AD-A250 527 - 4

Research and Development Technical ReportSLCET-TR-92-2

Movement of Dislocations in Quartz

R. Aaron MurrayElectronics Technology and Devices Laboratory

April 1992

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Movement of Dislocations in Quartz PE: ILIPR: 62705

G. AUTHOR(S) TA: AHc4

R. Aaron Murray

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US Army Laboratory Command (LABCOM)Electronics Technology and Devices Laboratory (ETDL) SLCET-TR-92-2ATTN: SLCET-EFFort Monmouth, NJ 07703-5601

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11. SUPPLEMENTARY NOTESThis report is based on a paper presented and published in the Proceedings of the 45th Annual Symposium onFrequency Control, 1991, IEEE Cat. No. 91CH2965-2.

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13. ABSTRACT (Maximum 200 words)

Dislocations in quartz crystals have been known to cause problems in the fabrication of resonators by theformation of etch channels. The etch channels are known to weaken the physical strength of quartz blanks and toreduce the yield in photolithographic production processes. While it is possible to reduce the etch channel densityin quartz by post growth electro-diffusion, this does not reduce the dislocation density. It is suspected thatdislocationg contribute to acceleration sensitivity, thermal hysteresis, and possibly aging. The behavior ofdislocations in quartz is also of interest to the fields of geophysics, seismology, and plate tectonics because it affectsthe underground movement of rock. Specifically, the movement of dislocations in quartz is the mechanism throughwhich quartz can be plastically deformed. A large body of literature on the movement of dislocations in natural andcultured quartz has been published in various geophysical journals over the past thirty years. This paper is a reviewof this literature and its possible implications for frequency control.

14. SUBJECT TERMS 15. NUMUER OF PAGESQuartz, quartz crystal, dislocations, dislocation movement, etch 13

channels, water weakening, vibration sensitivity, aging, thermal hysteresis, 0, 1. PRICE cootresonators.

17. SCURI'Y CLASSIFICATION 11. SEURTY CLASSIFICATION 1. SECURTY CLASSIFIATON 12. UIMTATION OF ABSTRACT

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Table of Contents

Pate

Introduction 1

Observing Dislocations 1

Impact of Dislocations on Resonators 2

Characteristics of Dislocations 3

Movement of Dislocations in Quartz 4

Summary 6

Acknowledgments 6

References 7

Accesion ForNTIS CRA I

DT!C 1A -

Justifhcation

By ............ ...... ...............

Dist ibutior I

DOI

iii 4l

Fieures

Page

1. Edge and screw dislocations. 1

2. Determination of Burgers vector. 2

3. Edge dislocation in quartz. 4

4. Fractional stress drop vs. temperature for natural and cultured quartz. 5

5. Frank-Griggs mechanism of dislocation movement 5

6. McLaren model of dislocation formation. 6

iv

Introduction

Until recently, characterizing dislocations inquartz has not been a high priority in the frequencycontrol community. Early work indicated that dislocationdensities found in cultured quartz did not adversely affectresonator performance, and. since jhen, most of the workhasbeen focused on hoV dislocations affect the processingof resonators. Etch channels and pits, which result whenquartz containing decorated dislocations is chemicallyetched or polished, decrease the mechanical strength of theresonators and lower the yields in manufacturingprocesses-.' However, as the requirements for resonatorperformance become more stringent, the presence ofdislocations in resonators is likely to become more Asignificant. Recent work has shown that etch channels candramatically reduce the Q of high frequency bulk waveresonators? It has also been shown that the vibrationalmode shape can affect the acceleration sensitivity ofresonators and X-ray topographs clearly show that modeshapes are distorted by dislocations ' 7 Thermal hysteresisand aging may also be affected by the presence ofdislocations.'" A

The properties of dislocations in quartz are alsoof interest to researchers in the fields of geology,seismology, and plate tectonics. When quartz is subjectedto high stress and temperature, it flows (plasticallydeforms) through a mechanism involving the movement ofdislocations. It has been reported that the ease with whichthese dislocations move is linked to the amount of waterin the crystal 0 This effect has been studied extensivelyover the past twenty-five years, and a large body of Bliterature has been published in the geophysical andmineralogical journals.

The current interest in UHF resonators, low Figure 1. Edge and screw dislocations. (A) Edgeacceleration sensitivity resonators, low hysteresis and low dislocation, (B) screw dislocation.3aging resonators, and the relatively untapped geophysicalwork make this an ideal time for a review paper ondislocations. In this paper we discuss historicalbackground and current theories of dislocations in quartz.Some of the geophysical findings may be used to help (or planes) of atoms into an existing lattice (see Fig. IA).explain results reported in the frequency control A screw dislocation is generated by displacing the latticecommunity. on one side of the dislocation line relative to the other (see

Fig. IB).23 How a given dislocation distorts a crystallattice is given by the Burgers vector. The Burgers vector

Observint Dislocations can be determined by tracing a closed circut around thedislocation (see Fig. 2A). The path here consists of

A dislocation is defined as a linear lattice defect. segments M to N, N to O,O to P. and P to Q, where MAn edge dislocation is formed by inserting an extra plane and Q occupy the same lattice point. Next, trace the same

Another technique, used by Moriya and Ogawae is light

P OM scattering tomography. This method scans the quartzP sample with a low power (in this case a 3 mW) He-Ne

laser. The scattered ight is then recorded on film. Thisapparatus is sensitive enough to observe both decoratedand undecorated dislocations in quartz samples and it is

0N non-destructive. Other methods include transmissionelectron microscopy (TEM) 1

12 and X-ray topographyY25

A recent improvement on standard X-ray topography isthe use of synchrotron X-rays to attain very high

A resolution and high speed (I ns) pictures of dislocationsand strain fields.s O1 This is especially useful for lookingat the effects of dislocations on active resonators. If the

p M O quartz has been deformed sufficiently, as happens in someP_ P of the geophysical experiments, the bands of dislocationsSgers, ector can be seen with a polarizing microscope. 3

0 Impact of Dislocations on Resonators

The question of real interest for the firquency

B control community is how dislocations affect devicefabrication and performance. First, consider thefabrication process. As mentioned earlier, when quartz

Figure 2. Determination of Burgers vector. (A) containing decorated dislocations is etched, channels form.Closed circuit around a dislocation, (B) closed circuit In HF, etch channels about 1 micron in diameter canaround a perfect lattice. propagate from the surface at mom than 100 microns/hour.

This is much faster than the bulk etching rate. As statedin the previous section, sweeping can reduce the number

segments on the perfect lattice, Fig. 2B. The Burgers of etch channels that form during chemical polishing andvector is the vector Q to M required to close the circut on etching. However, this does not reduce the dislocationM. Thus the direction and magnitude a dislocation density. Hanson" took X-ray topographs before and afterdistorts the crystal lattice is the Burgers vector. The sweeping quartz samples and no decrease was seen in theBurgers vector of an edge dislocation is normal to the dislocations.dislocation line while for a screw dislocation it isparaliclY The next concern is the effect of dislocations on

performance. A resonator property that is often measuredThere are many ways to observe dislocations in and reported is Q. In the past it was commonly accepted

quartz, some direct and some indirect. The most common that dislocations did not affect resonator Q. In 1982,technique in the frequency control community is to use Iwasaki and Kurashige' fabricated 5 MHz AT-cutetching in order to produce etch channels." In this resonators and found no correlation between dislocationsmethod a chemical etchant, usually HF, ammonium and mechanical Q for quartz blanks with dislocationbifluoride, or a buffered oxide etchant (i.e., various densities up to 103/cmn. In a more extensive study,mixtures of NH4F.HF and HF) is used to etch the quartz. Meeker and Millern also looked for a correlation betweenThe etch channel density is then counted (see standard the dislocation density and the performance characteristicsEIA-477-A"). This method is indirect and insufficient in of 8 MHz fundamental AT-cut resonators cut from r-bars.that the etch channels only form if the dislocations are They found that not only were the Q's independent of thedecorated with impurities, and not all of the dislocations dislocation density, but so were the resistance andshow up as etch channels. Sweeping moves the impurities inductance of the resonators. However, they did correlateaway from the dislocation sites, and for this reason, the grown-in strain associated with dislocations toetching will not reveal dislocations in swept quartz. abnormal frequency vs. temperature (f-T) behavior. That

2

is, the dislocations were responsible for apparent angle type of accelerated aging can anticipate a type of defectshifts in resonators of up to several minutes of arc. In a that might show up, in time, in resonatom If this happensrecent article, Kent3 correlated Q degradation with etch gradually over months (and years) it could contribute tochannels in high frequency (45 to 140 MHz) bulk wave aging. Could dislocation movement also be a factor inresonators which were chemically etched as part of the hysteresis? As the temperature is increased and decreased,fabrication process. In these very thin resonators, a single the dislocations may move to different potential minima,etch channel in the active area reduced the Q by 46%. changing the crystal constants. Beaussier' has put forthFor these resonators, Kent states that low etch channel the proposition that slight plastic deformations, associatedquartz (either as grown or swept) is necessary to achieve with the movement of dislocations, can cause an intrinsicconsistent Q values. Since the dislocation density is hysteresis in bulk quartz. Certainly the quartz materialunaffected by the sweeping process, it would appear that appears to affect hysteresis.3 But, no link to dislocationfor these resonators it is the presence q.f the etch channels movement has been shown.rather than the dislocations that degrades the Q.

The apparent angle shifts in resonators found by Characteristics of Dislocations in QuartzMeeker and Miler32 suggest that dislocations can changethe material constants in quartz. In support of this In cultured quartz it has been observed thathypothesis, James3 3 stated that he found significant dislocations usually originate in the seed or at inclusionsdifferences in the elastic moduli in quartz of different within the growth zones. It has also been observed thatgrades. The difference between the grades was the level these dislocations propagate nearly perpendicularly to theof Al impurities and the dislocation densities (10/cm' for growth front in each of the growth regions (+x, -x, s andthe higher grade vs. 103 to 10'/cm 2 for the lower). Such z).2' The angular distribution of dislocations in the growthchanges in the elastic moduli would be likely to show up zones was used by Alter and Voigt to show how theas deviations in the f-T characteristics (apparent angle directions change when dislocations pass growthoffsets). boundaries. They cut blanks from -x, +x, z, r, and R

growth sectors and used them as seeds. The degree toRecent attempts to make resonators less sensitive which the dislocations would deviate from the growth

to acceleration have not been uniformly successful.? One front normal was predicted by an elastic energyreason for this seems to be that the vibrational modes are minimization per length model. The dislocations on thenot the correct shape or in the correct place to cancel the +x seeds were nearly parallel to the seed. Meeker andacceleration frequency offset' Several groups have MilerU 2 found two types of dislocations in cultured r bars.studied the mode shapes in active resonators using The first were uniform, slow etching, and after thesestandard and stroboscopic x-ray topography.- "7 They have dislocations had been etched into etch channels, there wasshown that the presence of dislocations in the active no disruption of f-T curves. The second type wereregions of the resonators distorts the mode shape, clustered, etched faster, and changed the f-T curves. Theenhances coupling among modes, and interferes with mode dislocations normally found in the z region of quartz barstrapping. This means that very low dislocation quartz is are thought to be edge type and those in the +x and -xnecessary for fabricating acceleration insensitive regions are screw type.2'3 7 Given that Meeker and Millerresonators. used r bars, and not z cut seeds, the two types of

dislocations they observed may be edge and screw type.Finally, consider the problems of hysteresis and It is not clear, however, why these dislocations should

aging. If dislocations change their positions during the behave so differently. Iwasaki" proposed two atomiclife of the device, this could contribute to aging. Gluer et models for the edge dislocations in quartz Z growth butal. saw apparent dislocation motion in stroboscopic X-ray the Burgers vectors of the models do not fit thosetopographs of a vibrating AT-cut resonator, but they determined recently by Epelboin and Patel.m X-raydismissed this as an illusion caused by the vibration topographs of Barns37 were examined by Epelboin andbecause they didn't believe the dislocations could be Patel using a computer simulation method. This allowedmobile at the stress levels present. In a related vein, them to determine that two different Burgers vectors areStephenson35 used electric potentials at elevated present in the Z region dislocations. These are [1210] andtemperatures (near the alpha-beta transition) to induce (21101, with the first being the most prevalent Andislocations in nearly perfect quartz. He states that this example of an edge dislocation with the [1210] vector is

3

shown in Fig. 3. Note that only the Si atoms have been grown bars was growing on seeds cut from the +x region.drawn. Armington's data were inconclusive on the effect of silver

liners on dislocations. Irvine et al" at Sawyer Research

Over the years various methods have been tried also had mixed results for silver liners. The typicalto reduce the dislocation density in quartz.-' Doherty et Sawyer quartz bar grown in a silver liner had 86aLe attempted to grow high purity quartz. Their specific dislocations/cm2 , showing that simply using inert linersobjective was low Al content and low dislocation density. does not automatically abolish dislocations. AnotherBy using very pure fused silica as the nutrient in gold aspect of dislocation effects was detected when Armingtonlined vessels and growing very slowly, (0.16 to 0.35 analyzed the material swept from quartz. They found,mm/side/day) the Al content was kept well below I ppm among other things, Al (this had also been reported by(0.01 to 02 ppm Al) and the number of dislocations Gualtieri and Vig45). Armington speculated that the Alintroduced duing growth was reduced. To reduce the was swept along dislocations since it is improbable that itnumber of dislocations originating from the seed, the seeds would be moving through the c (z) channels.were cut from high quality natural quartz which had beeninspected by X-ray topography for dislocations. Usingthese methods, the dislocation density of the grown bars Movement of Dislocations in Ouartzwas kept to less than 10/cm 2. This material also hadradiation induced offsets of less than 10"P Hz/rad. The properties of quartz, both mono-crystallineArmington et al.4 have made an extensive study of ways and as aggregates, have long been of interest to geologiststo reduce the number of inclusions and dislocations in and geophysicists. This is partly because of thecultured quartz. Some of the methods which did not abundance of this material in the earth and partly becauseimprove the quartz quality were sweeping the seeds before of its unusual properties. One of the more importantgrowth, doping the seeds to change the lattice dimensions, aspects of these is how quartz behaves at high stressand annealing the quartz bars. In fact, the annealing levels. The long term strengths and flow properties ofseemed to increase the strain around the inclusions. One rock are of major importance to geophysicists becausemethod that did decrease the dislocation density in the they are critical to the understanding of, e.g., earthquake

seismology.'s The goal of geophysical research on thehigh temperature deformation of rocks is to determine thestress and strain history of the Earth's crust and mantle.This will allow accurate modeling of rock movement."When quartz is permanently deformed by stress, it is done

B=a/3" [12 10 a, through the movement of dislocations. Geophysicists areinterested in using dislocation density to infer the stressesexperienced by the samples while underground.

Natural quartz is unusual in the sense that the- / / /- - / combination of high strength combined with low elastic

/ • /- - constants means that very large elastic deformation ofsingle crystals is possible. 0 With dry natural quartz, there

/ \ / \ Ais a change in the response to an applied strain at around700 degrees C.' At this temperature there is a change

thtallows plastic deformation. This yield temperature ismuch lower for cultured (and for natural quartz that has

/A. water added during the experiment).' *-" These yieldStemperatures are dependent on the amount of water in the

crystals (see Fig.-4). For cultured quartz the yieldStemperature ranges from 650 degrees C for 1000 ppm

H/Si to 380 degrees C for 90300 ppm M/i (here the Hcontent was calculated from the 3 pmn IR absorption

band).' In the plastic deformation of the quartz, thisthe Si atoms have been drawn, o 0 atoms are shown.propagated

4

quartz that had been permanently deformed at 300 to 400nlat. qz.-60 ppm IIS degrees C using TEM and found large numbers of tangled

dislocation lines' 7

1000 nat. qz. 140 ppm One of the first theories which considered the role

of water in dislocation movement was the Frank-Griggs1000 ppm model *°. In the Frank-Griggs model (Fig. 5), the effect of

water weakening is explained by the hydrolyzing of O-Si2550 ppm bonds. 0 This supposedly makes the movement of the

CL dislocations easier because the O-H bonds are easier toS2900 ppm break than O-Si. Recently, McLaren et aLI2 looked at the60 60 problem of water weakening using TEM. They found that

5000 ppm when wet quartz is heated, water bubbles expand andgenerate dislocation loops. These loops can, given time,

8800 ppm connect several water bubbles. They claim that the OH

terminations do not make the dislocations glide easier.Instead, when the quartz is heated, the bubbles expand

P = 15Kb (see Fig. 6) and generate the dislocations needed for200 dislocation propagated slip to occur. This explains the

0 0.5 1.0 incubation time (the delay between the time the sampleAG / o was loaded and when the first signs of strain are detected)

found in some experiments. This also explains the resultsFigure 4. Fractional stress drop vs. temperature for Armington et al03 reported after annealing cultured bars.natural and cultured quartz. As mentioned earlier, Armington et al. found that the

strain around the inclusions was increased after annealing,slip. 0" That is, the movement of dislocations allows bulk and in the same paper they stated that most of theplastic flow. The slip planes in quartz, which correspond dislocations in their quartz were voids, partially filled withto preferred directions for dislocation movement, have liquid. These may correspond to the bubbles seen bybeen detennincd.u '2 Tullis"6 notes that there is a critical McLaren. Brice2 has conducted experiments in which theweakening pressure in the same sense that there is a yield alpha ( the infra-red absorption coefficient at 3500 cm"1,temperature. After quartz is plastically deformed, high proportional to H content) is shown to be correlated todislocation densities appear. Hobbs examined cultured dislocation density. That is, the dislocation density can be

Si Si Si Si Si Si Si Si Si Si SiI I I I I I I I I I IO V 0 0 0 0 0 0I I I I I I I I t

Si Si Si Si Si Si Si Si Si Si SiI I I I I I -i I IO OH 0 0 OH OH 0 0 OH 0I I HHO

Si Si Si Si Si Si Si SiI I I I I I II 0 0 0 0 0 0 0I I I I I I I I

Si Si Si Si Si Si Si Si

A B C

Figure 5. Frank-Griggs mecmanism of dislocation movement. (A) Hydrolyzed edge dislocatiom with anhydrousneighbors. (B) Si-O-Si bond hydrolyzed by water migration. (C) Dislocation moves by exchange of hydrogen bond.

5

st Summary

It has been shown in the geophysical work thatdislocations definitely can move in quartz. However, allof that work was done at high temperatures and pressures.

(A) st- a a -Si It remains to be seen whether or not dislocations can beformed, or are mobile under the conditions present duringthe fabrication and operation of resonators. One area that

S was not covered in the publications reviewed here was theL possibility of reducing the dislocation density through post

growth pressure reatment The possibility of movingdislocations out of the active arms in resonator blanks isvery appealing and deserves to be investigated.

st st

I I In parallel with these experimental studies, a* o theoretical basis for the behavior of dislocations in quartz

needs to be developed. Heggie et al."'- have published* Nseveral papers studying the dislocation lines in alpha

( ) -0 N - s quartz using atomic models with Keating type interatomicpotentials. While this is useful for determining which

N mdislocations are possible, it is essentially a static process.* * Pontikise recently made the point that computer molecular

dynamics (MD) techniques are very well suited forSI sI examining the movement of dislocations in crystals. With

MD simulations it would be possible to better interpret thedislocation experiments suggested in the last paragraph.Also, it is possible to perform simulations of P-Tconditions that would be difficult and costly to do inexperiments.

Figure 6. McLaren model of dislocation formation.(A) Bubble in quartz prior to heating. (B) Expansionof bubble through the incorporation of water. Acknowledgements

The author wishes to thank John Vig forestimated from alpha (Q1,). Samples with higher alpha'a suggesting this study and for his help in editing this paper.(lower Q's) have higher dislocation densities. This can befit to the curve

ogi* N,, - 5.00 * 0.48 + 2.5 logio a

where N0 is the dislocation density (cm-) and a is in cm'.Furthermore, quartz material from different manufacturersyields different lines. Brice feels that this difference inthe alpha vs. dislocation density plots for quartz fromdifferent suppliers is more supportive of the Griggs-Frankmodel as opposed to the McLaren model.

6

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Wood, "Acceleration-InducedFrequency Shifts in T v. 19, pp. 1619-1623, 1984.Quartz Resonators," Proc. 43rd ASFC, pp. 388-395, 1989. [15] Neville L. Carter, "Steady State Flow of Rocks,"

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[8] Gary R. Johnson and Robert A. Irvine, "Etch [191 M. Heggie, R. Jon,,s, and M. Nyl~n, "ElectronicChannels in Single Crystal Cultured Quartz," Structure of Alpha Quartz and PerfectProc. 41st ASFC, pp. 175-182, 1987. Stoichiometric Dislocations," Phil. MaR. B, v. 51,

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[101 David Griggs, "Hydrolytic Weakening of Quartz [211 M. Heggie, and R. Jones, "Models of Hydrolyticand Other Silicates," Geophys. J. R. Astr. Soc., v. Weakening in Quartz," Phil. Mag. A, v. 53, no.14, pp. 19-31, 1967. 5, pp. L65-L70, 1986.

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7

(22) M. Heggie and R. Jones, "Computer Modelling [33] B1. James, "A New Mea- ..,ment of the Basicof Plasticity in Minerals - The Hydrolytic Elastic and Dielectric Constants of Quartz," proc.

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[341 Raymond L. Filler, John A. Kosinski, and John

[231 Derek Hull, Introduction to Dislocations, R. Vig, "Further Studies on the AccelerationPergamon Press Ltd., New York, 1965, pp. 13- Sensitivity of Quartz Resonators," Proc. 37th21. ASFC, pp. 265-271, 1983.

[241 M.W. Wegner and J.M. Christie, "Chemical [351 J.D. Stephenson, "Quasi-Realtime Observation ofEtching of Deformation Sub-structures in Partial Dislocation Growth in Synthetic QuartzQuartz," Phys. Chem. Minerals v. 9, pp. 67-78, Near the Alpha-Beta Transition Temperature1983. Using Electric Potential Switching," Phys. Stat.

Sol. A, v. 106, pp. 441-449, 1988.

[251 Fumiko Iwasaki, "Line Defects and Etch Tunnelsin Synthetic Quartz," J. of Cryst. Growth, v. 39, [36] John A. Kusters and John R. Vig, "Thermalpp. 291-298, 1977. Hysteresis in Quartz Resonators - A Review,"

Proc. 44th ASFC pp. 165-175, 1990.

(26] John R. Vig, John W. LeBus, and Raymond L.F'ller, "Chemically Polished Quartz," Proc. 31st [37] R.L. Barns, P.E. Freeland, E.D. Kolb, R.A.ASFC, pp. 131-143, 1977. Laudise, and J.R. Patel, "Dislocation-Free and

Low-Dislocation Quartz Prepared by

[271 Electronic Industries Association, Engineering Hydrothermal Crystallization," J. of Cryst.Dept., 2001 Pennsylvania Ave., N.W., Growth, v. 43, pp. 676-686, 1978.Washington, D.C. 20006.

[38] Y. Epelboin, J.R. Patel, "Determination of[281 Kazuo Moriya and Tomoya Ogawa, "Observation Burgers Vectors of Dislocations in Synthetic

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[29] Fmniko Iwasaki and Masakazu Kurashige, [391 R.A. Laudise, R.L. Barns, D.S. Stevens, E.E."Defects in Synthetic Quartz and Their Effects on Simpson, H. Brown, "High Performance Quartz,"the Vibrational Characterictics," Ferroelectrics, Proc. 42th ASFC, pp. 116-126, 1988.v. 43, pp. 43-50, 1982.

[40] S.P. Doherty, S.E. Morris, D.C. Andrews, D.F.

[301 C.C. Gliler, W. Graeff, and H. Moiller, Croxall, "Radiation Effects in High Purity"Stroboscopic Topography with Nanosecond Synthetic Quartz," Radiation Effects, v. 74, pp.Time Resolution," Nuclear Instruments and 145-150, 1983.Methods, v. 208, pp. 701-704, 1983.

[411 Alton F. Armington, John J. Larkin, John J.

[31] W. Hanson, "Transmission X-Ray Topography of O'Connor, J. Emery Cormier, and Jane A.Single Crystal Quartz Using White Beam Horrigan, "Effects of Seed Treatment on QuartzSynchrotron Radiation," Proc. 41st ASFC, pp. Dislocations," Proc. 37th ASFC, pp. 177-180,228-235, 1987. 1983.

[32] T.R. Meeker and AJ. Miller, "The Temperature [42] Alton F. Armington and Joseph F. Balascio, "TheCoefficient of Frequency of AT-Cut Resonators Growth of High Purity, Low Dislocation Quartz,"Made from Cultured r-Face Quartz," Proc. 34th Proc. 38th ASFC, pp. 3-6, 1984.ASFC, pp. 85-92, 1980.

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(43] Alton F. Armington, Jane A. Horrigan, M.T.Harris, and Joseph F. Balascio, "A Study ofDislocations and Inclusions in Alpha Quartz,"Proc. 41st ASFC, pp. 213-215, 1987.

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[451 John G. Gualtieri and John R. Vig, "Sweepingand Irradiation Studies in Quartz," Proc. 38thASFC pp. 42-49, 1984.

[46] Vassilis Pontikis, "Defect Dynamics Revealed,"Physics World, pp. 25-28, 1990.

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