INDUSTRIAL
ENGINEERING CHEMISTRY
AND
ANALYTICAL EDITION PUBLISHED
BY T H E
AMERICAN
CHEMICAL
SOCIETY
0
HARRISON
E.
HOWE,
EDITOR
Tabulated Diffraction Data for Cubic Isomorphs LUDO K. FREVEL, The Dow Chemical Company, Midland, bfich.
C
HEMICAL analysis by the Debye-Scherrer-Hull method consists of matching the diffraction pattern of an unknown material with one or more standard powder patterns (1-6, 11-13, 16, 16, 18-29). In applying this empirical method to a large number of actual analyses, one encounters cases where the patterns sought are not found in a collection of 1-2000 catalogued patterns. In those instances the matching method can be augmented by systematically comparing the diffraction pattern of an unidentified phase with representative patterns of the various known crystal structures in an attempt to establish isomorphism between the unknown phase and one of the standard structures. This comparison method is readily applicable in the case of cubic substances, since their diffraction patterns are recognized by the absence of “splitting” of lines-i. e., in the isotropic system the interplanar distance d h k l is independent of the sign and order of the indices h, li, and 1. The procedure for comparing the diffraction patterns of isomorphous substances has been described previously (8); hence only the tabulated diffraction data for cubic isomorphs are presented here. Figures 1 and 2 contain representative diffraction patterns of 33 cubic crystal structures designated as in the “Strukturbericht” (7, 9, 10, 14). Within each group-e. g., the Astructures-the patterns are arranged in increasing order of complexity. The averaged relative intensities, based predominantly on the Dow file of standard patterns, refer to MoK, radiation; for other radiations well-known corrections for the polarization factor and absorption factor must be considered. The logarithmic scale and index scale of Figures
TABLE11. X-RAYDIFFR-4CTION DATA [Filtered NoK, radiation was used to obtain the powder diffraction data. d = interplanar spacing. I is the intensity of a powder ieflection (in arbitrary units), while I / I I is the relative intensity. The lattice constant of Ag(Br, I) is 5.916 * 0.009 and corresponds to the approximate composition 60 AgBr.40 AgI.1
4.
d, A. 3.77 2.96 2.29 2.087 1.961 1.710 1.479 1.324 1 ,207
I 3 76 2 40 1 10 3 7 4
---. A d
...
111
1.0
... 220 ...
220
0.7
200
222 400 420 422
...
...
...
311
...
... ... ...
0:i3 0.04 0.09 0.05
... 0.3 ... ...
... .
.
I
1 and 2 are useful in the rapid identification of cubic diffraction patterns.
GENERAL PROCEDURE FOR IDENTIFYING A SONCATALOGUED PATTERN. (1) Plot the lo d values and corresponding relative intensities of the unidentiled pattern on a strip of translucent paper; (2) use the index scale of Figure 1 to check if the pattern is cubic; (3) find an isomorphic prototype from Figures 1 and 2, also check Table 111; (4) compute the lattice constant of the unidentified cubic phase and check Table I V ar “Tables of Cubic Crystal Structure” (17‘) * ( 5 ) confirm the identification of the unknown phase by a quaiitative spectroscopic analysis or by spot tests. In case the substance to be identified is not listed in Table IV, one may still establish its type of structure and then synthesize the unknown phase on the basis of the elements present. The following example illustrates the procedure. Columns 1 and 2 of Table I give the diffraction data of an unknown material. On plotting the log d values and checking the index scale of Figure 1, one recognizes that the material consists of two cubic phases, both of which are found t o be isomorphous with sodium chloride (structure B 1 . The res ective lattice constants for phases A and B are 6.96 and 6.64 %.,and according to Table I V the compounds BaTe (6.99 d.) and SrTe (6.65d.) are indicated. However, a qualitative spectroscopic analysis shows potassium t o be the only metallic element present. An examination of Table I V for potassium salts with the sodium chloride structure su gests a solid solution of potassium iodide for phase A and a soli2 solution of potassium bromide for phase B. The silver nitrate test with an aqueous solution of the unknown vields a typical silver halide precipitate, the diffraction pattern of which is identified as a solid solution of silver bromide and silver iodide (see Table 11). Assuming approximate validity for Vegard’s rule and using the crystal radii of theiodide ion (2.20 b.)and of the bromide ion (1.96 d.),one calculates the composition of the mixed silver halide circa 60 AgBr.40 AgI (spot tests on the original unknown for chloride and cyanide being negative), Havingcon-
TABLEI. X-RAYDIFFRACTION DATA [Filtered MoK, radiation was used to obtain the powder diffraction d a b . d = interplanar spacing. I is the intensity of a powder reflection (in arbitrary units) while I / I i ia the relative intensity. The lattice constants for the t w o cubic phases, A and B, are 6.964 * 0.005 A. and 6 , 6 4 3 * 0 , 0 0 9 A,, respectively.] hkl--I/I1-d . A. I Phase A Phase B Phase A Phase B ... 0.50 111 10 4.02 ... 111 0:io 6 3.83 l:oo ... 200 20 3.48 1:ao 200 ... 20 3.315 0:SS ... 220 17.5 2.460 0:ss 220 17.5 2.350 0:io .. iii 6 2.100 iii 0.40 222 2.010 S ... 222 .. 0:io -1 . 920 ”-1.740 2 400 0.10 1.660 2 ... io0 o:io 1.599 1.5 331 ... 0:os .. 1.559 6 420 ... 0.30 1.487 6 ... 420 0:io 1.421 4 422 ... 0:io
1.
--
..
687
INDUSTRIAL AND ENGINEERING CHEMISTRY
688
Vol. 14, No. 9
TABLE111. COMPARISON OF STRUCTURES [The structures having comparable powder patterns are listed in rows. I n the column below each structure are listed examples and criteria distinguishing it from the structure in the first column. ZA is the atomic number of element A. Ihkj refers to the intensity of reflection ( h k l ) . For some structures, such as B 1 two special cases are considered-namely, the CsH type for which the odd reflections (111, 311, 331, etc.) are strong and the RbBr type for which the odd reflections are extremely faint.] Structures Having Comparable Powder Patterns A4
A1
B 32
B3
c1
ZB > > Z A
ZA x ZB
ZA
NaTl. LiIn
InSb, CdTe
SrCly Pt(In, Gala
B1 ~.
B3
ZA
> > ZB
ZB
KH, RbH, CsH, TaC LiI
BeSe, BeTe
D 21
B2
> > ZB
ZA
ZB
.....
....
> > ZA
1200
> Illi
B 32
CI
ZB
> > ZA
NaTl See A 4
B 20
ZA
> > ZB
B2
ZA
> > ZB
-
HgLi, PdBe, BuMg
c1
ZA
> > 2zB
UOz, ThOz, ZrOa, PbFz BaFz, LiaTe MgzPb See A 1 C 15
ZA
> > ZB
AurNa c 2
ZA
.....
....
....
B3 InSb. CdTe
c1
c3
ZA > > ZB Check (110)
BeSe, BeTe, HgS See A 1
B 32
.....
c1
ZB
RbBr, KCl, NaF, SrSe, SnTe ( l l l ) ,(311) very nwak
CsH, RbH, K H See A 1 B3
... Check (110)
CaB6
CsI, CuZn ZA
> > 2zB
UOz, PbFi
.....
ZA x ZB
B1
c1 ZA
ThOz, ZrOa BaFz, Ce0z MgnPb
> Im
Izlo
A2
> > ZA
...
.....
2zB
Z A z ZB
F1 Check I:oo, IZZO
ZA
E 21
z=5
ZB
CSI, CuZn S e e A 2 ; CaBa See D 21
Check Imc
ZA
B3
S5
2zB
> ZA
... B 32
> > ZB
F1 Check (110)
.....
.....
...
J 11
c 3 ZA
> > ZB
Check (110)
H 11
...
(BezCu) See A 4
OsSn
...
CaFz, SrCI:
CaFm, SrClr See A 4
ZB
.....
K 61
G 21
B3 (110) absent
c1
an,
> ac1
...
..
...
.....
...
..
..,
See A 1 c 3
ZA
> > ZB
Agio See A 1
ZB
> > ZA
F1
B 20 Check Izw
G Os
D 5a
D 11
Tetrahedrite (110), (310) very weak
Check (1111, (210), (320)
H 21 (1111, (2211, (311) absent
..,..
c 15
D 11
Check 1311
Check (210), (211), (321)
H 11 Check Iaii
D 11
D 5s
D 61 (?lo), ( Z l l ) , (391) absent
Tetrahedrite (1111, (210) absent
E 21
B2
G 0:
B 20 Check Izoo
F1
G 21
c 2 Check IZOO,1222
K 61 Check 11.m
H 11
c 15
H 5s
c1
D 61
( l l l ) , (210), (320) absent
.....
Check 1111,IZZD,1222 Check
111~ 1222
H 41a
c 2 Check Iloo, IZZI
H 21
B 20 Check (1111, (311)
(110) absent
See A 2
.....
....
.....
.....
...
.....
....
.....
...
.....
.....
.....
...
.....
..... .....
.....
... ...
.... .....
... .....
... J 11 Check 1111,Izoo
J 21 Check
.....
...
.....
...
...
1111, I201
K 61 Check IZOO. Im F1 Check (1111, (311)
.....
S 62 Check 1~10,Iazo
...
..... .....
September 15, 1942
ANALYTICAL EDITION
689
TABLE 111 (Continued) H2r
c1
H 41s
(210), (221) absent
Check Iaii
>BB~
.....
.....
..,..
B3 aJ1,
c1 an1
c 15
> 8c1
(200) absent
an, J 21
.1 1 a54]
I< 61
>
B1 aJz,
ab1
>
B3 Check ajn, >
am
G 21
C 2
.....
.....
R 09
( T
P 0:
H 21
15 Check I d m , I m ,
1140
H 11 Cherk I l n , I m , 1:ro
B B ~
.....
..... ..... J 21
Check Im. 1x0,Im
Check 1200,
.....
.....
D 3s
TABLE IV.
CUBICSUBSTANCES
> BCIS
c 3 Check 1 2 2 2 , Iaon Check (110) ~JZ> ! ac3
Check Im a q > ac1
J 11
.....
Check IXO.Ii?o Tetrahedrite
I P X , 1400
.....
.....
.....
9 61
1200,
..... .....
Check I m , Ism
s la
c1
1220,
..... .....
I~UO
.....
,..
c 3 Check (110) a n l > ac3
J 21
H 5,
J 11
Check Isoo
..... ..... .....
..... .....
.....
..,..
.....
.....
.....
.....
...
...
.....
...
690
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 14, No. 9
TABLE IV (Coritinuedj
A.
5.60 5.63 5,635 5.655 5.68 5.82
Substance B 3 (Contd.' AInS (red) AlAs GaAs ZnSe CuBr 8-CdS
6.04 6.05 6.07 6.08 6.103 6.12 6.12 6.13 6.383 6.40 6.43 6.45 6.48
InAs CUI HgSe ZnTe a-CuzHgI4 AlSb GaSb SnSb OL-A~ZH~II HgTe CdTe InSb 4gI
a,
a,
B 32 LjGa LiZn LjAl LiCd LiIn
4.437 4.438 4.438
NiSi FeSi CoSi
7.297 2.373 /.373 7.473
SaIn (CeMgJ (PrMgs haT1
4.548 4.620
CrYi
B 20
Lrnai
NiBe CoBe CuBe PdBe AlNi CuZn CuPd AuZn AgZn AgLi AuMg
4.33 4.619 5,06 5.07 5.08 5.13 5.38 5.40
5.40 5.406 5.45 5.47 5.526
5,53 5.54 5I 5 5 5.58 5.59 5.704 5.749 5.782 5.796 5.838 5.91 5.91 5.935 5.99 6.005 6.06 6.19 6.34 6.35 6.368 6.379 6.436 6.50 6.50 6.526 6.763 6,809 6.81 6.98 7.314 7.38 7.65 7.676 8.162
: : ; 2
LizTe AuIn? NazS MgzSn NazSe MgzPb SrClz NazTe KzS RbS? KzSe KzTe
5.94 6.287 6.435 6.96 7.03 7.61 7.79
BezCu BelAg BezTi MgNiZn CuzMg WzZr AuzNa
5.41 5.42 5,57 5.57 5.57
FeSa (Fe, S i ) & (6.5% S i ) RhSr RuSz Bravoite (53.8% SiSz. 39.1% FeSz, 7.1% CoSz)
5.62 5.64 5.65 5.68 5.74 5.85 5.92 5.93 5.94 5.97 6.02 6.096 6.36 6.37 6.43 6.44 6.64 6.94
AgCd AuCd (670' E.) LiTl
2%
Prtn CeZn AlNd a-RbC1 (83' K.) LaZn TlCN PrCd TlSb TlCl CaTl NHaCl (< 457' I
