3
TABLE II. Factor group analysis for SiO2 crystalline polymorphs. Space group and number SiO2 polymorphs Crystal Total Activity • system Hermann- Schoen- Zt modes Species of vibrations and Mauguin flies (3nZ') ir R IA AC C numberb ,x-Quartz Hexagonal P3121 (~152) D~ 3 27 12 12 O 2 8 4Al + 5A~ + 9E (R) (IR) (IR, R) Stishkovite Tetragonal P4~ I mnm (~136) D~ 2 18 4 4 3 2 0 Alg + Bt~ + B2~ + Eg + A~ + 2A~ + 4E~ + 2B1~ -- B-Quartz Hexagonal P6~22(~180) D~ 3 27 6 9 5 2 4 A1 + 3A2 + 2B~ + 3B~ + 5Ex (I~) (IR) (IR, R) + 4El (R) ~x-Cristabolite Tetragonal P4x2t2 (~92) D~ 4 36 12 21 0 2 8 4AL + 5A2 + 5Bx + 4B2 + 9E (R) (IR) (R) (R) (IR, R) B-Cristabolite Cubic Fd3m ($ 227) 0~, 2 18 2 1 3 1 0 A2_...~ + E...2 " + 3F~ + F~ + Fj_ 2 Tridymite Hexagonal P63 ] mme ($194) D~h 4 36 6 4 11 2 0 Alg + Bt__.£ + B2___~ + E,g + 2Et, + Ai~ + 3A~ + 2BL~ + 3BI~ + 5Eu + 4E2u Activity of modes does not count degeneracy. Z', see Table I for definition. Abbreviations as in Table I. b Gerade species Raman active and ungerade species infrared active unless specified; line under species indicates inactivity. The Computer Conversion of a Sine Drive Spectrometer to Linear Wavenumber Drive* WILLIAM F. MURPHY Division of Chemistry, National Research Council of Canada, Ottawa, Canada KIA OR6 Index Headings: Computer-based spectrometer control; Digital spectrometer control; Nonlinear spectrometer con- trol. For various reasons, we have had only sine drive spectrometers in our Raman laboratory, in spite of the advantages of working with spectra plotted linearly with respect to frequency. Since the inception of a research program in resopance Raman spectroscopy, it became more desirable to re~ rd ~pectra on a linear wavenumber scale, in order to far Ate ~e comparison of spectra obtained with different exc: ati n wavelengths. We have interfaced one of our spec+.ometers to a minicomputer based data acqui- sition system/ which can record data on magnetic tape for further processing at our Computation Centre; it is, of course, straightforward to replot these data on a wave- number scale. However, for much of our work there is no other reason to acquire and store these spectra, and it is thus inconvenient to obtain a wavenumber plot in this manner. Therefore, it was decided to write a computer program for the system which would drive the sine drive spectrometer in a constant wavenumber per unit time mode, such that we could use normal detection methods to obtain a chart output which was linear in wavenumber. Using a digital drive system, there are two general Received 14 March 1975. * Issued as NRCC No. 14645. methods of producing a nonlinear displacement as a func- tion of time: take several steps at constant time inter-Cals or take a single step at variable time intervals. The num- ber of steps in the first instance and the time interval in the second are chosen to give the best approximation to the desired continuous, nonlinear drive function. A varia- tion of the first approach is available in a commercially available digital Raman spectrometer system/ while we have chosen the latter. The only apparent advantage of the latter is that the digitization error in producing a variable time delay is usually a small fraction of the total delay, while the digitization error in stepping a variable number of steps (±1/~ step), can be significant. Thus, by taking minimal length steps at variable time intervals, one more closely approximates the desired drive function. However, in practice, both of these approaches should have sufficient accuracy, so that the choice between them can be based on other considerations. Our data acquisition system includes a DEC PDP-8L computer (4K memory) and logic in the interface to recognize and carry out various input-output (IO) in- structions. The IO instructions used in the present ap- plication are to read the absolute shaft encoder and to operate the stepping motor, both of which are connected to the spectrometer lead screw. The computer cycle time was used as the time base for generating the delay between steps2 This is accomplished by loading the computer accumulator register with a nega- tive number whose magnitude is proportional to the de- sired delay and repetitively incrementing this number until it reaches zero. Thus, the encoder value is used to obtain the required delay constant, which is then used to produce the delay, the motor is stepped, and the process is continuously repeated in order to achieve the desired drive function. Detailed operation of the drive control routine is as follows: the current encoder value is read, converted from binary coded decimal format to a binary number, and used to fetch an entry from a table of delay constants. This previously calculated table contains the delay constants necessary to produce a basic speed on 480 cm-1/min as a Volume 29, Number 5, 1975 APPLIED SPECTROSCOPY 421

The Computer Conversion of a Sine Drive Spectrometer to Linear Wavenumber Drive

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TABLE II. Factor group analysis for SiO2 crysta l l ine polymorphs .

Space group and number SiO2 polymorphs Crystal Total Activity • system Hermann- Schoen- Zt modes Species of vibrations and

Mauguin flies (3nZ') ir R IA AC C numberb

,x-Quartz Hexagonal P3121 (~152) D~ 3 27 12 12 O 2 8 4Al + 5A~ + 9E (R) (IR) (IR, R)

Stishkovite Tetragonal P4~ I mnm (~136) D~ 2 18 4 4 3 2 0 Alg + Bt~ + B2~ + Eg + A~ + 2A~ + 4E~ + 2B1~ - -

B-Quartz Hexagonal P6~22 (~180) D~ 3 27 6 9 5 2 4 A1 + 3A2 + 2B~ + 3B~ + 5Ex (I~) (IR) (IR, R)

+ 4El (R)

~x-Cristabolite Tetragonal P4x2t2 (~92) D~ 4 36 12 21 0 2 8 4AL + 5A2 + 5Bx + 4B2 + 9E (R) (IR) (R) (R) (IR, R)

B-Cristabolite Cubic Fd3m ($ 227) 0~, 2 18 2 1 3 1 0 A2_...~ + E...2 " + 3F~ + F ~ + Fj_ 2 Tridymite Hexagonal P63 ] mme ($194) D~h 4 36 6 4 11 2 0 Alg + Bt__.£ + B2___~ + E,g + 2Et,

+ Ai~ + 3A~ + 2BL~ + 3BI~ + 5Eu + 4E2u

Activity of modes does not count degeneracy. Z', see Table I for definition. Abbreviations as in Table I. b Gerade species Raman active and ungerade species infrared active unless specified; line under species indicates inactivity.

The Computer Convers ion of a Sine

Drive Spectrometer to Linear

W a v e n u m b e r Drive*

W I L L I A M F. M U R P H Y

Division of Chemistry, National Research Council of Canada, Ottawa, Canada KIA OR6

Index Headings: Computer-based spectrometer control; Digital spectrometer control; Nonlinear spectrometer con- trol.

For various reasons, we have had only sine drive spectrometers in our Raman laboratory, in spite of the advantages of working with spectra plotted linearly with respect to frequency. Since the inception of a research program in resopance Raman spectroscopy, it became more desirable to re~ rd ~pectra on a linear wavenumber scale, in order to far Ate ~e comparison of spectra obtained with different exc: ati n wavelengths. We have interfaced one of our spec+.ometers to a minicomputer based data acqui- sition system/ which can record data on magnetic tape for further processing at our Computation Centre; it is, of course, straightforward to replot these data on a wave- number scale. However, for much of our work there is no other reason to acquire and store these spectra, and it is thus inconvenient to obtain a wavenumber plot in this manner. Therefore, it was decided to write a computer program for the system which would drive the sine drive spectrometer in a constant wavenumber per unit time mode, such that we could use normal detection methods to obtain a chart output which was linear in wavenumber.

Using a digital drive system, there are two general

Received 14 March 1975. * Issued as NRCC No. 14645.

methods of producing a nonlinear displacement as a func- tion of time: take several steps at constant time inter-Cals or take a single step at variable time intervals. The num- ber of steps in the first instance and the time interval in the second are chosen to give the best approximation to the desired continuous, nonlinear drive function. A varia- tion of the first approach is available in a commercially available digital Raman spectrometer sys tem/ while we have chosen the latter. The only apparent advantage of the latter is that the digitization error in producing a variable time delay is usually a small fraction of the total delay, while the digitization error in stepping a variable number of steps (±1/~ step), can be significant. Thus, by taking minimal length steps at variable time intervals, one more closely approximates the desired drive function. However, in practice, both of these approaches should have sufficient accuracy, so that the choice between them can be based on other considerations.

Our data acquisition system includes a DEC PDP-8L computer (4K memory) and logic in the interface to recognize and carry out various input-output (IO) in- structions. The IO instructions used in the present ap- plication are to read the absolute shaft encoder and to operate the stepping motor, both of which are connected to the spectrometer lead screw.

The computer cycle time was used as the time base for generating the delay between steps2 This is accomplished by loading the computer accumulator register with a nega- tive number whose magnitude is proportional to the de- sired delay and repetitively incrementing this number until it reaches zero. Thus, the encoder value is used to obtain the required delay constant, which is then used to produce the delay, the motor is stepped, and the process is continuously repeated in order to achieve the desired drive function.

Detailed operation of the drive control routine is as follows: the current encoder value is read, converted from binary coded decimal format to a binary number, and used to fetch an entry from a table of delay constants. This previously calculated table contains the delay constants necessary to produce a basic speed on 480 cm-1/min as a

Volume 29, Number 5, 1975 APPLIED SPECTROSCOPY 421

function of encoder value. This constant is then used to produce the required basic delay which is repeated n times to produce the desired speed, an integral fraction of the basic speed (480/n cm-Vmin, where n can vary from 1 to 4095). The stepping motor IO instruction is then executed in order to produce a step, and the entire procedure is continuously repeated until halted by the operator. Since the desired tota ldelay is the time between steps, it is necessary to compensate the initial basic delay for the time used to access the delay constant. This is done by adding a suitable constant to the (negative) table entry for the first cycle so that the actual delay produced during this cycle is reduced by the time taken to access the delay constant.

In a preliminary version of this program, the delay was calculated directly from the encoder value in real time using the DEC floating point software package. However, the calculation time depends on the arguments, and the delay constant production time fluctuated in a manner which could not be satisfactorily compensated. The present approach was then chosen in order to avoid this problem.

During execution of the drive control routine, checks are made to assure valid encoder values and proper step- ing motor operation. If an error is detected, an appropri- ate error message is printed on the teletype, and the teletype bell is then rung continuously to alert the oper- ator.

All operator control is carried out via the teletype. The desired scan speed may be entered directly, or the optimal spectral slitwidth, time constant, or scan speed may be calculated, the other two being entered by the operator. In either case, the scan speed is rounded to the nearest integral fraction of the basic speed, and the integer (n) is

saved for use in the drive control routine. The actual scan speed is also printed out for the operator's information.

There is a separate section of the program which is used to produce the table of delay constants, given the encoder calibration constants and the measured computer cycle time. On completion of this section of the program, it is overlaid by the operating program, and this program, in- cluding the table, is stored on a magnetic tape cassette for future use. Thus, the table need be regenerated only on recalibration of the encoder.

The table has 2048 entries corresponding to the wave- length region ,-.400 to 730 nm. Each entry corresponds to 64 consecutive encoder values, a range of 0.16 nm. The delay constant is calculated for the midpoint encoder value, giving a worst case delay error within a given range of 1.3 ~sec (at the long wavelength end), compared to the digi- tization error of ~-~2.4 psec. Since the delays range from ~'-~6 to 18 msec, the total worst case delay error is thus ~-~0.06 % and is noncumulative over a sufficiently long scan.

A problem had been anticipated with respect to the reproducibility of the computer cycle time, since the manufacturer's specification is ::E12%. However, this is apparently a model-to-model variation, since, for our computer, the measured day-to-day variation was less than 0.1% after allowing ~/.~ h for stabilization.

Operation of the drive system was checked by measur- ing the spectrum of a tungsten lamp continuum imaged through an air spaced Fabry-Perot etalon. The resulting spectra, which have peaks (fringes) evenly spaced in wavenumbers, were not superposable because of periodic and random errors present in the lead screw-grating link- age. However, in several trials the differences between the

3061

16o7

4579 A

1588

BENZENE SLIT 5¢m °~ TIME CONST. lace. SCAN SPEED SOcm'Vrnin.

5145 A RANGE 20K

1178

I

I i

9 9 2 6 0 8

FIG. 1. Demonstration benzene spectra obtained using the computer-controlled wavenumber drive, at two excitation frequencies. Note the nonlinearity in the wavelength marker spacings.

422 Volume 29, Number 5, 1975

mean fringe spacing over one period of the lead screw for wavelength regions separated by ,-~100 nm was con- sistently less than half of the standard deviation of the individual mean values.

The drive operation is demonstrated in Fig. 1, which shows the recorder chart tracings for the Raman spectra of benzene taken using the 457.9 and the 514.5 nm argon ion laser lines. The peak positions are seen to be virtually superposable, although the scan ranges are ~70 and 90 nm, respectively, in the two spectra. The effect of the ap- paratus spectral sensitivity is quite obvious here; it is mainly due to the wavelength response of the EMI 6256 photomultiplier.

The method used here is only one of several equally valid approaches to achieve a digital nonlinear spectrom- eter drive; it indicates the feasibility of driving a spec- trometer in a nonlinear fashion under computer control. The minicomputer is by no means required to achieve this goal; it should be quite possible to base such a system on one of the recently available microcomputers/ In this fashion, one could use the most accurate mechanical drive system available without having to consider the desired drive function. The spectrometer could then be driven under program control in any desired fashion, with dif- ferent drive functions only requiring a different program.

Copies of the program, written in PAL III assembler language, are available upon request. However, since the details of the data acquisition system are unique, suitable modifications would be necessary for application else- where.

1. W. F. Murphy, "A Data Acquisition System for Raman Spectros- copy," Paper D1, Symposium on Molecular Structure and Spectros- copy, Columbus, Ohio, 1969; unpublished.

2. J. F. Moore, Spex Industries, personal communication. 3. The Software Writing Group, Introduction to Programming (Digital

Equipment Corporation, Programming Dept., 1969), Chap. 3, p. 27. 4. See, for example, R. E. Dessy, P. Janse-Van Vuuren, and J. A. Titus,

Anal. Chem. 46, 917A (1974); Anal. Chem. 46, 1055A (1974).

Precision and Accuracy of an X-ray

Fluorescence Determination of Minor and Trace Elements in Silicate Rocks

I. B. BRENNER, L. ARGOV, and H. ELDAD Geochemistry Division, Geological Survey of Israel, 30 Malchei Israel, Jerusalem, Israel

Index Heading: X - r a y f l u o r e s c e n c e .

In order to overcome the various effects detrimental to precision and accuracy, such as compositional, lithological,

Received 23 March 1975; revision received 24 April 1975.

mineralogical and granulometric variations, fusions TM, tedious mathematical corrections,'. 5-s thin fihn techniques 9 and separate calibrations for each matrix type 1° are em- ployed in x-ray fluorescence (XRF) spectrometric analysis of major and minor components in silicate rocks. It is generally accepted that only by using such measures can quantative analytical data be obtained. However, the above mentioned procedures may not always be suitable for trace element analysis, since dilutions decrease the signals, giving poor detections. Consequently, there are numerous reports giving details of powder procedures for determining minor and trace elements in silicates.

In the presently described procedure, the precision and accuracy of Fe, Ti, K, Mn, Cr, Ni, Cu, Zn, Sr, Ba, and Rb determinations are discussed. The calibration curves were prepared from standard reference silicate rocks of varied lithological, mineralogical, and chemical composi- tions. In spite of the very large chemical and lithological variations, calibration curve statistics suggest that matrix effects of absorption and enhancement arc insignificant for the purposes of the present investigation.

Two types of samples were employed: (a) loosc powders wet-sieved in nylon sieves to less than 300 mesh and packed in Mylar-covered cells; (b) cellulose-bound pellets prepared by mixing 1.5 g of sample with 1.5 g of chro- matographie cellulose in polystyrene vials in a Spex mixer mill for 30 rain. The mixed material is then pelleted in aluminium caps at 25 tons in vacuum to give discs of 30 mm diameter and 1.5 mm thickness.

A Phillips PW 1410 spectrometer using Cr and W tubes was used. The analyzing crystals, counter, and other operating conditions for each element are listed in Table I. In each case the major Ka reflection was used with exception for Ba whose La line was employed. The lines used arc not significantly influenced by adjacent lines, and no corrections for line interference were made for the matrices used in this investigation.

Intercepts and slopes of the working curves were tested for significant shifts during each day. The intercept varied slightly while the slope remained substantially constant. This day-to-day movement was less than ~5 % of the average counting rate. Radiation was normally recorded in two to three 30- to 100-see counts and averaged. A standard reference material was measured every 10 samples. Background readings were made where necessary, and the background intensity was subtracted from peak intensity, yielding net peak intensity. Linear working curves for both methods were calculated by computing linear functions of net peak intensity and element con- centration in standard reference materials. The following standard reference materials wcrc used for calibration: T-1 tonalite, SY-1 syenite, W-1 diabase, BR basalt, BCR-1 basalt, JB-1 basalt, DN-R diorite, G-2 granite, AGV-1 andesite, and NIM-N noritc. The recommended values were listed by Flanagan n and Abbey. t~ The bulk chemical compositions given in Table II show the variety of the matrices.

In order to extend the working range of the Sr calibra- tion curve, several spiked basaltic samples were prepared. The Sr values for the basalts were determined by standard additions. 7 Table III lists the working ranges and the co-

Volume 29, Number 5, 1975 APPLIED SPECTROSCOPY 423