crystallographic tables for the rhombohedral … · don,+rr l. gnar, illinois slale geological...

THE AMERICAN MINERALOGIST. VOI,. 46. NOVEMBER_DECEMBER, 1961

CRYSTALLOGRAPHIC TABLES FOR THERHOMBOHEDRAL CARBONATES

DoN,+rr L. Gnar, Ill inois Slale Geological Surt'ey, Urbana, Ill inois.

Assrn,{cr

Cell constants are given for CaCO3, MgCOr, CaMg(COs)2, MnCO:, FeCO3, ZnCOs,

CoCOe, NiCOa, and CdCO3, together with listings of all possible d-values for powder

diagrams taken with CuKar radiation. Less complete information is presented for CuCOr,

MggCa(Co3)a, CaMn(COa)2, CdMs(CO3)2, and the hypothetical end member, caFe(coa)2.

Samples of some of these materials prepared at or near room temperature have unit cells

distinctly larger than those of equivalent samples prepared at higher temperature.

Amplitude contributions to the structure factors of calcite and dolomite powder re-

flections are given, based upon recently refined parameters cited in the literature. Front

reflection intensities, based upon a simplified model essentially involving spherical neutral

atoms at rest, are computed for a number of carbonates.

fxtnooucrroN

The rhombohedral carbonate solid solutions, because of their wide-

spread occurrence in a variety of geochemical environments' are im-

portant in evaluating the conditions under which various rocks formed.

They are also of theoretical interest in a variety of solid-state studies. X-

ray diffraction probably is the single most valuable technique for char-

acterizing these materials. The change of unit-cell size among rhombo-

hedral CaMg and CaMn carbonate solid solutions has been shown to be

sumcient to allow the positions of suitably located individual back reflec-

tions on fi lms taken with standard 114.59 mm. diameter powder cameras

to be used as accurate measures of composition (Goldsmith, Graf and

Joensuu, 1955; Goldsmith and Graf, 1957; Goldsmith and Graf, 1958b;

Goldsmith, Graf, and Heard, 1961). The Debye-Scherrer method is par-

ticularly suitable for samples too small to utilize the maximum potential

accuracy of the diffractometer.Such back reflection measurements will yield useful information re-

gardless of the indices of the particular reflection. Major'advantages'however, are derived from considering the indices of the various back

reflections:1) More accurate values of the cell constants, @o and cn, r"r'a,! be ob-

tained by making extrapolations using reflections having, respectively'

very large o-axis and c-axis components. Because reflections of this na-

ture are limited in number, the procedure is most efiective when various

characteristic X-radiations may be utilized in order to bring the desired

reflections as close as possible to 20:180';2) The change in c:a ratio between some pairs of carbonates is great

enough to cause appreciable differential shifts in the positions of nearby

reflections. The change of separation of such reflections becomes in itself

an accurate measure of the extent of solid solution; film shrinkage can be

1283

t284 DONALD L. GRAF

ignored over such a small portion of the film and errors varying with dcan be assumed to afiect the two reflections equally and thus to cancel.The differential shift will be a maximum if one of the reflections has astrong c-axis component and the other, a strong a-axis component;

3) The spacings of reflections with strong c-axis components fromcarbonates with mixed-layer progressions along the c-axis (Graf, Blyth,and Stemmler, 1957; Goldsmith and Graf, 19580; Graf, Blyth, andStemmler, 1958) are altered because of this arrangement, and composi-tional measurements of such materials are best carried out using reflec-tions with Iittle or no c-axis component.

The back reflections of the rhombohedral carbonates are numerousenough so that interference or superposition of two or more reflections isnot uncommon. Reliable unit-cell and d-spacing values for pure, wellcrystall ized end members and ordered 1:l compounds are, therefore, aprerequisite if difiraction diagrams of intermediate solid solutions andpoorly crystallized materials are to yield maximum information. Tables1 and 2 are a somewhat expanded version of a compilation of thesequantities which has proved its usefulness. The accurate values given inTable 3 of the angles between [c] and the various plane normals ofCaMg(COa)2 may be used to estimate the orientation of planes in theother carbonates.

Intensities are important in evaluating cation and anion disorder andin estimating compositions of solid solutions between carbonates whosecations are very similar in size, such as ZnCOt and CoCO3, and theferroan dolomites, Ca(Mg, Fe)(COa)c. The amplitude contributions ofthe several kinds of atoms to the structure factor are presented in Table 3for the various reflections of CaCOa and CaMg(COr)2, the only tworhombohedral carbonates for which variable parameters have been de-termined. These values were used in calculating the relative intensities ofcalcite and dolomite reflections out to {00.12} which are given in Table4. The parameter approximations made in calculating analogous inten-sities for the other carbonates of Table 4 are discussed in a later sectionof the paper.

Measurements of reflection profiles and of the amounts of carbonatespresent in mixtures typically utilize low-angle reflections. Table 5 givesthe 20 values for such reflections from the more common rhombohedralcarbonates for CuKar radiation.

UNrr- CBr,r, DrlrnNsrorvs

Table 6 summarizes the methods used in preparing the various mate-rials for which unit-cell dimensions were determined. It also gives spectro-

RHOM BO.H EDRA L CARBON AT ES 128s

TesrE 1. PnBlennr'o Crr,r. CorsteNTS roR TrrE REorr'rsoHnlnA'L C'e'nsoNATEs*

Material ao co co/ ao

CaCOs20" c.26" C.

CaMS(CO3)s(ordered)

CaroMgsotMgCOsMnCO:

CaMn(COr):(disordered)

CaroMnsotFeCOsCaooFesotZrCOzCdCO:CoCOrCdsoMgsotCdMe(COB)z

(ordered)

CdMg(COa)s(disordered)

NiCOs

4.99004.9899

4. 80794.8t1464. 63304 . 7 7 7 r

4.87974.88354.68874.83934.65284.92044.65814.7767

4 . 7 7 7 0+0.00091

4.7746+ 0.00091

4. 5975

17 .061517 .064

16.01016.03951 5 . 0 1 615.664

16.36716.364I J . J / J

16.2t8515 .02516.29814.95815 .657

t5.&l+ 0 .003I

1 5 . 6 7 8+ 0 .03 I

l + - l z J

6.3753 460 4 .6 '6.3760 46" 4.3',

6.0154 47" 6.6',6.0251 47 4.0',5.6752 48" 10.g',5.905C 47" 43.15',

6.14025 46" 51.86',5.7954 47" 43.s' ,6.0855 460 51.5',5.6833 48" 19.6',6.1306 47" 19.16'5 .66505 48 '33 .1 ' ,5.9028s 47" M.o'.

5.5795 48" 39.7',

3.4r9r3.4197

3.32993 .33363.241r3.2790

3 .35413 .35093 .27873 .35143.2292J . J I Z J

3.21123 .2778

3.2742

3.2836

3.2024

* Pistorius (1960) has synthesized what appear to be mixtures of malachite and the

anhydrous rhombohedral cupric carbonate, cucos. Seven powder diffraction l^"*^oi_,!"

latter material give, from least square analysis, ao:4.796+O'005 A, c6:15'48+0'01 A'

cof do:3.227, a:48"11' , a"r . :5.856 A.

t Hypothetical solid solutions with os and c6 midway between those of the two end

members.

{ The ranges given for ds and c6 of ordered and disordered CdMe(CO3)z indicate only

the uncertainiy that would result from a misreading of line position on the films (taken

with a Guiniei-type focusing camera) by the smailest unit measured, 0'05 mm' The pro-

cedure used in otiaining these CdMg(COg)z values is summarized in Table 7.

graphic analyses of those cations considered most likely to enter into

solid solution in the carbonates. The analyses are computed with all cat-

ions as carbonates in solid solution, the most severe assumption possible

inasmuch as some of the impurities may be present as traces of other com-

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d + s l o \ \ c ) : 4 m o o c | , O . N . O o o O \ r O \ \ \ O N * t Ho + + 6 6 i o . o 6 3 R 5 9 $ * 3 D K 5 ; S !S S E S S € f r S I + , + - D N N N E n e e a a* {ena *n* * * na lan annan a r

i < ] O d c ) Nc O O \ o O \ O N Oo o r r < r r c o \o : c o N d i

l n l nT n

D O \ < r O So \ o \ N N + r o

4 0 $ o N so o @ € c o € €

+ o @ N r q \ o o ' rO + @ o \ F - \ N Nm - = i l N + + N n No \ o € o \ @ r c N rr @ N T T N N T N

- N O O \ \ O < t

O = f l o < 1 \ O \ On o $ s N Nc o o o @ c o @ €

N @ c ) N i D 4 \ O a o o O \ c ) . < t - rJ - r = c o \ o \ o d i ' j J ; . ; i H N i i < 1 : o \ o \ - 4 O

- o - o ; * + o + ; o * ; : e o o n t " : + ; ^ a nN - o < r o i < r : - c ) c ) - N - i i C ) n i o O c O i : i H 4 o

$€RNs EEs;€3* s€Rtr€ s$s€Fs 8'3\ O \ O r j \ O b D + r D \ 6 r i N \ O s N i r \ O o r 4 \ O N 1 4 . O

€O]IN

80Jo3

€oJpl)

8jJw

eoJul\tr

*otuIAIoeeJ

80Jad

*0eag0e?J

( J "92) 'oJeJ

*0e3tr\Ioe"J

'Col)FT IBJ

eoJ3tr\I

'rq"tl

I . q 4

.DONALD L. GRAF

@ 4 € O r ( } i C ) N N o O € No q o o l F o o o o N c ; N 4 oD < l 0 0 + d o 4 \ o 4 0

H o o o o , @ a o a o o o r N€ € € € € o r r r N r N r

\ s o \ \ o rN - O o O O \6 € r o r€ € € 6 N

" : t : \ \ \

c O € O O - o \ O @ = N - 4 o + - r\ o < r \ o o o - + s \ o + F € o N + €N S € . , 4 A a O 4 4 N < t + i O \ O \ \ O OH d O O O O \ O . O \ O \ € o O o o N r N r€ @ € € 6 N S S r N N N r N r N

c o s l N

4 d NN N

\ \ \

r O \ S \ N \ O c O r C ) O O N O o o dA n q N H O N N 4 O O \ O c O -e € N s r O - @ o O O N N < r N Nc ) o o o o \ o \ a o @ o \ N N N N N€ € € N N T N N N N T N N T

N N O D N < . O \ r - N + < ' c O O \ c ) € O + \ O D c 4 No 4 o . o N o . o < o N N N 4 o o r o 6 € A o . \ o o4 Q N N Q N N @ - @ + € S - d \ O 4 h ! + N N de t { N Q H - o o o o o . o \ o , o \ o , € @ N N N N N@ € O O O O € C O € € € N T N T N T N N N N N N N

r Q a O n O N d O \ r O O +$ i O O 4 4 O - S r NO \ O \ n a r \ O q D N N Or O \ O \ O \ o O o O o O o O @ N r\ \ \ \ \ \ \ \ \ \ \

4 O O ! + r i O \ i 4 O d@ € 4 N € h 6 N i NO . O \ O \ O \ o O € @ c a € NN T \ T S N T N

n c r . O C { O F t t l A l : d 1 4 | c \ l N i l i N d S \ O h + N h N - H t H h 6 \ O O$ 4 c o i r F o : i r N \ o i N N i \ o \ o 4 N + r \ o o 4 i s N N Q€ r r { t N c t < r < r < t \ o \ o 4 r 4 N c o @ N N o o r \ o N 4 o a o 4

H b c O O O \ < r i \ O O @ a O . q O \ N N r C )i r : a . ) N i N N r < r r @ \ o N b H a { d F d H r r H r N N e

RNg 35*$B 8X889 8$ :Rg3 $F+J EN :=8v v

1290

sOJIN

EOJOJ

EOJPJ

toJuz

80luntr

x0eutr\Ioe?J

foJed

xoeagoez"

('1 .92) eo3sJ

x0e3r{0e"J

'('ol)BIAIBJ

EOJSIAI

t.Et't

IN

r.l

F

RHOM BOH ED RA L C A RBON AT ES

Tmle 3. Aupr,rrvon CoNrnrsurror.rs ro Srnucrunr FLcroRs, ello ANcrrsBnrwrnw lcl .tNt PllNr Nonuar,s, lon Car,crrn ,l'rrm Dorourrn

t29l

Angle be-tween planenormal and

[c], for dolo-mite, indegrees

h k . t h,kJ,

Amplitude contribu-tions* to structure

factors, F, for calcite

Amplitude contributions* tostructure factors. F. for dolomite

00.31 0 . 1o t .21 0 . 400.60 1 . 51 1 . 0

1 1 . 3

02.r20.2to.702.40 1 . 8

1 1 . 6

00.9 33320.5 311

21.1 207

12.2 2r1

02.7 33110.10 433

2 t , 4 3 1 0

20.8 422

11 .9 432

12.5

03 .00 1 . 1 130 .303 .3o0.12

21.7

fc" fc

+2 -2 -1.8040+2 +2 +1.8040+2 -2 -6.0000

+2 +2 -2.1864

+4 .1910

+2 -2 +1.9808

+2 +2 -1.9808+2 +2 +1.8040

+2 -2 +2.1864

+3.7802

+2 -2 + r .7954

+2 -2 -1.8040

+2 +2 - r .7954

+2 +2 -1.9808

+4 .1910

+3.7802

+2 +2 +2.s860

+2 +2 +6.0000

+3.7802

+1 -1 -0.2444+1 -r +0.0817+1 +1 -1.9933+1 +1 + t .9734+1 +1 -r .9402+1 -I +0.4056+1 +1 +2.0000

-0.677r-o.3761-r.7952+1 .8801-5.8472+0.7814-2.ro95+4.1187-3 .@26+r.6286+ 1.9509-0 04.82-2.3185+1.6189+1 .1798+2.9sr6+r.9969-2.0689-4.4674+2.7sffi+0.6004+2.87s3- 1.1053-r.8692- 1 .8669-1.2224-1.4839-4.3850+3.0204-2.8915+3.8184+r.9259-r.1467+0.8776-1.3123+5.3964+4.8888-2.484r

I-0.24M \

+0.0817-1.9933-0.5640+r.9734+r.8942

(-1.9402

\+0.7187+0.4056

+0.0817 {I-1 .ee33 t

-0.5640- 1 .8355

+r .sn4 {t

+r.8942

+0.7 f t7 {I

+0.40s6 i+2.0000-0. 8686-o.24M {

t+r .7e6-0.s640 /

t

1 1 11001102t r222221101

2ro117200322220332

32r

320

112443300\221J44

421

+r - t

+ t - 1+1 +1

t l 1

+1 +1+1 +1+1 +1+ 1 - 1+ 1 - 1

+ l + 1

+ 1 + 1

+ r - 1+ 1 + 1

+ 1 + 1

+ 1 + 1t l I

+ 1 - 1

+ 1 + 1

+ 1 - 1

+ 1 + 1

+ t - 1

075.42262.5 t943.869

037 .56290

6 5 . 7 5 1

82 .59175.42228.78262.5r825.672

47 .985

056.969

84.386

78.878

47 .6892r .036

68. 535

43.867

36.499

63.826

9019.271

75.422

0

55.468

* The amplitude contributions have been divided by 6 in order to obtain expressionscorresponding to the contents of the rhombghedral unit cell.

fcu Ju" Jc Jo

t292 DONALD L. GRAF

T awn 3-(continueil)

hk.I h,hJ,



02.10 M2

tz.8 431

30.6 411. I03.6 s30l

22.O 20220. I1 53310.13 544

22 .3 317

I l . l2 543

13 .1 2 r2

3 r .2 301

2 r . t 0 532

I J ' +

01.14

2 2 . 6

0 3 . 930.9

J I . . )

12.11 542

00.15 55502.13 55304.T 1130+.2 222

t3.7 430

40.4 40020.14 644

31.8 521

22 .8 531

04.5 337

+2 -2 +1.9808

+2 +2 -1.7954

+2 -2 -2 .5860

+2 +2 -2 .Or92

+ 2 + 2 ' 2 . 1 8 6 4

-o.3704

+2 -2 -2 . t 566

+2 -2 +1 .7954

+1 +2.0000-r -0.8686- | +r .0127-l -0.2444

+1 +1 .7646

-1 +0 .0817

+1 - r .9933

+1 -1 .8355

+1 + r .9734

+1 -1 .6819

+1 -r.9442

- l +0.7r87

-r +0.4056

Angle be-normal andnormal and

[r], for dolo-m i t c i n

degrees

37 .562

5 1 . 8 1 8

62.5 t9

9034. 95516.470

77 .307

29.O35

6 5 . 6 / )

8r.79r

45.493

73.905

15 .365

6 5 . 7 5 1

52.036

70.169

42.766

030.60386.28082 59r

$ .249

7 5 .42228.782

60.014

60. 155

7 | .99r

Amplitude contributions* to

structure factors, F, for dolomite

+rt 1

T I

+ l

-L1

I 1T r

t lT T

t l

-1- r

+1

+1

t 1T T

+ 1

+ 1

t r

+ l

I 1

t iT T

t 1

t lT r

t 1T r

+1+ l+1+ l

+1+ l

+1 -1 .8355 +2 .s679

+r +r.8s42 {*g g: : :\ _ r . t J t z

+1 -t.s4o2 \_?23t?

32I

554

420

nu\q11 |

410

t o r o

t a a

-)-) -')

- 1 .1830+2.4039+0.4701-o.2913+0. 5583-0. 1901-3.6045+0.0978-r.0696+0.4957-4.4963+0. 7635-L1 79.)',)

+4.4742-a.2543- 1 .3600+r.2488+ 1 .0570+1.6801-0.3982+0.9577+0 .9170+2.8797-2.9749

+2 rs66- 1 .8040

+2.0192

-4.3704

+3.7802

-5.9232

-0.370+

r ( o t l ?

+1.9808

+2.1566

-0 .7811

- l

- 1- I- 1

+ 1I

t 1

t 1

l lT r

- I

- 1

t 1 r tT L T L

-L'.' -7

-L) J-',)

-0 .8686

-1 .1500 -3 .21s0+r.or27 +o.5257+0.0817 +0.3301- 1 .9933 -4.8835

( t tn,tt-n \6l1n" ' " . ^ " l . +1 .1270+r.973+ +4.8089-1.6819 +0 9413

r_1 RoL) ! -o .z tto

l+4.28e3l+0.oogs-rv. t t6 t i_o.zooo

+0.4056 +0.7721

RHOM BOH EDRA L CARBON AT ES

Trwn 3-(continued.)

hk.t h,kJ,



Amplitude contributions+ tostructure factors. F. for dolomite

J C a J M e

r293


[r], for dolo-mite, indegrees

23.942

13.514

38.045

43.868

86.586

83.195

65.528

54.r97

l o . J t I

36 .005

62.5r9t 2 . 7 4 5

73.389

90

51 .570

25.67 t

80 .338

47 984

0

67 .332

56. 969

64.484

7 t . 1 9 6

1 1 . 1 5

1 0 . 1 6

2 t . 1 3

30.120 3 . 1 2

3 2 . 1

2 3 . 24A.7

1 3 . 1 0

3 2 . 4

12.14

01.8o t . 17

z 5 ' J

1 4 . 0

3 1 . 1 1

02.16

14.34 t . 3

2 2 . 1 2

00. 18

3 2 . 7

40. 10

2 3 . 8

4r.614.6

654

655

643

oJJ Iq ( ? r

302

OJJ

MO665

, t 1a

2r3

632

664

1,19l

4ot)

2 1 t

5 1 1

541

4rI

642

666

520

622

530

+4 .1910

+2 +2 +1.8040

+3.7802

+2 +2 +2.5860

-4. tt45

+2 -2 +2.1826

+2 -2 -2.1566

+2 +2 -2.1826

+2 -2 +r.7954

+2 +2 +5.9232

+ 1 - 1

+ 1 + 1t l I

+ 1 + 1

t l 1

+1 +1+ 1 - 1

+1 +1

+1 +1

+1 +1+1 + r+1 -1

t l 1

+1 +1

t l 1

+1 +1

+1 -1

+1 +1+r +1+1 - r

+ r +1+1 +1

+1 + r

. .-^^ l++.+zts- I ' - t r u u \ - z . t o z l

+ 1 . 5880 +1 .763t

-0 .5640 -1 .4156

. ^ - - - l -+ .zzsz' *"" f -o.oool

-Ll oj?,/ . [-s 'os+tf +0.32e4

-1 681e t;l:133i+t.8942 +4.7092+r.2797 +r.4537

+o 4os6 ill 3ll3( t z t t l t

+2.oooo t_;.;i l;_0 8686 t _?:l3ll+1.5880 -2.6866

f +o'zott

- 1 .4835 -4 .6708l. -a r sro-0.s640 t+i.i i is

- 1 .8355 -4.4894| -n qnqa

+r.8e42 t_i:;; jl+r .zszt

-r .s4021 - : i : : :

l - r . + 1 6 r[+0.4791

510 \431J

J- ' J-)

-L) -L'.)

+1.3784

-o.3704

- 1 .9808

+o.M69

+2 +2 -2.0192

+2 -2 -6.0000

-4.1t45

+2 -2 -5.9232

+2 +2 -2.1826

+2 -2 - t .3784

r294 DONALD L. GRAF

Trsr.r 3-(continued.)

hk.I h,kJ,



20.17 7550 4 . 1 1 5 5 103.15 663\30.15 7Ml

2 L . 1 6 7 5 4

13.13 652

1 1 . 1 80 5 . 1

0s.21 0 . 1 9

3 2 . 1 0

0 5 . 4

31.14

14.941.9

1 2 . 1 7

5 0 . 533 .0

2 3 . t |

22 .15 753

40.13 733

33.3 4r2

01 .20 776

24.1 313-

42.2 402

05.7 44102.19 775

-0.370r

+2 -2 +2.1864:

+2 -2 +2.1826

+2 +2 +1.0296

+2 -2 -2.1566

+o.4469

+3.7802

- 0 . 7 8 1 1

_3.3772

+2 +2 +1.8040

+o.7735

+2 -2 +r.9430

765223

r14766

631

332

743

540\621J

764

500303

04r

Amplitude contributionsx tostructure factors. F, for dolomite

J C a I M E

+ 1 - 1+ 1 - 1

+ 1 - 1

+ 1 + 1

+r .2797-0.8686

- 1 .1500

+1 .5880

+1.0127+1 -1

+ r +1+1 - r+1 +1+1 - r

+1 +1+1 +1+1 +1

+1 -1 +0 .7187

+ 1 - 1

+ 1 - 1+ 1 + 1

+ 1 - r

+ 1 - 1

+ 1 - 1

+ 1 - 1

+ 1 + 1

f I - I

-1 483s 1;l:333i

-2.6t63- 1 .8350-r.9624-0. 1016+0.3789-2.2512+2.0612-r.t270

+0.0817 +2.09s9-1 .9933 -0 .5718- 1.4008 -0.8681

. ^ - . - (++.ozzt- r '6r r r \ -o . rszz

+r.9734 +0.0988- 1 .6819 +0.8918

-3.8638+0.5795-1.9321+1 .3391+1 .6923-2 .7212

+r.27e7 \+i . r i r i+0.4056 -r .9669+2.0000 -r.7691

-0.8686 { . t -7^ ' - !?! +5 . E56uI J-(\ )714-1.1s00 t i0. ; ; ;

+1.0127 +2.4289_o ,AA4 [

-t.a+zz- ' - - - -

l + 2 . 0 4 7 0+1 .3691 +1 .0319

f - r a r r r+0 .0817

\ - ; . ; ; ; ;t + 1 3 8 0 8+1 +1 -1 .ee33 1 ; ; ' :l + 2 . 1 7 6 4

+1 - I - 0 .5640 + t . 7233+1 - r -1.4008 +0.0808


[c], for dolo-

degrees

24.34154.428

37 .561

32.450

46.842

20. 306

87 .02384.061tt.Mt

59. 178

78.247

44.720

62.944

30. 897

75.42290

56.723

41 .605

49.794

81.460

10. 883

87: 186

84.386

69.99322.036

RHOM BOH EDRA L CA RBON AT ES

Trnr.l. 3-Gonti,nu,ed.\

-fc" J." fc

r295


[c], for dolo-- i ra i .

degrees



Amplitude contributions* tostructure factors. F. for dolomitehh.t h,hJ,

fc" k f" l o

24.4 422

04.14 66250.8 6t l33.6 5214 2 . 5 5 1 11 3 . 1 6 7 6 320.20 86630.18 855\03 .18 774J3 2 . 1 3 7 4 221.19 86541.12 732\14.12 6sr|15 .T 2r424.7 s3Tr5.2 32311.21 87605.10 550

+2 -2 -5.9232+2 +2 +r.0296+2 -2 +r.3282

+0.7735+2 +2 +2.1s66+2 +2 -1.9808

+2 -2

-4.1145+3.7802

+2 -2 - r .3784

+4 .5175+a.77s5

+2 -2 +2 .4974+4.1910

+2 -2 -1.0296

. _ t _ t 4 t 3 2+1 +1 +1.97s4 I _n ' r r rot

- w . 78.878

48.448167 .943173.700176.54314r.66412r.s46I

33 .3soi

s2 .e37128.8051

56.4491

87 .39617r.+79184. 802 t18.040163.1381

t These angles are for calcite (26" C.).

and composition, 0.38 mol percent substituted CaCOa in MgCO3 wouldproduce a change of 0.0005 A i.r a 1 A basal reflection and 0.0003 Ain a 1 A reflection with no c-axis component. These difierences would bereadily measurable in the back reflection region of films taken with a114.59 mm. diameter powder camera such as that used in this work.*

The other impurities in Table 6, where they are greater than the limitof detection, would probably not produce detectable spacing changes.The LizCOr used to facilitate recrystallization of some of these samplesin runs made with a squeezer-type apparatus (Griggs and Kennedy,1956) has never been observed to lead to changed spacings in cases wherecarbonates were initially well crystallized and careful comparisons ofback-reflection spacings before and after the run could be made.

x The slight equilibrium substitution of CaCOa in MgCOs at higher temperatures(Harker and Tuttle, 1955) suggests that the 0.38 mol percent CaCOr here computed isprobably not all present in solid sotution.

DONALD L. GRAF

o . = ?f e r.

o 6 . :

E E . gA > qx '6 EY o ' -

# a e

D O O r N : \ i : b + D N : F o o € H

s x d S i R : : R 1 9 ; : j q l j dd i r $ 4 t s + @ s

o i o N N o o N N N D o g r + t r o F N + F - - 6 4 I s

" o N 'N : : - o @ 6 t s N o r O : O i O . - N ' e F o O N C . . N No . o @ 6 s r N . , t s H N N 4 € F = F <

+ o N - h N c : F N 0 6 N t € i o

: : a ' t d o i " i

= . i 9 : o J o d T 9 ; - ;i € O € - € + + - + : D N g H

O o N s N € O N H € 1 6 : € O € O- N i j . H- e : s 5 F Y € : d S 9 g : . d - ; S :

+N t s H : O O N + n @ + t s N O O + @ € 6 - N = + - b € O D, ; . o 4 s . . € . o o . . € € N . € o . - N a . N N 6+ . N N . O O - + O . ' 6 O € . 6 ' @ ' ' F ' A .- o + F . + + . i + l - + n . o N N * o - € o + N = . o

N € N € O + 6 + b A O N $O , H . d O F , .

o $ 9 + b 6 . o . . . r oo $ s - i $ + @ N N i A t s D

€ € o O r o i o 6 H + N < O N. , : ' .F @ + : € O . : N ' ' O€ 9 6 / + @ S O € - - 4 N 9 6

g $ o E o s 6 o o € < o n v N. f - . N . . t s € '

@ 6 ^ : : @ € . 6 F ' ' @4 - 4 \ r + N + - t s N F 4 ^ d 6

+ o h t s o o ' : - 6 @ o o o o N -. $ + . ; 6 . € . @ $ € . €

b N i o i 6 : : o 64 $ $ ( \ $ o 4 D h N o Q o N 6

+$ r : : b N e 6 0 € l 0 0 b r o N o N c @ o b D N q + D

. d . O . . . + O r . O + . 4 O N . $ F O9 d € N . o r N N H . O € H N . . 6 . . 6

= = + - 9 + + . + ^ N + o . : t € N - $ - € N + N = 3 o

B 5 €

- o € 6 6 0 0 6 t s N o @ @ o € ! b 6 € N o o 4 @ s + 6 t sN + - + € N . . O . € $ . . @ r O . H € $ O O F ' t 6 FO . . F . ' N + . O N . € @ . N . + $ t s . ' O r l + .

. N - € N q t € N . € N N F ' o F o . 6 $ 4 d F o . h

*t i o : t N t i , ^ ! o t i t m H l N o t Ni o r o l r ' N N H : - o o l N

n I N N - q q + + * N

b € o r o @ o € + € + No o . . . € . . o 3 0 € 6 .

N @ . o b . € . o+ : N i € o o € . r o

6 O q r $ o q N 6 O + + N € b O N 6€ . N O N d F N € 4 . -

€ € . . o Q : + @ . ' s . . ' . i. N 6 b O H s i i + € +

: o O F N F t F O l i o N 6 N d ! F l - l - - - O ^ ^ O t O - 5 l i +F o F F I N o : - o d - - N D F o : - - i d s N r + o N +< F - N N N - N - N - d q t 9 D N d - $ 9 $ + D i + 9 N $

EO

U

EEO

O

N

O

O

(-)z

(-)O

(J

E

O

(-)trEO

O

O

O

O

O

(.,)

O

^s*n

r296

F

ztr4

d

E

F Zd or-r H

a . HE r d< FN *

3 L . ,

* A

F A

H =

z , y

2 o

5 =h r'lp a

= zo H

E <.-. o

Fl

r.l^/.

g

=Q

+t

F

RHOM BOH EDRA L CARBON AT ES

T,lnlr 5. V.lluus or'20 ron Low-Axcr,n X-rlv Rrr,r-rcrroNs or.rnr CowonRrroMsornnnal CARBoNATEs, Coupurrn lon CuKar Rlorlrrox

1297

hk.l h,kJ, Mgcoa caMg(cot,3;.C3j Feco: MnCOr ZnCOt

00.31 0 . 101.210 .400 .60 t . 51 1 . 01 1 . 302.r20.2ro.702.40 1 . 811.600.920.52 t . lt 2 . 242.710. 102 1 . 420.8l t .9l z ' 5

03 .00 1 . 1 1

!so.sI03 .300.t2

1 1 11001102 l l22222r1072r011720032222033232133331120I2r IJ.t I

433310A a 1

432320rt2443300\2211444

t6 .59722.O39

25.I43 24.07132.637 30.96435.850 33 .557

35.33138.841 37 .37642.985 41.148

43.81246.832 44.950

45.19351.614 49 .29553.877 50.56053.884 51 .096

5 1 . 3 1 552.374

61.395 58 .91862.4 t7 59 .841

60.03966.420 62.05666.431 63.45968.386 64.53369'.354 65 .r8269.360 66.09770.329 67.4r9

68.199

23.0s1 24.77729.394 32.0383r.427 34.989

35.965 38.36339.402 42.362

43.r52 46.208

47.107 50.81547.494 52.65048.496 52.889

56.555 60.58157.39r 6r .567

58.063 &.78960.660 65.42360.983 66.99661.359 67.82863.042 68.239&.654 69.372

24.310 25.05631.428 32.56134.319 35.827

37.625 38.67041.539 42.822

45.302 46.633

49.8r2 51.42451.597 53.80651.835 53.733

59.346 61.10860.309 62.t35

63.448 66.34064.06s 66.14965.595 68.20466.405 69.2r066.806 69.08167.91r 69.981

69.981

7s.986 70 .52s 65 .595 7 3 .917 72 .327 75 .928

Table 6 also gives the a6 and r0 values obtained from cos2 d and

extrapolations for various samples of MgCO3, FeCO3, MnCOe, CoCO3,CdCOr, NiC03, ZnCOs, and CaMn(CO3)2, together with measurementsof CdMg(CO3)2 samples made on fi lms taken with a Guinier-type focus-ing camera. The comparable information for CaCOr and CaMg(COe)zhas been given in Goldsmith and Graf (195SA), together with a discussionof the extrapolation procedure, which involves successive approxima-tions.

In making spacing measurements, film shrinkage and camera radius

(#.Y)

.DONALD L. GKLF

Tlsrn 6. Mr,rnoo ol Pnnpmarrow, Punrtv, ,tm Cnr,r- CoNstaxrs orVauous RroMeoHrpnAl, CensoNA'tn Smnpr,ns

MgCOr, No. G-1219; basic Mg carbonatefCOs*H:O, 15 hours in Morey bomb at

300" C.; 0.38+0.O6Ta CaCOa, 0.01 *0.O0316 FeCOy <O0037o MnCOr, <O.047oCdCOB, <0.007/o CoCOa, <0.251s ZICU.

oo: 4.633O A, Cu radiationco:15.016 A (Goldsmith and Graf, 1958b)

co /ao :3 .2411MnCOa, reagent grade chemical; O.tt+O.037o CaCOa, 0.02f 0.O1516 CdCOz, <002To

CoCOa, (0.01/o FeCOu O.l+O.\|Ta MgCO3, <O.20/6 ZnCOt HrO (-110" C'),0.85o/s* ; HzO (t 1 10' C.), 3.327a4.

ao: 4.792 A, (94 *q'j) extrapolation, Fe radiation\ s i n d 0 /

ro :15 .71 A, /cos2 g , cos2 01co/ao: 3.278 (;; *

-t) extrapolation' Fe radiation

MnCOs, No. G-738; reagent grade MnCOr*COz, 3 hours at 722" C. in cold-seal bomb;

0.Og+0.02Vo CaCOa, 0.1+0.05/6 MgCOs, 0'01 +0008/e FeCO:, <0.027a CdCOt,

<O.02To CoCOz, 1O.27o ZnCOa.ao: 4.7771A, Fe radiat ionao: 4.7772 A, Cu radiationco:15.664 A, Fe radiation

cs /an :3 .2790FeCOr, No. G-613; FeSOrf NaICOs*CO:*H2O, 20 hours at 143' C' in Morey bomb;

ao: 4.69024, Co radiationco:15.369 A, Co radiation

co/an :3 .276tFeCOs, No. G-1219 FeSO4+NarCO3+COr+HrO, 15 hours at 300" C. in Morey bomb;

O.O38 + 0.O20To CaCOr, 0.072 * O'Ul4Ta MgCOr, 0.13 !.0.0137a MnCOr, <0'0870

CdCO3, 0 NS + 0.0O27o CoCO:, 0.18 +0.041s ZnCOs.at: 46887 A, Co radiationoo: 4.6888 A, Fe radiationco:t5.373 A, Co radiation

co/ao :3 .2787FeCOr, material from No. G-1219*NaHCO3, 3 hours in squeezer-type apparatus (Griggs

and Kennedy, 1956), 14 kb, 659" C.oo: 4.6889 A, Fe radiationco:15.373 A, Fe radiation

c s / a s : 3 ' 2 7 8 6CdCOs, reagent grade chemical ; <O.WYa CaCOu 10'O67o CoCOs, 0'01s * 0'009/6 FeCOa,

Unless otherwise noted, impurities reported in spectrographic analyses by Juanita

Witters as weight per cent metal have been recalculated to mol per cent carbonate. Ce]]

constants were obtained by cos2 0 extrapolations unless otherwise noted. The ranges given

for oo and ,0 of ordered and disordered cdMs(co3)z indicate only the uncertainty that

would result from a misreading of line position on the films by the smallest unit measured,

0.05 mm.* Analyst, L. D. McVicker.

RHOM BOH EDRA L CARBON AT ES 1299

'llrnrn 6-(continueil)

O.O38+0.0267a MgCOr, 0.06+003/6 MnCOz, <0.O8Vo ZnCOg. HrO (-110" C.),O.23/6*; HrO (+110" C.),2.87Ta*.

ao: 4.936 it, (94 * gl^j)

extrapolation, !'e radiation\ s i n d 0 /

co:16.29 A', /cos2 A cos2 0\co/ao: 33a0 (;; +

;-/ extrapolation' Fe radiation

CdCO:, No. G-1321; CdSO4+NarCOsf COz*HzO, 15 hours at 255" C. in Morey bomb;0.09 + O.O7 ok CaCOa, (0.01 t|o MgCOs, 0.009 + 0.007 ak FeCOs, 0.003 + O.002bTaMnCO3, <A.0670 CoCOr, (0.0801 ZnCOa.

ao: 4.9207 A, Co radiationco:16.295 A, Co radiation

co/ao: 3'3115CdCO3, material from No. G-1321 plus LizCOa in squeezer-type apparatus for 3 hours at

10 kb, 500" c.ao: 4.92044, Co radiationco:16.298 A, Co radiation

cn/an :3 .3123ZnCO:, No. G-1316; reagent grade chemical *HsO*COz, 15 hours at 250" C. in Morey

bomb; 0. 19+0.04/6 CaCOa, 0.01+0.008% MgCO3, 0 O4O+0.0207o FeCOe, 0.002+O.OU|ETy MnCO3, <0.02ok CdCOa, <0.0270 CoCO:; HzO (-110" C.), O.54l6t;HrO (+110. C.), 3.737ot.

ao: 4.6528 A, Cu radiationao: 4.6525 A, Co radiationco:15.O25 A, Cu radiationco: 15.0244, Co radiation

co/oo: 3 2292ZnCO3, transparent crystal from Broken Hill, Rbodesia; 0.03+0.Olsok CaCO:, 0.92

+0.097a FeCO:, 0.30*0.03/e MgCOr, 0.041+0.004ok MnCO:, <0.O27a CdCO4<0.0470 CoCOs, (0 004/6 NiCOs.


co/ao: 3'2293NiCOs (prepared by Thelma Isaacs), Niclr.6HrO+NaHCOa*HzOiCOz,2.5 months at

250' C. in Morey bomb; 0.06 + 0 .03/o CaCOz, 0.04 + O.OZTy FeCO:, 0.01r t 0.M87oMgCO3, 0.04+0.027a MnCOr, 0.09+0.05ok ZnCOt O.02 wt ls Cu,0.2 wt ls Na,O.02 wt /6 Si. Infrared absorption curve shows no water in excess of that for the KBrblank.


co/ao: 3.2024

2 5 ' C .CoCO3, No. G-1319; "Specpur'e" Co:Or*KHSO4--+ Co sulfate; Co sulfate*"Spec:

25" C.pure" NazCOa -+ basic Co carbonatel basic Co carbonate*HzO*COz for 15hours at 255" C. in Morey bomb; 1}.lsTo CaCOr, 0 O4+0.O3nok MgCOr, 0.01

t Microanalyst, D. R. Dickerson.

1300 DONALD L. GRAF

Taun 6-(continued.)

+0.008ok FeCOa, (0.0041o MnCOu <0.17a CdCOs' <0.0027a NiCO3' <0'09%ZnCOs. HzO (-110" C.), nonet; HzO (+110'C.), 8.10%1.


co/ao :3 '2121CoCO3, material from No. G-1319+LirCOa, 2 hours in squeezer-type apparatus at 10 kb.,

60 'c .ao: 4.65814, Co radiationco:14.958 A, Co radiation

co/ao :3 '2112CdMg(COs)r, ordered; LizCOs added to equimolar mixture of CdCOs and MgCO:, treated

in cold-seal bomb for 23 hours under 27,000 psi COz at 600" C.d1ar1 and d1ui1 measured on film taken with FeKar radiation, using a Guinier-typefocusing camera, and calibrated against the closely similar d1ru1 and dlni; valuesof synthetic MnCOr run on the adjoining strip of the same film.

do: 4.7770+0.0009 Aco:15.641+0.003 A

cn/as: 3.2742CdMg(CO)a disordered; equimolar mixture of CdCOr and MgCO3 treated at 10 kb. and

900" C. for 1.5 hours in sealed-tube gas system; spacing measurements made as forthe ordered material.

ao: 4.7746+O.0009 A.o: 15.678 + 0.003 A

co/ao: 3.2836CaMn(CO)n disordered; equimolar mixture of CaCOa and MnCOa reacted in cold-seal

bomb at 706-71O" C. under 14,000 psi CO2 pressure for 22 hours.Line coincidence of [400] and {644} used to obtain accurate cofaoratio, followedby o6 and d0 extrapolations of back reflections on film taken with Fe radiation.Ilroo]:I{eal is computed to be about 3, and observed as such on films of CaMncarbonate solid solutions containing 40 and 60 mol per cent MnCOa, for whichthe two reflections are resolved. Departure from coincidence in the CaMn(COa):sample would thus readily be observable as line broadening relative to the linebreadths of neighboring reflections.

ao: 4'8797 Ac.:16367 A,

co /ao :3 .3541

errors were taken into account by using the Straumanis film mount andcorrection procedure. Reflections in the range 0:60o-90o were used forthe cos2 0 extrapolations, in accordance with the finding of Taylor andSinclair (1945) that almost linear extrapolation curves which simultane-ously eliminate eccentricity and absorption errors are obtained withinthis angular range.

CoupanrsoN ol CELL CoNsrlNrs wrrH PuBLrsrrED VALUES

Cell constants cited in this paper are compared in Table 7 with values

obtaiqed from the literature. For most of the carbonates, the agreement

RHOMBOHEDRAL CARBONATES 1301

is excellent. The newly determined values for coarsely crystalline syn-thetic NiCO3 are preferred over those of Pistorious (1959), and there is asmall discrepancy for CdCOB.

The range of a6 values reported in Table 7 for several CdCOa samples,4.9204 to 4.936 A, includes the values published by Swanson et al. (1957)and Ramdohr and Strunz (1941), but the range of d0 values, 16.298 to16.29 A, is clearly distinct from their t6.27 A. Mr. Swanson (personalcommunicat ion) f inds ao:4.9279 A and co: t6.284 A on repeat ing theleast squares calculation for his CdCOa sample.

The several sets of CdCOa values in Tables 6 and 7 suggest that ao in-creases and co decreases with decreasing temperature of formation, al-though some of these differences are near the limit of error, and thatSwanson's sample was made at fairly low temperature.

ENr,encnn UNrr Cnr,r,s oF LowER Truppnarunn PnBpanerrol,rs

Effects analogous to the change in cell size of CdCOr prepared atIower temperatures are noted for other carbonates (Table 6). There is aconsiderable increase in both @o and co of CoCOa prepared at 255o C.,compared with that made at 600' C. Reagent-grade chemical MnCO3 asreceived has a markedly enlarged cell compared with that of materialcrystall ized at 722" C. Saint L6on Langlds (1952) reported values fortwo NiCO3 preparations that indicate the higher temperature producthas a smaller cell. Graf et al. (1961) have described a magnesite from theLake Bonneville sediments of Quaternary age in the Great Salt LakeDesert , Utah, which has ao:4.669 f t , cx:15.21 A, compared wi thao:4.6330 A and co: 15.016 A given in Table 7 for material prepared at250' C. The impurity content which could conceivably be in solid solu-tion in the magnesite of the Utah sample,0.7 wt/6 Fe, 0.01 wt/6Mn, andabout 0.2 wt/6 Ca (spectrographic analysis by Juanita Witters), failsby an order of magnitude to explain the change in cell size.

Calculations by Verwey (1946) for several alkali halides, which shouldbe similar enough to the rhombohedral carbonates for order-of-magni-tude comparison, indicated that near-surface shifts of position of posi-tive and negative ions and their electron clouds should occur, but onlyfor one or two atomic layers below the surface. The efiect would thus beinsignificant for particles of the order of 1 micron diameter such as thosemaking up the lowest-temperature carbonate preparations. Rymer'srecent (1957) review indicates extensive disagreement as to the size andmagnitude of the effect of small particle-size per se on cell constants.

Lehovec (1953) computed that the space-charge zone in NaCl par-ticles, which causes an electrostatic potential between the bulk and thesurface of the crystal and afiects the concentration of point defects,should extend inward from the surface about 0.013 micron at 627" C.,

DONALD L, GRAF

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1303RHO M BOH EDRA L CA RBON AT ES

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1304 DONALD L, GRAF

0.22 micron at 327" C. However, the vacancy concentrations observed inthe alkali halides even at high temperature hardly seem adequate to ex-plain the larger of the cell-size anomalies described in this paper.

Some of the samples prepared at lower temperatures include severalpercent of HzO or OH- that is not released in 12 to 15 hours at 110' C.(Table 6). The remarkably high value reported for CoCOa is from amicroanalysis that totals poorly and may be in error, but there is no

reason to doubt the results given for ZnCOz, CdCOa, and MnCOs. Thestructural location of this HrO or OH- (it may, of course, only be tightlyadsorbed) and its possible effect upon cell constants will be discussed ina subsequent communication.

It is possible that some of the cell enlargement of dolomite in fine-grained precipitates formed at room temperature, hitherto attributed ex-clusively to excess calcium (Graf and Goldsmith, 1956; Goldsmith andGraf, 1958a), -uy actually result from structurally incorporated H2Oor OH-. Such a hydration effect is, of course, ruled out for other dolo-mites with enlarged cells which were formed by high-temperature syn-thesis in an anhydrous system.

TrrB IJNrr CBr.r. or HuNrrro, MgrCa(COr)a

Graf and Bradley (In press) gave for the unit cell of huntite oo:9.565A, co:7.82I A, obtained from a powder diffraction fi lm of huntite fromCurrant Creek, Nevada, by making a least squares analysis involving adrift error term of the form

,i"'o(+-+)Their cell was of principal value in demonstrating the close agreementbetween observed and calculated d-spacings of front reflections. A more

accurate o0 value can be obtained by combining the cf a ratio obtainedfrom the least squares analysis with measurements on a film taken withiron radiation of the positions of the {71'3} and t.72'2]1 reflections, at20=149" and 168o, respectively, to make a two-point cosz 0 extrapolation.Then co is calculated from d166.61, the latter f irst corrected by theamount that the measured spacing of the adjacent {25'0} reflectiondifiers from the value calculated from os. Varying the c/a ratio by an

amount corresponding to oo fixed at 9.4980 A and c6 changing from 7'81

to 7.82 A changes the extrapolated as value by only *0.0003 A.Measurements for three huntite samples, all very fine-grained nat-

urally-occurring materials, are given in Table 8. The cell constants of

the two samples from Currant Creek, Nevada, are identical within thegeneral limits of error observed in such extrapolations for the other

RHOMBOHEDRAL CARBONAT'ES I3O5

rhombohedral carbonates. The sample from Tea Tree Gully has a sig-nificantly larger cell. Graf and Bradley estimated that the o6 of theCurrant Creek huntite was 0.6lT0 greater than predicted from astraight-line interpolation between the values for magnesite and calcite;cn,0.75/6 larger. The corresponding values for the more accurately de-termined unit cells in Table 8 are a(r,0.57-0.61Yo, co 0.664.707o.

Coarsely crystalline huntite will have to be found in nature or syn-thesized before it will be possible to attribute a particular cell size to

TAsr,n 8. UNrr Car,r, DrlroxsroNs ol rrre Hr'xacoN.lr-Srnucrunn Cnr-r or Hunrrrn

Sample

Currant Creek, Nevada(Collected by D. L. Graf)

Currant Creek, Nevada(Collected by G. T. Faust)

Tea Tree Gully, SouthAustralia

Aoby extra-polation

9.4981

9.4979

9.5020

Using oq and thec/o ratio of the

least squaresanalysis

7 . 8156

7 . 8155

7 . 8182

From dloo 6l correctedagainst dlzr.o)

material of strictly 3: 1 molar MgCO3: CaCOa composition, free of hydra-tion efiects.

Ellnct oF CATToN Onnpn oN CELL SrzE

Small but measurable changes in cell size take place with cation dis-ordering oI the 1:l compounds. Comparison of d.o and c6 values for theordered and disordered cells with those predicted by taking a0 ar'd c()values midway between those of the two end members is interesting.Thus far, the only composition for which all three sets of values areavailable is CdMg(COr)z (Goldsmith, 1958). The crystall inity of thesepreparations is not ideal, and back reflection measurements are there-fore not of the highest quality. The most accurate data available arethose obtained from films taken with a Guinier-type focusing camera.The change in o6 on disordering is -0.0024 A, that in co, *0.037 A(Table 1). One might suspect that these slight dif ierences resulted froma sampling or mixing error-it need involve only about 0.2 mol percentCdCO3-were it not for the fact that the two axial lengths change in

1306 DONALD L. GRAF

opposite directions and that comparable efiects, discussed below, are

observed for dolomite. Actually, Goldsmith's mixing was achieved byprolonged hand mulling of small portions under alcohol, a method that

Ieaves little reason to distrust the stated compositions.The oo and cs cited for dolomite in Table 1 and used in computations

elsewhere in this paper, 4.8079 and 16.010 A, respectively, are those de-

rived by Goldsmith and Graf (19530) from study of several analyzedsingle-crystal dolomite samples. Goldsmith and Graf have discussed the

relations between these values and those derived by averages of the oo

values and of the co values for calcite and magnesite. These averagesalso are included in Table 1.

The most probable Aoo and Ac6 values for largely but not completelydisordered materials having essentially the composition CaMg(COr)zare respectively, -0.003 A and +0.036 A (Gotdsmith et at., 196l).

Most of the measurements were made on films taken with a Guinier-type focusing camera; the uncertainty in Aoo resulting from a possible

Guinier measurement error on each pattern of the smallest unit recorded,0.05 mm, is * 0.0018 A, and in co is + 0.006 A.

The agreement among Aoo and Aco values for the various CaMg(COJzand CdMg(COa)z samples is good, in view of the difficulty in making

accurate measurements on imperfectly crystallized materials and thefact that neither the compositions of the several dolomite samples nor

the amounts of residual order remaining in them after quenching from

temperatures near 1125" C. are precisely the same. Any variation that

may exist in Aoo and Aco with slight departures from equimolar composi-

tion is masked by the experimental uncertainty.No 1:1 ordered calcium iron carbonate has yet been described, but oe

and cs values predicted from those for FeCOe and CaCOa are presented

in Table 1 because of their possible usefulness in studies of ferroan

dolomite. The ordered compound CaMn(COe)2, kutnahorite, is present

in nature in well crystallized specimens, but none of the single-phasesamples yet studied is sufficiently free of Mg and Fe in solid solution topermit precise comparison with predicted values. Order reflections for

this composition can be detected with certainty only in single-crystal

x-ray diagrams, so that it has not proved possible to determine whether

ordered synthetic powders have been prepared. However, at a sufficientlyhigh temperature, by analogy with single-crystal experiments (Gold-

smith and Graf , unpublished data), one can be certain that such a powder

is disordered, and values are given in Table 1 for a sample of this kind.

Rnrranrr,rtv on CBU CoNsreNrs

The extrapolated cell constants presented here and by Goldsmith and

Graf (19580) for materials recrystallized at high temperatures appear to

RHOMBOHEDRAL CARBONATES 1307

differ from comparable published data, and also among themselves wheremeasurements of the same constant were made with several radiations,by from 0.0001 to 0.0003 A in oo and by 0.001 or 0.0016 A in c6, or Irom2.5 to 10 parts per 100,000. The maximum uncertainty in the tem-perature for which cell constants are valid is 26*3" C., the range oftemperature encountered in the laboratory where the films were taken,which is air-conditioned in summer. The correction for these materialsfor a temperature difference of 5o C., based upon available thermal ex-pansion data, would be about 0.0001 A in ao and about 0.002 A in c6,values comparable with the differences mentioned above.

The ceII constants presented here should be satisfactory for most geo-chemical and mineralogical purposes, but they may not be adequate forsome studies of defects in these solids. The extent to which they can befurther refined appears to be limited by poor crystallinity for materialsformed at modeiate temperatures. Less than perfect cation ordering in1: 1 compounds such as dolomite appears, in principle, to be present ingreater or lesser amount at all temperatures (Goldsmith and Graf,19586), and places a further l imit on the accuracy with which cell con-stants can be obtained for these materials.

INrBnpr,lN.qn SpacrNcs

The o6 and c6 values selected for use in calculating d-values, typicallythose for weII crystallized high-temperature materials giving the mostaccurate cos2 I extrapolations, are given in Table 1 together with o.n ando values for the rhombohedral cells.

Table 2 includes all possible reflections of the carbonates listed thereusing CuKar radiation. A list of such reflections was first prepared for ahypothetical dolomite-type structure having the ao and ca of CaCOs.Deletions from this list were then made of reflections forbidden for cal-cite-type structures, and of reflections with d<0.77025 for the carbonateswith smaller cells. The spacings l isted for CaCOr by Andrews (1950)and Swanson and Fuyat (1953), for CaMg(COr), by Howie and Broad-hurst (1958), for MnCOg by Goldsmith and Graf (1957) and Swansonet al. (1957), for CdCO3 and MgCO3 by Swanson et aI. (1957),Ior ZnCOzby Swanson et al. (1959) and for CoCOr by Swanson et al. (1960) indi-cate which of the possible reflections for these compounds have sufficientintensity to be readily observed in routine diffraction analyses.

Srnucrunr Facrons

Calcite belongs to space group R3c, dolomite to R3, and the huntitemodel proposed by Graf and Bradley (In press) to R32. The unit cells ofthese materials contain, respectively, 2CaCO3, Ca)Mg(CO3)2, andMgaCa(COr)r. Att lh,k,l,\ are possible reflections for dolomite and for

1308 DONALD L. GKAF

huntite, but for calcite reflections having h,+k,+1, odd are forbiddenunless h,lh,*1,.

Structure factor computations like those which follow are simplifiedconsiderably by using the rhombohedral cell. The amplitude contribu-tions to the calcite structure factors, obtained by substituting in theappropriate expression (International Tables ior X-ray Crystallography,volume l, 1952, p. a73) for each atom in the rhombohedral unit cell andsumming, fall into three types that may be represented by greatly sim-plified expressions. The types are defined using sign changes of amplitudecontributions from atoms whose coordinates do not involve variableparameters, and the zero or non-zero character of amplitude contribu-tions in general. Further definitions involving variable parameters whichare very nearly equal to simple fractions could be made, but wouldbreak down for higher order reflections. The letter-designated subdivi-sions are not distinct types, but will be useful in a comparison of calcite,dolomite, and huntite reflection types which follow.

The calcite types are:

l. (h,+k,+l,) divisible by 42fc^*2sfcl2{olcos Zrr(h - k) lcos 2rtc(k -I) I cos2rx(l - h)l

(1a. Two or three indices alike)(rb. h+k+t)

2. (h,+k,+l,) even, but not divisible by 42Jc"- 2Jc- 2folcos 2rx(h- k) | cos 2r*(k -t) Icos 2r r(l - h)l

(2a. Two or three indices alike)(2b. htk-t)

3. (h,+k,+l,) odd, hlkll2Jolsn2or(h-k)*stn2rr(k-1,)*sinZrr(t,-h)1.

These expressions are analogous to those presented by Tahvonen 09a7)for the isostructural NaNO3, but with calcium rather than the anion atthe origin. Like the amplitude contributions which follow for dolomiteand huntite, those for calcite have been divided by an appropriate con-stant so that they refer to the contents of one unit cell.

From the expression for the dolomite space group, given on page 463of volume 1 of the International Tables f.or X-ray Crystallography, withcalcium at the origin, three simplified expressions for the various typesof dolomite reflections mav be obtained:

1. (l4lk,ll,) evenJs"lJal2Jclcos 2rx(h* klD ] Z7o [cos 2r (hx * ky I I'z) ! cos Zr(kr ! I'y I hz) * cos

2n(1.*-lhyl-kz)l(la. (h,*k,*l,) divisible by 4;2 ot 3 indices alike)(lb. (h,+k,+l,) divisible by 4; hlk+l)(1c. (h"-lk,+-\,) even but not divisible by 4;2 or 3 indices alike)(ld. (h+k,+l,) even but not divisible by 4; h*hfl)

RHOMBOEEDRAL CARBONATES 1309

2. (lh+k,+l,) odd, two or three indices alikef s"-Jy'l2Jclcos 2rx(h*kll) ]*2/o [as in t ]

s. (th+k,+l,) odd, htk+tJc,-Ju"t2|clcos 2nr.(hlhlt) ]*2/o[cos 2r(hr*kyllz)*cos 2r(ktctly'fhz)Icos

2n(txfhylhz)l;l.^-J*"*2f c[cos 2rx(hlhll) ]+z/o [.o. 2r(kxlhyIlz) lcos 2r(htc!ly*fr2) *cos

2r(Irthylhz)l

Dolomite reflections of type 2, a consequence of cation ordering, areforbidden in calcite. Those of dolomite type 3 are in calcite contributedto exclusively by oxygen.

From the expressions for the space group of the Graf-Bradley huntitemodel, given on pa,ge 466 of volume 1 of the International Tables for X-ray Crystallography, with calcium at the origin, the following four sim-plified expressions for the various types of reflections may be obtained.Lengthy trigonometric expressions which appear within the bracketshave been omitted; those indicated by asterisks include both sines andcosines, the others, only cosines:

l. (h+h+l) even, 2 or 3 indices the same

I c"I J c;t | / 3 [ ]J c,,I 1 / 3 | lfMc+ | / s [ ]/o,+ r / s | 1 7o r,+ z / s I Uo,,,(a. h, h,l all even numbers)(b. Only one even index)

2. (h+h+l ' ) even, h+kl l

1/A2lB2,whercA:Lhe expression given under 1B : | / sl*lfq[-+r / 3l*lfM'+ 1 / 3[*]1or+r/3 [*Uo rr+2 ftl*1fon,

(2a. h, k,l all even numbers)(2b. OnIy one even index)

3. (h+k+l,) odd, 2 or 3 indices the same

fc"-Jc1*' ' ' remainder as in 1(3a. h, k,l all odd numbers)(3b. Only one odd index)

4. (h+k+t) odd, h*ht l

J42*82, wltereA:lc"-Jc;l ' . ' remainder as in IB as i n2

(4a. h, k, I all odd numbers)(4b. Only one odd index)

Table 9 gives correlations among the several groups of reflectionswhich have been described for calcite, dolomite, and huntite.

The number of cooperating planes for the various types of calcite andhuntite powder reflections, expressed in hexagonal indices, is (See In-ternat ionale Tabel len, 1935, p. 502) : {hk i l l , 2 .12; lhh2hl l , t2 ; { \kL l \ ,2 .6; lhk i \ l , 12; {hh2i l01, 6; l }k6} l ,6 ; {0001}, 2. For dolomite powderreflections the analogous values arc lhhi.l l , 4.6; lhh2il l l , 2'6; l\kdll,2 , 6 ; { h k i 0 1 , 2 . 6 ; l h h 2 h 0 } , 6 ; { 0 e 8 0 } , 6 ; { 0 0 0 1 } , 2 . T h e 4 . 6 a n d 2 . 6

1310 DONALD L. GRAF

entries for dolomite indicate that atoms in general positions, namely,oxygens, will scatter with a different amplitude for some of the co-operating planes of a given \hhi\, lhh2hll, or lhhi.Ol reflection than forothers.

Zero amplitudes result for particular sets of planes whose hexagonalindices do not transform to whole-number rhombohedral indices. Thus,there are for dolomite only two non-zero oxygen amplitudes lor l2l.aland only one for i$2.7]1. These relations are somewhat more simplystated in terms of rhombohedral indices: two non-zero oxygen amplitudes

T.lslr 9. Connrr-lrroN or Pomrn Rrnr,rcrroN Typrs ronTrnnB RnoMsorrEDRAl Srnucrunn Crr,r,s (see text)

Dolomite lluntite

l atbl ctd

J

l atb2a2b

Ia2a3a4a

I O

2b3b4b

result for all dolomite Ih,k,t, l in which h"+k,+l,, except for lh\i l . l re-flections, which have a unique oxygen amplitude. The occurrence ofzero amplitudes for calcite and huntite is such that there is only onenon-zero oxygen amplitude for each lh,k,l, l .

The amplitude contributions for calcite given in Table 3 have beencalculated by using the value of r:0.2578 (corresponding to a C-Odistance oI t.286 A) giv"n by Chessin and Post (1958)" Sass el al. (1957)obtained closely similar values, r:O.2593+0.0008 and C-O: I.294+0.004 A. The amplitude contributions for dolomite derive from Stein-fink and Sans' (1959) oxygen parameters, r.:0.2374*0.O068,y: -0.0347 +0.0068, and z:0.2440+0.00017, and their value ofz:0.2435*0.00031 for carbon, all in terms of the hexagonal unit cell.The corresponding values for the rhombohedral unit cell upon which thediscussion in this paper is based are so:0.4814, ys: -0.0281, zo:0.2787,and nc:0.2435. The C-O distance for dolomite corresponding to theseparameters is 1.283 A, in particularly good agreement with Chessinand Post's value. All three of the parameter determinations are based

RHOMBOH EDRA L CA RBON AT ES 13rl

upon single-crystal measurements. Those for calcite involve oxygen-only

reflections, and those for dolomite are based on some 500 reflections of

all types.The variable parameters used for the other calcite structures (Table

10) were calculated by assuming that the C-O bond length remains con-

stant at 1.286 h; the parameter tc:C-O/oo. The dolomite r and y

hexagonal unit-cell parameters were multiplied by the ratio of ao for

CaMg(COr)z to that of oo for CdMg(COa)2' so as to retain in CdMg(COJz

the same c-o value of 1.283 A found for dolomite. In the absence of evi-

dence for making other assumptions, the dolomite a parameters for

"^MgCOa r :O.2776MnCOa r.:O.2692FeCOg r:0.2743ZnCOt x :0 .2764CaMn(COg)z r:O.2635

CdCOs r:0.2614CoCOa x :0 .2761NiCOe *:O.2797CuCO: x:O.2681*CaFe(COr)r *:O.2657

CaMn(COr)z xo:O.4779, !o: -0.0241, zo:0.2782, rc:A '2435

CaFe(COs)z ro:O.4799, lo: -O 'O264, zo:0 .2785, tc:O '2435

CdMg(COa)z ro:O.4829, yo: -A.0298, zo:O.2789, rc:0 '2435

x Using the oo value given by Pistorius (1960).

oxygen and carbon were retained for CdMg(COr)r, as was the slight rota-

tion of the carbonate group relative to the hexagonal @ axes, and the

parameters for the hexagonal cell were then converted to values for the

rhombohedral cell. Coplanarity of carbon with the oxygens of its car-

bonate group is not required by symmetry for the dolomite struclure as

is the case for calcite. The reality of the 0.0005 difference between the

Steinfink and Sans z parameters for oxygen and carbon is indeterminate,

because the uncertainty ranges attached to these values are just great

enough to allow for coplanarity at z:0.2438. The intensity difference

for this shift of carbon by about 0.01 A is, in any event, insignificant

compared with other sources of error.Parar-neter assumptions of the same type as those for CdMg(COa)z

were used in calculating the values given in Table 10 for dolomite

structures having the compositions CaMn(COa)z and CaFe(COe)r'

These parameters involve a further approximation because, as discussed

earlier, the a6 values available for the calculations were not measured on

ordered compounds. The oo available for CaMn(COs)z is that for dis-

ordered material, that for CaFe(CO)2, merely the mean of the values

for calcite and siderite. However, these parameters are the best that can

1312 DONALD L. GRAF

be derived at present for making intensity estimates for order reflections.Parameter estimates for calcite-type structures having the compositionsCaMn(CO)2 and CaFe(COs)z are also shown in Table 10.

The variable parameters given by Graf and Bradley (In press) for ahuntite structure model derived from powder r-ray difiraction data are,for the rhombohedral uni t ce l l , ry* :0.541, *srr : -0.039, rer :0.365,,orr :0.096, #orr r : -0.033, yorr r :0.180, zorr , :0 .37 I .

fNrnNsrrrBs

rntensities of front reflections in powder diagrams of the rhombohedralcarbonates, computed for copper radiation, are given in Table 4. Thechange of intensities in the solid solution series between CaMg(CO3),and the hypothetical end member, CaFe(CO3)2, is shown graphically inFig. 1. Estimated changes in cell size with composition ha.re been .orr-sidered in the ferroan dolomite computations, but these computations donot allow for departure of CaCO: content from 50 mol percent.

These intensities are simply the products of F2 times -ultiplicity ti-esthe combined Lorentz and polarization correction for Debye-scherre,lines on a cylindrical film,

| * cosz 20

sinr g cos g

Absorption and temperature factors have not been considered, but couldbe added as corrective multipliers suitable for a given experimental situa-tion. The scattering factors given by Berghius et at. (r95s) were used forC, O, Ca, and Mg++, all self-consistent field data with exchange, withthe curve for Mg++ at (sin 0/|\)<0.2s diverted toward the value-for theneutral Mg atom at sin d/tr:0. Watson and Freeman (1961) give self_consistent field data with exchange for Mn, Fe, Co, Ni, and Lu+; thelatter curve at (sin 0/\)<0.2s has-been diverted toward the value forthe neutral Cu atom at sin d/tr:0.

The curve of Berghius et ar,. for Zn, based on serf-consistent field datau)ithout exchange, gives expectably low varues relative to the curvescomputed with exchange; it is essentially coincident with the cu curveover part of the sin 0/\'range. The values forznused in this paper weretaken from a curve drawn, at each sin d/tr varue, the same distance abovethe cu curve as the separation between the cu and Ni curves at thatpoint. The scattering factor curve used for cd, the only recent one avail-able, was computed by Thomas and umeda (1957) from the Thomas-Fermi-Dirac model.

These scattering factor curves fall off in generally concordant fashionand make it possible to observe the effect of progressively heavier cationsupon the relative intensities of the various carbonate reflections. These

RHOMBOH EDRAL CARBON AT ES

4 0 6 0Mol 7" Co Fe (CO:)z

1313

-{: : z}- t r o r l

-{ zoo}

- { r r o }

- {z ro }

c

ooE

- { s r o }_ - t i l 2 i

- t 2 t | l

i sz r ]

- { z r r }

-{, , nI( - - - J

- { r r r }

{ i zo}

322

443

-{ roo}) ( - l- -<tzorJ

l 4 z 2 l .- t 444 )

- i+rz]lzzz{ r r l

{ r r r ] ,r - - ,1l J J r J ,

{ r oo }Jt . .1t--- -J

[roo'l

{.. r}

{oo.J

\\\-i-i

l\t, +L{rr,}

{ i r r }

{ r s r }.{zzz}f:ooll 22 t )r - - - l

, l" ""J80 60Mol 7 .

4 0Co Mg (CO:)z

Frc. 1. Computed relative intensities for powder reflections in the front reflection

region, using copper radiation, for the solid solution series between CaMg(COr)z and the

hypothetical end-member, CaFe(CO:)2. Order reflections are shown by dashed lines,

strong oxygen reflections by heavy lines. The intensity of the very strong {211} reflection

is plotted reduced by a factor of ten relative to those of the other reflectrons; that of [321 ]'reduced by a factor of two.

relations are modified somewhat by differences in atomic arrangement in

the related calcite, dolomite, and huntite structures. The increase in

intensity of the CdMg(CO)2 order reflections relative to those of the

other ordered 1: 1 carbonates is noteworthy.

t3l4 DONALD L, GRAF

The computed intensities of Table 4 and Fig. 1 are based upon asimplified model essentially involving spherical neutral atoms at rest, inaccord with the empirical observation that observed intensities are betterexplained using neutral-atom scattering factor curves than those for ions.The radically different solubil ity rates of, for example, CaCO3 andNico' in HCI solution indicate that an error is introduced for reflec-tions at (sin d/\) (0.25 by this uniform bonding approximation. Thedetermination of scattering factor curves appropriate for specific car-bonate structures is, however, beyond the scope of this paper. The thirdfigure given in the computed intensities is obviously not generally sig-nificant, but may have meaning, for example, in computing an intensityratio for two reflections of the same compound which lie at about thesame 20 angle and have similar structure factors.

It should be noted, in comparing observed intensities of two or morecarbonates with the equivalent computed values in Tabre 4, that theobserved values must be suitably corrected so that they all represent in-tensity difiracted from the same number of unit cells.

Acrwowr,ntcMENTS

I am particularly indebted to J. R. Goldsmith for treating some of thesamples in a squeezer-type apparatus and for taking many of the filmsupon which the measurements were made; to W. F. Bradley for manyhelpful suggestions made during the course of the calculations; to DanielAppleman for using a computer program to prepare a list of all possiblecalcite reflections, as a check on the list arrived at by hand calculation;and to Juanita Witters, L. D. McVicker, and D. R. Dickerson for spectro-graphic and chemical analyses. C. S. Hurlbut, Jr., supplied the sample ofsingle-crystal smithsonite from Broken Hil l, Rhodesia; Brian Skinner,huntite from Tea Tree Gully, South Australia; George T. Faust, huntitefrom Currant Creek, Nevada. Permission from Dr. Goldsmith and Missfsaacs to quote their results is gratefully acknowledged.

RBlrnnwcnsANDREwS, K. w. (1950), An r-ray examination of a sampleof pure calcite and of solid-

solution efiects in some natural calcites: Mineral,. Mag., Z9r 85-89.AusrrN, J. 8., Serxr, II., Wnrcr,r, J., aNo Prnncr, R. H. H. (19,10), Direct comparison on

a crystal of calcite ol the r.-ray and optical interferometer methods of determininglinear thermal expansion : P hys. Rn., 57, g3l-933.

Bnlcnrus, J., Jennrrre, I., HenNmner, M., Polrrns, M., Loorsrne, B. O., McGrr,r_avnv,C. H., and Vrnr.rnNoell, A. L. (1955), New calculation of atomic scattering factors:A cta Cr yst., 8, 478-483.

cnrssrx, HnNnv, aNo Posr, Beu (1958), Positional parameter and thermal motions ofoxygen atoms in calcite (Abst.): Annual Meeting of the American crystallographicAssociation, Milwaukee, Wisconsin, June 23-27, 1958.

RHOM BOH EDRA L CA RBON AT ES 1315

FnnnueN, A. J. (1959), Atomic scattering factors for spherical and aspherical charge

distributions: Acta Cryst., 12, 261-27 I.Fmruax, A. J., aNo Wooo, J. H. (1959), An atomic scattering factor for iron: Acto Cryst.,

12, 271-273.Gorosuttn, J. R. (1958), Cadmium-dolomite and the system CdCOa-MgCOr: Geol. Soc.

Amer. Bul,l,., 69, 1570-1571.Gotosutttt, J. R., .lNn Gnal, D. L. (1957), The system CaO-MnO-CO:: solid solution

and decomposition relations: Geochim. et Cosmochi.m. Acto,llr 310-334.

Gor.osurtr, J. R., aro Gner, D. L. (1958a), Structural and compositional variations in

some natural dolomites : J our. Geol,o gy, 66, 67 8-693.Gor-lsurtn, J. R., AND Gnel, D. L. (1958b), Relation between lattice constants and com-

position of the Ca-Mg carbonates: Am. Mi,nerol..,43, 8+101.Gor.osurru, J. R., Gner, D. L., aNo Hnaa.o, H. C. (1961), Celi constants of the calcium

magnesium carbonates: Am, Minerol., 46, 453457 .Gotosurttt, J. R., Gn,lr, D. L., eno Jonwsuu, O. I. (1955), The occurrence of magnesian

calcites in nafille Geoch. et Cosmoch. Acta,7,2l2-23O.Gnel, D. L., Br,vrn, C. R., eNo Srnuurnn, R. S. (1957), MixedJayer effects in the rhom-

bohedral carbonates: Geol. Soc. Amer. Bttll.,68, 1737-1738.Gnal, D. L., Brvru, C. R., ,lro Srnuur.nn, R. S. (1958), Mixed-layer computations using

ILLIAC: The threeJayer case: Geol. Soc. Arner. Bxtll.,69,1572.Grar, D. L., ero Breolrv, W. F., The crystal structure of huntite, MgrCa(COr)r: In

Press, Acta Cryst.Gner, D. L., E,trlr-av, A. J., lNo Snrur, N. F. (1961), A preliminary report on magnesium

carbonate formation in glacial Lake Bonneville: Joor. Geology,69' 219-223.

Gnar, D. L., aNo Gor.nsurru, J. R. (1956), Some hydrothermal syntheses of dolomite and

protodolomite: f our. Geol,ogy,64, 173-186.Gnar, D. L., aro Le.uan, J. E. (1955), Properties of calcium and magnesium carbonates

and their bearing on some use of carbonate rocks: Econ. Geol., Fiftietl Anniversary

Volume, 639-713.GmGGs, D. T., lxl KENNEDv, G. C. (1956), A simple apparatus for high pressures and

temperatures: Amer. J our. Sci., 254, 7 22-7 35.Henxrn, R. I.,,r.noTurrr.u, O. F. (1955), Studies in thesystem CaO-MgO-CO* Part2.

Limits of solid solution along thebinary join, CaCOa-MgCO3: Amer. Jour. Sci..,253,274-282.

Howrn, R. A., .lNo Bnoaorunsr, F. M. (1958), X-ray dala for dolomite and ankerite:

Am. M iner aJ., 43, I2lFl2l4.Ilunr.nur, C. S. (1954), Smithsonite from Broken Hill Mine, Rhodesia: Am. Mi'neral.,39,

47-50.INtnrNarroNel Tlnrcs lon X-nly Cnvsrll,rocnepny (1952), The Kynoch Press,

Birmingham, England, vol. LInrnnxnrroN.q.rr, Tlner.r.nr zuR BESTTMMUNG voN Knrsrlr,r-stnurruREN (1935),

Gebriider Borntraeger, Berlin, vol. II.Lnnovnc, Kunt (1953), Space-charge layer and distribution of lattice defects at the sur-

face of ionic crystals: Jow. Chem. Physics,2l, 1123-1128.Prstontus, C. W. F. T. (1959), High pressure preparation and structure of crystalline

nickelous carbonate: Erperimti,o, 15, 328-329.Prsrontus, C. W. F. T. (1960), Synthesis at high pressure and lattice constants of normal

cupric carbonate: Exper'imtia, 16, M7-448.Rruoonn, P., ewo Srruxz, H. (1941), Isomorphie von Otavite mit Kalkspat: Zentrol'bl.

Min. , A,97-98.

t3 l6 DONALD L. GRAF

Rvutn, T. B. (1957), The lattice constants of small crystals: Nuot:o Ci,mmto, VI (Suppl.),294-305.

Serxr LfoN LnNcris, Ran6 tc (1952), Pr6paration et structure du carbonate neutre denickel anhydre cristallis6: Ann. chim. (Paris), ser. 12,7,568-583.

Sass, R. L., Vroar,n, R., mlo Dororue, J. (1957), Interatomic distances and thermalanisotropy in sodium nitrate and calcite:. Acta Cryst.,10r 567-570.

Sueu, W. E. (1960), The cell constants of artificial siderite: Am. Mineral..,45, 241-243.StntNltrt<, H., nlro Sers, F. J. (1959), Refinement of the crystal structure of dolomite:

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r-ray diffraction powder patterns: U. S. National Bweou oJ Stondard.s, Circ. 539,lO.Swlnson, H. E., aNl Fuva.r, R. K. (1953), Standard r-ray diffraction powder patterns:

U. S. Nalionatr Bweau of Stand.ord.s, Ci,rc.539,2.Swnnson, H. E., Gnrnrcn, N. T., awo Coor, M. I. (1957), Standard *-ray difiraction

powder patterns: [/. S. NationaL Btaeau of Stand,ards, Cire . 539,7.Sw,tNsoN, H. E., Grllnrcu, N.'f., Coor, M. L, SnNcnunlo, RocnR, mln Pems, p. C.

(1959), Standard *-ray diffraction powder patterns: U. S. National Bu.reau oJ Stanil-ard.s, Circ. 539,8.

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Monuscri.pt receit;d. Jan. 17, 1961.

crystallographic tables for the rhombohedral … · don,+rr l. gnar, illinois slale geological...

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