Elastic moduli and brittleness of diamondlike and zinc blende structured solids

In this paper, semiempirical formulae for both bulk modulus (B in GPa) and shear modulus (G in GPa) of diamondlike and zinc blende (A^NB^8−N) covalent solids are elaborated in terms of nearest neighbour distance (d in Å), covalent fraction (f_c) and product of ionic charges (Z_aZ_c) of the bonding. The resulting expressions can be applied to a broad selection of covalent materials and their modulus predictions are in good agreement with the experimental data and those from ab initio calculations. Furthermore, the correlation between the ratio G/B and the aforementioned bonding parameters was investigated. The analysis of this relationship demonstrates that compared to the nearest neighbour distance (d in Å), covalent fraction (f_c) and product of ionic charges (Z_aZ_c) are predominant parameters responsible for the brittle features of covalent materials.     

B3–B1 phase transition and pressure dependence of elastic properties of ZnS

We have performed the ab initio calculations based on density functional theory to investigate the B3–B1 phase transition and mechanical properties of ZnS. The elastic stiffness coefficients, C₁₁, C₁₂, C₄₄, bulk modulus, Kleinman parameter, Shear modulus, Reuss modulus, Voigt modulus and anisotropy factor are calculated for two polymorphs of ZnS: zincblende (B3) and rocksalt (B1). Our results for the structural parameters and elastic constants at equilibrium phase are in good agreement with the available theoretical and experimental values. Using the enthalpy–pressure data, we have observed the B3 to B1 structural phase transition at 18.5 GPa pressure. In addition to the elastic coefficients under normal conditions, we investigate the pressure dependence of mechanical properties of both phases: up to 65 GPa for B1-phase and 20 GPa for B3-phase.     

Solid-state extrusion of nylons 11 and 12: processing,morphology and properties

Monofilaments of poly(11-amino-undecanoic acid) (nylon 11), and poly(laurylactam) (nylon 12) have been produced using solid-state extrusion methods in an Instron capillary rheometer. The resulting morphology, physical and mechanical properties were investigated. For nylon 11, at an extrusion ratio (ER) of 12, the crystalline melting-point temperature increased by 16° C, over the undrawn material, while the per cent crystallinity,X _c, increased by 23%. Nylon 12, extruded to a maximum ER of 6, realized an increase inT _m of 4° C at ER=5 and anX _c increase of 14%. Young's modulus for nylon 11 increased from 3 GPa at an ER=3 to 5.5 GPa at an ER=7 and levelled off at greater ER. For nylon 12, the Young's modulus climbed from 2.5 GPa at ER=3 to about 3.3 GPa at E R=5.5. Conventionally melt-spun and cold-drawn nylon 11 and nylon 12 fibres exhibited Young's modulus values of 2.7 GPa and 2.9 GPa respectively. Atmospheric moisture loss was found not to affect solid-state extrusion of these higher nylons. Increases in extrusion temperature and/or pressure increased the extrusion rate. The flow activation energy of nylon 11 was 73 kcal mol⁻¹ at 0.24 GPa extrusion pressure, and 124 kcal mol⁻¹ at 0.49 GPa extrusion pressure. Calculated apparent viscosities were about 10¹⁴ poise and 10¹⁵ poise, respectively. The morphologies were shown by electron microscopy to be microfibrillar and the resulting monofilaments were transparent to visible light.     

Preparation, thermal expansion, high pressure and high temperature behavior of Al2(WO4)3

The titled compound Al₂(WO₄)₃ was synthesized by a conventional solid state reaction and characterized by powder XRD. It crystallizes in an orthorhombic (Pbcn, No. 60) lattice, with unit cell parameters as 12.582(2), 9.051(1), 9.128(2) Å, and V = 1039.5(3) (Å)³. The compound was found to show negative thermal expansion (NTE) behavior in the temperature range of 25 to 850°C. The average linear NTE coefficient (₁), in this temperature range, was –1.5 × 10^–6 K^–1. The effect of pressure at ambient temperature, was studied by a Bridgman Anvil (BA) apparatus, to reveal that there is no irreversible phase transition up to 8 GPa. The effect of high pressure and high temperature on this compound was studied by a Toroid Anvil (TA) apparatus. This compound has a limited stability under high pressure and temperature, as it undergoes a decomposition to AlWO₄ and WO_3–x with a partial oxygen loss. As an off-shoot of this work, certain new modifications of WO_3–x under pressure and temperature were observed, viz., monoclinic, tetragonal and an orthorhombic modifications at 5 GPa/1400°C, 3 GPa/900°C and 1.8 GPa/1030°C, respectively. The detailed XRD studies of the products are presented here.     

Thermal conductivity and heat capacity per unit volume of poly(methyl methacrylate) under high pressure

The thermal conductivity and heat capacity per unit volume of poly(methyl methacrylate) (25 and 350 kg · mol^– in molecular weight) have been measured in the temperature range 155–358 K at pressures up to 2 GPa using the transient hot-wire method. The bulk modulus has been measured up to 1.0 GPa at 294 K and yielded a constant valueg = 3.4 ± 0.3 for the Bridgman parameter. No dependence on molecular weight could be detected in the properties we measured.     

Attainment of high specific hardness and specific modulus in spark plasma sintered aluminium-copper-silicon carbide-titanium carbide hybrid composite

Aluminium matrix hybrid composites have been consolidated effectively by spark plasma sintering with new combinations of reinforcement and high volume percentage of ceramic particulates to maximize specific hardness and specific modulus through the powder metallurgy route. The aforementioned techno-scientific accomplishment with regard to metal matrix composite aims to meet a continuous increase in the global demand for a material with minimum structural weight and high-modulus for structural (automotive and aerospace) applications. The new aluminium based hybrid composite developed by incorporating ceramic particulate reinforcements (12.5 wt.% silicon carbide and 12.5 wt.% titanium carbide) along with 22.5 wt.% copper as the metallic reinforcement attains significantly high specific hardness (85 HV/gcm⁻³), specific Young's modulus (33.56 GPa/g cm⁻³), specific bulk modulus (27.97 GPa/g cm⁻³) when compared with the reported range of specific hardness (13 HV/g cm⁻³–89 HV/g cm⁻³), specific Young's modulus (24 GPa/g cm⁻³–27 GPa/g cm⁻³) and specific bulk modulus (20 GPa/g cm⁻³–22 GPa/g cm⁻³) possessed by structural steels. This is accredited to the genesis of a novel microstructure that consists of fine copper, silicon carbide and titanium carbide particulates together with a nominal in-situ originated aluminium-copper equilibrium phases distributed in a highly substructured aluminium based matrix with a significant dislocation density (7.56 ⋅ 10¹⁴ m^-2).     

The first bulk synthesis of ReO3-type tungsten trioxide, WO3, from nanometric precursors

A perovskite form of WO₃ has been synthesized in bulk for the first time at 0.66 GPa and 973 K with a=3.7823(4) Å [a₀=3.7719(4) Å, at ambient conditions] from nanometric powder of WO₃ with an average crystallite size of 35 nm. Data collected during tests to determine both the likelihood of retaining the structure at room temperature and the effect of high pressure on distortion have afforded analysis of thermal expansivity and compressibility of this phase. These result in V_T=53.407(5)exp(−3.9(12)×10⁻⁶(T−298)+1.91(9)×10⁻⁸(T²−298²)) Å³ and equation of state parameters of V₀=53.67(4) Å³, K₀=41.8(19) GPa with ∂K/∂P=K′=5.6(12).     

Equation-of-state measurements for crude oils at pressures up to 1 GPa

Equation-of-state measurements of two crude oils with different compositions and viscosity were performed at room temperature in the pressure range 0<P<1.0 GPa. We found large compressibilities and a strong dependence of the compressibility on oil content and viscosity. The bulk modulus changed with pressure from 2.0 to 12.1 GPa for one oil and from 1.3 to 9.5 GPa for the other. We discuss the possibility of detecting phase transitions in the region under investigation. The Tait and Murnaghan equations of state were fitted to the data, and residuals are presented.     

A density functional study of structural and elastic properties of LaN under high pressure

Structural and elastic properties of LaN at normal and high pressures are investigated using ab initio calculations based on full-potential linearized augmented plane wave (FP-LAPW) within both local density approximation (LDA) and generalized gradient approximation (GGA). Our results concerning equilibrium lattice parameter and bulk modulus agree well with the available experimental and previous theoretical findings. The transition pressure from NaCl (B1) to CsCl (B2) phase is found to be 31.05 GPa from LDA, and 42.2 GPa from GGA. To the best of our knowledge, the elastic properties for LaN in the B1 structure in the presence of pressure have never been reported so far. The linear pressure coefficients of elastic constants and their related bulk modulus are determined from the pressure dependence of these parameters. Furthermore, the mechanical stability criteria for LaN in B1 phase are found to be fulfilled at normal conditions.     

The pressure-volume relation of ytterbium up to 9 GPa

The pressure-volume relation of ytterbium has been determined up to 9 Gpa using tungsten carbide opposed anvil high pressure x-ray camera. The fcc phase of ytterbium is observed between one atmosphere and 4 GPa and the bcc phase above 3·5 GPa. The bcc phase can be metastably retained down to 1 GPa by gradually decreasing the pressure from a region where only bcc phase alone is observed. The bulk modulus,B ₀, at zero pressure and the pressure derivative of the bulk modulus,B’ ₀, are determined by fitting Murnaghan equation to the pressure-volume data. The following values were obtained:B ₀=16·3 GPa andB’ ₀=3·6 for the fcc phase, andB ₀=14·7 GPa andB’ ₀=1·5 for the bcc phase. Based on the present data it is suggested that the thermodynamic equilibrium pressure for fcc ⇆ bcc transformation in ytterbium is below 3·5 GPa. The valence change under pressure has been discussed.     

Thermal equation of state of natural chromium spinel up to 26.8 GPa and 628 K

A pressure–volume–temperature data set has been obtained for natural chromium spinel, using synchrotron X-ray diffraction with a resistance heated diamond-anvil cell (RHDAC). The unit cell parameter of the chromium spinel was measured by energy dispersive X-ray diffraction up to pressures of 26.8 GPa and temperatures of 628 K. No phase change has been observed. The observed P–V–T data were fit to the high-temperature Birch-Murnaghan equation of state, with V ₀ fixed at its experimental value, yields K ₀ = 209 ± 9 GPa, (∂K/∂T)_P = −0.056 ± 0.035 GPa K⁻¹, and α₀ = 7±1 × 10⁻⁵ K⁻¹. The temperature derivative of the bulk modulus (∂K/∂T)_P of chromium spinel is determined here for the first time. The obtained K ₀ is slightly higher than the previous results of synthetic spinel. We suggest that Fe²⁺–Mg²⁺ substitution is responsible for the high bulk modulus of chromium spinel.     

Sc-strengthened commercial purity aluminum under high pressure

Aluminum alloyed with approximately 1,000 at. ppm Sc was studied by high-pressure energy dispersive X-ray diffraction in two different states, homogenized and aged to peak microhardness. The microhardness of the aged sample is about three times higher than the microhardness of the homogenized sample (as a result of the formation of nanosize Al₃Sc precipitates in the aged sample). The results, which were refined using the Rietveld analysis technique, indicate a single cubic phase with no phase transition up to a pressure of 32 GPa. The Vinet equation was used to fit the volume–pressure curve to the equation-of-state. The bulk modulus (B ₀) is found to be 73 ± 5 GPa, and is equal to the value measured for an unalloyed aluminum sample. The fact that the bulk modulus does not change, despite a large difference in microhardness between the samples, is the result of the different origins of the two quantities.     

Thermal conductivity of amorphous Teflon (AF 1600) at high pressure

The thermal conductivity, λ of amorphous Teflon AF 1600 [poly(1,3-dioxole-4,5-difluoro-2,2-bis(trifluoromethyl)-co-tetrafluoroethylene)] has been measured at pressures up to 2 GPa in the temperature range 93–392 K. At 295 K and atmospheric pressure, we obtained λ=0.116, W·m⁻¹·K⁻¹. The bulk modulus was measured up to 1.0 GPa in the temperature range 150–296 K and the combined data yielded the following values ofg=(∂ln λ ∂lnp) _r :2.8±0.2 at 296 K, 3.0±0.2 at 258 K, 3.0±0.2 at 236 K. 3.4±0.2 at 200 K. and 3.4±0.2 at 150 K.     

Growth of Bulk InBO3 Crystals

Conditions are optimized for top-seeded solution growth of bulk indium orthoborate, InBO₃, crystals using the Na₂O–BaO–B₂O₃ flux system. InBO₃ has a hexagonal unit cell and is isostructural with calcite; a= 4.812 Å, c = 15.47 Å, microhardness of 11 ± 0.70 GPa. InBO₃ crystals are essentially insoluble in common organic and inorganic solvents.     

Structural evaluation of phosphate bonded ceramic composite materials from nondestructive ultrasonic velocity and attenuation measurements

The fabrication of a ceramic consisting of a matrix of newberyite and aluminium orthophospate filled with alumina and lesser amounts of carbon and glass fibre, is described. This material, whilst combining excellent insulation properties with forgiving fracture, is easy to produce by moulding without sintering. The ceramic has been characterized by a number of complementary ultrasonic techniques in the frequency range 24 kHz to 5 MHz,Dynamic elastic moduli measurements have been found to agree well with elastic constants calculated theoretically by treating the matrix and filler as end members of a two-phase material whose properties obey the lower Hashin and Shtrikman bound. In addition the bulk modulus of the matrix computed theoretically from crystallographic data and making an allowance for porosity agreed closely with the experimental modulus. Thus ultrasound velocity (moduli) measurements combined with theory can be used for non-destructive monitoring and quality control of the ceramic composition which is subject to variation with the parameters governing the chemical reaction during preparation. The theoretical bulk modulus of the ideal (pore-free) matrix is 10.4 GPa. This matrix modulus is far less than that of the moduli of the constituent oxides in the starting mixture. The reason for this is the large expansion in the sizes of closed rings of cation-oxygen network bonds that takes place in the reaction, rather than structural weakening (breaking of rings of network bonds) by hydration.The frequency dependence of ultrasonic attenuation has been used to identify scattering regimes and thus determine the dimensions of the major scattering particles. Grain sizes determined ultrasonically for the three compositions showed excellent agreement with values determined by optical microscopy.The high frequency dependent absorption and scattering in this material, mean that good ultrasound propagation is obtained only at low frequencies. The lowest frequency at which the ultrasonic propagation and properties are dependent on the material structure alone, i.e. independent of sample size, has been established to be 2 MHz with conveniently sized test pieces of dimensions 1.5×1.5×6 cm³. Previous address: Department of Physics, Brunel University, Kingston Lane, Uxbridge, Middlesex, UK. Previous address: Department of Physics, Brunel University. Previous address: Thorn EMI Central Research Laboratories, Dawley Road, Hayes, Middlesex, the Mechanics Group, Department of Engineering, University of Reading. Now at Fison's Scientific Instruments, Manor Industrial Estate, Gatwick Road, Crawley, Surrey. UK.     

Transverse mechanical properties of collagen fibers from nanoindentation

The mechanical properties of collagenous tissues, such as tendon and ligaments, are of particular interest as they are found extensively in the human body. In the present study the transverse mechanical properties of collagen fibers are reported for the first time. The elastic modulus was found to be 63 ± 4 MPa, while the viscosity was estimated to be 14  \textGPa ￡ h ￡ 56  \textGPa  \texts 14\;{\text{GPa}} \le \eta \le 56\;{\text{GPa}}\;{\text{s}} . Comparison with similar data in the literature, for bulk tendon and collagen fibrils, suggests that the apparent modulus of a network of interconnected building blocks is reduced as compared to the modulus of the individual building blocks; in particular E _tendon < E _fiber < E _fibril; this is due to the fact that as the scale of the microstructure increases (i) slippage and sliding between the respective building blocks (fibrils or fibers) increases, (ii) the volume fraction of the stiff collagen proteins decreases.     

A study of the effect of molecular weight on the tensile strength of ultra-high modulus polyethylenes

In this paper the influence of molecular weight and molecular weight distribution on the tensile strength (tenacity) of melt spun and drawn linear polyethylene are investigated with the aim of outlining the requirements for a high strength fibre. The tenacity was investigated over the molecular weight average ¯M _w range 60×10³ to 330×10³ with polydispersities ¯M _w/¯M _n ranging from 1.1 to 13.3. It was found that both molecular weight and its distribution affected tensile strength. The drawing conditions were also found to be important, a high draw temperature and a high draw ratio being needed for a high strength, high modulus fibre. By using a polymer of high ¯M _w and low polydispersity, and drawing at the optimum conditions, strengths of 1.65 GPa and moduli of 85 GPa have been achieved for test temperatures of –55° C.     

Effect of nanostructuration on compressibility of cubic BN

Compressibility of high-purity nanostructured cBN has been studied under quasi-hydrostatic conditions at 300 K up to 35 GPa using diamond anvil cell and angle-dispersive synchrotron powder X-ray diffraction. It has been found that the data fit to the Vinet equation of state yields the values of the bulk modulus B ₀ of 375(4) GPa with its first pressure derivative B ₀?? of 2.3(3), thus, the nanometer grain size (??20 nm) results in a decrease of the bulk modulus by ??9%.     

Effects of composition on selected physical properties of SiO2-K2O-Na2O glasses

Physical properties were used to characterize a range of five, three-component glass formulations (SiO₂-K₂O-Na₂O) synthesized from spray-dried precursor powders in terms of their final bulk chemical compositions. Five specimens per composition were produced by mixing dry glass powder with methyl alcohol to form a slurry, then shaping the slurry in a cylindrical mould, using conventional methods. Specimens were fired under vacuum. Optimum firing conditions for each glass were determined by selecting holding times which produced the maximum Young's modulus. Fracture toughness, K _IC, values ranged from 0.92–0.99 MPa m^1/2 and Young's modulus, E, values ranged from 45.09–58.06 GPa. Linear regression analyses showed significant correlations between chemical composition and fusion temperature (n=5; P<0.001), opacity (n=5; P <0.01), specific gravity (n=5; P<0.02), dynamic Young's modulus (n=5; P<0.01) and fracture toughness (n=30; P<0.001). The selected physical properties were found to be very sensitive to small variations in chemical composition.     

Ring-diagram calculations of normal and spin-polarized3He using the Aziz interactions

We calculate the ground-state energy of normal and spin-polarized³He within a model-space ring diagram framework where the particle-particle hole-hole (pphh) ring diagrams of the ground-state energy shift are summed up to all orders. The Aziz HFDHE2 and HFD-B(HE) interactions are employed. We first calculate a model space reaction matrix(G ^M ) whose intermediate states are required to be outside the chosen model space. The pphh ring diagrams withG ^M -matrix vertices are then summed within the model space by way of a PRA-type secular equation. The continuous single-particle spectrum of Mahaux is chosen in the present work. It is found that the inclusion of the pphh ring diagrams gives a significant increase in the binding energy per particle(BE/A) as compared with Brueckner-Hartree-Fock calculations. For normal and spin-polarized³He our calculated values forBE/A and saturation densities are respectively (1.86 K, 0.72 Å^–1) and (1.59 K, 0.91 Å^–1), while the corresponding experimental values for normal³He are (2.47 K, 0.785 Å^–1).Supported by the National Science Council of Taiwan, R.O.C., during his visit of Tsing Hua University in 1990/91.