X-RAY SPECTROMETRY, VOL. 19, 203-206 (1990)

Glass Disk Fusion Method for the X-Ray Fluorescence Analysis of Rocks and Silicates

MoisLts Alvarez Physics Department Universidad Nacional Pedro Henriquez Ureiia, Santo Domingo, Dominican Republic

A study of the physical and practical aspects needed for a successful solid solution method for XRF analysis is presented in the light of the theory and practice of the glass-making industry. An inexpensive manual glass disk sample preparation method is proposed that gives a well annealed disk that can he ground and polished without any losses due to breakage.

INTRODUCTION

Fusion methods have many advantages compared with powder pressed pellets in the x-ray fluorescence (XRF) analysis of rocks and silicates, regardless of whether the solid solution is used directly, powdered or briquet- ted.’-3 The advantages are that the particle size and heterogeneity effects (i.e. mineralogical effects) are elimi- nated, the possibility of decreasing matrix effects or maximizing fluorescence intensities using a high or low specimen dilution, respectively, the possibility of adding compounds (e.g. heavy absorbers, standard additions or internal standards) to decrease or compensate for matrix effects and easily prepared synthetic standards.

The disadvantages of the fusion method are that analyte-line intensities from low-2 elements and trace and minor constituents are reduced by dilution and absorption, fusion requires considerable time and skill if manual glass bead disks are attempted and sometimes there are problems associated with fluxing, crucible sticking and bead cracking.

Many studies have been made of these problems and the fusion method has become widely applied. However, for the x-ray analyst trying to use the fusion procedure for the first time, contradictory advice in the literature may result in confusion and disappointment, and the impression that the method is more an art than a science. This situation prompted us4 to try to under- stand and systematize the physical processes behind the fusion method, using the knowledge accumulated in the glass-making i n d ~ s t r y . ~

THEORETICAL

Let us first define some useful terms: Annealing: The operation of removing or reducing

the strains in glass. Stress : force per unit area. Strain : relative deformation.

Since stress usually accompanies strain, the words are often used interchangeably, but it is important to remember that they are not synonymous.

Reason for annealing glass

Our previous work4 has shown that the removal or pre- vention of excessive stress is the most difficult problem encountered by the analyst using the glass disk method in XRF analysis. When glass disks are poorly annealed, large losses due to breakage may occur during the cooling process, and even if the glass disks have been completely cooled without fracturing, they may show an annoying tendency to breakage when handled or when attempts are made to grind or to polish them later. It is hence desirable to consider, in a general way, the cre- ation and release of internal stress.

Glass is an amorphous material which at ordinary temperature is as hard as a typical solid, but softens when it is gradually heated, until it becomes viscous and finally liquid. The reverse process takes place during cooling. This ‘wide’ range of temperatures in which con- tinuous solidification occurs is characteristic of under- cooled liquids but is never observed with crystalline solids.

In general, a temperature gradient established by heating will produce in the outer layers a longitudinal compression that changes continuously into tension in the inner layers (with a neutral zone, in the middle, with no stress), while a gradient established by cooling will cause the opposite to happen.

Annealing of glass Temporary and permanent stress

The following discussion is based mainly on the theo- retical and practical knowledge acquired in the glass- making industry5 and generally follows the trends indicated in the classical paper of Adams and William- son.6

When glass is cooled there are three possibilities: (1) cooling from a relatively high temperature with the pro- duction of permanent stress; (2) cooling from a rela- tively medium temperature, in which case stress is

0049-8246/90/040203-04 $05.00 0 1990 by John Wiley 8z Sons, Ltd.

Received 1 I September 1989 Accepted (revised) 6 February 1990

204 M. ALVAREZ

introduced, but less than in (1); and (3) cooling from a relatively low temperature, in which case no permanent stress is introduced, only temporary stress due to the temperature gradient.

Detection of stresses in glass disks and their interpretation

The device for detecting stresses in a glass disk is the polariscope. The simplest polariscope can be made by crossing two Polaroid filters in such a way that the background remains dark. Introducing a glass disk in the middle of the filters and looking through them, using white light, is a very useful way of testing if the disk is or is not well annealed, and of establishing the degree of annealing. This information can be used for choosing and/or optimizing the conditions established for annealing, such as annealing temperature and time.

A well annealed disk should look completely black through the polariscope. Sometimes annealed disks show a black cross pattern, whose line width is an indi- cation of the amount of stress present. Narrower lines indicate higher stress.'

Highly stressed glass disks show coloured patterns and these colours are directly related to the stress (see Table 1). Other more sophisticated means for accurately detecting and measuring stresses can be found in the glass-making literature.'

Adams and Williamson6 found empirically that the release of stress at constant temperature proceeds according to the equation

(1) 1/F - 1/Fo = At

where F is the stress at time t , F, is the initial stress and A is a constant for the particular glass at a particular temperature and is a measure of the rate at which stresses are relieved. The variation of A with tem- perature follows the equation

log A = M I T - M , (2)

where T is the temperature in "C and M , and M , are constants for a particular glass.

For the sake of convenience, the quantity experimen- tally measured is the birefringence, 6n, i.e. the optical

Table 1. Relationship between phase difference and colour with white light

Phase difference Phase difference (nm) Colour" (nm) Colour"

50 200 300 425 530 565 640 740 840

Iron grey Greyish white Yellow Orange Red Violet Blue Green Yellowish green

880 945

1030 1100 1200 1300 1425 1500

Yellow Orange Red Violet Bluish green Green Yellow Orange

"The colours become paler as the phase difference increases.

path difference per unit length (in nm cm-'), which is directly related to the stress F.

Rearranging Eqn (1) yields

1/6n - 1/6n, = Aft

where 6n, is the initial birefringence and A' is the varia- tion of stress with time (in optical units).

The birefringence can be obtained using a polari- scope, by measuring the optical path difference (in nm) and dividing this value by the length (in cm) of the glass in the line of sight.

A method for measuring the optical path difference is to observe the colours produced when the sample is placed in a polariscope and then using Table 1.

Annealing

Adams and Williamson6 pointed out that at any tem- perature, a glass requires a certain 'annealing time', and this is arbitrarily defined as the time required to reduce the stress, in optical unit, from 50 to 2.5 nm m-'.

The 'annealing temperature' is that temperature for which the annealing time is 2 min. The 150°C interval of temperature lying immediately below is called the 'annealing range.' At temperatures below the annealing range, very little permanent stress can be introduced.

Adams and Williamson6 showed that the best method for annealing requires that the glass be held at constant temperature, below its customary annealing point, for the appropriate time, and then cooled at an increased rate, as shown in Fig. 1. This seems to be in contradiction with some authors' claims.

At this point, a word of caution is advisable. It is well known that the strength of glass under tension is much less than that under compression; the tensile strength of glass is almost an order of magnitude less than its com- pressive strength. This means that although the cooling rate can be increased when one surpasses the lower part of the annealing range, one must be careful in doing this, and bear in mind that the glass could crack, even if it is well annealed, owing to the temporary stress induced by cooling. At no time during cooling should

\ I L ._

I 2 3

T I M E ( H O U R S )

Figure 1. Recommended annealing procedure: the top dashed line is the annealing temperature and the temperature range between the dashed lines is the annealing range.

GLASS DISK FUSION METHOD FOR XRF ANALYSIS 205

the hot glass disk be touched by an object cooler than itself.

Annealing temperature and time

The problem that arises is how to measure, experimen- tally, for a particular glass sample the annealing tem- perature and the annealing time. The annealing temperature has been determined by three method^,^.'^ involving either the disappearance of the stresses using a 'special' oven, differential thermal analysis (DTA) or the rate of thermal expansion. In the XRF field, only Bertin' has mentioned DTA

for determining the annealing temperature of glass disks, but without going deeper into the subject. Wilburn and Dawson," in the glass field, reported the use of DTA use for this purpose and stated that DTA is a rapid and convenient method for determining the annealing temperature of glasses.

]in general, when powdered glass is subjected to DTA, two peak temperatures are observed, one endothermic, at fairly low temperature, and the other exothermic at a higher temperature. These peaks depend on the glass composition. The first endothermic peak is the so-called 'annealing dip' and the temperature where this occurs is the annealing temperature. The exothermic peak is due to devitrification of the glassy material and this tem- perature must be avoided when annealing glass disks or crystallization may occur (see Fig. 2). Working below this temperature greatly reduces the risk of crys- tallization, although this seems to be in contradiction with some authors' claims.

Once the annealing temperature has been obtained,

the annealing time can be determined from Eqns ( 1 ) and (2) developed by Adams and Williamson.6 For this, one needs to know the constants MI and M , in Eqn (2), which are particular to each glass and are not known a priori.

A practical way of solving the problem is to create a series of highly stressed glass disks. This can easily be done by quickly cooling them from a temperature higher than the annealing temperature (i.e. > 600 "C). Subsequently each can be kept at different times (i.e. 0.5, 1, 2 h and so on) in a fixed temperature environment slightly below the annealing temperature (1.e. 500 "C in an oven). When this time has elapsed, the oven is turned off and allowed to cool slowly, keeping the disk inside the oven, without opening the door, until the lower part of the annealing range is reached (1 h is normally suffi- cient but one can experiment). Below this temperature, the disk may be removed and cooled to room tem- perature. If the annealing was properly done it can be established by viewing the disk through the polariscope. The time should be adjusted until one obtains a well annealed disk.

After optimization, the disks are quite sturdy and can be ground and/or polished with confidence. Disks pre- pared according to the steps described above have a zero breakage rate and can even be dropped without breakage.

It should be mentioned that the rate of annealing doubles approximately for each 10°C rise in tem- perature. This means that if 30 min are needed for annealing a particular glass disk at 500 "C, at 440 "C it requires more than 1 day! Therefore, it is very impor- tant to know as accurately as possible the annealing temperature of a particular glass

0 . 2

10 Temperature ("'2)

Figure 2. DTA curve for a glass disk formed from a rock sample-lithium tetraborate (1 : 9) mixture (<120 mesh). The endothermic peak A at ca. 500°C is the 'annealing dip' and this is the annealing temperature (heating rate 10°C min-'). The exothermic peak B above 600°C is due to devitrification or crystallization.

206 M. ALVAREZ

Lastly, it is also important to note that another means used for toughening glass in the glass-making industry is tempering, that is all glass surfaces are cooled so that they end up with compression balancing the tension forces, which must be completely buried under the surface." Tempering is normally done by fast, uniform cooling of the glass from a temperature close to its annealing temperature. The technique resembles some of the methods used for producing glass disks in XRF.13

PROCEDURE FOR PREPARATION OF GLASS DISK SAMPLE

This sample preparation method involves the use of lithium tetraborate in a flux-to-sample ratio of 9 : 1. If a different fluxing reactant or flux-to-sample ratio is used, the appropriate annealing temperature and time must be determined as indicated above.

1. Weigh 9.000 0.001 g of lithium tetraborate in a small plastic cup, previously weighed and tared.

2. Weigh 1.000 f 0.001 g of rock sample powder on a piece of weighing paper, previously weighed and tared.

3. Weigh 0.2 g of ammonium nitrate [to oxidize iron(I1) to iron(III)] on a piece of weighing paper, pre- viously weighed and tared. 4. Transfer the weighed rock sample powder from 2

and the ammonium nitrate from 3 to the small plastic cup with the flux from 1.

5. Manually mix the powders for 1-2 min. 6. Transfer the homogenized mixture to a graphite

crucible and heat at 1150°C in an electric muffle furnace for 15 min. Every 5 min swirl the crucibles for ca 10 s to eliminate bubbles and to ensure homogeneity.

7. Pour the melt into a graphite mould (with sloping walls) previously heated to ca. 500 "C.

8. Introduce the glass disk (on the graphite mould) into a second oven previously heated to ca. 500°C (the annealing temperature was ca. 525 "C, see Fig. 2). Keep it there for ca. 1 h, which is the annealing time, without opening the oven door.

9. Turn off the oven and wait until the temperature falls below 350°C (ca. 1 h with the oven door closed)

before removing the glass disk to cool to room tem- perature.

10. Steps 8 and 9 are essential to prevent shattering during grinding and polishing. Moreover, if grinding or polishing are not done, these steps prevent unpredict- able cracking of the glass disks. The rate of breakage is reduced almost to zero.

11. To establish whether the glass disk is properly annealed it can be viewed through crossed Polaroid filters, and should look black. Sometimes the glass disk looks completely white when examined through a polariscope, but appears completely black after being ground. This may be caused by graphite contamination in the lower surface.

12. Grinding and polishing are important and almost essential to avoid graphite contamination in the lower surface of the glass disks.

CONCLUSION

A detailed study of the physical and practical aspects that need to be considered in order to produce a suc- cessful glass disk for the XRF analysis of rocks and sili- cates has been made in light of the theory and practice developed in the glass-making industry. According to these there are only two methods for dealing with the stresses in a glass disk : annealing and tempering.

In this work the measurement and optimization of the annealing method have been stressed. It is proposed as an inexpensive method that gives well annealed disks and can be applied under a variety of conditions, e.g. with different fluxes, with only minor changes.

Acknowledgements

The author is indebted to the International Atomic Energy Agency for financial support in the form of a fellowship (C6/DOM/8803). For their kind cooperation in the supervision of this work the author thanks Dr W. Rose and Dr T. Bornhorst of the Geology Department of Michigan Technological University, where this project was carried out, and Mrs E. Ducy de Perez and Mrs V. Mazo of the Universidad Nacional Pedro Henriquez Uretia and Dr E. Greaves of the Uni- versidad Simon Bolivar for their many helpful suggestions concerning the text.

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