Contains research objectives and summary of research.National Science Foundation (Grant GP-13548)ARPA Contract DAHC15-67-C-022

Garland, C. W.

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VII. COOPERATIVE PHENOMENA IN SOLIDS AND FLUIDSAcademic and Research StaffProf. C. W. Garland Dr. L. MisturaDr. E. Litov Dr. R. J. PollinaGraduate StudentsA. Bonilla D. EdenCarolyn K. Choo B. B. WeinerRESEARCH OBJECTIVES AND SUMMARY OF RESEARCHThe general goal of our ultrasonic investigations is to obtain information about bulksystems near cooperative phase transitions or critical points. In particular, ultrasonicvelocities give direct information about the equilibrium thermodynamic properties, andultrasonic attenuation provides data about the dynamical behavior. The majority of thework is concerned with order-disorder lambda transitions in solids, but fluids neartheir liquid-vapor critical point are also being studied. During the past year, progresswas made on a variety of ultrasonic problems. Work on KH PO4 and BaTiO 3 near theirferroelectric Curie temperatures has been completed. The KDP results have been pub-lished, but the BaTiO3 data are still being analyzed. Considerable progress has alsobeen made on the study of xenon near its critical point. Data have been obtained alongseveral near-critical isochores and along several isotherms. A recent contribution toPhysical Review Letters describes the attenuation results and analyzes them in termsof current theories of dynamical critical phenomena.In addition to ultrasonic investigations, our group has carried out low-temperaturex-ray structural studies, and isothermal compressibility measurements. The latterare based on a new capacitance method of measuring the length of a single crystal asa function of pressure. This method was developed by B. B. Weiner and has been appliedto the order-disorder transition NH 4 C1. At low transition pressures (pt < 1500 bar),there is a small first-order discontinuity in the volume at the "lambda" line. For tran-sition pressures above 1500 bar, the variation V is continuous and becomes progress-ively more gradual as the pressure increases.Work continues on dynamical calorimetry, where phase-sensitive detection tech-niques are applied to the measurement of heat capacities near a critical point. Apparatushas been designed and tested; measurements on chromium near its antiferromagnetictransition are in progress.C. W. GarlandPublicationsA. Bonilla, C. W. Garland, and N. E. Schumaker, "Low Temperature X-Ray Investi-gation of NH Br," Acta Cryst. A26, 156 (1970).N. E. Schumaker and C. W. Garland, "Infrared Investigation of Structural and OrderingChanges in Ammonium Chloride and Ordering Changes in Ammonium Chloride and Bro-mide," J. Chem. Phys. 53, 392 (1970).C. W. Garland and B. B. Weiner, "Anharmonic Potential Function for Libration inAmmonium Chloride and Bromide," J. Chem. Phys. 53, 1609 (1970).This work is supported by the National Science Foundation (Grant GP-13548) andby ARPA Contract DAHC15-67-C-0222.QPR No. 100(VII. COOPERATIVE PHENOMENA IN SOLIDS AND FLUIDS)C. W. Garland and D. D. Snyder, "Ultrasonic Attenuation near the Lambda Transitionin NH 4Cl at High Pressures," J. Phys. Chem. Solids 31, 1759 (1970).C. W. Garland, "Ultrasonic Investigation of Phase Transitions and Critical Points," inPhysical Acoustics, W. P. Mason and R. N. Thurston (eds.) (Academic Press, New York,1970), Vol. 7, Chap. 2, pp. 51-148.C. W. Garland, D. Eden, and L. Mistura, "Critical Sound Absorption in Xenon," Phys.Rev. Letters 25, 1161 (1970).E. Litov and C. W. Garland, "Ultrasonic Investigation of the Ferroelectric TransitionRegion in KH PO 4," Phys. Rev. B 2, 4597 (1970).C. W. Garland and B. Weiner, "Changes in the Thermodynamic Character of the NH 4C1Order-Disorder Transition at High Pressures" (to appear in Phys. Rev. B, March 15,1971).ThesesB. B. Weiner, "Volume Anomalies in Ammonium Chloride along the Lambda Line,"Ph.D. Thesis, Department of Chemistry, M. I. T., September 1970.QPR No. 100

Cooperative Phenomena in Solids and Fluids

Contains research objectives and summary of research.National Science Foundation (Grant GP-35082X

VI. COOPERATIVE PHENOMENA IN SOLIDS AND FLUIDSAcademic and Research StaffProf. C. W. GarlandDr. R. J. PollinaDr. J. ThoenGraduate StudentsA. Bonilla Carolyn K. ChooD. E. Bruins G. E. MillerRESEARCH OBJECTIVES AND SUMMARY OF RESEARCHThe general goal of our work is to obtain information about bulk systems nearcooperative phase transitions or critical points. Primary emphasis is on ultrasonicinvestigations. In particular, ultrasonic velocities give direct information about theequilibrium thermodynamic properties and ultrasonic attenuation provides data about thedynamical behavior. The majority of the work has been concerned with order-disorderlambda transitions in solids, but critical points in fluids are also being studied. Duringthe past year progress was made on a variety of ultrasonic problems. Interesting datahave been obtained as a function of temperature for NH4Br at 1 atm and for NH 4C athigh pressures. In the case of NH 4 Br, where an antiparallel ordering occurs, thebehavior is quite different from that of NH 4 C 1, where a parallel ordering takes place.In the case of NH 4 C1, the critical variations in the velocity and attenuation undergo dis-tinct changes as the pressure is increased in the disordered phase.A recently completed ultrasonic investigation of the relaxation processes associatedwith the nematic-isotropic phase transition in liquid crystals was carried out on p-methoxybenzylidine-p-n-butylaniline (MBBA). Simultaneous measurements of the soundvelocity and absorption in samples of MBBA without any preferred orientation were madeat eight frequencies from 0. 3 to 23 MHz. The temperature range from 230 to 77 0 C wasstudied, with special attention given to the region near the transition at -44oC. Farfrom the transition the absorption and velocity dispersion can be well described by asingle relaxation process for which the relaxation time and the relaxation strength bothincrease substantially as the transition is approached. In the immediate vicinity of thetransition the acoustic properties are characteristic of a multiply relaxing fluid.In addition to ultrasonic investigations, experimental work has also been completedon the variations in the heat capacity C of chromium in the vicinity of its antiferromag-netic transition. An ac calorimetric technique was modified for high-pressure work,and four isotherms at 25, 32. 5, 34. 8, and 37. 4°C were investigated. The heat-capacitydata indicate a striking change in the thermodynamic character of the transition at highpressures. At 37.4°C the heat capacity shows a small X-like peak at 490 bar. At a"critical point" near 34. 8°C and 890 bar, the heat capacity peak is enormous and thereis experimental evidence to suggest that it tends to infinity at this point. At 32. 5 0 C, theC peak at the transition pressure (1060 bar) is finite and small. The peak in C seemsp pto decrease rapidly in magnitude as one proceeds farther along the transition line. At250C, there is no sign of any heat capacity anomaly at an expected transition pressureof 2900 bar. A detailed analysis of these data is in progress.C. W. GarlandThis work is supported by the National Science Foundation (Grant GP-35082X).QPR No. 108(VI. COOPERATIVE PHENOMENA IN SOLIDS AND FLUIDS)PublicationsB. B. Weiner and C. W. Garland, "Order-Disorder Phenomena. VII. Critical Varia-tions in the Length of NH4C1 Single Crystals at High Pressures," J. Chem. Phys. 56,155 (1972).D. Eden, C. W. Garland, and J. Thoen, "Sound Absorption and Dispersion along theCritical Isochore in Xenon," Phys. Rev. Letters 28, 726 (1972).P. E. Mueller, D. Eden, C. W. Garland, and R. C. Williamson, "Ultrasonic Attenu-ation and Dispersion in Xenon near Its Critical Point," Phys. Rev. A 6, 227(1972).D. Eden, C. W. Garland, and R. C. Williamson, "An Ultrasonic Investigation of theNematic-Isotropic Phase Transition in MBBA," J. Chem. Phys. (in press).C. W. Garland, "Ultrasonic Investigation of the Lambda Transitions in NH 4 C andNH4 Br," J. Physique Suppl. (in press).ThesesA. Bonilla, "High-Pressure Heat Capacity of Chromium near Its AntiferromagneticTransition Line," Ph.D. Thesis, Department of Chemistry, M. I. T., September 1972.QPR No. 108

VI. COOPERATIVE PHENOMENA IN SOLIDS AND FLUIDSAcademic and Research StaffProf. C. W. Garland Dr. R. J. PollinaDr. L. Mistura Dr. J. ThoenGraduate StudentsA. Bonilla Carolyn K. ChooD. E. Bruins D. EdenRESEARCH OBJECTIVES AND SUMMARY OF RESEARCHThe general goal of our work is to obtain information about bulk systems near coop-erative phase transitions or critical points. Primary emphasis is on ultrasonicinvestigations. In particular, ultrasonic velocities give direct information about theequilibrium thermodynamic properties and ultrasonic attenuation provides data aboutthe dynamical behavior. The majority of the work has been concerned with order-disorder lambda transitions in solids, but critical points in fluids are also being studied.During the past year progress was made on a variety of ultrasonic problems. Interestingdata have been obtained as a function of temperature for NH4Br at 1 atm and forNH4 C1 at high pressures. In the case of NH4Br, where an "antiparallel" orderingoccurs, the behavior is quite different from that of NH 4 C1, where a "parallel" orderingtakes place. In the case of NH4 C1, the velocity and attenuation undergo a distinct changeas the pressure is increased. This work is still being actively pursued. Our majorultrasonic results during 1971, however, involved investigations of fluids: xenon andthe liquid crystal MBBA. The highlights of that work are described below.A novel phase-sensitive detection technique with signal averaging has made pos-sible the measurement of velocity and attenuation in a critical region where acousticattenuation is very large. The critical attenuation per wavelength and the reduced veloc-ity dispersion along the critical isochore in xenon were found to depend on tempera-ture and frequency through a single, dimensionless variable c/0 D , where cD is thecharacteristic frequency for thermal diffusion. Overall agreement with recent theoreti-1cal predictions of Kawasaki is good but not perfect. The data seem to suggest thepresence of other relaxation processes very near the critical point. The same ultra-sonic method was also used to measure the ultrasonic velocity and attenuation over awide range of temperature and frequency in the region of the nematic-isotropic phasetransition in MBBA. In the nematic phase, the relaxation time becomes very long asthe clearing temperature is approached: T = 4. 1 X 10 - 7 IAT -0.40 s. In the isotropic-8phase, there is a less pronounced variation in the relaxation time: T = 9.0 X 10 - 8 (T-T ) s,where To is 2.4 deg below the clearing temperature. The data nearest the phase trans-ition exhibit a relaxation spectrum which is definitely broader than that of a singlerelaxation time. This work represents the first detailed ultrasonic study of the phasetransition in a liquid crystal.In addition to ultrasonic investigations, work has also been carried out on dynamicalcalorimetry and high-pressure compressibility. The latter work, which is now com-plete, involved the measurement of anomalous variations in the length L of anThis work is supported by the National Science Foundation (Grant GP-13548) andby ARPA Contract DAHC15-67-C-0222.QPR No. 104(VI. COOPERATIVE PHENOMENA IN SOLIDS AND FLUIDS)NH4 C1 single crystal in the vicinity of its order-disorder transition line. At low pres-sures, there is a small first-order discontinuity AL superimposed on the expectedlambda-like variation in L. At a "critical" point (255. 95*K and 1491. 8 bar), L variescontinuously but KT and a appear to diverge. At higher pressures, the variationin L at the transition becomes progressively more gradual as the pressure increases.The compressibility along the critical isotherm varies like (Ap)-Y in the immediatevicinity of the transition and the coefficient of thermal expansion along the critical-xisobar is fairly well represented by (AT) . The exponents x and y, which range from0. 4 to 0. 9, are much larger than those associated with an ideal Ising lattice. Thisinvestigation shows the important role of stress-strain variables in determining thebehavior near cooperative phase transitions in compressible solids.C. W. GarlandReferences1. K. Kawasaki, Phys. Rev. A 1, 1750 (1970); A 3, 1097 (1971).PublicationsC. W. Garland and B. B. Weiner, "Changes in the Thermodynamic Character of theNH4 Cl Order-Disorder Transition at High Pressures," Phys. Rev. B 3, 1634 (1971).Book Review: "Ultrasonic Methods in Solid State Physics," by R. Truell, C. Elbaum,and D. Chick, Physics Today 24, 77 (1971).B. B. Weiner and C. W. Garland, "Order-Disorder Phenomena. VII. Critical Varia-tions in the Length of NH 4 C1 Single Crystals at High Pressures" (accepted for publi-cation in J. Chem. Phys.).ThesesD. Eden, "Ultrasonic Investigations of Phase Transitions in Fluids: Xenon andp-methoxy-benzylidine, p-n-butyl-aniline, " Ph. D. Thesis, Department of Chemistry,M.I.T., September 1971.QPR No. 104

Contains research objectives and summary of research.Joint Services Electronics Programs (U. S. Army, U. S. Navy, and U. S. Air Force) under Contract DA 28-043-AMC-02536(E

XI. COOPERATIVE PHENOMENA IN SOLIDS AND FLUIDSAcademic and Research StaffProf. C. W. GarlandDr. E. LitovDr. B. A. StrukovGraduate StudentsA. Bonilla D. EdenCarolyn K. Choo B. B. WeinerRESEARCH OBJECTIVES AND SUMMARY OF RESEARCHThe general goal of our ultrasonic investigations is to obtain information about bulksystems near cooperative phase transitions or critical points. In particular, ultrasonicvelocities give direct information about the equilibrium thermodynamic properties, andultrasonic attenuation provides data about the dynamical behavior. The majority of thework is concerned with order-disorder lambda transitions in solids, but fluids neartheir liquid-vapor critical point are also being studied.During the past year, progress was made in a variety of areas. Ultrasonic investi-gations of xenon near its critical point and KHZPO4 near its ferroelectric Curie temper-ature have been actively pursued. Dr. Eliyahu Litov has completed a study of the tran--1sition region in KDP as a function of applied electric field. A field of at least 3 kV cm-was found necessary to obtain a single-domain crystal and avoid scattering losses. Themost interesting result of this work involves comparison of the polarization relaxationtimes in KDP with those in KD P (that is, KD 2 PO4). In the paraelectric phase T(KDP)0.1 T(KD P), whereas the two relaxation times are essentially equal in the ferroelectricphase. This indicates that hydrogen tunneling is an important mechanism above Tc forKDP. Considerable progress has also been made on the study of xenon. Data have beenobtained by Peter E. Mueller and Don Eden along the two near-critical isochores andalong several isotherms. Recently, the sensitivity of the ultrasonic equipment wasgreatly enhanced by modifying a coherent detection scheme for use in variable-path-1measurements. This permits velocity accuracy of ±0. 7 dB cm- , even when dealing-1with pulses that are attenuated as much as 1000 dB cm . The most important resultof the xenon work is the observation of appreciable velocity dispersion and nonclassicalattenuation behavior between 0.5 MHz and 5 MHz. Recently, Dr. Strukov and Dr. Litovhave begun an ultrasonic study of polarization fluctuations near the Curie point inBaTiO3 , which is a typical displacive ferroelectric.In addition to ultrasonic investigations, the group has carried out infrared measure-ments on ammonium halide crystals near order-disorder transitions, low-temperaturex-ray structural studies, and isothermal compressibility measurements. The last arebased on a new capacitance method of measuring the length of a single crystal as afunction of pressure. This method was developed by Bruce B. Weiner and has beenapplied to the order-disorder transition in NH 4 C1. At low transition pressures(pt < 1700 bar), there is a small first-order discontinuity in the volume at the "lambda"line. For transition pressures between 1700 bar and 2500 bar, the transition appearsto be of the classical lambda type (that is, V varies continuously but infinitely rapidly atThis work was supported by the Joint Services Electronics Programs (U. S. Army,U. S. Navy, and U. S. Air Force) under Contract DA 28-043-AMC-02536(E).QPR No. 96(XI. COOPERATIVE PHENOMENA IN SOLIDS AND FLUIDS)the transition). Above 2500 bar, the volume variation indicates that the transition issecond-order in the Ehrenfest sense.The newest work in our group involves dynamical calorimetry, where phase-sensitivedetection techniques have been applied to the measurement of heat capacities near a crit-ical point. The sample is subject to a heat input at a fixed frequency w, and its tempera-ture variation is detected with a thermocouple whose output is measured with a "lock-in"detector. This output signal, which is inversely proportional to the heat capacity of thesample, can be measured with considerable precision as a function of the mean sampletemperature. The dynamic behavior of a system with oscillatory heat input is deter-mined by two time constants. It is desirable that wT 1 > 1 and w 2 < 1, where T 1 is therelaxation time for heat flow between the sample and the surroundings, and T2 is thecharacteristic time for the sample to reach internal thermal equilibrium. Apparatushas been designed and test measurements are in progress on the application of thismethod to chromium near its antiferromagnetic transition.C. W. GarlandPublicationsC. W. Garland and R. A. Young, "Elastic Constants of Ammonium Bromide, II. High-Pressure Ultrasonic Investigation of the Phase Transitions," J. Chem. Phys. 49,5282 (1968).C. W. Garland and D. B. Novotny, "Ultrasonic Velocity and Attenuation in KH2PO ,"Phys. Rev. 177, 971 (1969).C. W. Garland and N. E. Schumaker, "Infrared Investigation of Ordering and StructuralChanges in Ammonium Halides," in Molecular Dynamics and Structure of Solids,NBS Special Publ. No. 301, 1969, p. 241.A. Bonilla, C. W. Garland, and N. E. Schumaker, "Low-Temperature x-Ray Investi-gation of NH4Br, " Acta Cryst. A25, 654 (1969).C. W. Garland and D. D. Snyder, "Ultrasonic Attenuation near the Lambda Transitionin NH4 C at High Pressures," (to appear in J. Phys. Chem. Solids).ThesesPeter E. Mueller, "Ultrasonic Velocity and Attenuation in Xenon near Its Liquid-VaporCritical Point," Ph. D. Thesis, Department of Chemistry, M. I. T. , June 1969.QPR No. 96

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