BSTJ 30: 2. April 1951: Zero Temperature Coefficient Quartz Crystals for Very High Temperatures. (Mason, W.P.)

4.7 MB·English

Zero Temperature Coeficient Quartz Crystals for Very
‘High Temperatures

(atone Rein on 15,1950)

pe thal evar nw tematic
‘Sistecar ender ens ede eve sea ae

1. Isrtoaeeaie

‘Mont quate crystal sed ca conti the frequency of eons oF time
messing devices are used in places where the ambiant temperate doe
hot ceed 0? to FOC. The cxystas ave sual adja ia ale so
they have s 20 fonperature coeficert at » temperntare of about 80°C
sn they ane tempente roniralled at this temperstors However §
fess ves eran or rhick the ambien tempentate iy be conderahy
bere sul for thee ass eninary AT nod BW cyst. fr exompty are
ant misony This even fom Ea 2 which abow tae fee
ttueney wart for Mes erga over temperate ran fm — 100°C
UU" 200°C, For exutpl, the Zale eyuensy temperstane sare for the
AT cut cecus at am suple of 8598" ration about Lie X ace ‘tom the
Y cat By going to 3556 reatation shout the X ana mio cecure
SC 100°C, Fur the HT cut sown by Fig. 2 the aagle of 40°10 oneal
tion gies nel pannboie sage centered a 20. Dy caging the ote
tacion (© 47°27 the pera caters et 75°C.

ence fore withes to ee the teperstur for wish the sey tee
tare ectiien arose histo inersee the eottion abot 2 forthe AT
tea decrege it forthe BE eat "ae doioune needed for either oat
Mion can hes be determined evalining the elastic sonst Sue
ie a ureaatinn sel temper, ae tht =the man pape of te
tue. The rests are seplied ta determining ce beet anges of eaten
Tarthe AT, DT, C1 and DY typ enysal natn seo temperature coe
oxo TEMUMRATCAR ooRRMCKESY QUOKD oRVREATS 36
268 cm mtr ment Treen Joey sea 9G

Cents for any arbiteary venpecstoe. These calculted values have been
her experines lly fe te AT lye eye an He se ad oes
{ies oe posiate iy the elevation. WS show ie thee eis]
Angle of FSS which real'< in he High tenperalure of 190°C fae
Seki i esi ty eis ores ania AT typecryetal

AE Beauzavius ov sue Enssnne Cuseasiy a 4 Suweriy

for Lumoustva

A emple method for taking ceoours of the temperntu tems i te
pend the frequencies for che known cate in portss of the temperstze
‘round some ference tomparatue. Since ke data of High Land 2 rt
fom IDC to FAC, 4 voesnlert lompencure SOC. “hur

eee ae ee

vee Cis enpeatute ange the Caquencies measured can be accaraey
repuctened by temss ‘Leading the cubic at che Lighest IT ston 25
SINC, equeion {Lean be alee for the conarants #0 apa

ied

hore che ebscripte ort Us Kerala for why the fosanacce
fre measure, IF ay thee eqeatons er he AT crt a 3515
fd the UT at 16) we find, forthe Sree, the eqaaione

fer — 161% UL + 22 HIME = 50)

$88 TE KT = SOP Ld
n= DST HOR — 9 3 UPI — 90) "
S58 XTRA) — NE — TH XC TIRE — St =

In onder ts ohio’ the fragceaey seal the wernion a equa with
engl ef made ofthe esaton fora thickness exeorvtantion

1 Lab oh fees ce OA intron fy
ray Say
wt # is the thickness of the eral p le demi, she angle of the
tural of the plate measure from the Y acs and ey sud ee ace of
the seven eatie constants of aria mre al cotstant acre eld
"This sin eval foro nite plate nt sae gal appeoxzation
fos erga wine exeesartioal mersions are 30 Uo 10 ines the ik
ness diersons, Sine ene ave Hines ess, the Low meastements for
{he AT aad DT cote il give only vo raha soa we ns measurement
far snother angle, Ae distie! in Chapter X, Setin 10.2 of "Preroacric
Crystals an Their Appleton br Civasoaie" the romairing ext ean
bc obtained by messing the Lrichacw dar mide of Yeut lte or the
face tent mode of« sus cxyta. The litter mei cnsierahiy easier
to dimension ole br stain 2 feaquensy earesponing to the shear
made, Teble I suies mssunenacs for the froqueney corstant ai © ¥
face shear mods for a crtal having the following simensions: Length
song the X as S080 mn, wih alng the Z axis — 7.628 mm; tides
Sng the ax fs 0990 wan, High Hares weve used and the frequency
foratat ne obssned Io dividing the fequeney ty the os

“Tas reqaoney svn by Une else anata accorsing ta thee

fo fy oe apt

In caleutting the of sown ors the sexta Eequonces esared,
aectccton is inoduce yy the serianvsere expansion constants le
frpatle Ths fll foes equation 5) sfage fc the Feeney
trsand p the dry nrc change with tenperiuce. From measunemeals
tquoied by Sosmus® forthe expansion along Ie Z aie popular
fe the Z axis, we fad

Lee alt h 18 x 104 my 4 28 x MrT sme
= 1s x rer so
fog = MUA MG MONT — $0) | 63x WHET — SHY °
= 19% MEN AF od
Multlyng tie tose the woke enn
Vee aL 9x MA IBA HT —

<5 x KT SM

nse ol Ts aan
310m ann seer recmsteat. Soran, APRS. 1981

Since the diy ste inven af evolu, the aguas of the frequency
‘onstant fora crystal whe mension is meaared at SOC mst be mal
Del hy de aco

hk

Lele

Jn onder to comect for the afeet of tomoersure expansion on the ehstie
‘constant. This eovectio is showa by the tid column of Table 1. The
orth column i tien the value uf cf for the various temperatures The
Aft: column shows th values af th a, 2, S04 ax constants Zo the tem
Dezatue yatation of ch,

“Table 1 ovaloats one ofthe cacti constants of the frequeney enuatin
(4). To ceauate the orber Ivo conto ss me the frequeney

peat otaw | ae | RIT eseaee
ms one Re
owatsts fa she AT aad BT eat gvea by equation (3). Over a tempers
tere rage the Usha # is given Ly the catia:
Fe MB eate tH aaa) 8

where and J are the vals of wil Neng long the F aad Z axis ex-
pessed aba function of tempersture, Inserting he values of (6) and (7)
Tn equation (8), the clastic shear constants for tae A end cats become

SINT) = 2904 x 100 — 12 tO-HEM — 50)
SEAR x 1 = 50 | 172 HET = SOI}

eE(BT) = 6807 x HL Dx IO-AT °
06 IT = 5 = 238 OT = 5)
rom epaton (2), the faqency equation, we ave
HON ~ OsR5R | OST G1 09m

AIAT) ~ 0.6861 ch + 03330 ch — 008 ch

Since cis steady knows, tke tvo equations cin be solved for ely and
iyand wo nd
reso iearenytman comnzrousa quire cewstts 371

= onmndtn + 09008 AT) ~ asa
cy = 0080 GT) — oa egiaty — o226e a ON
Ioscting the vans fn, Table Hates (8) he tae cate cone
tots Besos
S258 0 — 171 1-4 — 50)
= HYP = S865 X10 = SP]
HE M025 x 0 EB IO 3)
5X IPT = 50" 7 10 HUE = SPE)
= isan x10 + 905¢ 19 «Fh
= 20x LET — $0) — 6H MET SPF

Yo determine the frequency an perature cvelicets for any angle
one subtest vale ofthe ellie crassa the tempeteture cx
pansion clients iz the sroquency eyatiag fH), which sects in the
cxpresion

P= OMS MI 85526 n"d— $AD6sin gone) | IONE — 90)
Teco! & — 828 sin' @— S¥6 sinh emt — 13 Sia es" #— 46
sinacond| © IOUT — AOE ows sic + SEE (8)
fo Maintome a0 mr —
anaes? Sthsin?o+ Un Deena] FY

sin cose — 12 st tec

UL, Peomrerts or AT avy BT Cor Crvstane Lavi Zim
‘Traennazents Conveterses ar Hic Trewern

“Te proves for obtaining high frequees cate of the AV and BT type

that will have ae tempeminre concerts a Pigh tenperatare fe
sate 00°C isto eit for 7 in equation (5) the vane

T= x0" | ar ay,

Insettng this vale in (4) aed coleting the ems fn powers af AT, we
a

PX UP = [513 ce + SATS la 8 — 5405 sing ease — O0m23
sin cst — WIS vie? ewe A] | (AT) XE
[807 cos! 9 — 126 Sut @ = 186 end coe — IT xt
cos 88 x! y oma] | (ALEX IMIS cos? (15)
Iss! 6 862
sin? cas 1+ ATP XI STS ont # — A wa!
+ H130 a8 cos

in6 cos — [2s Bote =
37M rm we ever THCMACAL JOURNAL, APH 181

¥. Besemscmss so ti Rewanense 02 sues baste
Conenasts ove « Wrox Trasaxar0s RANGE

Th oud: wm evaluate the remain of te sestic constants ease:

iments were ace the equer a face Xa nti eres

Ger the seme tempore mage ftom —109°C to —20FC." The ong

Tone) eeytals teased vi lenge at 207 0", 30" xa 00°

Irom che Fas, For the dour crgtaleteasurcd too reels are shown, by

i ]

u |

i om _~ i JwOAMENTEL | rT |
ae

: 16,30 _ naa :

‘Teble The alysis fr fa = fa
"Po covet fe che temgertsite expansion catiiens the Inrease along
{inven by he ast eqotinn of 16) while P= 30° de ae
Pa 30° = 28 78h Rh} 129% 104 — 50)
AE SAR X(T = SOF = LE WET — SO) Fd

ral he the consents 045 oy an oy

09)
1a 60 = Fe 25 = ALF YS IONE — 0)
308 3¢ WT — SO M9 X HHT — 50) bo]
Sine the fequeney «lng chin bu ven Hy Wie equation
hag = a co
I> Zoe 8 J

tng the lenge correo fom (9) and the density orrestion
From (7) ca comes forthe ele if tenpessue expansion,

tha sgn ee my TO ey

536 nck Sve TRCISHEAL Ju ARIE BSD

Applying Use cortections to the frequency egeations of Tale TT the
esa rnplanee constants bere

Hoon) = A= LOT X I FS X IO — BF

ESAS IPH = SOS 383 HE BDH ed
aaann) = 8199 X 10H U1 X IO — 50)

$2165 x 10-%T — SOP + 219.4% 1-50)
Been = 1402 X10 AIL LLL x 108{r —

198. rH — 50} = 916 X HOME — SOF]
res = 86M X AOE | WHA LOR ~ 50

EM LOT ~ SF HE IC OC = SOP

The equation for the emapiance constant sf furan X-cut esta! aan
angled from the 2x fas been sh a le!

oy

SE = shomte + sflsin!'o— 26 on én
co)

oh (tabs + a) sat # caso
Solving for the sonst in torso the compliance forthe four unles
aca Ho

Scar = Bays Bon

= Mier —Fshewns Gat ado = — 2 ea
eace aang he reuse nd
fh aT 0 ML 163 3 1-H PS
$585 HET — SPH CIMT — 2 Lo]
Se MOT x AOL H ISS x IOUT ~ 50)
PM Me + SOIT SOE

A= 0496 x HT} 19S x10 UF = 8
SX = SOF Sx CE =

(eB 1 oh) = 1788 2 10-300 x 10-4 — SO)
FAO XT 50) — 98 KET OP Fo)

gif Pome sok Metin Wy se 2, ain
42330 TRMPEIATORY coREMENENT quawre cows SIT

AL the complince constants ane now detec erent sh fh and
fh. Brom the zéaion fr oerystl in the quarts eas!

-wh- aw

the remaining constants can be obtain Tseting the values of ech
and ef fom (12), we Gd
A= 1986 OM BOL x LOTT — sn)
$0 x 100 — SOF 28 x 10-4
Wha 28 x WM — 138 x OH —
= 8X 10H = OP FXO AEE EY]
0.8005 x 10-1 — sis 10 Her — su)
= 210 x 10-YP = 50394 610 3 10 MEF — SUE >)
sho 040 x 10-1 — 190 x APH — ry
= S18 IONE 50 285 9 1 38 Ho

8,

It is aesines desis use te vole ae eo of lempens
tare, The remsining vakee cn e obssined froma she elaioes vale for

ae = By tha Ba a gy
bere
mesh Oh tay — Mis a= chk yo

Hh= 00 Xx 10eL — es XIE = 59)
1ST x AOE = 50} — AO RAL = SUPE
Hh 96% 10 510 x ET sy
= OD ET = 504 eo x OAC
R635 x LOHME — $85 9c 1-47 — 50)
Hs xT = 50

is x wor
= 685 x 10TE — ato x I-40 — 50)
= 1300 10 EF = SOV HD x 10 EE —SO)E