Local Thermal Expansion Coefficient Research Articles

Nanoparticle surface charge-enhanced heat capacity in molten salt phase change materials for thermal energy storage

Nanoparticle-enhanced molten salt phase change materials have been used extensively for thermal energy storage. However, the role of nanoparticles in enhancing the specific heat capacity remains elusive with contradicting reports. In this work, to clarify the mechanism behind the specific heat enhancement in nanoparticle (SiO2) embedded nitrate (NaNO3–KNO3) and carbonate (Li2CO3–K2CO3) molten salts. Due to the surface charges on nanoparticles, an orderly layered distribution of molten salt ions near the surface is observed in molecular dynamics simulations, which lead to higher electrostatic potential energies near the nanoparticle surface. This makes the ionic layers with the same charge type easier to expand when temperature rises, leading to a larger local thermal expansion coefficient. Since the thermal expansion coefficient is positively correlated with the specific heat based on the phonon interpolation, the increased local thermal expansion coefficient is the main reason for the enhancement in the specific heat. The enhancement in the specific heat and the enrichment of charged functional groups on the nanoparticle surface are also confirmed experimentally. The specific heat can be significantly enhanced, by up to 19% here with 1 wt% nanoparticle, after we tailor the surface chemistry of nanoparticles, in particular, by coating active functional groups such as hydroxyl groups on the surface. This study clarifies the fundamental role of surface changes on nanoparticles in enhancing the specific heat of molten salts, and suggests that nanoparticles can have higher surface charge densities, if protonated in an acidic environment, can lead to larger specific heat enhancement in molten salts.

An efficient multi-scale computation of the macroscopic coefficient of thermal expansion: Application to the Resin Transfer Molding manufactured 3D woven composites

This paper presents a simple and computationally efficient multi-scale procedure to predict the macroscopic temperature dependent coefficient of thermal expansion (CTE) of any linearly thermoelastic material from isothermal mechanical simulations only. The approach relies on Levin’s demonstration that, in analytical homogenization, the effective coefficient of thermal expansion is related to the local coefficient of thermal expansion and the stress concentration tensor. For demonstration purposes, this procedure was applied to a 3D woven composite material. The proposed approach was successfully validated with full thermal simulations.

Structural evolution of fused silica below the glass-transition temperature revealed by in-situ neutron total scattering

The common belief that glass structure is completely frozen-in at room temperature is challenged at both macroscopic and atomic scales. Here, we demonstrate an analytical method to elucidate the fine details of a continuous structural change of fused silica (FS) at temperatures below the glass-transition temperature using in-situ neutron total scattering. We find that the SiO4 tetrahedron expands through the entire temperature range with a local coefficient of thermal expansion of 9.1 × 10−6 K−1, while the average medium-range distance, derived from the first sharp diffraction peak of the structure factor, expands at a rate of 21 × 10−6 K−1. Such an expansion difference reflects glass-structure changes within the “rigid-unit mode” model, where each tetrahedron behaves as a rigid unit and the flexible rotations between rigid units lead to more than two times higher medium-range thermal expansion. We further demonstrate that such rotations change the shape of individual rings, leading to a measurable change in the first sharp diffraction peak (FSDP). This study paves the way to measure the structural changes of other silicate glasses, especially through the glass transition.

An Investigation into the Package and Printed Circuit Board Assembly Solutions of an Ultrathin Coreless Flip-Chip Substrate

Flip-chip technology has been widely accepted as a solution for electronic packaging of high-pin-count devices. Due to the demand for smaller and thinner package dimensions, coreless build-up substrates will be used in industry to carry the die by solder bumps due to the advantages of shorter transmission route and lower inductance and thermal resistance. However, coefficient of thermal expansion (CTE) mismatch between the Cu trace and the laminate often causes the coreless substrate to warp, which leads to failures such as nonwetted solder bumps and interfacial cracking during assembly and reliability tests. In a previous study, assembly of a six-layer polyimide-based coreless flip-chip package was achieved by a 17 mm × 17 mm die with 4355 Sn-37Pb solder bumps, an amide-based underfill, and 1521 Sn-3.0Ag-0.5Cu solder balls. For determination of its board-level reliability characteristics, the component was mounted on a printed circuit board (PCB) using a conventional surface mount technology, and 10 test vehicles were assembled for assessment of their reliability under a temperature cycling environment. The experimental results show that the characteristic life of the PCB assembly exceeded 1500 cycles and that failure resulted from fracture of the outermost solder balls on the substrate side. This was different from the failure mode of die cracking when the package experienced hundreds of temperature cycles at the component level because the rigid PCB, through solder balls, moderated the deformation of the coreless flip-chip package. Hence, the concentrated bending stress at the die edge region was lowered. Finally, the local CTE mismatch between the stiffener and the PCB dominated the fatigue fracture of the outermost solder balls to become the main failure mode.

Local Thermal Expansion and the C-C Stretch Vibration of the Dicarbon Antisite in 4H SiC

The C-C stretch vibration associated with the dicarbon antisite in 4H SiC has been observed out to the fifth harmonic in the low temperature photoluminescence spectrum. The anharmonicity is accounted for reasonably well by fits to the data based on the Morse potential. We combine the observations from experiment, the analytically tractable Morse potential, and results obtained from first principles calculations on this defect to obtain an estimate of the thermal expansion coefficient of the C-C bond. This local thermal expansion coefficient is considerably smaller than the linear thermal expansion coefficient of bulk 4H SiC, in striking contrast with the recent result for the nitrogen-vacancy center in diamond that the local thermal expansion coefficient is larger than the bulk value.

Ultra low-k die crack study for lead free solder bump flip-chip packaging

Ultra low-K (ULK) dielectric has lower mechanical strength (E < 8 GPa), lower cohesive strength and lower adhesion (<5 J/m2) than low-K and SiO2 dielectric material. The packaging reliability test has shown that delamination between copper (Cu) and ULK is a major concern. In addition to the Cu and ULK delamination issue, the ULK die crack after temperature cycling test (TCT) showed die crack failure to be another issue. ULK die crack failure can be detected by C-mode scanning acoustic microscopy (CSAM). The CSAM image of the die crack mostly shows a crescent moon shape. The crack initiates at the upper edge of the underfill fillet penetrating the sidewall of the die, and then propagates toward the inside of the die. Finite element simulation indicates that the die crack failure starts at the backside edge of the die. The ULK die crack is caused by two mechanisms. First is the bending stress at the backside of the die, which is the result of the coefficient of thermal expansion (CTE) mismatch between the silicon die and the organic substrate. Second is the thermo-mechanical stress, which is the result of the local CTE mismatch between the silicon die and the underfill. The finite element simulation parametric study performed in this paper shows that a low underfill fillet height and a small fillet tip angle reduce the thermo-mechanical stress. In addition, attaching a heat sink to the surface of the flip-chip die increases packaging stiffness and resists the bending stress induced by the shrinkage of the substrate. Experimental results demonstrate that lowering the height of the underfill fillet, reducing the angle of the fillet tip and attaching a heat sink to the flip-chip die are effective ways to solve the ULK die crack issue.

Effect of temperature on the local angular thermal expansion and local structure for nickel-doped zinc fluosilicate

A theoretical method for studying the local properties about Ni 2+ ion in a trigonal ligand-field has been proposed by diagonalizing the complete energy matrix and considering the electron paramagnetic resonance (EPR) parameters D and g. For nickel-doped ZnSiF 6 · 6H 2O and ZnSiF 6 · 6D 2O systems, the local lattice distortion and local angular thermal expansion coefficient have been investigated at various temperatures. The calculated results indicate that the local structure around octahedral Ni 2+ centre has a compression distortion in the two systems. Moreover, the temperature dependence of the local angular thermal expansion coefficient has also been analysed.

The EPR Zero-Field Splitting D and its Pressure and Temperature Dependence for Trigonal Mn2+ Centers in [Zn(H2O)6](BF4)2:Mn2+ Crystal

The EPR zero-field splitting D (= b0 2 ) and its pressure and temperature dependence for trigonal Mn2+ centers in low and room temperature phases in [Zn(H2O)6](BF4)2 :Mn2+ crystal are studied by a high-order perturbation formula based on the dominant spin-orbit coupling mechanism. From the studies, the local trigonal distortion angles, the local angular compressibilities and the local angular thermal expansion coefficients for Mn2+ centers in both phases of the [Zn(H2O)6](BF4)2 crystal are estimated. The results are discussed

Theoretical studies of the spin-Hamiltonian parameters and the effects of the temperature and pressure on the zero-field splitting for Ni 2+: Zn(BF 4) 2·6H 2O crystal

The spin-Hamiltonian parameters (the g factors g ∥, g ⊥ and the zero-field splitting D) and the effects of the temperature and pressure on D for Ni 2+ ion at the trigonal Zn 2+ site in the low- and room-temperature phase of Zn(BF 4) 2·6H 2O crystal are calculated. The calculations are based on the microscopic spin Hamiltonian theory in teams of the diagonalization of the complete energy matrix of 3 d 8 ions in trigonal symmetry. The crystal-field parameters related to the impurity structure are obtained from the superposition model. Thus, the local trigonal distortion angle θ, the local angular thermal expansion coefficient and local angular compressibility for Ni 2+ impurity centers in Zn(BF 4) 2·6H 2O crystal are estimated. The reasonableness of these local values is discussed.

EPR Theoretical Study of Local Molecular Structure and Thermal Expansion Coefficient for Octahedral Mn2+ Centers in Zinc Fluosilicate

A theoretical method for studying the inter-relation between electronic and molecular structure has been proposed by diagonalizing the complete energy matrices for a d(5) configuration ion in a trigonal ligand field and considering the second-order and fourth-order EPR parameters D and (a - F) simultaneously. As for ZnSiF(6).6H(2)O:Mn(2+) and ZnSiF(6).6D(2)O:Mn(2+) complex molecules, the local lattice distortion and local thermal expansion coefficient for the octahedral Mn(2+) centers in zinc fluosilicate have been investigated, respectively. The calculations indicate that the local lattice structure around an octahedral Mn(2+) center has an expansion distortion, whether the Mn(2+) ion is doped in ZnSiF(6).6H(2)O or ZnSiF(6).6D(2)O. Moreover, the total tendency of the local lattice expansion distortion will be more and more obvious with the temperature rising, apart from some slight variations at T = 60 K for the ZnSiF(6).6H(2)O. By simulating the two low-symmetry EPR parameters D and (a - F) simultaneously, the local lattice structure parameters R and theta have been determined to vary from 2.204 Angstroms to 2.256 Angstroms and from 53.417 degrees to 52.710 degrees, respectively, in the temperature range 19-297 K for ZnSiF(6).6H(2)O:Mn(2+) and to vary from 2.215 Angstroms to 2.255 Angstroms and from 53.346 degrees to 52.714 degrees, respectively, in the temperature range 50-300 K for ZnSiF(6).6D(2)O:Mn(2+). Subsequently the dependence of local thermal expansion coefficients on the temperature is studied and the corresponding theoretical values of the local thermal expansion coefficients are reported firstly. Some characteristics of local thermal expansion coefficients of Mn(2+) in ZnSiF(6).6H(2)O:Mn(2+) and ZnSiF(6).6D(2)O:Mn(2+) systems are also analyzed.

Crystal field spectroscopy of Cr 3+ in glasses: Compositional dependence and thermal site expansion

Optical absorption (= crystal field) spectra of Cr 3+ in silicate glasses have been investigated as a function of chemical composition and temperature. In a large range of glass compositions, most spectra show a variation of Crystal Field Stabilization Energy (CFSE) as a function of glass chemistry. Cr 3+ CFSE ranges between 215 and 234 kJ/mol-Cr 3+ and it increases with the theoretical glass basicity. Alkali-bearing glasses make a noticeable exception, as CFSE only varies with the nature of the alkali and not with its concentration. In glasses representing simplified magmatic compositions, CFSE varies by 7 kJ/mol-Cr 3+ and the lowest CFSE values are observed in silica-rich compositions. This CFSE variation may contribute to the compositional dependence of mineral/liquid Cr-partition coefficients. Near UV–visible absorption spectra have been recorded up to 800 K, using a homemade diode array spectrometer fitted with a furnace. The modification of the optical spectra at high-temperature is characterized by a red shift of the Cr 3+ absorption bands. CFSE shows a nearly linear negative dependence on temperature, with an overall variation of about 7 kJ/mol-Cr 3+ over 500 K, a value similar to that characterizing the CFSE chemical dependence. This systematic red shift is related to the local thermal expansion of the Cr site and may be treated in glasses using a polyhedral approach. The Cr–O linear thermal expansion coefficient is 15–20 × 10 − 6 K − 1 in alkali-bearing silicate and borosilicate glasses and is similar to those determined in silicate minerals. The local thermal expansion coefficient exhibits a weak compositional dependence and is larger than the bulk thermal expansion coefficient of the glasses. The compositional and thermal dependence of the Cr 3+ crystal field spectra shows that this ion is a sensitive probe of the evolution of glass structure as a function of composition or temperature. These data are consistent with the location of Cr 3+ ions in cationic domains in glasses.

X-ray absorption fine structure: characterization of thermal and structural disorder in non-crystalline solids

A great progress has been made in the last years in the XAFS studies of thermal and structural disorder, due to the increased quality of measurements allowed by the intense third generation synchrotron radiation sources, and the refinement of the analysis techniques. A description of XAFS strengths and limits is given and some paradigmatic investigations on thermal and structural characterization of crystalline and non-crystalline solids are reported. In particular, the environments of the nearest neighbors of selected species in some germanium based compounds and silver borate glasses are described in terms of radial distribution functions and their main parameters, such as mean distance, variance and asymmetry. The determination of local thermal expansion coefficients in crystalline and non-crystalline solids by temperature dependent studies is shown.

Ultramicrostructure and microthermomechanics of biological IR detectors: materials properties from a biomimetic perspective.

Microstructural organization of the biological infrared (IR) receptors was studied to elucidate their materials properties useful for prospective biomimetic design of artificial IR sensors from organic/polymeric materials. The IR receptors in Melanophila acuminata beetles were studied with ultrahigh-resolution scanning probe microscopy (SPM) in a range of temperatures. By application of micromechanical mapping and thermal stage, we made attempts to reveal the micromechanical and thermomechanical properties of the cuticular apparatus of the IR sensillum. The main component of the cuticular apparatus is an internal endocuticular sphere with a diameter of about 15-20 microm. Highly ordered multilayered organization of the lamellated peripheral mantle of the sphere was confirmed and characterized. We observed that the interlayer spacing of this microstructure varied along the circumference and decreased to 300 nm in the vertex of the sphere. We demonstrated that the microlayered structure is composed of nanolayers with very different micromechanical properties and thermal behaviors. Thermal expansion of the outer mantle was observed, and the local thermal expansion coefficient under given preparation conditions was estimated to be below 1.5 x 10(-4) grad(-1).

Reliability Analysis of Flip Chip Designs Via Computer Simulation

A flip chip component is a silicon chip mounted to a substrate with the active area facing the substrate. This paper presents the results of an investigation into the relationship between a number of important material properties and geometric parameters on the thermal-mechanical fatigue reliability of a standard flip chip design and a flip chip design with the use of microvias. Computer modeling has been used to analyze the mechanical conditions of flip chips under cyclic thermal loading where the Coffin-Manson empirical relationship has been used to predict the life time of the solder interconnects. The material properties and geometry parameters that have been investigated are the Young’s modulus, the coefficient of thermal expansion (CTE) of the underfill, the out-of-plane CTE CTEz of the substrate, the thickness of the substrate, and the standoff height. When these parameters vary, the predicted life-times are calculated and some of the features of the results are explained. By comparing the predicted lifetimes of the two designs and the strain conditions under thermal loading, the local CTE mismatch has been found to be one of most important factors in defining the reliability of flip chips with microvias. [S1043-7398(00)01203-2]

Electronic absorption spectra of Fe3+ in andradite and epidote at different temperatures and pressures

Temperature, T, and pressure, P, behaviour of absorption bands caused by spin-forbidden dd -transitions of Fe 3+ in octahedral sites of the andradite and epidote structures were studied at T from 300 to 750 K and P up to 10 GPa. The temperature dependence of the integral intensity of the 6 A 1g → 4 T 1g ( 4 G) and 6 A 1g → 4 T 2g ( 4 G) bands resemble the behaviour of spin-allowed dd -bands of the other 3d N ions: an increase on heating in case of the centrosymmetric position of Fe 3+ in the Y-site of andradite and nearly constant values in the strongly distorted M3-site of the epidote structure. Increasing T lowers the intensity of the crystal field-independent band 6 A 1g → 4 A 1g 4 E g ( 4 G) in both minerals. The influence of P on the intensity of the dd -bands is insignificant. In andradite garnet, the local thermal expansion coefficient α loc of the Fe 3+ -centred octahedra Y, as derived from the high-T spectra, is much lower than that of Cr 3+ -centred octahedra Y in chromium-bearing garnets. On the other hand, judging from T-induced shifts of 6 A 1g → 4 T 1g ( 4 G) and 6 A 1g → 4 T 2g ( 4 G) bands, α loc of FeO 6 is much higher in epidote than in andradite, being comparable to values in AlO 6 - or CrO 6 -octahedra. This indicates that α loc values of Fe 3+ -centred octahedra may vary strongly between different structural matrices, possibly as a consequence of differences in covalent bonding of Fe 3+ compared to Cr 3+ . In andradites, T and P produce energy shifts of the crystal field-independent band 6 A 1g → 4 T 1g 4 E g ( 4 G) in opposite directions, thus showing a decrease and an increase, respectively, in the covalence of the Fe 3+ -O bonds. In epidote, the effect of both T and P on the energy of the crystal field independent transition is much smaller than in andradite. In epidote, on the other hand, P causes a strong high-energy shift of the 6 A 1g → 4 T 2g ( 4 G) transition, indicating a strong increase of the crystal-field strength Dq, and thus significant compressibility of the Fe 3+ -centred M3-octahedra with k ≅ 75 GPa. Up to ca. 10 GPa, there appear no additional bands in the NIR range of the high-P spectra of both minerals. This is indicative for the absence of P-induced reduction of Fe 3+ .

THERMAL STRESSES AND THERMAL EXPANSION IN A UNIFORMLY HEATED FUNCTIONALLY GRADED CYLINDER

The exact solution is derived for the problem of uniformly heating a cylinder whose elastic moduli and thermal expansion coefficient vary linearly with radius. The solution shows that the radial and tangential stresses are largest in magnitude at the center of the cylinder whereas the deviatoric stress is largest in magnitude at the outer edge of the cylinder. The effective thermal expansion coefficient is found to be essentially given by the volumetric average of the local thermal expansion coefficient, with the variation in moduli having only a small effect. In the case of a material with uniform moduli but a spatially variable thermal expansion coefficient, the effective thermal expansion coeffi cient is exactly equal to the volumetric average; this result is an extension of those derived by Levin and Schapery for n-component materials.

Pressure and temperature shifts of the zero-field splitting for and ions in MgO

The relationship between the EPR cubic parameter a-value and the local structure of ions in crystals has been established by utilizing the crystal-field-like model. A general method for calculating both the local compressibility and local thermal expansion coefficient of the impurities in crystals has been proposed. Results show that the EPR cubic parameter a-value and its pressure and temperature shifts for and can be interpreted uniformly. It is also shown that: (a) the local compressibility and local thermal expansion coefficients of and crystals deduced are close to those of the host lattice, within experimental errors, and that the local bond lengths deduced are quite close to those of the shell model calculation values; and (b) the relation is a good approximation.

EXAFS Study for Anharmonicity of CuBr

New formalism of EXAFS analysis for anharmonic system has been applied to anharmonic system of CuBr at temperatures, 150, 300, and 400 K. The new formalism gives the consistent results on the second cumulants with a previous work, and the additional constants such as the local thermal expansion coefficient, α L , force constant, k 0 , and anharmonic parameter, β has been derived. The obtained values were α L =(6.19±0.05)×10 -5 /K, k 0 =(41±5) N/m, and β=(6.0±0.5)×10 11 N/m 2 , respectively, for Br–Cu bond. The higher cumulants were derived in terms of anharmonic parameter, force constant and temperature.

Determination of an effective coefficient of thermal expansion of electronic packaging components: a whole-field approach

Moire interferometry is proposed as a tool for the coefficient of thermal expansion (CTE) measurement of electronic packaging components. The method is a whole-field displacement measurement technique with a sub-micron sensitivity, which can produce the overall CTE and the local CTE across the entire component with high accuracy. The large dynamic range of the method makes it compatible with CTE evaluation of a broad range of components. Two experimental procedures are suggested for 1) CTE over a fixed temperature range and 2) CTE as a function of temperature. The procedures are implemented for various thin small outline packages (TSOPs) a plastic ball grid array (PBGA) package, and a stacked memory cube. The results emphasize the importance of a whole-field measurement technique. A supplementary thermo-mechanical analyzer (TMA) test on an aluminum alloy is conducted and the results are compared with a Moire measurement to discuss the accuracy of the proposed measurement procedure.

THERMAL STRESSES AND EFFECTIVE THERMAL EXPANSION COEFFICIENT OF A FUNCTIONALLY GRADIENT SPHERE

We present the exact solution to the problem of uniform heating of a spherical body whose elastic moduli and thermal expansion coefficient vary linearly with the radius. The Frobenius series method is used to find exact expressions for the displacements and stresses. Both the radial and hoop stresses are largest in magnitude at the center of the sphere. The radial stress decays to zero at the outer edge, whereas the hoop stresses always change sign at some intermediate value of the radius. We also find an exact expression for the effective thermal expansion coefficient. For the special case where the thermal expansion coefficient varies with the radius but the elastic moduli are uniform, the effective thermal expansion coefficient of the sphere is equal to the volumetric average of the local thermal expansion coefficient. In the more general case, where the moduli also vary, the moduli variations have very little influence on the effective thermal expansion coefficient.