and related compounds is discussed next. The structures

of CaHP0 4 *2H2 0 and Ca (H 2 P0 4 ) 2 -H 2 0 contain corrugated sheets

made up of (CaHP0 4

) ° and (CaH 2 P0 4 ) + chains, respectively.

In CaS0 4 *2H 2 0, there are corresponding CaS0 4 chains and sheets.

In Ca (H 2 P0 4 ) 2

•

H

2 0, the Ca(H 2 P0 4 ) + sheets are separated by H 2 P0 4 ”

ions and water molecules. Sheets similar to those in the above

compounds may also be present in Ca 2 (NH 4 )H7 (P0 4 ) 4 -2H 2 0,

Ca 2 KH7 (P0 4 ) 4

• 2H2 0, and CaCl (H 2 P0 4

) •

H

2 0 (Brown, Smith Lehr

and Frazier, 1958) . The widespread occurrence of the corrugated sheet feature speaks for its stability.

The structures of CaHP0 4 and CaHP0 4 *2H 2 0 are closely

related if allowance is made for the water molecules; corrugated

sheets in CaHP0 4 may be imagined parallel to several planes,

e.g., (101), (101) and (001), with the Ca-P0 4 chains running

parallel to [010] (see Fig. 1). It is of interest to compare

the sheets in CaHP0 4 , CaS0 4 , CaHP0 4 -2H 2 0, CaS0 4 *2H 2 0, and

Ca (H 2 P0 4 ) 2

•

H

2 0. This comparison may be done in terms of the

Ca coordinations in the five compounds (Fig. 2a through 2f)

.

In Ca (H 2 P0 4 ) 2

• 2H 2 0 (Fig. 2f)

,

the shortest Ca...O bonds (2.3 , 2.326 A) are between chains in the same layer; the next shortest

(2.393, 2.475 A) are from the surface of the layer to the interlayer H 2 0/H 2 P0 4 n network; the next longest bonds (2.521, 2.538 A)

to but which are

are7 P0 4 oxygens^/in the same chain as the Ca ion^which have no

covalently bonded hydrogen atoms; the longest (2.626, 2.628 A)

13
are to the oxygens in the same chain which have covalently

bonded hydrogens. The pattern is the same in CaS0 4 (Fig. 2c)

,

CaHP0 4 *2H 2 0 (Fig. 2d), and CaS0 4 *2H 2 0 (Fig. 2e) though actual

distances are a little different.

For Ca(l) in CaHP04 , Ca(l)...0(7) is the longest bond,

and Ca(l) is so far away from 0(5) (3.427 A) that they are not

considered to be bonded. This is to be expected from the above

descriptions, because these atoms are in the same chain and

0(5) and 0(7) are covalently bonded to hydrogens. The

Ca...O however,

other ^/distances do not follow the previous pattern,^/ In particular,

the Ca(l)...0(6) distance, which is within the chain and

where half of the 0(6) atoms in the structure are considered

to be covalently bonded to hydrogen, is relatively short, 2.451 A.

(However, as was remarked earlier, the position of 0(6) is

believed to be an average of two slightly different positions

depending on the occupancy of the H(3) site.) In tie case of Ca.(2)

in CaHP0 4 , 0(1), which is covalently bonded to hydrogen and is

/is within the chain/ so far away that it is not considered to be

bonded to Ca(2); on the other hand, the other member, 0(3), of

the P04 edge 0(1,3) has the shortest Ca(2)...0 bond. CaS0 4 conforms to the general pattern; the formally analogous compound

CaHP0 4 does not, probably because of the deforming power of the

hydrogen bonds, two of which are very strong, and partly because of the averaged effects of hydrogen disorder.

14
Much of the disruptive effect on the Ca-P0 4 coordinations can

be traced to H(l) which, in forming the bond 0 ( 1) -H (11) . . . 0 ( 5)

apparently breaks up two edge sharing by pulling 0(1) away

from Ca(2) and 0(5) from Ca(l).

Two other possible factors in the non-conformity of CaHP0 4

are Ca. . .H repulsions and the size of the oxygen coordination

polyhedron round Ca. The distances Ca...O where 0 is coordinated

o o to hydrogen are (i) 2.390 a and 2.427 A to the water oxygens

in CaHP0 4 -2H 2 0, (ii) ~2 . 34 & to the water oxygens in CaS0 4 *2H 2 0,

and (iii) 2.476 A to the water oxygen in Ca (H ? P0 4 ) 2

•

H

s 0. These

Ca...O distances are all quite short, and involve repulsion of

two hydrogens per oxygen atom. This suggests that Ca. . .H

repulsions are not the main force in the distortion of CaHP0 4

. The mean 0...0 separation in an edge of the S0 4 group in

CaS0 4 is 2.43 A. In the P0 4 groups in CaHP0 4 , the average

0...0 separation is 2.509 A. Thus, although the CaS0 4 structure may not be stable for CaHP0 4 , a change of -0.075 a in

0...0 distances should not be drastic, and the difference in

coordination polyhedron size is probably not structuredetermining. We are then left with the reasonable conclusion

that the 0-H...0 hydrogen bonds distort the CaHP0 4 structure.

15

The deforming power of hydrogen bonds in calcium phosphates

is of interest if P0 4

3-

groups in the structures become HP0 4

2

or H 2 P0 4 groups to restore electroneutrality if some Ca 2+

ions are missing. In cases such as these, the structure probably

undergoes some local distortion, and in extreme cases, may

even be so distorted that it remains amorphous.

15a
Acknowledgement

L. W. Schroeder participated in helpful discussions and

P. B. Kingsbury give technical help. This investigation was

supported in part by research grant DE-00572 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 American Dental Association; the United States 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.

16
References

Atoji, M. and Rundle, R. E. (1958). J. Chem. Phys . 2_9, 1306.

Beevers, C. A. (1958). Acta Cryst. 11 , 273.

Brown, W. E. , Smith, J. P .

,

Lehr, J. R. and Frazier, A. W.

(1958). J. Phys. Chem. 6_2, 625.

Cheng, G. C. H. and Zussmann, J. (1963). Acta Cryst. JL6, 767.

Cromer, D. T. (1965) . Acta Cryst. 18 , 17.

Cromer, D. T. and Mann, J. B. (1968). Acta Cryst. A24 , 321.

Cruickshank, D. W. J. (1961). J. Chem. Soc. , 5486.

Curry, N. A., Denne, W. A. and Jones, D. W. (1968). Bull.

Soc. Chim. France, 1748.

Curry, N. A. and Jones, D. W. (1970). Private communication.

Darlow, S. F. and Cochran, W. (1961). Acta Cryst. L4, 1250.

Denne, W. A. and Jones, D. W. (1969) . Abstract XII -78,

VIII International Congress of Crystallography, Stony Brook,

New York, August, 1969.

de Schulten, M. A. 0901) . Bull. Soc. Min. 2j4, 323.

Dickens, B. and Bowen, J. S. (1971a). J. Res. Nat. Bur. Stands.

75A , 27.

Dickens, B. and Bowen, J. S. (1971b). Acta Cryst., in press.

Egan, E. P. and Wakefield, Z. T. (1964). J. Chem. Eng. Data

9, 541.

Ellison, R. D. and Levy, H. A. (1965) . Acta Cryst. JL9, 260.

Hamilton, W. C. (1965). Acta Cryst. _18, 502.

Hamilton, W. C. and Ibers, J. A. (1963). Acta Cryst. 16_. 1209.

Hohne, E. (1962). Monat. Deut. Akad. Wiss. Berlin, _4, 72.

17a
Jones, D. W. and Cruickshank, D. W. J. (1961) . Z. Krist. 116 , 101.

Jones, D. W. and Smith, J. A. S. (1962). J. Chem. Soc. , 1414.

MacLennan, G. and Beevers, C. A. (1955). Acta Cryst. £3, 579.

MacLennan, G. and Beevers, C. A. (1956). Acta Cryst. _9 ; 187.

Pauling, L. (1960) . The Nature of the Chemical Bond , 3rd Edition,

p. 559, Ithaca, New York: Cornell University Press.

Perloff, A. (1971) . Private communication.

Sime ; J. G. and Speakman, J. C. (1970). J. Chem. Soc., 1919.

Zachariasen, W. H. (1967) . Acta Cryst. 2J3, 558.

17b
Table 1

Atomic

Parameters

in

CaHPO

kO in ID

CO '

'— '— •—• CM CM CM CM CM 00 CM 00

ft 00 ID r" 00 ’ ^ 

'w' "—• PQ ID in CM H 00 ID

CM iH o o CM CM rH o 00 in o 00 1 i 1 1 + w

ID ID ID .. Q)

CO

——" —

— CM CM CM CM CM CM CM 00

U ft

»H tn 00 CM V—' CO H

PQ 03 03 03 CM in r-* o (T\ CM ID 3 pqI rH o o o O CM o CM H O O 0^ & *

CO rbl 1 1 v p co | ID in ID r- *. X—K

CO CM

ft

—1 — 1— 1—

CM CM CM CM CM CM CM 00 fC

rH <N o CM rH '

1 —«* '1 '

—’ '

1 >

Q) +

PQ O 03 r- 00 ID 00 n- 00 *-4 H CM H O o O rH CM rH iH H 00 <* uo ID ft H ^1 1 1 1 1 1 1 ro 03 C

•H poi

X—-s. 4H ft r- 00 00 03 *—V

re 01 —

— v— CM oo 00 oo 00 00 CM 00 Q) Ul

<0 r- o CO 03 £

PQ ID iH CO 00 ID 03 ID 00 oo 00 •P + O o ID ID ID 00 o 00 00 ID 00 ID C ft rH rH rH H H H •H ^1

ftft ,—. QJ pqI CO 03 ..—_

«^s

V ,—. ^ V -P ft

w

—

—

—

—

00 oo CM 00 oo 00 00 oo CO •Je ft 00 ID oo CM — — —

'— 

'—• '—' —• H i-Q | PQ CT> 00 00 oo rH a> ID o o in D

rH in CM 03 n- ID 00 CM

U + H

rH rH H H H H fO ro O

CO • rH CO CO 0s! x-v ,—. C P pqI * —• —

—

'

00 00 00 00 00 oo oo 0 c ro

rH o rH 1— '—

—' '

'

— '— '— •H Q) •re rH in 03 ID in 'vT H a> ID rH P g CO 1 PQ r- iH uo CO o o r" 0^ 0^ & CM rc 0) H c

iH rH rH CM > *H \ Cl) P H

Ti CD 1 u '—

T5 a, ,—

^—. ,—,—x

—

— P X v— —1 rH rH H H H CM H CM ns (D CM 00 in tj* — 1— — —1 — — 1— T3

uo CM oo CM o CM 00

m o C g N CM in rH CO 00 00 in U0 uo H 00 H fU P

o- ID CM o oo 00 H o ID uo p 0

CN ID C" CM 03 ID uo o 00 H oo CO P

CD 0) P X

co p

00 s — —

1— 1— rH rH H H H CM H CM CO CD ID 00 o in — —1 v— — •— — v— 1—1 CD >

00 00 o UO o r- oo o ID CO ro >i 00 ["• 03 CM CM CM H oo ID CM ID 0^ CD rC

00 00 oo 03 00 CM oo O ID 00 ,C

00 00 03 00 H in 00 H O r** P CO c P

CD CD P P

CO CD a g

sf fO '

1 -—• '—•

rH rH H H H H H CM c P

03 o rH

—1 — '

—1 —1 — '— '

1 •H (0 ID o 00 ID 00 00 OO CM uo 'st1 a X in CO in CM rH 00 0^ CM a> 0^ r- CO 03 o 03 CM in oo 00 00 uo 0^ 00 CD H

CN rH CM CM 00 oo H o 00 o CM P fO • d g

On p

•H CD • HH 4Q g rH CM ^—s ^ s x—

Eh 0 —1 '

rH CM rH CM oo UO ID r- 00 CD 4J rti rtf v—

< U U PH PH O o O o O O O o Eh Je

Mw

ml

•k*

rQl CM+

=H rC

03 H

ml**

01

<c| CM

00H

Table 2

Calculated and observed structure factors for CaHP0 4

O . ft.O

1 7 -22

2 29b 299

3 49b -481

4 2 b 7 -270

5 IbJ lbb

6 78 78

7 6b -66

0 lb** -1 b 9 9 201 -207

10 100 -107

11 22 30

O . ft.l -12 36 32

“11 lbl -172

-10 39 40 -9 15 10 -8 26 26

-7 76 77

-6 461 -470

-5 73 -70

-4 3 b9 -372

-3 579 565

-2 229 228

-1 135 140

0 19b -211

1 94 87

2 149 -130

3 132 122

4 347 340

5 152 -153

6 319 323

7 146 -147

8 7 b -73

9 8b 85

10 96 -98

11 90 93

0

» K » 2 -11 119 124 -10 oO 67

-9 92 97

-8 62 -59

-7 71 -72 -6 292 303 -5 7 -2

-4 1 U5 107 -3 74 -78

-2 oil -631

-1 78 71

0 854 -937

1 316 306

2 38b -360

3 21 b 209

4 122 113

5 158 -154

6 74 71

7 13b 133

8 159 157

9 101 102

10 77 78

11 132 -136

0 » ft * 3 -11 67 95 -10 91 -90 -9 17 16 -8 126 128

-7 16 -15

-6 479 487

-b 111 112

-4 109 112

-3 443 -456

-2 196 -185

-1 418 -408

0 650 obi

1 12 -15

2 270 -265

3 415 -399

4 492 -493

5 234 229

6 45 -45

7 261 258

8 19 -13

9 112 -110

10 90 89

11 11 * 6

0 » ft » 4 -11 121 -121 -10 60 -65

-9 15 -9

-8 129 128

-7 174 174 -6 272 -276

-5 132 135

-4 244 -247

-3 330 333

-2 583 595

-1 160 -154

0 196 202

1 355 -363

2 62 -81

3 9-1

4 26 22

5 31 -35

6 95 -93

7 118 -115

8 112 -110

9 82 82

10 25 -21

0

» ft » 5 -11 23 23 -10 106 107 -9 97 -97

-8 230 -232

-7 165 -150

-6 117 -121 -5 160 163 -4 61 53

-3 63 -56

-2 13b -141

-1 95 97

0 94 -91

1 473 476

2 206 205

3 25 24

4 292 292

5 333 -333

6 167 164

7 94 -91

8 21 19

9 37 -33

10 123 -123

0

»

ft » 6 -11 69 65 -10 100 -95

-9 24 -28

-8 11 3 -7 126 -128

-6 152 153 -5 212 -213

-4 46 -47

-3 285 -297

-2 271 -277

-1 185 191

0 23 22

1 421 422

2 31 28

3 11 -6

4 24 -19

b 159 158

7 138 140

8 18 -17

9 160 -160

0» ft »7 -10 45 -44

-9 60 59

-8 157 156 -7 91 84 -6 69 -70 -5 47 -45

-4 160 -158

-3 15 15 -2 162 181

-1 127 -127

0 34 30

1 265 -286

2 102 -103

3 38 43

4 114 -108

b 253 262

6 154 -154

7 74 75

8 17 -16

9 64 51

0» ft »8 -9 45 -42

-6 46 -48

-7 27 29 -5 327 329

-4 183 166 -3 24 13 -2 44 46

-1 242 -246

0 20 -17

1 77 -78

2 61 69

3 179 -177

4 45 -41

b 251 -252

o 51 50

7 21 15

6 99 98

0* ft »9 -* 77 -72

-6 33 -28

-7 78 61 -6 112 112 -5 27 26

—4 79 76 -3 46 -45

-2 92 -90

-1 258 263

0 72 -72

1 207 207

2 62 -64

3 162 “162

4 23 20

5 99 -98

b 73 75

7 42 -41

0 * ft . 10 »

b

23 19 -7 39 -44 -6 2b -28

-5 172 -170

-4 35 -34

-3 21 22

-2 18 13 -1 120 122

0 14 -10

1 28 25

2 41 36

3 108 109

4 3 b -29

b 163 lt>2 0» K »11 -b 91 -90 -5 41 37

-4 14 10 -3 73 -76

-2 30 -23

-1 216 -215

0 88 87

1 52 -53

2 161 158

3 86 83

4 40 -37

0

«

ft . 12 -3 80 -62

-2 93 -87

-1 31 29

0 18 -1

1 31 27

- l » ft »-12

1 18 -8

2 83 80

-ltft»-ll -3 14 -8

-2 s 88 88

-1 80 -82

0

110 -110

1 50 -51

2 76 -76

3 1

7

b 174

4 23 -14

b 49 49

”1 » ft » -10

-5 142 141 -4 155 153 -3 59 -60

-2 29 -34

-1 95 -96

0 36 -36

1 26 25

2 23 -19

3 126 -129

4 134 -132

5 62 —b4 b 10* 6

7

108 105

-1

»

ft • -9

-6 65 69

-5 46 -47

-4 45 -43

-3 150 149 -2 11 0 -1 204 207

0 14 10

1 180 -180

2 83 82

3 193 -195

4 62 64

5 40 -37

6 52 -51

7 33 -33

8 84 -81

-1 »ft t-8 -7 187 -189

-6 51 -48

-5 96 -94

-4 22 -21 -3 177 178 -2 9* 7 -1 83 86

0

16 -12

1 20 -17

2 47 27

3 256 261

4 18 13

5 73 71

6 91 -90

7 205 -202

8 84 82

9 13 -2

-1

#

ft »—

7

-8 146 -148

-7 16 -15

-6 96 -94 -5 22 -20

-4 101 104 -3 244 -243

-2 26 -23

-1 314 -314

0 60 58

1 213 216

2 50 54

3 232 233

4 111 -108

5 45 40

6 209 209

7 73 77

8 92 94

9 55 -44

10

116 -118

-1

»

ft »-6 -9 104 106 -8 8* 4 -7 256 260 -6 9* 8 -5 152 -149

-4 193 -193

-3 127 -129

-2 8* 6 -1 74 73

0 54 -50

1 286 -294

2 31 -28

3 86 -85

4 259 2 o4 5 94 97

6 45 43

7 101 97

8 178 -177

9 109 107

10

8* -1 -1

»

ft » -5 -10 95 98

-9 70 69

-8 133 135 -7 173 -175

-6 25 25

-5 65 67 -411 -9

-3 533 529

-2 19b -195

-1 181 182

0 142 -139

1 197 -201

2 9-6

3 62 -58

4 41 -42

5 122 -119

6 229 -231

7 104 -108

8 19 20 9 142 137

10 122 126

11 49 47

-10 31 -31 -9 176 -178

-8 21 22

-7 177 -180

-6 137 138 -5 98 99

-4 282 282 -3 176 176 -2 312 305

-1 225 -214

0 208 199

1 164 165

2 118 -125

3 93 91

4 405 -411

5 260 -270

6 89 87

7 153 -154

8 171 174

9 163 -160

10 33 -34

11 51 -56

- lift . -3 -11 61 -62

-10 170 -173

-9 22 20 -8 146 -147

-7 251 252

-6 45 -45

-5 146 -137

-4 128 -127

-3 372 -370

-2 538 529

-1 69 70

0 214 212

1 98 -99

2 394 -395

3 208 207

4 272 276

5 177 176

6 75 74

7 49 -46

8 283 -290

9 35 -26

10 46 -50

11 23 23

-1. K .-2 -11 10 * 10 -10 85 84 -9 292 296

-8 15 -2

-7 82 -83

-6 326 -332

-5 90 -89

-4 274 -263

-3 359 343

-2 480 -469

-1 152 -141

0 515 -488

1 65 -86

2 350 363

3 158 150

4 480 488

5 40 37

6 166 -168

7 183 185

8 79 -78

9 240 244

10 51 51

11 78 -77

— 1 » ft » — 1 -11 112 111 -10 114 112 -9 169 -174

-8 255 258

-7 202 -204

-6 262 261 -5 47 36

-4 206 -202 -3 70 64

-2 236 -268

-1 350 -333

0 167 -170

1 133 -146

2 21 -34

3 183 -183

4 65 -64

5 68 -46

6 235 240

7 111 113

8 272 284

9 85 -81

10 40 47

11 14 -11 -1# ft »0 -11 43 -50

-10 76 -77

-9 68 -72

-8 114 120 -7 188 189 -6 153 152 -5 28 30 -4 39 40 -3 409 -402

-2 831 819

-1 . 41 32

0 13 9

1 27 1 2 847 -940

3 201 206

4 59 -66

5 148 145

6 66 61

7 183 -184

8 78 -80

9 122 -124

10 41 41

11 125 126

“ If Kf 1 -11 83 -87

-10 88 -93

-9 231 237

-8 186 -191

-7 76 77

-6 406 -416

-5 35 -36

-4 284 285

-3 265 258

-2 706 701

-1 144 131

0 75 -70

1 161 157

2 373 365

3 99 93

4 310 314

5 249 -252

6 451 -462

7 122 -124

8 22 8 -237

9 159 162

10 49 47

11 76 -78

“1

»

ft »2 -11 80 81 -10 26 -15

-9 197 -206

-8 97 -102

-7 204 -206

-6 25 20 -5 88 82 -4 216 -221

-3 218 216

-2 231 -261

-1 499 507

0 263 293

1 203 21

2

2 508 519

3 518 -515

4 42 41

5 64 -62

6 15 13

7 174 174

8 28 -28

9

108 -109

10 83 -78

11 41 -40

-1» K »3 -11 25 -17

-10 39 36 -9 125 -128

-8 277 288

-7 7* 3 -6 49 50 -5 86 -89

-4 341 -340

-3 111 -107

-2 20 13

-1 248 244

0 448 -466

1 211 -204

2 572 -587

3 234 236

4 56 59

5 393 386

6 202 203

7 62 -58

8 139 139

9 119 -121

10 25 26

11 96 96

-11 19 -16

-10 98 104 -9 214 216

-8 81 83 -7 176 178 -6 108 -109

-5 106 -105

-4 355 363

-3 377 -382

-2 305 312

-1 483 -511

0 375 -384

1 260 -257

2 211 -213

3 174 170

4 115 120

5 44 45

6 52 -52

7 97 -95

8 78 76

9 159 160

10

143 145 —lfft .5 -11 54 55 -10 30 -34

-9 29 26

-8 183 -187

-7 141 1 4

1

-6 89 86 -5 136 129

-4 156 159 -3 38 -33

-2 130 -129

-1 79 72

0 126 124

1 13 -15

2 310 313

3 454 -463

4 118 -118

5 159 -158

6 81 -80

7 213 216

8 88 -86

9 26 25

10 71 -71

-1 » ft »6 -11 73 -76

-10 104 -108

-9 136 -136

-8 77 75 -7 25 -11 -6 14 -12

-5 44 -34

-4 331 -342

-3 326 336

-2 21 -22

-1 598 622

0 94 88

1 132 -128

2 28 -29

3 32 -18

4 94 93

5 149 150

6 52 -46

7 163 -161

8 79 -78

9 116 -117

— 1 » ft » 7 -10 113 115 -9 44 -46

-8 45 44 -7 184 -185

-6 147 -147

-5 167 -166

-4 110 109 -3 70 -68

-2 123 123

-1 89 -92

0 18 19

1 137 139

2 13 -8

3 348 350

4 31 30

5 81 80

6 43 42

7 225 -225

8 63 58

9 63 -63

-1 » ft » 8 -10 11* 13 -9 54 48 -8 149 -149

-7 116 112 -6 28 26 -5 72 -75

-4 110 114 -3 268 -272

-2 25 -19

-1 147 -151

0

12 11

1

60 61

2 48 43

3 19 -20

4 87 -88

5 15 -13

6 34 34

7 172 173

8 9* 5 -1

»

K » 9 -9 84 82

-8 38 31 -7 171 174 -6 108 108 -5 22 21 -4 156 -160

-3 106 106

-2 88 -90

-1 182 186

0

16 -1

1 329 -328

2 99 -99

3 256 -257

4 92 85

5 85 84

6 15 12

7 34 35

10

-8 120 117 -7 112 -110

-6 15 15 -5 52 55

-4 59 57 -3 228 230 -2 35 -31

-1 43 -39

0 44 -46

1 63 -62

2 24 -22

3 45 47

4 49 -46

5 57 -55

6 22 16

-6 30 29

-5 18 -18

-4 28 26 -3 105 -105

-2 69 65

-1 8* -6

0 73 70

1 182 183

2 64 -60

3 140 142

4 97 -94

12 -4 85 -82

-3 105 -102

-2 39 38

-1 60 61

0

110 108

1 38 -30

2 9* 4 -2» ft »- l 1 -2 82 -76

-1 32 34

0 39 -39

1 173 174

2 71 68

3 109 112

4 44 43

5 137 -136

-2. ft.-lO -4 38 36 -3 145 -144

-2 104 -105

-1 46 47

0 40 42

1 105 105

2 48 -46

3 55 -55

4 41 -43

5 57 56

6 82 81

7

104 102

-2. K .-9 -6 9 -2 -5 13 11 -4 45 -41 -3 100 102

-2 83 81

-1 142 -145

0 18 4

1 287 -290

2 84 -86

3 18 15

4 65 -66

5 147 143

6 97 -95

7 44 43

8 37 -35

-7 17 17 -6 20 -21 -5 298 295

-4 42 40 -3 102 101 -2 33 -31

-1 214 -216

0 17 16

1 12 -11

2 46 44

3 36 -35

4 60 -57

5 285 -287

6 41 40

7 35 -40

8 101 102

9 74 69

-2 »ft * -7

-8 20 -18

-7 39 -38

-6 98 101 -5 61 -58

-4 37 37

-3 105 -105

-2 48 -46

-1 232 234

0 24 23

1 366 370

2 82 -80

3 97 -98

4 69 63

5 164 -163

6 137 137

7 40 -32

8 62 “64

9 87 -89

10 55 -56

-2» ft »-6 -9 80 84 -8 20 -16

-7 108 -109

-6 51 -51 -5 262 -263

-4 71 -68

-3 21 22 -2 69 70

-1 119 119

0 49 -47

1 65 66

2 10 6

3 224 232

4 86 86

5 316 319

6 160 -162

7 70 71

8 165 -159

9 66 -58

10

108 108

-9 8* 5 -8 40 -41

-7 105 -104

-6 143 -143

-5 232 231

-4 33 -32

-3 57 -55

-2 79 -76

-1 618 -616

0 132 131

1 122 -120

2 391 393

3 150 151

4 40 -35

5 35 -35

6 61 -60

7 172 170

8 178 180

9 51 49

10 77 -78

11 59 -57

“11 144 144 -10 9* 3 -9 97 96

-8 71 -71 “7 164 -163

-6 299 299

-5 60 -80 -4 594 573 -3 79 68

-2 143 -144

-1 51 36

0 519 -551

1 229 -221

2 157 150

3 104 100

4 175 -162

5 111 -117

6 270 -279

7 63 66

8 235 243

9 23 25

10 143 144

11 164 -190

-10 71 68

-9 121 -122

-8 87 86 -7 193 196 -6 73 71 -5 217 219

-4 90 -93

-3 202 -195

-2 53 -55

-1 75 67

0 36 27

1 151 150

2 241 -233

3 401 “408

4 61 66

5 252 -256

6 240 243

7 60 -58

8 28 25

9 61 53

10 38 -41

11 135 130

-2. K .-3 -10 95 -95

-9 100 100 -8 30 30 -7 16 -11

-6 76 75 -5 129 -126

-4 317 315

-3 303 293

-2 158 153

-1 522 505

0 587 -575

1 236 229

2 338 -341

3 192 -193

4 77 —81

5 123 -127

6 145 -151

7 86 -81

8 82 -84

9 36 -39

10 192 196

11 31 28

-2# ft »-2 -11 94 100 -10 47 — 4

1

-9 9* -6

-8 121 -122

-7 240 -238

-6 21 0 -5 104 96

-4 354 358

-3 111 108 -2 116 113

-1 476 -455

0 70 -51

1 146 -140

2 551 548

3 297 298

4 232 -235

5 43 44

6 425 -433

7 142 146

8 134 138

9 65 -62

10 23 -24

11 201 -203

-2. K .-1 -11 25 -20 -10 66 65

-9 196 -192

-8 35 -33

-7 149 145

-6 164 -160

-5 225 220

-4 454 -447

-3 567 -541

-2 355 -331

-1 217 -211

0 649 644

1 184 174

2 231 230

3 84 -90

4 105 103

5 324 330

6 230 232

7 43 44

8 95 -94

9 36 -34

10 195 -201

11 128 127

-2» ft »0

-2. ft .

2

-11 9. 4 -10 134 -139

-9 115 -112

-8 9b -97

-7 120 118 -b 93 91 -5 410 406

-4 29 21 -3 94 78

-2 211 -176

-1 45 30

0 744 800

1 145 124

2 *16 -23

3 123 -129

4 631 -646

5 2b 3 288

6 202 -208

7 37 3h 8 179 -179

9 124 -124

10 72 -74

11 106 106

-2. ft .

3

-11 226 -230

-10 71 68

-9 49 -45

-8 59 55

-7 o9 67 -6 378 -382

-5 165 -163

-4 7 b -80

-3 403 396

-2 516 514

-1 49 55

0 9-2

1 223 -231

2 296 314

3 187 180

4 225 217

5 298 -297

o 12 5

7 267 -267

8 61 -63

9 120 118

10

101 -102

11 111 111

-11 89 82 -10 132 135 -9 2 b 24 -8 lbl -163

-7 242 -244

-6 121 123 -5 178 -177

-4 270 267

-3 128 -131

-2 3ol -373

-1 29 30

0 315 -339

1 120 128

2 100 105

3 73 72

4 241 241

5 177 -173

6 17o 171

7 2 b 22

8 175 174

9 6b 63

10 9* -1

-2. ft .

5

-11 137 134 -10 127 -127

-9 134 134

-8 34 35 -7 58 51 -6 202 204 -5 22 -21

-4 73 -74

-3 92 -94

-2 461 -475

-1 230 -236

0 45 -46

1 35 -35

2 109 -104

3 54 59

4 250 -249

5 351 351

6 50 48

7 232 228

8 46 46

9 104 -101

10

68 66 11 72 -77 10 151 1 52

-9 144 145

-8 131 130

-7 66 63

-6 260 -261

-5 354 -345

-4 12 -10

-3 59 53 -2 140 -135

-1 121 115

0 820 —884

1 144 134

2 260 228

3 24 14

4 395 397

5 208 -213

6 273 281

7 85 -85

8 102 101

9 89 91

10 35 39

11 69 68

-2» ft »6 -11 96 -88

-10 30 26

-9 49 54 -8 172 174 -7 162 161 -6 110 -116

-5 31 25

-4 174 -179

-3 186 189

-2 321 328

-1 249 -258

0 65 86

1 420 -435

2 27 -2b

3 149 152

4 13 -14

5 17 -3

6 146 -142

7 112 -110

8 42 -40

9 138 134

-10 141 136 -9 62 -60

-8 155 -157

-7 147 -145

-6 47 -45

-5 170 172

-4 204 205

-3 128 127 -2 15 15 -1 52 52

0 16 14

1 246 248

2 62 60

3 42 -40

4 29 30

5 368 -365

6 25 23

7 80 -78

8 16 -12

9 90 90

-2. ft .

8

-10 182 -180 -9 24 -23

-6 55 -52 -7 91 -64 -6 103 103 -5 162 -158

-4 22 20 -3 26 24

-2 57 -58

-1 215 2*0

0 7* 5

1 223 229

2 14 10

3 17 11

4 37 35

5 14 6

6 3 b 34

7 18 -7

6 40 -38

-2. ft .

9

-9 4 b 48

-6 94 96 -7 3b -36 -6 42 -40 -b lib -117

-4 142 — 1

4

l -3 lb 3 -2 130 1*9

-1 150 -150

0 56 56

1 194 -196

2 33 25

3 170 168

4 38 39

5 172 171 6 105 -100

7 14 -8

-2. ft. 10 -b 10* -13

-7 9* 6 -6 109 -107

-5 226 219

-4 6* 0 -3 15 10 -2 60 -55

-1 242 -241

0 74 -71

1 25 -22

2 14 -10

3 10* 9

4 35 -35

b 99 -95

e 10* 3 -2. ft * 11 -7 82 * 84 -6 9b 93 -b 19 18 -4 28 28

-3 21 -22

-2 23 -18

-1 99 98

0 119 -114

1 50 47

2 110 -109

3 144 -1 h 0 4 73 o8 -2. ft . 12 -b 106 -104

-3 39 40 -2 97 95

-1 63 56

0 2b -23

1 17 -16

2 28 28

-3. ft . -11

-1 37 34

0 66 83

1 50 50

2 70 b9

3 168 -167

-3. ft . -10

-4 135 -141 -3 109 112

-2 24 -23

-1 208 211

0 25 26

1 31 35

2 6* -2

3 14 -7

4 57 53

5 60 66

b 42 -35

-3» ft * -9 -b 88 -b 6 -4 9* -2 -3 69 -68

-2 111 109

-1 7** -74

0 37 -34

1 50 47

2 64 -63

3 207 208

4 31 29

5 66 b 3 6 41 -41

7 94 -98

-3. ft. -a

-7 94 90 -6 8* 3 -5 70 68

-4 122 126 -3 260 -260

-2 23

-1 204

0 21

1 35

2 16

3 178

4 66

5 40

6 128

7 206

8 44

-8

0

64 20159

60

151

12280 238

lbO 258

78 275

13567

47

6b 86

20

129

153

3426

9 18965

130

19

94

lb

132

234

7473

91

18 -210

1635 -12 -182

-65

-42

125 203

43

64 204

58

58 -150

121 -82 239

-151 -260

-80 -281

13667

-41

62 -82

132

•159 29

23

7 187 -62

128 -19

43

43

94

12 128

232

73 -72

91

-81 -57

-87

153 -305

166

11 59 60

-3. ft.-l -11 82 -82

-10 129 -133

-9 21 -20 -8 153 -154

-7 218 219

-6 80 79 -5 91 -85

-4 144 143

-3 376 -375

-2 564 550

-1 24 2 234

0 441 440

1 152 -149

2 599 -608

3 38 -31

4 72 -74

5 185 185

6 60 61

7 81 -80

8 241 -245

9 17 -11

10 66 -64

11 61 65

-3. K .0 -11 59 -58

-10 12 4 -9 175 180

-8 118 -119

-7 135 -134

-6 208 -207

-5 197 -187

-4 99 98 -3 152 149

-2 210 -201

-1 429 -417

0 189 186

1 246 -251

2 867 886

3 20 -18

4 504 507

5 91 -92

6 47 -42

7 26 28

8 132 -133

9 82 85

10 45 -45

11 135 -134

-3. K .1 -11 161 166

-10 32 34 -9 132 -137

-8 30 28 -7 109 -112

-6 126 123 -5 98 93

-4 670 -660

-3 81 75

-2 866 -864

-1 289 2 79

0 186 179

1 441 434

2 169 164

3 115 104

4 130 -126

5 53 52

6 225 232

7 104 104

8 161 163

9 121 -125

10 55 -54

11 30 - -30

-10 127 -132

-9 58 59 -8 152 -153

-7 255 262

-6 81 -82

-5 162 -161

-4 18** -183

-3 263 -259

-2 110 111

-1 264 262

0 117 116

1 251 -2 b 3 2 27 -22

3 149 -152

4 34 b 342

5 241 243

6 78 76

7 76 77

8 20 b -205

9 45 44

10 45 -44

11 32 32 -3. ft . -3 -10 111 117

-9 102 109 -8 124 127

-7 90 -90

-6 26 24 -5 81 79 -4 37 -15

-3 337 326

-2 508 -500

-1 54 -52

0 203 -198

1 319 -317

2 295 294

3 243 -243

4 112 108

5 63 -61

6 12 -9

7 43 -46

8 143 141 9 75 71

10 146 146

11 16 8 -3. ft . -2 -11 37 36 -10 40 42 -9 161 -167

-8 lib 117

-7 11 -3 -6 256 260 -5 169 164 -4 59 46

-3 93 88 -2 142 -140

-1 101 97

0 3b -39

1 237 240

2 397 -400

3 68 70

4 691 -706

5 98 -101

6 46 43

7 13 -10

8 229 228

9 56 -59

10 34 -33

-3. ft .

2

-11 27 -30

-10 30 23 -9 21 -22

-8 147 149

-7 78 74 -6 123 123 -5 28 -26

-4 85 -76 -3 246 -249

-2 279 269

-1 100 94

0 147 141

1 115 109

2 835 -897

3 127 135

4 265 -267

5 151 150

6 199 204

7 79 -78

8 61 64

9 41 -42

10 69 64

11 86 86

-3» ft » 3 -11 110 -106

-10 27 -25

-9 158 163

-8 62 -61 -7 59 60 -6 13 -2 -5 10 -1 -4 566 567

-3 58 59

-2 522 522

-1 452 -463

0 32 -28

1 181 -196

2 15 -22

3 88 -95

4 9-1

5 219 -221

6 237 -239

7 36 33

8 163 -161

9 212 212

10 35 32

11 23 -19

-11 86 97 -10 119 -119

-9 106 -103

-8 179 -183

-7 33 -31 -b 160 157 -5 301 303

-4 178 -184

-3 177 181 -2 334 -346

-1 202 203

0 335 353

1 185 190

2 354 375

3 378 -409

4 57 -60

5 211 -212

6 34 -35

7 142 139

6 104 -102

9 9] -90

10 93 -94

-11 27 -28

-10 11* -14

-9 116 -119

-8 190 1«6 -7 121 -123

-6 42 -43

-5 68 -66

-4 373 -383

-3 32 6 -2 17 -3

-1 196 203

0

100 108

1 83 «8

2 173 -189

3 106 111

4 105 104

5 119 116

6 198 195

7 151 -146

8 116 116

9

168 -165

10 44 4

1

-11 21 17 -10 115 115 -9 96 86

-a 32 32 -7 20 -23

-6 147 -147

-5 94 -91 -4 137 145 -3 255 -269

-2 89 89

-1 349 -370

0 280 -20

9

1 162 176

2 195 -206

3 306 317

4 20 18

5 142 lul

6 53 44

7 76 74

8 44 42

9 87 05

— 3 » ft » 12 -5 62 60

-4 11* 7 -3 155 150 -2 100 -103

-1 50 -47

0

106 -100

1 49 -50

2 37 32

-2 128 132

-1 13 -9

0 25 25

1 162 -163

2 21 17

3 20 17

4 32 -26

-4 116 120 -3 64 63

-2 28 23

-1 49 4 b

0 30 -32

1 104 103

2 7u 73

3 10 20

4 25 21

5 197 -194

-b 94 99

-5 143 -142

-4 52 40

-3 103 -106

-2 99 -103

-1 lb? 157

0

21 -10

1 154 158

2 0* -3

3 9* -0

4 0 • -H

b 86 PH

6 50 52

7 31 3 b

8 46 -48

-3. K .7 -10 24 -?1

-9 52 54

-8 130 -134

-7 130 132 -6 116 114 -5 135 134

-4 73 76 -3 204 -207

-2 156 -161

-1 130 -137

0 6* -5

1 36 38

2 157 165

3 253 -256

4 52 -51

5 69 -70

-6 78 -00 -5 149 -161

-4 116 -117

-3 45 46

-2 76 73

-1 115 -115

0 7 • 1 1 340 -342

2 37 35

3 113 114

4 37 37

5 223 220

o 67 -67

7 13 0 8 38 36

7 288 201

8 74 -69

9 50 50 -3. K .

8

-10 72 -67

-9 80 -76

-0 140 139

-7 18 -3

-6 76 78 -5 41 42 -4 127 -128

-3 160 160

-2 54 S3 -1 252 255

0 160 164

1 170 -174

2 40 -*3 3 271 -273

4 70 71 5 67 -r, 7

6 33 -33

7 133 -130

8 16 -12

-3. K .9 -9 69 -64

-8 14 0 -7 119 -116

-b 144 -143

-5 62 63

-4 100 103

-3 130 13b -2 85 05

-1 33 30

0 61 -57

1 215 216

2 52 —54

3 166 170

4 124 -1?4

5 43 -39

6 19 -17

7 122 -122

-3. ft .10 -8 150 -146

-7 61 59

-6 10* -6

-5 16 -13

-4 84 04 -3 234 -228

-2 9* -1

-1 53 -53

0 12 -9

1 163 163

2 41 36

3 62 62

4 50 -58

5 35 30

6 9* -5

-3. ft. 11

-8 21 -24 -7 13 6 -6 60 -70

-5 254 259

-4 17 1? -3 102 99

-2 107 -inn

-1 28? -203

0 56 -58

1 148 -149

2 11 -3

3 35 32

4 00 -0Q

5 119 -119

6 59 59

7 46 43

8 139 140

9 15P 158

-9 57 -62

-6 40 38 -7 91 06

-6 155 160 -5 32 -28

-4 53 53

-3 13 -11

-2 59 -62

-1 246 244

0 106 -106

1 203 200

2 216 -210

3 94 -94

4 20 29

5 135 -133

6 135 136

7 96 -90

8 110 -114

9 17 -13

10

62 -62

-9 95 95 -8 21 24 -7 131 -134

-6 47 47

-5 374 -301

-4 67 6 b -3 81 79

-2 289 205

-1 203 202

0 137 143

1 62 -61

2

122 121

3 144 146

4 109 111

5 50 51

6 183 —106

7 167 -167

8 137 -139

9 121 -119

10

159 154

•7 65 57 6 53 50 5 73 -76

-4 70 -65

-3 91 -92 2 81 -77 1 22 21

0 36 35

1 179 -179

2 60 b7

3 16b -166

4 112 111

-10 43 44 -9 32 29

-8 146 -150

-7 161 -161

-6 257 -257

-5 163 164

-4 109 -107

-3 184 185

-2 29 29

-1 321 -313

0 2b4 264 •10 121 125

Table 2 (continued)

1 64 -56

2 263 257

3 294 297

4 120 -121

5 49 43

6 143 -147

7 106 106

8 ttb 87

9 45 48

10 96 -95

— 4 # K » —2

-3 165 -lo7

-2 183 -lb2

-1 182 179

0 300 -313

1 127 133

2 93 -99

3 11 -9

4 34 -30

5 54 48

to 159 -157

7

127 126

6 134 136

9 58 58

10

134 133 -10 25 28 -9 115 -116

-6 d9 59

-7 226 230

-6 16 -8

-5 168 190

-4 313 -315

-3 lOo -99

-2 154 -150

-1 12 4

0 94 -96

1 22 18

2 399 -402

3 127 -133

4 170 173

5 33 28

6 354 358

7 32 17

8 68 -64

9 85 84

10 71 -72

11 146 138

-11 58 55 -10 119 -122

-9 4b -44

-6 59 60

-7 143 144 -b 145 143

-5 206 208

-4 67 b6

-3 61 -58

-2 177 169

-1 192 -203

0 346 358

1 352 -375

2 118 -121

3 380 -402

4 308 -322

5 192 199

6 13 -2

7 90 66

6

16 8

9 137 -135

10 64 80 -11 67 -71

-10 35 34 -9 138 139

-8 241 245

-7 18 -18

-e 230 226

-5 319 -318

-4 243 234

-3 lb -5

-2 171 166

-1 26 25

0 534 -544

1 155 -148

2 258 -262

3 101 -106

4 209 209

5 188 -192

6 16 10

7 56 -59

8 10 -3

9 6b 64

10 204 203

11 50 49

-4 * K » 0 -11 150 152 -10 87 -88

-9 98 94 -8 66 -70

-7 154 -154

-6 61 60

-5 98 93

-4 2U6 197

-3 196 188

-2 198 195

-1 142 -149

0 50 49

1 142 -139

2 34 36

3 100 98

4 251 -245

5 13 -7

6 390 -398

7 94 94

6 93 92

9 11 2 10 65 87

11 158 -157

-11 194 -190

-10 38 32 -9 40 -36

-8 79 80 -7 216 22

1

-6 241 -238

-5 113 111 -4 93 -94 -3 253 252

-2 354 362

-1 108 116

0 144 -156

1 244 -257

2 47 -48

3 64 e5

4 154 158

5 116 -121

6 91 -90

7 218 -212

6

80 -80

9 100 96

10 47 -43

-lU 88 86

-9 17 -18

-6 159 -le5

-7 134 -134

-o 19 -18

-5 52 -46

-4 124 121 “3 64 -65

-2 263 -272

-1 305 321

0 159 -170

1 378 400

2 58 59

3 41 34

4 101 107

5 87 -68

6 35 33

7 37 -34

8 8* -2

9 12 9 —4»K»7

•11 27 -23

•10 82 -90

-9 191 -194

-8 97 -98

-7 140 138

-6 203 -200

-5 313 307

-4 409 -394

-3 69 -81

-2 130 133

-1 11 -1

0 558 579

1 87 83

2 16 -6

3 lib -118

4 80 83

5 215 220

6 169 166

7 51 -52

8 191 -191

9 lb7 -164

10 128 -129

11 67 68

—4 # K # 2

•11 159 -165

•10 123 127 -9 10* 8 -8 143 143 -7 22 -18

-6 267 -264

-5 334 -332

-4 169 -165

-3 28 -22 -2 165 159

-1 190 193

0 489 -512

1 200 203

2 129 130

3 281 285

4 542 543

5 119 -117

6 99 103

7 131 -130

8 71 -72

9 59 57

10 54 -53

11 51 50

•11 172 174

•10 30 31 -9 104 98

-8 26 -24

-7 166 -163

-6 173 174

-5 157 -153

-4 206 195

-10 81 -66

-9 15 -18

-8 65 63 -7 77 -72

-6 140 140 -5 300 -302

-4 21 -20

-3 206 -211

-2 73 -74

-1 7* -6

0 111 119

1 54 -56

2 75 81

3 12 -9

4 36 -36

5 271 277

6 78 79

7 109 112

8 33 32 —4 » K »

8

-9 60 58 -6 72 74 -7 146 144

“6 108 -109

-5 14 6 -4 173 -177

-3 21 17 -2 127 129

-1 147 -150

0 36 38

1 348 -360

2 44 -40

3 114 113

4 45 43

5 168 171

6 47 -49

7 45 -47

6 20 -17 -4.K.9

-9 24 24 -8 102 -103

-7 41 42

-6 49 -50

-5 199 202

-4 107 1U3 -3 84 80 -2 103 -105

-1 25 24

0 42 -46

1 95 97

2 21 -20

3 106 -103

4 36 -37

5 214 -216

6 53 47

7 59 -57

-4#K» 10 -8 17 16 -7 17 -11 -6 173 174 -5 147 -143

-4 71 75

-3 39 35

-2 33 26

-1 249 2 46

0 21 17

1 73 75

2 84 -77

3 93 -95

4 42 -43

5 30 -32

6 21 20

-4 * K » 1

1

-6 13 -1 -5 84 -83

-4 60 -58

-3 33 41 -2 7b 76

-1 9* -1

0 85 83

1 103 -104

2 20 -13

3 127 124

4 19 -18

—4 * K t 12 -4 46 -44

-3 44 -42

-2 53 -52

-1 186 -183

0 68 60

1 23 -23

2 67 64 -5»K»-10

0 50 -50

1 9* -7

2 35 -33 -5»K*-9

-3 45 -39

-2 73 -72

-1 25 -26

0 79 78

1 49 51

2 40 42

3 163 -161

4 92 -92

5 108 -111 -5»K • -8 -5 10* 9 -4 69 -74

-3 207 209

-2 15 17

-1 178 185

0 63 66

1 101 -101

2 8* -4

3 131 -137

4 46 42

5 71 -71

6 16 -12

7 92 -93 -5#K»-7

-6 15 -14 -5 11* 9 -4 58 55 -3 63 61 -2 5b 57

-1 89 -87

0 29 -27

1 120 121

2 49 -51

3 254 260

4 38 -39

5 12 -2

6 34 -35

7 135 -131

8 55 55

—5» K » -6 -7 56 58 -6 44 -46

-5 45 41 -4 37 34 -3 283 -286

-2 62 -59

-1 220 -224

0 31 21

1 260 261

2 16 12

3 84 88

4 97 -96

5 8* 4 6 83 84

7 255 257

8 10* -13

9 42 41 -5 » K » -5

-8 74 74 -7 90 96

-6 28 29

-5 81 -83

-4 152 -152

-3 38 -40 -2 19 -17

-1 41 40

0 36 -32

1 307 -310

2 27 26

3 276 -283

4 289 298

5 44 43

6 45 47

7 107 105

8 64 -59

9 76 73

-9 26 -28

-8 119 121 -7 173 -182

-6 43 33 -5 162 167

-4 68 69

-3 305 305

-2 154 -155

-1 80 -79

0 173 -178

1 22 -21

2 49 48

3 7* -5

4 47 -46

5 99 -101

6 71 -71

7 118 -117

8 121 122

9 42 -37

10

111 112 -5»K»-3

-9 89 -94 -8 94 -90

-7 9* 12 -6 8* -5

-5 136 136

-4 131 131 -3 119 -117

-2 147 146

-1 25 -27

0 73 70

1 487 502

2 61 -60

3 216 226

4 343 -350

5 153 -154

6 75 -75

7 35 -31

8 55 54

9 136 -138

10

104 -104

-5»k #-2 -10 77 -79

-9 14 7

-8 122 -125

-7 101 103 -6 105 -106

-5 192 -193

-4 6* 6 -3 274 -271

-2 350 355

-1 228 233

0

244 250

111

0 2 18 19

3 137 -140

4 227 229

5 108 110

6 93 -96

7 30 27

8 249 -255

9 40 39

10 27 -28 -5#K»-1

-10 101 106 -9 80 87 -8 38 39 -7 191 -193

-6 146 -147

-5 27 28 -4 46 46

-3 323 330

-2 352 -361

-1 178 -179

0 331 -341

1 181 -193

2 433 448

3 101 -ill

4 180 182

5 7# 1 6 53 -54

7 147 147

8 93 96

9 96 100

10 23 22 -5»K »

0

-10 52 55

-9 128 -130

-8 132 133 -7 47 43

-6 221 214 -5 202 191 -4 78 -77

-3 116 -117

-2 320 -323

-1 191 -193

0

231 -239 19-6 2 76 -77

3 46 44

4 204 -210

5 46 -48

6 179 180

7 18 -17

8 349 355

9 103 -103

10 39 38 -5 » K #

1

-11 76 -75

-10 26 -9 -9 59 57 -8 13 -2 -7 219 211 -6 24 13 -5 59 -55

-4 199 195 -3 320 -322

-2 320 316

-1 70 69

0 57 58

1 43 44

2 388 -404

3 6* 2

4 149 -156

5 88 84

6 36 -30

7 97 -97

8 77 -77

9 17 19

10 52 48

-5 * K » 2 -11 48 -56

-10 18 -20 -9 145 146 -8 178 -177

-7 63 -61 -6 266 -261

-5 71 -69

-4 264 262

-3 395 398

-2 51 45

-1 48 46

0 156 -157

1 40 -16

2 453 474

3 46 53

4 55 55

5 94 -93

6 328 -326

7 88 89

8 171 -173

9 150 152

10 98 -94

-5#K »

3

-11 79 78 -10 20 13 -9 231 -229

-8 46 -<*7 -7 202 -195

-6 151 147 -5 37 34 -4 198 -198

-3 36 34

-2 347 -352

-1 111 110

0 280 289

1 25 17

2 451 474

3 27 -30

4 80 85

5 30 -32

6 115 114

7 49 -48

8 85 86

9 163 -166

10 100 -101

-11 43 -46

-10 49 52 -9 16 10 -8 143 147 -7 13 10 -6 43 -42

-5 150 -151

-4 98 -93

-3 162 -165

-2 42 38

-1 41 -45

0

10 6

1 51 50

2 27l -271

3 242 252

4 53 -53

5 110 112

6 168 168

7 172 -173

8 129 131

9 51 -50

10 70 69 -5»K»5

-10 15 14 -9 234 235

-8 100 -98

-7 153 150

-6 126 -120

-5 29 -12

-4 268 269

-3 95 100

-2 113 108

-1 208 -212

0 328 -342

1 110 -107

2 146 -156

3 90 95

4 117 -121

5 68 -65

6 140 -142

7 107 108

8 10* 2

9

247 238 -5.K.6

-10 24 -22

-9 65 -58

-8 86 -85

-7 24 -14

-6 250 251

-5 176 175 -4 80 80 -3 114 120 -2 178 -180

-1 27 -8

0 117 120

1 171 -179

2 182 191

3 294 -302

4 50 -SO

5 126 -132

6 46 -42

7 135 138

8 54 -52

9 26 27 —5 * K * 7 -10 36 -37

-9 80 -75

-8 159 163

-7 95 -94

-6 10 0 -5 54 -55

-4 188 -188

-3 172 172

-2 21 22

-1 132 132

0 114 118

1 7* -4

2 21 -22

3 130 131

4 69 67

5 22 16

e 29 30

7 210 -208

8 9* 6 -5 » K * 8 -9 69 61 -8 69 -65

-7 66 -70

-6 181 -185

-5 107 -105

-4 43 41 -3 58 —57

-2 118 117

-1 150 -148

0 69 -70

1 194 200

2 28 -27

3 307 318

4 19 19

5 16 -8

6 27 29

7 65 -64 -5#K»9

-8 113 -113

-7 23 20 -6 54 54 -5 12 -1 -4 33 29

-3 156 -152

-2 62 -62

-1 117 -115

0

11 1

1 12 -4

2 79 78

3 54 -54

4 43 37

5 10* -5

6 10* -5

—5#K #10 -7 31 29

-6 47 48

-5 46 46

-4 131 -131

-3 157 153 -2 55 -53

-1 78 79

0 23 -21

1 164 -160

2 44 -44

3 112 -112

4 67 58

5 16 18 -5.K.11

-6 26 -29

-5 60 61 -4 86 80 -3 126 121 -2 104 100

-1 55 -57

0 55 -53

1 47 45

2 47 -43

3 59 59

4 77 -67

12 -4 82 74

-3 125 -118

-2 99 96

-1 17 -14

0 20 18

1 95 93 -6»K»-9

-1 17 -9

0 63 67

1 16 9

2 10* -5

3 70 -69

-4 98 -96

-3 48 52 -2 126 128

-1 90 -93

0 30 31

1 217 -219

2 14 5

3 16 -12

* 26 27

5 29 30 —6 * K » —7

-5 196 196

-4 42 42 -3 86 86

-2 39 -36

-1 85 87

0 73 -75

1 138 139

2 74 -75

3 90 -91

4 74 -73

5 191 -193

6 10* -9

7 31 -34

-6 160 162 -5 119 -119

-4 122 126 -3 91 -93

-2 14 7 -1 227 226

0 27 -24

1 159 160

2 74 -72

3 127 -131

4 20 -10

5 39 38

6 54 54

7 16 20

8 72 -68 -6.K.-5

-7 9* 5 -6 25 -23

-5 182 -185

-4 84 -82

-3 84 -79

-2 94 92

-1 52 -55

0 75 75

1 201 -205

2 130 132

3 150 154

4 85 88

5 276 283

6 126 -127

7 16 11

8 32 -34

-8 76 -80 -7 32 32 -6 200 -201

-5 213 215

-4 138 -135

-3 55 -54

-2 184 -183

-1 240 -242

0

86 88

1 31 -24

2 160 157

3 14 11

4 29 -29

5 23 -20

6 102 107

7 65 62

8 162 160

9 71 68

—6» K » —3

-9 99 -100

-8 44 42

-7 133 134

-6 127 130 -5 20 -13

-4 12 4 -3 77 -74

-2 84 -86

-1 249 250

0 139 -142

1 78 81

2 240 -245

3 250 -250

4 30 29

5 86 -85

6 246 252

7 51 -47

8 19 -11

9 26 -24 -6*K »-2 -9 65 61

-8 38 37 -7 48 -47

-6 184 187

-5 185 -192

-4 205 202 -3 118 117 -2 86 85

-1 273 278

0 ill -112

1 29 -25

2 102 -104

3 70 74

4 123 -123

5 86 89

6 256 -258

7 78 .-73

8 131 -130

9 40 -38

10 89 90 -6*K#-1

-10 10* -2

-9 8* 3 -8 121 -125

-7 116 -117

-6 92 -91 -5 119 115

-4 49 47

-3 51 53

-2 74 74

-1 210 -217

0 470 493

1 50 -49

2 336 336

3 74 76

4 239 -245

5 19 -22

6 184 -185

7 8* 0

8 52 51

9 14 -15

10 72 -72 -6.K.0

-10 23 22 -9 157 -153

-8 47 -47

-7 151 150 -6 80 -79

-5 75 73

-4 293 -291 -3 156 -151

-2 33 -33

-1 43 41

0 266 273

1 10 -14

2 75 -84

3 192 -195

4 138 141

5 14 6

6 422 423

7 29 -29

8 29 -28

9 29 -23

10

116 -110

—6 # K • 1 -10 34 '5 -9 156 155 -8 76 77 -7 29 28

-6 60 60

-5 175 -172

-4 12 -3

-3 64 64

-2 288 -296

-1 132 134

0 587 -619

1 45 49

2 243 -262

3 151 154

4 176 178

5 28 25

6 131 131

7 52 52

8 33 33

9 86 83

10 57 56

-6» K »

2

-10 21 -17

-9 85 82

-8 35 28 -7 122 -122

-6 269 262 -5 7* -5

-4 183 177 -3 72 -76

-2 137 -138

-1 234 -241

0 103 109

1 53 -56

2 28 25

3 42 36

4 258 -264

5 54 52

6 198 -199

7 119 117

8 84 82

9 19 22

10 96 90 —6 » K » 3 -10 54 -61 -9 152 -151

-8 26 -28

-7 85 82 -6 15 -3

-5 196 195

-4 153 -147

-3 38 -37

-2 258 264

-1 85 -90

0 622 648

1 44 -44

2 7* 1 3 208 -218

4 201 -204

5 14 0 6 69 70

7 16 -10

8 150 -147

9 96 -93

10 97 -99

-10 11 * 0 -9 15 12 -8 56 -55

-7 19 21 -6 256 -251

-5 45 -8

-4 109 -110

-3 213 215

-2 136 136

-1 22 1 228

0 157 -163

1 150 161

2 6* 4 3 120 126

4 295 302

5 220 -224

6 75 74

7 164 -161

8 73 -70

9 30 24 -6 » K » 5 -10 16 16 -9 19 16 -8 53 -55

-7 202 -202

-6 163 160 -5 101 -96

-4 113 109 -3 151 -152

-2 268 -291

-1 33 33

0 lib -117

1 267 297

2 40 39

3 32 32

4 36 38

5 11 -1

6 20 19

7 77 74

8 67 63

9 4b -43 -6»K.6

-10 62 -60

-9 9* -7 -8 107 109 -7 56 48

-6 123 122 -5 30 29

-4 106 -102

-3 132 -133

-2 14 -11

-1 195 -203

0 140 14b

1 105 -107

2 107 -107

3 84 -88

4 260 -267

5 212 216

6 18 -14

7 228 228

8 11* 13 -6.K.7

-9 24 22 -8 b3 64 -7 151 153

-6 130 -130

-5 166 168 -4 56 -57

-3 60 80

-2 218 220

-1 117 -118

0 42 -46

1 234 -243

2 91 -95

3 63 -64

4 66 89

5 91 -92

6 13 -7

7 46 -47

8 10* 5 —6»K#8

-9 45 -40

-8 6b -88

-7 87 -85

-6 31 31 -5 81 86 -4 179 182 -3 32 -24

-2 123 -121

-1 82 84

0 66 -71

1 261 267

2 91 89

3 116 -119

4 71 76

5 204 -207

6 80 76

7 eO -50

—6» K t 9 -8 10* 0 -7 30 -34

-6 49 47

-5 141 -138

-4 73 -68

-3 46 -43

-2 47 -49

-1 177 174

0 32 31

1 170 176

2 42 40

3 69 67

4 63 -83

5 125 129

6 b3 —60 -6»K»lo

-7 10* -4 -6 104 -101

-5 17 -12

-4 81 -80 -3 54 -51 -2 100 99

-1 106 -101

0 88 87

1 135 -133

2 34 33

3 79 77

4 9* 5 5 130 130

-6 »K# 11 -6 35 -37

-5 118 112

-4 100 100 -3 40 -41

-2 75 -67

-1 126 -122

0 45 -44

1

16 12

2 60 55

3 1J2 -106

—6» K # 12 -3 24 22

-2 61 -59

-1 168 156

0 98 -93

1 40 41 -7.K.-8

-2 78 78

-1 84 -85

0 72 -73

1 31 32 2 11« -15

3 209 211 -7.K.-7

-4 51 51 -3 104 -104

-2 87 -89

-1 74 -78

0 20 13

1 18 -19

2 63 61

3 118 -117

4 32 -32

5 38 -40 -7#K»-6

-5 47 -44

-4 98 -102

-3 190 166 -2 30 -31

-1 168 175

0 35 -30

1 215 -214

2 51 -52

3 135 -138

4 29 25

5 8* 6

6 59 -58

7 57 -57

-7 # K » -5

-6 8* -7

-5 15 14 -4 99 lul -3 171 174

-2 82 81 -1 28 -26

0 39 -37

1 16 8 2 80 -78

3 169 168

4 110 -110

5 50 -48

6 28 -27

7 165 -164

—7 » K » —4

-7 42 38 -6 9* -10 -5 17 -17

-4 104 100 -3 22 7 -227

-2 88 87

-1 162 -166

U 119 117

1 155 155

2 56 53

3 137 137

4 13 -8

5 28 -26

6 101 103

7 56 57

8 16 -8 -7.K.-3

-8 16 13 -7 123 130 -6 77 -73

-5 152 -145

-4 280 -281 -3 19 -23

-2 60 -64

-1 149 153

0 7* 4

1 134 -134

2 34 34

3 22 -19

4 291 291

5 174 177

6 9* -10

7 62 63

8 192 -191

9 96 92 -7 » K

» -2 -9 20 21 -8 128 134 -7 201 -205

-6 17 -17 -5 29 30 -4 46 -44

-3 290 297

-2 163 -165

-1 71 -74

0 151 -151

1 101 -102

2 43 42

3 26 22

4 23 -21

5 71 -e9

6 17 -7

7 22 -24

6

112 112

9 37 38 —7 » K » —

1

-9 124 -132

-8 33 33 -7 8* -1 -6 179 179

-5 97 93

-4 176 177 -3 103 -105

-2 234 244

-1 134 -141

0 56 55

1 56 57

2 252 -256

3 49 49

4 215 -215

5 154 -154

b 43 42

7 80 -01

8 108 106

9 72 -08

-7#K» 0

-9 98 95

-8 107 -109

-7 218 213

-6 74 -70

-5 27 -24

-4 7. 2 -3 87 -91 -2 279 285

-1 174 182

0 113 115

1 30 34

2 177 -178

3 72 -70

4 117 112

5 54 53

6 113 -115

7 53 -53

8 282 -2 79

9 36 30 -7 » K »

1

-10 47 44 -9 80 85 -8 9* 3 -7 167 -le5

-6 194 -193

-5 53 -50 -4 85 -87

-3 296 302

-2 117 -120

-1 33 16

0 102 -107

1 51 -52

2 369 370

3 24 -26

4 204 201

5 70 -66

6 104 -101

7 92 88

8 10 * -11

9 53 50 -7#k »

2

-10 72 72

-9 193 -203

-8 126 126 -7 117 -110

-6 155 152 -5 43 41 -4 193 -194

-3 138 -142

-2 167 -165

-1 52 -53

0 47 -53

1 17 8

2 128 -126

3 87 85

4 20 19

5 138 134

6 187 186

7 42 39

8 182 176

9 82 -80

-7 » K » 3 -10 24 -21 -9 93 90 -8 75 72 -7 190 187 -6 26 -22 -5 51 -49

-4 5b 56 -3 282 -288

-2 190 189

-1 104 -106

0

106 -110

1 21 17

2 341 -350

3 70 68

4 15 13 5 158 153

6 69 64

7 55 -52

8 48 -47

9 9* -6

-10 20 -21 -9 143 139 -8 71 -70

-7 57 60 -6 114 -114

-5 41 -39

-4 189 189 -3 124 127

-2 193 192

-1 16 4

0

60 -62

1

122 -121

2 231 234

3 151 -152

4 75 75

5 184 -180

6 232 -231

7 16 15

8 84 -83

9 93 87

-9 185 -185

-8 60 -62

-7 102 -98

-6 79 81 -5 158 157

-4 139 -134

-3 170 170

-2 153 -150

-1 321 325

0

166 168

1 48 49

2 106 108

3 1 08 -167

4 46 -45

5 11 0 6 36 -39

7 17 -11

8 33 -33

-7 » K »

6

-9 63 -60

-8 121 122

-7 17 -13

-6 81 -75

-5 108 -104

-4 74 -76

-3 46 -50

-2 79 80 -1 64 66

0 3b -32

1 82 76

2 163 -170

3 192 193

4 18 15

5 162 161

6 95 91

7 145 -145

8 34 29 -7*K »

7

-9 102 100

-8 29 -28

-7 65 65

-6 47 -48

-5 154 -153

-4 163 161 -3 214 -214 -2 116 114

-1 203 -203

0 123 -123

1 77 -77

2 17 16

3 69 68

4 57 58

5 23 20

6 8« -2

7 46 43 —7 # K »

8

-8 85 -89

-7 88 86 -6 86 87 -5 118 114

-4 34 -34 -3 19 12 -2 201 -201

-1 59 58

0 36 15

1 133 -133

2 54 53

3 232 -233

4 24 -25

5 21 17

6 14 2 -7 » K »

9

-7 13 9 -6 12 14 -5 15 7 -4 105 -104

-3 186 180 -2 17 -12

-1 146 147

0 22 19

1 84 -84

2 71 -69

3 15 -9

4 9* 6 5 38 40 —7 * K » 1

0

-6 33 -30 -5 83 -80

-4 97 99

-3 46 -40

-2 126 125

-1 24 -25

0 31 28

1 126 122

2 18 -14

3 172 173

4 56 -44 -7.K.11

-5 35 -31

-4 12 3 -3 105 -102

-2 19 -20

-1 18 17

0 82 79

1 35 38

2 34 37

—8 » K # —7

-2 21 -19

-1 69 69

0 72 74

1 104 106

2 17 -14

3 15 7 —8 » K * -6

-4 83 -83

-3 58 58

-2 74 77

-1 156 -158

0 14 8

1 193 -195

2 14 2

3 93 94

4 29 24

5 90 88 -8.K.-5

-5 185 190

-4 48 49 -3 29 -27

-2 87 -85

-1 171 -170

0 35 -32

1 39 39

2 18 16

3 122 -122

4 13 5

5 230 -231

6 103 101 -8.K.-4

-6 116 110

-5 57 -58

-4 53 58

-3 8* 0 -2 15 -17

-1 209 215

0 118 -119

1 166 171

2 146 -148

3 123 -125

4 37 -39

5 74 -75

6 44 38

7 32 29 -8»K»-3

-7 67 -70 -6 29 -30 -5 72 -80

-4 27 19 -3 70 69

-2 118 122

-1 18 20

0 16 17

1 55 -60

2 58 56

3 164 166

4 16 14

5 175 176

6 207 -206

7 9* 5

8 59 -c 8 -8»K.-P

-8 41 —44 -7 69 -72

-6 152 -1 S3 -5 142 149

-4 33 -34

-3 91 -96

-2 48 -S3

-1 306 -318

0 175 141

1 66 63

2 295 299

3 92 94

4 20 20

5 23 -17

6 9* 2

7 59 S9

8 50 SO

—8*K » —

1

-8 30 33 -7 126 128

-6 17 -14 -5 37 -?7

-4 126 -126

-3 121 -120

-2 78 -82

-1 152 1S7

0 128 -132

1 128 128

2 95 -96

3 145 -146

4 115 117

5 92 -41

6 196 194

7 9* -2

8 16 8 —8 * K » 0 -9 104 105

-8 34 36 -7 61 -55

-6 100 103 -5 108 -110

-4 222 226

-3 105 111 -2 23 24

-1 120 126

0 283 -290

1 98 -99

2 112 -112

3 63 -61

4 30 -29

5 29 -27

o 129 -128

7 32 -33

8 79 77

—8 * K » 1 -9 24

-8 43

-7 50 -6 27 -5 178

-4 170 -3 90

-2 30

-1 206

0 132

1 73

2 147

3 47

4 285

5 34

6 251

7 54

8 44

9 22

-8 » K »

2

-9 123

-8 49

-7 147

-6 119 -5 96

-4 198

-3 70 -2 36

-1 77

0 193

1 79

2 54

3 27

4 33

5 12

6 117

7 32

8 96

—6# K * 3 -9 78 76

-8 29 27

-7 100 -°7

-6 72 -70

-5 258 -260

-4 77 74 -3 17 -11

-2 52 —55

-1 92 90

0 269 -2 73

1 18 14

2 94 93

3 80 79

4 293 299

5 85 -87

6 127 125

7 79 -75

8 97 94 -8 » K * 4 -9 68 69

-8 37 - '0 -7 88 -87

-6 133 130

-5 37 -'6

-4 115 113 -3 25 -25

-2 228 -233

-1 125 -128

0 104 -103

1 21 -19

2 53 SO

3 102 101

4 133 -129

5 130 130

6 75 -77

7 93 89

8 106 105

-8 * K »

5

-9 29 -26

-8 9# 4 -7 156 153

-19

-42

-53

-6 8* -1 -5 163 162

-4 116 -117

-3 36 '4 -2 60 67

-1 86 -87 0211 211

1 114 -112

2 53 -60

3 29 -23

4 232 -232

5 57 57

6 63 -68

7 31 26

8 70 -65

-8 25 22 -7 20 -9 -6 100 -9b

-5 3b -29

-u 79 76 -3 149 149

-2 205 208

-1 82 83

0

21 -20

1 58 -Sb

2 11 11 3 13 -8

4 130 131

5 2 46 -241

6 25 -23

7 167 -164

-8 99 -99

-7 141 -141 -6 82 80 -5 55 -54

-4 130 130 -3 39 36 -2 156 -166

-1 83 83

0 63 -81

1 188 185

2 47 60

3 29 28

4 18 18

5 55 -65

6 35 31

7 12 -4 —8 » K • 8 -7 26 20 -6 44 43 -5 54 -65

-4 129 -130

-3 59 -63

-2 36 -41

-1 105 -lOo

0 66 66

1 71 -68

2 16 8

3 107 104

4 60 -64

5 163 1 69

6 9* 0 —8 iK «9 -7 43 4 S -6 92 -89

-5 48 42

-4 77 -80

-3 14 3 -2 88 88

-1 152 -160

1 160 -160

2 47 -46

3 54 53

4 70 70

5 10 2 -8.K.10

-5 82 >8

-4 95 92 -3 56 *6

-2 75 -72

-1 18 IS

0 107 -103

1 124 117

2 18 -12

3 69 -63 -8.K.11

-3 17 12 -2 60 55

-1 101 96

0 21 20

1 34 31

-1 35 -40

0 31 32

1 89 89

2 10* 0

3

125 125

-3 155 -164

-2 23 -24

0 52 47

1 24 24

2 48 4 o 3115 -114

4 9* -1

5 28 23

-5 10* to -4 157 -167

-3 90 90

-2 137 - 1 3b

-1 105 112

0 92 -°2

1 205 -207

2 13 -11

3 156 — 1 6S

4 1 1 9 119

5 88 8 S 6 26 28

-6 51 46 -5 28 24

-4 56 68

-3 70 75

-2 40 -40

-1 29 -2to

0 63 -65
-
Table 2 (continued)

1 23 21

2 54 -54

3 67 68

4 148 -146

5 33 -34

6 10* -8

-9 » K#-2

-7 40 36

-6 18 11 -5 11 0 -4 131 133 -3 156 -162

-2 128 133

-1 13 7

0 122 122

1 172 173

2 72 -75

3 70 67

4 167 -165

5 9* 9 6 10* -2

7 41 40

-9 * 4. -1

-7 101 97 -6 38 -39

-5 106 -108

-4 84 -86

-3 51 -52

-2 38 32

-1 117 121

0 151 152

1 112 -114

2 150 150

3 109 -108

4 241 236

5 100 98

6 27 22

7 30 -28

-8 73 72 -7 145 -142

-6 34 -35

-5 8* 4 -4 107 -108

-3 172 180 -2 247 -255

-1 29 -30

0 52 -52

1 28 -28

2 196 198

3 38 34

4 20 16

5 56 -55

6 39 37

7 17 -15

8 116 111 -9 * 4*1

-8 19 19 -7 35 34 -6 111 115 -5 81 85 -4 18 -17

-3 78 -79

-2 40 -37

-1 7* -2

0 27 -28

1 101 101

2 329 -332

3 74 74

4 268 -270

5 20 16

6 82 82

7 20 18

8 125 122

-9 * 4*2

-4 174 -3 126 -2 225

-1 54

0 71

1 103

2 178

3 131

4 22

-42

178 -129

229

-101 -179 -129

-18

5 25 24

6 13 9 7 17 12

8 152 -145

-8 37 -34

-7 66 -68 -6 43 -48

-5 14 9 -4 8* -2

-3 194 197 -2 71 -72

-1 18 -18

0 39 38

1 66 -63

2 319 318

3 54 -55

4 112 106

5 140 -134

6 90 -89

7 41 40

-9»K »4 -8 7* -6

-7 87 -86

-6 30 30 -5 85 84 -4 255 -259

-3 9* 3 -2 204 -206

-1 118 119

0 128 127

1 181 177

2 18 -18

3 66 65

4 17 -15

5 42 40

6 142 140

7 37 -30

-8 71 -7 15 -6 28 -5 114 -4 32

71

8 -24 -no

31

-3 178 -181

-2 126 125 -1 111 -113

0 43 -41

1 96 92

2 213 -211

3 131 129

4 20 -15

5 106 105

6 109 108

7 15 5 —9 * 4*6

-8 50 -47

-7 59 57

-6 9* 0 -5 10 * 7 -4 120 120 -3 17 -13

-2 52 54

-1 116 -117

0 92 -91

1 74 -71

2 64 60

3 54 -53

4 11 8

5 71 -71

6 140 -135

- 9 * 4*7

-7 23 -22

-6 93 93 -5 173 173 -4 67 -63

-3 93 90 -2 114 -114

-1 101 99

0 148 144

1 20 -17

2 80 77

3 260 -248

4 39 -39

5 110 -107

6 10* 0 -9 » K.8

-6 40 -41

-5 28 -22

-4 33 -32 -3 54 51 -2 97 96

-l 57 56

0 12 -2

1 78 78

2 96 -95

3 64 61

4 30 -21

5 12 1 -9 * 4*9

-5 33 -33

-4 62 62

-3 128 -119

-2 32 33

-1 67 -69

0 100 -100

1 120 114

2 21 -18

3 150 144

4 10* -1

-9 * 4*10

-4 13 -5 -3 110 -105

-2 110 -106

-1 47 -45

0 53 48

1 46 -40

2 125 118

-10 . 4.-4

-3 60 60

-2 111 115

-1 78 -80

0 80 80

1 183 -186

2 36 35

3 106 103

- 10 * 4*-3

-4 37 -33

-3 26 21 -2 134 -139

-1 133 -138

0 75 -76

1 22 23

2 22 -21

3 25 22

4 13 6

5 46 -43

- 10 * 4. -2

-5 104 -108

-4 14 2 -3 64 -62

-2 34 -35

-1 109 108

0 121 -122

1 31 30

2 129 -128

3 67 -71

4 69 66

5 55 -55

-10 . 4.-I

-6 35 33 -5 114 -117

-4 69 66 -3 60 62

-2 155 161

-1 33 25

0 69 71

1 99 -102

2 9* -2

3 51 50

4 16 -10

5 44 44

6 157 -154

— 10 * 4*0

-6 159 -164

-5 179 186

-4 56 -56

-3 104 104

-2 38 36

-1 116 -119

0 153 155

1 54 55

2 109 109

3 88 90

-27 -148

-98

-66 -37

183 -39

149

-7 92 -87

-6 71 74 -5 173 -176

-4 95 95 -3 19 -18 -2 19 -13

-1 46 47

0 216 -218

1 28 -32

2 100 -95

3 8* -4

4 71 70

5 21 16 6 43 -41

-10 * 4*3

-7 11 * 2 -6 23 22 -5 115 119

-4 62 64

-3 39 43

-2 32 32

-1 155 -160

0 37 39

1 126 -125

2 14 -12

3 41 -40

4 169 *162

5 63 61

6 108 -101

—10 * 4*4

-7 130 133

-6 42 -46

-5 134 132 -4 110 -110 -3 38 -35

-2 115 113

-1 18 19

0 137 136

1 43 -41

2 18 -18

3 87 -84

4 55 51

5 13 -6

6 64 61

- 10 * 4*5

-7 46 -46

-6 98 -98

-5 123 -125

-4 12 2 -3 43 39 -2 16 -10

-1 195 196

0 164 -163

1 157 148

2 24 23

3 86 84

4 179 174

5 44 -41

6 20 -17

-10 * 4*6

-6 70 65

-5 107 -101

-2 78 -80

-1 15 9

0 13 -9

1 55 50

2 61 56

3 28 26

4 43 -37

5 110 103

-10 * 4*7

-6 20 20 -5 45 45

-4 56 -56

-3 75 -75

-2 79 74 -1 117 -113

0 128 124

1 196 -181

2 27 -17

3 63 -58

4 63 -62

—10 * 4*8

-5 79 75 -4 11 * -13

-3 99 94 -2 32 30 -1 62 63

0 93 -91

1 57 -53

2 70 -72

3 37 -32

- 10 * 4*9

-4 101 103 -3 29 24 -2 75 -74

-1 118 111

0 54 -49

1 113 106

2 14 4 -11 * 4. -3

-1 38 -36

0 71 69

1 106 103

- 11 * 4* -2 -3 38 33

-2 36 -38

-1 18 20 -3 172

0 30 -28 -2 138

1 167 -159 -1 7 * 2 85 82 0 55

3 108 -107 1 40

2 224

— 11 * K»—

1

3 21

4 56

-4 14 -1 5 57 -3 71 76 -2 132 -130 - ll»Ki -1 81 -85

0 141 -144 -6 72

1 26 25 -5 8* 2 18 9 -4 29

3 80 80 -3 138

4 33 -35 -2 61

-1 57

- 11 * 4*0 0 9*

1 43

-5 18 19 2 80 -4 93 96 3 62 -3 134 -138 4 49 -2 93 96 5 17

-1 20 -18

0 29 30 — 11 * 4i

1 134 135

2 92 -89 -6 33

3 34 33 -5 51

4 138 -132 -4 84

5 48 -45 -3 74

-2 76

- 11 * 4*1 -1 34

0 90

-5 57 -60 1 26

-4 45 43 2 144 -3 20 17 3 17

-2 121 120 4 72

-1 117 117 5 69

0 66 66

1 44 -40 - 11 * 4 . 2 62 60

3 95 -89 -5 41

4 45 47 -4 58

5 36 36 -3 153

-2 42

- 11 * 4*2 -1 12

0 42

-5 41 34 1 118

-4 22 -23 2 158

174 3 38 -33

-137 4 27 24 -6 -52 *11 * 4*6

-38

223 -5 29 ?9 23 -4 61 -62

53 -3 26 23 -52 -2 76 -73

-1 53 52

>3 0 150 147

1 42 37 72 2 84 82

1 3 15 -9 -30 4 13 8 -135

-60 -11 * 4.7 -57

2 -4 18 -17

41 -3 27 -23

-80 -2 86 79

55 -1 9* 0 -47 0 26 -23

11 1 106 96

2 85 -83

4 3 175 157 -33 -11 * 4*8

-49

79 -3 25 -20 -70 -2 19 16 76 -1 78 -74 -33 0 64 -66

-89 1 58 -54 -26 -144 - 12 * 4*0

17 -63 -1 122 122

66 0 120 -122

1 47 45

>5 -12 * 4.1 29

57 -3 26 28 153 -2 16 -11 -38 -1 17 16 -7 0 22 -21 -45 1 29 -26 -112 2 48 -47

155

- 12 * 4*2

-3 22 22 -2 100 96 -1 126 -127

0 216 215

1 50 -47

2 104 95

3 45 -40

- 12 * 4*3

-3 10 * 2 -2 10 * 7 -1 106 106

0 39 39

1 48 47

2 54 -47

3 65 -58

- 12 * 4.4

-3 22 19 -2 116 i-113 -1 52 52

0 166 -161

1 86 79

2 40 -37

- 12 * 4*5

-3 72 -68

-2 16 -17

-1 148 -148

0 63 60

1 47 -42

2 11 * 11 - 12 . 4*6

-2 73 68

-1 47 -44

0 108 103

Columns are k, 10Fo , 10F C . F0 and Fc are on an absolute

scale. These values do not include corrections for

extinction or anomalous dispersion. Unobserved reflections

are those less than 2 a (I) and are marked by*.

Table 3

Hydrogen

positions

in

CaHPO G • •H P

N| ro rH fd X

ro ro P 03 o & P • • t 0

T5 03

03 0 ,C P p P

fC r* ID rH

r— 'O t

>1 VD iH 00 TJ 3 CN O o 03 G U • • • 03 rd r-1 3 - f0

03 u 03 03 xl

'sJ1 vD VO 5-1 rH

in rH rH 03 rQ O in 2 rd • • • 03 P c 03 0 rG •H P P

in 00 •H C

03 N| o 03 •H

03 03 • • • 0

5-1 P X

fd G 03 3 03 G G w e

>\

r- n- 03 0

03 03 CN o rH tr> •H G t • • 0 P P -H 5-1 c

03 P 03

rd 03 >i e

<U 5-1 XI

VO ,G 1—1 o in 03 • • • TO 03

03

U P G

rd rd i—1 P

03 3 03 •H O •H

>t 03 N|

VD ro i—1 T3 P 03 0^ o rd •H ,G • t • u

03 P G C 03

03 >i x:

Ti 03

N

0^ Eh CN o i—1 C 03 0 U • • • H G P 03 U 5-1 m

03 03 xl o in

iH P

03 • • • •H

T3

rH CN ro

S3 S3 S3

22

Table 4

Interatomic distances and angles

in CaHP04

Atoms Distance, A, or angle

p(D

,

0(1) . 1.5925(g) A

p (i)

,

0(2) 1.5397(8)

p(D

,

0(3) 1.5177(9)

p(D 0(4) 1.5147(9)

0(1) P (1) , 0(2) 108.10(5) 0

0(1)

,

P(l) , 0(3) 109.40(5)

0(1)

,

P(l) , 0(4) 106.59(5)

0(2) , P(l) , 0(3) 111.23(5)

0 2 , PI , 0 4 107.45(5)

olil: ^IslUri P 1 , 0(2)

0(4)

0(1)

,

0(3) 2.539(1)

0(1) , 0(4) 2.492(1)

0(2) , 0(3) 2.523(1)

0(2) , 0(4) 2.463(1)

0(3) , 0(4) 2.540(1)

P(2) , 0(5) 1.5244(9)

P (2) , 0(6) 1.5459 (LO)

P (2) , 0(7) 1.5482 (9)

P (2) , 0(8) 1.5125(iq

0(5) , P (2) , 0(6) 110.43 (6) 0

0(5) , P (2) , 0(7) 109.59(5)

0(5) , P (2) , 0(8) 110.64 (6)

0(6) , P (2) , 0(7) 104.78(6)

0(6) , P (2) , 0(8) 110.58 (7)

0(7) , P (2) , 0(8) 110.70(6)

0(5) , 0(6) 2.522(1) A

0(5) , 0(7) 2.511 (1)

0(5) , 0(8) 2.497 ( 1)

0(6) , 0(7) 2.451 (1)

0(6) , 0(8) 2.514 (1)

0(7) , 0(8) 2.518(1)

environments

0(1)

,

H ( 1) 1.00

j 0(6) , H ( 3) 1.00 r assumed

0(7) , H (2)

23

1.00 J

Table 4

( cont ' d)

0(1)

,

, Ca (1) 2.4142(9)

0(1)

,

, 0(5) 2.565(1)*

H ( 1) ,

. 0(5) 1.59**

0(1)

,

. H(l), 0(5) 165°

P(l)

,

0(1) , 0(5) 118.52(5)

0(2) , Ca (1) 2.4223(9)

0(2) , Ca ( 1

) 2.4482(9)

0(2) , Ca (2) 2.5718(9)

0(3) , Ca (2) 2.379 (1)

0(3) , Ca(2 ' ) 2.4785(9)

0(4) , Ca (1) 2.2951(9)

0(4) , Ca (2) 2.4796(9)

0(5) , Ca (2) 2.433(1)

0(5) , H (1) 1.59

0(5) , 0(1) 2.565(1)

0(6) , Ca (1) 2.450(1)

0(6) , Ca (2) .2.518(1)

0(6) , H ( 3) 2.24

0(6) , 0(8) 2.669(1)

H(3) , 0(8) 1.87

0(6) , H(3) , 0(8) 140°

1$

!

§§!

0(8') 139.53(7)

2176^

1 ?'

0(7) , o{i, 2.458(2)

0(7) , H ( 1) 1.46

0(7) , H(l) , 0(7') 178°

P(2) , 0(7) , 0(7 ') 108.29(6)

0(8) , Ca (1) 2.363(1)

0(8) , Ca (2) 2.483(1)

0(8) , 0(6') 2.669(1)*

0(8) , H(3) 1.87

* Hydrogen bond between these two oxygens.

** Distances and angles involving hydrogen were obtained using

the calculated hydrogen positions.

The figures in parentheses are standard deviations

in the last digit of the interatomic distances and angles, and

were calculated from the standard deviation in the atomic

positional parameters and the unit cell parameters. They include terms from the variance-covariance matrix*.

24
;
Figure Legends

1. A stereo illustration of the crystal structure of CaHP0 4 , viewed along [010] . The origin of the crystallographic

coordinate system is marked by *. The CaHP0 4 chains

are seen nearly end on.

2. The calcium ion coordinations in:

a) CaHP0 4 [Ca(l)]

b) CaHP0 4

[ Ca (2 )

]

c) CaS0 4

d) CaHP0 4

• 2H S 0

e) CaS0 4

• 2H 2 0

f) Ca (H 2 P0 4 ) s -H 2 0

The direction of the CaX0 4 chain runs from the top to

the bottom of the drawing in each case. The similarities

in the structures can be seen from the X0 4 -Ca-X0 4 sequences

in the centers of the drawings and from the two X0 4 groups

to the left of each of these sequences (in Fig. 2f, these

two X0 4 groups are shown behind rather than to the left

of the chain sequence) . The latter X0 4 groups define

the positions of the two chains in the corrugated sheet

which are adjacent to the chain that is shown.

3. The P0 4 ion environments in CaHP0 4

.

a) the P(1)0 4 group.

b) the P(2)0 4 group.

Two sites for H(2) are very close together. Only one of

these sites may be occupied at any given time. The same

is true for the two adjacent H(3) sites.

r

Figure 1. A stereo illustration of the crystal structure of

CaHP0 4 , viewed along [010]. The origin of the crystallographic

coordinate system is marked by *. The CaHP0 4 chains are

seen nearly end on.
Figure 2a. The calcium ion coordination in CaHP04

[ Ca(l) ]

. The direction of the CaX0 4 chain is

vertical

.
I

I

I

I

I

!

Figure 2b. The calcium ion coordination in CaHP0 4

[Ca(2)]

.

The direction of the CaX0 4 chain is vertical.
Figure 2c. The calcium ion coordination in CaS0 4

. The direction of the CaX0 4 chain is vertical.
Figure 2d. The calcium ion coordination in CaHP0 4 -2H 2 0.

The direction of the CaX0 4 chain is vertical.
Figure 2e. The calcium ion coordination in CaS0 4 «2H 2 0.

The direction of the CaX04 chain is vertical.
Figure 2f. The calcium ion coordination in Ca (H2 P0 4 ) s *H~0.

The direction of the CaX0 4 chain is vertical.
Figure 3a. The P0 4 environment in CaHP04 , the P(1)0 4 group.
Figure 3b. The P0 4 environment in CaHP0 4 , the P(2)0 4 group.