Zeitschrift
fUr Kristallographie,
Bd. 125, S. 437-449
(1967)
The crystal structure and refinement
of ferrimagnetic barium ferrite, BaFe12019*
By W. D. TOWNES, J. H. FANG ** and A. J. PERROTTA
Institute
for Exploratory
Fort
Research,
U. S. Army Electronics
Monmouth,
New Jersey
Command
Dedicated to Prof. Dr. G. Menzer on the occasion of his 70th birthday
(Received
March
15, 1967)
Auszug
Die Kristallstruktur
von BaFe12019 wurde bestimmt
und dreidimensional
verfeinert.
Die Raumgruppe
ist P63/mmc; die Elementarzelle,
mit a = 5,893 A,
Die Struktur
ist aufgebaut
aus
c = 23,194 A, enthiilt zwei Formeleinheiten.
kubischen
und hexagonalen
dichtesten
Kugelpackungsschichten
mit der Folge
BAB'ABOAO'AO in Richtung der c-Achse. (Die gestrichenen Buchstaben deuten
Schichten
im Verhiiltnis
von einem Ba-Atom
zu drei O-Atomen
an.) Die Verfeinerung beruht auf 900 beobachteten
Interferenzen;
sie wurde bis R = 0,059
getrieben.
Das Ergebnis
fiihrte zur Bestiitigung
der Isotypie
mit Magnetoplumbit PbFe12019' Das Anionengeriist
zeigt betriichtliche
Starung der dichtesten
Packung.
Die Struktur
ist ungewahnlich
in zweierlei Hinsicht.
Erstens:
Eisenatome, die ihrer Anzahl nach auf den horizontalen
Spiegelungsebenen
liegen
sollten, sind daraus urn 0,156 A, statistisch
in beiden c-Richtungen,
herausgeriickt. Zweitens:
Einige Oktaeder
urn Fe-Atome
kommen in Paaren mit gemeinsamer
Fliiche vor; sie bilden Koordinationsgruppen
Fe209, in denen der
Fe-Fe-Abstand
urn 0,45
ist. Eine beachtenswerte
A vergraBert,
Ausnahme
der O-O-Abstand
von einigen
urn 0,35
A verkleinert
Pauling-Regeln.
Abstract
The crystal structure of barium ferrite, BaFe12019, has been determined and
refined with the use of three-dimensional counter data. The symmetry is P63/mmc;
the unit cell whose dimensions
are a = 5.893 A and c = 23.194 A, contains two
formula units. The structure
is built up of ten close-packed
hexagonal)
layers of barium and oxygen atoms. The sequence
at the Austin, Texas, meeting of the American
* Presented
Association,
March 1966.
Permanent
address:
Department
of Geology, Southern
**
sity, Carbondale,
Illinois.
(both cubic and
of the layering in
Crystallographic
Illinois
Univer-
438
W. D. TOWNES, J. H. FANG and A. J. PERROTTA
the c axial direction is BAB'ABCAC'AC.
The primed lett3rs denote layers consisting of one barium to three oxygen atoms. The refinement
was based on 900
observed reflections
and was taken to a final R value of 5.9%, The result can.
firmed the isotypic relationship
with magnetoplumbite,
PbFe12019. The anion
framework
was found to be significantly
distorted
from close-packed
geometry.
The structure
is unusual in two respects:
(1) one set of iron atoms, which are
on the horizontal
mirror planes, is in trigonal-bipyramidal
coordination.
This
iron
atom
is split
into
two
half
atoms
0.156
A away
(2) some iron octahedra
occur in pairs which share a
coordination
groups. The distortion
that occurs in
Fe-Fe
distance by 0.45 A, while the decrease in the
face is 0.35 A. The compound
is a notable exception
from
the
mirror
plane,
and
common face to form FeP9
these groups increases the
0-0
distance in the shared
to some of PAULING'S rules.
Introduction
Barium ferrite (BaFe12019) has a mixed hexagonal and cubic
close-packed structure, with a barium atom substituting for an oxygen
position, and iron atoms occupying interstices. It is one of the so-called
hexagonal ferrites (ferroxdure) which have been extensively studied
in recent years because of their high coercive force as compared with
the well-known cubic ferrites (ferroxcube).
KOHN and ECKART (1964 a, b; 1965) of this laboratory have discovered a number of hexagonal ferrite mixed-layer structures, most
of which are based on the M phase (BaFe12019) and Y phase
(Ba2Me~+ Fe12022). BRAUN (1957) has refined the structure of the
Y phase; however, no refinement of the M phase has been carried out.
Therefore, it was decided to undertake the refinement of the crystal
structure of the M phase in order to establish a basis for further
analysis in the mixed-layer structures and also to aid in the magnetic
study of the M phase where iron is partially substituted
by other
transition elements. A least-squares
refinement using counter data
was thought desirable, permitting the determination
of more accurate
atomic positions.
Unit cell and space group
Precise lattice parameters for the hexagonal unit cell were determined with the General Electric single-crystal orienter using MoKa
radiation, a 0.02 degree detector slit and a 1.0 degree take-off angle.
The wavelength of MoKcx1 was taken to be 0.70926 A. Values from
four hO. 0 reflections in the range 330 < e < 570 were extrapolated
against the NELSON-RILEY (1945) function to obtain a = 5.893 A,
and a similar extrapolation based on six OO.l reflections in the range
440 < e < 720 yielded a value of c = 23.194 A. Laue and Weissenberg
The crystal
structure
of ferrimagnetic
barium
ferrite
439
photographs were consistent with the space groups P63mc, P62c, and
P63/mmc. The subsequent refinement of the structure has justified
the choice of the centrosymmetric
space group P 63/mmc.
Collection and corrections of intensity data
Two sets of intensity data were collected. Both sets were counter
data measured with a G. E. XRD-6 diffractometer
equipped with
a Tl-activated
NaI scintillation counter and pulse-height analyzer.
MoKiXradiation was used to record reflections within (sin fJ)/ A= 1.186.
The first set of data was two dimensional, namely hO. land hk. 0,
and a total of 578 reflections were measured by the stationary-crystal,
stational-counter
technique employing balanced filters. A constant
counting rate of 40 seconds was employed. The iXIiX2resolution was
corrected by using a curve similar to that of TULINSKY et al. (1959).
A standard reflection, 30.0, was measured at the beginning of each
day throughout the experiment. The day-to-day fluctuations in this
reflection were found to be less than 4 °/0. Also a few equivalent
reflections were measured, and their differences did not exceed 10%.
A second set of intensity data, which was three-dimensional,
was
measured by the moving-crystal,
moving-counter
technique,
and
a total of 900 reflections were collected.
The crystal used in this study was a sphere with a radius of 0.26mm.
The linear absorption coefficient is 155.9 cm-I. The data were corrected
for absorption and the usual Lorentz-polarization
effect in order to
obtain a set of structure factors.
Structure determination and refinement
Barium ferrite is isotypic with magnetoplumbite
(PbFe120I9)' whose
structure has been determined by ADELSKOLD (1938) from powder
data. The positional parameters reported by him were used as a starting point for the subsequent refinement. The scattering curve for
Fe+3 was taken from the International tables tor x-ray crystallography
(1962) and for Ba2+ from THOMAS and UMEDA (1957); both were
corrected for the real part of dispersion. The form factor for 02- was
obtained from SUZUKI (1960).
The unusually large number of unobserved reflections (about 1/3 of
all the reciprocal-lattice
points within 2 fJ = 115°) can be attributed
to the fact that the majority of the atoms are located at or near special
positions of the type (x, 2x, z) with x = t and l. There was little
or no contribution to reflections of the type h-k = 3n, l = 2n + l.
Table 1. Final atomic coordinates and isotropic temperature factors
Left columns are from three-dimensional
data and right from two-dimensional
Atom
Ba
B
z
I
I
Ba
y
x
Equipoint
data
2c
2c
1
1.
3
"3
2
"3
2
"3
1
4"
I
1
4"
.31 (1) A.2
.46(5)A.2
I
Fe(1)
Fe(1)
2a
2a
0
0
0
0
0
0
.20(3)
.36(10)
!Fe (2)
Fe(2)
4e
2b
0
0
0
0
.2567 (1)
1
4"
.36(5)
1.30 (11)
Fe(3)
Fe(3)
4f
4/
2
2
"3
t
1
"3
"3
.0272 (1)
.0272 (2)
.21 (2)
.44(7)
Fe(4)
Fe (4)
4f
4f
2
2
1
1
"3
"3
"3
"3
.1902(1)
.1901
.22(2)
.35(7)
Fe(5)
Fe(5)
12k
12k
2x
2x
.1083(1)
.1082(1)
.23(1)
.41 (3)
0(1)
0(1)
4e
4e
0
0
0
0
.1501 (4)
.1499(14)
.29(10)
.07 (38)
0(2)
0(2)
4f
4/
1
"3
1.
3
2
"3
3
~.0546(4)
.0528(12)
.46(11)
.75 (35)
0(3)
0(3)
6h
6h
.8159 (10)
.8166(34)
2x
2x
4"
t
.44(9)
.52 (23)
0(4)
0(4)
12k
12k
.8447 (7)
.8480 (21)
2x
2x
.0522 (2)
.0521 (5)
.31 (6)
.78(16)
0(5)
0(5)
12k
12k
.4967 (8)
.4980 (24)
2x
2x
.1495 (2)
.1495 (6)
.41 (5)
.63 (16)
.1687(1)
.1691(5)
1
(2)
The crystal
structure
of ferrimagnctic
barium
ferrite
441
Table 2. Interatomic distances in BaFe12019
(a) Fe-O distances:
Fe(l) octahedron
Fe(4) octahedron
Fe(5)
Fc-0(4)
Fe-O (3)
-0(5)
Fc-O(l)
-0(2)
-0(4)
-0(5)
octahedron
Weighted-mean
Fe-O
octahedral
Fe (3) tetrahedra
Fe (2) trigonal
(b) Ba-O
distance:
Fe-O (2)
-0(4)
bipyramids
Fe' -0 (1) *
Fe"-O(l)
Fe' -0 (3)
Fe" -0 (3)
(d) Fe-Fe
1.975
:::!::0.008
1.977
::!:: 0.005
2.091
::!:: 0.006
2.106
:::!::0.004
1.928
:::!::0.005
A
2.012
1.897
::!:: 0.011
1.936
::!:: 0.009
2.170
:::!::0.011
2.472
::!:: 0.011
1.886
::!:: 0.010
1.886
:::!::0.010
2.952
::!:: 0.001
2.865
::!:: 0.006
2.982
:::!::0.010
distances
(within
2.769
::!:: 0.010
2.947
::!:: 0.001
2.949
:::!::0.001
3.049
2.762
::!:: 0.001
::!:: 0.011
3.255
:::!::0.017
2.625
::!:: 0.017
2.849
::!:: 0.006
2.746
::!:: 0.012
3.147
::!:: 0.012
2.896
::!:: 0.009
2.872
::!:: 0.007
2.888
:::!::0.014
3.005
:::!::0.014
Fe (i)-Fe (3)
-Fe(5)
Fe (3)-Fe (5)
Fe (4)-Fe (4)
3.460
3.045
3.495
2.778
:::!::0.001
:::!::0.001
:::!::0.001
:::!::0.001
Fe (5)-Fe (5)
2.910
:::!::
3.5 A):
-Fe
*
::!:: 0.007
distances:
0(1)-0(3)
-0(4)
-0(5)
0(2)-0(4)
-0(4)
-0 (5)**
0(3)-0
(3)
--0(3)
-0(5)
0(4)-0
(4)**
-0(4)
-0(5)
-0(5)
0(5)-0(5)
-0(5)
If Fe(2)
is on the
mirror
(3) = 1.893 A. See the text
** Denotes shared edges.
Fe-O
::!:: 0.006
distances:
Ba-O (3)
-0(5)
(c) 0-0
1.995
2.060
plane
at
z =
for details.
(5)
t,
0.003
2.983 ::!::0.003
then
Fe-O(l)
= 2.316A
and
442
W.D.
TOWNES,
J.H.
Table 3. Observed
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379 "9
7 511
1 o 12
"8
2
1062
'" 1127
5
6
7
558
"7
201
213
396
3"0
227
251
663
777
370
325
148
215
402
328
1183 1139
863
890
258
"9
612
605
21/t
15')
1,70
397
651
450
structure
531
492
'07
}42
262
2(';67
',01
217
1776
1255
730
2465
2126
1606
1330
,
364
1
1175
200
A. J. PERROTTA
583
501
397
327
"3
218
397
281
418
201,
330
637
348
216
}115
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1611
197
6
7
8
212
353
660
398
229
365
1535
245
5
',187
265
788
8
5
6
1.96
367
311,
1048
289
802
\
3
603
290
1
,3
271
1369
218
925
211
485
11')
3)1j
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5
8
9
10
t
,.
270
1336
203
8Y3
205
296
6
8
6
58'1
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370
,
5
7
8
10
IFol IF,/
395
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321
274
583 5'6
897
863
325
220
203
3
5
6
8
9
10
IFol IF,I
363 335
286
284
2040 2165
2
3,
and
and calculated
3
4"
6
"9
"8
472
3';!6
207
5
239
'"
4~3
366
353
'04
291
293
20')
367
590
43')
210
27B
223
376
"3
652
220
311
5
6
7
10
3
5
9
!:!5':I
23
FANG
378
276
219
,
19
o 20
575
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358
2917
496
"9
3"
2799
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~375
1 20
380
289
621
1641
257
228
510
1.40
36,
408
282
"3
302
229
2 20 2239
J31
269
263
1015
371
3 20
315
208
238
211
20 1348
238
"5 20 250
486
396
350
1549
251
212
"8
"7
358
372
278
309
'"
211
2151
329
271
258
1011
389
293
218
2"
182
1365
231
3"
The
crystal
structure
of ferrimagnetic
barium
443
ferrite
Table 3. (Continued)
k 1 IF,I
520
021
1 21
233
14"8
224
220
842
799
1211t
lu6
8"
815
221
,
7
5
6
6
0
1
2
3
4
6
7
8
10
1
2
3
4
6
7
2
3
4
5
6
8
3
5
6
4
5
6
1
4
5
7
8
2
3
5
6
8
3
4
6
7
4
5
7
0
1
2
3
4
6
7
8
9
10
1
3
4
7
2
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21
421
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o 22
122
2 22
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4 22
o 23
123
22,
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024
124
224
570
594
1050
220
521,
756
IF,I
219
1271
234
200
815
771
1102
1068
838
8"
568
608
1010
187
525
731
71,8 766
~;/II
603
5
717
71')
188
211
437
1t57
2109
2012
452
388
1087
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358
328
869
790
1312
1237
388
379
541
528
407
395
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422
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237
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332
301
292
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321
207
213
1735
425
768
266
1640
413
691
234
562
836
297
229
205
1094
331
494
476
356
548
856
287
237
189
1108
340
482
447
357
444
190
209
486
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246
277
304
307
250
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391
272
237
1171
269
640
516
559
777
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391
253
371
565
213
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339
973
44'
208
230
496
390
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262
272
302
299
239
284
379
257
230
1297
279
609
508
530
856
229
375
230
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610
231
474
344
1073
k 1
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4
5
6
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6
4
5
b
5
1
2
4
5
7
8
10
2
3
5
6
8
3
4
6
7
4
5
7
5
6
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1
2
3
224
3 24
4. 24
521,
025
125
2 25
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25
425
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4
5
6
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1 26
4
226
326
4 26
o 27
1 27
2 27
327
4 27
o 28
1 28
228
k 1 I F,I IF, I
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224
211
495
351
lItO
615
161
289
753
220
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2875
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1164
916
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618
3 28
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725
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382
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795'
694
571,
490
700
2073
1582
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626
538
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429
1377
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416
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827
2699
2295
681
435
11,89
1197
811
737
667
537
517
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2008
1632
499
625
577
514
413
1382
305
340
406
250
401
304
309
218
339
290
261
173
285
345
349
200
290
248
215
357
302
220
233
257
252
201
261
589
503
3111
585
520
1138
3110
291
11/13
315
1117
328
277
292
1978
331
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437
1270
208
231
417
320
292
1687
282
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307
236
286
220
235
281
259
229
2106
272
244
226
262
51111
461
307
535
1178
1122
3117
J07
421
332
1111
352
289
285
1832
300
257
432
1271
1')2
207
385
299
306
1582
129
229
:; 29
29
o }O
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130
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30
4 }O
031
4
5
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8
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229
210
382
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562
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711,
665
979
389
288
216
237
287
632
247
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264
294
216
863
265
224
214
269
234
522
321
1029
894
274
289
534
359
302
305
278
239
2",
743
559
226
247
232
271
329
511
369
1632
219
388
347
916
1729
476
457
1454
390
327
1049
233
411
1184
213
1305
327
373
955
308
557
235
179
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389
1164
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791
707
964
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783
741
577
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573
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927
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263
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262
243
3 34
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524
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269
276
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318
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282
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210
200
208
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242
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255
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292
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364
315
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1189
316
415
312
602
349
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803
400
295
513
257
298
211
283
513
331
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4 36
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137
2 37
3 37
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775
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652
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281
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206
260
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335
291
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725
239
211
275
289
233
246
859
322
252
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1364
1196
271
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200
216
k 1 IF,I IF,I
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281
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280
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261
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603
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235
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308
310
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196
724
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298
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187
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1275
1167
248
863
262
226
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2 39
3 39
o 40
1 40
2 40
340
o 41
4
5
7
2
3
5
3
4
0
2
3
4
6
1
4
2
3
1
5
7
2
3
3
0
1 41
241
042
1 42
2 42
3 42
043
1
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2 43
o 44
3
1
4
2
2
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1
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1
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2
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3
6
1
2
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0
1
2
3
4
5
2
4
3
2
1
2
1 .-
2 .-
045
o 46
146
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1 47
o 48
1 48
o 49
o 50
051
052
o 53
054
2"
1040
241
265
581
218
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648
550
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201
448
549
499
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276
352
349
426
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375
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254
588
491
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402
381
539
482
516
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906
770
578
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808
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242
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200
320
399
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360
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407
464
288
713
635
265
327
629
320
440
357
634
606
1195
339
638
250
570
255
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205
420
420
374
277
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230
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232
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606
542
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225
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545
ItS3
293
250
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214
585
460
509
421
435
519
481
527
460
878
799
646
867
817
771
215
241
255
225
192
747
679
529
428
179
324
440
490
3"
452
404
517
268
730
678
274
286
634
328
517
340
713
679
1364
}69
689
221
637
281
237
206
421
503
444
317
The two-dimensional
data were used initially In the refinement.
Using the full-matrix least-squares program of BUSING et al. (1962),
as translated to extended ALGOL by GALLAHER and KAY (1964),
convergence was achieved in 6 cycles using unit weight. The number
of observed reflections per variable IS about 15. In the last cycle,
individual isotropic temperature
factors were varied. The value of
R was 11.7% for 395 observed reflections. The final parameters are
444
W. D. TOWNES, J. H. FANG and A. J. PERROTTA
given in the right columns of Table 1. As seen in the table, the temperature factors of all iron atoms are within a narrow range of 0.36 to
0.44, and that of oxygen from 0.52 to 0.75. Two exceptions are noted,
however. They are: B [Fe(2)] = 1.30 and B [0(1)] = 0.07. This iron
atom is in five-fold coordination, and 0(1) atoms are equatorially
bonded to Fe(2). When this paper was presented at the Austin meeting
of the American Crystallographic
Assocation on March 1966, Dr.
DAVID HARKER pointed out that the Fe(2) atom might be disordered.
At about the same time, two of us (A.J.P. and W.D. T.) had calculated the two-dimensional
Fourier map and found that the Fe(2)
peak was elongated along the c axis, supporting Dr. HARKER'S suggestion.
When the three-dimensional
scan data became available, the
refinement was initiated with the coordinates obtained from the
two-dimensional
refinement. Also the Fe(2) atom was moved 0.2 A
away from the horizontal mirror plane (from equipoint 2b to 4e,
thus making them half atoms), the
R factor dropped immediately, and
the temperature
factors of Fe(2)
and 0(1) also became very reasonable.
The final R value for
the 900 observed reflections was
5.9%, The parameters
from the
last cycle are given in the right
columns of Table 1. The corresponding bond lengths, calculated from
the three-dimensional
refinement,
are listed in Table 2. The observed
and calculated structure factors are
in Table 3.
Description of the structure
The structure of barium ferrite
can be derived from that of magnetite. It might
be visualized
as
composed of four double layers of
oxygens, plus two single layers, in
which
Fig. 1. Packing model of oxygen
(and barium) atoms
t
of the oxygens
are replaced
by barium atoms. The latter two
layers are interleaved between the
The crystal
structure
of ferrimagnetic
barium
445
ferrite
first and the second, and the third and fourth double layers, delineating
the magnetite block (the second and the third). These two layers are
located at the horizontal mirror planes at !e and ie. Figure 1 shows
a packing model of oxygen (and barium) atoms. The iron atoms are
in the octahedral and tetJ.'ahedral holes as in magnetite*, except for
one set of iron atoms which are coordinated to five oxygens. Thus
the unit cell contains eighteen octahedral, two trigonal bipyramidal,
and four tetrahedral
iron atoms. They are illustrated in Fig. 2. The
Fig.2a.
Smaller
Bottom:
C layer (belonging
to the unit cell below). Top: B layer.
solid circles are octahedral
Fe atoms, and the larger tetrahedral
iron
Fig. 2 b
Fig.2b.
Fig.2c.
Bottom:
Fig.2c
B layer
(the same B as in Fig.2a).
Top: A layer
Bottom:
A layer (the same A as in Fig.2b).
Top: B' layer.
solid circles at the unit-cell corners are 5-fold Fe atoms
The small
Fig. 2. A portion of layer stacking in BaFe12019 showing 6-, 5-, and 4-fold coordinations of iron atoms in projection
along the c axis
packing of the oxygen atoms in the middle two double layers are
cubic, and in the plates above and below the magnetite block, starting
from the barium-containing
layers, it is hexagonal close packing.
Thus the notation, BAB'ABOAO'AO,
can be used to denote the
layer sequence along the c axis, where the primed letters indicate
Ba-substituted
layers.
----
is made here to distinguish
between normal and inverse
* No distinction
spinel, for no divalent iron is involved. Thus "magnetite"
structure,
as used here,
refers to the degree of filling of octahedral
and tetrahedral
interstices
only.
2*
446
w. D. TOWNES, J. H. FANG and A. J. PERROTTA
There are two remarkable structural features in barium ferrite;
namely the five-fold coordination of Fe(2) and the sharing of Fe(4)
octahedral faces. These unusual coordinations can be seen clearly in
the polyhedral model of Fig. 3. For the sake of clarity, however, four
octahedra,
at 000, 00 t, 1 1 t, and 1 1 1, are omitted from the
drawing. Both of these unusual configurations are brought about by
Fig. 3. Polyhedral
model
of BaFe1Z019
the mirror planes at ic and ic. In the Fe209 coordination group,
there are two Fe(4) atoms, three 0(3) atoms in the shared face, and
six 0(5) atoms in layers of three, above and below the Fe(4) atoms.
The theoretical
and observed distances between the octahedral
centers are shown in Table 4. The per cent shortening of 0.71 and
0.58 are given by PAULING (1960, p.560). The last column shows
the percentage distortion due to cation-cation
repulsion from the
The crystal
Table 4. Fe-Fe
Shared
element
Corner*
Edge
Face
*
structure
distances
of ferrimagnetic
for octahedra
Theoretical
distance
4.00
X 1.00 = 4.00
= 2.84
4.00
X 0.71
4.00
X 0.58
barium
sharing
ferrite
various
elements
Observed
distance
A
= 2.32
4.00
Distortion
X 1.00 = 4.00
= 2.97
4.00
X 0.74
4.00
X 0.69
447
A
= 2.77
0%
4%
19%
Not observed in BaFe12019.
undistorted polyhedra. Since no octahedra share corners in barium
ferrite, the theoretical Fe-Fe distance is obtained by using Pauling's
octahedral radii or r(Fe3+) = 0.60 A and r(02-) = 1.40 A. The compensating distortion increases almost five times as polyhedra goes
from edge-sharing to face-sharing. This trend is also found to be the
case in hexagonal barium titanate (BURBANK and EVANS, 1948).
The 0-0
distances are all reasonable, except one short distance
of 2.625 A and one long distance of 3.225 A. The shortest distance
is exhibited by the 0(3)-0(3)
in the shared face, and the longest
between the 0(3) atoms not sharing the face. Looked at differently,
the six oxygen atoms surrounding the central barium atom are not
arranged as a regular hexagon, but rather as a truncated triangle,
with short edges alternating
with long edges, reminiscent of the
Kekule's structure of benzene. On the average, the intralayer (same
layer) 0-0 distances are slightly longer than the interlayer (between
the layers above and below) distances, as exhibited in many closepacked structures.
The charges surrounding the anions have been
calculated and are listed in Table 5. It is noted that the charge surrounding the 0(2) and 0(4) are in excess of 10%, respectively. These
two oxygen
atoms
make
up the layers
sandwiching
the plane
at c =
t.
The disposition of Fe(2) atom can be described in two different
ways. On the one hand, if the disorder of the iron atom is disregarded
for the time being, the coordination is that of a trigonal bipyramid,
with the Fe-O distance of 1.893 A (equatorial) and 2.316 A (apical).
The trigonal bipyramidal coordination of Fe3+ is a unique feature of
the M phase, not found in other hexagonal ferrites. Its bonding is
usually designated as d3sp with some dSp3 hybrids. However, the lengthening of the apical Fe-O distances, indicating a localized ionic
character, might considerably affect the nature of this hybrid bond.
On the other hand, as pointed out in the structure-determination
section, the Fe(2) atom is split into two half-atoms with the Fe-Fe
W. D. TOWNES, J. H. FANG and A. J. PERROTTA
448
Table
5. Electrostatic-valency
B a I'ancmg
Anion
.
catlOns
Charges of cation
Coordination number
I
Fe(2)
0(3)
"
6"
6"
6"
Fe(3)
~~Fe(5)
"
Fe(5)
Fe(5)
6.
"
2.
1.:£
Ba
1.93
1i
"
Fe(2)
Fe(4)
Fe(4)
"5
6"
6"
,
Fe(l)
Fe(3)
Fe(5)
Fe(5)
0(5)
2.25
6"
6"
Ba
0(4)
2.10
.5
Fe(5)
Fe(5)
Fe(5)
0(2)
Total charges
_~
surrounding anion
-.
I
I
0(1)
I
table
2.25
6
:1
.<
6"
6"
2
1 ~f
Ba
Fe(4)
Fe(5)
Fe(5)
1.67
6"
6"
6.
"
distance of 0.312 A. Considered in this way, we have a case of two
tetrahedra sharing a face, a clear violation of PAULING'S third rule.
Therefore the Fe(2) atom is either oscillating along the c axis or is
statistically distributed on two sites displaced 0.156 A from the central
position on the mirror plane.
Since the magnetic properties of barium ferrite are of some interest,
a speculation on its plausible magnetic structure is therefore in order.
A theoretical value of 20flB per formula unit can be obtained, for
instance if Fe(1), Fe(2), and Fe(4) are coupled ferromagnetically,
giving
+ 4flB'
and
between
Fe(3)
and
Fe(5),
giving
-20flB'
But
this
spin arrangement
would make the linear Fe(1)-O-Fe(2)
coupling
ferromagnetic,
in violation of the superexchange
interaction.
Thus,
a possibility arises that!
of Fe(3) and Fe(4), and i of Fe(5) might
couple ferromagnetically
with Fe(2), still giving the net moment of
though
the
magnetic
cell would then be doubled in this spin
20flB'
configuration.
The crystal
structure
of ferrimagnetic
barium
ferrite
449
Acknowledgments
The authors are grateful to Dr. J. A. KOHN for suggesting the
problem, and for his advice and encouragement
throughout
this
investigation, to Mr. R. O. SAVAGE for growing the crystal, to Mr.
D. W. ECKART for grinding the sphere and his assistance in some of
the data processing, to Mr. A. TAUBER for Laue and Weissenberg
photographs
of barium ferrite, to Mr. ESKANDERNAHOURAY of
Southern Illinois University for the illustrations, and to Dr. H. A. LEVY
of Oak Ridge Laboratory for his instructions in coding the PATCH
subroutine.
References
V. ADELSKOLD (1938), X-ray studies on magneto-plum
bite, PbO . 6Fe20a, and
other substances
resembling
"beta-alumina,"
Na20. 11 Al20a.
Ark. Kern
Mineralog. Geol. Ser. A 12, No. 29, 1-9.
P. B. BRAUN (1957), The crystal structures
of a new group of ferromagnetic
compounds.
Philips Res. Rep. 12, 491-548.
R. D. BURBANK and H. T. EVANS, JR. (1948), The crystal structure
ofhe:xa~onal
barium titanate.
Acta Crystallogr.
6, 330-336.
W. R. BUSING, K. 0. MARTIN and H. A. LEVY (1962), OR FLS, a FORTRAN
crystallographic
least-squares
program.
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