The growth of high acoustic Q quartz at high growth rates

Journal o f Crystal Growth 18 (1973) 1-6 © North-Holland Publishing Co.

THE G R O W T H O F H I G H ACOUSTIC Q Q U A R T Z AT H I G H G R O W T H RATES N. C. LIAS and Ms. E. E. GRUDENSKI Western Electric Company, Merrimack Valley Works, North Andover, Massachusetts 0184.5, U.S.A. and E. D. KOLB and R. A. LAUDISE Bell Laboratories, Murray Hill, New lergey 07974, U.S.A.

Received 5 .luly 1972; revised manuscript received 1 September 1972 A technique for the hydro0"qrmal Vowth of high acoustic Q (> 10e) quartz at rates above 100 mi~/day (2.5 ram/day) is reported. This technique hinge" uoon the fact that the solid soluW":~ .y in quartz of the proton which causes loss is d ~ as the growth temperature increases. Typical conditions for high Q-hillh rate Igrowth are: 3"/4 °C, crystallization temperature; 23°, temperature difference (AT) between dissolving and ffrowth zones; 88% fill; 40000psi (2759 bar) and 103 rail/day growth rate on a surface within

5° of a basal (0001) plane. The Q is 1.4× 10e. The concept of effective distribution constant developed to describe impurity segregation in melt growth is shown to be applicable to solution growth with appropriate modifications. A new quantity, the effective equilibrium constant for the segrelgation o f (M + s) ionsand (H +) in quartz is shown at constant temperature to depend on rate (where rate changes are brought about by fill and AT changes) in a manner analogous to the dependence of the effective distribution constant in melt

growth. It is suggested that the concent of effective equilibrium constant can be extended to polycomponent growth in general. 1. Introduction High acoustic loss ill hydrothermal!y grown synthetic quartz severely degrazles its usefulness especially for high frequency applications. It has been known for some time that acoustic loss is associated with interstitial !) H + which enters the lattice as ( O H ) - from the basic growth solution to charge compensate nonplus four ions such as Fe +j, Fe +2, Cu *a a n d AI ÷3 present in the lattice at Si +4 sites2). Growth from solutions containing Li + salts haz been shown to repress H + uptake and increase Q3,4), as has reduction in the concentration of nonplus four substituents at Si +4 sitesS). it has also been known for some time that qualitatively acoustic Q is inversely proportional to growth rate. For example, for growth on surface normal to (0001) (basal plane growth) or on samples 5 ° from (0001) (+ 5 ° X cut surface), high Q quartz (Q > 10 o) can be grown at rates* below 20 rail/day (0.5 mm/dey) while even i~ the presence of Li ~, Q's above ~ I0 ~ have ordinarily not been obtained at growth rates much above 60 rail/day (1.5 ram/day). Techniques for obtaining high Q at high rates have obvious economic * Growth rate is de~erminedas: [increase in thickness seed]/ltime of run].

importance. In pa:ticular, rate~ a b o v e about 100 rail/day (2.5 ram/day) with Q's > 10 6 would provide significant savings in both capital and ~ ~,~erating expenses in commercial quartz growth. We, thLrefore, carried out a systema*ic search for conditions where high Q-high rate q u a r t z could be produced. In addition, in the course o f this work, we have discovered that proton and other impurity segregation in hydrothermal growth and coupled substitution in general in polycomponent crystal growth can be described b y equilibrium and effective equilibrium constants where the effective equilibrium constant depends on g r o w t h rate a~d other growth conditions in a m, nner analogous to the effective distribution constant in liquid-solid monocomponent growth. 2. E x p e r i m e n t a l

The conditions of growth a~,~d the equipment were those ordinarily used in the commercial production of quartz except that to extend the pressure-temperature range, the autoclave shown in fig. 1, purchased from Autoclave Engineers, Erie, Pennsylvania, was employed for the higher pressure experiments. This autoclave utilized a laminated construction so t h a t the inner shell was o f either 4340E or HY-100 while the outer shell

2

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ZO

40

60

ppm H + ( w g t ) 80 t 0 0 120 t40 160

180 200

201" t9-

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i VENT

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140E OR ;T~-EL " OD HELICAL IOOVE

140"

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15"

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Laminated constr~ction ~utoclavc.

w~s of high strength I-l-l~ steel. Its pressure-temperature limit was 40000 ?si (,-~2760 bar) at 475 "C. A microgroove was machined in the outer shell and led to a series of vent holes for pressure relief. Thus in the event of a failure of the inner skell, pressure would be relieved and any metal fragments would be retained by the outer shell. Hence, the outer covering serves as an explosion barrier and the autoclave design is |o be recommended from the x.fewpoint of safety even for normal growth pressures and temperatures. In a, few cases growth was conducted in a silver tube s) contained within a similar autoclave. Acoustic Q was measured oy the infrared technique at 2.t;o rim (3500 c m :)') and was confirmed in some instances by acoustic Q loss meas~-arements on 5 MHz plates using the logarithmic decrement method6.7). Recently Sawyer s) has used both the logar/th~ic decrement and transmWsion 9) procedures to study the relationship between *'/:,rd "nfrared absorption.

-,.o 1

I 1 I I I I I I i I l - 2.O 0.4 0.8 1.2. 1.6 2'.O 2,4 E'~TINCTION COEFFICIENT (:It AT !,~Ou cm°1 (2.86/J.m)

Fig. 2. R e c i p r o c a l o f a c o u s t i c loss at 5 MiHz as a f u n c t i o n o f c x t i n c t i o n coeffi,:ient at 3 5 0 0 c m - ' (2,86 lain).

3. Results ~nd discussion

Table 1 lists the growth conditions and properties* of typical crystals. In all cases the percent baffle opening was 4 ~/o and the orientation unless otherwise indicate6 was 5 ° from the (0001) face ( + 5° X). The reciprocal relationship between acoustic Q at 5 MHz and the extinction coefficient at 3500 c m - 1 (2.8(5 ~tm) demonstrated in fig. 2 was used to determine the Q values of table 1. The a values of fig. 2 were measured at 2.86 I~m on polished specimens of varying thickness** using a Perkin-Elmer-257 spectrophotometer, while acoustic Q was measured by the logarithmic decrement method. As has been pointed out, at low Q's ~) there ;ends to be some departure from the reciprocal :'clatt~aship be* T h e Q values o f t a b l e I a r e a v e r a g e values. M ~ x i m u m and minimum Q's typically arc no n'ore than ~ 10% di~fe~nt from t h e avera[~e Q's, ** T r a n s m i u i o n s t u d i e s in s a m p l e s o f v a r i o u s thick;~ess verified t L a m b e r t ' s law.

THE G R O W T H OF HIGH A C O U S T I C Q QUARTZ. AT H I G H GROWTH RATES

3

Tsmta I Conditions of growth and properties of hydrothermaily grown quartz Run No.

Growth Pressure Temp. differential Per' Growth 0~ssoo Q H+ temp. (psD between growth cent rate (cm -x) ( x 10e) (ppm) (°C) and dissolving fill (mil/day). . . . . 'L .

zmm, AT('C)

X-450-2 X-455-2 X-469-2 X-475-2 LC-2434-12 LC-2583-12 LCo2630-12 LC-2632-13

Kerr

Remarks*

. . . .

350 348 350 352 350 352 352 352

21700 25300 31000 35000 25000 20000 20000 .21500

36 47 47 45 39 38 25 21

82 84 86 88 84 83 82 82

55 77 87 89 55 49 42 40

0.4641.0 0.60 0.68 0.212 0.07 0.066 0.06

0.65 0.15 0.22 0.195 !.08 1.5 1.3 1.5

37.5 83 49.8 56.4 17.6 6.05 5.48 5.0

6.6 14.6 8.8 0.95 3.1 1.06 0.965 0.67

Y,2 352 350 ~345

21300 40"/00 -12000

25 28 52 10

83 83 90 77

45 43 105 16

0.10~ 0.07 0.53 0.026

1.0 1.3 0.24 2.8

8.95 5.8 44 2.15

1.52 1.02 7.75 0.378

X-501-2 X-489-2 X-497-2 X-261-22 X-493-2 X-505-?

357 364 363 363 374 374

45000 36300 34100 28000 40000 40000

36 33 27 39 22 23

90 88 88 82.5 88 88

96 93 92 66 100 103

0.095 0.097 0.56 0.16 0.04 0.05

1.1 1 ~1 0.214 0.87 1.6 1.4

7.89 8,05 50 13.3 3.4 4.15

1.39 1.41 7.8 1.15 0.586 0.734

X-508-2

374

39300

22

88

104

0.107

1.0

X-440-3"** X452-3 X.487-2 SARP II, 39**

8.95

i.52

Some crevice flawing Some crevice flawing NaNO= not used NaNO2 not used NaNO= not used NaNO:~ not used; growth on "r" (10[1) face Growth on "r" face Growth 6n "r'" face Solvent 0.83 M NazCOa-k Li + salt Some crevice flawing Top seeds dissolved Solvent 1.2 M NaOH Some crevice flawing Number crystalsingrowth zone reduced in comparison with X-493-2 Some crevice flawing

* Unless otherwi~ noted basa ! plane or +5 ° X ,~¢d, 1.0 M NaOH+0.025 M Li=CO3+0.1 M NaNO2. ** We would like to thank Dr. D. B. Sawyer of Sawyer Research Products, Inc., Eastlake, Ohio, for this specimen. *** Silver tube run.

twcen a and Q but within the a~.~curacy of our present measurements we feel that no special importance can I~e attributed to this departure so that the points of fig. 1 were fitted to a straight line. In some instances, an expanded plot using a computer fit to the data was used for estimating the high Q's6). The proton concentrations of fig. 2 and table 1 were estimated assuming I o) a molar extinction coefficient of 77.5 l/mole cm for H +. All of the entries of table 1 atrove the line are for growth temperatures in the vicinity of 350°C. Those below the line are for higher temperatures. As can be seen, it is only at temperatures above 350~C, that rates above 90 rail/day (2.25 ram/day) and Q's above 10e are obtained, z ne lower ~ of X--497-2 m a y nmvc z-~rsu,~ from poor temperature control as evidenced by the fact that the ~eds in the upper part of the autoclave di,,solved. Attempt~ to achieve rates approaching 90 rail~ day by increasing the temperature difference between the dissolving and growth zones (AT) or the percent fill (with a ~ u l t a n t increase in pressure) result in Q's

below l0 s . Crevice flawing, that is, the growth of faceted dendrite-like quartz, was a problem in some runs. The data of table ! indicate that flawing seems more pronounced at high rates (due to high AT or temt'erature) when the fill is moderate. In laboratory si::,.ed 1 inch diameter autoclaves (the present commen:ial autoclaves are 6 inch and 10 inch diameter) where the surface area of quartz growing per unit volume of the gnu,wing zone is considerably less, we have found that raising the fill will often tend to repress flawingI ~). For this reason high temperature-high growth rate low fill conditions were hot investigated. However, flawing in runs X-493-2 and X-501-2 was surprising in view of the --..~..A~--A.'~I ~Ul[,7~|i[liiILIBi[

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'l'll,','dl,e*l'St 1.J,l'~lu~u~.

aCS wza

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constitutional supersaturation when the growth rate at the in:efface is so fast that the slower diffusion of solute causes a large concentration gradient. Consequently, its dependence upon experimental parameters might be expected to be rather complicated. As can be seen, high quality quartz (Q > 10s) can now be grown

4

N.C.

LIAS et

at conditions near 90 rail/day and (Run X-505-2) when the number of crystals in the growth zone is reduced somewhat so as to mitigate diffusion problems highQ-flawless quartz can be grown at rates over 100 rail/day (2..5 mm/day) at the conditions: crystallization temperature, 374 °C; AT, 23 °C; % fill, 88; pressure, 40000 psi (2759 bar). Thus, high rate-high quality quartz can now be grown at conditions well within the reach of commercial equipment at high enough Q's to be especially useful for most piezoelectric applications. It is now worthwhile, examining the details of the dependence of the partition of H + during hydrothermal growth. The entry of proton into the quartz lattice can be described by the reaction 2) (M+3)z-I-(H+)z ~ (H + • M+3)s ,

(1)

where (/) and (s) refer to the liquid and solid, re:~pectively, and the M +3 ions go to Si '~4 sites where they are compensated for by interstitial H + which enters the lattice as ( O H ) - . Reactions involving M + 2 ions can be ignored as insignificant contributors to charge compensation2). The principal charge compensating io~ q are AI +3 and Fe +3 from the natural Brazili:m lascas quartz nutrient. Quartz grown in a properly conditioned steel autoclave has optical loss at i.06 and 2.86 ~tm (the wavelepgths for Fe +2 and Fe +3 absorption, repectively) no different t h a quartz grown in a silver tube, showing that the rrincipa! source of Fe is the nutrient2). Na + from t, ~ NaOH mineralizer will also compensate M + ' but it~ eTect has been ignored. The equilibrium constant ~ ,r eq. (1) is

al.

effective and equilibrium distribution constants are related to one another in melt growth, i.e., by a treatment ~ analogous to that of Barton and Slichter 12.13), K K,ff =

K + (l - K ) e

-(~61D) ,

(4)

where ~ is the growth rate, ~ is the average diffusion layer thickness for M ÷ 3 and (OH)- and D is the average of the diffusion constants for M ÷3 and (OH)- in the hydrothermal medium. It has been shown 11) that the growth rate of quartz for a particular growth direction under hydrothermal conditions follows the equation ~hu ffi kal~ AS,

(5)

where k at is a velocity constant for a particular direction and obeys the Arrhenius equation, AS is the supersaturation, and a is a constant. Over small temperature intervals AS oc AT, the temperature difference between dissolving and erowth zoves, and over modest pressure intervals the effect of .ncreases in fill (pressure) on growth rate is to change the slope of the solubility-ten,perature curve, i.e., change AS. Now since in fig. 2 we established that Q ~ l/(H+h,

(6)

by substitution and rearrangement of eq. (3) 1 Q = K,.~.(M +'),_~(Ot-1),~"

(7)

If (OH)[ ano (M + 3)~ are kept constant,

(H + • M+a)s

K,

(M "3)~(H+)l'

(2)

where equilibrium activities havt been approximated by equilibrium concentrations. Since essentially all of the (H+)~ is associated with (M+3),,, (H+)~ ~_ (H+.M+3),, arid since the source of the proton is the (OH)- mineralizer, (H+)~ should be replaced with (OH)7. Now K~ is analcgous to an ordinary equilibrium distribution constanll in that we may define an eff"cdve equilibrium constant (H[ + • M + 3 ) s _ a

K t o r r = ( M ~'3 - , ' h-~(OH),_~

(3)

where the subscripts a indicate actu 4 ¢~,n~entrations. Kc~r will be related to K in the .~amc m~.:ner that the

Q = ~/KI.,f f

(8)

where fl is a constant. Substituting for K, ff from eq. (4) and rearranging:

[,+ By the use ofeq, (9) we may consider the possible effect of changes in experimental growth parameters on Q. The possible experimental changes which may be used to increase rate on a particular crystallographic face according to eq. (4) include: (I) Increase AT and hence AS; (2) Increase fill, hence pressure and AS; (3) Increase T and hence k.

THE G R O W T H OF HI~3H A C O U S T I C Q Q U A R T Z A T H I G H G R O W T H P.ATES

0.5

GROWTH RAI"E IN mm/OA. ",.0 1.5 Z.O 4.0

I/o OA

t0

100 t000 GROWTH RATE IN roll IDA.

40,000

Fig. 3. Effective equilibrium constant for (H +)t versus growth rate on + 5 ° X and r surfaces of quartz.

It is useful now to calculate KofVWe express concentrations in atoms/cm 3 (or its equivalent moles/I). (H+)o is easily calculated from the values of table I. (OH)~ is taken to be the initial molality of the hydrothermal solution*. The (M+3)~ concentration was taken to be equal to (Ai+3)I+(Fe+3) v It was assumed that all (Ai *'~) and (Fe +3) came from the fusing quality Brazilian quartz lascas used as nutrient. Typical analyses give 50ppm of each impurity in natural Brazilian quartzt4), assuming a typical solubility of 5 g/100 cm a for quartz at the condition of our experiments ! s) we estimated (M +~) as 1.5 x 10 -4 moles/l. The values of Ktff calculated on the above assumptions are summarized in ~able 1 and plotted in fig. 3. The K~ff = 48 asymptote of fig. 3 was calculated on the assumption that (H +). at high rate was limited by (Fe+3).+(Al+3). and that at high growth rates all of * The (OH)" will be depleted by reaction with SiO2 and so will be considerably less than the initial (OH)-. This e K ~ t will alter valuca of K,, only by a constant and can be ignored, in addition, ~OH)- will also be to ~ m e degree temperature dependent be. c a u ~ both the pertinent ionization constants and the solubility of StOa are temperature dependent. This effect has been ignored be,:ause preliminary estimates showed its magnitude to be an unimportant contribution to the observed changes in K,,-~. In one ~ase where a (CO.O" mineralizer was used, complete carbonate hydrolysis to (OH)- wa~ assumed in estimating the ( O H ) - concentration. This assumption s~vms valid because (H ÷), concentrations for quartz, grown from equi-nor,:ml (CO~)" and (OH)solutions appear comparable.

5

the Fe +3 and AI +3 in the nutrient would be incorporated in the grown quartz, that is, at high rates the concentration of M +3 in the grown quartz wouid be the same as in the nutTient. This is perfectly analogous to the high rate case i~' melt growth where the concentration of the impurky in the liquid and the solid becomes eqm'l. However, in the coupled substitution polycon:ponent growth situation which we have under present consideration, this does not result in Keff =-* 1.0, Any error in the magnitude of our impurity estimates for AI and Fe would be unimportant as long as the impurity levels were constant in our samples. As can be seen from fig. 3, the plot of log Kaf versus log,~ shows the typical "S" shaped dependence of the Burton and Slichter/~fts), with K,n approaching K1 at low ra+es, and Kaf approaching a value where the solid incorporales all available impurities at high rates. It should be noted that departures from this functional dependence occur only at temperatures above 350 °C where K, rr is uniformly lower than would be expected*. This is as would be expected if K~ decreases with temperature, Since there is a finite solubility of (OH) in SiO2, it is not unreasonable to expect the temperature dependence of thi~ solubility to be negative over some temperature range, Thus, the principal reason for our ob.~erved increase in Q is that as the temperature is rai~ed Kt is decrea.~ed. Kopp and Statt: t6) have recently pointed out that in the case of quartz grown from RbOH the absorption coefficients at 3500 cm- ~ and 3800 cm- t decrease as temperature is raised and that temperature increases will improye quality. In addition they present data suggesting that absorption coefficient is approximately linear with growth rate. We show elsewhere that the dependence ~7) of Kopp and Statts' absorption coefficient on growth rate is the same as that observed in this work and that at low growth rates the coefficient follows a Van 't Heft dependence on temperature as might be expected. A further consideration of eq. (9) and fig. 3 is worthwhile in under~,tanding the ett-ect of AT and fill on Q. * The important result of this, of course is that (H ~), is low aJld Q is high ~r~ t h e e coaditions. It is interesting to point out that no d e p a r t u ~ from the " S " shaped functional dependence occurs in several instances where the s ~ d orientation was an " r " face (IOI l). Thus the overriding variable is growth rate and its effect on diffusion. Differences, if any, in the structure of adsorbed layers on the growing faces must be negligible.

6

N.C.

LIAS et al.

(a) An increase in AT will effect only ~ and fi in eCi. (9) increasing both so as to increase Kcff and decrease Q. An examination of the data of table 1 and fig. 3 confirms that a AT increase raises Kaf and lowers Q. 03) Ir~creasing till besides increasing ~ , raising Kefe and lowering Q might be expected to also increase (d~p/dT)*, the temperature coefficient of fluid density with temperature, so as to increase convective circulation, decrease fi and K, cf and increase Q. In addition, an increase ir~ fill and pressure would be expected to shift eq. (1) to the right, i.e., increases Kl, increase (H +)~ and decrease Q. Which of these effects would be overriding cannot be ew:luated without detailed knowledge of the appropriate constants. However, examination of table 1 shows that increases in fill have a negli~ble effect on Q suggesting that the effe:t on 6 apparently cancels the effect on ~ and K. (c) Increasing T will, of course, increase ~ with an ir~tcrease in Kaf and an adverse effect on Q. If, however, as mentioned above the slope of the solubility curve of (H+)~ in quartz is negative, then increasing T will dec:t~ease K~ and (H +)~ and increase Q. The data of fig. 3 shows that the effect of temperature on K~ is overriding. 4 Conclusions

High temperature growth probably because of retrog'ade H ÷ solubility in quartz favors high Q. At 374 "C a Q of > 10 6 at a rate of > 100 mil/day (2.5 mm/day) ~.m be obtained. Effective equilibrium constants analog3us to effective distribution constants in monccomponent growth are applicable to the partition of H + between the solid and the solution. Other impurities in quartz, such as Ge +4 seem t 7) to have a K~ft which follow the Burton-Slichter depend* Effect:, of p and T on D are negligible in comparison with the effects ofp and T on other variables.

ence on ~ and it would be reasonable to expect our treatment to be generally applicable to solution growth and other polycomponent growth. Acknowledgments We would like to thank J. R. Carruthers for discussions and D. R. Fredrick of AutocLave Engineers for his design of the laminated construction autoclave. We would also like to thank F. T. Coder for his interest throughout this work. References I) D. M. Dodd and D. B. Fraser, J. Phys. Chem. Solids 26 (1965) 673. 2) E. D. Kolb, D. A. Pinnow, T. C. Rich, N. C. Lias, E. E. Grudenski and R. A. Laudise, Mater. Res. Bull. 7 (1972) 397. 3) J. C. King, A. A. Ballman and R. A. Laudise, J. Phys. Ch,'m. Solids 23 (1962) 1019. 4) A. A. Ballman, R. A. Laudise and D. W. Rudd, Appl. Phys. Letters 8 (1966) 53. 5) A. A. BaUman, D. M. Dodd, N. A. Kuebler, R. A. Laudiseo D. L. Wood and D. W. Rudd, Apr, l. Opt. 7 (1968) 1387. 6) D. W Rudd, E. E. Houghton and W. J. Carrol, Western Electric Engineer (Jan. 1966) 22. 7) J. C. King, Fundamental S'udies of the Properties of Natm al and Synthetic Quartz, 10 June 1960 (Contract DA-36-039SC-64586). 8) B. Sawyer, Trans. Sonics and Ultrasonics IEEE SU 9 (1972) 44. 9) R. A. Heising. Quartz C'r),staL~.[or Electrical Circuits (Van Nostrand, New York, 1946) p. 488. 10) D. M. Dodd and D. B. Fraser, J. Appl. Phys. 37 (1966) 391 !. !!) R. A. Laudise, J. Am. ('hem. Soc. 81 11959) 562. 12) C. D. Thurmond, in: Semiconductors, Ed. N. B. Hannay, (Reinhold, New York, 1959) p. 165. 13) J. Burton and W. P. Slichter, in: Transistor Technology, Vol. 5, Eds, H. E. Bridgers, J. H Scarf and J. N. Shive (Van Nostrand, Princeton, 1958)oh. 5. 14) R. A. Laudise, A. A. Ballman and J. C. King, J. Phys. Chem. Solids 26 (1965) 1035, 15) R. A. Laudise and A. A. Ballman, J. Phys, Chem. 65 (1961) 1396. 16) O. C. Kopp and P. A. Statts, J. Phys. Chem. Solids 31 (1970) 2469. 17) R. A. Laudise, in: Proc. IVth All-Union Crystal Growth Conf., to be published.