A study of indentation annealing of (111)p-type single crystal silicon

The indentation rosette size in (111)p-type Czochralski grown silicon was measured as a function of annealing temperature (450 to 1100° C), time (600 to 9300 sec) and indentation load (0.147 to 2.94 N). The indentations were made with the silicon surface immersed in an electrolytic solution containing Nal ions with concentrations in the range of 10^?5 to 10^?1 MI^?1. The rosette size,2L, was found to depend on the experimental variables as $$\left\langle {2L} \right\rangle = Ct^{1/2} P^{1.15} exp\left( {\frac{U}{{kT}}} \right)$$ whereC is a constant andt, T, P, andU are the annealing time, temperature, indentation load and energy, respectively, andk is Boltzmann's constant. The energy U has at least three different values depending on the annealing temperature interval and varies to a lesser extent on the indentation load.     

Orientation dependence of fracture toughness measured by indentation methods and its relation to surface energy in single crystal silicon

Fracture toughness of silicon crystals has been investigated using indentation methods, and their surface energies have been calculated by molecular dynamics (MD). In order to determine the most preferential fracture plane at room temperature among the crystallographic planes containing the 〈001〉, 〈110〉 and 〈111〉 directions, a conical indenter was forced into (001), (110) and (111) silicon wafers at room temperature. Dominant {110}, {111} and {110} cracks were introduced from the indents on (001), (011) and (111) wafers, respectively. Fracture occurs most easily along {110}, {111} and {110} planes among the crystallographic planes containing the 〈001〉, 〈011〉 and 〈111〉 directions, respectively. A series of surface energies of those planes were calculated by MD to confirm the orientation dependence of fracture toughness. The surface energy of the {110} plane is the minimum of 1.50 Jm⁻² among planes containing the 〈001〉 and 〈111〉 directions, respectively, and that of the {111} plane is the minimum of 1.19 Jm⁻² among the planes containing the 〈011〉 direction. Fracture toughness of those planes was also derived from the calculated surface energies. It was shown that the K _IC value of the {110} crack plane was the minimum among those for the planes containing the 〈001〉 and 〈111〉 directions, respectively, and that K _IC value of the {111} crack plane was the minimum among those for the planes containing the 〈011〉 direction. These results are in good agreement with that obtained conical indentation.     

Theory and application of microindentation in studies of glide and cracking in single crystals of elemental and compound semiconductors

The microhardness of Si (MP 1688 K), GaP (1623 K), GaAs (1510 K) and InP (1327 K) single crystals was determined by indentation (Vicker's hardness, VHN) of low-index facets at loads of 5–100g at 296–673 K, complementing earlier work on Ge and InSb. In the brittle range, extending up to about 0.35 T _melt (K), cracking occurred preferentially along the diagonals of the indentations, and was observed at all loads, with the possible exception of the lowest (5 g) in the case of InP at 289 K. At higher temperatures the relative orientations of crack and slip traces on the crystal surface, as observed by SEM, suggested that cracks nucleated preferentially at the slip-band intersection, as was also noted by Hirsch et al. (Phil. Mag. 3 (1985) 759) in GaAs above 600 K. As earlier in Ge, the VHN was found to depend on the load, L, as L ^p , and on the indentation diameter, d, as dⁿ, with p = 1/2 and n = 2, as required by the model of indentation plasticity of Banerjee and Feltham [4, 5], but higher p and n values were found if chipping at the indentation edges was evident. The effect was related to the resulting decrease in indentation diameter due to the work lost, through chipping, by the indenter. Above about 0.35 T _melt (K), relaxation of the dislocation structures entails a decrease of p and n; both parameters tend to zero as T T _melt. Shear and tensile stresses seem to co-operate in the process of plastic deformation, the role of normal stresses, acting across slip planes, predominating in the brittle range.     

Studies on microhardness of quenched mesolite crystals

Observations and results on studies of the microhardness of {1 0 1} and {1 0 ¯1} faces of natural mesolite crystals are illustrated and explained. Variations in Vickers hardness number (VHN) with temperature of quenching and also with the applied load are discussed.     

Growth mechanism of NaBrO3 crystals from aqueous solutions

To study the growth mechanism of {111} faces of NaBrO₃, crystals were grown at different supersaturations ranging from 2% to 8%. The growth mechanisms were investigated based on the growth rate versus supersaturation relation and from the surface features observed on {111} faces. The growth mechanism of these crystals appear to be due to 2D nucleation. The growth rate curve has been further investigated using Ohara and Reid equations. Polynucleation model in two-dimensional nucleation growth theory is suggested as the most possible growth mechanism for these crystals in the present supersaturation range.     

Epitaxial growth of CoSi2 on Si(001) by reactive deposition epitaxy: Island growth and coalescence

Epitaxial CoSi₂ layers, which are phase pure but contain {111} twins, are grown on Si(001) at 700 °C by reactive deposition epitaxy. Transmission electron microscopy analyses show that the initial formation of CoSi₂(001) follows the Volmer-Weber mode characterized by the independent nucleation and growth of three-dimensional islands whose evolution we follow as a function of deposited Co thickness t_Co in order to understand the origin of the observed twin density. We find that there are two families of island shapes: inverse pyramids and platelets. The rectangular-based pyramidal islands extend along orthogonal 〈110〉 directions, bounded by four {111} CoSi₂/Si interfaces, and grow with a cube-on-cube orientation with respect to the substrate: (001)_CoSi2||(001)_Si and [100]_CoSi2||[100]_Si. Platelet-shaped CoSi₂ islands are bounded across their long 〈110〉 directions by {111} twin planes (i.e. {111}(001)_CoSi2||{111}_Si) and their narrow 〈110〉 directions by {511}_CoSi2||{111}_Si interfaces. The top and bottom surfaces are {22¯1}, with {22¯1}_CoSi2||(001)_Si, and {1¯1¯1}, with {1¯1¯1}_CoSi2||{11¯1}_Si, respectively. The early stages of film growth (t_Co ≤ 13 Å) are dominated by the twinned platelets due to a combination of higher nucleation rates resulting from a larger number of favorable adsorption sites in the Si(001)2 × 1 surface unit cell and rapid elongation of the platelets along preferred 〈110〉 directions. However, at t_Co ≥ 13 Å island coalescence becomes significant as orthogonal platelets intersect and block elongation along fast growth directions. In this regime, where both twinned and untwinned island number densities have saturated, further island growth becomes dominated by the untwinned islands. A continuous epitaxial CoSi₂(001) layer, with a twin density of 2.8 × 10¹⁰ cm^− 2, is obtained at t_Co = 50 Å.     

Morphology of C60 Crystals Grown from the Vapor Phase

Abstract

The morphology of C₆₀ crystals grown from the vapor phase have been studied. In all observations, only hexagonal and rectangular shaped crystal faces were found. Very different morphology, highly faceted {111} faces and flat {100} faces were observed using scanning electron microscopy (SEM) and atomic force microscopy (AFM). the highly regular shape and similar distance between all neighboring macrosteps observed for the {111} faces can be explained by taking into account that edges of two adjacent {111} and {100} planes can act as step sources.     

The microhardness indentation load/size effect in rutile and cassiterite single crystals

The microhardness indentation load/size effect (ISE) on the Knoop microhardness of single crystals of TiO₂ and SnO₂ has been investigated. Experimental results have been analysed using the classical power law approach and from an effective indentation test load viewpoint. The Hays/Kendall concept of a critical applied test load for the initiation of plastic deformation was considered, but rejected to explain the ISE. A proportional specimen resistance (PSR) model has been proposed that consists of the elastic resistance of the test specimen and frictional effects at the indentor facet/specimen interface during microindentation. The microhardness test load, P, and the resulting indentation size, d, have been found to follow the relationship $$P = a_1 d + a_2 d^2 = a_1 d + (P_c /d_0^2 ) d^2$$ The ISE is a consequence of the indentation-size proportional resistance of the test specimen as described by a ₁. a ₂ is found to be related to the load-independent indentation hardness. It consists of the critical indentation load, P _c, and the characteristic indentation size, d _o.     

Heterogeneous nucleation of solidification of cadmium particles embedded in an aluminium matrix

A hypomonotectic alloy of Al-4.5wt%Cd has been manufactured by melt spinning and the resulting microstructure examined by transmission electron microscopy. As-melt spun hypomonotectic Al-4.5wt%Cd consists of a homogeneous distribution of faceted 5 to 120 nm diameter cadmium particles embedded in a matrix of aluminium, formed during the monotectic solidification reaction. The cadmium particles exhibit an orientation relationship with the aluminium matrix of {111}_Al//{0001}_Cd and 110_AlAl//11¯20> _Cd, with four cadmium particle variants depending upon which of the four {111}_Al planes is parallel to {0001}_Cd. The cadmium particles exibit a distorted cuboctahedral shape, bounded by six curved {100}_Al//{20¯23}_Cd facets, six curved {111}_Al/{40¯43}_Cd facets and two flat {111}_Al//{0001}_Cd facets. The as-melt spun cadmium particle shape is metastable and the cadmium particles equilibrate during heat treatment below the cadmium melting point, becoming elongated to increase the surface area and decrease the separation of the {111}_Al//{0001}_Cd facets.The equilibrium cadmium particle shape and, therefore, the anisotropy of solid aluminium-solid cadmium and solid aluminium -liquid cadmium surface energies have been monitored by in situ heating in the transmission electron microscope over the temperature range between room temperature and 420 °C. The anisotropy of solid aluminium-solid cadmium surface energy is constant between room temperature and the cadmium melting point, with the {100}_Al//{20¯23}_Cd surface energy on average 40% greater than the {111}_Al//{0001}_Cd surface energy, and 10% greater than the {111}_Al//{40¯43_Cd surface energy. When the cadmium particles melt at temperatures above 321 °C, the {100}_Al//{20¯23}_Cd facets disappear and the {111}_Al//{40¯43}_Cd and {111}_A1//{0001}_Cd surface energies become equal. The {111}_Al facets do not disappear when the cadmium particles melt, and the anisotropy of solid aluminium-liquid cadmium surface energy decreases gradually with increasing temperature above the cadmium melting point.The kinetics of cadmium solidification have been examined by heating and cooling experiments in a differential scanning calorimeter over a range of heating and cooling rates. Cadmium particle solidification is nucleated catalytically by the surrounding aluminium matrix on the {111}_Al faceted surfaces, with an undercooling of 56 K and a contact angle of 42 °. The nucleation kinetics of cadmium particle solidification are in good agreement with the hemispherical cap model of heterogeneous nucleation.     

Relationship of hardness to load on the indentor and hardness with a fixed diagonal of the indentation

For high-hardness materials, particularly for ceramics, the relationship of hardness to load is revealed very strongly. An equation is proposed for conversion of Vickers hardness from one load to another: $$HV = HV_1 \left( {\frac{P}{{P_1 }}} \right)^{1 - 2/n}$$ where HV and HV₁ are the hardness with loads on the indentor of P and P₁ respectively. The parameter n is determined from the equation P = const dⁿ, where d is the indentation diagonal. The parameter n may also be determined on the basis of a normalized curve of the value of HV/E (E is Young's modulus). The physical nature of the relationship of hardness to load is discussed and the hardness \(HV_{d_f }\) is introduced with a fixed indentation diagonal d_f (and not with a fixed load) calculated using the equation $$HV_{d_f } = HV\left( {\frac{d}{{d_f }}} \right)^{2 - n}$$ . The introduction of \(HV_{d_f }\) makes it possible to unify measurement of microhardness for different materials at different temperatures. Curves are given simplifying conversion of hardness from one load to another and determination of the hardness \(HV_{d_f }\) .     

Mechanism of nanostructuring in fluorite-like Ca<Subscript>1 − <Emphasis Type="Italic">x</Emphasis></Subscript>La<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>F<Subscript>2 + <Emphasis Type="Italic">x</Emphasis></Subscript>

Nanostructuring in fluorite-like Ca_{1 ? x} La _x F_{2 + x} is shown to be associated with the precipitation of an CuAu-ordered phase. The shape of the precipitates is governed by the energetics of the {001} and {111} faces of tetragonal inclusions in highly anisotropic media and is nearly cuboctahedral. The misfit strain relaxes through the generation of twins, which nucleate along the intersection lines of {001} and {111} faces. The twins impede facial development and further growth and ordering of precipitates, thereby freezing the precipitation process in its initial stage. For this reason, the phase segregation is difficult to reveal, and Ca_{1 ? x} La _x F_{2 + x} crystals appear homogeneous.     

Hardness anisotropy,deformation mechanisms and brittle-to-ductile transition in carbide

The slip plane for TiC_0.8 VC_0.84 and substoichiometric tantalum carbide has been determined as {110} using microhardness indentation at room temperature. Under the same conditions, HfC_0.98 also slips on {110} but TaC_0.96 slips on {111}. At low temperatures {110} slip is characteristic of the Group IV and substoichiometric Group V transition metal carbides while stoichiometric Group V carbides probably deform preferentially on {111} at all temperatures. This behaviour is explained in terms of two models for the crystal structures of the carbides. The Group IV carbides are described by a close-packed metal lattice whereas the structure of stoichiometric Group V carbides is more open. Various physical and mechanical properties and the effects of changing carbon content have been correlated on the basis of the models. In particular, an explanation of the brittle-to-ductile transition in carbides is proposed.     

Thermodynamic modeling of the initial microstructural evolution of oxide films grown on bare copper

A thermodynamic model is presented that predicts the initial growth of either a (semi-) coherent crystalline oxide phase or an amorphous oxide phase (with a subsequent amorphous-to-crystalline transition) on a bare metal as function of the substrate orientation, growth temperature and film thickness. The model accounts for possible relaxation of growth stresses by plastic deformation. The direct formation and growth of semi-coherent, crystalline Cu₂O is predicted by application of the model to oxide overgrowth on bare Cu{111}, Cu{100} and Cu{110}. For oxide overgrowths on Cu{111} and Cu{110}, a square grid of misfit dislocations with a dislocation distance of about six Cu₂O unit cells would occur on the basis of the model calculations, which agrees with experimental observations reported for Cu{111} in the literature. On Cu{100} an array of misfit dislocations is formed along the single direction of high lattice mismatch.     

Dislocations in energetic materials

An assessment has been made of the primary dislocation slip systems in the explosives pentaerythritol tetranitrate (PETN) and cyclotrimethylene trinitramine (RDX) using a combination of dislocation etching and microhardness indentation techniques. Hardness measurements were made on all major habit faces as a function of temperature and load. These showed that, within the attainable temperature range (PETN 293 to 353 K, RDX 293 to 373 K) no change in hardness occurred which could be associated with the development of deformation mechanisms additional to those operating at room temperature. The hardness values of both materials were consistent with values obtained in some previous measurements (PETN 17 kg mm^–2, RDX 39 kg mm^–2). Solvent etching with acetone (5 sec at 274 K) proved to be an excellent method for revealing the emergent ends of growth and mechanically induced dislocations in PETN. Etching of microhardness indentations confirmed that observable slip traces comprised dislocations. These migrated up to 160m (20g load) from the indentation point on both {110} and {101} faces. The alignments defined a {110} primary slip plane. Parallel experiments with RDX yielded evidence of highly localized slip around the indentation mark (90m, 50g load). Two alignments of etch pits were noticeable. The better defined of these lay at the intersection of the (010) plane with the habit faces. The second could not be defined absolutely but most probably corresponds to the intersection of either the (011) or (012) plane with the surfaces. Consideration of the Burgers vectors of dislocations which are likely to glide in these planes lead us to speculate that the primary slip systems are, PETN {110} [001], and RDX (010) [001]. Such an assignment would be consistent with the relative hardness of the two materials.     

Hardness anisotropy in niobium carbide

Measurements of hardness anisotropy by Knoop diamond indentation on the {100} surfaces of Nb₆C₅ crystals show that the hardness is determined by crystallographic slip on {111} 〈1¯10〉 and {110} 〈1¯10〉 systems. {111} is the preferred slip plane for Nb₆C₅ and crystals with higher carbon content which show a marked decrease in Knoop hardness. The carbon atom/vacancy arrangement in these crystals is shown, by electron diffraction, to possess short-range order. Crystals annealed at low temperatures contain domains of non-cubic long-range order which increase the Knoop hardness and eliminate the anisotropy in hardness. Dislocation arrangements around Knoop indentations have been directly observed by electron microscopy in an attempt to confirm the slip processes deduced from hardness anisotropy.     

Solidification of tin droplets embedded in an aluminium matrix

The solidification behaviour of tin droplets embedded in an aluminium matrix in a rapidly solidified Al-5 wt % Sn alloy has been investigated by a combination of transmission electron microscopy and differential scanning calorimetry. Detailed transmission electron microscopy shows that rapidly solidified Al-5 wt % Sn consists of about 5 μm diameter columnar aluminium grains, with a fine-scale distribution of 20–300 nm sized tin particles embedded within the aluminium grains, and 100–400 nm sized tin particles at the aluminium grain boundaries. The tin particles exhibit two different orientation relationships with the aluminium matrix and a variety of different faceted shapes: {1 1 1}_Al∥{1 0 0}_Sn and 〈¯2 1 1〉_Al∥〈0 1 0〉_Sn, with the main facet parallel to {1 1 1}_Al, and {1 0 0}_Sn; and {1 0 0}_Al∥{1 0 0}_Sn and 〈0 1 1〉_Al∥〈0 1 1〉_Sn, with the main facet parallel to {1 0 0}_Al and {1 0 0}_Sn.In situ heating in the transmission electron microscope shows that the different tin particle shapes are not affected by heat treatment in the solid state, but change into a truncated octahedral shape bounded by {1 1 1}_Al and {1 0 0}_Al facets when the tin particles melt. The {1 0 0}_Al-liquid Sn interfacial energy is about 9% larger than the {1 1 1}_Al-liquid Sn interfacial energy just above the tin particle melting point, and the {1 0 0}_Al/{1 1 1}_Al interfacial energy anisotropy decreases gradually as the temperature increases above the melting point. Differential scanning calorimeter experiments show that the liquid tin droplets solidify in three stages. Firstly, the larger tin droplets at the aluminium grain boundaries solidify by nucleation on catalytic trace impurities, over a temperature range of 170–140 °C. Secondly and thirdly, the smaller tin particles embedded within the aluminium grains solidify by catalytic nucleation on the {1 0 0}_Al and {1 1 1}_Al facets, over the two temperature ranges of 140–128 °C and 128-115°C. Catalytic nucleation of the solidification of tin takes place at special sites such as steps or dislocations on the {1 0 0}_Al and {1 1 1}_Al facets with contact angles of 55° and 59°.     

An approximate approach for the calculation ofM s in iron-base alloys

Having estimated the critical driving force associated with martensitic transformation,ΔG ^α→M, as $$\Delta G^{\alpha \to M} = 2.1 \sigma + 900$$ whereσ is the yield strength of austenite atM _s, in MN m^?2, we can directly deduce theM _s by the following equation: $$\Delta G^{\gamma \to {\rm M}} |_{M_S } = \Delta G^{\gamma \to \alpha } + \Delta G^{\alpha \to M} = 0.$$ The calculatedM _s are in good agreement with the experimental results in Fe-C, Fe-Ni-C and Fe-Cr-C, and are consistent with part of the data in Fe-Ni, Fe-Cr and Fe-Mn alloys. Some higher “M _s” determined in previous works may be identified asM _a,M _s of surface martensite or bainitic temperature. TheM _s of pure iron is about 800 K. TheM _s in Fe-C can be approximately expressed as $$M_S (^\circ {\text{C}}) = 520 {\text{--- }}\left[ {{\text{\% C}}} \right]{\text{ }}x 320.$$ In Fe-X, the effect of the alloying element onM _s depends on its effect onT ₀ and on the strengthening of austenite. An approach for calculation of ΔG ^γ→α in Fe-X-C is suggested. Thus dM _s/dx _c in Fe-X-C is found to increase with the decrease of the activity coefficient of carbon in austenite.     

Microstructure and electrical properties of ultrathin gold films prepared by DC sputtering

Ultrathin gold films with different thicknesses were prepared by direct current magnetron sputtering technique and analyzed by X-ray diffraction, atomic force microscopy, transmission electron microscopy and temperature-varying four-wire technique. For thicknesses d < 24.1 nm, both D_{avg {111}} and D_{avg {220}} increase rapidly with the thickness. For 24.1 ≤ d ≤ 97.8 nm, D_{avg {220}} increases at a slower rate than before but D_{avg {111}} remains the same. Surface morphology analysis shows that, as the thickness increases, the average particle size changes from 22.1 to 54.3 nm; at the same time, rms roughness decreases to a minimum and then increases. The electrical properties of the thin films from 80 to 300 K were measured. The results show that the temperature coefficient of resistance of the thin films is positive, and increases from 2.2 × 10⁻⁴ to 8.5 × 10⁻⁴ K⁻¹ with increasing film thickness.     

Scaling of the Temperature Dependent Resistivity in 111 Iron-Pnictide Superconductors

In Li_1?x FeAs, Li_1?x FeP, and Na111 (Na_1?δ FeAs, Na_0.9FeAs, NaFe_0.95Co_0.05As, NaFeAs_0.8P_0.2) members of the 111-iron-pnictide superconductor family, the temperature dependent resistivity ρ can be scaled into a single curve described by a scaling function. In particular, the ρ(T) dependences can be reproduced by the expressions $\rho(T) = \rho_{0} + cT\exp( - \frac{2\varDelta }{T})$ and $\rho(T) = \rho_{0} + (a/T)\exp( - \frac{2\varDelta }{T}) + bT$ for Li_1?x FeP and Li_1?x FeAs, Na-111 crystals, respectively. The scaling was performed using the energy scale 2Δ, the parameters a, b, c, and the residual resistivity ρ ₀ as scaling parameters. The existence of a single metallic ρ(T) curve is interpreted as an indication of a few mechanisms in various compounds, which dominates the different scattering of charge carriers in 111-iron-pnictide superconductors studied so far. Thus, the scaling of the normal-state properties seems to be a general feature not only for high-T _c cuprates, but also for the iron-pnictides superconductor family.     

A method for the calculation of interfacial energies in Al2O3 and ZrO2/liquid-metal and liquid-alloy systems

A method is proposed by which the interfacial energy, γ_SL, of polycrystalline solid oxides (Al₂O₃, ZrO₂) in contact with liquid metals and certain binary liquid alloys can be calculated from the values of the surface energy of the oxides, γ_SV, and the liquid metals or liquid alloys, γ_LV, respectively. According to this method, the interfacial energy depends on the geometric mean of surface interactions, (γ_SV γ_LV)^1/2, the molar volumes, V, of the solid and liquid phases, and a parameter, K, which depends on the geometric details of the oxide surface defined by the ion sites in the oxide as well as the stoichiometry of the elements in the oxide and is given by the equation, $$\gamma _{SL} = \left( {K\frac{{V_{metal} }}{{V_{oxide} }} + 1} \right)^{2/3} (\gamma _{SV} \gamma _{LV} )^{1/2}$$ The method was verified using interfacial energy data obtained by measurements of the contact angle, θ, formed between the oxides and the liquid metals and liquid alloys with the sessile drop technique. A good agreement was observed between the calculated and the experimentally estimated values of γ_SL at the melting point of the metals and alloys.