Chen1.
Anal. (Warsaw), 44, 1033 (1999)
by Rafal Sitko and JerzyJurczyk
Institute o/ChenlistJy, Silesian University, 40-006 Katowice, Poland
Key words: XRF analysis, thin layer n1ethod, inhoillogeneity
The authors have presented a sin1ple lllethod for the detern1ination of possible inhon10geneity of thin san1ples in a wavedispersive XRF analysis after previous exan1ination of intensity distribution of exciting radiation on sa111ple's surface. Investigations were carried out using as an exa111ple 111icrosan1ples of1110no- and polycrystals. Sa111ples were prepared by digesting an analyzed n1aterial directly on the substrate. The obtained results have been presented in a graphical way.
Autorzy przedstawili prosty spos6b wyznaczania ewentualnej niejednorodnosci cienkich pr6bek w falowodyspersyjnej analizie XRF po uprzednin1 przebadaniu rozkladu nat((zenia pron1ieniowania wzbudzaj'tcego na powierzchni pr6bki.·Badania przeprowadzono na przykladzie n1ikropr6bek n10no- i polikryszta16w. Pr6bki przygotowywano poprzez roztwarzanie badanego n1aterialu bezposrednio na podlozu. Uzyskane wyniki przedstawiono graficznie.
Application of thin layer Inethod in XRF analysis allows to IniniInize to a large extent the inter-elelnent influences; effects connected with the Inorphology of salnpIe, such as granulation, Inineralogical effect or inholnogeneityof the Inass per unit area renlain and their elilnination is possible by appropriate preparation of the salnpIe. The first two sources of error are frequently elilninated by a wet Inethod through digestion of the investigated Inaterial and dropping the obtained solution onto the substrate. However, a granularity effect Inay occur then as a result ofrecrystallization
[1]. Minilnization of the aforelnentioned effects in the case of powder salnples consists in hOlnogenization and disintegration of Inaterial to achieve appropriate grain

1034 R. Sitko and J Jurczyk size, ensuring salnple' s representativeness with respect to the entire population studied [2]. An inholnogeneity effect connected with uneven distribution of a Inaterial
011 the substrate lllay relnain. There are nUlnerous techniques used that require application of appropriate apparatus to filter or precipitate a disintegrated lnaterial on the substrate, e.g.
under pressure [3]. In the case of dropping standard solutions there is, alnong other things, a probleln of selecting conditions of drying [4]. Apart froln a traditionallnethod of dropping solutions authors ofpaper [5J present a Inethod of depositing standard solutions in the forln of an aerosol using a specially constructed apparatus. Paper [6J presents a silnple Inethod of determination of intensity distribution of exciting radiation in EDXRS analysis and a l11ethod of analysis of thin inholnogeneous salnples precipitated and deposited on a Millipore filter. Having in
Inind an inhomogeneity of exciting radiation distribution on salnple' s surface one can
expect varied intensities of fluorescent radiation froln various places of dropping the standard solution onto the salnple [7], e.g.
at investigating the chelnical cOlnposition of environlnental salnples. Preparation of lnicrosalnples for XRF analysis by the thin layer lnethod, both in the case of lnineralogical lnaterials [8,9] and llluitieleinent lnono- and polycrystals [9,10], by digesting the lnaterial directly on the substrate not always leads to obtaining salnples of hOlnogeneous thickness and the control of the analyzed Inaterial distribution on the substrate is especially difficult, hence the at...
telnpt presented in this paper to study the inholnogeneity of salnples' lnass per unit area.
EXPERIMERNTAL
Apparatus and conditions of measurement
PW1410 and PW 1450 wavedispersive sequential spectro111eters with Mo and W X-ray tubes, respectively; 45° angle of primary radiation incidence on the san1ple, angle of reflection depending 011 the deternlined elel11ent; LiF 200 analyzing crystal; 150 I-1n1 fine collinlator; n1easuren1ents in vacuun1 with rotation of sa111ple; detection tin1e t = 100 s; analytical lines: K a eu (0.1542 n111, flow counter), K a
Se
(0.1106 n111, flow and scintillation counter).
PROCEDURES AND DISCUSSION OF RESULTS
Authors of papers [9,10] have presented a quick lnethod for the preparation of lnicrosalnples (weig11ing fractions of lnilligraln) of lnultielelnent lnono- and polycrystals ofMINICrlSe cOlnpositions, where M,N - Cu, Zn, Ga, Co, Ni and Yb/Zn/Sb.
Material disintegrated and weighed on a lnicrobalance C--JO.5 n1g with accuracy of
0.001 lng) was digested directly on the substrate used by dosing portions of concentrated nitric and hydrochloric acids. The choice of a digesting agent depended on the studied lnaterial and conditions of the reaction carried out. A Millipore filter was the

Deterlnination o.fnzass per unit area inholnogeneity a/thin salnples 1035 substrate (AA type, Bedford, Mass., USA; 025 lnln) glued onto a glass plate by lneans of a two-sided adhesive tape.
During digestion of disintegrated natural salnples of the aforelnentioned lnonoand polycrystals a convection of still not digested lnaterial to the edges of a filter by added acids and a chrolnatographic effect were observed. Theseprocesses lnay result in concentration ofthe digested lnaterials on filter edges or in various places ofits surface. The observation of the described phenolnenon was possible due to a green color of chrolniuln (Cr
3
+) cations originating indigestion of spinels containing this elelnent. The described phenomenon occurring also in the case of other lnaterials was studied having in lTIind its likely consequences inter alia in deterioration of the precision of obtained results as an effect ofinholnogeneity of salnple's lnass per unit area.
The other effect considered was the possible intensification· of inter-elelnent influences in various parts of the filter as a result of concentration of elelnents and a local increase of saillpies' thickness in this area.
Studying the iniloillogeneity ofprepared thin salnples in XRF analysis the authors have initially deterillined the distribution ofprilnary radiation incident on the surface ofthe saillple. A silnple and quick procedure was used. The substrate was prepared - a polystyrene disk with a glued on two-sided adhesive tape op which a lllillilnetre scale was superilnp
0 sed.
A disk of 5 Cln dialneter was fitted to diInensionsofthe spectrolneter cassette. MeaSllrelnentswere carried out as follows: a copper elelnent ofdilnensions aboutO.7x3 mIn was glued on the substrate according to the superiInposed scale starting froln the centre of the disk (radius = 0), two lneasurelnents were carried out, theaforelnentioned elelnent was detached, glued on the saIne place and two lneasurelnents were carried out again. This procedure allowed to reduce errors resultingfrOlTI inaccuracy of the place ofgluing the copper elelnent. The subsequent points ofme asurelnents were obtained in an analogous waylnoving the copper sheet by one lnillilnetre (radius = 1, 2, 3, ... 20 lnln). Measurelnents were carried out during rotation of the spectrolneter cassette, hence in the range froln ---20 to 20 lnln at location ofthe copperelelnent for r = 0 ... 20 lnln. The obtained results, for both spectrolneters, averaged for four lneasurelnents (K u
Cu line) are presented in a graphical way in Figure 1 after norlnalization. The substrate itselfwithout copper was a blank sample. For PW 1410 spectrometer with a lnolybdenuln tube a slightly larger area covered by the exciting radiation was found. The obtained results provide not only the inforlnation on the geolnetry of radiation incidence on the salnple but also on its detection.
Having the inforlnation on the distribution ofradiation incident on the salnple and on its detection the authors have investigated the inholnogeneity of a typical salnple prepared for previous analyzes by digesting the analysed lllaterial - Cu/Zn/Cr/Se spinel (about 14% eu, 30/0 Zn, 22% Cr and 61 % Se) directly on the substrate. Measureillents of intensity of fluorescent radiation originating frolll various points of the saillple were carried out.
A copper lnasking fralne with a sliding aperture of2 mIll dialneter was used for that and the nleasured salnple was placed behind it. The location of lneasuring points is shown in Figure 2. Measurelnents were carried out for sele-

1036
1.0
0.8
.6'
~ 0.6
(])
.5
@!
.,6
0.4
.~
~
0.2
R. Sitko and J Jurczyk o -
PW 1450, X-ray tube with a W anode
- PW 1410, X-ray tube with a Mo anode
-10 10 20 f,IIlIn
Figure 1. Distribution of X-ray tube radiation distribution on the surface of the·
S atl1P Ie nilun, concentration ofwhich in the analyzed lnaterial was the largest (about 61 %). In the case of relnaining elelnents, i.
e.
copper, zinc and chrolniuln, that OCCl~r at slnaller concentrations, the obtained intensities offluorescent radiation were insufficient due to a very slnall area covered with analysis (0 2 lnln) at a sinallinass of the analyzed salnple, i.e. 0.13 lng cln-
2
(weight of salTIpleabout 0.61ng on a filter of 4.52 cln
2 area).
The lnasking fralne lnade of copper was thicker than the critical thickness for K a
Se line for which lneasurelnents were carried out (PW 1410 spectrolneter with an Mo tube). The obtaiped average results for individual points of radial r == 0, 2, 4,6,8 and
10 lnln and angular a == 0°,45°,90°,135°,180°,225°,270° and 315° coordinates are
135
0 tit
.:trl(l
- e
180°· . . .
-.
e e
It e
.. ..
e e l
2e ..
" e
• •
45
0 a ...
e
6 . .--.._
/
225(1 e e
8
~
1Onuu"'---.
•
I
\
,I r
-....
a e
0
270 e
315
(I
Figure 2. Location of 111easuring points

Deterl'nination o.f111aSS per unit area inhol'nogeneity o.fthin salnples 1037 given in Table 1. Table 2 presents a relative seleniuln concentration in various points of the salnple. Calculation were carried out taking into account the proportionality of fluorescent radiation to the intensity of exciting radiation: lr--J C· 1
0
The relative intesity ofthe priInary radiation for individual areas ofradiation Ineasurelnent wasdeterlnined by calculating the area under the curve of radiation distribution(Fig. 1) for PW 1410 spectrolneter.
Table 1.
Results of seleniul11 (K a ) radiation intensity 111eaSllrel11ents perfor111ed in various places of the sat11ple
1, countsll 00 s (net) a
0
45
90
135
180
225
270
315
0111111
7417 r.= 2111n1
8033
7050
9573
8148
7543
8373
8583
7695 r = 4 111111
8170
9700
9 140
9893
9 510
8445
8808
8 185 r = 6 111111
7993
8328
9610
10363
10415
9818
9433
8 818 r = 8 111111
9023
9778
10300
14805
13943
10550
11 840
9803 r = 10 n1111
10783
10723
13 560
16405
13 720
14068
12433
11 983
Table 2.
Relative concentration of selenium in individual areas of the sm11ple
--1
1 f
1
0 r =
0 111111
(r)dr = 1
3 f
1
0
1 r = 2
(r)dr
111111 r =
4 n1111 r =6 111111 r
=
8 111n1 r = 10 111n1
5 7 9 11
0.99] f 1
0
(r)dr = 0.965
f 1
0
(r)dr = 0.928
fI o
(r)dr = 0.856
f 1
0
(r)dr =0.746
3 5 7 9
45
90
135
180
225
270
315
0.337
0.369
0.324
0.440
0.374
0.346
0.384
0.394
0.353
0.385
0.457
0.431
0.466
0.448
0.398
0.415
0.386
0.39]
0.408
0.471
0.508
0.510
0.481
0.462
0.432
0.479
0.519
0.547
0.786
0.74]
0.560
0.629
0.521
0.657
0.654
0.827
1.000
0.837
0.858
0.758
0.730
Relative values of individual integrals are also given in Table 2. The selenilun concentration was calculated with respect to the area of the highest concentration of this elelnent:

1038 R. Sitko and J Jurczyk
Cmaxo..r
fa,r
1'+1 J
1
0
(r)dr
1'-1
1"+1 J
1
0 r'-1
(r' )dr' fa',r' fa,r r-J r+1 J
1
0
(r)dr
In the case ofthe studied salnple it was the area ofcoordinates a == 135°, r == 10 lnnl:
9
II J
1
0
(r)dr f135.10
1'-1
1'+1 J
1
0
(r)dr
0.746.
f a,r
4.547 .10-
5 • _ _ f_a,_r_
16405 r+1 J
1
0
(r)dr
1'+1 J
1
0
(r)dr
1'-1 1'-1 where: a, r - coordinates of the lneasuring point; C rc1a, r concentration ofthe elelnent in the place of coordinates a andr; fa, rintensity offluorescent radiation; a' and r' - coordinates of the lTIeasuring point corresponding to the highest concentration of the elelnent
CmaXa',rl;
(r 1, r + 1) - integration range (2 lnln dialneter of the lTIeaSUrelnent area).
Taking into account the intensity distribution of the prilnary radiation allows to obtain a real distribution of the studied lnaterial concentration after its direct digestion on the filter. As predicted, the obtained results indicate that there is a preconcentration of the salnple on edges of the filter. The described phenolnenon is presented in a grapllical way in Figure 3.
The inholnogeneity of the lnass per unit area ofprepared thin salnples or interlnediate salnples lnay be the source of errors of the perforlned analysis due to local interelelnent influences in the areas, where the concentration of the salnple increases and due to the inholTIogeneity of intensity distribution of the exciting radiation - the elelnent of diversified concentration in individual areas is excited to fluorescence with various intensity. In previous papers [9,1 OJ the authors have analyzed
Cu/Zn/Cr/Se, Zn/Ga/Cr/Se, Cu/Co/Cr/Se, Cu/Ni/Cr/Ce, Yb/Zn/Sb Inono- and polycrystals of diversified chelnical cOlnpositions. The calibration .carried out using synthetic reference salnples with a silnilar distribution of the analyzed Inaterial concentration allowed to avoid a likely systelnatic error. The precision ofpreparation a natural salnples was deterlnined. Thirteen lnaterials were altogether analyzed,for each lnaterial three salnples were prepared and three Ineasurelnents were perforlned for each salnple. The obtained values of standard deviations are deterlnined not only by salnple's preparation (inter alia inholnogeneity of lnass per unit area) but also by inholnogeneity of the lnaterial itself (salnples of 0.5 lng weight) and to a slnaller extent by lneasurelnent's precision. For seleniuln existing in studied Inaterials on average at the level of 620/0 the relative standard deviation (RSD) alnounts on average to
0.87%, for chrolnilull with average concentration of 19%, RSD on average is equal to
1.7%. The lnetals being deterlnined Zn, Ga, Cu, Co, Ni, Yb, Sb existed in the studied

Detennination ofl'nass per unit area inholnogeneity
0.1
thin sanlples 1039
1,3
15
Figure 3. Distribution of concentration of the analyzed tnaterial digested directly
011 a filter; X, axes - situation of n1easuring points (Cartesian coordinates) lnaterials at very diversified levels frolntenths ofa percent to several dozens of percent. For lnetal contents of about a few or a dozen or so percent the RSD usually does not exceed the value of 3.5%. A relative standard deviation for slnall contents of elelTIents, i.
e.
one percellt and less, reaches very diversified values of a few or a dozen or so percent what Inay result froln a large inhomogeneity of the Inaterial. The obtained results ofprecision ofpreparation of natural salnples were considered as satisfactory taking into account its silnplicity, slnall weights of the analyzed lnaterial (about 0.5
lng) and a large inholTIogeneity of studied crystals resulting froln thelnethod of their synthesis.
CONCLUSIONS
The described ·lnethod allows to deterlnine a likely lnass per unt area inhomogeneity of the salnples in a quick andsilnple way, after previous deterlnination ofexciting radiation distribution on the salnple's surface. The knowledge of inholnogeneity of sa In pIe distributiori on the substrate is needed considering its effect on the reproducibility of results. A likely deterioration of precision and accuracy of results arises froin various intensities ofelelnent's fluorescence in individual areas of the salnple (inhoinogeneity of the exciting radiation distribution). A silnilar distribution of the luaterial on the substrate both in standard and in studied salnples (as in the worked-outlnethod [9,10]) causes cOlnpensation of the aforelnentioned errors. However, ifthe accuracy of the obtained results is unsatisfactory, e.g. as a result of various distribution of the Inaterial in standards and in the analyzed salnples, the lnethods of preparation allowing to obtain salnples of better hOlnogeneity of salnples' Inass per unit area are looked for or there are attelnpts to use lnathelnaticallnethods taking into

1040 R. Sitko and J Jurczyk account the aforelnentioned inholnogeneity and the excitation radiation distribution on the salnple' s surface [6].
Classification of sainples to the class ofthin layer method according to frequently assuined criteria on the basis ofknowledge ofInass coefficients values and the geoInet~y ofineasureinents [11,12] Inay be erroneous for sainples that are inhoinogeneous with respect to Inass per unit area. Local preconcentration of the analyzed Inaterial
Inay be not only the cause for intensification of intereleinent influences but in an extreine case also a local excess of critical thickness ofthe sainple (t max ).
These were the reasons that while classifying samples authors deterinined their relative thicknesses
(treI.
== tsample/tmax) Ineasuring the eleinent's radiation intensity in the studied sainple and in the reference sainple of lnuch higher weight, situated outside the area of thin layer, but prepared in the identical way as the studied salnple [9]. The obtained results indicated that the values of errors resulting froln lnatrix effects were sinaller than one percent. In places where the Ineasureinents were carried out the salnple thicknesses were lnany tilnes slnaller than the critical thickness.
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Received Septen1ber 1998
Accepted May 1999