US2440694A - Piezoelectric crystal apparatus - Google Patents

Description

May 4, 1948. R MASON 2,440,694

PIEZOELECTRIC CRYSTAL APPARATUS Filed April 4, 1946 //v l E/VTOR W P MASON Patented May 4, 1948 UNITED STATES PATENT OFFICE PIEZOELECTRIC CRYSTAL APPARATUS Warren P. Mason, West Orange, N. J assignor to Bell Telephone Laboratories, Incorporated, New York, N. Y., a corporation of New York Application April 4, 1946, Serial No. 659,468

1'7 Claims. 1

This invention relates to crystal apparatus and particularly to piezoelectric crystal elements comprising di-potassium tartrate hemihydrate (KzC4I-I4Ot- (H20)). Such crystal elements may be used as frequency controlling circuit elements in electric wave filter systems, oscillation generator systems and amplifier systems. Also, they may be utilized as modulators, or as harmonic producers, or as electromechanical transducers in sonic or supersonic projectors, microphones, pick-up devices and detectors.

One of the objects of this invention is to provide advantageous orientations and modes of motion in crystal elements made from synthetic crystalline di-potassium tartrate hemihydrate. 7

Other objects of this invention are to provide crystal elements comprising di-potassium tartrate hemihydrate that may possess useful characteristics, such as efiective piezoelectric constants and minimum coupling of the desired longitudinal mode of motion to undesired modes of motion therein.

A particular object of this invention is to provide a di-potassium tartrate hemihydrate crystal element having a zero or nearly zero coupling between the longitudinal lengthwise mode of motion and the face shear mode of motion therein.

Di-potassi-um tartrate hemihydrate is a salt of dextrotartaric acid having a molecule which lacks symmetry elements. In its crystalline form, it lacks a center of symmetry and belongs to a crystal class which is piezoelectric and which in this instance is the monoclinic sphenoidal crystal class. By virtue of its chemical structure, di-potassium tartrate hemihydrate will form ionic and hydrogen bonded crystals offering high piezoelectric constants. In addition, the crystalline material affords certain cuts with l w coupling to other modes of motion therein, and a fairly high Q or low dielectric loss and mechanical dissipation.

Crystal elements of suitable orientation cut from crystalline di-potassium tartrate hemihydrate may be excited indifferent modes of motion such as the longitudinal length or the longitudinal width modes of motion, or the face shear mode of motion controlled mainly by the major face dimensions, or the thickness shear mode of motion controlled mainly by the thickness dimension. Also, low frequency fiexural modes of motion of either the Width bending flexure' type or the thickness bending flexure duplex type may be obtained. These various modes of motion are similar in the general form of their motion to those of similar or corresponding names that are already known in connection with other crystalline substances such as quartz, Rochelle salt and ammonium dihydrogen phosphate crystals.

It is useful to have a synthetic type of piezoelectric crystal element having a low or zero coupling to other modes of motion therein. In accordance with this invention, such synthetic type crystal cuts may be provided in the form of tartrate crystals and the tartrate crystals may be suitable cuts taken from crystalline di-potassium tartrate hemihydrate adapted to operate in a face longitudinal mode of motion. Such crystal elements cut from di-potassium tartrate hemihydrate may have advantageous elastic properties whereby the longitudinal mode of motion therein may be free from coupling or interference with the face shear mode of motion therein, or the face shear mode of motion may be free from coupling with other modes of motion therein.

In accordance with this invention, the crystal elements cut from the crystalline di-potassium tartrate hemihydrate may be Z-cut type crystal elements having their major faces perpendicular or nearly perpendicular to the Z or c axis and operating in the longitudinal mode of motion along the longest or length dimension thereof, the length dimension being inclined at an angle 0 of about +52% degrees with respect to the +X or +a axis. Where the angle 0 is an angle in the region from +30 to +45 degrees, a zero temperature coefiiclent of frequency may be obtained at ordinary temperatures, as disclosed and claimed in my copending application for Piezoelectric crystal apparatus, Serial No. 646,639 filed February 9, 1946. Where the angle 0 is an angle between +22 and +53 degrees, the piezoelectric coupling is of high value at all such 0 angles, and has its maximum value at the 0 angle of about 45 degrees. As disclosed in my application referred to above, the temperature at which the zero temperature coefiicient of frequency occurs for the longitudinal length mode of motion varies according to the value of the angle of selected, and is at about +16% degrees centigrade for a 0 angle of about 45 degrees at about +30 degrees centigrade for a 0 angle of about +37 /2 degrees, and at a value of about -45 degrees centigrade for values of 0 angles in the region of +52 /2 degrees. The coupling of the longitudinal length mode of motion to the face shear mode of motion in crystal elements having the 0 angle of about +52% degrees is zero, as disclosed and claimed in the present application.

The synthetic tartrate crystalelements pro,- vided in accordance with this invention have a high electromechanical coupling of the order of 20 to 25 per cent, have a high reactance-resistance ratio Q at resonance, and a small or zero coupling of between the longitudinal length mode of motion and the faceshear mode of motion therein. These advantageous properties together with the low cost freedom from} supply troubles indicate that these cr stal ele ments may be used as circuit elements in'cryst-a filters and oscillators. 7 electromechanical coupling existing in these crystals allows the ,circuitfrequency to be varied in much largeramounts by,a reactanoe tube, than canbe done forthe. frequency of quartz, such tartrate, crystal cuts maybe advantageously. used for frequency modulatingan oscillation generator;

The tartrate crystal elements provided in accordance with thislinvention may be especially useful in filter systems for example. Elorus'e in channel filters for example, the..electro-mechanical coupling in these crystalelementsisso high that regular channel .widthsof about 3600cycles per second for example may banbtained without the use of auxiliarycoils.fonfrequencies as low as 60 ,to 100 kilocycleaper secondfor example. Accordingly, such .a crystal channel filter may. be produced more cheaply'and put intoa smaller space than onewhich is usedwith bulky. and expensive .coilsand condensers, When such crystal filters .areto beparalleled, a terminating:net.- worlr; comprisingcoils and condensers-may be used therewith in order, to, obtain no paralleling loss; on terminating; resistances may be -used therewith and the .1paralleling loss made up forty anadded stagepf, amplification, 'The tartrate crystal elements provided in accordance with this invention have a low ratio of capacitiesand ac.- cordingly; may berused in wide-band filters suchas for example in program .fi-lters, where the .tartrate type crystal element may beused to con trol the loss peaks located atsomedistanceffrorn the. passband, while. using, quartzcrystalsforthe sharpest peaks nearestthegpass band. The .tartrate crystal elementsdn accordancewith thisin vention have high coupling and aeeordingly may be ,used to extend the rangeof ;.cryst a l filters to lower frequencies than have been obtainedin the past. For exampl .,-,v0i6 channels down to about 12 kilocycles-per secondorless-may be obtained usinga flexure mode tartratecrystal element, the flexure modesbeing. obtainedby methods presently used in connectionwith quartz crystal elements. The. tartrate; crystal elements provided in accordance-with this inyen tion -may also e used cr n ro of re uencrmo u t d cillators. Qnaccountof the large electromeh mical; c u i g,v he fre u ncy. va t on. a hi t my be mad ozbe l rger c ue nd m y e on ro led br n-arm d d rect c rr n olta e .0 b a ui blereacta ev u for; exampl F r lea er.- nd an...:ns h ;-na:t e this invention and the additional advantages, f ea- Moreover, since the high 4 tures and objects thereof, reference is made to the following description taken in connection with the accompanying drawings, in which like reference characters represent like or similar parts and in i which:

Fig. 1 is a perspective view illustrating the form and growth habit in which a monoclinic crystal of di-potassium tartrate hemihydrate may be crystallized, and also illustrating the relation of the surfaces of the mother crystal with respect to the mutually perpendicular X, Y and Z axes, and the crystallographic a, band 0 axes;

Fig. 2 isanother .view illustrating the rectangular X, Y and Z and the crystallographic a, b and 0 systems of axes for monoclinic crystals, and also illustrating the plane of the optic axes of di-potassiurn-tartrate hemihydrate crystals; and

Fig. 3, is aperspective View illustrating longitudinal-anode-Z-cut type di-potassium tartrate hernihydratacrystal elements rotated in effect 7 about the Zor c axis to a position corresponding to anangleof-=about+52 degrees with respect to the X axis.

This specification follows the conventional terminolo y, as. ppl dto piezoelect ic crystalline substan s. which mploys as stem of threemutuallyperpendicularX, Y andZ; axes asreference, axes for definingihe angular orientation of a crystal element. As ,used .in. .this specif cation and as shown in jtheclrawing, theJZ axis corresponds to thecaXistheY axis corresponds to the b axis, and theX lXIiS'is inclinedat an angle with respect totheo axiswhich, in the case of crystallinev di potassiurn tartrate hemihydrate, is a small angle of about ,5l, m inutes., Thecrystallographic a, band 0, axesrepresent conventional terminology as used by ,clystallographers,

Referringto the,.drawing, F-ig.,1gis a perspective View, illustrating, thegeneralform and-growth habit in which ,diepotassium tartrate. hemihydrate maycrystallize, thenatural faces of the dipotassiurn tartrate, hemihydratecrystal I, being designated iaFig. .1 in --terms of conventional terminology as, used-by crystal ographers. For example, thetopsur'faceof the crystal body l is designated as a 001 plane, and the bottom surface thereof-as,a-00-l;plane, and other surfaces cr et a e e h n E s The mother :crystal'l, as illustra-ted in Fig. 1, may srownhomero m-table nutrient solution 1 by suitable crystallizes apparatus or met od. he u ri n e uticn sed: for r in he y a b i a' ren redr r m anysuitable chemical substances-and, thecrystahl being grown from such nutrient solution in any suitable mannor a n-smother c ysta l of :a: s e and pe that s su tabl r-fo cutt nather m pie oelectri crystal elements in accordance with this invention, Themothe ystalJ fro-rn wh-ich the crystal elements are.;-to--be cut is-relatively easy to growin -shapesandsizes-that are suitable for cu t ng se l. r sta p atesr--el me tshe from. Such;mothercrystal, rmay be conveniently grown to. sizesaround ;2 inches orimore for the X and Y dimensions or,o-. -ar;1;ysuiiicient size t u t he desi eder ize. r e iezoe ct cuit elements that are tobecut therefrom. It will be unde stood hat he m the cr st I ay be grown; to size-by any. suitable, crystalliz er appaa u -suc a orxexemm s ar c ne ta k t pe ry ia l r- 5 esipm et ng: tar syr n rystal-1 er..-.

.- ta1. 1 compr in ii-potassium tart ate monoclinic sphenoidal class of crystals which has as its element of symmetry the Y or b crystallographic axis, the-Y or b axis being an axis of binary symmetry. There are four dielectric constants, eight piezoelectric constants and 13 elastic constants involved in such crystalline material. Di-potassium tartrate hemihydrate crystals l have /2 molecule of water of crystallization, as compared to 4 for Rochelle salt crystals. As a result, the water of crystallization is much more tightly bound for crystals of di-potassium tartrate hemihydrate than those of Rochelle salt. When held at about 80 degrees centigrade, there appears to be no observable dehydration of the crystalline di-potassium tartrate hemihydrate; but at about 150 degrees centigrade the vapor pressure of the crystal reaches atmospheric pressure and will cause bubbling that may be observed in an oil bath. If the di-potassium tartrate hemihydrate crystal is placed in a sealed container that is evacuated or filled with dry air, it will give off enough moisture to establish its equilibrium vapor pressure, which may be around per cent relative humidity, and it will be stable from then on. Sudden changes of temperature do not appreciably affect the crystal l since the stable relative humidity at room temperature is so low.

Di-potassium tartrate hemihydrate crystals l have three cleavage planes'which lie along the three planes determined by the three crystal-lographic axes a, b and 0. While such cleavage planes may make the crystals 1 somewhat more difiicult to cut and process, nevertheless satisfactory processing may be done, as by using a sanding or abrasive belt cooled by oil or by a solution of water and ethylene glycol, for example.

As illustrated in Fig. 1, monoclinic crystals l comprising di-potassium tartrate hemihydrate are characterized by having two crystallographic axes b and c, which are disposed at right angles with respect to each other, and a third crystallographic axis a which makes an angle different than 90 degrees from the other two crystallographic axes b and c. The c axis lies along the longest direction of the unit cell of the crystalline material. The b axis is an axis of two-fold or binary symmetry. In dealing with the axes and the properties of such a monoclinic crystal 1, it is convenient and simpler to use a right-angled or mutually perpendicular system of X, Y and Z coordinates. Accordingly, as illustrated in Fig. l the method chosen for relating the conventional right-angled X, Y and Z-system of axes to the a, b and 0 system of crystallographic axes of the crystallographer, is to make the Z axis coincide with the c axis and the Y axis coincide with the b axis, and to have the X axis in the plane of the a and c crystallographic axes at an angle with'respect to the a axis, the X-axis angle being about 51 minutes above the a axis for di-potassium tartrate hemihydrate, as shown in Fig. 1. The X, Y and Z axes form a mutually perpendicular system of axes, the b or Y axis being a polar axis which is positive by a tension at one of its ends, as shown in Fig. 1. In order to specify which end of the Y axis is the positive end, the plane of the optic axes of the crystal I may be located. A monoclinic crystal 1 is an optically biaxial crystal and for di-potassium t-artrate hemihydrate the plane that contains these optic axes is found to be parallel to the b or Y crystallographic axis and inclined at an angle of about 21 degrees with respect to the Y axis, as illustrated in Fig. 2.

Fig. 2 is a diagram illustrating the plane of the 6 optic axes for crystals l comprisin (ll-potassium tartrate hemihydrate. As shown in Fig. 2, the plane of the optic axes of a di-potassium tartnate hemihydrate crystal l is parallel to the Y or b axis,

, which in Fig. 2 is perpendicular to the surface of the drawing; and is inclined in a clockwise direction at an angle of about 21 degrees from the +0 or +2 crystallographic axis. Since the +X axis lies at a counter-clockwise angle of degrees from the +0 or +Z axis, and the +b=+Y axis makes a right angle system of coordinates with the X and Z axes, the system illustrated in Figs 1 and 2 determines the positive directions of all three of the X, Y and Z axes. Hence the positive directions of all three X, Y and Z axes may be specified with reference to the plane of the optic axes of the crystal I A similar optical method of procedure may be used for orienting and specifying the direction of the three mutually perpendicular X, Y and Z axes of other types of monoclinic crystals. Oriented crystal cuts are usually specified in practice by known X-ray orientation procedures.

Fig. 3 is a perspective view illustrating a crystal element 2 comprising di-potassium tartrate hemihydrate that has been cut from a suitable mother crystal l as shown in Fig. 1. The crystal element 2 as shown in Fig. 3 may be made into the form of an elongated plate of substantially rectangular parallelepiped shaped having a longest or length dimension L, a breadth or width dimension W, and a thickness or thin dimension T, the directions of the dimensions L, W and T being mutually perpendicular, and the thin or thickness dimension T being measured between the opposite major or electrode faces of the crystal element 2. The length dimension L and the width dimension W of the crystal element 2 may be made of values to suit the desired frequency thereof. The thickness or thin dimension T may be made of a value to suit the impedance of the system in which the crystal element 2 may be utilized as a circuit element; and also it may be made of a suitable value to avoid nearby spurious modes of motion which, by proper dimensioning of the thickness dimension T relative to the larger length and width dimensions L and W, may be placed in a location that is relatively remote from the desired longitudinal mode of motion along the largest or length dimension L.

Suitable conductive electrodes 4 and 5 may be provided adjacent the two opposite major or electrode faces of the crystal element 2 in order to apply electric field excitation thereto. The electrodes 4 and 5 when formed integral with the faces of the crystal element 2 may consist of gold, platinum, silver, aluminum or other suitable conductive material deposited upon the surface of the crystal element 2 by evaporation in vacuum or by other suitable process. The electrodes 4 and 5 may be electrodes wholly or partially covering the major faces of the crystal element 2, and may be provided in divided or non-divided form as already known. Accordingly, it will be understood that the crystal element 2 disclosed in this specification may be provided with conductive electrodes or coatings 4 and 5 on their faces of any suitable composition, shape, and arrangement, such as those already known in connection with Rochelle salt or quartz crystals for example, and that they may be nodally mounted and electrically connected by any suitable means, such as for example, by a pair of coaxial pressure type clamping pins or by conductive supporting spring wires 6 each cemented by a spot of cononeness.-

Elective. Ceme t V1. to the pective metallic. coat.- n l .4; and 5: pos ted 1. on theo fital;element-. as; already. kno n. connection With one z; och l e salt and; th r ystals. hav nasim a or. corresp n in on it di l mo es: of motion As i lustrated inFi 7 nearly; perpendicular to the Z;;or caxis and has espect to th r +a-ax s ein very: nea to th a. a i

+X; axis; as particularly illustrated in Fig; 3, ho tal, element 2. has; a la g Piezoelectric ouplin a r em erat co ifi ient f; i equ y ab 45 de esnti ad for. its longitudinal modeof motionalong the length;

dimension L, and at that angleofabout 529/; degrees the mechanical coupling of that longitudinal mode of motionto-the, face shear mode of;-m 0tion therein is Zero; At angles of 0. above andhelow' about 52% degrees, the piezoelectriccoupling is of efiective Values, the mechanical coupling of the longitudinal length L mode, of

motion to, the face shear and'other modes of motiontherein is small, andthe position oi" the, temperature at which thezero temperature coeificient of frequency occurs for the longitudinal length L mode of motion is raised or loweredaccprding to the angle of 0 selected;

ItxWill be noted that the, naturaltopand- bottom surfaces 001 and 001 respectively-of the.

mother. crystal 1 of Fig. 1 extend in the plane.

of the a and b-axes which consequently has -a normal which makes an angle .of about 51 minutes. from the Z ore axis, as illustratedin Figs. land 2. For practical purposes and ease -in processing, the major faces of the crystal element 2?.1I1Z1Y1fOHOW the natural (1 axis and b axis surfacedirections of the mother crystal I, in which case .they willnot be quite perpendicular to the Z.-'and c. axisby the, angleof about 51 minutes. However, they properties ofthe crystal element 2 do not. vary much with such a. small changewin the. orientation angle. Accordingly, the crystal element 2 of Fig. 3 may have itsmajor faces nearly perpendicular to the Z axis. andin the plane formed by the crystallographicaxesaand As-particularly illustrated in Fig. 3, the length or longest dimension .L of the major faces or". thecrystal element 2 lies substantially in the plane of'theX and Yaxes and is inclined at anlangle ofabout-+52 /2 degrees with respect to the +2 axis; The width dimension W of the majorfaces oi -the crystal element 2 being perpendicularto the -length dimension L thereof will make an angle of about 52% degrees with respect-to the Y axis. The thickness dimension T. extends along or nearly along theZor c axis. The elece trodes s and 5 disposed adjacent theopposite major-faces of the crystal element 2 provide an electric field in the direction of the thicknessdi: mension- T of the crystal element 2.:thereby pro.-. ducing a useful longitudinal mode of motion along-the length dimension L ofthe crystal. element '2'With high piezoelectric or high electromechanical coupling'and a low mechanical cou-v pling-to the face shear mode ofrmotion therein.

Thedimensional ratio of the width dimension W with respectto the length dimension L' of the crystal-element 2 maybe madeof any suitable- 3, the crystal element-, as ts. ma or fa s disposed p pendi ularvalueinathe re ion-Je s tan -7; o exam l n as norti u a lr d 6fibedi he einmar e made of the: order; or; abo t 0.5 or nsit di a length mode c rstalieleroentol. he smaller-va ues-of he:dimens onali a so he WidthEW with'r spect; to; the len th: L5. as.- o the der- -5 moreorless; have-the e ect- OKSPaQine-the widt W modegohmotion-atajreguency; which is remote: rom; the; undamental lo g t d nal mod of.- m tion: along the -.1en th m n ion-L.-

When-t e x t olementi is op ated th fundament 1;. ong ti di a1 m derof, motion along the; len th dimension-L L thereo t e. nodal line ocssiirai.atvv th center: of andren ve se: t t ength im n ion oft eorystal ielemontz about midw yybetw nth r opposite sme l ends th o and the crystal1element}may-bewthere mounted ndri leotrioally: connected y an uitable e ns. so 'h: s;by ner. more pairs of op os te Sprin Wire w i h. may lo cemented to: the metallic oatin s; 4 and. 5: the. no al: i n- T of: t

rlstal.:. lem ntz ,zi

Whi e. ha r sta e emont Z is pa t lar y esor beti;h rein sbe n perat d in t e; funda.-

ment llongituoinal; mode, of motion along its ensthoim nsionh itwili aheiunderstood that. it

ma be operated in any even or odd order-sharm nio ho. o :in-a.known. mannenbr means of: a plura ity f pa rsloftonposite interc nn cted elecodess naoed: a n the l n th-L t ereof Als f .-desired,.;the; rystal le ent 2;-.may-;he.- p rated imul aneouslyin he-lon tud n len h Lan width -modos.- t motion-by: a ran ement s di closed o xamr le in W. P.. Mason-PatentzNol ,292 85, dated Aueustll; 9.4.2; or simu taneoujs -.th.e.-1onsit dina; en th-L mode of, ouandt ewidthw flexur mode fm ti n by arrangements as. isolo ed' orre amp einiW P. MasomPatent N 2,'292,88. .datedAusust:

The electrodehoatings 41 and;v 5 :disposed adjacent thetopnosit imaio fa s :05 the r stalelee it-2; prov de anelectriofield in he-senemldie t on .of thozthi kness.d mension T: o h =Q 5" tal; e1ement;2-.;- thereby: producin a u efu 1oneitudinal; modeioi; m tion alon the: n t mensionhoI the crystol..; 1ementc22wi ha h h electromechanica couplin elicit. a: low or: e o. moohanioal-coup h zit rth qfaoo h ar mod of motion. therein;.. ae is hown: hr t e: fre uenc nectrumro. ;a;.l 2; /2 de ree ,Z- out :o'i-p a s u tartrate h.omihrdrato. crystal elem nt of Flieforwarious dimensional; ratios ither wi th W with-.I8.SPe t;to;;:the ylength L within e ra e between abo i:0..1:5,:and;0 .65 for example. The main modesoi =motiontwhich1is; the .iu ament iongitudinarmodeloii b at on alon the len th dimension; has equen y. onstant whi varies. fromabout ,1560 to;lilo kilocyclespersecndper centimeterrofi; th ns.t.hj d m ns n dependin -uponzthet.dimensionaL ot o f' w t W; tolensthzll selecte -1 h s; a an e l a 2%;deeree4 cutmrystai elementfi hav ng a len h di ensiontI-i .oeo ez ent m enand a dimensional-;ra tio;ot;width W-to length-Lv of about 0.5;"'Wi ;:h@.V6: s i t finfiy oiiabout ;1, 5. o y.o per secondi nitsifunda ontal longitudinal mode or. motion 1 nar h len t m n o L- A similar o eZ out c ys a element 2 haying; a; length dimension .-L. of another value re p ndin a reou n yi io va the; lengthdimension L. ,,m, de.: otimotion has no coupling to the main, length L longitudinal mode ofv motionat the 10-. anslegot about +5 de r es.

9. At a dimensional ratio of width W to length L of around 0.5, for example, the main length L longitudinal mode of motion has a ratio of ca pacities around 19.5 to 20, while the secondary face shear mode of motion has a ratio of capacities of around 5,000 to 10,000. The efiect of the secondary face shear mode of motion on the main length L longitudinal mode of motion is negligible.

The still higher frequency secondary modes of motion are related to the width W longitudinal mode of motion and are,'for a +52% degree Z cut crystal element 2 having a width dimension W equal to about one-half of its length dimension L, disposed above twice as high in frequency as the frequency of the main longitudi nal mode of motion along the length dimensional L, anddo not produce any troublesome interference therewith.

The longitudinally clamped dielectric constant of Z cut type di-potassium tartrate hemihydrate crystal elements 2 over a temperature range from 80 to +100 degrees centigrade is of the order of 6.0 expressed in .centimeter-gram-seconds (c. g. s.) units. f

A feature of special interest is that at the angle of about +52% degrees, the crystal element 2 has a longitudinal length L mode of. motion that has no coupling to the face shear mode of motion, and accordingly corresponds, in respect to the feature of freedom from coupling effect,

to the 18.5 degree Xcut'quartz crystal element:

of W. P. Mason et a1." United States 'Patent 2,173,589, dated September 10, 'i939, and 'to-the 42 degree 26' Y cut Rochelle salt crystal element Of W. P. Mason United States Patent. 2,292,885, dated August 11, -1942,'Figl 2. It will be under stood that a coupling between the le'ngth -L'1ongitudinal mode of motion andthefac shear mode of motion produces an 'extra resonance which is often undesirable for filter purposes. The cause of the coupling between the longitudinal length L mode of motion and the face shear mode of motion is the shear-longitudinal elastic constant. In this case, since the length L longitudinal motion is along the X axis and the face shear motion is in the XY or XY' plane; the shear coupling constant is 3'16, and vanishes when the 6 angle is in the region of +52% degrees, with respect to +X axis as illustrated in Fig. 3. -f

It will be noted that'the 0=+52% degree Z cut crystal element as illustrated in Fig. 3 is an orientation for which the frequency variation -'is such over ordinary room temperature ranges as to be useful for example in filter systems, and that the low or zero coupling therein with undesired modes of motion together with the high electromechanical coupling, the high Q, the ease of procurement and the low cost of production are advantages of interest for use as circuit elements in electrical systems generally.

Although this invention has'been described and illustrated in relation to specific arrangements, it is to be understood that it is capable of application in other organizations and is therefore not to be limited to the particular embodiments disclosed.

What is claimed is:

1. A Z-cut type di-potassium tartrate hemihydrate crystal element having its major plane section disposed substantially perpendicular to the Z axis, the lengthwise axis dimension of said i 10 +X axis to obtain substantially zero coupling between the longitudinal motion along said lengthwise dimension and the shear motion in said major plane section.

2. A Z-cut type di-potassium tartrate hemihydrate crystal element having its substantially rectangular major plane section disposed substantially perpendicular to the Z axis, the lengthwise axis dimension of said major plane section being inclined at an angle of substantially +52% degrees with respect to the +X axis to obtain substantially zero coupling between the longitudinal motion along said lengthwise dimension and the shear motion in said major plane secion.

3.A Z-cut type di-potassium tartrate hemihydrate crystal element having its major faces disposed substantially perpendicular to the Z axis, the lengthwise axis dimension of said major faces being inclined at an angle of substantially +52% degrees with respect to the +X axis to obtain substantially zero coupling between the longitudinal motion along said lengthwise dimension and the shear motion in said major faces.

4. A Z-cut type di-potassium tartrate hemihydrate crystal element having its substantially rectangular major faces disposed substantially perpendicular to the Z axis, the lengthwise or longest axis dimension of said major faces being inclined at an angle of substantially +52% dees with respect to the +X axis to obtain substantially zerocoupling between the longitudinal motion along said lengthwise dimension and the shear motion in said major faces.

- 5.'Piezoelectric crystal apparatus comprising a di-potassium 'tartrate hemihydrate crystal element havingmajorfaces, said major faces being disposed substantially perpendicular to the Z axis, the lengthwise'ax'is dimension of said major faces being' inclined at an angle of substantially +52% degrees with respect to the +X axis to obtain substantially zero coupling between the longitudinal-i'notion along said lengthwise dimension and the shear motion in said major faces, and means comprising electrodes disposed adjacent said major faces for operating said crystal element in said longitudinal mode of motion along said lengthwise dimension of said crystal element.

6. Piezoelectric crystal apparatus comprising a di-potassium tartrate hemihydrate crystal element having substantially rectangular major faces, said major faces being disposed substantially perpendicular to the Z axis, the lengthwise axis dimension and longest edges of said major faces being inclined at an angle of substantially +52% degrees with respect to the +X axis, to obtain substantially zero coupling between the longitudinal motion along said lengthwise dimension and the shear motion in said major faces, and means comprising electrodes disposed adjacent said major faces for operating said crystal element in said longitudinal mode of motion along said lengthwise dimension of said crystal element, the ratio of the width dimension of said major faces with respect to said lengthwise dimension thereof being one of the values less than 0.7.

7. Piezoelectric crystal apparatus comprising a iii-potassium tartrate hemihydrate crystal element having substantially rectangular major faces, said major faces being disposed substana y perpendicular to the Z axis, the lengthwise axis dimension and longest edges of said major facesbeing inclined at one of the angles from substantially +50 to +55 degrees withlrespectto the +Xaxis to obtain substantially zero coupling between the longitudinal motion alongzsaid lengthwise dimension and the shear motion in saidmajor faces, and means comprising-electrodes disposed adjacent said major faceswfor operating said crystal element in said 'longitudinal mode of motion along said lengthwise dimension of said crystal element.

8. Piezoelectric crystal .apparatus comprising a dipotassium tartrate hemihydratecrystal-element having substantially rectangular major. faces, said major faces being disposed substan tially perpendicular to the Z axis. thelengthwise axis dimension and longest edges of said major faces being inclined at one of the angles from substantially +50 to +55 degrees with respect to the +2! axis to-obtain substantially no coupling between the longitudinal-motion along said lengthwise dimension and the shear motion-in said major faces, and means comprising :electrodes disposed adjacent saidzmajor-faces-for operating said crystal element in-said longitudi nalmode of motion along said lengthwise di mension of said crystal element, the ratio of the width dimension of saidrmajor faces with respectto said lengthwise dimension thereofibeingone of the values less than 0.7.

9. Piezoelectric crystalapparatus comprising -a dipotassium tartrate hemihydrate crystal. ele-- ment having substantially rectangulan. major faces; said major faces beingdisposed substantially perpendicular to the Z axis, the lengthwise axis dimension-and'longestedges of said-major faces being inclined atone of: the angles from substantially +50 to +55 degrees with. respect.

to-the +X axis to obtain substantially -no cou-. pling between .the fundamental longitudinal.motion along said lengthwise dimension *andl:the shear motion in saidmajor faces; and means comprising electrodes disposed adjacent. said major faces for operating sald.crystal element. in said fundamental longitudinal mode of rum-- tion along said lengthwise dimension. ofwsaid crystal element.

10. Piezoelectric crystal apparatus comprising a di-potassinmtartrate hemlhydrate crystalele-- ment having substantially rectangulan major faces, said major faces being disposed substantially perpendicular to the Z axis, the lengthwise axis dimension and longest edges of saidmajor [aces being inclined at one of the-angles from substantially +50 to +65 degrees with respect to the +3: axis to obtain substantially no coupling between the fundamental longitudinal motion along said iengthwise dimension and the shear motion in said major faces, and means comprising electrodes disposed adjacent said majorfaces for operating said crystal element in said-fundamental longitudinal mode of motion along said lengthwise dimension of said crystal element, the ratio of the width dimension of. said-major faces with respect to said lengthwise dimension there, of being one of the values lessrthan 0.7.

11. Piezoelectric crystal apparatus comprising a-di-potassium tartrate hemihydratem'ystal element having substantially rectangular: major faces. said major faces being disposed substan tially perpendicular to theZ axis. the. lengthwise axis dimension and longest .edges of 'saidtmajor faces being inclined at one of the angles from substantially +50 to +55 degrees wlthrespect to the +X axis to obtain substantially no coupling between the longitudinal motion-along said lengthwise dimension andthe shear: motion in said major-faces. and :means comprising electlOdESEidl-SIJOSBG. adjacent-said major faces for operating-said crystal element in said longitudinalimode of motion along said lengthwise dimensionroi-said crystal-element, the ratio of the width-dimension-of: said-.major faces with re spectr-to.saiddengthwise dimension thereof being substantially-0.5.

12. Crystal apparatus comprising a di-potassium.tartrate hemihydrate. crystal element; the major-faces: of; said-crystalelement being substantially perpendicular to the Z axis, the lengthwisc'axisldimension of said major faces being inclined'eaiz. anzangle'izot-isubstantially +52% degrees 'withrrespect -to::the -.+X axis, and means comprising electrodes disposed adjacent said majorfacesrfot operatinggsaid-crystal element in a longitudinal mode; 10f: motion along said lengthwise dimension with substantially no coupling to the face shear: mode" ofmotion therein.

13." Crystal apparatus comprising a di-potassiurnitartrateihemihydrate 4 crystal element, the major faces-hf saidicrystal-element being substantiallymectangularrshaped and disposed substantially perpendicular to the Z axis. the lengthwise a s. dimension .of-said major faces being inclined at an-angleof.substantially +52% degrees withn'espcct to-the +X- axis; and means comprising-electrodes-disposed adjacent said major facesfor-operatingsaid crystal element in a longitudinal-.modemfimotiomalong said lengthwise dimensionrwith: substantially no 'ccupling to the face shear mode :of: motion therein 14.- Piezoeleetric crystal apparatus comprising as azecut dirpotassinmgtartrate. hemihydrate crystalelanentzadapted'fon longitudinal motion along the length'axis dimensionzof-its: substantially rectangular majdn faces; zsaidemaiorfaces-being substantiallyperpendicularto the Zaxis. of the three mutuallrpemendicular QL-ZY-and Z.axes thereof, and-saidaiengtlt axis dimension being inclined at an-angleofzsubstantiaflyr-tfli d s h specttosaidri-l-x-axisa thematic ofthe ,width di; mensionn'f-said-zmajorfaceswithrespect to said length dlmensionzbelngza value not greater than substantially:0.6;;saidzlngth:.dimension being a valuecorrespondingitolthe. frequency-for said longitudinal mode ,of motionrosaid lengthdimension expressed inz'ceniflmeters-rbeing one of the values substantially from-1160 to 180 dividcdby the value of said frequency expressed in kilocycles per second,; and-:means. comprising electrodes disposed adjacent said.mai or faces-for operating said crystal element-Yin saidz-longitndinal mode of motion.

15.- Piezoeiectriczcrystal apparatus comprising a Z.-:cut dt-potassium:tartrate hemihydrate crystal'elementradaptedior longitudinal motion along the lengthmxis dimension-:of its substantially rectangulai: major faces, said major faces being substantiaily=per ndiculan to the -Z axis of the three mutually-.perpendicular-X,.Y and Z axes thereof. and said length'aids-dimensionbeing inclined at an angle.=ofwsuhstantially;+52A degrees with respect'to solidi-Hi"- axis: the -.ratio .of the width dimension of sald-maior faceswith respect to said length dimension-being a value not greater than substantially;0:6,=.said length;- dimension being a value corresponding to the frequency for said longitudinal mode of motion, said length dimension-expressed "in-centimeters being one of the values substantially: from to divided by the -value =of said frequency-expressed in kilocycles :per tsecond, .and .means. comprising electrodes dlsposedrndjacent said majorfaces for operstinjgmaidrcnystalwelement in said longitudinal 13 mode of motion with substantially no coupling to the face shear mode of motion therein.

16. Crystal apparatus comprising a di-potassium tartrate hemihydrate crystal element having mutually perpendicular width and length axis dimensions for its major faces, said major faces being substantially perpendicular to the Z axis, and said length axis dimension being inclined at an angle of substantially +52 degrees with respect to the +X axis, said width dimension being substantially less than said length dimension.

17. Crystal apparatus comprising a di-potassium tartrate hemihydrate crystal element having mutually perpendicular width and length axis dimensions for its substantially rectangular major faces, said major faces being substantially perpendicular to the Z axis, and said length aXis dimension being inclined at an angle of substantially +52 degrees with respect to the +X axis, said width dimension being substantially less than 10 said length dimension.

WARREN P. MASON.

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