3E 
 
 E 
 
 O 
 

 

 Piezo- Electric Activity of Rochelle 
 Salt Under Various Conditions 
 
 BY 
 
 J. VALASEK 
 
 A THESIS 
 
 SUBMITTED TO THE FACULTY OF THE GRADUATE SCHOOL OF THE UNIVERSITY 
 
 OF MINNESOTA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS 
 
 FOR THE DEGREE OF DOCTOR OF PHILOSOPHY. 
 
 Reprinted from PHYSICAL REVIEW, Vol. XIX. X<>. 5 
 
Piezo- Electric Activity of Rochelle 
 Salt Under Various Conditions 
 
 BY 
 
 J. VALASEK 
 
 A THESIS 
 
 SUBMITTED TO THE FACULTY OF THE GRADUATE SCHOOL OF THE UNIVERSITY 
 
 OF MINNESOTA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS 
 
 FOR THE DEGREE OF DOCTOR OF PHILOSOPHY. 
 
 Reprinted from PHYSICAL REVIEW, Vol. XIX, No. 5, May, 1922, 
 
- 
 
 . 
 
PIEZO-ELECTRIC ACTIVITY OF ROCHELLE SALT UNDER 
 VARIOUS CONDITIONS. 
 
 BY J. VALASEK. 
 
 SYNOPSIS. 
 
 Electrical Properties of Rochelle Salt Crystal are analogous to the magnetic prop- 
 erties of iron, the dielectric displacement D and polarization P varying with the 
 electric field E in the same general manner as B and / vary with H for iron, and 
 showing an electric hysteresis with loops distorted by an amount corresponding to 
 the permanent polarization Po, whose value is about 30 e.s.u./cm. 3 but varies for 
 different crystals. The dielectric constant (K = dD/dE) was measured from 70 
 to 30 C. and found to be surprisingly large, increasing from about 50 at 70 to a 
 maximum of about 1,000 near o. The modulus of piezo-electric activity for shearing 
 stresses (5) varies with temperature, 70 to 40 C., in a very similar manner, increas- 
 ing from less than io~ 6 at 70 to a maximum of about io~ 4 at o. The ratio 
 d/K varied with the electrode material, being greater for tin foil than for mercury elec- 
 trodes. The difference may be due to the alcohol used in shellacking the tin-foil elec- 
 trodes on. There are other indications that 5 and K are related. The variation of 
 8 with humidity is such as can be accounted for by the decrease in the dielectric con- 
 stant of the outer layer as a result of dehydration. The change of polarization 
 produced by pressure as measured by the change in the hysteresis loop agrees with the 
 value found directly from the piezo-electric response, as required by Lord Kelvin's 
 theory. Also fatigue effects on 5 produced by temporarily applied fields are traceable 
 to fatigue in the polarization. The electrical conductivity below 45 is less than 
 5 X io~ 9 mhos/cm. 3 but from 43 to 57 increases rapidly to 5 X io~ 4 . 
 
 Optical Properties of Rochelle Salt as Calculated from the Natural Polarization. 
 Assuming only one electron is displaced the natural period corresponds to a wave- 
 length of 4.2 n and the specific rotation for sodium light comes out 10, the observed 
 value being 22.!. 
 
 T3 ECENTLY 1 the writer described some experiments on the dielectric 
 A V and piezo-electric properties of Rochelle salt, which were made 
 for the purpose of correlating and explaining the effects observed chiefly 
 by Cady and by Anderson. The plates used were cut wrth faces per- 
 pendicular to the 3. axis and with edges at 45 with the b and c axes. 
 The present paper is a continuation of the work, the variations in the 
 electrical properties having been studied more extensively. The appa- 
 ratus and method of observation have been already described in the paper 
 referred to above. The more important results obtained at that time 
 can be summarized as follows: 
 
 In the case of Rochelle salt the dielectric displacement D, electric 
 intensity , and polarization P behave in a manner analogous to B, 
 H, and / in the case of magnetism. Rochelle salt shows an electric 
 
 1 J. Valasek, PHYS. REV. (2), XVII, p. 475. 
 
 478648 
 
479 
 
 J. VALASEK. 
 
 ("SECOND 
 
 [SERIES. 
 
 hysteresis in P analogous to the magnetic hysteresis in the case of iron, 
 the loops however being distorted by an amount corresponding to the 
 permanent polaiization of the crystal in the natural state. This point 
 of view is very effective in accounting for many of the peculiarities 
 observed. 
 
 In an electric field the piezo-electric activity has a maximum for a 
 definite value of the field and decreases to a small value in both directions. 
 The position of the maximum corresponds to the greatest rate of change 
 of polarization with electric field in the case of the condenser experiments. 
 In fact if force and electric field are equivalent in changing the piezo- 
 electric polarization then the response for a given force in various applied 
 fields must necessarily give curves of the same general nature as curves 
 of dP/dE or dD/dE against E. It is permissible to interchange D and 
 P in most cases because of the large dielectric constant of Rochelle salt. 
 
 RELATION BETWEEN POLARIZATION AND PIEZO-ELECTRIC ACTIVITY. 
 
 The activity of a piezo-electric crystal is intimately related to the 
 natural polarization. According to Lord Kelvin this natural moment 
 is masked by surface charges so that the crystal appears to be uncharged. 
 This polarization or piezo-electric moment can be measured independ- 
 ently of the charges on the electrodes, through the distortion of the 
 hysteresis loop. The center A of the loop is found by a consideration of 
 symmetry and may be assumed to represent the condition of no polariza- 
 tion. If the natural condition of polarization is assumed to be half way 
 between the two branches of the loop at zero field then the value of the 
 permanent polarization P is proportional to AB, Fig. i. There being 
 
 60 60 100 
 
 VOLTS 
 
 . 1. 
 
 no field applied, the equation for the work done per unit charge carried 
 through the condenser is: 
 
VoL.^XIX.J P2EZO-ELECTRIC ACTIVITY OF ROCHELLE SALTS. 480 
 
 SO that 
 
 where Q is the apparent average permanent charge at zero field given by 
 AB (Fig. i) and where 5 is the area of the plate. Calculation gives the 
 value: 30 e.s.v./cm 2 . 
 
 According to Lord Kelvin's theory an applied stress will change this 
 polarization so as to create free charges on the electrodes. A force of 
 250 grams applied to the crystal should consequently shift the loop by an 
 amount equivalent to the piezo-electric response for 250 grams. When 
 this experiment was performed another, but more unsymmetrical loop, 
 was obtained. The change in polarization by the loop method was 
 114 e.s.u./cm. 2 while the piezo-electric response amounted to 121 
 e.s.u./cm. 2 
 
 The value of P obtained from the hysteresis loops is only approximate 
 because of the assumptions involved in its determination. It cannot, 
 moreover, be fixed definitely enough \.o be put down as a physical constant 
 of Rochelle salt because it varies with different specimens, besides chang- 
 ing with temperature, pressure and fatigue. The value P = 30 e.s.u./cm. 2 
 is thought to be a representative value and is checked by other 
 measurements. The writer would not be surprised, however, to find 
 other specimens giving several times this value. The change in polariza- 
 tion due to pressure however is derived by a differential method eliminat- 
 ing much of the uncertainty in measurements on one loop. The result 
 in this case should be fairly definite, as indeed it seems to be. 
 
 Piezo-electric activity depends on both the crystalline structure and 
 on the polarization. It is greatest for a polarization somewhat larger 
 than normal and decreases in both directions for changes in this quantity, 
 the polarization being changed by applying an electric field. It has been 
 shown by the writer that this relation between activity and applied 
 field is approximately like that of the derivative dD/dE of the curve 
 relating the dielectric displacement D and the electric field E of the 
 crystal used as a condenser. Since this latter relation is in the form of a 
 hysteresis loop it follows that the activity is also a double- valued function 
 of the applied field depending on the direction of variation of the field. 
 A curve illustrating this effect is reproduced in Fig. 2. The readings 
 were taken in as short a time as possible to eliminate fatigue. These 
 curves show that the piezo-electric response at zero field depends on the 
 previous electrical treatment of the crystal. The latter fact has also 
 been noted by W. G. Cady in the report previously referred to. 
 
48 1 
 
 J. VALASEK. 
 
 [SECOND 
 
 [SERIES. 
 
 This after-effect does not persist very long but dies off exponentially 
 with the time. The piezo-electric response or ballistic throw of the 
 galvanometer for 250 grams has been observed to return to half value in 
 I minute and to normal in over 20 minutes after fields of 150 volts have 
 been applied for 3 minutes previously. There is a much greater after- 
 effect in the direction of increased activity. 
 
 !* 
 
 g// 
 * 
 
 * 
 
 j- 
 
 o 1 
 
 
 
 
 
 
 '/\ 
 
 
 
 
 
 
 
 
 
 / 
 
 3 
 
 i 
 
 
 
 
 
 
 
 
 / 
 
 
 
 \ 
 
 
 
 
 
 
 
 
 / 
 
 / 
 
 \\ 
 
 
 
 
 
 
 
 
 // 
 
 
 
 i 
 
 
 
 
 
 
 ^ 
 
 2 
 
 
 
 ^ 
 
 ^ 
 
 ^^_ 
 
 
 
 jo-*" 
 
 ^ 
 
 / 
 
 
 
 
 
 
 /20 -90 -60 -JO O JO 60 &O UO 
 
 2. 
 
 Fig. 2. 
 
 A corresponding dielectric effect is indicated by the double value of the 
 condenser charge at zero field in the hysteresis loops. This is clearly 
 due to a fatigue in the polarization and it also dies off exponentially with 
 time. Herein is probably found the explanation of the "storage battery 
 effect" described by W. G. Cady who observed that after applying a 
 field of 100 volts for some time there was, on removal of the field, a small 
 current which decreased gradually and flowed from the crystal as from a 
 miniature storage battery. 
 
 The piezo-electric fatigue may well be a direct result of the fatigue in 
 the polarization, as there seems to be a close relation between piezo- 
 electric activity and polarization. It appears that the activity is approxi- 
 mately proportional to the rate of change of polarization with applied 
 field and hence proportional to the dielectric constant. An examination 
 of the temperature variation of the two quantities leads to this conclusion. 
 It is further confirmed as regards field variation by the fact that the 
 relation of activity to applied field is like dD/dE vs. E where dD/dE is 
 merely the instantaneous value of the dielectric constant K. As an 
 approximation we can write the piezo-electric modulus 8 proportional 
 to K: 
 
 d = A-K. 
 
VOL. XIX. 
 No. 5. 
 
 ] PIEZO-ELECTRIC ACTIVITY OF ROCHELLE SALTS. 
 
 482 
 
 If this equation were exact A would be a fundamental piezo-electric 
 constant of the substance, being of the order of I X io~ 7 between 20 
 C. and + 20 C. At some temperatures and for some exceptional 
 specimens the relation does not seem to be so simple. 
 
 EFFECT OF MOISTURE ON PIEZO-ELECTRIC PROPERTIES. 
 In order to investigate the effect of dryness on the activity of Rochelle 
 salt, some phosphorus pentoxide was enclosed in the chamber containing 
 the crystal. The crystal soon started to dehydrate and after a few days 
 was covered by a white coating. The piezo-electric throw for a load of 
 250 grams continually diminished. When the response was tested at 
 different fields a more interesting fact was observed. Besides the de- 
 crease in response, the maxima were displaced along the field axis into a 
 condition of greater polarization. This is shown by Fig. 3, the curves 
 
 "200 -160 -120 -60 -40 O 40 30 
 
 TlGURf S, 
 EFFECT Or DffYING 
 
 Fig. 3. 
 
 IZO 160 ZOO )/OLTS 
 
 being taken after the lapse of the following times: (b) I day, (c) 3 days, 
 (d) 12 days. 
 
 The decrease in the maxima and also their displacement is in the same 
 direction as, and may be entirely due to, the effect of different dielectric 
 properties of the crystal and of the dehydrated layer. In other words 
 the presence of a layer of inactive dielectric of relatively low specific 
 inductive capacity will diminish the charge on the plates due to the 
 polarization of the central active layer, and thus decrease the piezo- 
 electric response. It will also diminish the effective field across the 
 active layer making it necessary to increase the potential difference 
 
J. VALASEK. 
 
 [SECOND 
 
 [SERIES. 
 
 between the plates to produce 'the same field across the inner layer, thus 
 shifting the position of maximum activity. The effects due to uniform 
 layers can be readily calculated. Let P be the polarization produced in 
 the middle layer by pressure, let PI and PI be the 
 electrically induced polarizations in the dielectrics 
 I and 2 respectively (Fig. 4). Since the dielectric 
 displacement is solenoidalwe have: 
 
 D' = E! + 47rPi -f 
 Since 
 
 we can write 
 
 D' = 
 
 o = E 2 + 47rP 2 = 47r<7. 
 
 and 
 
 X* 
 
 d 
 
 Fig. 4. 
 
 The difference of potential between the plates is zero so that, replacing 
 PO by (TO : 
 
 = E 2 (d - ./) + Erf 
 
 giving : 
 
 -+3* 
 
 TO Q 
 
 KI) + Kid 
 
 This gives us a relation between the piezo-electric response at zero field 
 of the crystal with the dry shell and of the same crystal before it dried. 
 The assumption is made that the elasticity of the shell is equal to that 
 of the crystal so that a given total force produces the same polarization 
 in the crystalline portion. 
 
 The position of the maximum will be changed to another value of total 
 potential difference on the crystal. Let V be the total potential drop 
 and V be the drop across the crystalline part. When there is no de- 
 hydrated layer present 
 
 V = V = dE, 
 
 where E is the field strength in the dielectric. When there is a layer of 
 uniform thickness (d J)/2 on both faces then 
 
 V = (d - 
 
 + tE', 
 
 where E" and E f are the field strengths in the dielectrics 2 and I respec- 
 tively. The dielectric displacement 
 
 D 
 
 Kl E' 
 
VoL.^XIX.j PIEZO-ELECTRIC ACTIVITY OF ROCHELLE SALTS. 484 
 
 is solenoidal, and we can eliminate E" from equations above and write: 
 V' = dE = (d - t) - 1 E' + tE f + 47rP 
 
 Since the last term is small compared to the rest of the expression, this 
 gives : 
 
 E t( K2 - KI) + <fi- 
 
 The following quantities were measured and substituted in these equa- 
 tions. 
 
 KI = looo, d = 0.22 cm., 
 
 K 2 = 180, t 0.14. 
 
 The quantity t is an average obtained by breaking the crystal in several 
 places and it is probably not very accurate because of the irregularity 
 of the outer layer. We should, however, get a rough check on the 
 plausibility of the proposed explanation. We find that 
 
 and that 
 
 While the values of Q'/Q and E'/E from the maxima of curves a and d 
 of Fig. 3 are respectively 0.39 and 0.33. The agreement is not as good 
 as could be desired even after making allowance for the difficulties in 
 estimating t. Possibly there is a true humidity effect with respect to 
 piezo-electric activity but the above shows, at least, that it is quite small. 
 
 PIEZO-ELECTRIC ACTIVITY AND TEMPERATURE. 
 
 In order to investigate the variation of activity with temperature, the 
 chamber holding the crystal was immersed in CO 2 snow. After every- 
 thing was thoroughly cooled and at 75 C., the chamber was allowed 
 to heat up. Above 35 C. an electric heater was used. It was wound 
 on a glass jar and insulated from the crystal chamber by a felt jacket. 
 This jar was immersed in an oil bath to steady the heating rate while the 
 felt eliminated any rapid changes of heating of the crystal. The current 
 was gradually increased so as to keep the rate of heating uniformly between 
 | and i C. per minute so as to eliminate thermoelastic stresses. The 
 temperature was measured by means of a copper-constantan thermo- 
 couple directly soldered to an electrode on the crystal. In this way the 
 actual temperature of the crystal itself was measured. 
 
J. VALASEK. 
 
 [SECOND 
 
 [SERIES. 
 
 When the piezo-electric response or galvanometer throw for 250 grams 
 was measured at the various temperatures for the first specimen the 
 curve of Fig. 5 was obtained. This was duplicated to check the second 
 
 -6o -so -to -30 -zo -/o 
 
 PlZOLCTJ?lC 
 
 /o 20 Jo 4o 
 
 TFffffffA TURC 
 
 Fig. 5. 
 
 maximum. At 70 C. the piezo-electric activity is comparatively 
 negligible. As the temperature is raised slowly the activity stays small 
 until 30 C. is reached. At 20 C. it is rising very rapidly, reaching 
 a maximum at about o C. It decreases again but at 23 C. comes to a 
 small but sharp maximum from which it diminishes slowly, becoming very 
 small at + 50 C. The magnitude of the second maximum varies with 
 the temperature at which heating begins. This, second maximum was 
 found in the case of two crystal plates provided with tinfoil electrodes 
 attached by shellac. 
 
 Three other crystals were prepared with electrodes of mercury held 
 against the crystal by two rectangular cups attached by wax. The 
 thermocouple wires were immersed in the mercury. None of the crystals 
 so prepared gave the second maximum. Moreover, none of them were 
 as active as those used above. The variation of piezo-electric response 
 of these specimens is shown in Fig. 6. The increase at 30 to 15 C. 
 and the decrease at +20 C. to + 30 C. are remarkably consistent. 
 Between 15 and + 20 C., however, they each show different char- 
 acteristics. These mercury electrode crystals seemed to give more con- 
 stant results than the crystals with tinfoil electrodes attached by shellac. 
 
 It was then suspected that the increased response of the crystal with 
 
VOL. XIX. 
 No. 5. 
 
 ] PIEZO-ELECTRIC ACTIVITY OF ROCHELLE SALTS. 
 
 486 
 
 -70 
 
 to 
 
 /O ZO JO 
 \ 
 
 - SA*erir&T/i#r 
 
 Fig. 6. 
 
 tin foil[ electrodes and the presence of the second maximum was in some 
 way due to the penetration into the crystal of the alcohol solvent of 
 shellac. Accordingly one of the crystals originally with mercury elec- 
 trodes[was provided with the other type. As soon as the shellac was 
 sufficiently dry, Curve b, Fig. 7 was obtained, the response originally 
 
 Fig. 7. 
 
 having followed Curve a. The sensitivity increased seven-fold at some 
 temperatures but there was no second maximum. In two weeks the 
 characteristics had changed to those shown in Curve c, seemingly checking 
 the suspicion that alcohol was responsible for the second maximum and 
 for the increased sensitivity. It would be interesting to use alcohol cup 
 electrodes and investigate the continuous effect of alcohol soaking into 
 the crystal. Tlie effect is probably not chemical. 
 
J- VALASEK. 
 
 In a paper on the piezo-electric effect on Rochelle salt/A. M. Nicolson 1 
 describes a method for desiccating the crystals by soaking in alcohol and 
 heating, thus making them stronger and more sensitive. 'The writer is 
 certain, from his work on the subject, that complete desiccation will make 
 the crystal entirely inactive. In the above method, apparently, the 
 treatment is not prolonged enough to completely dehydrate more than 
 a shell around the crystal and its effectiveness may be connected with 
 the penetration of the alcohol into the crystal. The heating at 40 C. 
 may also be effective in allowing a rearrangement and recrystallization 
 of some of the molecules or groups not properly oriented. W. G. Cady, 
 as well as the writer, has observed that heating the crystal will usually 
 increase its sensitivity permanently, although sometimes the reverse 
 is true. 
 
 An interesting side-light on the temperature variation of piezo-electric 
 activity is offered by a study of curves like that of Fig. 2 but at different 
 temperatures. They show that the effect of temperature is not so much 
 to change the piezo-electric activity as to shift the position of the maxi- 
 mum from one value of the field to another. This is probably connected 
 with the variation of the dielectric constant with temperature which 
 will be taken up presently. 
 
 The charging throws of the crystal used as a condenser show variations 
 similar to those of the activity except that they do not tend to zero but to 
 a constant value at the lower temperatures. The crystals giving the 
 second maximum on the piezo-electric curve show a similar peculiarity 
 here. The crystals with the mercury electrodes give more regular curves. 
 At 20 to 25 C. the crystals of both types begin to conduct, causing a 
 steady drift of the galvanometer. Experiments seem to indicate that 
 Ohm's law holds at least approximately. The conduction was at first 
 thought to be electrolytic because of the manner in which Rochelle salt 
 melts. Instead of real melting it appears that the crystal dissolves in 
 its water of crystallization which is set free at 55 C. The desiccated 
 crystal, however, decomposes into a tarry product and emits heavy white 
 fumes above 150 C., without melting. The dehydrated crystal also 
 begins to conduct above 20 C., making it probable that electronic and 
 not electrolytic conduction is observed. 
 
 Measurements of conductivity were made on the natural crystal at 
 various temperatures up to its liquefying point. The values obtained 
 after the conductivity was sufficiently large to use a Wheatstone bridge 
 are as follows : 
 
 1 A. M. Nicolson, Proc. Am. Inst. Ele. Eng., Vol. 38, p. 1315 (1919). 
 
VOL. XIX.' 
 No. 5. 
 
 PIEZO-ELECTRIC ACTIVITY OF ROCHELLE SALTS. 
 
 488 
 
 TABLE I. 
 
 Temperature. Conductivity. 
 
 Less than 43 C Less than 0.5 X l-0- mhos/cm 3 . 
 
 43 0.5 X 1C- 8 
 
 45 1.0 X 10-8 
 
 47 . . 0.3 X 10- 7 
 
 49 0.5 X 10- 7 
 
 51 , 0.5 X 10-6 
 
 53 0.6 X 10~ 4 
 
 54 1.7 X 10-< 
 
 57 5.0 X 10-4 
 
 Greater than 57 1 5.0 X 10' 4 
 
 At temperatures below 20 the dry crystal is a fairly good insulator 
 having a specific conductivity of 5 X io~ 12 mhos/cm. 3 at o C. The 
 conductivity decreases slightly at still lower temperatures. In all these 
 measurements the surfaces were thoroughly dried by the presence of 
 phosphorus pentoxide in the crystal chamber. 
 
 TABLE II. 
 
 Temp. 
 Cent. 
 
 Dielectric Constant. 
 
 Piezoelectric Modulus. 
 
 A 
 
 B 
 
 A 
 
 B 
 
 70 
 
 71 
 85 
 140 
 386 
 943 
 1,380 
 1,100 
 688 
 423 
 Conduction 
 
 42 
 50 
 146 
 252 
 924 
 956 
 928 
 645 
 146 
 commences 
 
 0.041 X 10~ 5 
 0.068 " 
 0.41 
 5.4 
 18.9 
 22.9 
 18.9 
 13.5 
 2.2 
 0.41 
 
 0.017 X 10~ 5 
 0.017 " 
 0.065 " 
 1.08 
 6.07 
 6.75 
 7.42 
 8.10 
 1.08 
 0.41 
 
 -50 
 -30 . . 
 
 -20 
 
 10 
 
 
 10 
 20 
 
 30 
 
 
 Table II. gives values of the dielectric constants for a field changing 
 from o to 880 volts/cm, and of the piezo-electric modulus 5u for shearing 
 stresses of 220 grams/cm. 2 . The modulus 614 is defined by the relation 
 given by Voigt en = S^F, where <TI is the surface density of charge 
 and F z is the shearing stress producing it. The given values are thought 
 to be the most representative in each case. They are subdivided into 
 two classes, according to whether the electrodes were tinfoil attached 
 by shellac (column A) or mercury in direct contact with the crystal 
 (column B). The former method is the most convenient to use in 
 general practice, but the latter is thought to give more exactly the prop- 
 erties of Rochelle salt in the direction of the a axis. The dielectric 
 
4 8 9 
 
 VALASEK. 
 
 constants are surprisingly large, a fact noticed by Pockels 1 who supposes 
 that this is due to "internal conductivity." The writer however has 
 measured separately the conductivity at these temperatures and is of 
 the opinion that this is a true dielectric constant arising from polarization 
 of the dielectric, and for this reason being so closely related to the piezo- 
 electric effect. Because of the relatively low specific inductive capacity 
 of the desiccated crystal it is thought that the high specific inductive 
 capacity of Rochelle salt is partly due to the water molecule. 
 
 MAGNETIC ANALOGY. 
 
 There seems to be a strong analogy between the behavior of Rochelle 
 salt as a dielectric possessing hysteresis and having an exceptionally 
 large dielectric constant, and the phenomena of ferromagnetism. Ac- 
 cordingly some of the features of Weiss's theory of magnetism may find 
 their counterpart in the phenomena in Rochelle salt. Weiss 2 plots the 
 susceptibility against the reciprocal of the absolute temperature and finds 
 that the curve may be represented by a succession of straight lines. He 
 interprets the sudden changes in slope as due to changes in the number 
 of magnetons. If the data of Figs. 8a and 12 are plotted against the 
 reciprocal of the absolute temperature one likewise gets what may be 
 considered to be a succession of straight lines. Actually however there 
 occur rounded corners where the curves suddenly change direction. 
 This may be due to slight non-uniformity in heating which occurred in 
 spite of the precautions taken. It is considered that the straight portions 
 are at least as definite as those shown in Weiss's paper. The most abrupt 
 changes are at 20 C. and at +20 C. These may accordingly be 
 considered as the "Curie points" in Rochelle salt. 
 
 RELATION TO OPTICAL PROPERTIES. 
 
 Some of the optical properties of Rochelle salt can be at least approxi- 
 mately found from the electrical data given. In the course of this 
 calculation it is of course necessary to introduce some assumptions notably 
 as to the nature of the permanent polarization. If one knew just how the 
 permanent polarization was pioduced he could find the free period of this 
 mechanism. The data needed are the force per unit displacement / 
 and the mass m of that part of the molecule. The wave-length corre- 
 sponding to the free period is given by the expression 
 
 X = 271 
 
 c being the velocity of light. 
 
 1 Pockels, Lehrbuch der Krystaloptik, p. 508. 
 
 2 P. Weiss, J. de Physique, Vol. i, p. 968 (1911). 
 
No L ' 5 XIX '] PIEZO-ELECTRIC ACTIVITY OF ROCHELLE SALTS. 490 
 
 Let us assume for simplicity that only one electron is involved in the 
 creation of the permanent moment. The quantity / can be derived from 
 the value of the permanent moment PQ = 30 e.s.u./cm. 2 and from the 
 displacement of the electron producing it. Since the force on an electron 
 inside a dielectiic of polarization P is roughly equal to fPo^ 1 the expres- 
 sion for the wave-length may be put in the form : 
 
 The value of d, the displacement of the electron, can be found as follows: 
 Taking 30 e.s.u./cm. 2 as the natural polarization, the moment per 
 molecule is obtained by dividing by the number of molecules per c.c., 
 the result being 7.1 X io~ 21 e.s.u. In each of these molecules there are 
 140 electrons, this being the sum of the atomic numbers of the constituent 
 elements in Rochelle salt. If we suppose as above that only one of these 
 is effective in producing the piezo-electric moment, its displacement from 
 the center of force of the rest of the molecule will be d = 2.7 X io~ n cm. 
 It would of course be more reasonable to suppose that at least several 
 of the electrons are displaced by different amounts, and to the extent 
 that we do this the value calculated above becomes smaller. 
 
 Using these values of P and d for the simple case treated above we 
 find for the wave-length the Value: 
 
 X = 4.2 p. 
 
 Coblentz 2 shows the presence of fairly strong absorption in this region of 
 the infra-red. This may, however, be due to the water of crystallization 
 and not to the cause cited above. These two possibilities should be dis- 
 tinguishable experimentally because the character of the absorption due 
 to these electrons should change greatly with the temperature, as the 
 piezo-electric elasticity or force per unit displacement of the electrons 
 changes. 
 
 The natural period as found above should be the same as that involved 
 in rotatory dispersion formulae, since both the piezo-electric effect and 
 optical rotation are due to an unsymmetrical or twisted structure of the 
 molecule. J. J. Thomson 3 gives an approximate formula for the specific 
 rotation, namely: 
 
 1 H. A. Lorentz, Theory of Electrons, p. 306. 
 
 - W. W. Coblentz, Infra Red Spectra, Vol. 2, p. 38. 
 
 3 J. J. Thomson, Phil. Mag., Dec., 1920. 
 
491 J. VALASEK. 
 
 in which e is the charge of the electron, c is the velocity of light and M 
 and m are the masses of the molecule and of the electron, d is the radius 
 of the molecule, p is the free period, and n is the frequency for which p 
 is to be calculated. Using the value of .p derived from piezo-electric data 
 we find for sodium light the specific rotation of the order of magnitude of 
 10, the tables giving 22.1. Considering the fact that so little is known 
 of the structure of the Rochelle salt molecule, the approximation is fair. 
 The writer is indebted to Professor W. F. G. Swann, who initiated this 
 research and gave many helpful suggestions, and to Dr. W. R. Whitney, 
 Director of the Research Laboratory of the General Electric Company, 
 whose presentation of two beautifql crystals made the work possible. 
 
 PHYSICAL LABORATORY, 
 
 UNIVERSITY OF MINNESOTA. 
 
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