1. IntroductionAn important and often overlooked aspect of

diffraction work is proper diffractometer align-ment. Residual stress determinations require awell-aligned goniometer, particularly with fo-cusing or Bragg-Brentano optics. A well-alignedgoniometer means that the X-ray source, go-niometer center and back slit are all co-planarand that the ability to reproducibly place thesample surface on the goniometer’s center ofrotation has been demonstrated. The use ofnew parallel beam optics (PBO) such as multi-layer parabolic mirrors or polycapillary opticsfor residual stress measurements is preferredsince PBO can reduce or eliminate peak shiftsdue to sample displacement, specimen trans-parency, and flat specimen errors. Though par-allel beam optics may have relaxed the align-ment rigor necessary to do residual stress de-terminations, it is still vital for the practitioner toknow where the beam is going in order to haveconfidence in data interpretation [1].

The subject of this paper is not new, and thecited references are not exhaustive. Also, itshould be noted that depending upon theequipment involved, the outlined steps mayvary. Rather than an extensive discussion ofalignment found elsewhere [2, 3], the objectivehere is to emphasize “down-and-dirty” practicalusage and techniques necessary to safely aligna typical powder diffractometer for a residualstress determination. That is, essentially, whatone does when confronted with a new machineto ensure it is running properly, how to use

standards in this effort, what are the related er-rors and practical examples. This paperevolved, in part, out of portions of workshopsgiven at the Denver X-ray Conference [4, 5].After a brief discussion of safety, this paperseeks to answer four questions:1. How to know when the alignment is good

enough? (What do I want to do with this in-strument?)

2. How to check the alignment of a goniome-ter? (What tests do I perform?)

3. How to improve the alignment of a go-niometer? (What should I change?)

4. How do I maintain the alignment?In order to clearly illustrate these tests, real

data will be discussed from a 4-circle/axis sys-tem [6] that has just had the tube changed fromCo to Cu and a 2-circle/axis system that was duefor an alignment check (see Fig. A1 in AppendixA#). Appendix A provides details about the in-struments and data collection. Since the baseconfiguration of the 4-axis system is basicallythat of a Q –2Q system, this unit will also be re-ferred to as either the 4-axis or Q –2Q system,depending on the nature of the testing beingdiscussed.

2. SafetyThe greatest likelihood of a personal X-ray ex-

posure is during alignment. Today, live-beamalignment, while quick, is no longer considered

THE RIGAKU JOURNALVOL. 23 / 2006, 25–39

Vol. 23 2006 25

CONSIDERATIONS REGARDING THE ALIGNMENT OF DIFFRACTOMETERS FOR RESIDUAL STRESS ANALYSIS

THOMAS R. WATKINS1, O. BURL CAVIN2, CAMDEN R. HUBBARD1, BETH MATLOCK3, ANDROGER D. ENGLAND4

1 Metals Materials Science & Ceramics Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831-6064, U.S.A.2 Center for Materials Processing, University of Tennessee, Knoxville, TN 37996-0750, U.S.A.3 TEC/Materials Testing Division, 10737 Lexington Drive, Knoxville, TN 37932, U.S.A.4 Cummins Inc., Columbus, IN 47201, U.S.A.

Proper alignment of an X-ray diffractometer is critical to performing credible measure-ments, particularly for residual stress determinations. This article will emphasize practical as-pects of diffractometer alignment and standards usage with regards to residual strain mea-surement. Essentially, what to do when one is confronted with a residual stress problem andan unfamiliar goniometer. Various alignment techniques, use of standards, and related issueswill be discussed.

# Appendices available at www.rigakumsc.com/journal/index.jsp

a safe option; thus, a slower, safer, incrementalalignment methodology is utilized. Still careand caution must be exercised. Since the custo-dian is in and out of the X-ray enclosure/hutchfrequently making small adjustments to the sys-tem, he/she must be vigilant as to the status ofthe shutter. It is understood in the following dis-cussion that any changes made by the custo-dian inside the X-ray enclosure/hutch are doneso with the shutter closed.

There are other points to consider. The fail-safe circuit with a clear performance descriptionshould be obtained from manufacturer, whichneeds to be understood and tested periodically(see Table I). The custodian should obtain anduse a survey meter/Geiger counter for labora-tory use to check for leaks around tube headsand more general surveys. In particular, if thetarget/X-ray tube is changed from a longer toshorter wavelength (viz. lower to higher en-ergy), a radiological survey should be con-ducted at full power with the shutter closedaround the tube head and again with the enclo-sure closed and the shutter open to check forleaks and/or inadequate shielding. The materialfrom which the shutter is made needs to be de-termined. In the past, lead was commonly usedfor shutter material. Unfortunately, time and ex-perience have shown that lead is a particularlypoor shutter material, as lead shutters areknown to stick, jam or freeze open or closed [7].X-rays produce ozone in an ambient atmos-

phere [8], and ozone is very corrosive, particu-larly in humid atmospheres [9]. The lead cor-rodes, likely due to the ozone, forming a stickygrayish white corrosion product. Empirical ob-servation has revealed that shutter assemblycomponents made of Ni-coated brass also cor-rode. In the past and with less intense X-raysources, the user simply cleaned the shutter fre-quently to alleviate the problem. Today, thereare better solutions available. If your shuttercontains lead, it should be replaced with a suffi-ciently thick piece of tantalum or 304L stainlesssteel (perhaps lead filled). Periodic inspectionsof the shutter are still recommended. Mechani-cal binding or solenoid failure can also causethe shutter to jam open or closed. Again, lead isa soft and malleable metal, which can deform/wear over time to cause a jam. A secondarysafety circuit is often desirable [7, 10]. Finally,one should never rely solely on the software todetermine the status of the shutter.

3. How to know when the alignment isgood enough? (What do I want to do withthis instrument?)

While well-aligned and well maintained in-struments are necessary to do any good work, itis important to know just how “good” the align-ment needs to be for the task at hand, given thetime and financial constraints we all face. TableII lists some general guidelines or “rules ofthumb” when checking the alignment regarding

26 The Rigaku Journal

Table I. Elements of testing the fail-safe or interlock circuit of an X-ray diffractometer.

peak position and resolution with a standard/reference material, preferably a powder of �325mesh/�45 mm particle size. For residual stressdeterminations, the relative differences in peakposition are more important than the absoluteposition. As always, sample knowledge (com-position, etc.) and good software help im-mensely.

Peak resolution here refers to the relationshipbetween peak width or full width at half maxi-mum (FWHM) with respect to peak overlap.That is, for a given FWHM, the resolution is de-fined by how close can two peaks overlap be-fore they are indistinguishable and resemble asingle broadened peak. Today there are oftenmany choices of optics all of which have certainadvantages and disadvantages relative to eachother. Generally for a given diffractometer sys-tem, improving the resolution results in the re-duction of the intensity of the peaks, which cansignificantly increase the data collection time,particularly in the high two theta region wheredata for stress determinations are acquired andwhere peaks are inherently much weaker. Whilehigh resolution may be required when workingwith multiphase samples and/or low symmetryphases, most stress determinations are per-formed on predominantly single-phase engi-neering materials, which generally have highsymmetry crystallographic structures, and thusdo not require high resolution.

4. How to check the alignment of a go-niometer? (What tests do I perform?)

First, the custodian collects a set of diffractiondata covering a wide 2Q angle (see Appendix Bfor details). This involves collecting a diffractionpattern from a standard/reference powder orstress-free sample via a Q –2Q scan. The peakpositions and calculated lattice parameters arecompared relative to the standard values in adatabase and prior instrument records. Fig. 1shows a portion of a LaB6 diffraction patterntaken on the 4-axis unit, wherein the low 2Qpeak positions are low relative to the PDF card#34-427 [11]. The refined lattice parameter de-termined from this scan was 4.1598(4) as com-

Vol. 23 2006 27

Table II. General guidelines or “rules of thumb” regarding alignment using a standard/referencepowder.

Fig. 1. 4-axis unit: Diffraction pattern of LaB6

shows peak positions are systematically low at low2Q (see full pattern in Fig. B1) relative to PDF card#34-427.

pared to the PDF value of 4.15690 Å (see TableBI). Likewise, the data in Fig. 2 from the Q –Qunit shows LaB6 peak positions are systemati-cally high in the high 2Q region with a refinedlattice parameter of 4.1518(2) Å (see Table BII). Itis obvious that some re-alignment is needed onboth instruments.

Next the custodian conducts intensity, FWHM/resolution and X-ray wavelength contaminationtests (see Appendix C for details). This involvescollecting a diffraction pattern from a polycrys-talline quartz plate via a Q –2Q scan over se-lected 2Q regions. Fig. 3 indicates that the de-tector electronics and diffraction side mono-chromator are set properly as no kb peak is ob-served. Further, the tube potentially has a lot of

life left given the high intensity and negligibleWLa lines caused by target contamination. Theintensity test was not done on the 4-axis unit asa brand new tube was installed. The five fingersof quartz were examined using both instru-ments, wherein the ka1–a2

of three reflectionsoverlap in such a way as to resemble the fin-gers of a hand. A figure of merit (FOM) is calcu-lated from the intensity of the (212) minus thebackground intensity divided by the average in-tensity of the valleys surrounding the (212) line[i.e., trough between (212)a1–a2

, (212)a2–(203)a1

,(301)a1–a2

] minus the background intensity. Gen-erally, an acceptable performance the FOMshould be greater than 2. The test result for the4-axis unit was particularly bad (see Fig. 4) andresembled a mitten. This poor resolution is dueto the 0.25° radial divergence limiting (RDL) slitson the diffraction side. These RDL slits present atradeoff: reduced sensitivity to sample surfacedisplacement and in this case enhanced inten-sity versus resolution. As was pointed outabove, good resolution is often not needed forresidual stress determinations and texture stud-ies. In contrast, the FOM from the Q –Q is good,exceeding 2 (see Fig. 5). Although not critical toresidual stress determinations, Appendix D cov-ers how to handle dead time corrections for de-tectors.

The “tilt” test [12] quickly checks for X-raybeam misalignment and/or sample surface dis-placement (with Bragg-Brentano optics), whichis required prior to residual stress determina-tions. If parallel beam optics (PBO) are used, theconfounding influence of slight sample surface

28 The Rigaku Journal

Fig. 2. Q –Q unit: Diffraction pattern of LaB6 showspeak positions are systematically high at high 2Q (seefull pattern in Fig. B2) relative to PDF card # 34-427.

Fig. 3. Q –Q unit: Diffraction pattern of Quartz shows no kb and negligible W contamination.Inset: good peak intensity for (101) reflection of quartz.

displacement is removed. Here, a strain/stress-free sample, usually a powder, is mounted onthe goniometer and tilted the same as in astress determination. If the goniometer isaligned and the sample surface is on the centerof rotation of the goniometer, the amount ofpeak shift will be very small. A LaB6 powdersample was slurry-mounted on a zero back-ground plate. This sample was placed on the 4-axis unit, which has both c and W axis move-ments (the goniometer movements are shownin Figs. A2 and A3, respectively, wherein c�Y

and W�2Q /2�Y ). The sample was oscillated toimprove particle statistics; if available, oscilla-tion is recommended as it improves peakshape. The (510) reflection was examined at�141.8°2Q with only three Y tilts (more may berequired/desired as in a stress determination).Tilt tests should include both positive and nega-tive Y tilts covering as large an angular rangeas possible. The results for each are shown inFigs. 6 and 7, respectively, all of which showvery small relative peak shifts despite an errorin absolute peak position relative to the PDF

Vol. 23 2006 29

Fig. 4. 4-axis unit: The “mitten” of Quartz. Inset shows a schematic representation of theoptics. Not shown: incident Soller slits.

Fig. 5. Q –Q unit: The five fingers of quartz, FOM�3IA/(IB�IC�ID)�2.29. Inset shows aschematic representation of the optics. Not shown: incident and receiving Soller slits and dif-fraction side monochromator.

card.

5. How to improve the alignment of agoniometer? (What should I change?)

The generic step-by-step re-alignment of a 4-axis and Q –Q goniometers will be described inthree broad overlapping steps: goniometer in-spection, 4 “physical” alignment (no diffraction)and diffraction alignment. Since the custodiantypically has little or no recourse, misalignmentof goniometer axes relative to each other or rel-ative to the position to the center of rotation willbe assumed to be negligible and not discussed.Prior to beginning alignment for the first time,the custodian should inspect his goniometerand construct a functional schematic drawing ofhis goniometer (see Fig. 8), which shows all theparts that can be adjusted or moved relative tothe others. Usually there is one spot on the go-niometer/beam path which cannot be moved orwhich the custodian has only limited controlover its position, such as the center of rotationon the goniometer (as is the case for both ex-

amples here) or the focal spot, respectively.These become important as it usually definesthe sequence of the alignment.

The physical alignment involves leveling,physical settings and using the X-ray beamwithout doing any diffraction. The following arehandy alignment tools to have: fluorescentscreen, dial indicator, mounting hardware andpin, sample situated alignment pieces (e.g.,“glass slit,” knife edge(s), flat plate), referencepowders and materials, attenuating foils, level,“X-ray sensitive burn paper,” telescope/cathetometer, direct beam detector, and othertools specially fabricated for you. A good dealof patience and courage is also needed.

First, level the goniometer. This may be ac-complished by pre-existing adjustment screwsor may require shims. Confirm or adjust thetake off angle from the focal spot, which is typi-cally, but not always, 6° (purple arc in Fig. 9).Alignment should always be performed at thenormal power settings you intend to use to col-lect data, as the focal spot generally will move

30 The Rigaku Journal

Fig. 6. 4-axis unit: Tilt test using chi axis shows acceptable tilting alignment.

Fig. 7. 4-axis unit: Tilt test using omega axis shows acceptable tilting alignment.

with power level. As always, be aware of theshutter status. Because you will likely need toscan the primary beam, foils to attenuate thebeam need to be placed somewhere in thebeam path. Copper foils usually work well; thetotal thickness of the foils should be empiricallydetermined with care so as to not damage thedetector. Until one is experienced, gradual in-creases in power, quick scans and correspond-ing increases in foil thickness should accom-plish this. If applicable, set the energy windowon the detector electronics as wide as possibleto detect all the X-ray energies emitted from thetube as these contribute to dead time. Once thetake-off angle is set and with no sample inplace, adjust the mechanisms available (right-most green ⇔ in Fig. 9) to get the most intensebeam possible through the widest slits avail-able. The intensity can be checked either by adirect beam detector or by using the pre-exist-

ing detector with attenuating foils. For the latter,0° 2Q may have moved substantially necessitat-ing a broad scan range to locate the beam.Next, incrementally insert narrower incidentand anti-scatter slit sets, observing the intensitydecrease proportionally to reduced angular di-vergence of the incident slit. Deviations fromthis proportional reduction likely indicate somemisalignment with the incident slit assembly;that is, the beam path is not parallel with the di-rection of beam travel. The custodian must ad-just the position of the slit assembly so as toachieve this proportional reduction in intensity.The tilt on the incident Soller slits should thenbe optimized with respect to intensity.

The approximate center of rotation of the go-niometer must be known or located. Usually thediffractometer comes with either some fiducialsurface or a mechanism for placing the sampleon the center of rotation of the goniometer (seeFig. A4). The fluorescent screen needs to bemounted such that the fiducial mark on the fluo-rescing surface is on the center of rotation ofthe goniometer, and if possible level this sur-face. A telescope/cathetometer with cross hairscan be very useful here, particularly for the 4-axis unit. The horizontal cross hair can bealigned to the leveled surface of the fluorescentscreen at �90°c and the vertical cross hair at0°c . Make sure the sample surface stays on thecross hair as the sample is rotated about thesurface normal. The visible fiducial mark on thecenter of the fluorescent screen must be trans-lated (via XY stages here such that it coincideswith the cross hairs of the telescope/cathetome-ter, which are set on the center of the goniome-ter. The intersection of the cross hairs is now onthe center of rotation, but should be doublechecked with c movements to confirm. Alterna-tively, a laser pointer may be mounted to the

Vol. 23 2006 31

Fig. 9. Q–Q unit: Photographs show the locationsof the adjustments for setting the take-off angle andaligning incident slit assembly as well as the move-ments available.

Fig. 8. The functional schematic drawings for the (A) 4-axis (overhead view) and (B) Q–Qgoniometers (side view) showing relative motions of various parts of the goniometers.

detector arm to point at the center of rotation.Iterative adjustments of the sample surfaceheight, the laser spot position and detector armposition are made until the spot no longermoves with detector arm movement (see Fig.A5). Another method for determining the centerof rotation is presented in Table III.

The fluorescent screen is a powerful align-ment tool in that one can “see” the X-ray beam.Interpretation of the image as a function ofangle of incidence provides the key to what ad-justments need to be made to obtain a goodalignment. We will first consider the 4-axis unit.Figs. 10A and B show that initially the beamwas hitting to the right of center and that thiseffect was reduced as the angle of incidence in-creased. Further, the slits were rotated aboutthe beam such that the image was of a trape-zoid rather than a rectangle. This effect was alsoreduced as the angle of incidence increased,demonstrating the lack of sensitivity to these ef-fects at higher angular positions. Fig. 11 illus-trates this condition showing that the positionof the observed diffraction peaks would belower than the correct positions. In particular,the D2Q (�2Qobserved�2Qcorrect) of low anglepeaks would be larger than those at higher 2Qas was observed in Figs. 1 and B1. The slit as-sembly was moved perpendicular to the X-raybeam in the X/horizontal direction in order tocenter the image (see Fig. 10C). Fig. 12 showsthe adjustments possible to move the slit as-

sembly relative to the X-ray beam. The slit as-sembly was then rotated to align the slits to thescreen transforming the image from a trapezoidto a rectangle. In order to be more sensitive toany misalignments, the angle of incidence wasreduced as in Fig. 10D. Because of poor designof the slit assembly, many back and forth move-ments over 30 mm were required in order to

32 The Rigaku Journal

Table III. An alternative method for a Q –2Q goniometer to experimentally find the center of rota-tion of the goniometer provided W can rotate over 180°.

Fig. 10. 4-axis unit: Drawings of the fluoresced im-ages as a function of angle of incidence and incidentslit movement perpendicular to beam path. Thearrow indicated the direction of the X-ray beamtravel. Fig. 11. 4-axis unit: Schematic of initial alignment

condition relative to the desired.

Fig. 12. 4-axis unit: Photograph of the incident slitassembly and the available adjustments to move theslit assembly relative to the X-ray beam. Note: thedial gauge probe to monitor X direction (or other)movements, the 0.2 mm divergence and 0.5 anti-scat-ter slits bracketing the Soller slits, and the snout/colli-mator holder where the beam exits.

center the beam at a 1° angle of incidence.Since the vertical placement of the image wasgood no changes in the vertical/Y directionwere needed.

To finish off the “physical” alignment, the flu-orescent screen was removed and the sampleposition was left empty. The detector wasscanned to find 2Q zero after Cu foils were in-serted on the incident side to attenuate thebeam. The acceptance angle of the RDL slitswas adjusted to align the long Soller foils paral-lel to the X-ray beam. This improved the inten-sity and peak shape (see Fig. 13A). The 2Q zeroposition was reset physically and electronically.An alignment slit was placed in the sample po-sition with care so that the slit opening was onthe center of rotation. In order to find 0° W , Wwas scanned through zero with the detector at0° 2Q (see Fig. 13B). The W zero position wasreset physically and electronically. With thealignment slit and Cu foils still in place and ç atthe new 0°, the detector was rescanned to find2Q zero. Fig. 13C confirms a good physicalalignment showing the primary beam bracketedby two smaller peaks, which are due to reflec-tion of the X-ray beam from the sides of thealignment slit. The intensities of these reflectionpeaks are effectively equal indicating a well-centered slit around the beam. Any significantdifference in intensity between these two reflec-tion peaks indicates some degree of imperfec-tion in the alignment.

Similarly, the fluorescent screen was used on

the Q –Q unit. Figs. 14A and B show that initiallythe beam was centered at low 2Q and to the leftof center at high 2Q . Fig. 15 illustrates this con-dition showing that the position of the observeddiffraction peaks would be lower than the cor-rect positions. In particular, the positions of thehigh angle peaks are lower than the correct po-

Vol. 23 2006 33

Fig. 13. 4-axis unit: (A) 2Q zero scans with an empty sample position; (B) W zero scan withan alignment slit in the sample position; (C) 2Q zero scan with an alignment slit in the sampleposition.

Fig. 14. Q –Q unit: Drawings of the fluoresced im-ages as a function of angle of incidence. The arrowindicated the direction of the X-ray beam travel.

Fig. 15. Q –Q unit: Schematic of initial alignmentcondition relative to the desired.

sitions as was observed in Figs. 2 and B2. Fortu-itously, we discovered after careful observationthat one of the counterweights was miss-setsuch that the detector arm was missing steps athigh 2Q . Thus with no shaft encoder feed-back,the software “thought” the detector was at ahigher 2Q than actual, but still low, and record-ing data as such. The goniometer arm whichheld the X-ray source was moved to 90° Q1 orangle of incidence, and the tube plus slit assem-bly was translated (left-most purple and greenarrows in Fig. 9) such that the image was cen-tered (see Fig. 14C). The goniometer was thenmoved back to 10° Q1, and the image was offcenter. The image was recentered by raising theheight of the sample holder (see Fig. A4B),which required adjusting red-painted screws.This adjustment was iterative and not conve-nient; it required partial disassembly of thesample holder in order to determine the correctscrews to turn. In synopsis, Cu foils were in-serted to attenuate the beam. The X-ray sourceand detector were each moved to 0° (�Q1�Q2),and the detector was then scanned with thetube fixed. A flat plate was then inserted intothe sample holder. First the detector wasscanned with the tube fixed and vice versa asthe plate bisected the beam. This was done iter-atively with sample holder adjustment to opti-mize the intensity, which should be nominallyhalf that from the scan without the plate. If not,one should start with the fluorescent screen tocheck for what is misaligned. With both anglesset at 0°, the flat plate is replaced with the align-ment slit, which is rocked iteratively with sam-ple holder screws to maximize the intensity.

This aligns the sample and source with respectto each other. Again, the detector was scannedwith the tube fixed and vice versa iteratively inorder to optimize the intensity. Once optimized,this defines 0° Q1 and 0° Q2 as well as 0° 2Q and0°W with direct beam detector. The W and 2Qzero axis positions were reset physically andelectronically.

If everything has been done correctly, the dif-fractometer is ready to perform the tests out-lined in section 4 to further refine the align-ment. With the shutter closed, the custodianshould remove any attenuating foils and if ap-plicable, narrow the energy window on the de-tector electronics so as to detect only X-ray en-ergies corresponding to ka lines. This is usuallyaccomplished by scanning an intense peak,such as the (101) quartz with the lower level ofthe SCA set very low (but above backgroundnoise) and the window wide open. After scan-ning, the custodian should raise the lower leveland repeat until 5% of the net intensity hasbeen removed. Next, the custodian should nar-row the window and scan again, repeating thisuntil another 5% of the net intensity has beenremoved. Upon completion, the custodianshould rescan and make sure the kb has beenremoved (see Fig. C1).

Diffraction from standard materials is nextused to correct 2Q zero errors, perform tilt testsfor stress determinations and to check the align-ment using the procedures outlined in Appen-dices B and C. Figs. 16 and 17 each show por-tions of a LaB6 diffraction pattern taken on the4-axis and Q –Q units, respectively. When com-pared to Figs. 1 and 2, respectively, prior to re-

34 The Rigaku Journal

Fig. 16. 4-axis unit: Diffraction pattern of LaB6 shows peak positions are near PDF card #34-427 values at low 2Q (see full pattern in Fig. B3).

alignment, it can be seen that the alignment ofthe goniometers has improved the quality ofthe data considerably. The refined lattice para-meters determined from the scans in Figs. B3and B4 were 4.1566(1) and 4.1569(1) Å for the 4-axis and Q –Q units, respectively, which com-pare favorably to the PDF value of 4.15690 Å[11] (also see Tables BIII and BIV). Neither Ta-bles BIII nor BIV present peaks outside thestated D2Q window of 0.05° as given in Table II.Tables BIII and BIV do reveal 1 and 7 peak posi-tions, respectively, which fall outside the morestringent D2Q window of 0.02° as given in Ap-pendix B for Diffraction angle calibration. Theformer alignment in this regard was acceptedas good. The latter was accepted because onlyphase ID work was being done at low 2Q onthat instrument. Otherwise another round of re-alignment would be required. When evaluatingyour alignment, one should consider the pri-mary uses of the instrument. For example whenperforming stress determinations, absolutepeak positions are not as important as relativechanges in peak position as a function of sam-ple tilt.

As an aside, the first Q –2Q scan of LaB6 afterre-alignment of the Q –Q unit revealed the peakpositions were systematically off. This requiredgoing back and rescanning with the alignmentslit to define 0° Q1 and 0° Q2 and the location ofthe fiducial surface corresponding to the centerof rotation of the goniometer. The subsequentQ –2Q scan of LaB6 revealed the peak positions

were systematically offset by a constant 0.04°,which is consistent with 2Q zero error. The de-tector arm was moved to the experimentally de-termined angular value for 8 the (510) LaB6.This position was reset physically and electroni-cally to the 2Q value listed for the (510) LaB6 onPDF card #34-427, which corrected the 2Q zeroerror.

Next, the custodian rechecks the intensity,FWHM/resolution and X-ray wavelength conta-mination (see Appendix C for details and Fig.C1). Neither W contamination (viz. new tube)nor kb peaks were observed, indicating that theelectronics are set properly on the 4-axis unitfor kb discrimination. Similar results were alsofound for the Q –Q unit with the maximum in-tensity of 3670 cps for the (101) quartz peak. TheFWHM/resolution decreased somewhat on bothunits (see Fig. C2). This was not a concern forthe 4-axis unit given the choice of optic and thesingle-phase samples with high symmetry usu-ally examined by this instrument. Althoughthere was 16% reduction in resolution for theQ –Q unit, the FOM was close enough to 2 thatanother re-alignment was not performed.

The tilt tests on the 4-axis unit, critical forresidual stress determinations, improvedslightly indicating negligible sample surface dis-placement error and beam misalignment forboth c and . tilting in Figs. 18A and B, respec-tively. Figs. 19A and B show the same when theincident optic is a 1.5 mm diameter pin-hole col-limator rather than slits as in Fig. 18. The 0.07°

Vol. 23 2006 35

Fig. 17. Q –Q unit: Diffraction pattern of LaB6 shows peak positions are near PDF card #34-427 values at high 2Q (see full pattern in Fig. B4).

2Q change in peak position is due to a smallmisalignment of the collimator with respect tothe focal spot. The 4-axis unit has positioningscrews to move the snout (see Fig. 12) indepen-dent of the slits. Although not shown, once thealignment appears to be finalized, the authorstypically use seven Y tilts and apply the criteriain Table II. Often the tilt tests reveal large differ-ences in peak position indicating that the align-ment is not good enough. The relative differ-ences can qualitatively tell you what is off andneeds to be adjusted. Figs. 20 and 21 providesome guidance in this regard by consideringthe four most basic situations:1. the X-ray beam is hitting behind the center

of rotation AND the sample surface is lo-cated on the center of rotation

2. the X-ray beam is hitting in front of the cen-ter of rotation AND the sample surface is lo-cated on the center of rotation

3. the X-ray beam is hitting on the center ofrotation AND the sample surface is locatedbehind the center of rotation

4. the X-ray beam is hitting on the center ofrotation AND the sample surface is locatedin front of the center of rotation.

The schematics in these figures attempt to illus-trate these conditions for W and c tilting, re-spectively. These figures based on the fact thatwhen the diffracting point on the sample sur-face is behind the center of rotation the ob-

served peak position (2Q) will be at a lowerangle than when the diffracting point on thesample surface is at/on the center of rotation.Likewise, when the diffracting point on the sam-ple surface is in front of the center of rotationthe observed peak position (2Q) will be at ahigher angle than when the diffracting point onthe sample surface is at/on the center of rota-tion. As is shown, sometimes the sample sur-face displaced from the center of rotation. Thezero tilt condition is the least sensitive to sam-ple surface displacement,15 due in part to thehigh 2Q (�130°) at which stress determinationsare normally done. Since there is usually asmall measurable effect of sample surface dis-placement, the relative peak position is desig-nated as �0. When two of these condition com-bine, the qualitative “additions” provide a guideas to the relative peak positions with tilt. Obvi-ously, the use of both positive and negative Ytilts is essential to this testing. Based on this,the custodian can determine what to adjust onthe goniometer. Of note, Vermeulen providesanalytical equations quantitatively modeling theabove [13].

Some comments about ASTM E915 are mer-ited as it describes tilt tests with some statisticalrigor for alignment verification only. Unfortu-nately, this standard procedure does not requirethe use of both positive and negative Y tilts,which could allow goniometer misalignment

36 The Rigaku Journal

Fig. 18. 4-axis unit: Tilt tests using (A) chi and (B) omega axes showing acceptable align-ment.

Fig. 19. 4-axis unit: Tilt tests using (A) chi and (B) omega axes showing acceptable align-ment using an incident 1.5 mm diameter pin-hole collimator.

Vol. 23 2006 37

Fig. 21. Schematics to help interpret c tilt tests. The peak positions (2Q) are relative to thatof Y�0° tilt condition; COR���center of rotation; diffraction plane is perpendicular to theplane of the paper; incident beams are going to the left, diffracted to the right; SS�, SS0 andSS� are the sample surfaces for the negative, zero and positive tilts, respectively. The c axis isperpendicular to the plane of the paper and passes through the COR. When in combination, therelative peak positions for the individual conditions can be added to get a qualitative summa-tion.

Fig. 20. Schematics to help interpret W tilt tests. The peak positions (2Q) are relative to thatof Y�0°. COR���center of rotation; diffraction plane is in the plane of the paper; incidentbeams are going to the left, diffracted to the right; SS�, SS0 and SS� are the sample surfacesfor the negative, zero and positive tilts, respectively. The W axis is perpendicular to the plane ofthe paper and passes through the COR. When in combination, the relative peak positions forthe individual conditions can be added to get a qualitative summation.

and/or sample surface displacement to go un-detected, resulting in erroneous residual stressvalues [14]. Another problem with ASTM E915is that it specifies that correct alignment is ac-complished once the average of five stressmeasurements is 0�14 MPa. As the elastic con-stant is not specified in the standard, differentstress values can possibly be calculated fromthe same set of strain measurements depend-ing on the elastic constant chosen. Since peakposition or interplanar spacing is measured, it isproposed that better criteria would be based onthese. Provided the stress free interplanar spac-ing is reported, crystallographic strain wouldalso be an acceptable alternative. While thepractitioner would need to be aware of thechanging sensitivity to strain with 2Q , thiswould allow the flexibility to use other materi-als/powders instead of just iron powder irradi-ated with chromium ka X-rays. Since most lab-oratory X-ray units use copper radiation, whichcauses fluorescence in iron, this flexibility isneeded. However, the fluorescence interferencecan be dramatically reduced by a diffractedbeam monochromator. Within ASTM E915,there is a need to consider the uncertainty asso-ciated with the individual measurements. Forexample, the five individual measurements allhave stress values near 0 MPa, but have individ-ual standard deviations greater than 14 MPa. Inthis instance, while the alignment is correct ac-cording to the standard, the authors maintainthat there is probably an alignment problem inthis situation.

6. How do I maintain the alignment?Periodic checks every 1 to 8 weeks is a rea-

sonable interval between alignment checks de-pending upon what you are doing and theamount of usage. Frequently, these checks canlapse and undue effort is expended trying to ex-plain data confounded by an instrument that isout of alignment. Alignment adjustments andalignment check results should be recorded forfuture comparison and troubleshooting.

7. Standards/Reference Materials forAlignment of Goniometers for Stress De-terminations

In order to assure that the X-ray machine isrunning properly, the custodian must have a setof standards. For powder diffraction, these stan-dards must be polycrystalline, crystallographi-cally random and strain free. As can be inferredfrom this work, suitable powder standards in-clude Si, LaB6 and Al2O3. Suitable solid stan-

dards include polycrystalline quartz and Al2O3.These can be obtained from a variety ofsources. The necessity of certified standards de-pends upon your customer base and corporaterequirements. Given the expense of certifiedstandards, uncertified standards can be used formost alignments without any compromise. LaB6is favored here because of its excellent scatter-ing power due to the high atomic number of Laand numerous, intense peaks present over awide range of 2Q due to its simple cubic struc-ture and relatively large lattice. Alternatively,ASTM E915 procedure describes the prepara-tion of a stress-free iron powder standard [12].

Alignment for stress determinations, particu-larly the aforementioned tilt tests, single-phasepowders with a 10 mm grain size are regardedas ideal. Since powders cannot support long-range stresses, they have zero macro stress. Ifthere were appreciable crystallographic an-isotropy or cold work, the peaks would bebroadened due to microstresses (micron scalestrains) or r.m.s. strains (nano scale strains) andsmall crystallite size, respectively. Although amaterial with sharper peaks is preferable, gen-erally speaking, these problems would not pre-clude using them for alignment. To be clear,these powders do not replace the need for apiece/powder of the material that you are study-ing in order to obtain a stress-free interplanarspacing, d0.

Solid samples of known stress values areproblematic as testing by numerous laborato-ries usually produces a wide range of results forthe same sample. Still, there is a need/desire forsuch a standard when equipment or situationswarrant. For example, if extensive physical con-tact is needed to position the sample surface onthe center of rotation, a powder would not suf-fice. One such commercial standard was testedrecently.* Iron powder samples were made bygently compressing �325 mesh, 99.9% ferritepowder mixed with a few drops of oil. The re-sultant disk was glued onto a flat plastic disk.This type sample has a flat, hard surface that iseasy to handle. The oil enhances the com-paction process and provides some oxidationprotection for the sample. LaB6 powder wasmixed with acetone. This slurry was thenpainted on the surface of the compacted irondisc. Once the acetone evaporated, a thin layerof LaB6 powder adhered on the surface of theiron disc. Using the same methods as described

38 The Rigaku Journal

* TEC/Materials Testing Division, 10737 Lexington Drive,Knoxville, TN 37932, USA.

previously (see Table A.I), several iron diskswith and without LaB6 powder painted on wereexamined. Table IV lists the results in terms ofstress, strain and maximum minus minimumpeak position. The results from sample #04042meet the stress-free criteria of ASTM E915 withan average stress of �11�8 MPa. In all casesbut one, the strain in the LaB6 was less than thatin the iron disk. Seventeen of the 20 values ofD 2Q were less than twice the guidelines inTable II. The overall average for the commercialiron disk was �15�9 MPa.

8. SummaryAlignment criteria, test procedures and main-

tenance checks have been described with em-phasis on residual strain measurement. The useof standards has also been discussed. Thoughtersely discussed, important safety considera-tions were mentioned. It is hoped that thispaper will provide insights to safely improvethe alignment of instruments to yield more ac-curate data for the engineering and sciencecommunities.

9. AcknowledgementsWhen performing an alignment, it is often

critical to discuss options, scenarios and solu-tions with others who have a fresh outlook.Thus, this work represents the summation of

numerous conversations with many people.The authors are particularly indebted to Dr.’sAndrew Payzant, Claudia Rawn, Scott Misture,Tom Ely, Xiaojing Zhu, Paul Predecki, CevNoyan, and Kris Kozaczek for their help and in-sight. Research sponsored by the Assistant Sec-retary for Energy Efficiency and Renewable En-ergy, Office of FreedomCAR and Vehicle Tech-nologies, as part of the High Temperature Mate-rials Laboratory User Program, Oak Ridge Na-tional Laboratory, managed by UT-Battelle, LLC,for the U.S. Department of Energy under con-tract number DE-AC05-00OR22725.

References

[ 1 ] T. R. Watkins, O. B. Cavin, J. Bai and J. A. Chediak:Advances in X-ray Analysis, 46 (2003), 119–129.

[ 2 ] R. Jenkins and R. L. Snyder: Introduction to X-rayPowder Diffractometry, John Wiley & Sons, Inc., NewYork (1996), 123, 205–230.

[ 3 ] J. P. Cline and R. W. Cheary: “The Design, Alignment,Calibration and Performance Characteristics of theConventional Laboratory Diffractometer,” Workshophandout, Denver X-ray Conference, 26 July 2000.

[ 4 ] T. R. Watkins and R. D. England: “Workshop W13-Alignment: Maintenance & Alignment Section,” Den-ver X-ray Conference, Steamboat Springs, CO, 31 July2001.

[ 5 ] T. R. Watkins: “Workshop W8-Diffraction Analysis ofStress and Strain: Practical Application Section,” Den-ver X-ray Conference, Colorado Springs, CO, 2 August2005.

[ 6 ] H. Krause and A. Haase: “X-ray Diffraction SystemPTS for Powder, Texture and Stress Analysis,” Experi-mental Techniques of Texture Analysis, DGM Informa-tionsgesellschaft Verlag, H. J. Bunge, Editor, (1986),405–408.

[ 7 ] F. X. Masse, J. Coutu-Reilly, M. Galanek and A. Ducat-man: Health Physics, 58 (1990) [2] 219.

[ 8 ] C. Weilandics, N. Rohrig, and N. F. Gmur: Nucl. Inst.Meth. Phys, Res., A266 (1988), 691–698.

[ 9 ] S. Oesch and M. Faller: Corr. Sci., 39 (1997), 1505–1530.

[10] T. R. Watkins, G. K. Schulze and C. R. Hubbard: ORNLTM to be published.

[11] Powder Diffraction File, ICDD, Newtown Square, PA19073–3273 U.S.A.

[12] ASTM E915-Verifying the Alignment of X-ray Diffrac-tion Instrumentation for Residual Stress Measure-ment, ASTM, West Conshohocken, PA, 1996.

[13] A. C. Vermeulen, “Instrument Aberrations in a 4-circlePowder Diffractometer,” Accepted to Zeitschrift fuerKristallographie, May 2006.

[14] E. B. S. Pardue and L. A. Lowery: “Assessment ofComponent Condition from X-ray Diffraction DataEmploying the Sin-Squared-Psi Stress MeasurementTechnique,” Practical Applications of Residual StressTechnology, ASM, (1991), 39–46.

[15] I. C. Noyan and J. B. Cohen: Residual Stress, Mea-surement by Diffraction and Interpretation, Springer-Verlag, New York, (1987), 101–102.

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Table IV. The stress determinations for a stress-freeiron disk, LaB6 and iron powders.