Planes de mantenimiento de los sistemas evaporativos

Bolts, e

_{Disk , E}

Disk , D

Bolts , c

Disk, C

Ceramic disk , A

Bolts, a

Sample holder, S

Sample

Thermocouple

Fig. 3.3 This is » diagram of th* sinplt manipulator which was specially designed to fa cilita te the centering o f the axis of the cylindrical single crystals on the axis of rotation of the rotary drive. Using this device, the eccentricity in the sample rotation could easily be reduced to as little as 0.25mm, and the resultant angular distortions in the data were negligible. The operation of this device is fully described on the previous page.

AES on cylin d rical singla crystals Chapter 3

tungsten filam ent fo r ra d ia tive heatin g. A rm itage1 had clamped the samples between stainless steel plates, but th is was found to be ra th e r u n s a tisfa c to ry in the present in vestig a tio n as the samples had a tendency to move on h ea tin g. The problem seemed to lie in the axial (rather than radial) expansion o f the cylinders on annealing to 700-800*C a ft e r argon ion bombardment. A special sample holder was designed which permitted some lon gitu d in a l expansion o f the crystal w hilst preventing any motion o ff axis. Two variants o f th e design are shown in f ig . 3.4a and b. Sample holder a was used fo r the copper crystal whilst sample holder b was used fo r the nickel crystal.

(3.12) T h e c o m p u t e r i n t e r f a c e .

In itia lly , a ll th e data were taken b y recordin g Auger spectra in th e derivative mode on a c h a rt recorder and measuring th e p eak-to-peak h eigh ts. As an experiment in which spectra were taken every 5 degrees o f a rc around th e sample circum ference entailed th e recording o f 74 spectra, and th e spectrometer had to be reset and the crystal turned by 5 degrees between each datum, experimental time would seldom be less than th ree and a h a lf hours and the subsequent processing o f th e data could easily take as long as two. This procedure was very slow, tedious and inaccurate and so it was decided to computerize the experiment.

The oomputer used was a GEC 4080 which is a multi user system equipped with d ig ita l, d ig ita l to analogue (DA), and analogue to d igital (AD) ports with 12 b it resolution. A schem atio o f the computer in te rfa c in g is shown in f i g . 3.3. Basically, one 12 b it AD p o rt was used to sample the analogue output o f th e Brookdeal lock-in amplifier, one 12 b it DA p o rt was used to provide a programming voltage fo r the modified ramp generator, and two 8 b it DACs were used to provide TTL compatible control outputs fo r the stepper motor control unit (which was built by the Author from a schematic by WD Technologies).

AES on cylin d rica l single crysta ls Chapter 3

tungsten filam ent fo r ra d ia tiv e h eatin g. A rm ita ge1 had clamped the samples between stainless steel plates, but th is was found to be ra th e r u n s a tisfa c to ry in the present in v e s tig a tio n as the samples had a tendency to move on h eatin g. The problem seemed to lie in the axial (rather than radial) expansion o f the cylinders on annealing to 700-800*C a ft e r a rgon ion bombardment. A special sample holder was designed which permitted some lo n gitu d in a l expansion o f the crystal whilst preventing any motion o ff axis. Two variants o f th e design are shown in f ig . 3.4a and b. Sample holder a was used fo r the copper crystal whilst sample holder b was used fo r the nickel crystal.

<3.12) T h e c o m p u t e r i n t e r f a c e .

In itia lly , all th e data were taken by record in g Auger spectra in th e derivative mode on a ch a rt re cord er and measuring the p ea k -to -p ea k heigh ts. As an experiment in which spectra were taken every 5 degrees o f a rc around th e sample circum ference en tailed th e recording o f 74 spectra, and the spectrometer had to be reset and the crystal turned by 5 degrees between each datum, experim ental time would seldom be less than th ree and a h a lf hours and the subsequent processing o f th e data could easily take as long as two. This procedure was very slow, tedious and inaccurate and so it was decided to computerize the experiment.

The computer used was a OEC 4080 which is a multi user system equipped with d ig ita l, d ig ita l to analogue (DA), and analogue to d igital (AD) ports with 12 b it resolution. A schem atic o f the computer in te rfa c in g is shown in f ig . 3.3. Basically, one 12 b it AD p o rt was used to sample th e analogue output o f th e Brookdeal lock-in amplifier, one 12 b it DA p o rt was used to provide a programming voltage fo r the modified ramp generator, and two 8 b it DACs were used to provid e TTL compatible control outputs fo r the stepper motor control unit (which was built by the Author from a schematic by UD Technologies).

AES on cylin drical singla crysta ls Chapter 3

F ig . 3.4 This fig u r e shows th e two sample holders used in this investigation in cross- section. The hollow cylindrical samples are pushed onto hollow cy lin d ric a l tubes as shown, and clamped between the two end plates. This completely elim inated the problem o f the samples moving o f f axis during annealing.

Sample holder <a> was used fo r the copper sample, and it can be seen that the cu rren t to the filam en t tra v e ls down throu gh the cy lin d ric a l sample which is part o f the circuit.

Sample holder (b) was used fo r the nickel sample, and in this sample holder sample and filament are completely isolated.

Filament

AES on cylin d rica l single crystals Chapter 3

F ig . 3.3 This fig u r e is a fu n ction al diagram o f the apparatus used in this in v e s tig a tio n . The letters P.M. stand fo r photomultiplier, the letters DVM stand fo r digital v o lt meter and the QEC4080 computer to which the apparatus was interfaced is denoted simply as 4080. The PSD used throu ghou t th is work was a Brookdeal lo ck -in amplifier, and th e spectra were d ig itiz e d to 12 b it resolution using analog to d ig ita l converters a tta ch ed to th e computer.

AES on cylindrical single crystals Chapter 3

(3.13) T h e s o f t w a r e .

A ll the o peratin g softw are fo r the computer controlled spectrometer was written in FORTRAN on the OEC 4080 computer in th e physics department. The program ASPEC8 was th e main con trol program fo r the spectrometer and this was supplemented by several simple utilities. BOMBARD was a simple program which allowed the crystal to be continuously rota ted during argon ion bombardment and gas dosing whilst XTALC measured the sample cu rren t at 1* in te rva ls around the 360* o f sample rotation. JPLOT2 was used to normalize the Auger peak-to-peak heigh ts to the average peak-to-peak height of a reference peak recorded around th e sample circumference and JIMPLOT simply p lotted out previously recorded Auger spectra. A Televideo 912C terminal with G raffix 4010 emulation interfaced to an Epson FX-BO dot matrix p rin ter provided th e plots. When hard copy o f the data was not required, a BBC model B microcomputer with th e Sussex U n iv ersity term inal emulation ROM was used as a graphics term inal. Several programs were w ritten on the BBC microcomputer and also on a Sinclair Spectrum 48X microcomputer to allow file transfer from the 4080 fo r fu rth e r data processing and archiving as space on the GEC cartridge drives was often limited. Two programs, SL1CE18 and 110CYL were w ritte n on th e microcomputers to plot out an a rb itr a r y c r y s ta l plane in an a rb itr a r y la t tic e (of not more than 128 atoms) and to plot out all the crystal planes at 5 degree intervals around the crysta l circumference. All the diagrams o f crystal planes in this thesis were generated using one o f these programs. A ll th e calcu lation s fo r the models presented in the later chapters of this thesis were performed on Spectrum and AppleX+ microcomputers.

AES on cylin drical sin gla crystals Chapter 3

(3.14) D i g i t a l s m o o t h in g f i l t e r s .

One o f the major advantages gained by computerizing the experiment was the ability to apply d ig ita l sig n a l processing techniques to the digitized spectra. Digital smoothing filt e r s can markedly increase the signal to noise ratio o f a noisy signal (as demonstrated fo r AES by Prutton 2), and are much more versatile, accurate and controllable than their analogue cou nterparts. Two d ig ita l filt e r s were considered fo r use in the current work, each o f which fit t e d a smoothing th ird o rd er polynomial to th e data. The smoothing spline algorithm (Reinsch^) has been recommended by Prutton2 and was already implemented on the GEC 4080 at Warwick. The smoothing spline gives a very good subjective smooth to the data, but has th e disadvantage o f bein g a long and slow algorithm, and requires the input o f two param eters by th e operator, th e ’s t iffn e s s ’ and th e 'sign a l to noise r a t io ’, which con trol th e amount o f smoothing. The s tiffn e s s should be in the interval Ni«/N, where N is t h e number o f points in th e peak to be fitte d , and the signal to noise ra tio should be estimated from the s c a tte r on th e data. The problem encountered w ith th is routine was that fo r a given Auger peak, spectra o f d ifferen t intensities seemed to require widely d iffe r e n t sign a l to noise ra tio s or s tiffn e s s e s fo r a good fit . In the present work on c y lin d ric a l sin gle crysta ls where th e re is a large anisotropy in Auger peak-to-peak h e ig h ts around th e sample, this necessitated input from the operator after every spectrum, and o fte n several guesses had to be made to fin d th e co rrect signal to noise ra tio . P ru tto n has approached th is problem by estim atin g the signal to noise r a tio from least squares s t r a ig h t lines fit t e d to the beginnings and ends of the spectra and has had grea t success. This approach was tried in the present work, but still seemed incapable o f coping w ith th e marked v a ria tio n s in Auger intensity observed around the cylinders. The reasons fo r this were never fu lly understood.

AES on cylin d rical single crystals Chapter 3

The d ig ita l smoothing f ilt e r fin a lly chosen was a variation o f the Savitsky/Golay slid in g least squares d ig ita l smoothing algorith m 4. This algorithm is based on equation 3.1, where the smoothed point y(0) is in the cen tre o f an odd number interval of points P, where P»2m+i and m is any in teger. The experimental data points in the interval, ytt), are convoluted with appropriate integers Cj, and normalized by the fa cto r NORM.

y<0> g C t / t t ) NORM t=-m

(3.1)

The simplest case is with Ct,*l (fo r a ll t) and NORM*P when the equation reduces to a slidin g average. A least squares f i t o f an nth order polynomial to the data over th e in te rva l w ill allow the calcu lation o f the in tegers and o f NORM to giv e an exact lea st squares f i t o f y(0). Values o f C{, and NORM fo r polynomials o f order 2 to 5 and in te rv a ls in th e range 1 to 25 points are given in referen ce 4, and corrections to some o f these by Steinier et al can be found in reference 5.

An u nfortunate aspect o f this central point smoothing mechanism is that m points are o f necessity lost from each end o f the spectrum a ft e r each smooth. In the extended slid in g least squares f i t used in the cu rren t work, P rocto r and Sherwood4 f i t the firs t and la st m spectral points w ith a smoothing parabola and add th is to the smoothed data. This approximation works extremely well in practice, producing only very small end distortions, and it also makes possible iteration o f the smooth as the number o f spectral points is conserved. S avitsky and Oolay sta te th a t ite ra tio n o f the smooth, such as a 2a+l follow ed by a 2b+i point smooth, should be ex a ctly th e same as a smooth with an in te rv a l o f 2(a+b)+l points. P rocto r and Sherwood clea rly demonstrate that this is not th e case, and indeed recommend the use o f the smallest smoothing interval possible with many iterations. In the present work, perhaps due to the low number o f points per spectrum

AES on cylin d rica l single crystals Chapter 3

The d ig ita l smoothing f i l t e r fin a lly chosen was a variation o f the Savitsky/Golay slid in g lea st squares d ig ita l smoothing a lgo rith m 4. This algorithm is based on equation 3.1, where th e smoothed point y(0) is in t h e centre o f an odd number interval o f points P, where P»2m+i and m is any in teger. The experimental data points in the interval, ytt), are convoluted with appropriate integers Cf, and normalized by the fa ctor NORM.

m

y(0) * E Cj^tt) (

3

1

y , NORM

t=-m

The simplest case is w ith C (,"l ( f o r a ll t) and NORM*P when the equation reduces to a slid in g average. A least squares f i t o f an n ^ 1 o rd er polynomial to the data over th e in te rv a l w ill allow the calculation o f th e in tegers and o f NORM to giv e an exact lea st squares f i t o f y(0). Values o f C{, and NORM fo r polynomials o f order 2 to 5 and in te rv a ls in th e ran ge 1 to 25 points a re giv en in re fere n ce 4, and corrections to some o f these by Steinier et al can be found in reference 5.

An u nfortu n ate aspect o f this cen tral point smoothing mechanism is that m points are o f necessity lo st from each end o f th e spectrum a ft e r each smooth. In the extended slid in g lea st squares f i t used in the cu rre n t work, P ro c to r and Sherwood4 f i t the firs t and la st m spectral points w ith a sm oothing parabola and add th is to the smoothed data. This approximation works extremely well in practice, producing only very small end d istortion s, and it also makes possible iteration of the smooth as the number o f spectral points is conserved. S avitsk y and Oolay s ta te th a t ite ra tio n o f th e smooth, such as a 2a+l follow ed by a 2b+i point smooth, should be ex a ctly the same as a smooth with an in te rv a l o f 2(a+b)+l points. P ro cto r and Sherwood c le a rly demonstrate that this is not th e case, and indeed recommend the use o f the smallest smoothing interval possible with many iterations. In the present work, perhaps due to the low number of points par spectrum

AES on c y lin d ric a l s in g le c r y s ta ls C h ap ter 3

(a )

F ig . 3.6 Th is fig u r e shows <•> an A u ger survey o f a carbon and sulphur contaminated