ANALYST, MAY 1988, VOL. 113

Microanalysis of Urinary Calculi by Quantitative X-ray Diffraction Procedures

783

Michael Alexander Erich Wandt* and Allen Lawrence Rodgers Department of Physical Chemistry, University of Cape Town, Private Bag, Rondebosch 7700, Republic of South Africa

Ten urinary calculi were quantitatively analysed using two microanalytical X-ray diffraction techniques. The first employs a combination of separate diffraction and absorption measurements whereas the second uses silver peak attenuation to determine constituent concentrations. Both approaches show good agreement with each other and with results obtained independently by elemental analysis of the same specimens. Keywords: Urinary calculi; X-ray diffraction; microanalysis

Urinary calculus disease is one of the oldest known medical disorders of mankind. Although the bladder stone was the typical urinary concrement of history, renal and ureteric stones are very common today.1 Over the past 30 years, the world-wide prevalence of renal calculi in particular has multiplied, paralleled by increasing prosperity.

Urinary stone formation is a complex process involving many variables, the pathogenesis of which is not completely clear.2 The investigation of the fundamental causes of urolithiasis involves both clinical and scientific approaches, the latter essentially embracing two areas: crystallisation experiments and stone analysis.

The crystallisation approach considers stone formation to be part of the field of biomineralisation and investigates the influence of physico-chemical parameters such as concentra- tion and pH on the crystallisation process. On the other hand, stone analysis allows the investigator to characterise accu- rately the chemical conditions prevailing at the time of nucleation and growth. Accurate knowledge of the chemical composition of a calculus is important not only with regard to understanding its genesis, but also for the prescription of suitable prophylactic measures.

As urinary calculi are composed mainly of relatively insoluble crystalline substances, the constituents can be easily identified by X-ray diffraction (XRD) analytical techniques. Moreover, XRD has the potential of being truly quantitative, although this aspect has been largely neglected in its applica- tion to urolithiasis studies.

Probably the most versatile and widely known instrument employed in quantitative X-ray diffraction analysis (QXRDA) is the powder diffractometer with Bragg - Bren- tan0 geometry. Most QXRDA techniques using this instru- ment require the sample to be of “infinite” thickness. Assuming a mean irradiated area of 1.0 X 0.5 cm2 and a “practically infinitely thick” specimen of 2 mm depth (stan- dard sample holder), and a mean urinary stone density of approximately 2.5 g cm-3, a minimum of 250 mg of stone powder is imperative. However, only a few calculi will be of a size large enough to meet this demand, because 55% of all stones weigh less than 100 mg and 40% weigh less than 25 mg.34 There is therefore a need for a procedure which will permit the quantitative analysis of small calculi. This paper describes the development and application of microanalytical XRD techniques which allow calculi with a mass as low as 1 mg to be investigated.

* Present address: Council for Scientific and Industrial Research, National Accelerator Centre, Van de Graaff Group, PO Box 72, Faure 7131, Republic of South Africa.

Theory Most QXRDA methods using the powder diffractometer are based on an equation which was first deduced by Alexander and Klags:

xj=kfi-lb*z,j . . . . - . (1)

This equation relates the mass fraction XJ of component J with the diffracted intensity ZJ of a reflex i of this component via the mixture’s mass absorption coefficient F*. The value of the instrument sensitive constant, kJ, depends on the nature of the component, J, and on the geometry of the diffractometer. Two years later, Wilson6 published the theoretical equation permitting analyses from less than “infinitely thick” samples. In this instance, the intensity - concentration relationship [equation (l)] is complemented by an exponential factor that takes into account the absorption and reflection properties of the specimen which are functions of the diffraction angle 85:

XJ = ktJ-1ziJ~*[1-exp(-2~*asin-1eiJ)]-1 . I (2)

In contrast to other methods of QXRDA, the appearance of the mass absorption coefficient, p, and the sample’s (mass) surface density, a, in the exponential expression [equation (2)] does not allow the “flushing out” of absorption-related phenomena from the concentration-determining equation.

In order to overcome this problem, Talvitie and Brewer7 and Bradley8 limited the surface density of their samples, thereby yielding XJ independent of F* and linear in ZJ:

XJ = (8kfip-lM-1Asine~)Z~ . . . . (3)

where M is the total sample mass and A is the area over which it is distributed. However, the implementation of this proce- dure in stone analysis is impeded by the difficulty in obtaining uniform powder layers of suitable thickness.

An alternative approach is either to determine the attenua- tion coefficient, p, directly by transmittance measurements9 or to use the internal standard method.10 Another alternative is to mount the sample on a metal specimen holder and to compensate for absorption effects using the intensity of a reflection from the holder.11 An advantage of this technique over the previously described diffraction - absorption method12 is that both the absorption and diffraction measure- ments are made in the same way and on the same sample.

Because of their extremely low diffracted background intensities, silver filters have found wide application as sample mounts.13 The mass absorption coefficient can be expressed using the measured silver peak intensity for any reflection OAg before (I**) and after (Z’A~) deposition of the sample:

ItAB = IAgexp(-2~*asin-l~iJ) . . . . (4)

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784

Solving equation (4) for F*o and substituting the result in equation (2) allows the calculation of X, from measured quantities only:

ANALYST, MAY 1988, VOL. 113

alpha-alumina (internal) standard (BDH, Poole, Dorset, UK, 0.3 pm).

A variety of membrane filters for use as sample mounts were investigated to establish their diffraction properties; Table 1 gives the observed diffraction patterns. It was decided to use pure silver filters because these produce only two sharp diffraction maxima against an otherwise extremely low background in the 20 region of interest. For this purpose, silver membranes (25 mm diameter, 0.2 pm pore size) were obtained from Selas-Flotronics, Huntingdon Valley, PA, USA.

Although dust chambers of different technical complexity have been used for sample collection in the field of occupa- tional health,l0,15 a filtering technique7916 was considered to be more applicable for the preparation of stone samples. Portions of the powdered stone, with or without internal standard, were dispersed and filtered under suction. Water and acetone were used as the liquid medium. The suspension was applied to the filter by means of a syringe connected to a Millipore microsyringe filter holder. The latter was fitted to a filter flask under vacuum. Proper distribution of the material was ensured by the use of a wetting agent (Triton X-100, BDH). Small non-uniformities in the deposition of the samples on the silver filters were compensated for by rotating the sample about the diffraction vector (PW 1064120 rotating specimen holder). This procedure smoothed those intensity fluctuations which were due to different particle sizes and also averaged the preferred orientation of the particles. Sample masses ranging from 1 to 100 mg were tested, but were found to have little effect on the mass distribution on the filter.

X, = #kiJ-l M-1 ALsineA, I,, [l-exp(-LsinOA, sin-1Os>]-l where ( 5 )

A practical problem with this microanalytical technique is the need to measure the intensity of each silver filter before use. As a result, one approach has been to employ a different filter type of negligible absorption on which the samples are precipitated and then placed on the same silver membrane each time.14

In this work, constituent concentrations were derived using two of the described techniques {diffraction - absorption with separate determination of the absorption coefficient [equation (2)] and silver peak attenuation measurement [equation (31). The values obtained were compared with concentrations obtained from independent inductively coupled plasma atomic emission spectrometric determinations.

Experimental Instrumentation and Apparatus A Philips automatic X-ray powder diffractometer equipped with a PW 1050/70 vertical goniometer, a PW 1390 channel control, a PW 1394 motor control, a PW 8203 pen recorder and a PW 1395 programmer was employed. Radiation was produced by a PW 2233120 Cu normal focus tube set at 50 kV and 30 mA. The take-off angle was 6". Soller slits, a 0.5" divergence slit, a 0.2 mm receiving slit, a 0.5" anti-scatter slit and a monochromatising graphite crystal (Model E3-202 6VW 2OC-800, Advanced Metals Research, Burlington, MA, USA) were used in the beam path. Diffracted radiation was detected with a PW 1964/60 NaI scintillation detector. The ambient temperature was maintained at 19 "C and the supply voltage was allowed to stabilise for 30 min before measurements were started.

The grinding and mixing equipment which was used to reduce the mean particle size and to obtain homogeneous mixtures of standard and stone samples included a Micro- Dismembrator I1 (B. Braun, FRG) and a Turbular mixer (Type T2C, W.A. Bachofen, Basle, Switzerland).

Attenuation coefficient measurements were conducted on a Philips PW 1220 spectrometer, equipped with a molyb- denum X-ray tube, which was operated at 45 kV and 28 mA. An Sr specimen [2 g SrC03 + 3 g A1203 + 1 g wax C micropowder (Hoechst, Frankfurt, FRG)] was used as the standard target. The generated Sr Ka radiation was diffracted by an LiF(220) crystal and measured with a scintillation detector at an angle of 36.865 "20.

Samples and Specimen Preparation Whole stones were pulverised with an agate mortar and pestle. Portions of the powdered sample were enclosed in a PTFE container together with a PTFE coated ball. The container and its contents were immersed in liquid nitrogen for ca. 20-30 min, after which the container was mounted on the Micro Dismembrator I1 and the grinding action was commenced. The low temperature permitted crushing to be continued for long periods without the sample temperature ever rising above 0 "C, and also rendered the sample very brittle thereby making it easier to grind. Heat-induced changes were also prevented from occurring. [Dehydration of calcium oxalate dihydrate (COD) and struvite (STR) was observed when using auto- matic mortar grinders for sample preparation.] Some of the resultant powder was then mixed with ca. 35-45% mlm

Phase and Intensity Determination Specimens were first scanned continuously (2 "28 min-1, 2 cm min-1) and the phases present were identified from characteristic peaks. Thereafter, those regions of the X-ray pattern which included the stronger reflections of each component and the (111) and (200) silver peaks were step-scanned (step size, 0.01 "20; fixed time, 10 s). Patterns were processed using the NBS*QUANT82 system17 and the QXDA program.18

The proportionality constants, k,J, in the intensity - concen- tration relationship were obtained by applying the internal standard technique. Reference intensity ratios19 were measured for six substances: calcium oxalate monohydrate (COM, 1.25), calcium oxalate dihydrate (COD, 0.81), hydroxyapatite (HAP, 0.45), brushite (BRU, 1-56), struvite (STR. 0.90) and uric acid (UA, 1.03).2"

Mass absorption coefficients for pelleted samples were determined in transmission. A blank reading was first recorded at the strontium KLY wavelength followed by three readings with the sample inserted. A further blank reading was then recorded for each sample. Photons were counted for 40 s or until 106 counts had been registered. Counts were dead-time corrected and the mass absorption coefficients were calculated with the aid of the sample masses and absorption area (1.267 cm*). To attain higher accuracy, this procedure (including the preparation of a new pellet) was repeated.

Because the ratios of two absorption coefficients measured at two different wavelengths are the same for all compounds (provided that there is no absorption edge between), it was possible to convert the mass attenuation coefficients measured at the strontium wavelength to those at the Cu KLY wavelength. To achieve this, pure alpha-alumina and uric acid samples were subjected to the described procedure. A conversion factor was then calculated from the mass attenuation coef- ficients measured at the Sr Ka wavelength and from the mass absorption coefficients derived from International Tables21 for the Cu Ka wavelength. This factor was used to convert all measured absorption coefficients to the Cu K a wavelength when calculating constituent concentrations according to equation (2).

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ANALYST, MAY 1988, VOL. 113 785 ~

Table 1. Diffraction patterns of membrane filters (1CL5Oo28 scanning range, Cu Kar radiation and diffractometer settings as described in the text)

Pore sii Pm

0.2

0.45

0.2

0.2

0.45

0.45

0.4

0.2 0.4

0.65

0.2

0.2

10.0

0.2

0.2 0.2

0.2

0.8

0.2

!el Filter material Regenerated

cellulose

Mixed cellulose

Mixed cellulose ester

ester

Cellulose

Cellulose nitrate triacetate

Diffraction pattern characteristics* Low background ( 4 0 cps) at large diffraction angles (>30 "28); two

distinct broad maxima (FWHM ca. 3 '28) at 12.0 and20.5 "28 (cu. 250,400 cps, respectively)

Slightly structured background of relatively low intensity, decreasing from cu. 300 cps at 10 '28 to 4 0 cps for angles larger than 30 2 8

Background intensity decreasing from cu. 300 cps at 10 '28 to <150 cps for angles larger than 30 "28 with broad peak (cu. 400 cps) at cu. 20 '28

Slightly structured background, decreasing from cu. 400 cps at 10 "28 to <50 cps for angles >30 "28, with small peaks at cu. 17 "28

Background intensity increasing from cu. 250 cps at small angles to 400 cps at ca. 20 28, but steadily decreasing to 4 0 0 cps for angles

Low background intensity (<50 cps) except for broad peak between 16 and 26"28 with superimposed peaks (cu. 400 cps) at 20.3 and

Low angle background of ca. 500 cps up to 18 "28; broad peak (2800 cps) at 26 "28; very low background (ca. 20 cps) on high angle side of this peak (>32 28)

Low background intensity (ca. 50 cps) up to 14 "28; broad peak (65CLllOOcps) around 17.6 '28; extremely low background (cu. 10 cps) for angles >30 "28

Very low background with average intensity of 50 cps over entire diffraction angle range; very broad peak of low intensity (<150 cps) between 14 and 28 "28

Very low background (25-50 cps) over entire diffraction angle range, except for somewhat elevated region ( 4 0 0 cps) between 16 and 26 "28

Broad maximum between 15 and 22 "28 with superimposed sharp peaks (>lo00 cps) at 17.8,18.4 and 20.0 "28; smaller peaks at 25 S,

Broad maximum between 10 and 20"28 with superimposed sharp peak of high intensity (ca. 8000 cps) at 18.0 "28; broad hump in background from 30 to 50 '28 with superimposed minor sharp peaksat31.6,37.0and41.4"28

Lowbackgroundwithsharppeaksat 18.0,21.9,24.1,31.8,36.7and 49.3 "28, the intensity of which decreases by a factor of 20 with increasing diffraction angle (from ca. 7000 cps for the first peak)

Same as Millipore FGLP (Fluoropore) High background on low angle side of sharp peak (cu. 220 000 cps) at

18.0"28; otherwiselow backgroundwithsharppeaksat31.8,36.7

Low background with high intensity maxima at 14.0 (6OOOcps), 17.0 (4000 cps) and 18.0 "28 (40 000 cps); peaks of lower intensity at 25.7,27.2,28.6,31.8,36.7and49.3"2€1

Extremely low background ( 4 0 cps) over entire diffraction angle range; two strong sharp silver peaks (100% = 5000 cps) and 3 further peaks (10CL150 cps) at 27.8,30.3 and 46.3 "28

Extremely low background over entire diffraction angle range; displays only silver pattern (PDF 4-0783)

>3402e

23.7028

36.0 and 38.8028

49.3 028

Manufacturer Sartorius

5 P e SM 11607

Gelman

Schleicher & Schull

Gelman

Sartorius

Metricel

ME 24 GA-6

TCM-200

SM 11306

Sartorius SM 11906 Polyamide

Nuclepore Polyester

Nuclepore Polycarbonate

Millipore BDWP Polyvic PVC

Sartorius SM 12807 PVC

Millipore GVWP Durapore Poly(viny1idene difluoride)

PTFE Millipore LCWP Mitex

Millipore FGLP Fluoropore PTFE

Nuclepore Sartorius

Filinert SM 11807

PTFE PTFE

Gelman Teflon PTFE

Millipore Silver

Selas Flotronics FM-25 Silver

* Cps = counts s-1.

cellulose filters display a rich spectrum, in particular at lower diffraction angles. As this range (<25 '20) is generally used to identify unequivocally urinary stone constituents, these filters cannot be utilised in such investigations. On the other hand, filters made from poly(viny1 chloride) (PVC) show a very low and almost flat background over the entire diffraction angle range, which should make them ideal substrates for stone powder suspensions. However, the Millipore PVC filter is not manufactured with a pore size small enough to prevent passage of the small corundum particles, and the Sartorius variety is no longer manufactured owing to difficulties in production (Sartorius, personal communication). Therefore, silver filters are currently the most suitable despite their high cost.

Table 2 displays the results for the ten stones investigated with the two XRD techniques and by an elemental method, viz., inductively coupled plasma atomic emission spec-

Results and Discussion

The most difficult problem in QXRDA is that of specimen preparation. Urinary calculi for XRD analysis must be air-dried and not subjected to heat. Selection of a particular portion has a decisive influence on the results of the analysis as samples from different regions of a stone are likely to yield different concentration values. Therefore, the approach in this work was to crush whole stones and to use portions of the powdered mixture for specimen preparation.

One of the practical problems encountered in the use of membrane filters as substrate materials is that these filters are produced from a diversity of materials, most of which cause substantial scatter of the X-rays. The high background radiation commonly observed in the diffractograms of these filters generally makes them unsuitable as sample mounts for QXRDA. It can be seen from Table 1 that the common

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786 ANALYST, MAY 1988, VOL. 113

determinations. However, it can be seen that discrepancies occur with apatite, which is not detected by XRD at concentrations below 20%. This constituent is generally regarded as being difficult to determine by XRD owing to its small particle size and amorphous nature.23 Inaccuracies also arise in the determination of this constituent using the ICP-AES data, because it is assumed to be present in those stone samples in which phosphorus is detected but in which no corresponding phosphatic component can be demonstrated. A systematic bias in the microanalytical method, especially when employing absorption correction by means of silver peak attenuation, is also evident. It appears that alpha-alumina values are often larger than the true concentrations added to the sample.

trometry (ICP-AES).22 In the first diffraction - absorption technique (p), the absorption coefficient was determined directly in transmission, whereas in the second instance (Ag) use was made of silver peak attenuation measurements. The phase concentrations derived from ICP-AES analysis (elemental) were calculated from the concentrations of the major elements, calcium, magnesium and phosphorus, with additional structural information from XRD powder photo- graphs.

Table 2 shows that there is good agreement between the two XRD techniques. Good correlations also exist with the ICP-AES data, thereby lending confidence to our QXRDA

~ ~ ~

Table 2. Comparison of constituent concentrations (YO m/m) derived from different techniques

Mass absorption

filter/ Phases Mass on coefficient, Constituent concentration$

mg cm2g-l* detected? G*i? Agv Elemental// 8.1 20.8 A1203 41 54 (44)

COM 7 8 10 UA

COM COD APA

COM APA STR

APA STR

COM COD UA

COM APA STR

23.4 48.7 &O3

11.6 54.7 A1203

8.8 33.9 A1203

22.3 28.0 MZ03

11.1 56.9 &O3

22.6 47.3 AlaOs

63 74 39 37 25 23 72 70

40 45 12 14 32 50 8 13 43 46

46 52 38 48 6 9 44 31 31 42 41 48 24 20 50 41 14 12 48 46

- -

- -

- (39) >.) 10

22 49 25

(35)

80 (36) p o - (36) 33 48 14 (35)

COM 35 44 43 40 $85 COD - 10 14.1 48.8 A1203 50 52 (40)

APA - COM COD APA -

28 56 51 34 180 COM 24 36 j35

15 19 24 23 137

- 17 25.6 52.5 A1203 46 48 (41)

COD 7 11 APA 29 24 48

COM COD UA 39 40

25.4 29.0 A 1 2 0 3 46 44 (40)

- * Determined by transmission measurements from separate spe-

cimens. t Identified from XRD strip-chart or implied by elemental content

of specimen. $. The concentration of A1203 internal standard is its concentration

as measured in the specimen; concentrations of stone components expressed as percentage of stone mass.

5 Concentrations calculated according to equation (2) using mass values from column 1, a filter area of 4.52 cmz and separately measured p* values from column 2.

7 Concentrations calculated according to equation (5 ) using atte- nuation of silver diffraction maxima.

IIThe A1203 concentration is the true amount added to the specimen; concentrations of stone components obtained from ICP- A E S elemental analysis2 in conjunction with semi-quantitative XRD analysis (Debye - Schemer).

Conclusion It can be concluded that for the application of the membrane mount microanalytical technique, the use of an internal standard for correction purposes is indispensable, especially when studying small (<lo mg) samples. In addition, the use of the silver maxima suffices for the correction of changing absorption effects in the samples and a separate determination of the attenuation coefficient is unnecessary. However, each filter must be scanned before and after the deposition of the sample, because great variations in the intensity (34004700 counts s-1) can occur in the different filters. At very low filter loads (i .e. , <1 mg), quantitative measurements cannot be made. Also, the positive identification of all materials in a sample is hampered when peak maxima are within the 3a limit of background scatter.

The inaccuracies of the described procedure also arise from a non-uniform distribution of the sample on the filter; this could represent a systematic error in the analysis. Further, when handling very small samples, the reproducibility in weighing is a major factor in the over-all error incurred. Hence, various figures of merit have been published for this technique, generally ranging from 10 to 30% reproducibility.

The quantitative determination of constituents from differ- ent sections of a urinary stone is vital for the understanding of its aetiology. As XRD is regarded as the first method of choice for qualitative analysis,z3 the results of this work suggest that it should also be selected for quantitative determinations. Although other techniques such as ICP-AES can also be employed for this purpose, many are limited in certain respects. For example, element-sensitive techniques cannot identify the purely organic components of a stone, nor can they distinguish between the various calcium oxalates and phosphates; distinctions of this type are of clinical importance. The results of this work show that serious scientific investiga- tions of urinary stone pathogenesis can confidently include quantitative investigations of small calculi using a micro- analytical XRD technique.

The financial support of the Council for Scientific and Industrial Research (CSIR, South Africa), the Medical Research Council (MRC, South Africa) and the University of Cape Town is gratefully acknowledged.

References 1. Blacklock, N. J., in Williams, D. I., and Chisholm, G. D.,

Editors, “Scientific Foundations of Urology,” Volume I, Heinemann, London, 1982, p. 235.

2. Finlayson, B., Urol. Clin. N. Am., 1974, 1, 181. 3. Gundlach, G., Urologe, 1968,7, 353. 4. Maurer, C., Urologe, 1969,8, 189. 5 Alexander, L., and Klug, H., Anal. Chem., 1948,20, 886. 6. Wilson, A. J. C., J . Sci. Instrum., 1950,27, 321. 7. Talvitie, N. A., and Brewer, L. W., Am. Ind. Hyg. Assoc. J . ,

1962,23,58.

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ANALYST, MAY 1988, VOL. 113 787

8. 9. 10.

11. 12.

13. 14.

15. 16. 17.

18.

Bradley, A. A., J. Sci. Instrum., 1967,44,287. Leroux, J., and Powers, C., Occup. Health Rev., 1970,21,26. Donovan, D. T., Knauber, J. W., and von der Heiden, F. V., Prog. Anal. Chem., 1973,6, 61. Williams, P. P., Anal. Chem., 1959, 31, 1842. Leroux, J., Lennox, D. H., and Kay, K., Anal. Chem., 1953, 25,740. Altree-Williams, S., Anal. Chem., 1977,49,429. Altree-Williams, S . , Lee, J., and Mezin, N. V., Ann. Occup. Hyg., 1977,20, 109. Leroux, J., Occup. Health Rev., 1970,21, 19. Quakernaat, J., J. Sediment. Petrol., 1970,40, 506. Hubbard, C. R., Robbins, C. R., and Snyder, R. L., Adv. X-Ray Anal., 1983,26, 149. Heck, H. G., “QXDA-Program for Quantitative X-ray Dif- fraction Analysis of Powder Mixtures,” DSM Central Labora- tory, Geleen, The Netherlands, 1975.

19. Hubbard, C. R., Natl. Bur. Stand. (US), Spec. Publ., 1980, No. 567,489.

20. Wandt, M. A. E., and Rodgers, A. L., Clin. Chem., in the press.

21. Ibers, J. A., and Hamilton, W. C., Editors, “International Tables for X-Ray Crystallography,” Volume IV, International Union of Crystallography, Kynoch Press, Birmingham, 1974, p. 61.

22. Wandt, M. A. E., and Pougnet, M. A. B., Analyst, 1986,111, 1249.

23. Rodgers, A. L., Scanning Electron Microsc., 1985,II, 745.

Paper A71467 Received November 18th, 1987

Accepted January 12th, 1988

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