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Abstract

PowderCell contains a comfortable, user friendly visualization and modification tool for crystal structures. It provides on-line calculation of the corresponding powder diffraction patterns simulating a variety of experimental conditions. The common ICSD and Shelx file formats are supported for importing crystal structure information. It has control of automatic cell transformation and also derivation of subgroups. More than 740 different settings of the 230 space-group types are supported. Up to ten crystal structures can be considered simultaneously. A full pattern refinement enables the direct comparison with experimental diffractograms for quantitative phase analysis, lattice parameter refinement, polynomial background estimation, etc.
user-friendly
program can be dowdoadcd
lbr the "cost" of
yoü modem
time, and it will off€r many teäturcs
not even
found in comnercial Packäges
I $ä1. ro
rhdnk t\e
!trhor\'or
lherr
reddne*
ro
gi\e a
brief description
of their progräm. and
I encourage
other
au-
thors of sofrware^Veb
pages/manuah
etc io follow their €x-
ample.
To keep üis section
ful] of life and up-to-date,
your
inpul is absoiutely
necessary
Besl
wishes,
Robert
E. Dinnebie.
Laboratory
of Crystallography
Univ€rsity
of Bayrcoth
D 954-40
Bayreutlr
Gernany
E nail: roben.dinnebier@uni-bayreuth.de
Powdercell
2.0
for windows
G. Nolze & w Klaus, Federal
Institute for Materials
Research and Testing (BAM), Unter den Eichen 87,
D-12205
Berlin,
Gernany,
e:mail:
gert.nolze@bap.de
Abstract
Po$'de{etl .onunr:s
z colnfortable,
user
friendlv visual-
izalion and modification tool fo. crystal structures lt plo
vides oniine catcutation
of the corresponding
powder dif
fraction patterns simulating a variety of experimental
conditions.
The common
ICSD änd Shelx {ile lotmats are
,upponed lor rmporung
Lrliul strucldre
inlormrrion
ll ha'
co;nol ol auromäric
cell rranifoßtralion
and al\o deri!Jlion
of subgroups.
More thän 740 different settings
of the 230
5pare-grout
'ype5
siU be
rupponeJ
Uo lo len
crlslal
\ruc-
Lures can be
considcred
.itruluneou\l)
A lull
panem ßnoe
menl enables
the direct comparison
with experimental
dil-
fractogams
for quantitative
phase analysis'
lattice parämeter
refinemenl,
polynomial background
estimaion' etc-
Key words: refinemenl,
subgroups,
unit cell transforma-
rion, quantitative
phase
analysrs,
stnrcture
vlewer
l. lntroduction
Po d€det represenls
the dircct successor
of the DOS
prosram
POWDER
CELL (Kraus & Nolze,
1996).
even
ihoueh
it was not a sinple conversion
to the windows envi
ronrnent
usine
Borland's
Delphj
l 0 Using
Microsofi
win-
dows
has some
significant
advantages.
Tbe most important
is
the indeDendence
of speciäl
hardware
adaplatrons
such as
ootimal icreen resolution
or existing
printer d'ivers The use
ri rhe
.lrpborrLl
oaen
a comronJble
po'rbili'v for sinple
,.1ps11
,,. r...u11.
lprcrure,.
oalr.
erc
I
inlo olli(e
appLcali,,n..
runheimore. *uitiple .t u"tu." processing
is implemenled
with the ability
to produce a theoretical
mixture
of up
lo 10
seemingly
small details
were considered
during
the
planning stage. for €xalnple,
different
oxidation
states of a
eiven element in one and the same
crystal structure
can be
Aefned by diffetent properties,
e g.. alomic scattering
fac'
256 Powder Difir.,
vol.
13, No
4, December
1998
toIS. colors: either the powdef pattem simulation or the crys
tal slructure
drawing may be switched
off if desired These
considerations led to a principle .econstruction of the code,
while the aim of the program was rehined: the suppolt ot
crvstal anrlvsis b! the intuilive creätion of structure nlodels'
rn'"nnt.ost lo ueriion 1.0. the second
release
is charactenzed
bv e6\ Io-handle
rehnemerr
\ d a Gruptucal
U'er Inle'{ace
rfre'mponarr
teature'
ol qhrch
ale
de'cnbed
belo$
ll. Crystal
Structure
Generation
and
Manipulation
The st uctüe data
imporl has been exlended
in PovdT '
Cel. In additional !o lhe POWDER CBl-]-'specilic jnitial
data {iles (with erlension + cel), ICSD and SHELX files
(*.txt and
*.res
extensions
respectively)
can be imported For
üe ICSD
impon
rn aulomalic
unil
cell lran'for'nation
pro-
cedwe is implemented
since many crystal srmcturcs arc
aiven in non-conventional
settings.
However,
the cell trans-
iormation procedure
is appljcable
in anv other case
where a
nonconventional
choice of basis
vectors
has been used for
üe description
of the unit celt. The program distinguishes
between
more than 740 different settings
of üe 230 space
gmup types. The transformation
procedurc fot nonocljnic,
onhorhombic,
and rhombohe&a1
space-goup
types constd-
ers a pelmulation or superposition
of basis
vectors An addi_
tional shift of all atomic coordinätes
in the asymmetnc
umt
allows settings
where
rhe
new basis
veciors are
chamcterized
by a new origin (necessa./ for some
monoclinic
se$ings) ln
contrast.
the SI{ELX converter
transforms
the glven sy1nme-
try operatols
inlo a predefined setting
ofÄpace_group
types
This is necessary
because
of the setting
sensitjve
extmcton
Ialus used
h Powde{e . Figure 1 shows
the implemerted
crystdl structure
editor which can be used
for the input of a
new data set or to show and edit imported
crystal slructure
wlereäs in the DOS version. the complete
set
of general
po\flrons wa\ defrned
In üe \ymmery ble lo geremle äll
;rodric
po'irion' $nhin rhe
rtü cell.
Poüetcell 2.0 a2plie'
the generätors listed in the Intemätionäl
Tables
for Crystal-
logaphy (IT) (Hann,
1995) This fact means that the genera-
rion p.ocedure derives
the general or special
posltons re-
Fieur L cry$al *ru.rurc data crn b€ edited in ! very simple N2v. Add'
tioml inbrmalion can b. added as a coment
lrtemariona
Bepons 256
quired, üsing eirher aU or a subser
ol rhe posrrron-retated
generJlor\.
One
udvdnrage
of
lhi. pro,edure
is
,he
&c,"r.ed
odrd
'or
ezcn
rerrjog given
;n
lhe
.)
mmer)
hle pcq
spgr.dor.
Alco. the pu.sibiliry
of ryping
enor. h \er) \ma which
b
rmpodant.
cunsidering
rhe
polen
al] trrge
number
of \et_
rng\. rünhermore.
il decredses
lbe
run rime
and
enäbles
üe
user
to undersrand
and check
the locat syrnmetry
of special
^ Regffding skucture
modeling,
one of the most interest
n8, 'eature\
i\ 'he fu y auromäric
generar;on
of.ubgroups
and
(panidlly) .upergoupc.
Ttus
feature
offeN
a con orrable
derivaloo
of cubgroup,
b' sradual
decred\e
or,)mmery
1as. ror rhe de.cnprion of crysLauog,aphir
phase
Ijansrtron.t.
see
Figure
). the
ddu used
are an
exrraclron
oI
:: !.ctj
.".q
^T !h: tompreret)
denved
and l?butared
b] U.
Muler {19q4)
I .ing rhe.e
dara.
üe prog|am
catcutale\
rhe
ne$
Dasß \ec,or\.
u-arclorms
äll alomic po.irion..
and
detel
mlnes
me asymmerfic
unit in reiation
ro ihe new space group
symnetry. Additiomly. the Wyckoff positions
are identined
rn .one.\pondence
ro lho,e g'ven in üe IT. All e(i.rjng
wlcLofi posrüons
hä\e been classified.
As menüoned
ubole.
lhe,)nmeLry dependenl
Wyckofi ,olarion
$i be
useo
ror sere(_Lrte
generadon
of üe atonxc posirioo,.
The
oenveo
crysral \trucrure
parajnelerr
can be
€dited
dd sa\ed
rn änalog)
to u.uät
"üucrure
darä ra\ in Figüre
, we sanr
ro poinr
our tiar in rhe progam
a u\er_fäendly
oel'tce ex$ts ro manipulate
crystal srructures,
onty by ro;
tron and transtation
of atoms.
Therefore,
rhe desired
atoms
must
be selected
before
using
difierenr tools.
The aroms
wlx
FieüE 2. The po$ibte naxin2r subsronps
of a gild
space group qpe can be selated ea\jly.
be
displayeJ
b) harcbng
'.ee
Frgure
l). For
rhe maniputr
rion
thal
lbliou..
rhe
Drogrrm
reduce\
lhe.etecred
om, ro
lho.e
in
lhe
a.)mmeLnc
unir.
i.e..
ontJ
üe dronxc
p,biLron\
or $e ,,) orJnernc
unir s;ll be changed.
The ,ynmero of üe
crysral
$t be
consened.
.Powdet(e enable,
'ülarior, atong
lhe bä5r5 \eclors
and
also
aloog
a predeijned
düeclion
bel$een
lso aromic
posrtions,
i.e., a bond.
The rotarion
is carried
out arorind
rhe
center
of graviry,
a predefined
atom,
or a vecror given by the
l$o dlonlc
po.ir;un\
fFi$re lj. Airer
nänipuldri.n
lhe;n-
nueoce
oo
rhe
calculated
po$der
em cän
be ünmedrdrely
srudied.
__. The cryslal srrucrure
rcpresenration
can be eiponeo as a
Windows
Meta
Fite (*.wmf),
as a posrscript
fite, or as
a
POVRä)
,cripr.
fhe la e. i\ e,pec,ajtJ
"urraLle
for rhe
cre
alion
of pboto
realislic piclure.
b) üe u\e ol pOVRay.
a
ree$are
raylrar
Ing progTdm ravaitabte
är $wk.porm).orgr.
lll. Powder
Pattern
and Retinement
In conrasr
ro rhe
DOS
version,
powierce[ 2.0 is able
to
simulale
nor only X ray panems
but also neurror difftaclion
pattems_
Arnong
orher
things,
the influence
of a variable
pri_
mary sür .]srem hä' been
cor\rdered.
the seneralron ol
equivulenr
Debye
Wa er tä,ror,
r.rng r}e coni.pondng
an_
'$ffoprc component\
gilen rn üe |CSD ha5
been
rtnpte-
menreJ.
dnd
üe $eI+nown
p,eudo_
Vo ig1 pron
te runcrron
i.
ävarlable
ro
describe
üe reflecuon
prohte\.
funh(more. ,r
r.
FiguE:1. The crysrd stücture is Epresenred
by tne cont€ni
or hr trlmeb. urur Tbe
Dnr ce e,lges
m trdcd
uur.
r he hJlc,ted
pan
of thc
AJmeLnc untr
ua be
rcrired
$
Powder
Dtffr., Vot. 13,
No.4,
December
1998
liielrc.1. Thc scrco duDp shows i rypr
c.i aüangenent conr.rnmg rwo crlnlr
{rrrurer and
rhe corestonding ponder
diffra.noi taden. The di1Lrcn.c.une
sho*s thc lood agr.Dc betweer n.x
ruEd and Enned poqder prlrenr.
possible
lo enlafge rhe
paLtem
lo tirll screer. a lunction oftcn
requested
in the DOS version.
| , r'ts r\. . d\a n:ree. oi w:r!1.
$.. rhr pr^ts a r. i. .u r-
able
for rhc calcularion of powder paLlcms of phase
nixtures
ll-igure .1).
Thc da$,ing possibilities hälc bccn extended to
alkrw üe cokrrs ol points
or lines
to bc ser by the user. Ody
tlrc differerlt crystal slfucture dai! nlusl be loaded to get
the
resulting po\lder panem. Thc sum as well as the single
..I\' , .. r be .l plJrel I Jhrl n. ol relecr:o.r. roJ il
cludes Nliller nolation. lt{iller-Bravais notalion. d values.
Brngg nngle\. strucLure
anplitudes. integral ini.nsitics, and
FwHNl. Addition.rlly a lisling of ail reflections combined
$ith a line
cuhor allo$,s an eas) identilicttlo! in the
po\)"der
Another new Lature is the implementation of a full pat-
|em refinement
procedure
to optimjze selected
parameters
using the Marquard aleorithm.
Allhough the Marquard algo
dthm {see
for examplc
Young. 1995) is rclatively
slow and
needs a nininum of I itcrrtions fo. convergence.
the con
vergence is -cenerally
morc st.rble. The proeram
rcfines
back
ground,
lattice
t{ramctcrs, FI'HM in dcpcndence of 24 i!
tcnsity scalc facror, deg.ee of pre-setected prefened
o.ientalion,
7e.o shift, and samplc displacemcnl
(\cc Figurc
5). Rcfincmcnt of .{omic positions
has not
)el been included.
Once convergence has been ßached. all parameters
can be
retined simultaneously. Thus, a phase
mirture can be ana-
lyzed
quandtatively
without any inlernai or external standrrd
if the cryslal sructures of all phases
are known. The raw
Figtrrö 5 Relinible td mete6 c$ be switched on oroL
tnr ca.h cLynal i0ctrri..
258 Powder Diilf, Vol. l3 Nc. ,1 Decenber 19sB IntemalionalRepots 258
powder can be loaded in several different file formats includ-
ing Siemens, Philips, Sietronics CPI and XY (angle, inten-
sity) format. The optional display of the difference plot and
the agreement factors supports the goodness-of-fit visually.
A message box shows important R-values during the refine-
ment process. A comparison of R-values before and after the
refinement is possible on the result screen. The diagrams can
be saved or exported in *.wmf format using the Windows
clipboard.
PowderCell is free of charge and can be downloaded
from the following Web site:
http://www.bam.de/a_v/v_l/powder/e_cell.html
The program, all essential data, and some example files of
crystal structures are included in the compressed file. Be-
cause of the intensive calculations during refinement, a PC
with Pentium CPU is recommended.
Acknowledgments
The authors wish to thank U. Miiller for his cooperation
with regard to the implementation of subgroups. Further-
more, we are grateful to R. Allmann, L. Cranswick, and B.
Miiller for inspired discussions and to all users who helped
us in debugging the program.
Hahn, T. (1995). International Tables for Crystallography Volume A -
Space group symmetry (Kluver Academic Publisher, Dordrecht/Boston/
London).
Kraus, W., and Nolze, G. (1996). "POWDERCELL - a program for the
representation and manipulation of crystal structures and calculation of
the X-ray powder pattern," J. Appl. Crystallogr. 29, 301-302.
Miiller, U. (1994). "Relations between Wyckoff positions among crystallo-
graphic group-subgroup relations," Suppl. Issue No. 8, XV. European
Crystallographic Meeting, Dresden, 28. August-2. September, Book of
Abstracts, Z. Krist., 203.
Young, R. A. (1995). IUCr Monographs on Crystallography: The Rietveld
Method (Oxford University Press, Oxford), 3rd ed.
Calendar of Meetings
Donald R. Petersen
Greenleaf Associates
6210 Siebert Street
Midland, MI 48640-2724
23-29 January 1999
23rd Annual Conference on Composites, Advanced Ce-
ramics, Materials and Structures. Cocoa Beach, Florida,
USA. [Contact: American Ceramic Society, Post Office Box
6136,
Westerville, OH 43086-6136, USA. Fax:
1.614.794.5882; E-mail: customersrvc@acers.org; Info:
http://www.acers.org].
8-12 February 1999
AXAA99 Eleventh National Workshops and Conference
of the Australian X-ray Analytical Association: Analyti-
cal X-rays for Industry and Science. Parkville (near Mel-
bourne) Victoria, Australia. Held at the Victorian College of
Pharmacy. Emphasis on XRD, XRF, and X-ray surface
analysis. February 8-9 devoted to workshops, February
10-12 to the conference proper. [Contact: Dr. Mick Gould,
13 Jeffrey Street, Mt. Waverley, Vic. 3149, Australia. Tel:
61.3.9887.8003;
Fax: 61.3.9887.8773; E-mail:
ca@netwide.com.au; Info: http://www.latrobe.edu.au/www/
axaa].
28 February-4 March 1999
128th Annual Meeting and Exhibition: The Minerals,
Metals and Materials Society (TMS). San Diego, Califor-
nia, USA. [Contact: TMS, 420 Commonwealth Drive, War-
rendale, PA 15086-7514, USA. Tel: 1.724.776.9000; Fax:
1.724.776.3770; E-mail: tmsgeneral@tms.org; Info: http://
www.tms.org].
8-10 March 1999
7. Jahrestagung der Deutschen Gesellschaft fur Kristal-
lographie. Leipzig, Germany. [Contact: Frauen B. Kahnt, H.
Schwarzer, Universitat Leipzig, Institut fur Mineralogie, Kri-
stallographie, und Materialwissenschaft, Scharnhorststrasse
20,
D-04275 Leipzig, Germany. Tel: 49.341.973.6250; Fax:
49.341.973.6299; E-mail: dgk99@rz.uni-leipzig.de; Info:
http://www.uni-leipzig.de].
15-19 March 1999
International Centre for Diffraction Data, Spring Meet-
ing. Newtown Square, Pennsylvania, USA. Annual member-
ship meeting. [Contact: Linda Shertz, International Centre
for Diffraction Data, 12 Campus Boulevard, Newtown
Square, PA 19073-3273, USA. Tel: 1.610.325.9814; Fax:
1.610.325.9823; E-mail: shertz@icdd.com; Info: http://
www.icdd.com].
259 Powder Diffr., Vol. 13, No. 4, December 1998International Reports 259
http://dx.doi.org/10.1017/S0885715600020856
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Intergranular and intragranular cracks that usually form during sintering of yttrium manganite (YMnO3) ceramic samples hinder the densification process of this ceramic and deteriorate its magnetic and ferroelectric properties. To overcome this problem, mechanochemically synthesized YMnO3 powder was sintered using two different processes: Conventional Sintering (CS) and Pulsed Electric Current Sintering (PECS). All samples were characterized by XRD, SEM and FESEM and their magnetic and ferroelectric properties were investigated. Apart from their phase composition, conventionally sintered ceramic samples showed cracks throughout their whole volume, reaching a maximum relative density of 85 %. However, it was found that PECS process could significantly reduce the presence of cracks within samples whose relative density reached 99.8 %.
... The calculated powder diffraction patterns were simulated based on the reference structural data with the use of the program PowderCell 2.4 [25]. The experimental diffraction patterns obtained at Kurchatov's source of synchrotron radiation were integrated in the program Fit2D [26]; the same program was used for calibrating the distance between the sample and the detector. ...
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This article opens a series of publications devoted to the preparation and stabilization of new high-temperature (HT) semiconductor phases A (III) - B (VI), which have a large number of vacancies and possess a number of unique properties. In this first work from the proposed series, the T-x diagram of the Ga – S system was investigated in the composition range x = (30.0 – 60.7) mol % S, and then the structural identification of new HT phases was carried out. For the Ga – S system, four polymorphic (α-, α'-, β-, γ-) Ga2S3 phases of different symmetry were found and displayed on the phase diagram near the Ga2S3 composition (x ∼ 60.0 mol% S). For the first time, it became possible to obtain in-situ a reliable direct proof for the existence of equilibrium in narrow temperature range for the re-opened cubic phase γ-Ga2+δS3 (x ≈ 59.0 mol % S), which was isolated at room temperature in a fairly pure form. We also confirmed the presence of other hexagonal (α-, β-) Ga2S3 modifications, existing at much higher temperatures than the cubic γ-Ga2+δS3 phase. It was shown that the polymorphic α-Ga2S3 and α′-Ga2S3 phases mentioned in the literature form superstructures from the parent β-Ga2S3 phase. The observed structural variants for all four Ga2S3 polymorphic phases, containing up to ¹/3 of vacancies in the Ga sub-lattices, are closely related to different methods of ordering Ga vacancies. The reliability of our studies follows from the combination of the methods used: differential thermal analysis (DTA), microstructural local analysis (TEM, HREM, SAED), powder X-ray diffractometry (XRD), including high-temperature synchrotron XRD.
... Afhankelijk van de procesparameters komen verschillende fasen voor in de uiteindelijke absorberlaag. Nolz98], dat niet alleen toelaat het theoretisch XRD-spectrum te berekenen aan de hand van een ingegeven kristalstructuur, maar dat hierbij ook rekening houd met een aantal experimentele parameters (zoals geometrie van de opstelling, gebruikte stralingsbron, gebruik monochromator, slits...), teneinde het spectrum waarheidsgetrouw te kunnen simuleren. Daarnaast is het met deze software mogelijk een zogenaamde 'verfijning' door te voeren waarbij het berekende spectrum gefit wordt aan het experimentele spectrum door variatie vanéén of meerdere parameters. ...
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Mathematical models for microalgae and cyanobacteria are seldomly validated for different algal species, as such limiting their applicability. Therefore, in this research, a previously developed kinetic model describing the growth of the green microalgae species Chlorella vulgaris was used to simulate the growth of the cyanobacterium Arthrospira platensis and the red alga Porphyridium purpureum. Based on a global sensitivity analysis, the model parameter µmax,A was calibrated using respirometric-titrimetric data. Calibration yielded values of 5.76 ± 0.17 d-1, 2.06 ± 0.16 d-1 and 1.06 ± 0.09 d-1 for Chlorella vulgaris, Arthrospira platensis and Porphyridium purpureum, respectively. Model simulations revealed that the biological growth equations in this model are adequate. However, increased light intensities triggered a survival mechanism for Arthrospira platensis, which is currently not taken into account by the model, leading to bad model accuracy under these circumstances. Future work should address the most important survival mechanisms and include those in the model to widen its applicability.
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Silver carbonate (Ag2CO3) is a material currently used for artificial carbon storage. In this work, we report synchrotron X-ray powder diffraction (XRD) experiments under high pressure and high temperature in combination with density-functional theory (DFT) calculations on silver carbonate up to 13.3 GPa. Two pressure-induced phase transitions were observed at room temperature: at 2.9 GPa to a high-pressure (HP1) phase and at 10.5 GPa to a second high-pressure phase (HP2). The facts that a) the HP2 phase can be indexed with the initial P21/m structure, b) our DFT calculations predict the initial structure is stable in the entire pressure range, and c) the HP2 phase is stable under decompression suggest that the intermediate HP1 phase is a product of the appearance of non-hydrostatic stresses in the sample. The observed structural transformations are associated to a high sensitivity of this compound to non-hydrostatic conditions. The compressibility of Ag2CO3 has also been determined, showing the c axis is the most compressible and that the bulk modulus increases quickly with applied pressure. We attribute both observations to the weak nature of the closed-shell Ag–Ag interactions in this material. The behavior of Ag2CO3 under heating at approximately 3 GPa was also studied. No temperature-induced phase transitions were found at this pressure, and the thermal expansion was determined to be relatively high for a carbonate.
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A new method is proposed for controlling the composition (nonstoichiometry) of low-volatile inorganic compounds. The basic principle of the method is the introduction (or removal) of one of the components into the low-volatile compound using reversible selective chemical vapor transport (CVT). Theoretical analysis is used to identify the process parameters determining the direction of mass transport: source temperature T1, source composition x1, and sample temperature T2. Using nonequilibrium thermodynamics concepts, steadystate conditions are found under which mass transport ceases. A new type of phase diagram, x2–T1–T2, is proposed, which describes the state of CVT systems under steady-state conditions without mass transport. The CVT process is used to prepare GaSe crystals with different deviations from stoichiometry. The crystals are characterized using x-ray diffraction and cathodoluminescence spectroscopy. The stability regions of two GaSe polytypes in the T-x phase diagram are located. CVT is used to control the compositions of phases in the In–S system. The advantages of the CVT method are analyzed with application to control over the composition of inorganic compounds.
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We studied the effect of Mn on the structure and properties of Cd3−xMnxAs2 crystals with x = 0–0.24, synthesized by direct fusion of high-purity elements. Obtained X-ray diffraction patters suggest that the incorporation of Mn promotes a structural phase transition from primary α-Cd3As2 (x = 0) phase to the α''– Cd3As2 (x = 0.24) phase, while at intermediate compositions both phases can coexist. In addition, the increase of Mn content results in the decrease of lattice cell parameters, which effectively saturates for x > 0.13. Microstructural, calorimetric and magnetometry studies suggest that at high Mn content (x = 0.24) secondary MnAs phase appears. Using obtained results, we estimated the solubility limit of Mn in Cd3As2 as x~0.13, which corresponds to the formation of ternary Cd3−xMnxAs2 compound where Cd atoms are partially substituted by Mn. Formation of ternary compound was also suggested by the results for Cd3As2 + MnAs composite systems, where we also observed the presence of CdAs2 phase, which is a byproduct of corresponding reaction. Additional studies suggested that the CdAs2 phase formation in composite system can be prevented if one uses the Cd3−xMnxAs2 compound instead of pure Cd3As2 as a matrix material.
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The main component of this program is a simultaneous representation of the unit cell and the calculated powder pattern. It allows the manipulation of the crystal structure by moving selected atoms of the asymmetric unit. The resulting powder pattern can be directly compared to experimental data in order to obtain reliable starting values for further computations in refinement programs.
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The first edition of this volume appeared in 1983 and a Brief Teaching Edition appeared in 1985 (M.A. 86M/0069). It deals specifically with crystallographic symmetry in 'direct space' but moves away somewhat from the special topic of X-ray structure determination, to provide data and text which are useful for all aspects of crystallography. Apart from corrections of errors from the first edition, this edition incorporates two new sections on normalizers of space groups.-R.A.H. Inst. fur Kristallographie, Rheinisch-Westfalische Technische Hochschule, Aachen, West Germany.
Relations between Wyckoff positions among crystallographic group-subgroup relations
  • U Miiller
Miiller, U. (1994). "Relations between Wyckoff positions among crystallographic group-subgroup relations," Suppl. Issue No. 8, XV. European Crystallographic Meeting, Dresden, 28. August-2. September, Book of Abstracts, Z. Krist., 203.
IUCr Monographs on Crystallography: The Rietveld Method
  • R A Young
Young, R. A. (1995). IUCr Monographs on Crystallography: The Rietveld Method (Oxford University Press, Oxford), 3rd ed.