INDUSTRIAL
AND
ENGINEERING CHEMISTRY PUBLISHED BY THE A M E R I C A N C H E M I C A L S O C I E T Y W A L T E R J. M U R P H Y , EDITOR
Chemical Analysis by Powder Diffraction LUDO K. FREVEL, The Dow Chemical Company, Midland, Mich. This paper cites examples of use of the powder diffraction method in the chemical identification of solids, and discusses some of the general difficulties that may be encountered in its use.
COMPLICATIONS IN REGISTRATION OF POWDER DIFFRACTION PATTERNS ABSORPTION EDGES. In view of the fact that most x-ray diffraction work is being done with filtered radiation, characteristic
Table I. Data on Boiler Scale
I
N T H E past ten years the powder diffraction method has been
Powder Diffraction
Chemical Analysia
Microscopic Analysis Analysis used to an increasing extent in the chemical identification of 70 % solids (4, 6, 9, 18, 18, 16, 24, 96, SO, 3.4, 46, 47, 59, 60, 62). The Fe 28.32 Black shiny powder, -40 FeFelO4 utility of the method resides in its ability to detect the state of Ca 22.30 heterogeneous: par-30 CaCOa, calcite S 6.21 ticles too small for re-30 Cas04 chemical combination for each crystalline component in a mixture Cos-22.10 fractive index measureIgnition loss 16.70 ments (80). The present paper cites a few typical examples and discusses some of the general difficulties that may be encountered Advantages Accurate quantitative High sensitivity for deDirect identification of in this physical method of chemical analysis. data, method of analytecting minor phases, compounds, nondeIdentification of boiler deposits is a general problem that is sis independent of state morphological details structive method a of aggregation of Samreadily ascertainable ilicable to extremef; conveniently handled by the powder method.de (29) ne powders A particular scale submitted for identification was examined by chemical analysis, by miTable 11. Powder Diffraction Data on Boiler Scale croscopic examination, and by powder diffracFiltered M o K a radiation used to obtain powder diffraction patterns. d interdanar tion. Table I lists the data ascertained by spacing measured in A. I peak intensity-of a diffraction line as estimated with a-direct each method. comparison intensity scale (arbitrary units). I / I I = relative intensity of a diffraction line, where XI is intensity of strongest line of particular phase in question. Moat representative The information obtained by the diffraction value for XI of phase 1 is taken as 33 and is obtained by multiplying intensitias of aix unambiguous reflections (483 2.95 2.41, 1.705 0 967 0 855 A ) by corres onding relative intensities method is of evident value to the chemist of FeFelOI and t'aklng ahthmetic mian'of bomputed values of PI (36,. 55, 37, 22, 25, 20). interested in selecting the correct treatment The average value for the strongest line of phase 2 is 22, for hase 3 it IS 38. Spectroscopic analysis o f scale: Fe, Ca, chief constituehts; 80, Mo, Cu, Na, 0.001 to0.01%. for the removal of scale or in devising methods FeFerOl Phase 1 CaSOi Boiler Scale Phase 2 CaCOa Phase 3 to diminish scaling. The manner in which d , A . I/Ii d, A . 1 1/11 d . '1. I / I i 1/11 d , A . I/II 1/11 Z I the diffraction data are conveniently com5.80 1 .. .. .. .... 4:i5 0106 0:09 4.83 3 'pared with published powder data is illustrated 3.87 4 ., . . 3:89 0:03 4 3186 0108 in Table 11. 3.49 25 .. .. 3.49 1.00 .. 3.03 30 .. .. 3:04 l:oo . Other typical problems solved by the diffrac0:io 2.95 10 2:97 0128 .. .. ... 2.84 15 2:85 0:67 tion method are: the identification of corrosion 2:i3 1:oo (33) 2.52 75 .. .. 2:49 0:io 41 products, the constitution of fluxes, the de2.41 6 2 42 0.11 0.18 .. .. .. . . . . .. 2.33 8 2:32 0:33 .. tection of pigments or fillers in plastics or 2.27 '10 .. .. 2 . 2 6 0.01 2:is 0:24 .. 2.21 8 2 . 2 0 0.33 .. elastomers, the analysis of minerals, the recogni2.08 30 2:io 0 :32 (ii) 2 . 0 8 0.11 2 :09 21 0 :io 1.99 1 .. .. . . tion of allotropic modifications, and the study 1.99 0.11 .. .. 1.91 10 .. .. 1.93 0.04 1:92 0:32 .. of chemical reactions in the solid state. .. 1.865 12.5 . . .. 1.86 0.27 1.87 0.24 15 1.745 4 1.74 0.20 . . . . .. As illustrated in Table 11, chemical analysis 1.705 6 I171 o:ie o:is .. .. .. 1.640 4 1164 0:27 .. by the powder method consists of matching 1.606 20 1:sl 0:64 (ii) 1.59 0.03 1 :60 o:i6 28 1,560 1 .. .. .. 1.56 0.05 the diffraction pattern of an unknown material 1.518 6 1.52 0.07 1:51 0 : i2 7 with one or more standard powder patterns. 1.480 30 11483 0 : s o (26) 1.487 0.08 1.475 0.05 30 1.439 4 . . . . . . . . . 1.439 0.08 This requires (1) a correct registration and 1,420 1 1,'420 0 : 0 8 4 1.425 0.05 1.320 2 11326 0 : 0 6 1.318 0.09 1.350 0.03 5 (2) measurement of the diffraction lines and (2) 1.278 6 1.275 0.09 1.279 0.20 .. 9 (7) 1.210 2 1.210 0.05 1.215 0.05 3 a careful interpretation and evaluation of (2) 1.150 2 1: i i o 0:05 .. these data as applied to chemical analysis. 1,120 2 1 :iii 0 : io 0:06 ... .. 1,090 7 1.092 0.32 0.21 .. The first part of the problem has received 1.047 6 1.049 0.10 1: 045 0:06 (3) 1.010 2 . . . . . ..5.. 1.011 0.03 considerable attention in the literature and 0,967 4 o:iz 0:970 01 is . . . . . ... .. 0.938 2 0.940 0.06 0.06 . . . . . ... .. .. only a few points require enumeration. .The 0.879 2 0.06 0.880 0.10 . . . . . ... .. .. second part, however, has not been treated 0.855 4 0.859 0.20 0.12 . . . . . ... .. .. 0.850 1 0.853 0.08 0.03 . . . . . . . . .. . . extensively in previous publications and de0.810 1 0.814 0 . 1 0 0.03 . . . . . .. .. serves detailed discussion.
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I
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209
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210
INDUSTRIAL AND ENGINEERING CHEMISTRY Table
Method of Preparing Powder Specimen Grinding or filing
111.
Vol. 16, No. 4
Preparation of Powder Specimens
Pre!cautions to Be ObservedAbrasion contamination Mechanical strain Volatilization Grind hard nonferrous Vacuum-anneal meGrind sample containmaterials in an agate tallic filings a t suiting sublimable submortar. (Micromicroable temperature stances in a small closed system or in an nizer may be useful in (Sf) atmose uilibrium the pulverization of or grind sample under pfere [NHlHCO: abrasives.) Remove dry benzene and load ( N H ~ ) ~ C ONHdOCO: J, metallic iron contamwet powder into a thinNHI, NHlNa. NHaCN. nation from steel morwalled glass capillary (Si.13.9) NHISH, etc.: ammotar bv maenetic methodi nates or alcoholates may lose NH: or ROH on erindinnl Coprecipitation or co- Oxidation Solvation cryetalliration Load precipitate in wet Vacuum-dry washed Make qualitative speccondition--e.g., pyroprecipitate horic catalysts such as troscopic analysis and ftaney nickel spot tests on washed precipitate Preferred orientation Oxidation .., Check condensed film (Adsorbed 01, HzO, for preferred orientaetc., on substrate) tion of crystallites by taking ex osurea a t varioua incinations
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Preci itation or crystalisation
Condensation, electrodeposition, or sputbring
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Phase decomposition (Supersaturated solid solutions, quenohed alloys, pressure-sensitive substances such as w u r t ~ i t e or brookite chemical reaction in solid state (f4. 68). For alloys a structureinteeratine camera of micro de&n may be adaptable
..........
.........
Tabk IV. Powder Diffraction Pattern of Magnesium Oxide
(m)ob..
dar ddd. (I/Ii)dd. extremely poor powder pattern with MoKa but a normal intense 0.08 2.425 2.428 0.08 pattern with CuKa. Specimens containing elements of high 2.103 1.00 (50) 2.103 1.00 1.487 0.50 (25) 1.487 0.55 atomic number*.g., gold, mercury, thallium, lead, bismuth-show 1.268 0.04 1.268 0.06 0.15 (1.216) 1.214 8"") L-fluorescence with MoK. These fluorescence considerations 0.06 (1.053) 1.052 apply not only to filtered K a radiation but also to crystal-mono(0.9661) 0.9649 0.01 B 0.03 0.9405 0.9405 .... chromatized x-rays. In the case of filtered x-rays, the distribu0.9404 0.9405 .... 0.8583 0.8585 .... tion of the continuous radiation may noticeably affect fluores0.8587 0.8585 cence. Thus if a zirconium oxide screen is placed in front of the 4.206 0.001 A. (25' 3' C.) T e B1: a EXPO%URX. R t e r e d MoKa radiation; camera radius, 20.477 * 0.010 film to filter the diffracted MoK radiation, the resultant diffracom., calibrated with spectroscopically pure Mg (a 3.2026 A., c 5.1998 tion pattern from a molybdenum specimen has a background 3.5 a t 25' C.); slit dimensions, 0 2 , X 5 x 50 mm.; specimen radius, 0.2 mm.; duplex film without Intens!fying screen. times as high as in the case when the filter is placed in front of the PREPARATION OF MgO. Sublimed magnesium metal, s ectroscopically slit system. For general routine analysis by powder diffraction, pure was diasolved in = 10% HC1 (c.P. @fadedistilled). Gagneaium hydroxhe was preci itated by dropwise addition of freshly prepared C.P. amtwo sources of K a radiationv-cg., MoKa and CuK-are monium hydrorig. The precipitate was washed twice by decantation, folusually adequate to avoid serious cases of fluorescence. The wet hydroxide was transferred to a lowed by filtration and waahjn clean i nited sillimanite orucibfe and vacuum-dried over Mg(C103z. The RESOLUTION. The geometrical factors deciding the resolution Mg(O&a was then converted to M 0 by heating to 890' C. for 1 hour in an oxygen atmos here free of carbon tioxide. of a Debye-Scherrer-Hull pattern are: R, radius of the camera; CHEMICAL % Mg = 60.22 * 0.05 (pyrophosphate method); r, radius of the powder specimen; h, length of the specimen; calcd. % Mg = 60.32. SPECTROSCOPIC ANALYSIS FOR IMPURITIES. Si 0.01 to 0.176,A1 0.005 to 6, divergence of the impinging x-ray beam; and U, difference in 0.05%, B 0,001 to 0.005%, Cu 0.001 to 0.005%. PARTICLESIZ: DISTRIBUTION.Electron microscope, 200 to 1200 i.;wave length of the K a doublet. For a fixed camera radius the avara e diameter 650 A., very uniform; particles are not of regular sha e, optimum resolution corresponds to the limiting condition: r, h, thoup% crvstalline in character: neneral tendency is for platelike ParticTes LZO; A. chick (see Figure 1). 6, u + 0. In general, however, the hardness of the primary (hkl)
111
200 220 311 222 400 33 1 420 ai 420 (12 422 ai 422 ai
"03;
-
f
A.
-
-
.. .. ..
-
.
XNALYSIS.
x-ray absorption manifests itself in four ways: (1) in the silver bromide emulsion (AgK, = 0.4845 A., BrK, = 0.9181 A.); (2) in the filter (17) (ZrK, = 0.6874 A., NiK, = 1.484 A,); (3) in the specimen containing elements, the characteristic absorption edges of which fall within the transmitted background radiation; and (4) in the tungsten contamination of the target (WL1 = 1.022 A.) ( 2 ) . There also exists the possibility that the zinc edge (1.281 A.) may introduce a discontinuity in the response of fluorazure intensifying screens. For powder diffraction work these effects are observed only for the more intense reflections. For example, using a sealed-off Mo tube operated a t 35 kv., one finds that the intense (111) reflection of cubic silver iodide produces one spectrum toward the longer wave-length end of AgK, and another corresponding to IK,. In the case of silver phosphate the intense portion of the continuous spectrum from (210) is slightly stronger than the (220) MoKa reflection. For powder patterns the sharpness of the edge of the transmitted spectrum is often blurred; consequently care must be exercised in distinguishing these edges from weak K a reflections. Fluorescence excited in the sample by priFLUORESCENCE. mary K a radiation is readily detected by a general enhancement of the background and a corresponding decline in the.prominence of the desired diffraction pattern. Using MoKa radiation for specimens containing yttrium, strontium, rubidium, biomine, or selenium, one obtains relatively weak diffraction patterns with high background. For example, carbon tetrabromide gives an
radiation used and the time required for the registration of a good diffraction pattern are the limiting factors in the design of a suitable camera. The geometrical resolution for a camera of radius R can be expressed approximately as the sum of 6, the divergence of the diffracted beam due to the divergence or convergence of the impinging rimary beam, and ~ , h the , angular spread of the diffracted lea, due to the dimensions of the powder specimen ( u , , ~= radian, for parallel x-rays) (8, 32, 41). Accordingly, twq powder reflections d and (d A d ) will be resolved if
$
(ea2
+
- 8al)d
(6 + W r , h ) e
where 8 is the Bragg angle for the interplanar s acing, d, and a denotes the wave length under consideration (SSf For example, with MoKa, radiation the two powder reflections corresponding to 2,260 A. and 2.274 A. will be separated by 3.4', which interval is equal to the MoKa doublet separation, (ea2- eal)2.0s. Evidently the use of very narrow slits does not aid greatly in the resolution of a noncubic powder pattern because of the disturbing doublet separation. (The utility and precision of powder diffraction work would be greatly enhanced if an intense source of strictly monochromatic WLal could be made available for precision-focusing cameras). Convenient standards for testing and calibrating powder cameras are 200-mesh powders of the following substances: pure fused magnesium oxide, pure crystallized silicon, annealed 99.9% molybdenum metal, C.P. thallous chloride, and indium sesquioxide prepared by the direct oxidation of 99.95% indium metal.
ABSORPTION.The intensity distribution of a powder diffraction line is markedly influenced by absorption in the powder
ANALYTICAL EDITION
April, 1944
Table
V.
Substance Pb
d,
A.
2 . 8 5 2.47 1.00 0.50 d, A. 2.85 2.47 1/11 1.00 0.37 Examples: In, In-Ag; Mg, 1/11
85Pb. 15Na
d, A. 2.36 1/11 1.00 d, 2.35 l/Il 1.00 Examples: Co, Ni;
Ag
A.
Au
CUCl
A.
1.74 1.490 1.428 1.134 0.50 0.50 0.17 0.17 1.74 1.487 1.424 1.131 0.20 0.31 0.07 0.07 Mg-In; Pd, Pd-An; Fe, Fe-Cr
2.04 1.445 0.53 0.27 2.03 1.440 0 . 5 3 0.33 Cr, Fe; Pd, P t ;
d
-
or Isomorphism
interplanar spacing; 1/11
relative intensity
1.105 0.17 1.102 0.07
1.232 1.179 1.022 0.53 0.05 0.01 1.227 1.173 1.019 0.40 0.09 0.03 Rh, I r ; Mo, W ;Cb, Ta
2.70 1.91 1.83 1.353 1.240 i.104 0.08 0 . 8 0 0.30 0.08 0.08 0.06 d , A. 2.89 1.91 1.83 1.353 1.242 1.104 I/Il 0.05 0.75 0.50 0.05 0.18 0.15 Examples: NaBr, PbS; NaC1, Ag(C1, Br); KCN, RbCI; MgrSn, MgrPb; FeF:04, NiMnrOd, ZnFerO6; Enol, Y:Oa d,
IIIl
8-ZnS
ZnFt
d,
A.
I/Il ICoFa
d,
A.
I/Il [SnOa
d,
A.
I/Il (NHdrCrO4
d, A. I/Il
(NHdrSeO4
d,
A.
IIII (CoClz.6HrO
I
-
Ambiguities Arising from Solid Solution
Diffraotion patterns taken with filtered MoKa radiation.
211
A. I/II d , A. d,
IIIl
3.12 1.00 3.12 1.00
3.33 1.00 3.37 1.00 3.34 1.00
2.80 0.80 2.84 0.88 2.64 0.83
2.35 0.06
2.27 0.20 2.30 0.29 2.30 0.03
2.10 0.05
5.8 0.82 5.5 0.60
4.80 1.00 4.80 1.00
3.91 0.35 3.89 0.40
3.74 0.10
5.8 1.00 5.5 1.00
4.85 1.00 4.85 1.00
3.52 0.31 3.53 0.50
3.11
..
..
2.38 0.18
..
,.
0.10
3.08 0.04
1.75 0.80 1.75 0.86 1.75 0.83
1.87 0.20 1.67 0.29 1.67 0.10
1.58 0.08 1.58 0.14 1.58 0.05
1.492 0.11 1.496 0.14 1.492 0.10
1.412 0.32 1.420 0.14 1.435 0.10
3.85 0.10
.. ..
3.45 0.40 3.45 0.40
3.18 0.75 3.17 0.80
2.94 0.40 2.95 0.40
2.84 0.20
2.77 0.10 2.75 0.20
2.32 0.62 2.33 0.40
2.01 0.15 1.98 0.20
1.87 0.05 1.87 0.10
2.94 0.83 2.95 0.50
2.73 0.50 2.70 0.50
2.58 0.20 2.54 0.30
2.40 0.83 2.40 0.50
2.20 0.50 2.18 0.50
2.07 0.05 2.05
2.02 0.03 2.02 0.06
1.98 0.31 1.97 0.20
1.89 0.20 1.90 0.20
.. ..
2.11 0.02
..
..
0.M
1.88 0.10 1.86
1.81 0.03 1.81
0.14
0.02
Examplen: COSOI.HZO(?),ZnSO4.Ht0, NiSO4.7Hr0, ZnSOr,7H,O Co(NHdc(SOdr.BHr0. Fe(NHMSO4);.8HtO, Zn(NH3~(SOdr.8HrO,C ~ ( N H I ~ ( S O ~ ) ~ . B H ~ O
(e,
specimen 4.9). With an eaeentially parallel x-ray beam and a suitable combination of a b s o r p t i o n coefficient a n d diameter of the powder rod, the resulting diffraction lines for low values of 8 can appear as pseudo-doublets (40). For MoKa radiation and a specimen radius of 0.2 mm., only the denser powders containing elements of highatomicnumber exhibit this effect--e.g., mercuric bromide, tungsten, bismuth, etc. Dilution with flour or reducing the specimen diameter will overcome this complication. T h e standard wedge technique used in many laboratories does not lead to pseudo-doublets. PREPARATION OF SPECIMEN. The two most common factors influencing the quality of a powder diffraction pattern are particle size distribution and instability of the sample. The g r a t i n g l i m i t a t i o n s of a powder specimen are manifested in the breadths of the resulting diffraction lines (IO). Thus materials of colloidal
d
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- Vi.
Table interplanar spacing; 1/11
Substance ZnSOd.Ht0
d,A. 1/11
MgSOd.Hc0
d,A. 1/11
4.80 0.84 4.82 0.40 5.9
MgSO4.7HzO
d,A.
0.20
ZnS067H10
I/II d,A. I/Ii
coca04
d,
A.
Zn A It 04
1/11 d, A.
4.88 0.08
1/11
MmAldSiOS, MgaAlr (si04)a (NHr)AWOd:.12H:O
d.A. I/II d,A. 1/11 d, A. 1/11
.. ..
..
.. 2.89 0.30 2.88
0.50
I/II
7.0 0.30 7.0 0.04 7.0 0.12
ItCaFe(CN)I
a,A.
8.0
0.07
KICUFZ(CN)I
I/Il d,A. 1/11
As401
&A.
Sbr Asr01
I/II d,A. I/Ii
8.3 0 2 8.4 0.25
KAl(SOSi.12HrO KCr(SOh.12H:O
A.
d, 1/11 d, A.
Partial Ambiguities Due to isomorphism In the case of mixtures the above differencen are more difaoult
relative intensity.
7
.. ..
to check 3.80 3.40 3.08 1.00 0.40 ,. 3.38 3.07 . , 1.00 0.20 5 . 3 4.50 4.22 0.20 0.08 1.00 5 . 3 4.50 4.20 0 2 0.18.1.00 2.88 2.43 2.34 0.20 1.00 0 . 0 8 2.85 2.44 , 0.53 1.00 2.99 2.46 2.38 1.00 0.02 0.20 2.58 2.45 2.35 1.00 0 2 8 0.20 5 . 4 4.97 4.30 0.60 0.30 0.80 5.4 4.98 4.29 0.20 0.08 1.00 5 . 5 4.98 4.31 0.16 0.08 1.00 5.1 4.60 3.72 0.30 0.03 %3 5.1 0.38 3.18 2.75 2.53 1.00 0.24 3.18 2.75 2.52 1.00 0.25 0.13
. ..
-
-
.. ..
.. ..
0.32
2.52 0.40 2.55 0.40 3.78 0.10 3.76
0.20
2.02 0.13 2.02 0.07 2.27 0.13 2.28 0.20 4.07 0.80 4.05 0.40 4.08 0.30 3.64 1.00 3:83 1.00 2.24 0.08 2.24 0.02
2.40 0.06 2.40 0.05 3.41 0.12 3.44 0 2
..
.. 1.91 0.07 2.10 0.15 2.10 0.15 3.87 0.40 3.85 0.04 3.88
0.60 3.07 0.10 3.06 0.20 2.12 0.16 2.11 0.04
2.34 2.19
0." 2.33 0.03 2.98 0.18 2.99 0.12
. .,
,
1.85 0.07 2.04 0.05 2.03 0.02 3.26 1.00 3.24 0.40 3.28 0.35 2.85 0.03 2.88 0.08 1.95 0.24 1.95 0.30
2.19 0.05 2.87 0.20 2.87 0.30 1.65 0.04 1.85 0.13 1.88 0.26 1.87 0.25 3.05 0.30 3.03 0.18 3.04 0.30 2.57 0.42 2.67 0.75
2.10 0.10 2.10 0.04 2.74 0.08 2.75 0.10 1.58 0.25 1.55 0.33 1.87 0.15 1.86
0.13 2.95 0.08 2.93 0.12
.. ..
2.05 0.05 2.05 0.17 2.88 0 2 0 2.88 0.25
.. ..
1.480 0.07 1.60 0.30 1.595 0.40 2.79 0.12 2.78 0.20 2.81 0.12 2.80 0.10 2.29 0.31 1.64 0.18 1.54
2.35 0.03 2.36 0.15 1.86 1.59 0.18 0.08 1.88 1.58 0.30 - 0.06 0.10
--
1.97 0.18 1.97 0.05 2.48 . 0 2 2.50 0.12 1.432 0.30 1.431 0.40 1.545 0.40 1.54
0.83
1.91 0.08 1.90 0.05 2.88 0.05 2.37 0.08 1.235 0.02 1.283 0.07 1.44 0.085 1.440 0.13
..
2.80 0.12 .. 2.58 .. 0.08 .. 2.59 0.06 2.13 2.08 0.07 0.10 2.13 2.06
.. ..
0.25 0.83
1.438 0.08 1.430 0.07
.. ..' .. ..
212
INDUSTRIAL A N D ENGINEERING CHEMISTRY
subdivisiion, such as coprecipitated oxides of the spinel type, apecially prepared catalysts, or clays give rather diRuse diffraotion pat!m s that may appear insignificant in the p-nce of an intense sharply delined pattern. A similar situation is encountered in the field of high polymers. I n order to obtain information of greater value in the d s e of these idiosyncracies, the use of crystal-monochromatizedradiation has been advocated by a number of diffractionish.
Vol. 16, No. 4
The uniqueness of this inference is not evident and requires further examination. VALIDITYOF S T A ~ A R PATTERNS. U It is convenient to cansider first the validity of the standard patterns, pr (4, $35, 86). From the results of x-ray diffraction analysis it is well reoogniaed that the powder diffraction pattern of a single phase is ayunction of the particular crystal structure, the elements present, and the crystallite-size distribution of the powder. To he acceptable as a standard each substance should be subjected to a precise analysis to substantiate the assigned chemical formula. The method of preparation of the powder specimen should also be stated. Table IV illustrates a satisfactory presentation of a powder diffraction standard. On exmining the published tabulated powder data (4, M ,$8) one finds the labeled standards usually have not been examined for the correctness of the ascribed chemical formulas. This d e fieiency was realized when the first 1000 Dow standards were published (&5). The rnurr frrqucnt typr9 of errors art,: ( I ) incorrect dcarce of hydratioil [pilltern 210 is CsSOa.2lIrO; pattern 338, Cn9O4.H:O. oattern 623. U i F ~ . I H ~ OD : B T I 8C1. ~ ~ Sa,S.rll*Ol: f2) clirrnid reaction h&tween stan$.&d substance and watkr. 'akgeu. or carbon dioxide [pattern 193 is mixture of CaC08, &(OH)*, 'and graphite (7); pattern 227, Ca,,(OH),(PO,), and &(OH) ' nattern 21.5. vatente olus oaloitel: (3, ~ ~ and ~ ~ ~~, ,rnoorred , - ~ chemic3 . ormula [ &tern 13 is Al(OH)s, gibbsite; patterns 68 and 69 are AS)~O~ patterns ; 132 aud 143 are largely Bi(OH),. largely p t t e r u 269 refers t o a mixture containing minor amount 01 examethylene tetramine]. Some errors in the diffraction data have been noted--ex.. the most intense line for FeCI&?HxO (pattern 409) is 5.5 x.'(40);the (020) reflection for NazSOIIII (pattern 859) should read 4.47 1. ~~~~~~
~~
~~~~
~~~~
~
~
~~~~~
~~
~~
~
~~
(&,
Figurel. Electron Micrograph of Magnesium OxidoStandard
The problem of the instability of a sample -Illy csn be overcome without serious difficulty (see Table 111). Hygroscopic substances are readily powdered in a drying box and loaded into thin-walled glass capillaries that can be sealed easily. Efflorescent materials can be loaded wet (to prevent extreme crystal growth, a little amorphous material, either starch or charcoal, is admixed with the wet powder). In the esse of complex organic compounds the existence of two or more allotropic modifications must he kept in mind; thus a m a t e d crystallized from a melt may give an entirely different powder pattern than the same substance crystallized from a solution. Other cases of 'less general occurrence are: allotropic transformation an grinding or filing (wurtzite, brookite, supersrtturated solid solutions); photoseusitivity (BaNe, P,); and chemical interaction of the substance with glass capillaries [acid fluorides, such as NHtFHF to form (NH,),SiF,I. Polystyrene capillaries, developed for the study of acid fluorides, have proved useful for powder diffraction with soft radiation such as CuKa and FeKa.
An examination of the useful compilation of powder data on minerals ($6) reveals a similar state of affairs for these tabulated standards: Pattern 3 (dabandite, HnS) lists in additiun 72 thr diffrxction data for cutiir manganrsr sulfide the lines 2.83 A. nnd 1.993 A. (probably SaCI). Pattern 23 [brxvoitc. (Fr, Xi)%] ~ v .the w arwntmi ( 2Uattcin nluq the noncubir r~Ileotiunq3.On.2.18. 2.04. 1.86; and 1.682 A. Pattern 35 (chromite, FeOCnO;) does not correspond t o the HI1 structure for FeCnO,. Pattern 37 ( c l a w thalite, PbSe) lists an extraneous 2.86 b. reflection. I n pattern 39 (coloradoite HgTe) the strong (111) reflection is missing and the lines 2.82 and 2.52 A. appear extraneous, BS does the line 2.79 b. in pattern 95 (magnetite, Fe.0,). Pattern 93 (lollingite FeAm) does not check the published data (58); the specimen used may have been an impure form of arsenopyrite. Pattern 137 (sphalerite, ZnS) checks the 9 3 structure except line 3.95 A. Pattern 143 (sulvauite, Cu8VS4)omits the (220) reflection (1.90 1.)and lists the extraneous lines 5.2,4.15,3.70, and 2.84 A. For f~ nnmber of substances the innermost reflections have not been recorded: pattern 9 (srgentite, Ag.S) Bhould include the line 3.91 b. (57); pattern 16 (berthierite; FeS.SlhSd, 8.0, 7.2, 5.7, 5.1 1.; pattern 66 ( ersdorffite;NiAsS), 3.99 1.;pattern 76 fhmerite, MnS2), 3.52 pattern 77 (hsusmannite, Mn804), 1 ~ :n*t,t,em 9.5 (mametit,e. Fe.0~).4.8.5 1.:nsttern 141
A.
~~
~~
~
~
1.;
'the (220) klection. COMPUCAnONS IN METHOD OF ANALYSIS
Chemical analysis by the Debye-Schemer-Hull method consists of matching the diffraction pattern of an unknown material with one or more standard powder patterns. When a match is found (see Table 11) one infers that compounds A, B, C. . are present in the unkuowu. If p denotes the powder diffraction data. of the unkuown material; p,, the diffraction data of all the cataloged standard pattern; and n', the composite operation of matching the unknown with the standards A, B, C one may express the mode of analysis symbolically as
.
.. .
n'(p.p,) 3 A , B, C
...
While the experimental inaccuracies Jisoussed can be remedied (the A.S.T.M. has an organization set up t o issue new pattern periodically and correct old ones), there remain inherent limitations ta the uniqueness of an established standard pattern. Solid solution, isomorphism, or structural similarity can contribute to the ambiguity of a standard pattern (see Tables V, VI, and VII). The absence of solid solution in au identified phase should alwayn be checked by qualitative spectroscopic analysis and spot tests. If solid solution is indicated, a sensitive back-reflectiontechnique is required to measure the d-shifts between standard and solid 8olution. Ambiguities sttributed t o isomorphism (see Tables V
April, 1944
213
ANALYTICAL EDITION
and VI) or S t N C t d similarity (Table Table VII. Ambiguities Arising from Sbudural Similarities VII) usually are resolvable by spectroscopic analysis, spot testa, or some d interplanar spacing: 1/11 relative intansity Subatanaa simple physical criterion such as solusi d . A. 3.12 .. 1.91 1.m 1.3541.2421.104 .. 0.958 0.918 bility in water, melting point, etc. , _ 1.00 0.63 0.18 0.25 0.40 0.06 0.13 1.00 I/I, In the identificationof multicomponent 3.12 8-ZnS d, A. 2.69 1.81 1.63 1.353 1.242 1.104 1.044 0.957 0.913 mixtures the intrinsic limitations illus0.05 0.03 0.04 1.00 0.05 0.75 0.50 0.05 0.18 0.15 VI, tratedin Tables V to VI1 become pro3.12 2.70 1.91 CUCl d , A. 1.63 1.353 1.240 1.104 1.043 .. .. .. nounced because of superposition of .. 0.06 0.08 0.06 0.04 .. .. 1.00 0.08 0.60 0.30 IlI, L lines (see Tables 11 and XI). d . A. .. 2.45 2.12 1.50 1.281 1227 1.060 0.975 0.951 0.868 0.818 COO The phases present in an unknown 0 . 2 0 0.07 I/I, .. 0.67 1.00 1 0 0 0.40 0.40 0.10 0.10 o* may be formed under rather haphazard d. A. 3.00 2.45 2.12 1.51 1.283 1.228 1.065 0.917 O T i i 0.869 0.819 C"l0 or 'unequilihrated conditions con0.03 1.00 0.31 0.44 0.31 0.05 0.03 0.05 0.03 0.03 0.03 I/II ducive to the formation of defect struo.. .. FeO d . A. 2 x 2.14 1.51 1.293 1.238 1.072 0.984 0.959 .. tures (6, 87, 51, 58). The differences .. 0.50 1.00 0.63 0.15 0.08 0.03 0.03 0.05 .. 1/11 between the diffraction pattern of .. .. .. d, A. 2.70 2.34 1.65 1.412 1.352 1.171 1.015 .. .. .. .. .. such a defect structure and that of a 1.00 1.00 1.00 0.75 0.30 0.15 0.30 I/I, .. .. .. normal standard may be subtle and d , A. 2.72 2.36 1.67 1.422 1.360 1.179 1.082 .. .. .. .. .. 1.00 0.40 0.24 0.16 0.03 0.01 0.02 I/I> escape the notice of the analyst. I n .. .. .. .. general, structural irregularities in .. .. d , A. 2.33 2.02 1.43 1.218 1.188 .. .. .. .. .. .. 1.00 0.40 0.30 0 3 0 0.07 I/I* crystalline phases may be detected by .. .. .. .. .. d. 2.32 2.00 1.42 1.211 1.160 changes in intensities of the diffrac0.67 i.00 I/I, - 0.23 0.03 0.03 .. .. .. .. .. tion lines (as compared to an ordered .. .. .. d, 1 . 2.97 2.57 1.815 1.55 1.481 1.288 1.179 .. standard), by an increase of diffuse .. .. .. 0.28 0.12 0.16 1.00 0.60 0.40 0.40 I/I, scattering, by the appearance of broad .. .. .. 2.96 2.56 1.81 1.55 1.482 1.283 1.178 .. d . A. diffraction ghosts (6), by a hroaden.. .. .. .. 1.00 1.00 0.60 0.32 0.12 0.05 0.12 I/Il ing of one or more types of reflections, .. 1.245 1.140 .. 1.398 1.280 2.80 1.97 1.68 d . A. 3.22 and by B change in the small angle .. .. 0.38 0.25 0.38 0.13 l.CO 0.380.75 0.88 I/Ix scattering. Serious refinements in the x 1.68 1.61 1.28 1.246 1.1 d . A. 3.21 2.80 l normal powder technique, however, .. 0.05 0.03 0.0 1.00 0.300.20 0.20 0.10 I/Il are required to gain information of 1.67 1.60 1.385 1.270 1.240 1.1 3.20 2.77 1.96 d. A. sufficient reliability to justify an 0.1 0.40 1.00 0.75 0.20 0.25 0.09 0.06 0.20 I/I, evaluation of the type of randomness in a particular phase. In a careful analysis of an unknown, due considercurrenee. Figure 2 illustrates the sensitivity uu.l yo*sation should be given to the possible presence of defect S t N C reflection method for ascertaining this effect. tures (see Table VIII). The formation of a continuous range CLASSIPICATION OF STANDARDS. u p b the p163Sent ahout 2500 of solid solutions of cocrystallized salts is a rather common oc-. patterns have been cataloged at Dow. When one deals with this number of standards the identification of-unknownsby the group classification system (84) is adequate, as has been amply demonstrated st Dow during the past ten years. However, it is of theoretical interest to consider what probable limitations may arise when a comparatively larger number of standards is considered. A statisticd study of this problem has been made and is presented here purely as a guide to any modified index that might be considered by the diffraction analyst. To arrive at a tentative answer to the above query it is instructive to examine how the three most intense diffraction linea (reference lines) for each of the cataloged pattern are distributed with respect to interplanar spacing. Figure 3 shows
-
-
.. .. .. ..
__
~~
..
.. ..
a.
..
_._ _
Table
__
VIII. Dofod Sbuctures
EX*mple
Diffraction Effects
Continvow range of d i d 80i"ti0IlB K(I Br) Btru0iurea with "Leerstellen" Fel.=R (R 0.S . Se. Te) NazW01
Merging of Km doublet on bank-refleetiom
-
Mgi-=AL,O~-r
ooovrrenoe of 8"PerstlUh turelinesandanomalovs change in lattice constante with 2 Broadening of diffraction
Referenew
... (20-8s)
...
Pseudomorphism M (OH)zo-ziO= Ranfomneas in layer structurea CdBm (Weobdtruktur)
Figure 9.
Back-Reflection Patterns
Taken with unllterod Fe< r d d t i o n . Specimen-to-him distance 7.50cm. Sector 1 refon to d mechsn'csl mixOlre 01 98% KI
md
(1. 37) X-ray d & ' & b? a h (S. 87 28, 56. counted foron baau of II 33, i 9 . 46) unit of strvotvre containinz B fractional st& ohiomztric weight Mioss. olayanCddImmCd(0A)n Broadening of diffraction 187.2S. 58) !!nee, ohangea in intensilwter carbon Oea
Alloy ayetern with transition stlYCtYlea AI-CU, ALA.. CuFeNir. AvCur
Broad diffraction ghosts (6)
(8. I1 IS. 86. 66. 68. 81)
214
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 16, No. 4
8
f ~
d
e
:. :. :. :. :. :. :. :. :. :. :. .: .: .: .: . :. :. :. :. .: .: .: .: .: . :. :. :. :. .: .: :. :. : :
.-
:. .: . :. ;.-: .s.%*: :. .6. :. ; : ; v
a e I)
ly
215
ANALYTICAL EDITION
ApA, 1944
se
Y E0
216
N
m
217
ANALYTICAL EDITION
April, 1944 0.7K
0.600
0.W
of reference lines for one component [for an n-component mixture there are 3n(3n - 1)(3n - 2) - (n - 1) combinations]. In the general case of a binary mixture, allowance must also be made for the following possibilities: (1) the superposition of reference lines, for example, the second reference line of phase A and the third reference line of phase B so that 1 2 {a > I , or (2) the superposition of a reference line of phase A and a moderately intense reflection of phase B (13 I, > 12); and (3) the presence of prominent nonreference lines for phase A , so that 1, or I , + > r 2 . These considerations are general and apply to any scheme of classification. In case the number of standards exceeds 10,000 to 20,000, the problem may arise as to how to circumvent the probable congestion of reference lines and the multiplicity of trial reference lines for multicomponent mixtures. I n view of the fact that the great majority of analyses are supplemented or confinned by qualitative spectroscopic analysis, it may be expedient to reverse the procedure and obtain the spectroscopic data first to facilitate finding the appropriate diffraction standards.
+
0.400
L&)
r,;
+
0.302
0.m
0.100
0
Figure 3.
Distribution of Interplanar Spacings of Reference Lines
I refers to distribution of first reference line of various standards with respect to d, interplanar spacing; II and Ill pertain to second and third reference lines, respectively. No = total number of cataloged standards = 9100. (dN)l.d = number of standards having their first reference line located in of clarity experimental points are shown only for I. M a x i m a for I, 11, and * .08,9.75 * .eo, and 9.60 * .30 A., respectively. n = number of diffraction lines per pattern; 4 G n 45; "=,,19. I, = intensity of r t h reference line; 9 4 I1 919 based on / I (NaCI) = 150. /1:/2:/3 = 49.3:95.7:90.9 for -I cos2 ee, MoKa (when corrected for factor continued ratio is proportional to 96.0:-
+
sin2e cos e 99.0:19.9>. V I expresses probability that dl > d2 or da; G1:Tz:Ta = 1.00:50:0.98. above a letter signifies an arithmetic average for No standards.
A bar
For example, all compounds containing aluminum would be grouped under aluminum as shown in Table IX. Those substances containing both aluminum and iron would be listed under
that for most common inorganic substances the reference lines fall within the interval 2.0 t i 3.5 A. Considering the first reference line, one finds 15 patterns listed in the interval 15 to 20 A. and 74 patterns in the interval Table XI. Powder Diffraction Data 2.95 to 3.00 A. (of course, the Filtered M o K a used t o obtain diffraction atterns. d = interplanar spacing. I = ,peak intensity of a difsecond and third reference lines of I1 is intensity of strongest line of particular phase in question fraction line. I / I i = relative intensity, ,!ere a substance materially reduce the (values in parentheses refer to calculated intensities). Diffraction pattern of albite, Amelia Court Houae, Va., was taken with a 0.1-mm. slit to resolve some of the broader reflections. number of standards to be conSPCCTROSCOPIC ANALYSIS OF UNKNOWN.Fe, Al, Si, Na chief constituents: niinor constituents P 0.1 to sidered). I n the identification of 0.572,K 0.01 to O.l%, Ca 0.001 to 0.01%. mixtures, however, a crowding of XaAlSisOa, Albite, UnAlbite: Goethite, Amelia Court House, reference in the relatively narrow known NaAlSirOs Phase I a-FeO.OH Phase II Va. interval from 2.6 to 3.0 A. might I/Ii TI d , A. 1/11 d, 2 . I d,A. I/Il I/Ii d , 2. I/Ii 6.5 necessitate an undue amount of 1 6.4 0.08 .. 6.4 0.06 5.0 6 .. .. 0: 09 .. 5 9 0.04 4:98 0 : 0 4 searching to locate the sought 4.20 25 0.76 .. 5.5 0.02 4.21 1.oo (25) 4.02 0:35 12.5 4:05 .. . . 4.01 0 . 5 0 (50) standard patterns in a very large 3.80 3 3.80 0.16 .. . . 3.84 0.06 collection of standards. The point 0.25 9B 3.66 3.67 . . 3 . 7 6 0.08 4 3.38 o:i2 0: 12 . . 3 . 6 6 0 . 4 0 (40) 3:39 may be visualized by the diffrac3.19 50 3120 1:00(50) .. .. .. . . 3.50 0.10 2 . 9 5 1 2 . 5 2 . 9 6 0 . 2 5 . . 3 . 3 7 0 .os tion pattern of a binary mixture 12.5 2.65 0.02 2.69 0:3s 3.19 1 . 0 0 B (100) 2:70 0136 2.57 12.5 2.56 0.12 i i 2.94 0.20B for which there are six reference 2.58 0.24 (8) 2.44 30 2.44 0.14 32 2 . 8 5 0.10 0.80 2.45 (26) lines, the intensities of which may 2.37 .. .. . . 2 64 0 . 0 4 2.32 . . 2 . 5 5 0.10 where be denoted by I, and 2.25 o:iz 0 : 15 2.43 2:25 0.10 2.18 2.19 0.20 io 2 . 3 8 0.04 T , s = 1, 2, 3. Assuming (1) that (7) 2.10 .. . . . . 2.31 0.10B there are no superpositions of lines, 2.01 . . 2.24 0 . 0 1 1 . 9 0 1 . 9 1 0:os 8 2 . 1 9 0 .02 (2) that the six most intense re1.81 0.08 11 2.12 1.80 0.08 1.72 flections are also the six reference 0.36 16 2.06 0.06 1.72 1.60 4 1.98 0.063 1 . 6 0 0.08 lines for the binary mixture, and 15 1.56 i:bs o:iz 0.28 1.56 i i 1 . 8 9 0.10 1 . 5 1 1 2 . 5 1 . 5 0 0 . 0 8 0 . 2 4 1 . 5 0 12 1 . 8 5 0.08 (3) that ZI 2 ZI 2 I t 2 61 > CZ 1 . 4 5 5 10 1.460 0 . 1 6 11 1 . 8 2 1.455 0.12 0.10 1:419 9 1.425 0 . 1 6 2 Cs; 0,one may have to exhaust 8 1.782 0.08 1.420 0 . 0 4 4 1.350 1.350 0 . 1 4 1.355 0.08 9 1.713 0 . 0 4 from 1 to 119 possible combins, 1.720 0.04 tions to find the appropriate set
r,
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
218
aluminum and iron-ag., FeAlrO, is listed in Tables I X and X (there are nine such substances listed). Under the nonmetalsH, C, N, 0,F,S, C1, &, Br Te I - o n e would list only those compounds which do not contah efements detectable by the conventional arc spectra-i.e., which do not contain any of the following: Li, Be, B, Ne, Mg, Al, Si, P, K, Ca, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Ga, Ge As Rb, Sr,Y, Zr, Cb, Mo, Ru, Rh, Pd, Ag, Cd, In,Sn,Sb, Cs, b a , La Ce, Pr, Nd, Sm, Eu, Gd Tb, Dy, Ho, Er, Tm, Lu, Hf, Ta, W, he, Os, Ir, Pt, Au, Hg,. Ti, Pb, Bi, Rs,Th, U. Chemical tests are convenient to identify the nonmetals-e.g., the use of aqueous sodium hydroxide and Nessler’s reagent to detect ammonium salts. Organic compounds may also be detected in the arc (using copper-electrodes) b the 2478.5 A. emiasion line of carbon and the cyanogen b a r d For routine analysis it would be advisable to check the diffraction standards listed under carbon and nitrogen, The procedure for identifying an unknown by this modification of the triple index system (,t?flis illustrated by Table XI. Qualitative spectroscopic analysis of the unknown shows the following chief constituents: iron, aluminum, silicon, sodium. The more prominent diffraction lines of the unknown (column 1, Table XI) are: 4.20,4.02, 3.19,2.95,.2.69,2.57, 2.44, 1.72 A. Looking under Table X to locate the iron-containing phase(s), one finds a-FeO(0H) as a likely component of the unknown. Checking the complete data of standard pattern 424 one establishes the presence of goethite in the mixture. In a like manner Table IX indicates albite, NaA1Si808,as the second phase of the unknown. The presence of albite also could have been ascertained by looking under the index for sodium or silicon. As all the diffraction lines of the unknown are satisfactorily accounted for, the qualitative compound analysis is considered complete and there is no need to check the diffraction standards listed under carbon, nitrogen, etc. The extent to which the suggested classification of diffraction standards by elements circumvents the anticipated congestion of reference lines can be estimated by an examination of Tables I X and X in regard to the number of times the average compound is listed under more than one element. For aluminum (Table IX) there are 18 substances listed only once (under aluminum), 47 substances listed twice (distributed over 23 elements), 11 substanceslisted three times (distributedover 8 elements), and two substances listed 4 times (distributed over 5 elements). For Table X there are 39 substances indexed only under iron, 60 substances indexed twice (distributed over 23 elements), 13 substances listed three times (distributed over 19 elements), and five minerals listed 4 times (distributed over 11 elements). A calculation of the quotient
Em
r NZn, b
where n, = number of substances listed r times N = total number of elements under which the various substances are indexed
shows that the congestion of references lines has been reduced by H factor of 12.7 for the aluminum compounds and 13.9 for the iron compounds. However, it appears that the intrinsic advantage of combining spectroscopic information with diffraction data is the natural incorporation of isomorphous groups in the various tables. This combination of empirical standards and structural types into one index should broaden the scope and utility of chemical analysis by powder dzraction. ACKNOWLEDGMENT
The author wishes to acknowledge with appreciation the pertinent criticism of this paper by J. D. Hanawalt.
Vol. 16, No. 4
LITERATURE CITED
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