448RARIES
CRYSTAL STRUCTURES OF THE TURQUOIS-GROUP MINERALS
by
HILDA CID-DRESDNER
Diploma, Universidad de Chile
(1958)
S.M., Massachusetts Institute of Technology
(1962)
SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
June 1964
Signature of Author...............~.'....
.......
'..
Department of Geology and GeohWsics. June 22, 1964
Certified by..............
Theis 'Supervisor
.
.....-... a
Accepted byair ....
Chairman, Departmen' 1 Com
.-...-.. 'on.............
ttee on Graduate Students
Structures of the turquois-group minerals
by
Hilda Cid-Dresdner
Submitted to the Department of Geology and Geophysics on
June 22, 1964, on partial fulfillment of the requirement
for the degree of Doctor of Philosophy
Abstract
The turquois group includes turquois, henwoodite,
rashleighite, alumo-chalcosiderite, chalcosiderite and faustite.
Turquois and chalcosiderite are the only members of the group
that present single crystals. They are isomorphous and the
similarity of their x-ray diffraction photographs indicate that
they have the same structure.
Turquois is triclinic, space group Pl, with cell
dimensions a
7.424A, b = 7.629R, c = 9,9101, c, 68.610,
/3=69.71o, '
65.080 . The cell contains one formula of
CuA1 6 (P 4 )4 (OH)8 .4H2 0, so that the Cu atom is fixed in an inversion center. Three-dimensional intensity data were collected
on a single-crystal diffractometer using a proportional counter
as detector, and were corrected for Lorentz-polarization factors
and absorption. The interpretation of a three-dimensional Patterson function and of a three-dimensional electron-density
function based on signs due to the Cu contribution only, gave a
trial structure that was refined by Fourier methods and then by
least-squares methods to R
7%.
The structure can be described in terms of planes
of approximately close-packed oxygen atoms oriented parallel to
(001). Planes containing the Al in octahedral coordination and
planes containing the Cu in a 4 + 2 octahedral coordination alternate between oxygen layers. The octahedral groups of anions
around the aluminum are single and double; two phosphorus tetrahdra link each double group to its translational equivalent,
forming a tetrahedra-octahedra chain parallel to the b axis.
The PO tetrahedra together with the single aluminum octahedra
constitute a zig-zag chain in the directIon of the c axis. The
water content has been determined to be four molecules per cell.
Chalcosideritets cell constants are a = 7.68a,
=64.8 0 . Chalb =782A, c = 10.211, c . 67.50, 3 = 69.l0,
cosiderite crystals present a very curious phenomenon that can
be interpreted as epitaxial growth of turquois on chalcosiderite.
Thesis supervisor: Martin J. Buerger
Title: Institute Professor
Preface
This thesis is divided into two sections.
The first
section consists of three parts which are intended for publication.
The second section is presented in the form of two appen-
dices.
The first appendix gives an account of work done in con-
nection with the thesis and is not intended for publication.
The first part of Appendix I is a review of the literature related to the subject of this work.
The second part gives a de-
tailed description of the method used in the solution of the
structure of turquois.
Appendix II is
a list
of observed and
calculated structure factors for turquois as obtained from the
last cycle of refinement, and might be included in the turquois
paper.
Aknowledgements
This work would have not been aone without the constant
encouragement provided by Professor Martin J. Buerger,my thesis
supervisor.He also proposed the problem and contributed to it
with many helpful suggestions.
Mr. Wayne Dollase And Mrs. Isabel Garaycochea-Wittke,
from the Crystallographic Laboratory of the Geology Department,
are thanked for their friendly interest in the problem.They contributed to it through many constructive discussions.
Miss Erica Moore read the manuscript and corrected the
Gnglish of the text.She typedfrom my handwritten originals,
the first and seond drafts of this work, as well as all the final
versions of the tables.Her help is gratefully aknowledged.
Professor Clifford Frondel at Harvard University and
Dr. George Switzer of the U.S.National Museum, kindly provided
the crystals utilized in this investigation. Dr.Charles T. Prewitt
of E. I. Du Pont de Nemours made the piezoelectric test to confirm
the existence of a center of symmetry in turquois.
While this work was donethe author was on leave of absence
from the Laboratorio de Cristalograffa de la Universidad de Chile.
Financial support during this time was provided by fellowships
from the Agency for International Development of the U. S. State
Department, and from the Organization of American States, in this
order.
This work was partially supported by a grant of the National Science Foundation.All the computations were carried out on
the IBM 7094 computer of the massachusetts Institute of Technology Computation Center.
This work is dedicated to my husband, George.
Table of contents.
Abstract
Preface
iii
Acknowledgements
iv
Table of contents
v
List of figures
vii
List of tables
viii
Part I-A
Abstract
1
Introduction
2
Unit cell and space group
3
Intensity data
6
Structure determination
7
Refinement of the structure
12
Results from the refinement
18
Description and discussion of the structure
33
Acknowledgements
48
References
49
Part I-B
Abstract
54
Introduction
54
Precession work
54
Cylindrical film measurements
62
Acknowledgements
66
References
68
v i.
Part I-C
Abstract
69
Introduction
69
Appendix I-A
a.
The minerals of the turquois group
References
b.
The anion configuration around the
Cu+2 ion
References
81
87
Appendix I-B
89
Appendix II
99
Biographical note
125
vii
List of figures
Part I-A
8
1.
Minimum function M (yz)
2.
The eight hydrogens of the turquois structure.
3.
Composite of sections from the final electron density
.
21
function.
4.
The structure of turquois projected parallel to the a axis.
5.
Polyhedral chains, view parallel to the a axis, sections
from x
6.
= 0 to x =
31
34
.
Polyhedral chains, view parallel to the a axis, sections
1.
36
Polyhdral chains in turquois, view parallel to the b axis.
42
from x
7.
14
-
to x
Part I-B
1.
Rotation photograph of chalcosideite .
55
2.
Zero-level Weissenberg photograph of chalcosiderite.
58
3.
The two reciprocal lattices of the chalcosiderite crystal.
63
Part I-C
1.
Absorption of Mo radiation by lead.
71
2.
Experimental results from four pinhole systems.
74
Appendix I-B
1.
Results from the electron density function p1 (xyz).
Composite of sections showing the environment of the peaks chosen as A1l,
PI
2.
PV, and
(peak 12).
90
Results from the electron density function pl(xyz).
Composite of sections showing the environment of the peaks chosen as Al 2 and P2.
93
VLL I
List of tables
Part I-A.
1.
Turquois cell constants
2.
Discrepancy index R for the different stages of determination
and refinement of the turquois structure
4
17
3.
Coordinates for the non hydrogen atoms of turquois
19
4.
Anisotropic temperature coefficients
23
5.
Atomic coordinates of the hydrogen atoms in turquois
29
6.
Distances in hydrogen bonds
30
7.
The interatomic distances in the turquois structure
38
8.
Bond angles in the turquois structure
42
Part I-B
1.
Direct and inverse transformation for the three reported unit
cells of chalcosiderite
60
2.
Comparison of chalcosiderite and turquois unit cells
61
3.
Identification of the two lattices found in rotating crystal
65
photographs of chalcosiderite
Appendices
Appendix I-A
1.
Available data for the minerals of the turquois group
78
2.
The Cu+2 coordination
82
Appendix I-B
1.
Results from the electron density function, pl(xyz)
Part I A
Determination and refinement of the crystal structure of turquois,
CuAl 6 (PO 4) (OH) .4H20
By Hilda Cid-Dresdner
Massachusetts Institute of Technology
Cambridge, Massachusetts
Abstract
Turquois is triclinic, space group P1, with cell
dimensions a=7.424 A, b=7.629
=65.080 .
0
X, g 09,910
A,d=
0
68.61,
I=79.71
The cell contains one formula of CuAl 6 (PO414)(OH)
so the Cu atom is fixed in an inversion center.
8
0
4H2 0,
Three-dimensional
intensity data were collected on a single-crystal diffractometer
using a proportional counter as detector, and were corrected for
Lorentz-polarization factors and absorption.
The interpretation
of a three-dimensional Patterson function and of a three-dimensional electron-density function based on signs due to the Cu contribution only, gave a trial structure that was refined by Fourier
methods and then by least-squares methods to an R factor of 7%.
The structure can be described in terms of planes of
approximately close-packed oxygen atoms oriented parallel to
(001).
Planes containing the Al in octahedral coordination and
planes containing the Cu in a 4+ 2 octahedral coordination alternate between two oxygen layers.
The octahedral groups of anions
around the aluminum are simple and double; two phosphorus tetrahdra link each double group to its translational equivalent,
building a tetrahedra-octahedra chain parallel to the b axis.
The PO
tetrahedra together with the simple aluminum octahedra
,
constitute a zig-zag chain in the direction of the Q axis.
The
water content has been determined to be four molecules per cell.
Introduction
The turquois group is one of the few examples of a
well known mineral family whose crystal structures have not been
worked out up to the present time.
distinguished in this group.
Two isomorphous series can be
One is the turquois-chalcosiderite
series, characterized by isomorphous substitution of A1 2 03 by
2
1
rashFe 203; this includes as members turquois, henwoodite,
leighite, 3 alumo-chalcosiderite,4 and chalcosiderite.5 The other
series is formed by isomorphous substitution of Cu by Zn and only
the two end members, turquois and faustite,6 are known.
Of the whole group, single crystals suitable for x-ray
structure determination have been reported only for chalcosiderite
and turquois.
A recent x-ray study of chalcosiderite crystals, 7
has shown a curious feature that can be explained as a very thin
epitaxial growth of turquois on all crystals examined.
This fact
made chalcosiderite an unfavorable case for structure determination.
For almost eighty centuries turquois had been known
to occur in the cryptocrystalline state only.
It was not until
1912 that the first single crystals of turquois were described
by Schaller.1
Crystals from Schaller's original sample were
kindly provided by Professor Clifford Frondel, of Harvard University, and by Dr. George Switzer, of the U.S. National Museum, for
use in the crystal structure determination reported here.
Unit cell and space group
Turquois is triclinic and the space group is P 1, as
1
10
reported by Schaller and Graham.
The determination of the unit
cell was based on data from two precession photographs, Grahamts
a and b axes being the precession axes.
As is customarily done
for triclinic crystals, a reduced cell was chosen according to
Buerger's and Balashov's convention.
This convention uses
the three shortest non-coplanar translations of the lattice as
crystallographic axes and requires the interaxial angles to be
all acute or all obtuse.
The orientation of the set is completely
defined by the condition
a < b < c
The relations of the chosen reduced cell to the previous work of Schaller and Graham are given below.
It should be
noted that Graham's cell is a reduced cell that satisfied Peacock's
conventions for the setting of a triclinic crystal.11
His set in-
cludes the three shortest non-coplanar translations of the lattice
and satisfies the relations a ( c ( b;
L<,
Direct transformation
Schaller to Graham
Graham to Cid-Dresdner
}
-l
0
0
1
0
0
0 owl
L0
Cid-Dresdner
0
>
900,
1
r < 900.
Inverse transformation
-1
-1
l
11
0
0
1
O'
1
0
0q
-
0,
-bMa'
Schaller to
/3
0
-l
No
-h
-b
0 0 1
-1
~
L
l
0
0
-l
0
l'
01
Table 1.
Graham's values for
the all-acute cell
This work
Turquoise cell- constants
7.46A
7.424
± .004A
7.629
0
e003A
9.91A
68.35 0
69.430
64.62*
9.910
68.61
69.71
65.08
+
00042
t o0
0
e.04
i
.03
Final cell constants were obtained by refinement of
data from three axial photographs taken with a back-reflexion
precision Weissenberg camera2 *
Five cycles of least- squares
refinement using Burnham's LCLSQ 3 program13 for the IBM 7094
computer yielded the lattice constants listed in Table 1, where
they are compared with Graham's values.
The centro-symmetric
space group was confirmed by a piezoelectric test.
The refined cell parameters of Table 1 and Schaller's
analysis of crystalline turquois from Virginia1 were used to determine the unit cell contents.
The original formula of tur-
quoise 1 was given as Cu A16 (P04)4 04 . 9H2 0, since the chemical
analysis reported 20 non-water oxygens.
The values listed below
have been normalized to 20 oxygens since the available values of
the specific gravity 10, were not considered satisfactory.
Cu
0.94
P
4.02
Al
5.99
Fe
0.02
0
20.00
H20
9.33
This formula corresponds to the ideal composition CuAl (PO )
6
4 4
(OH)8 .(4H20 H2). Whether or not this extra water molecule belonged in the atomic arrangement of turquois was to be elucidated
from the structure determination.
Intensity data
A small turquois crystal of average dimension 0.18 mm
was selected for intensity measurements.
The shape of the crystal
was an irregular tetrahedron with truncated corners.
Although
this irregular shape precluded an accurate absorption correction,
the choice of this particular crystal was made on account of its
transparency, perfect extinction under the polarizing microscope,
and the good shape of the x-ray diffraction spots that were obtained with it.
Of the 2600 reflections in the positive hemisphere of
the Ewald sphere for CuK
radiation, 1650 which were within the
instrument limit were measured on a single-crystal counter difThe instrument was based on equi-inclination,
fractometer.
Weissenberg geometry
,
and the parameters
I
and ) as well as
the Lorentz-polarization factor for each reflection were obtained
using a program written by Prewitt15 for the IBM 7094 computer.
A proportional counter was used as a detector.
Counter intensity data for each reflection consisted
of the scan count (i.e., the total number of counts while the
crystal was rotated through the maxima, from a positionf1 to
for
Y 2, wheree 1( hklf2) and fixed-time background counts
the positions f1 and f 2 . The average background count from
these last two measurements was subtracted from the total scan
count.
The calibration of the absorbing foil was made in the
following way.
The integrated intensities of ten medium-sized
reflections were measured twice; first with the Al foil and then
without it. The ratio between the two measurements gave a good
approximation of the factor by which the strongest reflection had
been reduced.
In addition, a separate scale factor for these re-
flections was allowed in the last cycles of refinement.
The calculation of the observed structure factors was
16
made through two data-reduction programs
written for the IBM
7094 computer.
The first computed the integrated intensities,
allowing appropriate scaling adjustments for the reflections
measured with Al foils; the second one applied Lorentz-polarization and absorption corrections to the integrated intensities.
In this case an approximation to the absorption correction was
made by applying a spherical absorption correction since the lack
of well-developed crystal faces made it impossible to use a prismatic correction.16
Since the product of the linear-absorption
coefficient and the average radius of the "sphere" was 0.835, the
error introduced by this approximation was not expected to affect
the results greatly, even if it showed up as a temperature effect.
Structure determination
a. Two-dimensional work
An attempt was made to solve the structure in projections.
The three Patterson projections
P(xy), P(xz) and P(yz)
were calculated with the FORTRAN program ERFR217 on the IBM 7094
computer.
The projection P(yz) was studied first since it should
show less superposition.
The two strongest peaks were assumed to
define the interatomic vectors from the copper atom to two other
cations.
Two minimum functions M2 (yz), based on the correspond-
ing inversion peaks, were calculated and combined to produce the
function M (yz) which is illustrated in Fig. 1. The maxima from
-.-
~
U
Fig . 1
Minimum
function
(yz)
M (4
49
.1 I .1.
0
/3,
10
M (yz) provided the coordinates y and z for a model structure, the
x coordinates being obtained by correlation of M (yz) with the
other two Patterson projections.
This model structure was refined
independently in the three projections by successive Fourier syntheses followed by structure-factor calculations to discrepancy
factors R=
(yz).
49.3%
for ((xy),
R
=53.0%
for
'(xz),
and R
36.5% for
At this stage the three projections could not be corre-
lated any longer, and neither the Fourier refinement nor leastsquares refinement succeeded in attaining further convergence.
It was decided then that full three-dimensional data were necessary to solve the structure.
Accordingly the model structure was
discarded and a new start in three dimensions was made.
b.
Three-dimensional work
A three-dimensional Patterson function, based on the
1600 intensities collected, was calculated.
In the interpreta-
tion of the Patterson function the following features were taken
into consideration:
1. Turquois can be treated as a structure composed of a heavy atom at the origin and a residual structure of
atoms randomly distributed through the unit cell.
The ratio of
the contribution from the heavy atom and the maximum contribution
of the residue is only 12%.
Nevertheless, it must be considered
that the heavy atom is always making a maximum positive contribution.
On the other hand, the contribution of residual atoms will
newer attain more than a fraction of their maximum value due to
the fact that they are randomly distributed.
Hence, in spite of
the small ratio, the probabilities are that most of the structure
factor signs will be positive.
tion calculated with
(F
If so, an electron density func-
hkl as coefficients will approximate the
real structure.
2.
In the absence of a substructure the strong-
est peaks in the Patterson map should correspond to vectors from
the Cu atom to the Al and P atoms.
The next highest peaks should
be the Cu-O interactions of approximately the same height as an
Al-P peak, but both about
i
of the Cu-Al peak.
(Actually it was
not expected that this would hold rigorously since structures
based on oxygen are likely to show some kind of a substructure.)
3.
The Cu is expected
to be in a distorted
octahedral coordination with four oxygens at an approximate distance of 2A and the other two at a distance of 2.5
X.
The Al is
expected to be in octahedral coordination with approximate Al-0
distances of 1.9 A, and the P will be surrounded by an oxygen
0
tetrahedron with approximate P-0 distances of 1.5A.
4.
At least the peaks chosen as the cations in
the structure should project as a peak in the old M4 (yz) function.
An electron-density function, with all signs positive,
was calculated, and from it a model structure which fulfilled all
the preceding conditions was chosen.
This model was refined by
four successive electron-density functions followed by structurefactor calculations from the original discrepancy factor R =62%
to R= 27%.
In the course of the Fourier refinement five of the
oxygens and one of the phosphorus atoms from the original model
were found to be incorrect.
The peak erroneously assumed to be
a phosphorus was a substructure peak due to the superposition of
the almost identical Al(l) - P (1) and Al(2) - P(2) vectors.
At this point the Fourier refinement had converged.
The electron-density function whose atomic coordinates gave an R
of 27% showed round peaks of correct relative heights in the atomic locations and no spurious peaks.
Consequently the structure
was considered solved and the model was submitted to least-squares
refinement.
Only four water molecules were included in the struc-
ture, since no extra peak that could be attributed to the other
oxygen had been found.
On the other hand, the 28 oxygens per cell
fulfilled the coordination requirements of all the cations, and
if
a fifth water molecule were to be placed in the unit cell it
could not be attached to the cations in any of the usual ways.
Refinement of the structure
Least-squares refinement of the turquois structure
was done on an IBM 7094 computer using the full-matrix program
written by Prewitt.19
Atomic scattering factors for Cu 2, 0,
Al+1, P, together with individual isotropic temperature factors,
were used in the first four cycles of least-squares refinement.
The initial temperature coefficients were taken from the pseudomalachite structure,20 for Cu, 0 and P, and from the andalusite21
structure for Al.
These values were 0.5 for Cu, 0.15 for P, 0.6
for 0 and 0.25 for Al.
Only one scale factor for all reflections was used in
the initial stages of the refinement.
No rejection test was in-
cluded, but, at this point, a special weighting scheme was used.
The product of the discrepancy factor of a group of reflections
and the weight of these reflections was maintained constant by
22
this weighting scheme.
It was designed to give a larger weight
L
13
to those structure factors that showed a better agreement, because
this is desirable in the initial stages of the refinement.
One cycle of least-squares refinement, varying the
atomic coordinates and the scale factor but not the temperature
factors, improved the R factor from 27% to 14.2%.
Three more
cycles in the same conditions gave an R of 13.5% and no movement
in the atomic positions larger than the standard deviation was
observed.
At this point the weighting scheme was changed.
All
reflections were given the same weight in order to allow more reflections to influence the refinement.
Three more cycles of re-
finement only improved the R factor to 13.2%.
Two scale factors, one for the reflections measured
with an Al. absorber and one for all the rest, were used from this
point on.
One cycle, varying isotropic temperature factors to-
gether with both scale factors, was run in order to study the
interaction among these parameters.
This was done through the
23
Geller matrix coefficients
finement program.
obtained from the least-squares re-
Rather large correlation coefficients were
obtained for interactions between scale factor (1) and scale
factor (2), and for interactions between scale factors and temperature factors.
Accordingly, the scale factors and tempera-
ture factors were varied in consecutive independent cycles.
After three cycles of refinement of the isotropic
temperature coefficients the discrepancy index R had attained
10%.
A three-dimensional difference-Fourier synthesis was cal-
culated in order to see the hydrogen atoms.
There are eight
-1
Fig . 2
The eight hydrogens of the turquois structure.
HH
H2
HaH
H5
H7
16
hydrogens in the asymmetric unit of turquois, four are attached
to two water molecules and the other four belong to OH radicals;
If those hydrogens were found, it would be the best way to differentiate an OH radical from an H20 molecule.
The difference-synthesis maps showed two types of
anomcllies; these were, peaks in six out of the eight expected
locations of the hydrogens, and also the characteristic combination of positive and negative peaks attributed to anisotropic
motion of the atoms.
Again, no peak that could be interpreted as
the fifth water molecule was found.
When the six hydrogens were
included, but not varied in a final cycle of isotropic refinement, the resulting R factor became 9.5%.
Four cycles of anisotropic refinement with the six
hydrogens, included but not varied, converged to an R factor of
7.2%. During this refinement five oxygens did not maintain a definite positive character, even though their equivalent isotropic
temperature factors were always positive.
This was attributed
to errors in the absorption correction due to the deviation of
the shape of the crystal from a sphere.
A final three-dimensional difference-Fourier synthesis, using the results from the final cycle of anisotropic refinement, with the six hydrogen excluded, was calculated.
The
positions from the six hydrogens plus two others were recovered
from it. The eight hydrogen peaks are shown in Fig. 2. When the
hydrogen coordinates obtained from the last three-dimensional
difference-Fourier synthesis were included in the refinement, a
final discrepancy index of 7% was attained.
17
Table 2
Discrepancy index R for the different stages of determination
and refinement of the structure of turquois
R
Original coordinates
62%
Results of Fourier refinement
27%
Least-squares isotropic refinement
9.5%
Least-squares anisotropic refinement
7%
Results from the refinement
Table 2 lists the discrepancy indices R as obtained
These values were ob-
at the various stages of the refinement.
tained from the relation
FZ
-
F
In Table 3 are listed the final refined coordinates
for the non-hydrogen atoms in turquois together with the standard
deviations as given by the least-squares program.
the refined anysotropic coefficients/
Table 14 lists
for the non-hydrogen
atoms together with the equivalent isotropic temperature factor
as calculated from Hamilton's formula
B3
i
j
ij
(i i .i*)
j
Values marked with a star correspond to those coefficients responsible for the non-definitive positive character of the temperature vibration.
Usually an arbitrary change of approxim-
ately , of the standard deviation will give a positive character.
In
regard to the fact that the absorption correction
was not accurate enough, no attempt was made to interpret the
vibration ellipsoids of the atoms.
The only remark that can be
made is that the Cu vibration is in the direction of the longer
bond (Cu-H 2 0) which is approximately perpendicular to the plane
of the square arrangement of OH radicals.
Table 5 gives the hydrogen coordinates unrefined, as
19
Table 3
Coordinates for the non hydrogen atoms of turquois
z
Atom
Cu
0
0
T(z)
0
Pi
o.3504
0.0006
0.3867
0.0006
0.9429
0.0004
P2
0.8423
0.0006
0.3866
o.ooo5
0.4570
0.0004
At
0.2843
0.0006
0.1766
0.0006
0.7521
0.0005
AL2
0.7520
0.0006
0.1862
o.ooo6
0.2736
0.0005
AL3
0.2448
0.0007
o.5023
0.0007
0.2438
0.0005
0.0675
0.0014
0.3633
0.0014
0.3841
0.0011
02
o.8058
0.0014
0.3435
0.0014
0.6262
0.0011
03
0.2757
0.0663
0.0014
0.3554
0.0014
0.1129
0.0011
0.0015
0.0639
0.0015
0.1973
0.0011
0.2375
0.0015
0.0739
0.0015
0.6287
0.0012
06
07
0.7334
0.2978
0.0014
0.0857
0.0014
0.1243
0.0011
0.0015
0.4016
0.0014
0.6060
0.0011
08
0.3249
0.0014
0.2227
0.0014
0.9049
0.0011
09
0.9857
0.0014
0.2807
0.0014
0.8471
0.0011
010
0.5756
0.0016
o.o467
0.0015
0.6855
0.0012
Oil
0.7866
0.0014
0.4067
0.0015
0.1319
0.0011
012
0.4630
0.0014
0.2950
0.0014
0.3277
0.0011
013
0.7864
0.0014
0.2281
0.0014
0.4323
0.0011
0i4
0.5779
0.0014
0.366o
0.014
o.8987
0.0011
04
20
obtained from the last three-dimensional electron-density function using F0 -F
as coefficients.
An arbitrary isotropic tem-
perature coefficient of 2.0 was assigned to all hydrogens when
included in the refinement, but no attempt was made to change it.
The largest 0-H distance is 1.17 and the shortest
0.72.
Taking the average value 0.95 as the normal 0-H distance,
a standard deviation of the hydrogen coordinates can be estimated
in
0.2A.
bonding.
All 8 hydrogen atoms seem to be involved in hydrogen
Table 6 gives the relation between them and the atoms
they contribute to bind.
Interatomic distances and bond angles were computed
with Shoemaker's program DISTAN.
Interatomic distances are list-
ed on Table 7 and bond angles on Table 8.
In both tables the
atoms designated with a single prime represent the centrosymmetrical equivalent of the unprimed atom whose coordinates are
listed on Table 3, plus or minus a cell translation.
The short
distance 05-06 corresponds to the share edge of the Al and Al
1
2
octahedra.
Fig .
Composition
final
of
3
sections
electron
from
density
the
function
b/2
23
Table
Anisotropic
Atom
4
temperature coefficients.
p..
B
0.0076
1.6
Cu
P1
P220.0079
p33
0.0047
p12
-0.0027
p13
0.0012
p23
-0.0012
P11
0.0015
pz
0.0015
p33
0.0008
s12
-0.0005
P133
-0.0003
p23
-0.0003
P11
0.0012
p22
0.0012
p33
0.0006
P12
piz
-0.0004
-0.0002
P23
-0.0002
P1
P2
0.26
0.21
T"L *0
TONo 00+
Lid
9700 *0+
Zi 00 01400
Z1VO0 *0
.L~d
ZT d
Vd
6000
1o
z000 *0zo00 '0'000 '0
4000 '0
Zoo
s2
0
ZTO
*0
EIV
LeOQO .0Z0 '09000 0-
Ld
Ld
Zd
9i00 '0
9000 '0
6L7 o
zIV
OOO
oioo
Lid
Zid
00
LZd
'0-
'0-
zloo 0
LLd
8000 00
8z00 *0
i i~j
ITV
(I
tUOT0V
t1
25
Atom
p..
B
0.0038
0.56
02
p22
0.0036
p3 3
0.0007*
p12
-0. 0032*
p1 3
0.0016
p23
0.0001
p
0.0032
p22
0.0040
p3 3
0.0011
P12
-0.0027
p1 3
p2 3
0.0019
03
0.62
-0.0003
04
p11
p22
0.0058
p3 3
0.0024
p1 2
-0.0016
p1 3
p2 3
-0.0008
5p
0.82
0.0029
0.0002
0.0048
0.0011
p22
p33
p12
-0.0012
P3
-0.0003
P23
-0.0002
0.0027
0.68
19 *0
1000 '0
9000'0
6000o0
IT
££E00 00
60
1'00, 0
ZTd
1000 0
N1~
000 0-
£L00.0
l£00 '0
17L *0
z1z
80
SLOO '0
s£000 0
17100
91O00
LUd
11700
Z100 .0
98,0o
1z
LE00 *0
1000 0
U
d
CL
d
100 0-
0200 0
99*0
U£00 *0
t-l0o
27
Atom
010
p11
0. 0043
p22
p33
p1 2
0. 0016
0. 0043
-0. 0011
P13
p23
0. 0002
p1
0.0054
p22
p33
p12
0.0018
p13
0.95
0. 0001
0.66
0.0021
-0.0016
0.0008
-0.0001
012
Pli
0. 0016
p22
0. 0026
p33
0. 0025
0.61
-0. 0003
p13
0. 0012
-0. 0010
013
p1
P2
P33
p12
p13
p23
0.0025
0.0038
0.0015
-0.0026
0.0009
0.0003
0.59
28
P..
Atom
O 4
p
0.0007*
P22
0.0042
P33
0.0002*
-0.0015
p13
0.0024
-0.0008
0.41
Table 5
Atomic coordinates of the hydrogen atoms in turquois.
I8
Atom
x
y
z
H
0.8667
0.0333
0.7533
H
0.1500
0.1567
0.1500
H3
0.6333
0.1433
0.5900
H4
0.3933
0.0833
0.2900
H
0 .1433
0.1167
0.5933
H
0.6500
0.1433
0.1000
H7
H8
0.9800
0.4500
0.3500
0.9000
0.2767
0.4233
30
Table 6
Distances in hydrogen bonds.
. . . ....
0.I
4 - H
.
4 - H2
0 10-
H
0 10 -H
3
.4
Ok
0. - H.
02
0. 869
03
1.150
1.901
2. 950
013
1. 172
1.567
2.688
1.004
1.881
2.780
0.743
2.292
2.883
0.716
2.062
2.670
0.844
2.220
2.970
0 .725
2. 173
2. 862
...
1
j
X
k - H
j
2. 067
AX
0-0
k
2. 871
A
0 12
0
- H ......
0 - H4
09- H7
012
0O.
0 11
0
- H8... .. .0 027
31
Fig * 4
The structure of turquois , a axis projection
--.
l
-
.
.
,
33
Ir
Description and discussion of the structure
A final three-dimensional electron-density function
was calculated after the last cycle of refinement of the turquois
A composite of sections of the structure which contains
structure.
maxima, as seen looking down the a axis is shown in Fig. 3.
If
this composite section is compared to the minimum function M (yz)
of Fig. 1, a close correspondence can be recognized.
The false
peak that projects on the inversion center of coordinates (0,I)
on M (yz), is due to the pseudo symmetry C 1 of the crystal.
In
a first approximation turquois can be described as a C-centered
structure with a Cu deficiency in the inversion center (*,
0,
).
Actually the biggest hole in the structure corresponds to this
location, as can be seen from Figs. 4 to 7.
Figure
4 is the interpretation of the three-dimension-
al electron-density function projected parallel to the a axis.
Figures
5
and 6 are views of the structure represented as linked
polyhedra as seen looking in the direction of the a axis.
For
simplicity, the structure has been divided into two parts, centrosymmetrically related.
The first half of the structure, consid-
ered from z = 0 to z = I is represented on Fig. 5; the second half,
from z=
to z =l is represented in Fig. 6.
The structure can be described in terms of single and
double octahedral groups of oxygen atoms, OH radicals, and water
around the aluminum atoms.
The double group consists of two Al
octahedra sharing an edge.
It is linked by four P0
tetrahedra
to the two translational-equivalent groups in the direction of
the b axis.
These tetrahedra are attached to the four free cor-
ners of the square sections with the common edge, as shown in
34
Fig
.
5
Polyhedral chains in turquois. View parallel
to the a axis . Sections from x
=
0 to x - 1/2
bsiny
c sin
36
Fig.
6
Polyhedral chains in turquois. View parallel
to the a axis. Sections from
x= 1/2 to x = 2/2
~7
38
Table
7
The interatomic distances in the turquois structure.
Atom
pair
Multiplicity
Distance
Cu pseudo octahedron
Cu
(H 2 0)
2.422
(OH)
1.915
(OH)
2.109
Cu
-0 6
-0 9
04
-06
2.748
04
-
3.420
Cu
04
016
3.420
-09
3.029
04
06
-09
06
-0
2.690
3.025
9
Al 1 octahedron
Al 1
-05
Al 1
-
(OH)
6 (OH)
1.858
1. 963
Al
-
07
1.812
Al 1
-08
1.817
Al 1
- 0'
Al 1
-
010 (H 2 0)
0 5
-
O76
05
05
05
(OH)
2.011
1.943
2.340
-0 7
- O
0
- 010
2. 623
2.808
2.668
39
Atom
pair
1
- 08
O6
Multiplicity
2.690
- O
O'6
08
07
07
-
0
-o
08
-
2.699
2.722
010
O'6
Distance
10
1
2.834
1
2.675
2.875
08
10
1
2.704
9
1
2.584
1
2.084
At2 octahedron
Al
- O'
Al 2
-
(H2 0)
0'5 (OH)
1.844
Al2 - 06 (OH)
1.963
A12 Al 2 - 012 (OH)
1
1.899
1.832
A12 - O13
O' - '5
04
- 06
O'1 '4-
1.805
2.681
1
2.748
1
2.606
13
2.815
' 5 - 06
2.340
O 5 - 012
2.752
O'5 - 013
0
-O
2.676
06 - 012
11 - 012
1
2.669
2.725
1
2.759
11 -
13
1
2.752
012 -
13
1
2.720
40
Atom
Al
3
pair
Multiplicity
Distance
octahedron
A13 -0 1
Al3 -0'2
A13 -
3
1.903
1.893
1.904
Al 3 - O'9 (OH)
2.164
Al
1.906
- 012 (OH)
3
A13 - O0 14
O
- O
01
2
1.878
2.734
2.593
2.811
02 -O
Of
Of
- O9
O' -O03
2.797
2.702
2.702
012
91
012 -0
3
012
014
O
012
- O3 1
4
2.647
2.730
2.730
2.729
12 1403
O
P
- O'2
2.709
2. 667
tetrahedron
P
- O '3
1.541
P
P
- 08
- O'
1.521
P1
O 11
P1
014
1.539
1.556
41
Atom
013
pair
2.489
O'3
03
~
08
-0
11
4
2.501
2.504
2.531
08
OQ
Distance
2.458
08
-
Multiplicity
- O4
1
2.591
P2 tetrahedron
-
01
1.. 534
-
02
1. 533
-
o'7
1.543
-
013
-
02
2. 527
-
07
2.524
-
0.3
2.528
02
-
0'7
2.507
02
-
01.3
2.470
07
-
01.3
2. 538
P2
P2
P2
P
O'f
O'f
O'f
1. 550
A maximum error of 0. 005 can be assumed on all distances.
4z
Fig
.
7
Polyhedral chains in turquois . View parallel to
the b
axis
C Sina
44
Table 8
Bond angles in the turquois structure.
Atoms,
Multiplicity
Angle
Cu pseudo octahedron
0'6 - Cu -O
(H2O)
O' 6 - Cu - O14 (H 2 0)
77.40
102. 60
O'
- Cu -
0'
- Cu - O'4 (H 2 0)
83. 30
06
- Cu - O'9
96. 50
O'6 - Cu - O'9
83.50
4 (H 2 0)
96. 70
Al 1 octahedron
05 - Al
05 - Al
- 0'6
O 6-
06 - Al
- 08
07 - Al
- 08
0 5 - Al 1- 0 9
7 ~
1 - 98
o'6
75. 60
91.40
90.80
102. 20
93. 30
85. 20
0
- Al
- O
97.30
0
- Al
- O
84. 60
05 -
l1-
O'6 07 - A
08 -Al
0 10 (H2O)
89. 00
(H2O)
010
9
(H2O)
10
9
- 010 (H2O)
88. 00
90. 30
91.30
(shared edge)
4.5
Multiplicity
Atoms
'9 - A1 - 010 (H2O)
O'6
05
1
7
-Al - 08
Angle
172. 0
166. 90
166.40
Al2 octahedron
85. 30
04- Al2
0
4
- Al2
06
06
05 - A2
06-- Al
Al2 0
4
2
0 - Al 2
6
0' - Al
5
2
- Al
O
6
2
-Al
0
11
2
0- Al
2
4
011
75.7 0
83. 20
90. 0
012
94.40
012
89. 90
012
96.00
013
91. 30
013
05
2
013
-A1l
0
11
2 -0O
13
012 -A2
011
O5 -A2
O0
- At2 012
06
85.20
013
2
93.40
100.20
93.70
162.40
175. 0
168.80
Al3 octahedron
0
1
- Al
3
13
1
- Al3
1
3
0' - Al
3
2
-A1l
0
3
3
0
-
-
01 2
92.40
-
03
85. 90
01
91.8
~09
89.40
-0 9
019
87.20
(shared edge)
46
Multiplicity
Atoms
01
Al
O 2
3
A.13
03
Al 3
O'2
Al 3
0 3
Angle
0
012
88.
012
92. 00
012
91. 50
Of 1
90.20
01 14
91. 50
O'
88. 00
019
Al 3
Al 3
01.2
Al 3
012
O' 2
03
176. 1
019
Al
.3
Al
0 12
178.6
01
Al 3
014
177.40
P
01 14
92.1
tetrahedron
013 ~
01
0
11.4
3
8
01
3
106. 80
1 - 08
- P
1
-P
1
- P
- O'
-0O'
11
11
-O
1.
1.4
-0O
0
-P
8
.
1.4
-0O
0'
-P
1.1
1.
1.4
107.80
109.80
107.70
110.70
113.70
P2 tetrahedron
O'f
01
02
01
02
2
2
-P
- O'
2
7
- P -0'
2
7
2
13
2
13
110.60
110.70
109.70
110.00
105.60
f7
Atoms
O'
- P2 - 013
Multiplicity
Angle
1
110.10
1
143.40
Oxygen coordination angle
- Al3
P'2 - O
P2
-O 2 - Al'3
1
134.10
P'
- O3 - Al3
1
133.20
- A2
1
88.20
1
108.10
1
98.60
-O 6 - Al'2
1
108.40
Al'1 - 06 - Al2
1
99.80
P' 2 - 07 - Al 1
1
Cu -O
(H 20)
Al1 - 05 - Al'2
Cu' -0
Cu
P1
6
- Al 1
- Al
Cu' - 0
- Al'3
Al
140.20
- 08 - Al
Cu' - O'
140.1
1
91.30
130.90
- 0'
- Al'3
I
-0
- Al
-
129.9"
-
(H2O)
P'
I
137.30
Al2 - 012 - Al3
1
138.80
0 13 - Al2
1
135.70
1
139.60
P2
P
- 01
- 0
- Al
- Al'3
--------
48
Figs.
5 to 7.
The single aluminum octahedron shares the four oxy-
gens at the corners of a square section with four PO
tetrahedra.
Of the two remaining vertices, one is shared with the double octahedral group, and the other is also common to an octahedron of the
double group and to the Cu octahedron.
There are only two OH
radicals in the asymmetric unit that are common to the coordination polyhedra of three cations.
One is OH(6), in the shared
edge of the double group which also belongs to the Cu polyhedron.
The other is OH(9), common to one single octahedral group, to a
double octahedral group, and to the Cu octahedron.
The Cu octahedron has the expected
predicted by the Jahn-Teller effect.
18
4+
2 coordination
The square coordination
is formed by two OH radicals and their centrosymetrical equivalents.
The two long bonds are directed to two water molecules,
related by an inversion center, which also integrate the Al(2)
octahedron.
The location of the water molecules in the Cu coordination agrees with the distribution found in eucroite26 and liro27
28
conite.
However, the results reported for krbhnkite
place
the H 0 molecules as integrating the square coordination of the
2
Cu.
The values of the interatomic distances and angles
for the PO
tetrahedra agree well with the reported values in
related compounds.
The single Al octahedron is also regular;
the average Al-O distance is 1.94A, the longest value is 2.164A
0
and the shortest value is 1#878A.
The average octahedral angle
49
for the single octahedron is 90.01
85.9
0
to 92.5
with values ranging from
0
The larger departures from regularity are found in
the interatomic distances and angles of the double octahedral
group.
The shared edge 0506 shows an extremely short bond dis-
tance of 2.34 0A, coupled with octahedral
angles 75.7 (0 -Al -0 )
for
and 75.6 (05~l1~.06 ). Bonds of 2.43 02had been reported5221
shared octahedral edges in andalusite
and in anatase and ru29
but they are seldom found. A possible reason for this
tile,
rather remarkable distortion is that the double octahedral group
also has two edges (one from each octahedron) in common with the
Cu pseudo octahedron.
These edges are 0 -0
06-0
of the Al2 octahedron.
of the Al
octahedron and
2
One of the OH radicals (06) be-
6 4
longing to the share edge also integrates the Cu square coordination, thus becoming one of the two anions actually bonded to
three cations.
The second negative ion coordinated to three
cations is 09.
It can be observed from Table 8, that the oxygen
bond angles which agree the least with the ideal values are the
ones including 0
6
and 0 .
9
The only exception is the value 88.20
for one of the water molecules, in the coordination angle Cu 0
- A12.
so
Acknowiedgements
The author wishes to thank Professor M.J. Buerger of
the Massachusetts Institute of Technology for his constant
encouragement and helpful suggestions and Dr. C.T.Prewitt of
E.I. Du Pont de Nemours for making the piezoelectric test .
Professor C. Frondel from Harvard University and Dr. G.Switzer
of the U.S. National Museum kindly provided the turquois
crystals used in this investigation . This work was done while
the author was on leave of absence from the Laboratorio de Cristalograff a de la Universidad de Chile under an OAS fellowship.
All the computations were carried out on the IBM 7094 computer
of the Computation Center of the Massachusetts Institute of
Technology. The work was partially supported by a grant of the
National Science Foundation.
51
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52
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Subrata Ghose.
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Act Uryst. 16
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Charles W. Burnham and M.J. Buerger.
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Bernhardt J. Wuensch.
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David P. Shoemaker.
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53
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Period. Mineral 31 No. 1 (1962) 19-42.
28.
B. Rama Rao. Die Verfeinerung der Kristallstruktur von
Krohnkit, N 2 Cu(SO4 )2 w 2H2 0'
Acta Cryst
29.
-
14 (1961) 738-743.
Ralph W.G. Wyckoff. Crystal structures, vol. 1 (1963).
Interscience Publishers, 2d ed. 252-255.
A
54Part I-B
X-ray study of chalcosiderite, CuFe6 (P4 4 (OH) .4H 0
8
2
By Hilda Cid-Dresdner
Massachusetts Institute of Technology
Cambridge,
Massachusetts
Abstract
Chalcosiderite is triclinic, space group P1, with cell
dimensions a = 7.68A, b - 7.82A, c :10.21A, c - 67.50, /3= 69.10,
X-ray rotation and Weissenberg photographs show the
'e= 64.8.0
existence of two slightly different lattices for each chalcosiderite
crystal. A possible interpretation for the phenomenon is given.
Introduction
Chalcosideritel,2 is related to turquois by isomorphous substitution of Al by Fe. The structure of turquois was
recently determined by the author , and a determination of the
structure of chalcosiderite was considered desirable. Chalcosiderite crystals from West Phoenix, England, were kindly provided
by Professor Clifford Frondel of Harvard University for this investigation.
Precession work
Several single crystals of chalcosiderite were examined optically before one satisfactory for x-ray study was
found. The crystals tend to form groups in which they maintain
nearly parallel orientations, building a sort of sheaf.
The
Fig . 1
Rotation photograph of chalcosiderite
56
smaller crystals presented rounded faces which were mostly striated, but the striations disappeared when the crystal was immersed
in a liquid with a refractive index similar to its own.
A small crystal which gave good extinction under the
polarizing microscope was chosen for the determination of the lattice constants.
The crystal was oriented on the optical gonio-
meter so that a normal to one of the best-developed faces was
parallel to the spindle axis.
The crystal was then transferred
to the procession camera and the orientation was corrected by
Evans' method*
Two precession photographs were taken using as precessing axes the crystallographic directions analogous to the a
and b axes of turquois.3
As expected, the reduced cell56 of
chalcosiderite retained the orientation of the turquois cell.
The relations of the reduced cell of chalcosiderite with respect
to the previous cells reported by Maskelyne1 and Graham
given on Table 1.
are
The transformation matrices for chalcosiderite
are identical to the transformation formulas used for turquois 3
to obtain Schaller's2 and Grahams 7 settings.
This is due to
the fact that both authors2,7 based their choice of the turquois
cell on the values reported for chalcosiderite.
Table 2 gives the lattice constants for chalcosider.ite obtained from precession photographs.
Graham's values for
chalcosiderite and the turquois parameters are also included for
comparison.
The isomorphism of both minerals is evident from
the similarity of the lattice constants.
5S
Fig.
2
Zero - level Weissenberg photograph of chalcosiderite.
b is the rotation axis
59
-4
60
Table 1
Direct and inverse transformations for the three
reported unit cells of chalcosiderite
Direct transformation
Inverse transformation
1
-1
Maskelyne to
Graham
0
1
0
01
0
Graham to
Cid-Dresdner
1
-l
0
10
1
0
0
0
01
0
-ol
1
0
0
0
-l
Maskelyne to
Cid-Dresdner
0
1
0
0 -*1
0
o11
61
Table 2
Comparison of chalcosiderite and turquois unit cells
Turquois
Chalcosiderite
Graham
Cid Dresdner
Graham
Cid Dresdner
7.46AX
7.424A
7.65A
7.629A
9.031
9.910AO
a
7 .68A
b
7.90A
c
10.20A
10.21
68 *35
68.610
69.00
67.5"0
69.1 0
69.430
69.710
64.70
64.80
64.620
65.080
0
0
7. 82A
0
62
Cylindrical-film measurements
In
order to transfer the chalcosiderite crystal to
the single-crystal counter diffractomer, a reorientation of the
crystal was necessary.
The orientation was made by the use of
the double-oscillation technique of Weiss and Cole.
A rotation
photograph of the chalcosiderite crystal showed the existence of
two parallel lattice translations of similar dimensions.
One of
them corresponded to the value of the b axis determined by precession photographs.
The other was a slightly smaller translation
and included the weaker diffraction spots (Fig. 1).
A zero-
level Weissenberg photograph (Fig. 2) of the same crystal also
showed the existence of the slightly smaller lattice.
In order to understand the relationship between the
two lattices, the Weissenberg photograph of Fig. 2 was plotted
in reciprocal space, as shown in Fig. 3. When the data from the
rotation and the Weissenberg photographs were combined, it
turned out that the parameters corresponding to the smaller
translations were very close to the turquois lattice constants.
Table 3 compares the results of the cylindrical film method with
the previous known data for chalcosiderite and turquois.
The
comparison is made in terms of reciprocal-lattice constants
since no information about the other two angles was included in
these photographs.
The results from Table 3 pointed out that the "single" crystals of chalcosiderite also include turquois crystals.
A well-known mechanism that could explain this fact is epitaxial
growth of turquois on chalcosiderite.
Attempts were made to see
the two minerals under the polarizing microscope.
It was thought
63
Fig * 3
The two reciprocal lattices of the chalcosiderite
crystal
64-
-a'
65
Table 3
Identification of the two lattices found in rotating crystal photographs of
chalcosiderite.
Lattice I
Chalcosiderite
Turquois
0.230 r.1. u.
0.238 r. 1. u.
0.228
0.2353
0.168 r. 1. u.
0.173 r.1.u.
0.169
0.1721
102 0'
7.856 R
t
Lattice 2
103015,
1020301
7.620
A
7.82
A
From precession photographs
$From back-reflection Weissenberg least-squares method
1030
7. 629
X
~
-
66
that it should be possible to differentiate between the refractive indexes of chalcosiderite and turquois.
Chalcosiderate's
lowest refractive index is 1.775 and turquois' highest index of
refraction is 1.65.
Chalcosiderite crystals were immersed in a
liquid of refractive index 1.75 to look for an edge that would
possibly show a lower index.
Even if this was actually observed
in some cases, the evidence was not considered conclusive due to
the limitations of the method used. 9
Four other crystals were examined by x-ray methods.
All of them presented evidence of the existence of the two structures.
Two of those crystals were cut but in both cases the
useable fragments still showed the two characteristic translations corresponding to turquois and chalcosiderite.
Under these conditions the structural study of chalcosiderite was postponed.
It is, however, certain that chalco-
siderite and turquois have the same structure.
Both of the re-
placeable elements accept octahedral coordination.
The reported
Fe-C distance for Fe in octahedral coordination 1 0 '1 1 is 2.02A,
while the average Al-0 in octahedral coordination is
1.9R.
This
difference could very well account for the larger cell presented
by chalcosiderite.
Acknowledgements
The author wishes to thank Professor M.J. Buerger
from the Massachusetts Institute of Technology for his interest
in this work and many helpful suggestions.
While this work was
done the author was on leave of absence from the Universidad de
Chile, Santiago, Chile under an OAS fellowship.
This work was
6?
partially supported by a grant from the National Science Foundation.
68
References
1
Maskelyne, N.S. (1875). On andrewsite and chalcosiderite.
Jour. Chem. Soc. London, 28, 586-591.
2
Schaller, W.T. (1912). Crystallized turquois from Virginia.
Am. Jour. Sci. 33, 35-40.
3
Cid-Dresdner, H. (1964). The determination and refinement of
the crystal structure of turquois, Cu A1 6 (PO4)4 (OH)8
. 4H2). In preparation.
4
Evans, Jr., H.T., Tilden, S.G., Adams, D.P. (1949). New
Techniques applied to the Buerger precession camera
for x-ray diffraction studies. Rev. Sci. Inst. 20,
155-159.
5
Buerger, M.J. (1957).
42-60.
6
Balashov, V. (1956).
The choice of the reduced cell in the
triclinic system. Acta Cryst. 9, 319-320.
7
Graham,
Reduced cells.
Z. Kristallogr. 109,
X-ray study of chalcosiderite and
A.R. (1948).
turquois. Univ. Toronto Studies, Geol. Ser., No.
52,39-53.
8 Weiss, 0., Cole, W.F. (1948).
An improved technique for
setting single crystals from zero layer-line photographs. J. Sci. Instrum. 25, 213-214.
9
Walstrom, E.E. (1943).
Optical crystallography.
10
Ito, T., Mori, H. (1951). The crystal structure of ludlamite. Acta Cryst. 4, 412-416.
11
Mori, H., Ito, T. (1950). The structure of vivianite and
symphlesite. Acta Cryst. 3, 1-6.
69
Part I-C
An improved pinhole system for single-crystal
x-ray diffraction work
By Hilda Cid-Dresdner
Crystallographic Laboratory
Massachusetts Institute of Technology
Abstract
A collimator system consisting of a borehole in a
solid aluminum rod is proposed for use in single-crystal x-ray
diffraction work.
Such a collimator is free from the fluores-
cent-scattering characteristic of the usual lead-pinhole systems
and therefore insures a lower background for reflections of small
sin Q values.
Introduction
Some precession photographs, which were made using
abnormally long exposures because of the tiny specimens, showed
circular blackened areas centered in the direct-beam location.
Examination of other precession photographs showed the same feature except that, due to much shorter exposures, it was subdued
and, hence, had been overlooked.
It was evident that the pheno-
menon was inherent in the experimental conditions currently used
in taking precession photographs.
In order to determine the origin of the dark circle
careful measurements of its diameter were made on precession
photographs taken under different conditions.
It was found that
the diameter of the shadow did not depend on the value of the
precessing angle or on the presence of a layer-line screen, but
70
was a function of the position of the film.
The dark area seemed
to be produced by a point source located at a constant distance
from the crystal.
The position of this point source was determined from
two values of the shadow diameter measured at two known crystalto-film distances.
The proportion:
D2
Dy
2
where D and D
distances d
crystal.
are the diameters measured for crystal-to-film
and d2, gives the distance x from the source to the
For the type of collimator used, the position of the
source was found to coincide with the second pinhole of the system.
We considered several interpretations of this phenomenon.
A possible explanation might be that some radiation, strik-
ing the interior of the tube in which the pinholes were mounted,
may have been scattered from the interior of the tube, through
the second pinhole, to the film.
In this case the dark circle
would be the part of the x-ray cone limited by the guard slit.
To test this hypothesis an experimental pinhole system was designed which permitted the use of several intermediate baffle pinholes to eliminate the possibility of internal reflection.
The
circular shadow was not changed by this procedure.
The second and more reasonable explanation was that
fluorescent radiation was emitted by the second lead slit, and it
was limited by the guard slit.
Figure 2 is a graph of the absorp-
tion coefficient of lead for different wave lengths; the spectral
Fig . 1
The absorption of the Mo radiation by lead
300
Mo
Kcc
200
too
11o white radiation
at
.3
.A
.'
.
7
.1
1- .0
1
.2
1.3
3S k V.
1.4
T3
distribution of the Mo radiation is also included.
from this graph that Pb strongly absorbs the MoK
It is evident
radiation and a
good amount of the white radiation, this energy being released as
fluorescent radiation.
If an element heavier than lead were used to make the
second pinhole in the collimator system, the situation would not
be very much improved.
The absorption of the Mo radiation by
this element would be smaller, and consequently the intensity of
the fluorescent radiation emitted would also be smaller.
Never-
theless, the fluorescent radiation would have a shorter wavelength and the absorption of it
by the air would be minimized.
On the other hand if the second pinhole were made of a sufficiently light element its fluorescent radiation would be expected
to be strongly absorbed by air before reaching the film.
In
order that a system made in this way would still be able to limit
the Mo x-ray beam, a solid rod, instead of limiting slits, should
be employed.
A number of experimental pinhole systems made with
elements of atomic numbers less than 82 were tried; the results
for four of them are shown in Fig. 2. The aluminum pinhole system gives the most satisfactory results.
The graphite rod was
not able to completely absorb the direct beam so that the film
showed powder rings from the carbon itself.
This work was partially supported by a grant from the
National Science Foundation.
The author was the holder of a fel-
lowship from the Organization of American States, and was on leave
of absence from the Laboratorio de Cristalografia of the Universidad de Chile, Santiago, Chile.
74
Fig . 2
Results from four experimental pinhole systems
T5
Brass
Groj&h. ie
At vnovvn
76
APPENDICES
T7
Appendix I-A
a.
The minerals of the turquois group
The turquois group includes two series of minerals.
The turquois chalcosiderite series is formed by isomorphous substitution of Al by Fe.
The known members of the series are:
turquois,12,3 henwoodit,
rashleighite,5 alumo-chalcosiderite
and chalcosiderite.
The second series is the turquois-
faustite9 series,
6
formed by isomorphous substitution of Zn by
Cu.
A summary of the physical and chemical properties
known from the minerals of this group,
follows in Table 1.
Further possibilities of study: Chalcosiderite
crystals are not good enough for an independent structure determination.
Nevertheless, single-crystal counter-data using
iron radiation could be collected for reflections with sinG large
enough to completely resolve the two maxima.
The data obtained
in this way could be used to attempt a least-squares refinement
using turquois coordinates as a starting point.
Another possi-
bility would be to build up a three-dimensional differenceFourier syntheses using as coefficients (Fobs)turquois-(Fobs)
chalcosiderite).
A third possibility is to calculate an electron
density function with the available values of Fobd, for chalcosiderite combined with the corresponding turquois signs.
From the comparison of the x-ray diffraction spectra
obtained for chalcosiderite and turquois, it is certain that both
minerals have the same structure.
A prediction can be made, how-
Table 1
Available data for the minerals of the
turquois
Mineral
Optical data
Density
Turquoi s
2.84
Henwoodit
2.67
group.
X-ray data
nx
ny
nz
2V
1.61
1.62
1.65 220
powder
single crystal
no single
crystal
Rashleighite
no single
crystal
Alumo-chalcosiderite
no single
crystal
Chatco siderite
3.22
Faustite
2. 92
1. 775
1. 84 1. 844 400
1. 613 (average)
no single
crystal
Results
cell dimensions
structure
ever, that any departure of the chalcosiderite structure from the
turquois model will tend to improve the oxygen packing.
This
prediction is based on the comparison of the refractive indices
for chalcosiderite and turquois.
The rest of the group do not present single crystals,
and this is the reason why their unit cells are not yet known.
Available powder diagrams show very close correspondence with
the turquois diagram in both position and intensity, revealing
that they are probably isostructures with turquois.
The only
possible way to prove this would be to collect good counter data
for rashleghite, henwoodite and faustite using a powder diffractomer.
In order to index these reflections a turquois standard
should be run in the same conditions.
Since the lattice constants
for turquois are known, the values of sin 0 for any reflection
10
can be calculated
using Prewitt's program. By comparison, the
maxima could be indexed.
Given (hkl) and d
it should be poshkl
sible to determine the lattice parameters by a l.s.p.
References
1.
Waldemar T. Schaller. Crystallized turquois from Virginia.
Am. Jour. Sci. 2
35-40.
2.
A.R. Graham. X-ray studies of chalcosiderite and turquois.
Univ. Toronto Studies Geol. Ser. 52 (1948) 39-53.
3.
Hilda Cid-Dresdner. The determination and refinement of
the crystal structure of turquois, CuAl (PO4)4
(OH)8 .4H2 0'
6
In preparation.
4.
E. Fischer. Henwoodit, ein Glied der Turkis-ChalcosideritReihe.
Chemie der Erde 21 (1961) 97-110.
5.
Arthur Russel, Bart. On rashleighite, a new mineral from
Cornwall, intermediate between turquois and chalcosiderite.
Min. Mag. 28 (1948) 353-388.
so
6. A. Jahn and E. Gruner.
Saxony.
Mitt.
Vogtland.
Alumo-chalkosiderit, Schnekenstein,
Gesell. Naturfor.
1 (1933)
19.
7. N.S. Maskelyne.
On andrewsite and chalkosiderite.
Jour. Chem. Soc. London 28 (1875) 586-591.
8. Hilda Cid-Dresdner.
X-ray study of chalcosiderite.
In preparation.
9. Richard C. Erd, Maragaret D. Foster and Paul D. Proctor.
Faustite, a new mineral, the zinc analog of turquois.
Am. Min. 38 (1953) 964-971.
10.
C.T. Prewitt. The parameters T and f for equi-inclination
with application to the single crystal-counter diffractomer.
F. Kristallogr. l4 (1960) 355-360.
+2
b.
The anion configuration around the Cu
ion.
Cu+2ion conforms itself to a distorted octahedral
coordination.
It has four nearest neighbors at the corners of a
square, with copper-anion distances regularly of the order of
2.0A.
Two farther neighbors complete the octahedron at dis-
tances going from 2.4 to 2.7A, in a few cases still larger.
This special type of distortion is predicted by a
theorem formally proved by Jahn and Teller in 1937.
This theorem
states that any non-linear molecular system in a degenerate electronic state will be unstable and will undergo some kind of distortion that will lower its symmetry. The Jahn-Teller theorem
has a direct application to the Cu+2 ion placed in the center of
an octahedron of anions.
Cu+2 has the configuration
s22s2 p63s2 6d9.
The
nine d electrons are distributed in the five d orbitals.
Because
of the presence of the negative ions surrounding the metal, the
five d orbitals are no longer equivalents.
The orbitals in which
the electrons can be as far as possible from the negative ions,
namely dxy , d
dYZ, become the most favourable.
In the two remaining orbitals, dz2 and dx
2, the
electrons are exactly located in the direction of the anioncation bond, thus screening their interaction.
Consequently,
three electron pairs of the Cu +2ion always occupy the three
favourable orbitals,
and one of the unfavourable orbitals will
be occupied by a single electron.
If
d 2
2 is
the orbital that
gets the single electron, the cation-anion attraction will be
-
-
82
Table 2
The Cu+2 coordination.
Compound
Nearest neighbors
Farther neighbors
Atacamite
Cu - OH
2.04 (X2)
Cu
CuC1 2 3Cu(OH 2 )
Cu
2. 00 (X2)
- OH
2.76 (X2)
Cl
-
Cu
- OH
1. 94 ER(X2)
Cu
- OH
2.36
Cu
- OH
2.07 k(X2)
Cu
- Cl
2.75
Cu - O
2.41 (X2)
Krohenkite
Cu - O
2.14 (X2)
Na2 Cu(SO )2- 2H 2 0
Cu - H O
2. 05 (X2)
Cu - N
2. 06 (X2)
Cu -H2O
3.37
Cu - N
2.04 (X2)
Cu -H2O
2.59
1.98 (X2)
Cu -O
2. 90 (X2)
Cu(NH 3
4
SO*-HO
-OH
Azurite
Cu
Cu 3 (OH) 2 (CO3)2
Cu -O
1.88 (X2)
Cu
2. 04.R
- OH'
CuTI-
OH'''
1.99
Cu 11-
O'''
1.92
CuII - o
Cu
'
-0
2.38
2.83
2.01
Brochantite
Cu 4 (OH) 6
4
Cu
-OH "
1.98 (X2)
Cu-
Cu
- OH'
2.05 (X2)
Cu-
Cum - OH
1. 99 (X2)
Cui
- OH'
2. 02 (X2)
CuII
O
2.38
a
0-
-O
2.35
2.32
2.52
Reference
number
85
Compound
Nearest neighbors
Cu 2 (OH) 3 Br
Cu
-OH
Farther neighbors
1. 92 (X2)
Cu -Br
2. 93 (X2)
1. 93 (X2)
Cu
-OH
2. 05 (X2)
Cu
- OH
2.41
Cu
-I OHI
2.01
Cu
- Br
2.80
2.05
CuOHC1
-Cl
2.30
Cu - Cl
2.73
Cu -OH
2.01
Cu - Cl1
2.70
Cu -OH
2.03
Cu
2.0
1. 96 (X2)
Cu - OH
2.30
2.06 (X2)
Cu - OH
2.49
Cu - 0
2.33
Cu - O
2.37
Cu - 0 1
2. 37 (X2)
Cu - 0 1 1
2. 41 (X2)
Cu - O
2. 53 (X2)
Cu
-
OHm
Antlerite
Cu 3 (SO )(OH) 4
CuSO 4
Cu
- OHm
Cu
-O
1.90
Cu
- OH'
1.96
Cu
- OH"
1.97
Cu
- OH"'"
1.97
X
(x2)
Cu - O11
2.00
Cu - Om
1.89
Cu - Om
1. 99 (x2)
Cu -H20
1. 95 (X2)
Cu
-
(OH)1
1. 93 (X2)
Cu
-
(OH)1
1. 98 (X2)
(x2)
Kr Bhnkit
Na 2 Cu(SO )2 2H2 0
Linarit
PbCuSO4 (OH)
2
Reference
number
84
Compound
Nearest neighbors
Reference
number
Farther neighbors
' 12
S.alesite
CuIO 3(OH)
k (X2)
X
Cu - (OH)
1. 95
Cu - 0 1 1
2. 01 (X2)
Cu - O
1. 86 (X2)
Cu - O
I
2. 06 (X2)
Cu - OH
1. 93 (X2)
Cu - OH I
1. 96 (X2)
Cu - 0
1.99
Cu -0
Cu - O 1 1
1.79
Cu - Ov(H2O) 3.34
Cu - Om
1.93
Cu - 0
2. 59
1
(x2)
Dolerophanit
Cu 2O(SO )
Cu - O 1
2. 53 (X2)
Cu - O
2.47 (X2)
Linarite
PbCu(SO )(OH)2
Teineit
CuTeO 32H2 0
1
(H 2 O)
Cu - O
(H2 0)
2.35
1.97
Liroconite
Cu 2 Al[ (As 1 P)O 4
(OH) 4 ] - 4H 2 0
Cu - O 1 1
1.99
Cu -0
(H2 0) 2.76
Cu - O
1.98
Cu - O
(H2 0)2.46
Cu - 0
11
1.87
1
Cu - ON
1.94
Eurcroite
Cu 2 (AsO4 )(OH)- 3H 0 Cu, ON
2
Cu - O
Cu - O
Cu - O
1.92
CuI - O
2.08
Cu
1.96
2.01
I
- 0
(H 0) 2.51
VI
(H 0) 2. 42
2
85
Compound
Nearest neighbors
Farther neighbors,
Cu
- 0 1 (H 20) 1.99XA
Cu
-o
Cu
-O
1.97
Cu
-O
Cu
- O
1.92
Cu
-o
2.01
Reference
number
(H2O) 2.74,
2.47
Pseudomalachite
Cu 5 (PO) 2 (OH) 4
Cu
-
(OH)1
Cu
-OH)
Cu
CU
-O
- II
Cu
-
Cu- ON
2. 69 (X2)
1.91
Cu
-O
2.39
2.02
Cu
- ON
2.70
2.02 (X2)
1. 94 (X2)
(OH)
1.98
Cu
- (OH)1
1.99
Cu
-
(OH
2.00
Cu
1.94
Cu
-O
- (OH)
Cu
- (OH)
1.96
,Cu
-
Cu - O
2.36
2.51
1.95
Turquois
CuA16 (PO 4 ) 4 (OH) 8 '
4H2 0
Cu - Ov
(OH) 1. 92 (X2)
Cu - OIX (OH)2. 11 (X2)
Cu - O
(H 2 0)
2. 42 (X2)
86
more screened along the z axis, and the octahedron will become
elongated in the z direction.
If d 2 is singly occupied, the
octahedron will become shortened in the z direction.
In all the Cu compounds listed on Table 2 the octahedron has become elongated in the z direction.
This probably
is the best proof that the elongated octahedron represents a
lower energy state compared to the shortened octPhedron.
It is interesting to observe in Table 2 the disposition that the water molecules of the hydrated compounds take in
the Cu coordination polyhedron.
The water molecule can go eith-
er in the square coordination or become one of the farther neighbors in the Cu polyhedron.
The common feature to its behavior
is that always the water presents only one tight bond to a cation,
if
any.
87
References
1.
A.F. Wells. Crystal structure of atacamite and crystal
chemistry of cupric compounds.
Acta Cryst. 2 (1949) 175-180.
2.
M. Leone and F. Sgarlata. Struttura della kroehnkite e
contributto alla cristallo chimica del rame.
Period. Mineral 23 (1954) 223-233.
3.
F. Mazzi. The crystal structure of Cu(NH 3)4 So4 H 20.
Acta Cryst. 8 (1955) 137-141.
4.
G. Gattow und J. Zemann. Neubestimmung der Kristallstrukter von Azurit, Cu 3 (OH2 )C03 )*
Acta Cryst. 11 (1958) 866-870.
5,
G. Cocco and F. Mazzi. La struttura della brochantite.
Period. Mineral 28 (1959) 121-149.
6.
H.R. Oswala, Y. Iitaka, S. Locchi und A. Ludi. Die Kristall strukturen von Cu2 (OH)3 Br und Cu2 (OH)3J*
Helvetica chim. acta "j No. 7 (1961) 2103-2109.
7,
Y. Iitaka, S. Locchi und H.R. Oswald. Die Kristallstruktur von CuOHCl.
Helvetica chim.acta. 4, n. 7 (1961) 2095-2103.
8. Takaharu Araki.
Min.
9.
The crystal structure of antlerite.
Jour. 3 (1961) 223-235.
B. Rama Rao. A note on the crystal structure of anhydrous
copper sulphate.
Acta Cryst. 14 (1961) 321.
10.
B. Rama Rao. Die Verfeinerung der Kristallstruktur von
Kroehnkit, Na 2 Cu(S04 )2 .2H 2 0*
Acts Cryst. l4 (1961) 738-743.
11.
H.G. Bachmann und J. Zemann. Die Kristallstruktur von
Linarit, PbCuSO 4 (OH) *
2
Acta Cryst. l4 (1961) 747-753.
12.
Subrata Ghose.
CuIO 3 (OH).
The crystal structure of salesite,
Acta Cryst.
13.
15 (1962)
1105-1109.
Die Kristallstruktur von Dolerophanit,
E. Kahler.
Cu 2 0(SO4 ) ein Beispiel fur s-koordiniertes Kupfer.
Die Naturwissenschaften 13 (1962)
14.
1-3.
Takaharu Araki. The crystal structure of linarite, reexamined. Min. Jour. 3 (1962) 282-295.
T
8
15.
Die Kristallstruktur von
Anna Zemann und J. Zemann.
die Korrektur einer chemisfur
Beispiel
Fin
Teineit.
chen Formel auf Grund der Strukturbestimmung.
Acta Cryst. 15 (1962) 698-702.
16.
G. Guiseppetti - A. Coda - F. Mazzi -
C. Tadini.
La strut-
tura crystallina della liroconite, Cu2 Al[(As P)O
(OH) 1.
4H2r)*
Period. Mineral, 31 (1962) 19-42.
17.
Guiseppe Guiseppetti. La struttura cristallina dell'eucroite
Cu 2 (A3 04 )(OH).3H 2 0'
Period. Mineral. 32 (1963) 131-156.
18.
Subrata Ghose. The crystal structure of pseudomalachite,
Cu5(PO42(O)2*
Acta Cryst. 16 (1963) 124.
19.
Hilda Cid-Dresdner. The determination and refinement of
the crystal structure of turquois, CuA16(POh44(OH)s.
4H 2 0.
In preparation.
89
Appendix I-B
Interpretation of the first electron density (>ljxyz) function
in the solution of the crystal structure of turquois
In the course of the crystal structure determination
of turquois, the first electron-density function was calculated
using positive signs for all the structure factors.
This assump-
tion was based on the consideration that the positive contributions from the Cu atom located at the origin would control most
of the signs.
This section intends to give the successive steps
followed in the interpretation of this electron density function
leading to the solutioa of the structure of turquois.
Table 1 lists the eighteen highest peaks of a threedimensional electron density function calculated with all signs
positive.
The coordinates of the peak maxima in Fl(Xz) are
given in one thirtieths of the cell edges, since this was the
interval used for the calculation of all Patterson and electron
density maps.
To a first approximation, the five highest peaks
should correspond to the three Al and two P of the asymmetric
unit.
If the relative heights were taken into account, peaks
3 and 8 should be P and peaks 1, 16 and 17 should be Al.
A more careful study showed that peak 1 could not be
anything else but an oxygen because its distance to the Cu atom
was approximately 2A,
too short for an Al-Cu distance but just
right for an 0-Cu distance.
Also, since peak
8
showed a square
arrangement of peaks around it at distances close enough to the
length of the Al-0 bond, it was chosen as an Al.
Moreover, peak
90
Fig . l
Results from the electron density function
f
( xyz)
Composite of sections showing the peaks chosen as
All,
P
and
P',
( peak 12)
ZA
"-0lo
17 showed a nice tetrahedral coordination and was chosen as the
P. Figure 1 is a composite of sections of
1 xyz)
environment of the peaks chosen as A 1(peak 8),
showing the
P1 (peak 3), and
Pi(peak 12).
The highest peaks left to be considered for the third
aluminum were peaks 10, 13, 15 and 18.
Peak 13 was discarded be-
cause it was too close to peak 8 to give a correct Al-Al distance.
Peak 10 was chosen as the third aluminum since it ful-
filled the condition of homogeneous distribution of the aluminum
through the cell.
It also corresponded to one of the strong
peaks in the minimum function M 4 (yz) which was always used as
a check.
Peak 18 was chosen as the second aluminum atom instead
of peak 16 because it showed a good octahedral environment; also,
it was at the right distance to share one oxygen with each of P2
and Cu.
Figure 2 shows the aspect of the peaks chosen as Al(2),
Al(3) and P(2) together with the peaks that were assumed to represent some of the oxygens from their coordination polyhedra.
The coordinates of a model structure, including the six cations
and thirteen possible oxygens, were submitted for structurefactor calculation; this gave an R factor of 62%.
The signs de-
termined by this model were used to calculate a second threedimensional electron density
function, f2(xyz)
The main changes inferred from the electron density
were:
a.
Four out of the thirteen oxygen atoms included came back
at approximately half of the height of the average oxygen peak,
and could accordingly be eliminated.
93
Fig . 2
Results from the electron density function
( xyz)
Composite of sections showing the environement of
the peaks chosen,. as Al
2
and P2
Table I
Results from the electron density function r1 (xyz)
No.
Max. height
arbitrary units
(In 1/30 of cell edges)
875
29.87
25*8
539
29.5
14.5
932
Peak designation
Based on height and
Based on
chemical considerations
height only
Al
P1
2.4
603
10.
509
17.5
405
10.
388
949
8.8
9.0
21.
22.
Al
Table 1.(continued)
Results from the electron density function ],(xyz)
No.
Max. height
arbitrary units
10
789
7.4
11
590
10.7
12
695
10.5
13
748
11,8
14
614
11.4
13.
9.
15
794
26.4
13.
23.8
16
891
26*8
17
869
25.3
11.5
14 .
18
830
(In 1/30 of cell edges)
22.4
Peak designation
Based on
Based on height and
height only
chemical considerations
Al 3
7.2
28.
12*0
28.
24.
8.4
Al
Al2
97
b.
Five other maxima,
also about half of the height of an
oxygen peak and at the right distances to complete the coordination polyhedra of the cations, were found.
They accounted for
the oxygens that had been eliminated and for the oxygen missing
in the first structure-factor calculation.
c. Peak 12 from Fl(xyz),
which had not been included as an
atom because it was too close to peak 11 to be either an oxygen
or an aluminum, came back with a height equal to the average
oxygen peak.
The only possibility for peak 12 was phosphorus,
but both Pl and P2 had come back at full height in the second
electron-density map.
It was observed, however, that if peak 12
was assumed to be a phosphorus, then the peak called Pl could be
explained as a substructure peak; it would correspond to the
superimposed interatomic vectors from Al
Al 2 to
A12
1 to peak 12 and from
2*
Two structure-factor calculation were made, one considering only the changes affecting the oxygens and the other
including also the change in the position of the phosphorus atom.
The R factors were
57% for the first and 48% for the second.
The signs from the last were used to calculate a third electrondensity function.
P3 (xyz) gave the following results:
One oxygen was
found to be misplaced, three other experienced rather large displacements, and all the rest of the atoms showed small displacements from their original positions.
The discrepancy factor for
these atomic positions was 38% and the signs they determined were
used to form the electron-density function
4
(xyz).
The appearance of this electron-density map was very
satisfactory.
The peaks looked round, the relative heights
matched well the scattering power of the atoms they were supposed
to represent, and no spurious peaks were found.
The only anoma-
lies detected were a rather large displacement showed by one oxygen and slight displacements of the rest of the atoms.
When the atomic coordinates from f4(xyz) were submitted for a structure factor calculation an R factor of 27% was
obtained, the structure was considered solved and the model was
submitted for least-squares refinement.
99
Appendix
II
Observed and calculated structure factors
of turquois
h
k
0
-0
-O
4
-0
1
0
0
0
5
7
-0
-0
8
-0
0
0
0
1
1
2
2
3
3
4
-4
5
5
6
6
7
7
8
0
1
1
2
2
3
3
4
4
5
5
6
6
7
8
0
-1
1
2
2
3
3
4
4
5
6
5
5
6
1
-1
1
-1
1
-1
1
1
1
-1
1
-1
1
-1
1
2
2
-2
2
-2
2
-2
2
-2
2
-2
2
-2
2
2
3
-3
-3
3
-3
3
-3
3
-3
-4
4
3
-3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
3
0
F
0
19.71
-87.13
35.48
74.85
19.00
14.35
12.73
23.26
20.68
93.48
-15.77
13.44
41.23
-40.00
78.85
9.89
-3.88
12.99
-27.98
6.53
25.01
14.54
7.17
23.78
24.10
-43.17
59.19
4.14
9.05
47.75
-27.53
32.25
8.08
-6.14
-6.01
-9.37
-8.27
48.92
18.16
23.20
75.05
61.71
14.99
-1.68
-68.56
8.66
26.75
-24.49
21.58
27.92
17.96
F
C
20.21
-82.18
34.94
69.45
16.96
13*97
12*13
25.62
20.41
100.02
-5.93
15.70
41.33
-31.87
84.46
10.65
-2.26
12.20
-27.96
5.50
24.01
13.82
8.82
24.72
24.15
-33.17
58*00
8.17
11.03
44.96
-25.40
32.03
6*46
-4.06
-4.96
-8.83
-8.99
47.46
19.24
24.03
76.30
60.01
15.32
-0.92
-65.93
7.86
26.87
-21.25
21.73
27.14
16.83
100
6
7
8
0
1
1
2
2
3
3
4
4
5
7
8
0
1
1
2
2
3
3
4
4
5
6
7
8
0
1
1
2
2
3
3
4
5
6
7
-3
3
3
4
4
-4
4
-4
4
-4
4
-4
4
4
4
5
5
-5
5
-5
5
-5
5
-5
5
5
5
5
6
6
-6
6
-6
6
-6
6
6
6
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
48.72
15.12
4.78
-31.60
14.47
18.03
3.04
56.93
20.87
5.88
66.04
19.45
-1.49
16.41
36.25
56.28
14.09
2.91
-38.71
-4.91
18.03
19.58
5.04
-24.56
12.79
26.95
9.05
-2.07
14.09
8.47
6.72
17.90
-21.71
13.12
6.91
-20.94
9.31
-23.59
14.41
48.52
14.55
3.41
-25.43
15.00
19.47
0.91
56.15
22.97
4.64
64.27
19.57
-0.41
15.98
35.81
53.69
12.19
1.85
-36.23
-2.49
19.80
19.90
6.59
-24.88
12.70
25.40
8.33
-1.12
12.86
7.70
5.23
16.35
-19.91
12.08
7.03
-21.69
10.47
-22.83
12.91
0
7
0
-33.28
-34.36
1
1
2
2
3
4
5
6
7
0
1
2
3
4
5
-2
2
-3
3
-4
4
7
-7
7
-7
7
7
7
7
7
8
8
8
8
8
8
-0
-0
-0
-0
-0
-0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-1
-1
-1
-1
-1
-1
9.37
6.85
17.90
48.85
12.34
13.18
7.43
47.88
7.82
16.93
5.43
22.88
13.25
-20.23
15.70
15.74
45.78
10.80
146.02
33.93
-6.85
8*93
6.03
17.94
51.57
11.91
12.22
7.14
46.46
6.90
15.26
4.31
20.86
13.15
-20.00
14.52
16.94
44.50
14.03
140.24
33.27
-5.51
102
-5
5
-6
6
-7
7
-8
0
0
1
-1
1
2
-2
-2
2
3
-3
-3
3
4
-4
-4
4
-5
6
6
6
-6
-6
6
7
-70
-7
7
-8
0
0
1
1
-1
-1
2
-2
-2
2
3
-3
-3
3
4
-4
-4
4
5
-5
-5
6
6
-6
-6
-o
-0o
-o0
-0
-0
-0
-0
1
-1
1
-1
-1
1
-1
-1
1
-1
-1
1
1
-1
-1
-1
-1
1
12
-1
-1
1
1
-12
-1
-1
2
-2
221
-2
-2
2
2
2
-2
-2
2
2
-2
-2
2
2
-2
-2
2
2
-2
-2
2
2
-2
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-12.45
24.90
5.34
21.48
-5.93
3.56
17.39
20.22
21.87
-11.53
53.36
49.41
19.50
24.70
23.65
28*46
36.17
-90.97
2.24
67.00
28.33
22.60
5.99
-2.50
3.89
65.74
-58.37
1.91
4.68
25.36
41.70
19.83
-2.64
8.37
51.25
-3.23
21.74
25.16
94.81
26.68
12.78
-27.40
15.22
12.45
26.02
3.43
-36.89
45.13
-20.55
-15.42
25.36
14.30
10.41
31.29
17.06
34.78
-50.07
54.22
4.41
0.86
9.55
-10.82
24.13
0.33
19.88
-5.28
5.09
19.82
22.24
23.60
-8.88
51.27
46.23
20.58
25.03
26.07
28.40
34.71
-85.52
2.17
63.27
28.67
22.87
7.35
-2.43
0.08
65.16
-53.71
1.60
3.64
25.50
42.37
22.14
-2.68
7.72
55.81
-3.50
23.06
26.55
95.39
28.01
15.90
-32.39
15.04
13.82
28.21
1.50
-29.88
46.51
-9.64
-13.11
25.56
13.76
11.74
30.63
17.98
34.99
-47.59
52*74
3.76
1.95
9.64
102
6
7
-7
-8
0
0
1
-1
-1
2
-2
-2
2
3
-3
-3
3
4
-4
-4
4
5
-5
-5
5
6
-6
-6
6
7
-7
-8
0
0
1
-1
-1
1
2
-2
-2
2
3
-3
-3
3
4
-4
-4
4
5
-5
-5
5
6
-6
7
-7
-8
0
0
-2
2
-2
-2
3
-3
3
3
-3
3
3
-3
-3
3
3
-3
-3
3
3
-3
-3
3
3
-3
-3
3
3
-3
-3
3
-3
-3
4
-4
4
4
-4
-4
4
4
-4
-4
4
4
-4
-4
4
4
-4
-4
4
4
-4
-4
4
-4
4
-4
-4
5
-5
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
2.24
-26.15
31.55
2.31
17.85
15.81
91.94
-3.82
-57.71
10.67
29.58
18.64
4.81
21.21
62.58
-15.74
49.41
33.47
7.44
17.26
17.65
65.28
-31.36
31.75
8.30
-3.56
17.59
13.37
-9.16
-1.38
-14.36
3.56
15.74
14.43
77.27
2.37
50.00
65.15
18.38
27.27
17.00
9.29
-2.64
30.83
-6.65
-37.55
4.28
4.22
19.04
11.40
-21.94
-22.73
37.29
33040
27.67
19.76
24.18
24.44
10.28
11.07
12.38
3.69
-28.10
33.50
1.64
18.58
16.84
90.21
-0.82
-52.15
10.12
29.91
20.17
5.29
19.69
61.66
-7.80
48.72
32.94
6.67
18.42
17.73
62.51
-35 o 66
31.25
9.37
-1.11
17.28
12.87
-12.71
-1.30
-14.61
2.36
15.55
14.66
78.36
1.47
47.46
61.94
19.41
28.24
18.86
9.55
-0*46
30.54
-1.86
-34.37
4.35
4.51
20.93
12.12
-20.51
-24.20
37.18
35.98
29.13
20.49
25.08
24.59
9.55
9.45
11.99
103
1
5
5
-1
1
2
-2
-2
2
3
-3
-3
3
4
-4
-4
4
5
-5
6
-6
7
-7
-8
0
0
1
-1
-1
1
-2
-2
2
2
3
-3
-3
3
4
-4
5
-5
6
-6
-7
0
0
1
-1
-1
1
2
-2
3
-3
4
-4
5
-5
-6
0
-1
-5
-5
5
5
-5
-5
5
5
-5
-5
5
5
-5
-5
5
-5
5
-5
5
-5
-5
6
-6
6
6
~6
-6
-6
6
6
-6
6
6
-6
-6
6
-6
6
-6
6
-6
-6
7
-7
7
7
-7
-7
7
-7
7
-7
7
-7
7
-7
-7
-8
-8
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
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36.70
9.69
-19.29
1.40
9.45
6.78
21.16
37.41
9.31
12.27
11.23
3.22
19.68
-1836
6.85
10.77
-1.90
15.65
0
-8
-3
-2.90
-3.37
-1
-2
-3
-4
-5
-6
-3
-4
0
-1
1
-2
2
-3
3
-4
4
-5
-8
-8
-8
-8
-8
-8
-9
-9
-0
-0
-0
-0
-0
-0
-0
-0
-0
-0
-3
-3
-3
-3
-3
-3
-3
-3
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
32.38
9.71
8.84
11.26
3.37
3.37
-8.57
-2.16
-25.03
15.24
22.66
-9.98
17.47
7.08
15.72
62.19
-28.13
-1.01
33.58
9.60
8.66
10.79
0.04
2.08
-12.96
-1.37
-14.08
16.09
21.34
-9.83
15.37
7.74
16.13
65.17
-23.41
-1.23
5
-6
6
-0
-0
-4
5.06
4.30
-4
23.14
23.22
-0
-4
-0
-0
-4
-4
6.81
4.79
6.66
5.29
0
0
1
-1
-4
-4
-1
1
-1
1
8.23
62.93
6.83
58.41
1
1
-1
-1
-4
-4
-4
-4
20.84
15.04
37.77
7.02
21.49
16.24
36.59
8.16
-7
-8
-16.53
-15.34
111
-2
2
-2
2
-3
3
-3
3
-4
4
-4
4
-5
5
-5
5
-6
6
-6
6
-7
-7
0
0
-1
1
-1
1
-2
2
-2
2
-3
3
-3
3
-4
4
-4
4
-5
5
-5
5
-6
6
-6
6
-7
-8
0
0
1
-1
1
2
-2
-2
2
3
1
1
-1
-1
1
1
-1
-1
1
-1
-1
1
-1
-1
1
12
-1
-1
-12
2
-2
2
2
-22
-2
2
2
-2
-2
2
2
-2
-2
2
2
-2
-2
2
2
-2
-2
2
2
-2
-2
-2
-2
3
-3
3
3
-3
-3
3
3
-3
-3
3
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
61.11
17.74
55.45
-16.12
20.37
31.43
18.75
30.56
28.47
52.95
-15.85
-15.18
2.56
-4.99
21.38
7.15
-8.57
4.79
13*49
33.66
23.34
2.56
45.19
7.89
27.32
12.28
20.24
37.50
19.02
4.25
77.85
44.92
9.98
10.99
20.98
15.18
13.69
-40.00
-12.41
59.56
24.55
26.64
17.74
8.84
8.90
51.13
36.90
-25.16
4.11
-31.97
-80.79
-16.59
27.86
4.72
1.55
33.12
51.67
23.54
99.89
57.47
4.65
65.79
18.51
53.87
-11.72
22.06
28.28
21.20
28.31
26.46
48.91
-14.88
-13.81
0.59
-3.41
22.57
6.51
-10.03
4*26
13*66
32.52
25.81
1.03
44.94
8.70
28.78
15.80
21.68
34.60
18.91
5.08
71 * 44
43.06
9.52
10*35
22.26
14.39
13.87
-33.87
-7.51
54.58
27.14
24.56
21.08
7.38
8.65
50.10
36.56
-23.62
0.99
-34.46
-82*46
-12.54
27.92
2050
0.73
31.85
49.50
24.87
102.59
55.26
4.49
112
-3
-3
3
4
-4
-4
4
5
-5
-5
5
6
-6
-6
-8
0
0
1
-1
-1
1
2
-2
-2
2
3
-3
-3
3
4
-4
-4
4
5
-5
6
-6
-7
-8
0
0
1
-1
-1
1
2
-2
-2
2
3
-3
-3
3
4
-4
-4
5
-5
6
-6
-7
3
-3
-3
3
3
-3
-3
3
3
-3
-3
3
3
-3
-3
4
-4
4
4
-4
-4
4
4
-4
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4
4
-4
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4
4
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4
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4
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5
5
5
-5
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5
5
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5
5
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-5
5
5
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5
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5
-5
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-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
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-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
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-4
-4
-4
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-4
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-4
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-4
-4
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-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
-4
10.39
12.95
1.01
-26.85
-3.78
-24.82
-61.38
16.26
1.48
6.95
31.57
11.40
37.44
63.61
-2.09
35.55
46*75
7.15
12.88
17.74
15.72
-28.80
15.72
4.92
-23.68
11.74
2.63
12.55
17.20
40.88
9.58
42.77
39.12
14.91
15.11
9.31
-70.42
7*96
33.59
18.68
28.67
18.15
7.96
21.11
9.78
26.71
-5.26
-44.86
39.66
6.21
12.68
8.50
10.32
-14.64
15.04
36.90
4.05
-3.17
20.03
-1.08
21.79
9.66
13.78
0.54
-24.09
-1#54
-20.45
-57.38
14.74
0664
8.56
30.30
11.77
37.52
67.75
-0.22
34.77
46.12
3.93
1278
18.85
16.17
-26.41
15.92
5.40
-21.78
11.37
2644
7*48
16.70
36.75
7.38
42.57
35.43
14.43
15.49
9.45
-75.45
7.08
36.48
16.63
28,22
17#90
7.71
21.84
11.29
25.16
-5.69
-41.77
37.17
5.67
12.21
9.47
9.46
-12.42
15.33
38.71
2.99
-1.87
19.80
-1.03
23.17
-~
113
-8
0
0
1
-1
-1
1
2
-2
-2
2
3
-3
3
4
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-5
-6
-7
-8
0
-1
1
-2
2
-3
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-5
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-8
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-1
-2
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0
1
-1
-2
2
-3
3
-4
4
-5
5
-6
6
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-8
0
0
-1
1
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1
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2
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6
-6
6
6
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6
6
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6
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6
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-5
-5
-5
-5
-5
-5
-5
-5
-5
-5
-5
-5
-5
-5
-14.50
5.60
90.25
11.94
7.02
20.84
-16.73
-31.64
-25.16
-1.96
-38.45
24.89
4.32
30.29
72.31
29.61
17.13
-3.31
4.72
27.93
-19.36
-5.13
13.49
32.85
20.37
14.30
-15.04
9.24
6.54
-6.34
-18.21
4.92
-0.88
-16.12
-15.11
2.69
88658
11.89
5.82
20.72
-16.19
-31.02
-24.93
-3.06
-37.32
24.30
2.85
30.19
74.04
31.67
18.28
-0.79
4.90
29.73
-17.84
-1.61
12.80
31.74
20.84
12.53
-15.64
9.67
5.91
-0.77
-21.05
3.92
-0.93
-16.00
6*48
4*65
7.35
19.43
38.79
-7.96
17.54
93.34
7.32
19.69
17*47
30.69
34.74
3.44
16.19
7.08
-14.23
20.91
4.79
17.61
12.41
7.55
21.25
15.11
52.75
43.24
-18.89
1.48
22.73
18.62
40*15
-4&07
14.10
101.82
20.06
29.14
31.92
0.44
18.13
7.64
-13.47
25#60
4.87
16.50
14.24
7.37
18.12
15.92
52#33
41#20
-17.05
1*64
24.41
17.58
114
-2
2
-3
3
-3
3
-4
4
-4
4
5
-5
-5
5
-6
-1
-1
1
1
-1
-1
1
1
-1
-1
1
-1
1
-1
1
-5
-5
-5
-5
-5
-5
-5
-5
-5
-5
-5
-5
-5
-5
-5
12.68
38.11
-35.08
7.35
9.11
63.00
10.99
11.33
1.55
1.42
-7.76
0.88
67.12
-26.51
10.66
14.34
34.09
-35.25
6.91
10.21
55.96
11692
10.94
0.44
0.67
-6.20
2.51
83.30
-23.01
10.82
6
1
-5
18.41
-6
6
-7
-7
-8
0
0
-1
1
-1
1
-2
2
-2
2
-3
3
-3
3
-4
4
-4
4
-5
5
-5
5
-6
6
-6
-7
-8
0
0
1
-1
-1
1
2
-2
-2
2
3
16.44
-1
-1
1
-1
-1
2
-2
2
2
-2
-2
2
2
-2
-2
2
2
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2
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3
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3
3
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3
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-5
-5
-5
-5
-5
-5
-5
-5
-5
-5
-5
-5
-5
-5
-5
9.71
14.17
-18.08
-5.67
-7.55
35.35
33.12
-37.17
26.44
-33.66
95.51
5.80
13.02
2.16
6.14
51.74
17.74
73.65
-50.46
19.63
21.72
20.71
20.03
-13.15
26.10
-60.71
34.60
-3*44
-5.46
17.67
59.49
7.08
2.23
28.40
-4.92
58.62
16.59
53.02
4.32
15.45
9.11
-6.41
-28.47
7.60
13.49
-21.27
-6.00
-8.73
32*87
28.99
-35.23
26.88
-30.53
90.77
5.85
13.04
5.60
5.91
54.69
15.87
77.59
-43.28
20.48
20.45
21.97
17.65
-15.83
23.66
-61.34
32.91
-6.29
-5.75
18.12
65.34
6.61
2.22
29.38
-2.52
59.52
19.77
51.29
5.61
16.07
11.51
-5.04
-26.61
-
4
3
-5
8.36
8.84
3
-5
20.51
18.59
115
-4
-4
4
5
-5
5
6
-6
-7
-8
0
0
1
-1
-1
1
2
-2
-2
2
3
-3
-3
3
4
-4
-4
4
5
-5
-6
-7
-8
-9
0
0
1
-1
-1
1
2
-2
-2
2
3
-3
-3
3
4
-4
-556
-6
-7
-8
0
0
1
-1
-1
1
3
'-3
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3
3
-3
3
-3
-3
-3
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4
4
4
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-4
4
4
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4
4
-4
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4
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5
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5
5
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6
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6
6
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-5
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-5
-5
-5
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-3.84
13.02
32.38
2.70
1.82
29.14
3.71
21.65
-24.42
5.87
10.05
23.95
42.02
-28.13
-22.80
40.74
2.90
-3.31
10.19
6.34
2.63
32.78
-32.11
3.37
10.99
11.33
4.72
17.47
4.79
40.20
-8.23
11.67
18.35
-5.80
3.84
-15.38
-46.21
49.31
67.99
-35.21
21.18
14.91
20.30
21.99
52.41
2.23
-35.28
10.25
7.35
13.96
-4.99
5.06
14.91
-3.51
4.18
9.51
3.64
-2.23
23.27
9.11
4.45
-5.82
13.85
30.58
0.05
1.10
27*81
3*74
23*27
-27.68
4.58
11.74
23.50
39.92
-26o26
-20.69
38.44
3.58
-3.26
11.65
5.88
1.63
33.09
-29.40
3.70
9.80
10.75
3.41
17.67
5.09
40.60
-9430
11.12
19.18
-7.04
4.59
-15.26
-43.90
47.73
69.87
-33.81
21.49
14.17
21.40
23.10
50.58
0*38
-35o51
11.44
6.94
14.25
-5.57
2.92
15.38
-0.65
3.04
8.23
2.03
-0.60
21.68
8.80
5.43
116
2
-2
2
3
-3
3
-4
-5
-6
-7
-8
0
-1
1
-2
-3
-4
-5
-6
-7
-8
0
-1
-2
-3
-4
-5
-6
-7
-2
-3
-4
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0
1
-1
-2
2
-3
3
-4
4
-5
5
-6
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0
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1
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1
-2
2
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2
-3
3
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3
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6
-6
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6
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-7
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-6
2.50
15.18
21.85
-20.98
14.77
52.55
13.22
2.90
15.72
-6.27
7.02
11.74
5.53
11.06
5.80
-3.71
9.11
8.43
6.88
49.31
8.03
13.15
-16.93
-2.83
38.18
16.80
-20.84
10.05
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84*01
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27.79
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117
4
-4
4
-5
5
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5
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2
-6
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51.31
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0
-2
-6
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-1
1
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2
2
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3
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22.62
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50.45
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0
-3
-6
84.93
85.91
-1
1
-1
1
-2
2
-2
2
-3
3
3
-4
4
-4
4
-5
5
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3
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13.69
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799
40.98
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24.35
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3.82
8.94
32.53
118
0
1
-1
-1
1
-2
-2
2
3
-3
-3
3
4
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4
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23047
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6.04
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8.12
35.46
11.17
13.65
16.55
11.27
1.08
20.33
12.04
47.87
21.20
-28.89
8.25
34.24
0.84
23.82
119
-2
-3
-4
-5
-6
-7
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-4
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0
-1
1
-2
2
-3
3
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4
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5
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1
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2
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7.55
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40.34
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26.31
9.51
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17.20
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9.50
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3.94
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26.23
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4.27
24.06
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34.42
35.10
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10.22
9.24
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120
4
-5
-5
-6
-7
-8
0
0
-1
1
-1
1
-2
2
-2
2
-3
3
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3
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4
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4
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0
1
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1
2
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3
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3
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0
1
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2
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2
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3
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3
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3.88
3.36
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3.06
2.85
121
-1
1
-2
2
-3
-4
-5
-6
-7
-8
0
-1
-2
-3
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-m 5
-6
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0
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1
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13660
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122
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0
0
1
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1
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29.88
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Biographical Note
Hilda Cid-Dresdner,
nee Hilda Cid Araneda,
on February 20, 1933 in Talcahuano, Chile.
was born
She is the daughter
of Jose Cid Bastidas and Hilda Araneda de Cid.
She attended pub-
lic school in Talcahuano, and graduated from the secondary school
Liceo Fiscal de Talcahuano in 1949.
Undergraduate studies were taken at the Universidad
de Concepcidn, Concepcion Chile, where she was given the University Prize in 1955.
From 1955 to 1958 she continued studies at
the University of Chile, towards the diploma of Profesora de
Estado en Ffsica y Matematicas (equivalent to a B.S.) which was
granted, with honors in 1958.
In 1955 the author joined the Laboratorio de Cristalograffa of the Universidad de Chile as a teaching assistant,
and became an associate researcher after graduation.
In 1960 she was granted a fellowship from the Agency
for International Development of the U.S. State Department and a
leave of absence from the Universidad de Chile to take graduate
studies at the Massachusetts Institute of Technology.
ceived an S.M. in Geology and Geophysics in June 1962.
She reShe was
permitted to continue a course of study leading to the degree of
Doctor of Philosophy in Crystallography under the guidance of an
interdepartmental committee.
From 1962 to 1964 she was the hold-
er of a fellowship from the Organization of American States.
In 1955 she became the wife of Dr. George W. Dresdner
of Santiago, Chile.
They have three children, Rodrigo Felipe,
born in 1956, Jorge David, born in 1957 and Rosanna Cecilia born
126
in 1962.
The author is
a member of the American Crystalle-
graphic Association, the Mineralogical Society of America, the
Sociedad Chilena de Fisica and the Society of the Sigma Xi.
Publications
Etude anx rayons X de la cyllindrite.
Bull. Soc. franc. Miner. Crist. (1960) 83.
On the setting of crystals for x-ray diffraction work.
Acta Cryst. (1961) l4,200-201.
(With Isabel Garaycochea)
The crystal structure of potassium hexatitanate,
K 2 Ti 6 01 3 .
Z. Kristallogr. (1962) 117, 411-430.
(With M.J. Buerger)