A S O T E O N T H E HIGH-LOW INTERSION O F QUARTZ AKD T H E HEAT CAPACITY OF LOW QUARTZ AT 573" BY R. E. GIBSON
It has been shown definitely' that the high-low inversion of a crystal of quartz is a phase change which is always accompanied by superheating. As the reaction is so rapid that it might be considered as proceeding adiabatically I thought it possible to calculate the heat capacity of low quartz a t j73'. This may be done as follows. Let TZ = the maximum temperature to which the crystal superheats = the minimum temp. to which it cools during the reaction Ti 1HTl = the heat content of the lower phase (low quartz) a t T I lHT9 = the heat content of low quartz a t T z a H T , = the heat content of high quartz at T 1 = the average heat capacity of low quartz between TI and T z CL L = the latent heat of inversion a t T1; L = ~ H T, zHT, Then iHT, C L ( T ~ TI) - = ~HT% But ~ H T ?= Z H T ~if the process is adiabatic. ... ~ H T , C L ( T ~ - T I )= ~ H T , L = CL(T?-Tl).
:.
+ +
If L and ( T z - Ti) are known we may make an estimate of CL. I n the preceding paper I have calculated a value of the latent heat of inversion from what seems to be the best value of the volume change and the pressure coefficient of the inversion temperature. This gives L = 3.x cal. per gram. T 2 - Tl has been measured by Bates and Phelps for many different specimens and is given the mean value of 0.j'. I n the following I shall outline several experiments made with blocks of quartz in which T 2- 2'1 seemed to be nearer 0.9'. Bates and Phelps do not indicate what steps were taken t'o ensure good contact between the thermocouple and the quartz but their results are consistent and so as an approximation I shall take 0.7 as a tentative value for T2 - Tl. Hence C L = 3.1,/0.7 = 4.4. The outside limits for CL, taking the extremes in the values for T Z- TI, are 3 and j cal. per gram per degree. We have therefore the result that the heat capacity of low quartz in the neighborhood of the high-low inversion is 4 i I. This is more than ten times the heat capacity of low quartz a t j j o o or of high quartz a t 600'. White, and Perrier and R O U Xhave , ~ shown that the heat capacity of quartz builds up with increasing rapidity above joo' and a very high value of the heat capacity is to be expected. Despite this effect, however, the value just obBates and Phelps, Bur. Standards Sci. Papers (No. 5j7) 22, 31j (1927). Properties of Silica," p. 337 (1927).
* Sosman: "The
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tained is astonishingly high and it was thought worth while examining the validity of the assumptions underlying the foregoing calculation. We have assumed in this calculation: (I) that the reaction is rapid. (2) that the whole block inverted while the temperature dropped from T:!to T,. Assumption number ( I ) , made necessary to avoid confusion with sluggish transformations, is borne out by experiment. A11 observers agree that the reaction is quite rapid. The second assumption will be reasonable if it can be shown that T I is always above the equilibrium temperature, Le., the temperature at which the change is thermodynamically reversible. I hope to demonstrate in this paper that the equilibrium temperature of the j j3' inversion of quartz is the maximum temperature reached during the high-low transbrmation on cooling, and as this is always several tenths of a degree below T,, we may say that the above calculation is fairly sound.
Experimental Heating and cooling curves j o r blocks of quartz. Two cylinders of quartz were studied. The first, cut from a crystal of vein quartz from Hot Springs, Arkansas (Xational Museum S o . 8 3 6 6 0 ) was 19 mm long and 1 2 mm in diameber. The seconci iTC2.S cut from a pebble of quartz from Brazil and was 19 mm long and I O mm in diameter. Both were drilled axially to a depth of 11 mm and in these holes thermocouples were placed. It should be emphasized that the thermocouple fitted tightly in the hole so that good contact was made between the element and the quartz. The blocks were enclosed in thick-walled silver crucibles, placed in a platinum furnace and heat.ing and cooling curves were made in the usual way, temperature readings being taken every quarter of a minute. Chromelalumel wuples were used. The sensitivity of these is quite high, 42.4 microvolts being equivalent to IT. The couples were calibrated a t the freezing point of antimony (630'). A series of orienting experiments confirmed Bates and Phelps' observations as to the superheating and supercooling phenomena. Curves I and 2 , Fig. I , show the results. It will be seen that the drop in temperature during the low-high transformation is as great as 1°C but that the rise of temperature during the high+low change never exceeds 0 . 2 ~ . The comparative flatness of the maxima on the cooling curves, taken in conjunction with the small supercooling, led to the thought that the equilibrium temperature was close to the highest temperature reached after supercooling. To test this hypothesis I tried to reverse the reaction during the high+ low inversion. The temperature of the furnace was allowed to fall slowly until the minimum on the heating curve indicated the change was taking place. Thereafter, a t a convenient time, the current through the furnace was doubled. The cooling stopped almost instantly and the block started to gain heat from the furnace. The results are given in curves 3, 4 and j
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(Fig. I ) . The arrows indicate when the reheating was started. I n cases 3 and 4 the heating was begun before the maximum temperature was reached. The temperature of the block remained practically constant for a fraction of a minute and then rose steadily and rapidly. In case 5 , however, where reheating was not begun until after the maximum on the cooling curve had been passed, the curve exhibited no preliminary flattening, the temperature rose immediately, the low quartz superheated and then inverted with the usual drop in temperature. About twenty experiments in all were made. The results were all entirely similar to those given in the figures.
2 TIMCI.UINUTEI
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I+
&
14
12
14
lb
I#
LO
12
24
FIG.I Heating and cooling curves for a block of quartz, illustrating reversal of the high +low inversion.
It would seem, therefore, that, if reheating of a quartz block is begun a t the maximum on the cooling curve or just before it, the low quartz present is converted to the high variety without appreciable superheating. If, however, the maximum is passed, indicating that the high-low inversion has gone to completion, then, on reheating, the low-high change is accompanied by superheating. The parallelism between this phenomenon and the presence or absence of the solid phase during the freezing of a liquid which supercools readily is too obvious to require emphasis. One is perhaps justified in saying that about the temperature of this maximum ( 5 7 2 . 3 & 0.2') low and high quartz coexist in equilibrium or a t any rate behave thermodynamically as if they did. We may also conclude that the difference in the observed temperature of the up and down inversions is solely a matter of superheating and supercooling, and is not due to a real difference in the temperatures of these two changes.' 1
For other explanations see Sosrnan: op. cit., p.
122.
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It should be emphasized that these experiments refer to a sound, solid block of quartz. The effect of shattering on a block is shown in Fig. 2 . Curres I and I’ were made with a sound block; curves 2 , 3 , 2 ’ and 3’ with exactly the same block half an hour later when it had been shattered by bringing it extremely rapidly through the inversion. The chief features of interest are the lessening of the temperature drop during the low-high inversion and the flattening of the cooling curve. I
TIHEuPIINUTES
--+ FIG.z
Heating and cooling curves for a broken block of quartz.
attribute these differences to the individual fragments’ inverting a t different times. The heat changes are thus distributed in time and the effect on the thermocouple is thereby diminished. In one series of experiments with a broken block of Arkansas quartz the cooling curves were almost parallel to the time axis during inversion. There was practically no supercooling. An example of this is seen in curve 2 , Fig. 3 , of the previous paper. There is a difference of 0 . 3 ~in the maxima on the heating curves before and after breaking but the maximum on the cooling curve is altered by only 0.05’. Curve 3’ gives another illustration of the reversal of the reaction during the high+low change. I have included the curves for a cracked block because they demonstrate that the constancy of the temperature of the maximum on the heating curve (573.3’) for a solid block is perhaps a matter of accident and that the fundamental temperature of this reaction is 572.3 ( * o . z ) , the equilibrium temperature of the reaction.
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Conclusion and Summary The high-low inversion of a crystal of quartz at one atmosphere pressure is a change of phase which is generally accompanied by superheating and supercooling. There seems, however, to be a temperature (572.3 + 0.2) a t which low quartz may be converted reversibly to high quartz and were it not for almost insuperable experimental difficulties it would be possible to have the two phases in equilibrium a t this temperature. This renders unnecessary any hypothesis of forced inversion. Before a block of low-quartz passes to the high variety it superheats so much that during the inversion its temperature never falls to the equilibrium value. Therefore, since the reaction is adiabatic, we may calculate the apparent heat capacity of low quartz around 573'. This is 4 f I cal. per gram per degree. On the changes in physical properties of quartz between 'o and 570' we can throw no light. Quartz a t 570' is certainly very different from quartz a t atmospheric temperature but quartz a t 570' is a definite and stable substance and the inversion a t ~ 7 2 . 3 'except ~ for the superheating or supercooling, is quite comparable with any rapid enantiotropic change. Geophysacal Laboratory, Carnegae Instztutaon o j Washanqton, Apral, 1928
