Higher order elastic constants and non-linear stress-strain relation for V3Si

Relations for the third and fourth order elastic constants are derived from a Landau-Devonshire type free energy function for crystals with the A15 structure which undergo the structural transformation at low temperature. Application to transforming V₃Si at 21° K gives in connection with experimental data for the pressure derivatives of the elastic constants unusually large numerical values for c₁₁₁, c₁₁₂, c₁₂₃ and c₁₁₁₁. The stress-' strain relation calculated from these data is in semiquantitative agreement with the directly measured, strongly non-linear behavior.     

The elastic constants of isomorphous sodium bromate and sodium chlorate from 77 to 350 K

The elastic constants of NaBrO₃ and NaClO₃ are evaluated from ultrasonic velocity measurements using pulse superposition techniques. The values of C₁₁, C₁₂ and C₄₄ for NaBrO₃ at 298°K are 5.57₈, 1.70₅, 1.51₀ (x 10¹⁰ N/m²) and for NaClO₃ the values are 4.89₇, 1.38₉, 1.17₄. The values at 77°K are respectively 6.35, 1.98 and 1.65 for NaBrO₃ and 6.15, 2.16 and 1.32 for NaClO₃.     

Anomalous thermoelastic behaviour of cubic potassium cyanide

The temperature dependence of all elastic constants of cubic potassium cyanide has been measured by ultrasonic methods in the range from -105.4 to 181°C. Until about 180°C all elastic wave velocities increase with higher temperatures. The behaviour of the shear constant c₄₄ is given by c₄₄ = a · logT/T₀ with a = 0.219 · 10¹¹dyn.cm^?2 and T₀ = 153.7°K with a good approximation. These unusual effects are assigned to the librational vibrations and orientational jumping processes of the CN-ions. The phase transition at -105.5°C is a consequence of the low c₄₄ value.     

The elastic constants and distance dependence of the magnetic interactions of Cr2O3

The six single crystal elastic stiffness constants of Cr₂O₃ have been determined at 20°C by a pulse-echo-overlap technique. The results are: c₁₁ = 3.74, c₁₂ = 1.48, c₁₃ = 1.75, c₃₃ = 3.62, c₄₄ = 1.59 and c₁₄ = 0.19 all in units of 10¹² dyne/cm². The magnetic anomalies in lattice parameters at 0 K were also determined. These results were used to approximately calculate the interatomic distance dependence of the magnetic interactions in Cr₂O₃.     

Low temperature polarization effects in ice

When an initially unpolarized HF doped ice specimen is warmed at a constant rate in an applied electric field two peaks are observed in the current. The low temperature peak occurs near 100°K and the temperature at which this peak occurs is seen to increase as the HF concentration decreases. The second peak appears to occur randomly in the temperature range 125–135°K. These peaks are also observed if the sample is cooled in an applied electric field and then warmed at a constant rate with the field removed. It is suggested that the first peak is due to a dielectric relaxation process which is governed by the L defects released from the HF molecules. This release of L defects is shown to obey the law of mass action with an activation energy for liberation of an L defect of 0.12±0.06 eV and a dissociation constantk _o ^L≈10²⁹ m^?3. A simple theoretical model of ice is also developed which predicts the current reversal phenomenon observed by Dengelet al. [11] suggesting that it is due to dipole relaxation and not to ferroelectric ordering.     

Lattice softening in K2Pt(CN)4Br0.3·3H2O

The temperature dependences of the elastic constants, c₁₁, c₃₃, c₄₄, and c₆₆, in KCP are described. In the temperature range 10–100 K softening is observed in c₄₄, while c₆₆ decreases almost linearly with decreasing temperature. These results indicate the presence of a new critical region.     

Elastic,piezoelectric and dielectric properties of ZnO and CdS single crystals in a wide range of temperatures

A complete set of elastic, piezoelectric and dielectric constants of ZnO and CdS at room temperature was determined by the method of resonance-antiresonance. Elastic constants s^E₁₁, s^E₁₂, s^E₅₅, c^D₃₃, c^D₅₅, coefficients of electromechanical couplingk₃₁, k₁₅, k_t and dielectric constants ε^T₁₁, ε^T₃₃ of ZnO single crystals were determined in the temperature range 4.2–800 K. Elastic constants s^E₁₁, s^E₁₂, s^D₃₃, s^E₅₅, s^D₃₃, s^D₅₅, coefficients of electromechanical coupling k₃₁, k₃₃, k₁₅, k_t and dielectric constants ε^T₁₁, ε^T₃₃ of CdS single crystals were determined in the temperature range 4.2–300 K.     

Ultrasound studies of single crystal thulium in an applied magnetic field

The paper reports the first measurements of the single crystal elastic constants of the heavy rare earth metal thulium as a function of temperature and magnetic field. The constants were obtained from ultrasonic velocity measurements over a temperature range of 4.2–296 K and in applied magnetic fields of up to 5 T. The elastic constants; C₁₁, C₃₃, C₄₄ and C₆₆=(C₁₁–C₁₂)/2 were determined from the ultrasonic velocities. Anomalies in the elastic constants were observed at 58 K from the c-axis propagated shear wave measurements and at 55 K from the c-axis propagated longitudinal wave measurements. Significant softening of the elastic constants C₃₃ and C₄₄ was observed close to T_N. Application of a magnetic field (>2 T) along the c-axis direction induced further softening of the material. Electromagnetic acoustic transducers (EMATs) were also employed in addition to conventional piezoelectric quartz transducers. A marked increase in the EMATs acoustic coupling efficiency (generation and detection efficiency) occurred close to T_N.     

Ferroelastic phase transition and anomalous elastic and thermal properties of betaine borate (CH3)3NCH2COO·H3BO3

The temperature and pressure derivatives of the elastic constants of orthorhombic betaine borate, (CH₃)₃NCH₂COO·H₃BO₃, have been determined by measuring temperature and stress induced shifts of resonance frequencies of thick plates at ca. 15 MHz in the range between 140 and 300 K and 0 and 3 kbar. The elastic ‘shear’ resistance c₄₄ exhibits a value as low as 0.0492×10¹⁰Nm^-2at 293 K. With decreasing temperature c₄₄ approaches zero at ca. 142.5 K, indicating an acoustic soft mode behaviour connected with a ferroelastic phase transition. The softening of c₄₄ is described in a good approximation by c₄₄(T)_p=0 =alogT/T₀ with a=0.0663×10¹⁰Nm^-2 and T₀ = 139.5 K. Further, c₄₄ decreases with increasing pressure according to the linear relation c₄₄(p)_{T=293 K} = 0.0492?0.184×10^-4p (p in bar, c₄₄ in 10¹⁰ Nm^-2). All other elastic constants show a quite normal temperature and pressure dependence. At 293 K the transition is induced by a pressure of 2.65 kbar. The transition temperature T_c depends linearly on pressure according to T_c = 142.5+0.0568 p (pinbar, T_cinK). Passing through the transition no discontinuous change of the lattice constants is observed. The three principal coefficients of thermal expansion and the pressure derivatives of the dielectric constants exhibit discontinuities at the transition. The transition is of strongly second order.     

Stiffness matrix and debye temperature of ReO3 from ultrasonic measurements

We have measured the propagation velocities of bulk acoustic waves in the simple cubic transition-metal oxide ReO₃ by ultrasonic pulse propagation. The elastic stiffness constants at 300 K are: C₁₁ = (47.9 ± 1.4) × 10¹¹ dyne/cm²; C₄₄ = (6.1 ± 0.2) × 10¹¹ dyne/cm²; C₁₂ = (?0.7 ± 2.8) × 10¹¹ dyne/cm². These elastic constants indicate a crystal with highly anisotropic shear propagation. The Debye temperature of the compound from these measurements is 528 K. This value is somewhat higher than previous results from specific heat and resistivity determinations.     

States of 12ΛC formed in the reaction 12C(K−, π−)

States of ¹²_ΛC formed in the (K^?, π^?) reaction have been studied for momentum transfers up to 260 MeV/c, using an incident K^? beam of 800 MeV/c momentum. The angular distributions for the g.s. and for a peak at 11 meV have been measured between 0° and 19° in the laboratory. Limits on the splitting of the 11 MeV peak and on the formation of low-lying excited states are given.     

Halleffekt und anisotropie der beweglichkeit der elektronen in ZnO

Hallconstant, conductivity and Hall mobility of ZnO crystals were measured as function of temperature (4 °K < T < 370 °K) and orientation. Value and anisotropy of mobility can be explained (50 °K < T < 370 °K) by polar optical scattering, deformation potential sc., piezoelectric sc. and sc. by ionized impurities. The anisotropy of mobility is caused only by piezoelectric sc. Maximum values of μ_H are reached for μ_H ⊥ c, with 2400 cm²/V sec at 40 °K and for μ_H ¦ c with 1350cm²/Vsec at 60 °. Below 50 °K Hallconstant, conductivity and Hall mobility are influenced by impurity band conduction processes. The crystals have impurity concentration in the 10¹⁶ cm^?3 range, but they show different donor activation energies depending on growth conditions: Type I: 38,4 meV (50 °K < T < 100 °K) and Type II: 20,3 meV (50 °K < T < 100 °K) and 6 meV (25 °K < T < 50 °K).     

Stereochemical studies of oligomers XXIX. Reinvestigation of the structure of N-m-tolyl phthalimide

C₁₅H₁₁NO₂, Mr 237.3, monoclinic, space groupC _c, a=8.539(2),b=19.865(4),c=7.599(2)?,β=111.44(2)°,V=1199.8 ?³,Z=4,D _c=1.31 gcm⁻³,λ(CuKα)=1.5418 ?,μ=6.74cm⁻¹,F(000)=496, room temperature. The structure was solved by direct methods with SHELX-86 and refined down to agreement valueR=0.046 for 1117 reflections above 2σ(I). The angle between the plane of the phthalimide group, which shows a little bent [1.2(2)°] between its two rings, and the tolyl group is 56.1(1)°. The packing of the molecules is stabilized by van der Waal’s forces only. Part XXVIII: Bocelli and Rizzoli (1990)     

The elastic behaviour of the ternary zincblende structure semiconductor CuGe2P3

A single crystal has been grown of CuGe₂P₃, a ternary semiconductor with a zincblende structure in which the copper and germanium atoms are randomly distributed on the cation sites. The second order elastic constants measured by the ultrasonic pulse echo overlap technique (C₁₁ = 13.66, C₁₂ = 6.17, C₄₄ = 6.66 and bulk modulus B = 8.67 in units of 10¹⁰Nm^?2 at 291 K) are closely similar to those of GaP and conform well to Keyes' correlation for zincblende structure crystals. The hydrostatic pressure derivatives of the second order elastic constants ($\text{?C}{}_{11}\text{?P}\text{= 4.40}$, $\text{?C}{}_{12}\text{?P}\text{= 3.9}$, $\text{?C}{}_{44}\text{?P}\text{= 0.93}$ and $\text{?B}\text{?P}\text{= 4.07}$) and the third order elastic constants (C₁₁₁ = ? 8.45, C₁₁₂ = ? 3.49, C₁₂₃ = ? 1.13, C₁₄₄ = ? 2.82, C₁₅₅ = ? 1.44 and C₄₅₆ = ? 0.69 in units of 10¹¹Nm^?2) also resemble those of GaP: even the anharmonicity of the long wavelength acoustic modes of this ternary semiconductor resembles that of its binary “parent” compound. The positive signs of the hydrostatic pressure derivatives and the negative signs of the third order elastic constants show that the acoustic modes at the long wavelength limit stiffen under pressure, an effect which is quantified here by computation of the mode Grüneisen parameters, which are all positive. The harmonic and anharmonic force constants, obtained in the valence force field model, fit well into the pattern shown by related zincblende structure compounds: the ratio ($\text{β}\text{α}$) for bond bending (β) to stretching (α) force constants is greater than 4:1; the dominating anharmonic force constant is γ: most of the anharmonicity is associated with nearest neighbour atoms. Analysis of the temperature dependence of the elastic constants on the basis of a simple anharmonic model again emphasises the similarity between the elastic behaviour of CuGe₂P₃ and GaP. The thermal expansion of CuGe₂P₃ varies almost linearly with temperature between 291 K and 1000 K, the linear coefficient of thermal expansion α being 8.21 ± 0.02 × 10^?6 °C^?1. The similar lattice parameters and elastic behaviour of CuGe₂P₃ and GaP indicate that semiconducting devices made of epitaxial deposits of CuGe₂P₃ on a GaP substrate should prove to be almost strain-free.     

Zeitliches Abklingen und Anisotropie von p-Terphenyl- undp-Terphenyl-Anthrazen-Mischkristallen bei Beschuß mit α-Teilchen

The time dependence of scintillation intensity from single crystals ofp-terphenyl and mixed crystals ofp-terphenyl and anthracene after bombarding with α-particles was investigated at the two temperaturesT=296 °K andT=92 °K. For the crystals ofp-terphenyl the time dependence of the scintillation anisotropy was also measured. Using the formulas given byKing andVoltz the decay curves ofp-terphenyl were decomposed into two components. Good agreement between experiment and theory was found. The ratio of the prompt intensity to the delayed intensity was determined to be 1∶2 atT=296 °K and 1∶3 atT=92 °K. The diffusion constants for triplet excitons were calculated to beD _T(296 °K)≈10^?5 cm² sec^?1 andD _T(92 °K)≈ 2×10^?6 cm² sec^?1, and the triplet-triplet interaction rate constantsχ _tt(296 °K)≈ 2.5×10^?11 cm³ sec^?1 andχ _tt(92 °K)≈0.5×10^?11 cm³ sec^?1.     

Proton spin relaxation in hexagonal ice

Measurements of the rotating frame proton spin relaxation timeT _1p in hexagonal ice single crystals as a function of temperature ? for various rotating magnetic field strengths reveal the expectedT _1p minimum at the lowest practicable field values. This allows a very precise determination of the proton correlation (? molecular jump) time τ_c and the related activation energy ΔE by means of the theoretical reasoning of relaxation spectroscopy. We find the Arrhenius-law temperature dependenceτ _c=1.99×10^?17exp(0.603/8.61×10^?5 ?)sec, which is in good agreement with our earlier indirect derivation.     

Anomalously low elastic stability of NaCl-H<Subscript>2</Subscript>O ice at low temperatures

Water-NaCl solid solutions with the salt weight fraction p = 0.0001–0.1000 subjected to high uniaxial compression exhibit elastic instability (similar to the Bridgman explosive effect) in the temperature range 100–260 K. At temperatures from 225 to 260 K, stability threshold P _c (or a critical pressure at which the explosive instability occurs) of these solutions is equal to, or higher than, P _c for pure water ice. However, in the temperature interval 100–225 K, thresholds P _c for the NaCl-water solid solutions with p ≥ 0.001 are anomalously low. The largest drop of P _c (by 15 to 30 times relative to P _c for pure water ice) is observed for low p, 0.001 ≤ p ≤ 0.010. The possible structure of the solid ice solutions in all the temperature ranges mentioned above is analyzed in terms of the percolation theory as applied to elastic networks.     

Amorphization of ice near the melting point

In addition to reflections of the hexagonal phase of ice I _h, the intense diffuse scattering of X-rays mainly due to the amorphization of ice is revealed on the X-ray diffraction patterns of water ice samples prepared at liquid nitrogen (studied by the authors earlier) and samples prepared at T = ?10°C (this work). The measurements are performed in the temperature range from ?25 to 0°C. The existence of reflections of the crystalline phase and intense diffuse scattering on the X-ray diffraction patterns makes it possible make a conclusion about the coexistence of crystalline and amorphous structures of ice. Splitting of the first maximum on the electron-density radial distribution function is detected on the basis of an X-ray diffraction pattern recorded at T = ?3°C. This splitting is explained by an increase in the interatomic distances between the nearest-neighbor atoms located at different levels. Similar splitting was also detected on a radial distribution function constructed using an X-ray diffraction pattern recorded at ?10°C.     

Elastic constants of 2H-MoS2 and 2H-NbSe2 extracted from measured dispersion curves and linear compressibilities

Recent neutron data on the dispersion curves and X-ray measurements of the linear compressibilities of the 2H polytypes of MoS₂ and NbSe₂ have been used to obtain approximate values of the five independent elastic constants of these materials. In the case of NbSe₂ sufficient information is available to over-determine the elastic constants and the results are self consistent within estimated uncertainties, although the uncertainties are especially large for c₃₃ and c₁₁. Additional related considerations such as Debye temperatures and model calculations of c₃₃, and c₄₄ are also made. It is found that there is significant and unexplained disagreement between the value of the low temperature specific heat Debye temperature of NbSe₂ and the value determined on the basis of the elastic constants, but that the model predictions of c₃₃ and c₄₄ are in satisfactory agreement with the values extracted from the neutron data for both MoS₂, and NbSe₂.