The Rigaku Journal
Vol. 16/ number 1/ 1999



Rigaku/USA, 199 Rosewood Drive, Danvers, MA 01923, USA

     Sources of calcium are generally widespread and quite extensive. These sources are of limestone, dolomite, marl,
chalk, and oyster shell. Cement plants account for nearly half the demand while more than two hundred lime plants in the
United States and Puerto Rico consume about twenty five percent. Since the chemical composition of the limestone or
other sources of calcium is critical in the cement and the lime industry, particularly for the deleterious compounds such as
Na2O, MgO, P2O5, and K2O, accurate determinations are critical. Due to the tonnage per hour, these determinations must
be made rapidly and accurately. X-ray fluorescence can thereby satisfy this need for accuracy and precision.
     Production of lime is performed by calcining limestone and the industry is generally located and concentrated in the
States of Michigan, Pennsylvania, and Missouri. The resulting product is quicklime-CaO, or hydrated lime-Ca(OH)2.
Substantial amounts of quicklime is further processed into calcium carbide in order to produce acetylene gas. In this case,
the determination of P2O5 is critical since minor amounts of phosphorous in the acetylene gas can cause premature
explosions. Other uses for lime are well known in the treatment of water, the paper and pulp industry, and the steel
industry for the production of slag to remove impurities. Dolomitic lime is heavily utilized in the manufacture of
magnesite refractories by reacting the dolomitic lime with brines from the Michigan basin to produce MgO and CaCl2.
     Sample preparation for these materials has been performed by grinding and pelletizing or fusion with Li2B4O7. In
addition to the chemistry, matrix and interelement effects will be discussed as related to the chemical analysis by X-ray

Introduction                                                                 fluence the intensities of the analytical lines.
     Calcium carbonate and calcium-magnesium                                 Consequently, relative intensities of a standard and an
carbonate in the form of limestone, dolomite, marl,                          unknown sample are often only approximate mea-
chalk, and Oyster shell are one of the most widely                           surements and not directly proportional to the
utilized non-metallic materials in the industrial world.                     concentration since the matrix, in addition to the
The largest use of limestone or calcium carbonate is in                      concentration of the assayed element as related to the
the cement industry where it is used as a source of                          measured characteristic radiation must be corrected
CaO and also in the concrete industry where it is used                       for enhancement, absorption, and possible peak
as the primary coarse aggregate. Following the                               overlaps. These matrix effects are generally
cement industry, the second largest user would be the                        considered as absorption, enhancement, peak over-
lime industry.                                                               laps, mineralogical differences, and inhomogenity of
    Geological materials present numerous problems                           the sample particles. Consideration of these problems,
as a result of the preponderance of low atomic                               thereby providing a useful and workable procedure by
numbered elements in a variable mineralogical and                            X-ray fluorescence, has been approached by the use
elemental matrix. X-ray fluorescence can provide the                         of internal standards [1], comparison to standards
analyst with an accurate and precise method providing                        approximate in composition to the unknowns [2],
the analytical techniques are properly addressed and                         fusion and dilution with transparent materials such a
are consistent from sample to sample. The most ser-                          lithium-tetra-borate [3-5], reduction of particle sized
ious problems to solve are absorption and enhance-                           by fine grinding [6-9], and mathematical corrections
ment effects, mineralogical differences among                                [10-14]. The method utilized by the author employs
samples, and particle size effects which often in-                           the powder method, fine grinding and pelletizing, and
                                                                             empirical calculations for corrections due to ab-
* Presented at the ASTM Committee on Lime, C-7, December 8,                  sorption, enhancement, and peak overlaps.
Nashville, Tennessee.

16                                                                                                                    The Rigaku Journal
    Analysis of any material by X-ray fluorescence is
best applied to materials where the compositional
range is reasonably small. Calcium/calcium-mag-
nesium carbonate rocks fall into this category even
though the calcium/ magnesium ratios plus the
argillaceous fractions are quite variable. In order to
successfully apply an X-ray fluorescence technique,
the characteristics affect the reproducibility and
accuracy must be identified and corrected. These
variables which can cause errors in the analysis are
deviations in the particle size, mineralogy, and
interelement effects due to varying chemical
composition among samples.
Particle Size
     Reproducible and accurate results by the powder
method in the quantitative analysis of mineralogical
samples requires proper sample preparation in order to
minimize intensity fluctuations as a function of
variations in the particle size and distribution. Burn-                Fig. 1 Grinding time versus intensity.
stein [16] has illustrated that the fluorescent intensity
from a pure material will increase as the particle size is
decreased. In limestone and dolomites the intensities
from several elements may all increase, decrease, or
one may decrease while others increase. Campbell
and Thatcher [17], measuring calcium in Wolframite
where the calcium may be present as a carbonate,
tungstate, or phosphate supported Burnstein's work.
Differences in intensities were observed for equal
concentrations of calcium in three chemical states
when the particle size is large as compared to the
effective depth of penetration of incident X-ray.
Extensive grinding illustrated the intensities from the
various mineralogical forms approach a common
value by reducing the absorption within the individual
particles to a small value (-325 mesh). Figure 1
illustrates the relation of intensity with grinding time
or a reduction in particle for Ca-Mg carbonate rocks.
Reduction in particle size causes a reduction in the
intensities of iron, sulfur, and potassium while the
intensities of calcium and silica are increased. As the            Fig. 2 Pelletizing pressure versus intensity.
size of the individual particles is reduced, the
intensities stabilize. Further reduction in particle size
through continued grinding does not promote any              Examination of Figure 2 reveals that in order to
additional improvement in the intensities, Referring to      reproduce a consistent pellet, a pelletizing pressure of
the example on Figure 1, the minimum grinding time           fifteen tons per square inch should be used.
would be five minutes. A lesser amount of time could         lnterelement Effects
cause significant intensity/concentration deviations
                                                                 Quantitative analysis by X-ray fluorescence of
among the standards and samples. Now that a grinding
                                                             any material requires that the measured intensity of a
time has been established, determining the proper
                                                             particular element is proportional to the percent com-
pelletizing pressure must be determined. A similar
                                                             position. A matrix such as a limestone or a dolomite
study was performed as illustrated on Figure 2.

Vol. 16 No. 1 1999                                                                                                 17
may reveal that the intensity of an element may not be                  RB = ( Cb ) (1+ Ca αBA)                               (2)
directly proportional to the concentration due to result
of an additional element within the sample. This non-              Defining αAB and αBA
linearity is frequently referred to as the interelement
effect and may also be referred to as enhancement or                             ( µ csc θ + µ csc θ ) ⋅ (B − 1)
                                                                        αAB =
                                                                                    1       1       2         2
absorption. When the characteristic radiation of one
element excites another element, enhancement oc-
                                                                                    ( µ csc θ + µ csc θ ) ⋅ A
                                                                                        1       1       2         2

curs. Absorption is observed when one element in the
sample matrix has an absorption edge on the low                                  ( µ csc θ + µ csc θ ) ⋅ ( A − 1)
                                                                                    1       1       2         2
                                                                        αBA =                                                 (4)
energy side of the element of interest or has a mass                                ( µ csc θ + µ csc θ ) ⋅ B
                                                                                        1       1       2         2
absorption coefficient larger than the element of
interest at the energy level of that element. Examples        where
of these effects are illustrated on Figure 3 (Mass
Absorption Coefficient vs Energy in KEV). Since the
Si Kα line occurs just on the high energy side of the         (µ1)A and (µ1)B= the mass absorption coefficients of elements A
                                                                               and B at the effective wavelength for the
Al K-edge, secondary fluorescence will take place                              excitation of the A radiation
and conversely, silica is strongly absorbed by
                                                              (µ2)A and (µ2)B=the mass absorption coefficients of elements A
aluminum. A similar case is observed in the po-                               and B at the effective wavelength for the
tassium-calcium System where calcium is strongly                              excitation of the B radiation
absorbed by potassium since the Ca Kα line lies just          θ1 and θ2 = the angle of incidence of the primary X-ray beam and
on the high energy side of the K K-edge as illustrated                           the take off angle of the secondary radiation
on Figure 3. An additional complication is the fact that      Ca and Cb =the weight fractions of elements A and B
iron has a high mass absorption coefficient at the            Ra and Rb = the relative intensities of elements A and B expressed
energy levels of the lower Z elements, thereby acting                            as ratios of net intensities of the elements A and
                                                                                 B in the sample to the net intensities for the pure
as a strong absorber.                                                            elements A and B
     Although absorption and enhancement effects                   Calibration of the standards involves an iterative
can be severe, mathematical corrections can easily be         process according to Equations 3 and 4 which estab-
applied. Numerous methods have been proposed [10-             lishes the a coefficients which are then assigned to
14]. The author has proposed a method described by            Equations 1 and 2. The unknown sample data is then
LaChance [11] where a relationship is established that        processed through multiple regression analysis
the relative intensity of a characteristic line in a binary   utilizing Equations 1 and 2.
system is directly proportional to the weight fraction
of a given element (A) plus (B) however must sum to           Sample Preparation
unity. The expression would be as follows;                         As previously discussed, particle size and
                                                              distribution can have an effect on the intensities of
        RA = (Ca ) ( 1+ Cb αAB )                      (1)     most elements with the most severe being at the low Z
                                                              end of the periodic table. An illustration of this fact,
                                                              Figure 1, displays the effect of grinding time trans-
                                                              lated into smaller sized particles with increased
                                                              grinding time. Eight (8) separate samples of single
                                                              standard of five (5) grams and 0.1 grams of Na-
                                                              stearate as a grinding aid were placed in a tungsten
                                                              carbide rotary swing mill and ground for one (1) to
                                                              eight (8) minutes. The resulting powder was then
                                                              pelletized under 15 tons per square inch with boric
                                                              acid as a backing material. Each pellet was analyzed
                                                              with the resulting intensities plotted as a function of
                                                              grinding time (Figure 1). The grinding curve indi-
                                                              cated a minimum grinding time plus one (1) minute
                                                              for a total of six (6) minutes.
           Fig. 3 Elemental absorption curve.

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                         Table 1. Instrumental Operating Conditions for Limestones and Dolomites.

 Element                   Na2O    MgO     Al2O3    SiO2     P2O5     SO3      K2O     CaO     TiO2    MnO     Fe2O3   SrO

 ANODE                                                       Rh

 ANODE VOLTAGE, KV                 30                        50

 ANODE CURRENT, MA                 130                       80

 SLIT                                                        Coarse

 CRYSTAL                           RX-40   PET                        Ge                               LiF

 DETECTOR                                  FP-C                                                        SC

 FILTER                                                      None

 PEAK 2θ ANGLE             17.05   14.15   144.65   109.04   141.10   110.80   70.00   61.95   86.18   62.96   57.49   25.13

 COUNTING TIME, S                  40                                          20

 PHA LOWER                         50                                          100

 PHA-UPPER                         450                                         300

 ATMOSPHERE                                                  Vacuum

Instrumentation                                                       that the CaO in the unknowns was initially
    A Rigaku RIX 3100 X-ray spectrometer with a 4                     determined by a KMnO4 titration with no attempt to
kW generator was utilized for this analysis and was                   differentiate between CaO and SrO. In the KMnO4
operated under the instrumental operating parameters                  titrimetric determination of CaO, both the CaO and
as described on Table 1.                                              SrO are both precipitated as a calcium-strontium
                                                                      oxalate and when titrated with KMnO4, the oxalate
Results and Conclusions                                               ion is being determined. As a result, the determined
     The samples utilized in this study were seven (7)                value by this method will be CaO plus SrO. In a
standards supplied by the National Bureau of                          limestone or a dolomite, the SrO could be from 0.05
Standards [18], Ash Grove Cement Company [19].                        to 0.3 percent. Therefore, since X-ray fluorescence
Hercules Cement Company [20], and well charac-                        determines CaO and SrO separately, the SrO and CaO
terized unknown samples from Medusa Cement                            determination by X-ray fluorescence must be com-
Company [21]. The standards and unknowns were                         bined in order to agree with the KMnO4 titrimetric
derived from diverse geographical and geological                      calculation.
areas. In addition the mineralogical structure varied                 Conclusions
from calcite (rhomboidal-R-3c), vaterite (hexagonal-
P63mmc), aragonite (orthorhombic-Pnm), and ara-                           The results of analysis illustrate that X-ray
gonite (orthorhombic-Pmca) as listed in appendix A.                   fluorescence is a viable technique for the analysis of
                                                                      limestone and dolomite. It further illustrates that, with
     The results of analysis is contained on Table 2,                 proper sample preparation, mineralogical differences
while the individual calibration curves are contained                 become insignificant. Data reduction the use of
in appendix B. A typical spectra of limestone is con-                 theoretical alphas automatically solves the problems
tained in appendix C. Calcium oxide and magnesium                     associated with absorption and enhancement effect.
oxide, the main components in Ca/Mg carbonate
rocks, exhibited absolute errors of approximately two                 References
to four percent relative utilizing a simple least squares             [1] Dwiggins, C. W. Jr., and Dunning, N. H., Quantitative
regression analysis. Utilizing the theoretical alpha                      Determination of Traces of Vanadium, Iron, and Nickel
                                                                          in Oils by X-ray Spectrography, Anal. Chem. 32, 1137-
routine as outlined by LaChance [11] with a multiple                      1141, 1960.
least squared analysis, these errors were reduced to
0.07 and 0.05 percent respectively. It should be noted

Vol. 16 No. 1 1999                                                                                                             19
     [2] Brown, 0. E., “Use of X-ray Emission Spectroscopy in
         Chemical Analysis of Cement, Raw Materials”, And Raw
         Mix, ASTM Annual Meeting, 1963.
     [3] Moore, C., “Suggested Method for Spectrochemical
         Analysis of Portland Cement by Fusion with Lithium
         Tetraborate Using an X-ray Spectrometer", ASTM
         Report No. E-2, 5MlO-26.
     [4] Harvy, P. K., Taylor, D. M., Hendry, R. D., and Bancroft,
         F., “An Accurate Fusion Method for the Analysis of
         Rocks and Chemically Related Materials by X-ray
         Fluorescence”, X-ray Spectrometry, 2, 33-34, 1972.
     [5] Claisse, F., “Accurate X-ray Fluorescence Analysis
         Without Internal Standards", Norelco Rep. 4, 1957.
     [6] Wheeler, B. D., “Cement Raw Mix Control through X-ray
         Emission Spectroscopy”, Proc. Third Forum the geology
         of Industrial Minerals, Spec. Dist. 34, University of
         Kansas, 1967.
     [7] Hooper, P. R., “Rapid Analysis of Rocks by X-ray
         Fluorescence”, Analytical Chemistry, 36, 1964.
     [8] Wheeler, B. D., “Accuracy in X-ray Spectrochemical
         Analysis as Related to Sample Preparation”,
         Spectroscopy, vol. 3, No. 3, pp 24-33, March, 1998.
     [9] Kester, B., AIEE Cement Industry Conference,
         Milwaukee, Wisconsin, 1960.
     [10] Wheeler, B. D., and Newell, D., “Chemical Analysis of
         Mg-Cr Refractories by X-ray Fluorescence, Fall Meeting
         of the American Ceramic SOCIETY, Refractories
         Division, Paper #13-RI-76F, October 9, 1972.
     [11] LaChance, G. R., and Traill, R. J., “A Practical Solution
         to the Matrix Problem in X-ray Analysis”, Canadian
         Spectroscopy, vol. 11, nos. 2-3, March-May, 1966.
     [12] Lucus-Tooth, H. J., and Price, B. J., “A Mathematical
         Method for the Investigation of Interelement Effects in X-
         ray Fluorescence Analysis”, Metallurgia, vol. LXIV, no.
         383, Sept., 1961.
     [13] Rasberry, S. D., and Heinrich, K. F. J., Calibration of
         Interelement Effects in X-ray Fluorescence Analysis,
         Analytical Chemistry, vol. 46, no. 1, Jan., 1974.
     [14] Hasler, M. R., and Kemp, J. W., “Suggested Practices
         for Spectrochemical Computations”, ASTM Committee
         E-3, Report SM 2-3, American Society for Testing &
         Materials, Philadelphia, PA, pp 72-82, 1957.
     [15] Sherman, J., “The Correlation Between Fluorescent X-
         ray Intensity and the Chemical Composition”, ASTM
         Special Publication, no. 157, pp 27-33, 1954.
     [16] Burnstein, F., Particle Size and Mineralogical Effects in
         Mining Applications of X-ray Analysis, Denver Research
         Institute, University of Denver, 1962.
     [17] Campbell, W. J., and Thatcher, D., Advances in X-ray
         Analysis, vol. 2, University of Denver, 1958.
     [18] National Bureau of Standards, Washington, D.C.
     [19] Ash Grove Cement Company, Kansas City,MO.
     [20] Hercules Cement Company, Bethlehem, PA.
     [21] Medusa Cement Company, Dixon, IL.

20                                        The Rigaku Journal
                         Appendix A. Listing of Standards and Source

             STD       GEOLOGIC FORMATION                   REGION               SOURCE

             LS-1    Burlington                  Missouri              Ash Grove Cement Co.

             LS-2    Raytown                     Kansas                Ash Grove Cement Co.

             LS-3    Squamish                    British Columbia      Ash Grove Cement Co.

             LS-4    Kimswick                    Missouri              Ash Grove Cement Co.

             LS-5    Jacksonburg                 Pennsylvania          NBC

             LS-6    Jacksonburg                 Pennsylvania          Hercules Cement Co.

             LS-7    Farley                      Nebraska              Ash Grove Cement Co.

                              Appendix B. Typical Limestone Spectra

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