Etude comparative des structures des alumines β stoechiometrique et non stoechiometrique: Transition de phase dans l'alumine β stoechiometrique (II)

The usual preparation methods of β alumina lead to a non stoichiometric compound $\text{(β“N.S.”)}$ of formula 11Al₂O₃?(1 + x) B₂O with x ≈-0.3; a metastable phase with a composition close to stoichiometry $\text{(β“S”}\text{and}\text{x ? 0)}$ can however also be obtained. X-Ray diffuse scattering studies of this stoichiometric form of silver β alumina reveals a sharp order—disorder phase transition at about 307 K. The low temperature ordered state of the silver ions is found to correspond to a 3D hexagonal superstructure with the lattice constants $\text{a}\text{3}\text{, a}\text{3}\text{, c}$. Above the transition temperature 3D short range order is observed up to about 315 K, where a cross over occurs towards a higher temperature 2D short range state, similar to that previously observed at low temperature in $\text{β}{}_{\mathrm{<mtext>Ag</mtext>}}\text{“N.S.”}$. Above 500 K the conducting silver ions are found to be in a 2D quasi liquid state. A similar type of order—disorder phase transition seems to occur in stoichiometric sodium β alumina at lower temperature. It is concluded that the very particular behaviour namely the absence of phase transition in the usual forms of β alumina is a direct consequence of non stoichiometry.     

Neutron scattering study of the phase transition in s-triazine at high pressure

The elastic transition in s-triazine (C₃N₃H₃) from a trigonal ($\text{R}\text{3}\text{c}$) high temperature (low pressure) structure to a monoclinic (C2/c) low temperature (high pressure) phase has been investigated at pressures up to 5 kbar using neutron scattering techniques. Neutron diffraction was used to measure the pressure dependence of the order parameter and inelastic scattering to study the softening of the transverse acoustic phonon modes on three isotherms. In both cases the effect of pressure on the transition is found to be described primarily by that on the temperature of the transition.     

Pressure dependence of c-axis elastic parameters of oriented graphite

The elastic c-axis moduli C₃₃ and C₄₄ of compression-annealed pyrolytic graphite and their derivatives with hydrostatic pressure have been measured at room temperature over a pressure range from 1 to 7000 bars (700 MNm^?2) using an ultrasonic pulse-echo technique. The experiments were also made with material irradiated with fast neutrons. The pressure dependence of the c-axis compressibility of these materials was calculated from the experimental data, enabling pressure derivatives of the c-axis moduli to be also expressed as c-axis strain derivatives.     

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.     

Orientational motion and the elastic anomaly of sodium azide

A microscopic model is developed to discuss the nature of the α-β structural transformation in sodium azide. The model is a mean field treatment of the coupling of the orientational motion of the azide ions to the lattice strains. The apparent second order nature of the transition is examined. Predictions regarding the temperature dependence of the elastic constants c₄₄ and $\text{1}\text{2}$(c₁₁–c₁₂) are made. Sodium azide differs from other molecular crystals with elastic anomalies such as KCN in that the associated change in orientational ordering seems to be quite small.     

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 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.     

Deviations of Matthiessen's rule in some PdAu alloys

The low temperature electrical resistivity of Pd_1?cAu_c alloys (c = 0.1, 0.22, 0.38, 0.69, 0.82 and 1.1 at.%) have been studied in detail between 1.5 and 300 K. Deviations from Matthiessen's rule (DMR) have been analysed on the basis of a two-band model, and the agreement is found to be reasonably good. The parameter λ was found to decrease monotonically with temperature, and no anomalous maximum was observed as with earlier studies of $\text{Pd}$Ti. The variation of β shows a weak temperature dependence. The limitations of the model are also discussed.     

High pressure X-ray diffraction study on p-FeS2, m-FeS2 and MnS2 to 340 kbar: A possible high spin-low spin transition in MnS2

Pyrite p-FeS₂, marcasite m-FeS₂ and MnS₂2 have been investigated using the high-pressure X-ray diffraction technique to 340 kbar. MnS2 undergoes a pressure-induced phase transition at about 140 kbar from the pyrite to the marcasite type phase with a volume contraction of about 15%. The high-pressure marcasite type m-MnS₂ is found to belong to the B type of marcasite with an axial ratio $\text{c}\text{a}\text{= 0.76}$ and $\text{c}\text{b}\text{= 0.62.}$ p-FeS₂ and m-FeS₂ do not undergo any phase transition in the pressure range investigated. The high spin p-MnS₂ has been found to be much more compressible (B_o = 760 kbar, B′_o = 5.4) than the low spin p-FeS₂ (B_o = 2154 kbar, B′_o = 5.5) and m-FeS₂ (B₀ = 1465 kbar, B′_o = 4.9) while the high-pressure m-MnS₂ has comparable compressibility (B_o = 2138 kbar, B′₀ = 5.0) with those of low spin p-FeS₂ and m-FeS₂. The p-MnS₂-m-MnS₂ phase transition might be accompanied by a high spin-low spin transition of Mn²⁺.     

Chaleur spécifique et transformation martensitique dans le système Nb1−xSnx

Experimental data on the superconducting temperature, and low temperature specific heat, together with X-ray and neutron investigations are reported for two sets of Nb_xSn_1?x, samples with the A15 type structure. The first one, intended for a study of the effect of stoichiometry, consists of cast alloys with lattice constants ranging from 5.273 to 5.289 Å, γ's from 4.9 to $\text{9}\text{mJ}\text{K}{}^2$ g-at and T_c's from 6 to 17.9 K. The second one consists of nearly stoichiometric sintered alloys with lattice constants ranging from 5.288 to 5.291 Å, γ's from 5.6 to 13.5 $\text{mJ}\text{K}{}^2$ g-at and T_c's close to 18 K. The martensitic transformation ratio has been determined by neutron diffraction in the latter set and the values 32, 77 and 95% were obtained. The analysis of the specific heat jumps at T_c shows that the superconducting T_c of the tetragonal phase is 17.9 K and both T_c and γ are reduced in the cubic phase.Phonon information inferred from specific heat data are indicative of a structure with a typical energy of 9 meV in the density of states. The agreement with spectra obtained by inelastic neutron scattering is good.     

Soft phonon mode at the martensitic phase transformation of AuCuZn2

The lattice dynamical property of AuCuZn₂ has been investigated by means of inelastic neutron scattering technique in connection with its martensitic phase transformation. The temperature dependent soft phonon was observed transformation. The temperature dependent soft phonon was observed around $\text{q =}\text{2}\text{3}\text{[110]}$ of TA₂ phonon branch. We have also found a premartensitic metastable phase, in which new satellite reflections at (H± $\text{2}\text{3}$, K ? $\text{2}\text{3}$, 0) have been observed around fundamental reflections with H + K = 4n. The atomic displacements of the soft phonon mode correspond to the atomic arrangement of the premartensitic phase.     

Combined experimental and theoretical study on the effect of Nb content on martensitic transformation of NbRu shape memory alloys

The effect of Nb content on the martensitic transformation of NbRu high-temperature shape memory alloys is investigated by experiments and first-principles calculations. We calculate the lattice parameters, density of states, charge density, and heats of formation of Nb_50+xRu_50-x β phase. The results show that an increase in Nb content increases the stability of Nb_50+xRu_50-x β phase, leading to a significant decrease of the β to β' martensitic transformation temperature. In addition, the mechanism of the effects of Nb content on phase stability and martensitic transformation temperature is studied on the basis of electronic structure.     

Structural instability and superconductivity in niobium-titanium alloys

Niobium-titanium is the most widely used technical superconductor. Titaniumrich transition metal alloys, quenched from high temperatures, can generally be retained in the bccβ phase. This phase is metastable and the instability is relieved by a variety of low temperature structural transformations. This aspect has been investigated using x-ray, TEM, low temperature resistivity,T _c and dH _c2/dT studies, in a series of Nb-Ti alloys. The instability has been characterized by the normal state resistivityρ _n and dρ/dT. The commercially used Nb-Ti alloys are Ti rich per atom-wise. This stems basically from the anomalous increase in the normal state resistivityρ _n as the Ti concentration is increased. This is a consequence of a dynamical process through which theβ phase instability tends to be relieved leading to athermal ω precipitation. The resulting anomalous resistivity behaviour can be understood in terms of a ‘two-level system’ model generally invoked for amorphous materials. It has also been possible to induce instability towards athermal ω precipitation in a system spontaneously undergoing a martensitic transformation to become stable. Thus in an alloy of Nb-83 at % Ti, addition of 1% nitrogen has suppressed the martensitic transformation, giving a three-fold increase inρ _n (about 150µΘ cm), the highest known in Nb-Ti so far. The increase in the normal state resistivity has beneficial effects on the upper critical field. From studies on several Nb-Ti alloys, it is inferred that a peak inH _c2(0) occurs at 17–18 tesla at aρ _n value of 100µΘ cm. It is pointed out that in the present commercial alloys, the sequence of thermo-mechanical treatments given to optimizeJ _c, restrictsρ _n, perhaps owing to the partial relieving of the metastability of theβ phase. They are therefore non-optimized with respect toH _c2.     

The elastic moduli and their pressure and temperature derivatives for calcium oxide

The room temperature adiabatic elastic moduli of CaO were obtained using a pulse superposition technique to measure the ultrasonic velocities. The elastic moduli were found to be (in GPa) at 298 K.

     

15.

Longitudinal polarization transfer in the T→p, →n)3He reaction     

J.J. Jarmer  J.C. Martin  G.G. Ohlsen  G.C. Salzman  J.E. Simmons 《Physics letters. [Part B]》1974,48(3):215-217

The longitudinal polarization of neutrons has been measured for the reaction $\text{T}\text{→p}\text{,}\text{→n}\text{)}{}^3\text{He}$ with the incident proton beam longitudinally polarized. Measurements were performed at 0° for proton energies from 4 to 15 MeV and an angular distribution was measured at 10 MeV. The data determine the polarization transfer coefficient K_z^z′, which is equivalent to the Wolfenstein A′ parameter for nucleon-nucleon scattering. The quantity K_z^z′ at 0° increases from about 0.3 at 3 MeV incident energy to 0.9 at 9 MeV, and then decreases to 0.5 at 15 MeV. The data are computed with R-matrix calculations which reproduce the qualitative shape of the data at 0° and the angular distribution at 10 MeV.     

16.

Metastability and phase transitions in field theory     

《Physics letters. [Part B]》1986,169(4):398-401

λφ⁴ theory is investigated at finite temperature in the presence of an external current, j. Metastable situations are studied that may arise as the sign of j is reversed and they are related to the phase transition that takes place as j→0, β→β_c. A semiclassical approximation to the theory is used, which corresponds, in statistical mechanics, to the “droplet-bubble”.     

17.

Attenuation of longitudinal ultrasonic wave near the diffuse phase transition in CdF₂     

M.O. Manasreh  D.O. Pederson 《Solid State Ionics》1985,15(1):65-69

The attenuation of a longitudinal ultrasonic wave propagating in the [111] direction in CdF₂ is studied as function of temperature from 300K to 1030K. An ultrasonic attenuation peak has been observed for the first time near 983K. This peak is used to define the diffuse transition temperature (T_c = 983K) in CdF₂ which is well below its melting temperature of 1372K. The Arrhenius activation energy of anion motion above T_c was obtained from the temperature dependence of the attenuation and the theory of the dynamics of the coupled crystalline-cage-charged-liquid fluctuations. The elastic constant, $\text{C}{}_{11}\text{+2}\text{C}{}_{12}\text{+4}\text{C}{}_{44}\text{)}\text{3}$, measured simulataneously with the ultrasonic attenuation displays a large decrease near 983K in addition to the nearly linear decrease in the elastic constant with temperature.     

18.

Temperature and pressure derivatives of the elastic constants of cubic rubidium cyanide     

S. Haussühl 《Solid State Communications》1979,32(2):181-183

The temperature and pressure derivatives of all elastic constants of rubidium cyanide have been measured from 133 to 380 K respectively from 0 to 1500 × 10⁵ Nm^-2 by ultrasonic methods. The thermoelastic behaviour resembles that of KCN and NaCN. A strong softening of the shear resistance c₄₄ approaching the transition temperature from higher temperatures is observed. The pressure derivatives are also quite similar to those of KCN and NaCN, but fully different from those of normal alkali halides of rocksalt-type. This behaviour confirms a rule already observed in other isotypic crystal groups: the quasi-invariant pressure derivatives are shifted in a characteristic way for a certain structure type, if rare-gas-like ions are replaced by asymmetric ions. The nonlinear elastic behaviour is qualitatively interpreted by interactions of volume-conserving type as existing in fluids.     

19.

Study of phase transitions and properties of tetragonal (Pb,La)(Zr,Ti)O3 ceramics—I: Phase diagram and β-phase     

C.G.F. Stenger  A.J. Burggraaf 《Journal of Physics and Chemistry of Solids》1980,41(1):17-23

The phase diagram (T?x plot) of thermally depoled tetragonal PLZT materials has been investigated by means of X-ray diffraction, Capacitance and DSC measurements. Materials with a low La content show a classical Fe_t?PE_c transition. This transition has first or second order character, dependent on the Zr/Ti ratio.Materials with a medium and high La content show a diffuse transition from the cubic high temperature phase to a tetragonal, so called β phase. This β phase has no clear FE properties and a spontaneous transition to the FE_t phase on lowering the temperature only takes place for materials with a medium La content. For materials with a high La content a spontaneous β_t→ FE_t transition is not observed.     

20.

Elastic constants and softening of acoustic modes in A2MX6-crystals observed by Brillouin scattering     

W. Henkel  J. Pelzl  K. H. Höck  H. Thomas 《Zeitschrift für Physik B Condensed Matter》1980,37(4):321-332

Room-temperature Brillouin-scattering measurements of the longitudinal and transverse sound velocities for the cubic crystals K₂SnCl₆, K₂ReCl₆, (NH₄)₂SnCl₆ and (NH₄)₂SiF₆ are presented. The elastic constantsc ₁₁,c ₁₂ andc ₄₄ are determined from the angular variation of the Brillouin line shifts. Furthermore, for K₂SnCl₆ the sound velocities in the [100]- and [111]-direction are investigated as a function of temperature, 256K≦T≦330K. A strong softening of thec ₁₁–c ₁₂ mode is observed in the para-distortive phase as the temperature approaches the phase transition temperatureT _c1=262K from above, whilec ₄₄ shows no anomaly within the experimental error. These acoustic anomalies are interpreted theoretically by a mechanism based on the coupling of the elastic strain field to the fluctuations of the soft-mode coordinates.     

c11	c12	c44
226.2 ±0.9	62.4 ±0.9	80.6 ±0.3 The pressure derivatives of the elastic moduli, which were measured at and below room temperature, decrease with decreasing temperature. The temperature derivatives of the elastic moduli were also obtained for several temperatures below room temperature.

Longitudinal polarization transfer in the T→p, →n)3He reaction

The longitudinal polarization of neutrons has been measured for the reaction $\text{T}\text{→p}\text{,}\text{→n}\text{)}{}^3\text{He}$ with the incident proton beam longitudinally polarized. Measurements were performed at 0° for proton energies from 4 to 15 MeV and an angular distribution was measured at 10 MeV. The data determine the polarization transfer coefficient K_z^z′, which is equivalent to the Wolfenstein A′ parameter for nucleon-nucleon scattering. The quantity K_z^z′ at 0° increases from about 0.3 at 3 MeV incident energy to 0.9 at 9 MeV, and then decreases to 0.5 at 15 MeV. The data are computed with R-matrix calculations which reproduce the qualitative shape of the data at 0° and the angular distribution at 10 MeV.     

Metastability and phase transitions in field theory

λφ⁴ theory is investigated at finite temperature in the presence of an external current, j. Metastable situations are studied that may arise as the sign of j is reversed and they are related to the phase transition that takes place as j→0, β→β_c. A semiclassical approximation to the theory is used, which corresponds, in statistical mechanics, to the “droplet-bubble”.     

Attenuation of longitudinal ultrasonic wave near the diffuse phase transition in CdF2

The attenuation of a longitudinal ultrasonic wave propagating in the [111] direction in CdF₂ is studied as function of temperature from 300K to 1030K. An ultrasonic attenuation peak has been observed for the first time near 983K. This peak is used to define the diffuse transition temperature (T_c = 983K) in CdF₂ which is well below its melting temperature of 1372K. The Arrhenius activation energy of anion motion above T_c was obtained from the temperature dependence of the attenuation and the theory of the dynamics of the coupled crystalline-cage-charged-liquid fluctuations. The elastic constant, $\text{C}{}_{11}\text{+2}\text{C}{}_{12}\text{+4}\text{C}{}_{44}\text{)}\text{3}$, measured simulataneously with the ultrasonic attenuation displays a large decrease near 983K in addition to the nearly linear decrease in the elastic constant with temperature.     

Temperature and pressure derivatives of the elastic constants of cubic rubidium cyanide

The temperature and pressure derivatives of all elastic constants of rubidium cyanide have been measured from 133 to 380 K respectively from 0 to 1500 × 10⁵ Nm^-2 by ultrasonic methods. The thermoelastic behaviour resembles that of KCN and NaCN. A strong softening of the shear resistance c₄₄ approaching the transition temperature from higher temperatures is observed. The pressure derivatives are also quite similar to those of KCN and NaCN, but fully different from those of normal alkali halides of rocksalt-type. This behaviour confirms a rule already observed in other isotypic crystal groups: the quasi-invariant pressure derivatives are shifted in a characteristic way for a certain structure type, if rare-gas-like ions are replaced by asymmetric ions. The nonlinear elastic behaviour is qualitatively interpreted by interactions of volume-conserving type as existing in fluids.     

Study of phase transitions and properties of tetragonal (Pb,La)(Zr,Ti)O3 ceramics—I: Phase diagram and β-phase

The phase diagram (T?x plot) of thermally depoled tetragonal PLZT materials has been investigated by means of X-ray diffraction, Capacitance and DSC measurements. Materials with a low La content show a classical Fe_t?PE_c transition. This transition has first or second order character, dependent on the Zr/Ti ratio.Materials with a medium and high La content show a diffuse transition from the cubic high temperature phase to a tetragonal, so called β phase. This β phase has no clear FE properties and a spontaneous transition to the FE_t phase on lowering the temperature only takes place for materials with a medium La content. For materials with a high La content a spontaneous β_t→ FE_t transition is not observed.     

Elastic constants and softening of acoustic modes in A2MX6-crystals observed by Brillouin scattering

Room-temperature Brillouin-scattering measurements of the longitudinal and transverse sound velocities for the cubic crystals K₂SnCl₆, K₂ReCl₆, (NH₄)₂SnCl₆ and (NH₄)₂SiF₆ are presented. The elastic constantsc ₁₁,c ₁₂ andc ₄₄ are determined from the angular variation of the Brillouin line shifts. Furthermore, for K₂SnCl₆ the sound velocities in the [100]- and [111]-direction are investigated as a function of temperature, 256K≦T≦330K. A strong softening of thec ₁₁–c ₁₂ mode is observed in the para-distortive phase as the temperature approaches the phase transition temperatureT _c1=262K from above, whilec ₄₄ shows no anomaly within the experimental error. These acoustic anomalies are interpreted theoretically by a mechanism based on the coupling of the elastic strain field to the fluctuations of the soft-mode coordinates.