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Table 450. Dielectric Constant of Crystals

Table 450. Dielectric Constant of Crystals

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431

T A B L E 450.-DIELECTRIC

Name



Tartrates :

Ro$elle s;!t



C O N S T A N T O F C R Y S T A L S (concluded)



........ NaKC4H4Oe.4H20



30°C 5 .



.



KE



Kb



K.



Composition



...



8.0

300

NaNH;C4H40a.4Hz0 9.0

LiKC4H40e.H,0

5.84

LiNH4C4H,0e*Hz0 7.2



Frequency



...



9.4

8.9

7.32

8.0



2.5x10'0

free

free

free

free



9.6

10.0

7.4

6.9



Authority



h

c, j

h

h

h



Monoclinic crystals

Lithium sulfate ........

Tartaric acid .........

Potassium tartrate ....

Ammonium tartrate ...

Ethylene diamine

tartrate (EDT) .....



LizS04.Hz0

C4H,0R

K2C4H40s-jH20

(NH4)zC4H40e



5.6

4.3

6.44

6.45



10.3

4.3

5.80

8.2



6.5

4.5

6.49

6.0



free

free

free

free



h

h

h



CzN1Ha.GHeOe



5.0



8.22



6.0



free



h



h



8 See also figure 16.

REFERENCES:

a, Bechmann, H., and Lynch, A. C., Nature vol. 163 p. 915 1949.

b, Cady, W. G.,

Piezoelectricity, McCraw-Hill, New York, 1946.

c, Hablitzel, J. Helvet. Phys. Acta vol. 12. p. 489,

d. Taffe. H.. The Brush Develooment co. Reoort to U.5. Sirrnal Corm on kvnthetic watersoluble piezoelectric crystals April I 1948.

e, Jaffe' H. personal cGmmunication.

f Laboratory

for Insulation Research, Mlssachuseks Inst. Techn. Tables 6 Dielectric Materials I11 1948. and perg, Landolt Bornstein Tables, 5th ed.

sonal communication.

h, Mason, W. P., Pie&electr& crystals

and their application to ultrasonics, Van Nostrand Co., New York, 1950.

i, M e n , W. J., Phys. Rev.,

vol. 75. D. 687. 1949.

i , Mueller. H.. Phys. Rev.. vol. 47. I). 175, 1935: vol. 58. D. 565. 1940.

k.

I,, S itzer, F., Dissertation, m t t h g e n , 1938.

m;

Naval Research Laboratory, Crystal Section.

Standards on piezoelectric crystals, Proc. Inst. Radio kng., vol. 37, p. 1378, 1949.

n, International

0, Bever and Sproul, Phys. Rev., vol. 53, p. 801, 1951.

Critical Tables, vol. 6.

1939.



~



10



- 60



-40



-20



20

temper.1ure



40



60



or



FIG.16.-Dielectric constant K. of Rochelle salt. Curve A : free condition (audio

frequency) ; curve B : clamped condition (radio frequency).



SMITHSONIAN PHYSICAL TABLES



432



T A B L E 451.-PIEZOELECTRICITY



In this table are listed piezoelectric strain coefficients * d,, which are ratios of piezoelectric polarization components to components of applied stress a t constant electric field

(direct piezoelectric effect) and also ratios between piezoelectric strain components to a p

lied electric field components at constant mechanical stress (converse effect). The subcripts n = 1 to 3 indicate electric field components, m = 1 to 6 mechanical stress or strain

components. These components are referred to orthogonal coordinate axes. For correlation of these to crystallographic axes, we follow Standards on Piezoelectric Crystals.”’

In the monoclinic system, indices 2 and 5 refer to the symmetry ( b ) axis, in distinction

from the older convention relating indices 3 and 6 to the symmetry axis. Crystal classes

are designated by international (Hermann-Mauguin) symbols. A dot in place of a coefficient indicates that it is equal by symmetry from another listed coefficient ; a blank space

indicates that the coefficient is zero by symmetry. If the sign of a coefficient is not given

it is unknown, not necessarily positive.



3



1



Unit for d., = lo-’ statcoulomb/dyne = i< lo-” coulomb/newton

3

1

= 10.’ cm/statvolt = x lo-’’ meter/volt

3

. T h e coefficient d14 of Rochelle salt is extremely dependent on temperature and on amplitude. The

ratio of d14 to dielectric constant K (for the latter see figure 16) i s , however, nearly constant; 4 u d d K =

old = 6.4X10-1 statvolt cm/dyne.

m Letters refer to references, p. 431.



Cubic and tetragonal crystals

Name



Composition



Sphalerite ............

Sodium chlorate .......

Sodium bromate .......

“ADP” ...............

“KDP” ...............

“ADA” ..............

“KDA” ..............



Class



Authority“O



dsa



dl4



b

1

1

d



9.7



43m

23

23

42m

g m

42m

42m



ZnS

NaCIOa

NaBrOa

NH4HzPO

I< HzPO4

NH4H2As04

K HASO,



5.2

7.3

+48.0



- 1.5

1.3

+41

+23.5



+



+31



+22



d



Trigonal crystals

Name



Class



dii



Quartz ............... 32

Tourmaline ........... 3m



+6.9



dis



dl4



d2z



dR3 Authority



dal



-2.0

+11.0



-.94



+.96



$5.4



b

b



Orthorhombic crystals

Substance



Class



Epsomite ............. 222

Iodic acid ............. 222

Rochelle salt (30°C) ... 222

NaNH. tartrate ....... 222

LiK tartrate .......... 222

LiNH, tartrate ....... 222

(NH.)z oxalate ....... 222



d 25



dir



-6.2

57

1500*

+56

9.6

13.2

50



-8.2

46

-160

-150

33.6

19.6

11



+



dai



dir



4 6



K pentaborate ......... mm



9.5



1.7



dso



Authority



-11.5

70

+35

+28

22.8

14.8

25



1

h

b

b

h

h

e



da?



fi23



0



-5.4



Authority



d



+5.6



Monoclinic crystals (Class 2)

d14



Substance



Lithium sulfate ........ t 1 4 . 0

Tartaric acid .......... +24.0

Kz tartrate ( D K T ) .... -25

+9.3

(NH.), tartrate

E D T ................. -31.1

(Ethylene diamine tartrate)

Cane sugar ........... -3.7



.......



dle



dn



dT1



-7.2



+4.4 -10



(continued)



SMITHSONIAN PHYSICAL TABLES



d2,



dZG



d,



-12.5 +11.6 -45.0

-5.5 +16.5 -26.4

+15.8 -2.3

-6.5

-6.3

$1.1 -32.4

+6.5 -2.2

+8.5 -10.4 -22.5 +29.4

-8.5 +17.6 -26.2

+1.8 -5.9 -14.0

-36.5 +30.6 +6.6 -33.8 -54.3 -51

+2.2



-2.6



-1.3



dss Authority



+10.0

+35.0

-66.0

+5.6

-56.9



h

h

h

1



+1.3



b



a



T A B L E 451.-PIEZOELECTRICITY



433



(concluded)



Polarized polycrystalline substance

dis



Barium titanate ceramic



K = 1700



...... .... 750



dsl



-235



&a



Authority



+570



e



T A B L E 452.-VALUES

FOR P O W E R FACTOR I N P E R C E N T F O R S E V E R A L

ELECTRICAL INSULATING MATERIALS A T RADIO FREQUENCIES



From the range of values given, an approximate figure can be taken for a particular

material and its relative position with respect to other materials seen. Data of this kind

are much affected by the condition and past treatment of the samples and by the conditions

of the tests. The power factor and dielectric constant of dry air may be taken as 0 and 1.00.

Fused quartz has the lowest power factor among the solid insulating materials, and is

used for supporting the insulated plates of standard air condensers.

Material



Fre uency

R C



Amber . . . . . . . .



187.5

300

600

1000

30

Glass . . . . . . . . . .

600

500

cobalt ... ..

500

flint . . . . . . .

890

100

photographic

235

1700

14

plate . . . . . .

100

500

635

1000

14

Pyrex ....

30

100

420

500

750

80-650

Marble .. . ..

600

Mica . . . . . . .



.



Power

factor



.459

.476

.495

.514

.35 - 2.98*

.040- .653t

.70



Material



Paraffin



.... ...



Phenolic

insulation :

laminated 11



.



Frequency

kC



14

100

500

1070



.74

.h7

4.72z

.93f



.



bay . . . . . .

birch . . . . . .

maple . .. . .

oak . . . . . . .



.042

.017.026

.034



.031



625

710

1000

1085

1126



2.62 - 8.0

3.85 - 6.65

1.64 -10.9

1.56 - 8.4

.68

.70

.62

.70

.88

.68

.74

1.05



870

500

500

300

635

1060



3.76

6.48

3.33 - 3.63

2.948-13.8

3.24n-10.1

4.20



190

1000

190

1000

135

315



600



.58 .50

.42 .68

.35 ,007-



Power

factor



f Range of a number

$ Range of 10 samples.

Range of 9 samples.

t Range of 27 samples.

8 After drying 48 hours at 80'C.

11 Range of several samples.

of samples from different localities.



SMITHSONIAN PHYSICAL TABLES



434



TABLES 453-465.-RXDIO



P R O P A G A T I O N DATA



*



Antenna a r r a y s (figs. 17-19).-The basis for all directivity control in antenna arrays is wave interference. Ey providing a large number of sources of

radiation, it is possible with a fixed amount of power greatly to reinforce radiation in a desired direction by suppressing the radiation in undesired directions.

The individual sources may be any type of antenna.

The radiation patterns of several common types of individual elements are

shown in figure 17. The expressions hold for linear radiators, rhombics, vees,

horn radiators, or other complex antennas when combined into arrays, provided a suitable expression is used for A,the radiatidn pattern of the individual

dir.cltriy



<""."I

dislribullon



Iyp. of

radiolor



horizontal

Fi8

ClOl



Holl-wov

dipole



=

fOS



(5



K



I,"



0)



c3s 0



Shortene<

dipole



Lengthene

dipole



Horizonic

loop



FM



z KIII



101 = K



cos @



Horizontc

turnstile



i,and i2

phased 9

0'



0 = horizontal



angle measured from perpendicular bisecting plane



@ = vertical angle measured from horizon



K and K' are constants and K' 2 0.T



FIG.17.-Radiation patterns of several common types of antennas.

antenna. The array expressions are multiplying factors. Starting with an individual antenna having a radiation pattern given by A,the result o f combining

it with similar antennas is obtained by multiplying A by a suitable array factor,

thus obtaining an A' for the group. The group may then be treated as a single

source of radiation. The result of combining the group with similar groups, or,

for instance, of placing the group above ground, is obtained by multiplying A'

by another of the array factors given.

The expressions given here assume negligible mutual coupling between individual antennas. When coupling is not negligible, the expressions apply only

if the feeding is adjusted to overcome the coupling and thus produce resultant

currents that are of the amplitude and relative phases indicated.



* Data arranged by Newbern Smith and Marcella Phillips, Central Radio Propagation

Laboratory, National Bureau of Standards.

(continued)



SMITHSONIAN PHYSICAL TABLES



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