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ABSTRACT

 A new method of measurement for elastic wave velocities in rocks at high temperatures by means of ultrasonic impulse transmission is presented.This method consists of the direct measurement of wave velocities by utilizing the piezoelectricity of a beta-quartz crystal.It is shown that there are several kinds of cut in the orientation of a beta-quartz crystal generating or receiving the longitudinal or transversal wave,or both waves.In our experiments,these beta-quartz crystal cuts did not change in phase to tridymite at 870℃,presumably due to a sluggish inversion.The efficiencies of transducers were not reduced even at 870℃,and the measurement could be made up to about 1000℃.Thus there is a possibility of using direct measurements for high temperatures above 1000℃.
 The rock specimens used are all volcanic rocks which were collected from several localities:Mihara volcano,Izu Oo-shima;Showa-shinzan and Usu volcano,Hokkaido;Hakone volcano,Kanagawa Prefecture;Shidara,Aichi Prefecture.Some of the results obtained are noted below:
 1)Longitudinal and transversal wave velocity through volcanic rocks from Showa-shinzan and Mihara volcanoes increases with a rise in temperature up to about 800℃,while that through volcanic rocks from Shidara and Hakone volcano decreases with a rise in temperature.The longitudinal wave velocity generally varies more than the transversal wave velocity.
 2)The increase of elasticity with a rise in temperature seems to be a characteristic of the recently erupted new volcanic rocks,while the decrease of elasticity is observed in the old volcanic rocks.This seems to be mostly due to the differences in the structures of volcanic rocks.
 3)The increase of Poisson’s ratio with a rise in temperature is generally remarkably large.

INTRODUCTION

 The elastic properties of rocks at high temperatures have not been duly studied,because of many difficulties in technique for measurements at such temperatures.In particular,there are quite a few experimental data on the rigidity modulus and Poisson’s ratio of rocks at elevated temperatures.Young’s modulus of rocks at high temperatures elevated up to about 1000℃ has been determined by several methods of measurement:the static measurement by the bending method [14],the dynamic measurement by the resonance method [1,3,7],and the longitudinal wave velocity measurement by the ultrasonic impulse transmission method [6,15] have been reported.In these,the static method is unsuitable for the measurement of elasticity of rheological substances such as rocks,because of the reciprocal action of their elasticity and viscosity.It is,therefore,desirable to use the dynamic measurement,a fact that is well known.However,even when the resonance method is used,it is rather difficult to derive the torsional vibration in rock samples,particularly at high temperatures;therefore Young’s modulus has been obtained mainly by the bending vibration method.On the other hand,Hughes,Pondrom,and Mims [5] have begun to use the method of measurement of wave velocity of ultrasonic impulse transmitted through rocks.This method has proved more effective from various view points,but it is mostly restricted to the temperatures of about 550℃ and below.This is because there is no suitable transducer which can sufficiently endure at higher temperatures.To overcome this difficulty,a scheme has been devised [2] for maintaining the transducer at room temperature and for transmitting the ultrasonic impulses through the rock samples by means of a rod wave guider,which has one end fixed to the transducer and the other end closely attached to the specimen.By such a method,only the longitudinal wave seems to be obtained because of the modification of the ultrasonic impulses in the wave guider mentioned above.
 The authors carried out the experiment by paying attention to the piezoelectricity of a high quartz,called beta-quartz,and found a possibility of direct measurement of both longitudinal and transversal wave velocities in rocks for high temperatures up to 1000℃ or higher.Accordingly,by this direct measurement,which differs from that used before,the measurement of elastic wave velocities in volcanic rocks was carried out.The present paper deals with the experimental method used and lists some of the results obtained.

EXPERIMENTAL APPARATUS AND PROCEDURE

Array The ultrasonic apparatus has been constructed for the measurement of elastic wave velocities in rocks.This principal apparatus is similar to that used by Nagumo [12].A block diagram of the apparatus is shown in Fig.1 and the photograph of the experimental arrangement of the apparatus in Fig.2.The apparatus is constructed as it is generally made and consists of a pulse generator,pulse amplifier,sweep circuit,time mark circuit,and cathode-ray oscillograph.Its main characteristics are the following:The pulse generator provides an output pulse accurately synchronized with the trigger.The output pulse has a rise time of about 0.1-0.5 μ sec and a peak amplitude of about 200 volts.Furthermore,the pulse is repeated at every 1 kc per second.The time marks are given at every 1.00 or 0.20μ sec,while the maximum sweep velocity is 5cm per microsecond at the trace on the screen of the oscilloscope.The pulses are impressed on a quartz crystal which generates very sharp elastic pulse waves in the rock specimen.These waves are received at the opposite end of the specimen by a similar crystal.The quartz crystals,as well as the bariumtitanates that were used for room temperatures,were employed commonly as a driver and a receiver.The output of the receiving crystal goes through an amplifier to a cathode ray oscilloscope.The amplifier has a flat response up to 1mc per second with a gain of 110db andthen gradually falls off.
 It has been proved that small rock specimen is convenient for the high temperature experiment,and therefore a pulse adjuster having a minimum variable rise time of 0.2μ sec and a time mark of 0.20 it sec have been made for the purpose of our experiments.In any event a device to increase sweep velocity and to amplify the gain for the high frequency region extending to 15-30mc per second is now under construction.
Transducer
 X- and Y-cut quartz crystals are mostly used for the experiment of ultrasonic impulse transmission;while low quartz,designated alpha-quartz,changes into high quartz,designated beta-quartz,at 573℃.The inversion is spontaneous and accompanied by an abrupt change in the directly observable properties,even though the change is not too great.Moreover,an electric twinning is easily producible in the neighbourhood of the transition point.From these circumstances the reliable measurement for high temperatures has been carried out in safety only at temperatures below about 550℃.It was found,however,that beta-quartz had piezoelectricity,so this beta-quartz was used as a transducer.In the case of beta-quartz,the so-called X- and Y-cut crystals like as in the case of alpha-quartz are available only for the transversal wave measurement,while a special transducer is needed only for the measurements of longitudinal waves or for both longitudinal and transversal waves.Various kinds of cuts in the orientation of the crystal axis of a quartz crystal are illustrated in Fig.3.Generally,we should like to call transducers made from such cuts as β-cut crystals.The β-X- and β-Y-cut crystals for longitudinal waves have the same characteristics at temperatures above 573℃ and they are used only for the measurement of longitudinal waves.However the characteristics of  β -X -cut crystal are different from those of β-Y-cut at temperatures below 573℃.The plane of the electrode of this type of transducer is perpendicular to the plane of the sound radiation,even though this may cause inconvenience in practical use.A ,β-45°-cut crystal is used for the measurement of both longitudinal and transversal waves;it is most effective to take about 40-50° for the angle θ in Fig.3.
 The piezoelectric constants of beta-quartz crystal up to 626℃ have been obtained by Cook and Weissler [4].As seen in Fig.4,the piezoelectric constant,d_14,of beta-quartz is of almost the same order as d_11 of alpha-quartz,and therefore it is sufficiently useful for practical purposes.As seen in Fig.4,d14,_β seems to have a tendency to decrease rapidly with a rise in temperature.It was found from the results obtained from practical use,however,that it did not change too much with a rise in temperature.
 At temperatures above 870℃ beta-quartz is usually inverted into tridymite which has no piezoelectricity,but in the present experiments beta-quartz did not change in phase to tridymite at 870℃,this being presumably due to a sluggish inversion.Thus the transition did not really take place.The measurements could be carried out with the beta-quartz in the same condition until a temperature of 960℃ was reached.This temperature of 960℃ is the melting point of silver,the substance used as a cementing material to fix the transducer to the rock specimen.Consequently,in this case the transducer became useless at 960℃ because of the melting of the silver.According to the results of differential thermal analysis,beta-quartz does not seem to be inverted into tridymite until at least 1200℃.Therefore this has opened a possibility to measure directly the elastic wave velocity of rocks by means of ultrasonic impulse transmission at temperatures above 1000℃.
 In the cooling process from temperatures above the inversion point of alpha- to beta-quartz(573℃),an electric twinning was generally produced in the alpha-quartz crystal under 573℃,and the experiment could not be continued under the same conditions.In some cases it is possible to prevent [16] the electric twinning by imparting a suitable static stress and electric field to the transducer before the temperature in question is attained.
 At high temperatures the transducer is sometimes broken down,so we made the transducer self-producing The dimension of the transducer used was changed according to the size of rock specimen,namely(1.0~1.5)×(1.0~ 1.5)×(0.2~0.4)cm3 for X-cut and Y-cut crystals and 1.0×1.0×1.0cm3 or 1.2x0.4×0.6cm3 for β-X- and β-Y-cut crystals.
Method of experiments
 First,a transducer and an electrode cemented to both ends of the rock specimen.A mixture of sodium silicate(water glass)and graphite powder or Dupont silver conductive coating was used for this cementing material.It was found that the silver conductive coating was fairly good for this experimental purpose,but that it could not be used above 960℃,its melting point.The sodium silicate in this mixture,however,was found to be a good substance to attach firmly the rock specimen to the transducer at high temperatures,particularly above 800℃,but was found to be somewhat inadequate at comparatively low temperatures,because the electrode or transducer cemented to the rock specimen is sometimes fall off due to an air bubble,probably caused by the dehydration of the sodium silicate.
 Both ends of the rock specimen having the electrode and transducer thus cemented were covered by a special fire brick,the outside of which was electrically shielded by painting the mixture of sodium silicate and powder of graphite over it.These features are illustrated by the photograph of the rock specimen prepared for the experiment,as shown in Fig.5.
 Since the elastic constants of alpha-and beta-quartz crystals are given by E.W.Kammer et al.[9,10] up to 800℃,the so-called response delay time of the transducer against a pulse can be calculated for various types of transducers up to 800℃.In the neighbourhood of a temperature of 573℃ the elastic property of the quartz crystal varies rapidly according to the variation in temperature.Moreover the elastic wave velocity of the rock specimen becomes rather large in the neighbourhood of 1-2cm away from the driver.To eliminate these influences,two rock specimens with a different length were measured at the same time during one experiment,and the delay time induced was cancelled out from the observation of apparent time difference of impulse transmission through them.Thus the velocities of longitudinal and transversal waves directly transmitted through the specimen were accurately determined.In this case,the uncertainty of the absolute velocity does not usually exceed 2 per cent and is no greater than 5 per cent even in the worst condition.The errors induced are chiefly due to the obscurity of the rise of the pulse and to the uncertainty of the identification of the pulse.Accordingly,our experimental apparatus is being continuously modified so as to increase the accuracy of measurements.
 To elevate the temperature an electric furnace about 35 cm in length and about 10 cm in diameter was used.This furnace was horizontally set and was filled with nitrogen gas for the purpose of preventing the oxidation of the specimen.The rock specimen was horizontally placed on a steel plate set in the center of the furnace.The temperature was always measured at about the center of the specimen.The thermocouple leads passed through insulated porcelain tubes to the cold junction,from which copper connections were carried to a potentiometer.Chromel-alumel or platinum-platinum rhodium thermocouples were used in conjunction with the manufacture’s calibration table;the temperature measurement was thus made with the maximum error of about ±5℃.It was necessary to allow a little time for the specimen itself to reach the temperature of the furnace;in this case the rate of change in temperature was 200-300℃ per hour.

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FIG.1.Block diagram of the experimental apparatus.TP:Trigger pulse generator.TM:Time mark generator.SG:Sweep generator.PD:Pulse delay.A:Attenuator.C.R.O:Cathode ray oscillograph.DPA:Driving pulse adju
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写真 FIG.2.General view of the experimental apparatus.
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FIG.3.β-cut transducer of quartz crystal for high temperatures.Shaded surface:plane of electrode.Dotted surface: plane of sound radiation.
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FIG.4.Temperature variations of piezoelectric constants of quartz(after R.K.Cook and P.G.Weissler [4]).
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写真 FIG.5.General view of the rock specimen used for the experiment.Upper two specimens: showing the inside view of the special fire brick covering the transducer which is cemented to each end of the spec

ROCK SPECIMEN

 The rock specimens used in this experiment were all volcanic rocks and were cut to suitable length by a diamond saw from solid rocks collected from several localities.The ends of the specimens were ground smoothly to a plain parallel finish before the measurements were made.The specimens were all rectangular prisms,1.2 to 1.5 cm in width and 2.0 to 6.0cm in length.The names of the rock specimens are listed in Table1 together with their localities,their longitudinal and transversal wave velocities at room temperature,their densities,and their cutting types from which the transducers were made.The names of the rock specimens listed are given according to the classification of volcanic rocks by Kuno [11].The chemical and petrographical studies of some kinds of rocks used were-already carried out by a number of investigators [11,13,17,18].Their chemical compositions are listed in Table2.The specimens,after the silver coating,were placed in the apparatus 
for ultrasonic impulse transmission.

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TABLE1.LONGITUDINAL AND TRANSVERSAL WAVE VELOCITIES AT RQOM TEMPERATURE,LOCALITY,AND DENSITY OF VOLCANIC ROCKS
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TABLE2.CHEMICAL COMPOSITION OF VARIOUS VOLCANIC ROCKS

RESULTS

Array By means of the apparatus iust mentioned above the elastic waves through the rock specimens were photographically taken on an oscilloscope screen.
 Top curve of each record represents time marks,1 microsecond.Middle and lowest curves of each record represent the longitudinal and transversal waves through the rock specimens,the lengths of which are 6.00 and 3.00 cm respectively.Fig.6 shows some examples of the records of the wave patterns obtained.The incident and received wave pulses are shown on the records.The wave trains received show two sharply distinguishable phases,the first,a smaller one corresponding to the longitudinal wave and,the second,a larger one corresponding to the transversal wave.
 The velocities of longitudinal and transversal waves,V_1 and V_t,were obtained from the relationship between the length of the specimen and the times of the first and the second phases respectively.The values of V_1 and V_t thus determined for some examples of specimens are given in Table3.The variations in these velocities with a rise in temperature are shown in Figs.7 and 8.Furthermore,Young’s modulus E,rigidity modulus μ,and Poisson’s ratio σ were computed from the longitudinal and transversal waves:

【数式】

These values were plotted against the temperatures,as shown in Figs.9 and 10.
 As seen in Figs.7 and 8,the longitudinal wave velocity of rocks such as the 1950 lava of Mihara and the 1944 lava of Showa-shinzan decreases slightly at a temperature around 100℃ or 200℃ and then increases somewhat more when the temperature rises to about 700-800℃;on the other hand,the velocities of rocks from Hakone and Usu volcanoes and Shidara decrease only with a rise in temperature.
 The velocity of the transversal wave varies with a rise in temperature in a similar way to the longitudinal wave,although its variation is not so great as that in V_1.The phenomenon of the increasing wave velocity with the increasing temperature may be seen in the recently erupted rocks,such as basalt from Mihara and hypersthene dacite from Showa-shinzan.On the contrary,a decreasing wave velocity may be seen in the comparatively old rocks,such as two-pyroxene andesite from Hakone and Usu volcanoes and rhyolite from Shidara.
 With respect to Young’s modulus Sakuma [14] found that the lava of Showa-shinzan and Oo-shima increased its value remarkably with a rise in temperature up to nearly 700-800℃,after which its value began to decrease;the maximum value it attained was about 1.5 to 2.0 times as great as its initial value at room temperature.The present results also show a tendency to increase E when the temperature rises as seen in Fig.9,but the value of increase is found to be a little less than the amounts above.The difference between the two cases depends upon the differences in the method and specimens used.The temperature variation of μ is also seen in Fig.9;the maximum increasing value it attained was about 1.8 times as great as its initial value.This increase of elasticity with a rising temperature will be seen also in the rocks from Showa-shinzan(S).On the other hand,a decreasing elastic constant with a rise in temperature may be seen in the rocks from Shidara(K)and Usu(G-1),as shown in Fig.10.
 The Poisson’s ratio σ varies rather greatly according to the increase of temperature,as shown in Figs.9 and 10.As a whole,a has a tendency to increase the value with a rise in temperature except for the rocks from Shidara.Since σ is a function of the ratio of V_1 to V_t,even a slight change in V_1 and V_t has much influence upon σ.This variation of σ is caused by a great increase of V_1 rather than by any decrease of V_t.Thus it is interesting to note in this phenomena that the rocks are in a sense to become harder,not softer,when a larger value of σ with a rise in temperature is given,so far as the present temperature ranges are concerned.
 In any event there are two kinds of variation types in the variation of the elasticity and temperature of volcanic rocks.The increase of elasticity is quite similar to the results concerning amorphous silica [8].It is,however,noted that this increase of elasticity does not always depend on only the amount of silicate,as given in Table 2.Then the increase of elasticity seems to be a characteristic of the new volcanic rocks recently erupted and the decrease of elasticity a characteristic of the old volcanic rocks.This may be considered the main differences in the structures of rocks.
 Furthermore,the thermohysteresis phenomena were observed in the andesite from Hakone.Its velocity,V_t,in the cooling process following a heating to about 1000℃ is quite different from that in the heating process above 600℃.Such phenomena were already observed in the case of the basalt from Oo-shima [14].Consequently,if the rocks are subjected to a high frequency region of ultrasonic impulse,a thermohysteresis has much influence upon their elastic constants.

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FIG.6a.Examples of records obtained by the experiment.Rock specimen:hypersthene dacite,lava of Showa-shinzan.
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FIG.6b.Examples of records obtained by the experiment(Continued).Rock specimen:hypersthene dacite,lava of Showa-shinzan.
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TABLE3.VARIATION OF LONGITUDINAL AND TRANSVERSAL WAVE VELOCITIES AND ELASTIC CONSTANTS OF VOLCANIC ROCKS WITH TEMPERATURE
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【数式】
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FIG.7.Variation of elastic wave velocity of recently erupted volcanic rocks from Showa-shinzan and Mihara with temperature.● V_1,▲ V_t,M-1,M-2: Basalt from Mihara volcano,S:Hypersthene dacite from Sho
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FIG.8.Variation of elastic wave velocity of volcanic rocks from Hakone,Usu,and Shidara with temperature.● V_1,▲ V_t,H:Two-pyroxene andesite from Hakone volcano.K: Rhyolite from Taguchi,Shidara.T:Bioti
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FIG.9.Variation of Young’s modulus,rigidity,and Poisson’s ratio of recently erupted volcanic rocks from Showa-shinzan and Mihara with temperature.● E,▲ μ,○ σ,M-1,M-2,S are the same as those in Fig.7.
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FIG.10.Variation of Young’s modulus,rigidity,and Poisson’s ratio of volcanic rocks with temperature.● E,▲ μ,○ σ,K,G-1 are the same as those in Fig.8.

SUMMARY

 An ultrasonic apparatus has been constructed for the measurement of elastic wave velocity in rocks.By utilizing the piezoelectricity of beta-quartz crystal the direct measurement of longitudinal and transversal wave velocities of ultrasonic impulses transmitted through rock specimens was carried out at high temperatures up to about 1000℃.The rock specimens used were all volcanic rocks such as hypersthene dacite,two-pyroxene andesite,basalt,and rhyolite.These were collected from several localities such as Mihara volcano,Oo-shima;Showa-shinzan and Usu volcano,Hokkaido;Hakone volcano,Kanagawa Prefecture;Shidara,Aichi Prefecture.The results obtained are summarized as follows:
 1)Longitudinal and transversal wave velocities through volcanic rocks from the Showa-shinzan and Mihara volcanoes increase with a rise in temperature up to about 800℃,while those through volcanic rocks from Shidara and Hakone volcano decrease with a rise in temperature.The longitudinal wave velocity generally varies more than the transversal wave velocity.
 2)The temperature variation of Young’s modulus of rocks is generally remarkable compared with that of the rigidity modulus.
 3)An increase of elasticity with a rising temperature seems to be a characteristic of the recently erupted new volcanic rocks and a decrease of elasticity a characteristic of the old volcanic rocks.This seems to be the main difference in the structures of volcanic rocks.
 4)Poisson’s ratio varies according to the temperature variation and generally increases with a rising temperature.The variation with temperature of the longitudinal wave velocity contributes to this phenomena more than the transversal wave velocity does.
 5)The thermohisteresis of volcanic rocks seems to have a great influence upon the variation in elasticity.

ACKNOWLEDGMENT

 In conclusion,the authors wish to express their thanks to Mr.K.Suwa,who made the classifications of the rock specimens.The expenses for the study were partly defrayed from the Grant in Aid for Scientific Research given by the Ministry of Education.

REFERENCES

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