PRINCIPLES OF PRECISION COLORIMETRY _Measuring Maximum Precision Attainable with Commercial Instruments C. F. HISKEY, JACOB RABINOWITZ,
AND
IRVIRG G . X-OUSG
Polytechnic Institic t e of Brooklyn, Brooklyn, S.
Y.
By the use of photoelectric colorimeters as null detectors in tlie comparison of a standard and an unknown, increased precision may be obtained as the absorbance of the standard is raised. The maximum precision obtained is proportional to the total radiant power available and to the way that power is distributed between absorbance and sensitivity. This study presents data on three widely differing commercial instruments whose characteristics were investigated, the purpose being to demonstrate the methods used in evaluating the m a u i m u m precision obtainable with any instrument.
I
S EARLIER papers (4,5 ) the basic fundamentals of colorimetric measurements as they apply to comparisons with standard saniples of finite absorbance were t,reated. I n genewl, it was established that enhanced precision could be achieved with any given commercial colorimeter if one could work with high absorbance standards. It was indicated that there were good reasons, theoretical as the ell as experimental, for believing that colorimetric determinations could be made with a precision equal to that of gravimetric and volumetric procedures. Since that time various applications of the method have been made, particularly to the determinat,ion of copper, permanganate, chromate, etc. ( I . 2 ) and, in the main, t'he above-mentioned predictions have been confirmed. There are, nevertheless, a number of important practical as well as theoretical matters to be treated in connection \ d h this experimental approach which, when clearly understood, Ti-ill assist t'he analyst in making a proper application of the transmittance ratio approach. A4 treatment of the principles m d niethods of evaluating the ult,imate precision which mal- be expected of any commercial instrument is one of the problems in this category. This is especially true because commerci:tl instruments are not generally designed for use with high absorbance reference standards. Consequently, this paper is devoted to t,hat, subject. Experimental data on three widely diff ering tj-pes of commercial instruments are given and these data are evaluated. The three instruments chosen were a Lumetron 402E colorimeter, a Coleman Model 14 spect'rophotomet'er, and a Beckman I I U spectrophotometer. This group covers both single- and doublebeam, as n.ell as barrier-layer and vacuum photocell instrunient~s. They represent types of instruments widely used in this country as well as abroad. Their selection for this study was governed entirely by availability to the authors and not' by choice. Consequently, these remarks are made without any consultation with t,he manufact,urers and are not intended either as criticisms or endorsements of the instruments. Instead, the intent,ion is to provide the analyst with the details of theory and procedure to be iollo\wd in evaluating his own instrument. The method described herein involves an evaluation of a quantit>- termed the intrinsic scale length of the colorimeter. Ot,her quantities associated with this concept include the transmitt'ance of the reference standard and the relative sensitivities of the instrument in a transmitt'ance and a transmittance ratio measurement. -411 introduction to these concept's may be made tiy defining t,he intrinsic scale length. INTRINSIC SCALE LENGTH
Every photoelectric colorimeter has some type of ruled scale or dial, usually reading in per cent transmittance and covering a iange from 0 to 1 0 0 ~ o .This is the real or normal scale of the in-
sti,ument,and may I) igneti arbiti,arily a value of iitiity. 11 :I relative transmitt:rnce measurement is made, the effrct.ivc sc:iIt: length, L, of thr colorimeter will be different from t,he mil ~ c l l g t h and will always lie larger. The correctness of this assertion ii1:iy he allowed momentarily, as an explicit, demonstration is gircn below. It follows then that there will be some maximum cffectivr scale length for any colorimeter. The ratio of the effect,ivc and tlic real scale length mal- be termed the intrinsic scale length. L . It is seen that L,,, rqiresents the maximum magnification of tlie real scale possible n-ith xn:~particular instrument. K h c n opei'ating with an intrinsic scale length of L, it is as though the c:ilibrated dial of the instrument were L times as long as that octunlly observed with the response characteristics of the instrumelit unchanged throughout t,his expanded dial. Associated with the intrinsic scale length are tn-o othnr qu:int ities of importance: the ti~a~ismittance of t,he referencc btaiidnrd to be employed in the analysis and the ratio of the sensitivities of the instrument in :itransmittsnce and in a transmitt:inctt ratio measurement'. The relation of each of these quantities to the iiitrinsic scale length is devrloped here in the order in which (hey :ire mentioned. At this point it is rirccwarj- to recall the fundamental ah,sorption law equation involvd in the ti.ansmit,tance ratio method. Thxt equation has becn givrn :IS
xhere d lis the absoit)tlnce of the standard, a: = c. r: -i.c-.. tho ratio of the unkno\vn and the st,andard concentratioii~--;111111, and 1, are the intensit'ies of the emerging light beams coming t'roir1 a source of identical flux and passing through identical cuvi'ttei which contain solutions of concentrations c2 and cI, respcctivcly. From Equat'ion 1, it is evident that as the absorbancc ot t l i r rrference standard is increased a smaller value of (a: - 1) n i q > - l ) r detected, and thus a t high absorbances increased precision ivill I>(* obtained in measuring the unknown concentration. -4direct consequence of Equation 1 is that the colorlrnetcr ticiirg used must be alilr to operate with high absorbance standardi.e., it must be possible t,o set the calibrated dial at' 100% transmittance and effect an electrical balancing of the circuit. It' can lie seen from this that the effective scale length is proportioiinl to the reciprocal of the transmittance of the reference standard and the intrinsic scale length to the reciprocal of Ihc Ion-est transmittance which can be halanced on the instrument. In a more explicit, fashion the validity of these definitions mi)lie demonstrated by considering Figure 1, where a real :md :in effective optical scale are compared.
If two solutions with ti~ansmittancesof 0.50 and 0.40 a r t ' fxken and examined hy ordinar>-colorimetry, the vertical lines lnhelcct 1464
V O L U M E 2 2 , NO. 1 2 , D E C E M B E R 1 9 5 0 I , I u aiitl I: 10 on the r e d (upper) s t i l e \rill correspond to the Soiv if instead of uning a solvent to set the was done above, the solution with a transen as the stnndard, this n-ould result in the rflective si,& as depicted. This effec,tivescale ivould lie twice that ot' the real scale. I l . I o is niatlr to read unity on the real scale. :ilthough on the effective scale its position is! of course, only 0.50. Similarly, li'10is 0.40 on the effei~tivcsc.ule Ibut on the real scale it- value i i 0.80 and on this i;c,:ile i t i. trmiect the relative transniit t:iuc,e--i.e..: I 2 !I:,
It is iio\\- :tppai'ent \vhj- t,he effrcti3 lc~iiptliis 1)roportion:tl also lie evidriit that to IU,'II :mtl L,,,, to (I"II,)n,n\.It inci,e:isiiig Tile effective scale Irrigth iiieiiiis th:it o i i e of several ~ i t . the light iiithing> hi.. kwvii done in tht, i ~ i s t i ~ u n i ~ ~1:itlier t wi>ity 01 tlie iiicidr,nt i)e:ini ha. I ) w n increasrti, or the amplifier gain 01' thv g:tlvaiionieter response has i i c ~ i iincreased. T l i t b otlir,i 1:iiatol, involved in thc intiinsir sc:ilc length, as \v:ia iiit1ic~:ilctl: t I > ~ v ei-, , tlie ixtio of thr> instrunieiitd sensitirities in 1 lit. t\vo liilitls oi i i l e : ~ s u i ' ~ " ~ iIwiiig i ~ ~ i ic~onsitlcretl t~ here. To under, s t : i i i t l the fu!~ctiori of' this r:itio consi(l(~r fiwt the meaning of the tc.1 111. >tAii>itivit>. il~liena ti~:iiisniitt:rnce 01' a ti~aiis.niitt:i~ice ratio measurement iu in:i~lerepeat rdly without iii any i\-a!. :iltering tlie instrument adjustinents, i t will be found that thew is a definite uncertainty obs ~ ~ i in~ tlw v ~\ ,td u e s foi, these tc'rnis. These uncertainties may be w i t t e n for thc~twoliinck of iiif,iisui,eiii('iits as A(Il/fo)and A ( I Z / l i ) , rc...liertivel\-, The niagnituclrs of' these quantities are determined i n 1):irt by tlw atii1it~-of the ('ye to discriminate the dial or gnlv;iiioiiieter position :mtl i n jxirt 1))- t l w staljility of t h e instrument. Iiistruineiital >t,:tbilit>.includrs not onl?- ~tc.:itlinessof the light sourre and o ~ h c i*ircuit ~r roniponriits hurl1 tis tlicx :implifiers and the ilit~~ absorption pliotowlls, t J U 7 : i l w the i ~ e ~ ~ i ~ o d u c ~ofi l ipositioning ~ ( ~ 1 1 s . I t i. I,OT 11o.sil~lc~t o sa^. i n :rdv;incc~ whether the visual tiiar1~imi1iatioiioi the inati,unieiit;il st:iljility is the doininant >., 1)ec:iusr the r r h t i v e r f f z c t of these tlvo source of uiii~ci~t:iiiit :ispets vat i i - irom (8:isc~t o c Y , In each in-tmce it is necessiii'y t o c~nlu:itr,r ! i w m ~ i " v of i-t;iljility i n ortlvr t o decide nliirli t ' O l l t I ' ~ ~ ~ \ l i1.tJ.T ~?to A(fi/It,) 01' A(/! 111.
?
0.15 0.15
1,5 ,,
I.? I.?
2.0
I
t
,
f
,
I
:
-
!EFFECTIVE
.
,.I SCALE(Ls2)
I
1
F
ipure 1.
Real and Effective Optical Scales
Tlic.qc. i i i i i ~ ~ ~ i ~ tterms ~ i i i i t: I~W~ tlicwi'oi~c~ impor,t:tnt measures oi t h c lwi,ioixi;lrlce of the in~ti~unierit arid repi'cbseiit the smallest detect:rl)lt~tiiflei e1lc.e in thrx ti,niiciiiitt:iric(, 01' the' ti,ansmittrtnce ratio cd. ivhicli c:in l w ~iicii~siii In niost instruments A ( I l i l o ) and A(/?; I , ) ui'e cquiil to e:ich o t l i q but this is not necessarily alxiys true.
T o understand why these quantities are iiot ahvays identical, c,nnbider the response of any photometer esposed to a relativel\band of radiant energy from a continuous source. will he proportional to the product of the light eiwi'gy from the source and the spectral sensitivity of the photoi , r l l . I n the most e1ement:try (,:ise-i.e., a photo element coni i w t c d directly to a galvanometer-this response may be indicated l i y 3 galviiiiometer deflection. Let us also assume t,hat, the i'c+ponse 01 the instrument is linear with respect to light energy. l-(i\vthe deflection of the galvanometer may be subdivided into 1 .OO unite corresponding to a transmittance of unity. A(Zl/Io) \vi11 of coiii's~represent the uncertainty of determining the transniitt:iiii~~ i.(.uding,
1465 S o w , if the energj- admitted is douhled, the galvanometer A ( I l i I o ) will, however, dedeflec,tion n-ill also be doubled. crease b?. one half, because the actual uncertainty of locating the gxlvanonieter position has not changed while the literal length of the new galvanometer scsale has been doubled. B!. this process the sensitivity and the precision of the instrument have tieen doubled. Suppose no\v that in the serond case, whrre the energy is tn-ice t,hat of the first. a n absorber with a transmittance of 0.50 is placed. Then the galvanometer deflection would be redured to what it \vas in the first ca5e and A(1, /Iji would also be identical to that of the first rase, but the precision of niensurcnient would not be identical hecause of the low trancmittance of our reference st:ind:ird and the (,onsequent prcrisinn g:iiii ;tii+ingtherefrom.
T1t.r~. i h t h e n :i simple illustration of thr n.ay the light enei'g>mu!. 1)e ttividcd between t,he production of electrical signal :inti ahsoi~l~aricc~. instrument manuf:icturer is limited in t h e mi3itii-ity which may be introduced into his instrument h ~the physiicxl requirement of keeping his scale to a reasonable size, liy the dr,sire to give maximum resolution, if a monochromator is t o tie H pai't of the instrument, by the desire t o avoid overloading tlie photocell out, of a linear response range, and by the need to kcel) costs within reason. On the ot'her hand: the analyst may in givrii situ:rtions be able to sacrifice some of these characteristics in the of greater precision. iritc~i~c~st Fi.oni what has been said above, L can be formulated matlienow, as the product of the reripi'ocal transmittance oi m:~tic~all>tile rc~i'crence standard and the ratio of these uncert:iiiities. Thus:
l.'or all those .situat,ions and instruments where the uncertaint,ji,atio i,clm:iins unity, L = I o ! I l = IO-'' and is controlled only 1)y thc, value of the absorhance of our standard. T h a t ahsorbmce oljviouply must be at a mnsimum for niasimum precision and for the intrinsic scale length to he defined. [This restricted definition is identical with that given I)>- Bastian, \\-ehrrling, and Palill:i ( 2 ) .] \Yhen a solvent is used t o srt the scale: L has a value equ:il to unit)., since A I = 0. On the other hand, with a standard solution \vlio.ze ti,:in,vnittancc is, Irt us say, 0.10, L will equul 10 and A i will, of course, equal unit!-. Thw, t h o smallcr the ti,ansniitt m c e of the standard sample, the mow must the radiant poner incidrnt on the cuvettes be increased :inti, therefore, the larger the valur of L required. The determination ot' L for such colorinietera thus becomes merely one of determining the lowest transniittaricr value which can he expanded to unity on the real scale. For :i fen. instruments the ratio A ( I , / / , , I A ( I J I , ) is not unit?.. In other words, as the transniittanrc~of t l w wfei,ence staildml cahanges, so too does the fraction of light energ!- usetl for t h i b generation of electrical unbalance. \I7hero this i.:itio brronies IC; th:in unity, it. obviously leads to ii diminution in ttic vuluc of I. ant1 ma:- e v ~ noutweigh the f o / f i term. I t is thei~ri'oi~r~ most essiriitiiil to tlvaluete this ratio brforc procrrding to t h e u s e of liigli :iii.wrlxiiic(i st:iiitl:ii+ nit11 : i : i > ~ ~ ) : i i ~ t i ( ~ i I :ci ro l o r i m c ~ t ( ~ori ~ slwct i~)~)hotonirtc~r. DISTI-perl,olic character of the reltition between sensitivity arid ZI !Io. -111 curves for all filters nti:illy the same, differiiig only in t h e value of the conht:ilii.
GI3 a
t
-
25
20
-
15
-
IO
-
Q5
-
-
I 2-
mu 365 515
3- 700
Na2CrOq
K Mn 0,
N ISO4
4- 575 GrG13 5 - 640 G U S 0 4
0
0
ance of the standard solutions. L is seen to remain at unity as the absorbance of the reference standard is increased. Another way to demonstrate this is by substitution of Equation 12 into Equation 2. On the ot'her hand, with a number of the filtei plied, it. is impossible t o work with the full light intensity uvaila1)le becnu,!e the rapid fatigue of the photocells results in poor tinie stability. I n those instances, where it is necessary to diminish the light intensity, the hett,er proccdure is to use a standicrtl >olution as the light ahsorber. In Figure 7 it is again seen that :I given amount of light e ~ ~ ( ' r g y should be divided so that 63.2% is absorbed by the standard used for comparison, with the remaining 36,8y0 used for genc,i,atinu electricd signal. This arrangement will give maximum precii;ion a t any particular light level. On the other hand, if the iriterisit!of light source can be increased at will, the sensitivity :ind pwcision will vary linearly with the light intensity. Thwc will, 01 course, be an upper limit a t which fatiguc or inst,:ibility of t h c l i t ) trctirig circuit viill vitiate any further attempt to incw:cw the pi,ecision. At this point an increasc in the absorbance \vi11 p r m i t :I further precision gain wit,h increasing light intensity. T h a t guiri in precision will tie logarithmic with respect to light intrt1sit.v a m i not linear as in the case of the light used for generating unl):il:iriw i n the circuit. .Is a consequence it will be undesirable t o iiirrc1:i-e inti,iiaities beyond those required t o handle absorbanccc 01 :iIiout 1.7, innsmuch as a fifty-fivefold increase of light intrnsit). \\ ciulii l i p nwtletl. This hecomes prohibitive in most work 8
7
8 .
0
2
4
6
8
10
I.'igure
6.
IO sensitivity of Reference Standard TS. Transmittance
6 LT 0
oc oc
w e W
2
I ~ I ~ t~l i vI standpoint, II of pwcisioii considerations, one can comI i u t e tlir I'rlative error of this e t ~in. a~ very simple manner merely l)y su1,atituting the relatioil L(1JZl) X 11/10= A(11/Z@)into t'he 1 c~l:rtivc~ ( ~ i ~ r ofunction i preriously given. With the substitut.ion vIi'c.rtri1 ttir ~t,lative error 1)ecomea:
+-a d 4 LT
2
~~
2
.4
.6
.e
IO
12 -
A 1)lot of This relative error as a iunct'ion of the relative transmitt:iriw i. given in Figure 7 and is seen to differ in several renliec't- Ti o i i l other relative transmittance functions previously giJ-en, It iq s('f.it that, when the absorbance of the standard is zero :i wI:itivc'ri 01 identical with the normal colorimetric case is 01)t:iintatl. This is to be expected, as the functions are ident,ical. .-is tlre LLI i c o i h n c e of the standard increases, hoir-ever, the niinimurn ri'i'e~rtloei: not diminish as might have been expected from previous treatments, but instead remains a t a constant valuc of f 1(11 l g b i . e . , 2.72A(Zl/lo)--until an absorbance of 0.4343 has I w i i reac:hrd. After t'his the niinimuin error increases with the : i ~ i ~ o i ~ l ) m rof ; r the standard. IVhile t'he absorbance of the st:iiiil:ird is being increased, it is observed th:it the value of I y ! I I cvi,i.cyoiiding t o minimum error moves from 0.368 a t zero abroi,i):inc.c t o unity when the absorlxmce equals 0.4343, and rei u : i i t i . unity as the absorbance is increased beyond this value. This indicates t,hat for :I tizcd light intensity as used here o11t' C:III c.\l)ect n o gain in p r , c . c 4 - i e i i i i i i e i ~ l yhj- inci~cvmingthe a1)sorl)-
I I
Figure 7 . 1. 2. 3.
KelatiFe Error
Curve 4 1 0.0 0.4343 11.1086 0.8686 0.2171 6. 1.303
4.
Tlic pi~o1)lcniof the light iritensity c a n I i ~ ~ v np:ii~tic~ulu:iy ic l~:i(l ivhcn \vorking ivith rare earth :thsorption hp'ctra or i n thr, ultrxviolet dierc. tlir :il)sorption Ijands ai'e very nai'roiv. 111 o d e : ro get sufficient rtidi:int poll-er to thr photoc.rll. one must often \r-itlci, t,he T W W length of the hand traiismittetl, This leads. iu the.>c eases, to a pronounred absorption Ian- dc ition due to the qtr:t>light effwt and uiider these circuinstitrices a n y precision g i i r i a i i t i r i p a t d hy :I high :tlisorbance approucah i x i y fail to nxitrhr,itilize. 4CKYOWLEI)C\IENT
Thi5 :iuthois r r i h to achioirledge thr genci'oun assistance given this study hy 11:ichlett and Pons and t h e Cloleriian I n ~ t r u n i r n t
ANALYTICAL CHEMISTRY
1470 Company. I n addition, they are thankful to the U. S. Electric lfanufacturing Corporation for permitting the use of its facilities in certain phases of the work. They are also indebted to D. Killiams, R. C. Hawes, and G. S.Haines for their friendly criticisms while the manuscript was in preparation. LITERATURE CITED (1)
Bastian, R., ANAL.CHEM.,21, 972 (1949).
(2) Bastian, R., Weberling, R., and Palilla, F., Ibid., 22, 160 (1950). (3) Brice, B. A., Reu. Sci. Instruments, 8 , 279 (1937).
(4) Hiskey, C. F., ANAL.CHEM.,21, 1440 (1949). ( 5 ) Hiskey,C. F., Trans. N.1’. Acad. Sci., 11, 223 (1949). RECEIVED May 4 , 1950. The nomenclature and method of approach used in this article are in conformity with those given in a previoua paper ( 4 ) . Reading of the above article will facilitate the understanding of many points which are only briefly treated in this paper. Some of this material was presented before the Fifth Annual Symposium of .halytical Chemistry, Pitts. burgh, February 1950. Other parts mere presented a t the 118th Meeting of the AMERICAX CHEMICAL SOCIETY.Chicago, 111.. September 1950. The erperimental material contained herein has been taken from theses to be s,tbmitted by Jacob Rabinowitz and I. G. Young to the Polytechnic Institute of Brooklyn in partial fulfillrnent of the rerj~~irelnent for the master’s degree in chemistry.
Evaluation of Three Iron Methods Using a Factorial Experiment I,. K. REITZ, A . S. O’BRIEN,
AND T.
L. D.IVIS
Paper Service Department, Eastnian Kodak Company, Rochester, V. Y . The classical method of designing experinients for testing the precision of an analytical nicthod is contrasted with Fisher’s factorial design technique. The advantages of the latter procedure from the point of view of econorn? of experiments and the detection of interactions are presented. The application of an anal!sis of variance to data obtained by a factorial experiment is discussed. These sta-
T
HE value of .staZtistivitl terhiiiqueb to the analytiral vhemist has become increasingly apparent. .I Symposium on Stat istical Methods in Experimental and Industrial Chemistry was SociEw held a t the 113th Meeting of the . ~ M E R I C A N CHEMICAL (8). The progress made in statistics as applied to analytical chemistry has been reviewed by Wernimont ( 9 ) ,who lists the statistieal tools that should be exploited by the analyst. These include control charts, teats of significance, analysis of variance, correlation, and design of experiments. Factorial design and the analysis of variance are described in this article. These techniques when applied to an analytical method yield information on precision but not necessarily on the absolute arcuracy of the p w cedure. If proof of the accuracy of a method is needed, the extrapolation technique of Youden (11)ran sometimes be applied. When a n analytical chemist investigates the precision of a test method, he almost always finds that several factors influence reproducibility. The classical approach to the problem of locating these sources of variability aould bc to alter one factor at a time while holding all others constant. Thus the significance of each factor is determined separately. However, if the factorial design technique originated by Fisher ( 2 )is used, a more reliablemeasure of the significance of factors can hc obtained from a relatively small number of experiments. The technique permits all factors to vary systematically according to a designed pattern. When the classical technique is used, only one estimate of variability is obtained from two cxperinients in which all factors but one are held constant. A repetition of these two experiments would give one more estimate of variability. However, with a factorial design, repeated estimates of the variability attributable to a certain factor are obtained because of the systematic manner in which the factors are varied. The explanation of the illcreased efficiency of a factorial design is given in various discussioiis of the subject (1,6). The classical technique and the factorial design may be contrasted a t another point-that of the detection of “interactions.”
tistical techniques are illustrated by a study of three colorimetric methods for iron-phenanthroline, thiocy anate, and sulfide. The variables included in the study were dictated bj the type of information desired. The o-phenan throline (1,lO-phenanthroline) tnethod proved superior to the thiocyanate method according to the criteria set up. The thiocyanate method was much better than the sulfide procedure.
-4simple interaction is pwseiit ~vhenthe rffect of one variable is not consistent at different levels of a second variable-for esample, the result of a test method may not he influenced by “time of standing” a t one “pH,” but may be strongly influenced at it second “pH.” This would I)e called a p H times time of standing interaction. When data are rollected from a factorially designed experiment, interactions can be detected and evaluated. Using a classical design the interaction is often missed and the variability improperly assigned unless certain experiments happen to he chosen. When an interaction is detected by classical design it is often impossible to measure the magnitude of the effect. Factorial design also systematically detects and evaluates “higher order” internction involving three or more t e r m . These a-ould be missed by rlassical technique or a t most would he detected only hy the most :igilc mind. VARIABLES OF THE-EXPERLMENTS
In this study a factorial experiment and an analysis of variance of the resulting data are illustrated by an evaluation of three colorinietric iron methods. The object was the selection of the most precise of three rapid methods for the testing of iron in raiv 1113 teri als . In the testing of raiv materials for iron it is necessary to measure iron a t several Ion- l c ~ c l s . Some products have very low iron specifications a.nd othrrs may contain considerably more. One variable included in thcsr (valuation experiments was therefore “level of iron.” The three levels scxlected were 0.05, 0.15, and 0.25 mg. of iron, which represent the amounts presrnt in a sample of reasonable size for matrrial ranging from low to high i n iron. Raw materials often contain ot,her heavy metals such its lead, which could possibly intrrfere in an iron method. .1 small quant,ity of lead (0.1 mg.) typical of the amount often cncount,ered was introduced as another factor in the study. The raw material itself, although essentially inert, could influence the results. Sodium sulfittr was selected as a test material and introduced as :mothrr factor in the designed experiments. Five grams of C . P . sotliuni sulf:ite were added to certain experimrnts and t,his is rcft~rrcdto iri this study as inert material.
