Anomalous temperature dependence of shear modulus c44 for platinum

MacFarlane, R.E.; Rayne, J.A.; Jones, C. K.

doi:10.1016/0031-9163(65)90659-1

Cited by 140 publications

(47 citation statements)

References 3 publications

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“…The calculations of the elastic constants are carried out at 0 K neglecting their temperature dependence, which according to Refs. [27,28] is very small in the temperature range of 0-300 K. The elastic properties have been calculated at both the theoretical (0 K) and experimental (room temperature) values of lattice parameter [19].…”

Section: Resultsmentioning

confidence: 99%

Ab initio calculations of elastic properties of Pt–Sc alloys

et al. 2008

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Section: Resultsmentioning

confidence: 99%

Ab initio calculations of elastic properties of Pt–Sc alloys

et al. 2008

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“…Table 8 gives the measured composite modulus, E C , for the addition of 0.10, 0.20, 0.30, and 0.40 volume fraction of tungsten particles with diameters of approximately 30 lm to a borosilicate glass [91], along with the predicted values of modulus calculated by the ROM, RCS, HP, HT models and the modulus of tungsten [92]. In addition, Table 8 lists the measured E C , for composite specimens from Fujieda et al [64], who measured the elastic modulus change induced by adding either 26 wt % platinum nanoparticles (Pt NP ) [93] or 26 wt % Ag NP [94,95] to a dental porcelain, where the mean diameters of the Pt NP and Ag NP nanoparticles were 5 nm and 10 nm, respectively. The measured composite moduli, E C , (Table 8) [64,91] agree quite well with the moduli calculated in this study using the Halpin-Tsai model (HT).…”

Section: Discussionmentioning

confidence: 96%

“…Over the indentation load range of 1.96 N to 9.8 N that is included in this study, both H and K C were independent of Table 7 For CoSb 3 -based thermoelectric materials, a comparison of the K C results from this study with the literature, including the porosity, P, the grain size, GS, of the specimens and the K C measurement technique [69][70][71] Material K C (MPam 0.5 ) P G S (lm) K C measurement method Reference [64,91] and E r is the Young's modulus of the reinforcing material [92][93][94][95] the load for Ba-skutterudite (Fig. 12).…”

Section: Hardness and Fracture Toughness As A Function Of Loadmentioning

confidence: 98%

Influence of silver nanoparticle addition, porosity, and processing technique on the mechanical properties of Ba0.3Co4Sb12 skutterudites

et al. 2014

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The thermoelectric skutterudite Ba 0.3 Co 4 Sb 12 is a promising candidate for waste heat recovery applications. Recently, it was demonstrated that the addition of silver nanoparticles (Ag NP ) to Ba 0.3 Co 4 Sb 12 increases both the thermoelectric figure of merit and electrical conductivity. This study is the first to examine the effect of Ag NP addition on the material's mechanical properties. This study also found that the Young's modulus, E, shear modulus, G, and bulk modulus, B, decreased linearly with increasing volume fraction porosity, P. Resonant ultrasound spectroscopy was employed to measure the elastic moduli, and Vickers indentation was used to determine the hardness, H, and fracture toughness, K C . Trends in the mechanical properties as a function of grain size, porosity, and the Ag NP are discussed in terms of the pertinent literature. While K C was independent of Ag NP addition, porosity, and grain size, both E and H decreased linearly with increasing porosity. In addition, this study is the first to identify (i) the Ag 3 Sb phase formed and (ii) the enhanced densification that occurs when the Ag NP is sintered with Ba 0.3 Co 4 Sb 12 powders, where both effects are consistent with the eutectic and peritectic reactions observed in the binary phase diagram Ag-Sb. These eutectic/peritectic reactions may also be linked to the enhancement of electrical conductivity previously observed when Ag is added to Ba 0.3 Co 4 Sb 12 . Also, similar beneficial eutectic/peritectic reactions may be available for other systems where conductive particles are added to other antimonides or other thermoelectric systems.

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“…On the basis of this model we have calculated phonon dispersion relations, frequency spectrum and the specifie heat of platinum. Ah independent stimulus to the present study was also imparted by the availability of experimental dispersion curves from neutron scattering [12] and specific heat data [10].…”

Section: Lntroduefionmentioning

confidence: 99%

Lattice dynamical study of platinum

Hemkar

1976

Acta Physica

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A modificd angular force model which takcs into aecount the effect of eleetron-ion interaction on the basis of S~ASMA and JOSHI model along with the ion-ion central and DE LAUNAY type angular intcraction, has been applied to investigate the phonon dispersion curvcs, vibrational spectrum and specific heat of platinum. The calculated results show satisfactory agreement with the experimental data. lntroduefionIn spite of the significant advances made in the recent past, the lattice dynamics of metallic crystals remains one of the most interesting field of investigation to undertake. The theory is still lar from a stage of completion and phenomenological force models based on empirical relations are still necessary for a proper understanding of the vibrational properties. It is well known that the Cauchy relation (C1~ = C44 ) does not hold for metals and FucHs [1] attributed the cause of this failure to the presence of conduction electrons. Quite recently, BEHAItl and TRIPATHI [2--5] have investigated the lattice dynamics of several body-centred and face-centred cubic metals using a modified forro of a non-central force model which takes into account DE LAUNAY [6] type angular forces and SHASMA and JOSHI [7] type volume forces along with the ion-ion central interaction, h was emphasized that the Cauchy discrepancy in metals arises because of the angular interaction between a pair of ions and the presence of electron gas. The frequencies calculated on this approaeh were found to show good agreement with the recent experimental neutron scattering data for almost all the cases. In a recent study, we have utilized this model as well to explain many other solid state phenomena f o r a number of cubic metals [8, 9]. In view of the relative success and simplicity of this model, it was thought of interest to employ it to other complicatcd cases of transition mctals. In the present communication we have considered platinum for lattice dynamical study, because of its high stiffness constants Cll and C12 and departure from Cauchy relation which is is vcry much greater in ir than in copper (C12/C442= 1.53 for Cu and 3.82 for Pt). It shows that angular forces ate more important in platinum. Thus platinum is a suitable metal to test the validity of modified angular force model. On the basis of this model we have

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Anomalous temperature dependence of shear modulus c44 for platinum

Cited by 140 publications

References 3 publications

Ab initio calculations of elastic properties of Pt–Sc alloys

Ab initio calculations of elastic properties of Pt–Sc alloys

Influence of silver nanoparticle addition, porosity, and processing technique on the mechanical properties of Ba0.3Co4Sb12 skutterudites

Lattice dynamical study of platinum

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