The Thermal Expansion of Anisotropic Metals

Childs, Barney

doi:10.1103/revmodphys.25.665

Cited by 50 publications

(7 citation statements)

References 22 publications

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“…The large undercooling can lead to excessive dissolution of the substrate [6] and large primary intermetallic compounds (IMCs) such as Ag3Sn blades, which can result in poor mechanical performance [3][4][5][7][8][9][10][11]. The variable undercooling causes the microstructure to vary from joint to joint [12] and the small number of grains per joint is a concern because βSn is tetragonal and has highly anisotropic properties such as thermal expansion [13] stiffness [14], and the diffusion of Ni and Cu [15,16]. The orientation of the βSn grain(s) plays an important role in electromigration resistance [17][18][19][20][21] and in the lifetime of a joint during thermal cycling [22,23].…”

Section: Introductionmentioning

confidence: 99%

Grain refinement of electronic solders: The potential of combining solute with nucleant particles

Shang

Belyakov

et al. 2017

Journal of Alloys and Compounds

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Sn-Ag-Cu electronic solder joints typically solidify from a single nucleation event producing either a single βSn grain or twinned grains. With so few and variable βSn orientations, each joint is mechanically unique due to the anisotropy of tetragonal βSn. Here we explore the potential of increasing the number of βSn orientations in solder joints by promoting heterogeneous nucleation during solidification. It is shown that large (60 g) samples can be grain refined effectively by combining growth restricting solute with potent heterogeneous nucleant particles introduced by alloying additions of Zn, Ti, Co, Ir, Pd, or Pt. These mechanisms are discussed with reference to the grain refinement of structural casting alloys.In 500 μm solder balls, these grain refinement approaches were less effective and a relatively high cooling rate of 17 K/s combined with solute and nucleant particles were required to trigger multiple nucleation events. With this approach, up to 12 independent grains formed in 500 μm balls of Sn-3Ag-0.5Cu alloyed with Pt, Co, or Ti, compared with one independent grain in balls without nucleant particle additions.

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Section: Introductionmentioning

confidence: 99%

Grain refinement of electronic solders: The potential of combining solute with nucleant particles

Shang

Belyakov

et al. 2017

Journal of Alloys and Compounds

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“…48 For a crystal with anisotropic lattice parameters, contraction along one crystal direction could be accompanied with expansion along another direction. 49,50 This is due to the impact of the potential energy curve on the crystal direction. Along the direction of high compressibility in the lattice, normal modes of vibrations with high frequencies are excited at a certain temperature at the expense of those with low frequencies.…”

Section: Discussionmentioning

confidence: 99%

Nonuniformity in lattice contraction of bismuth nanoclusters heated near its melting point

Esmail

Abdel-Fattah

Elsayed-Ali

2011

Journal of Applied Physics

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The structural properties of bismuth nanoclusters were investigated with transmission high-energy electron diffraction from room temperature up to 525 6 6 K. The Bi nanoclusters were fabricated by thermal evaporation at room temperature on transmission electron microscope grids coated with an ultrathin carbon film, followed by thermal and femtosecond laser annealing. The annealed sample had an average cluster size of $14 nm along the minor axis and $16 nm along the major axis. The Debye temperature of the annealed nanoclusters was found to be 53 6 6 K along the [012] direction and 86 6 9 K along the [110] direction. At T ¼ 464 6 6 K, the diffraction intensity started to deviate from Debye-Waller behavior due to increased lattice anharmonicity. The onset of the melting of the Bi nanoclusters was T $ 500 6 6 K, as measured by the reduction of the nanocluster size through the formation of a liquid shell detected by the width of the diffraction rings. The thermal expansion coefficient of the Bi (012) and (110) planes is positive up to $ 499 6 11 K. However, the expansion coefficient of the Bi (012) planes showed a transition from a positive to a negative value that occurs over the temperature range T c $ 499 6 11 K to 511 6 8 K. For the Bi (110) planes, the thermal expansion coefficient is positive up to their melting point, which is 525 6 6 K. V

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“…Mechanical tests [4,5] and modelling efforts [6] on polycrystal SAC305 specimens have been conducted, such that isotropic, macroscopic material properties have been obtained and used to quantify behaviour in an averaged, homogenised sense. However, the strong anisotropic behaviour of solder joints [7][8][9][10][11] that commonly contain only one to three β-Sn grains [12][13][14][15][16] requires the determination of the anisotropic single crystal properties for β-Sn and SAC305.…”

Section: Introductionmentioning

confidence: 99%

Multi-scale plasticity homogenization of Sn–3Ag-0.5Cu: From β-Sn micropillars to polycrystals with intermetallics

Xian

et al. 2022

Materials Science and Engineering: A

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The Thermal Expansion of Anisotropic Metals

Cited by 50 publications

References 22 publications

Grain refinement of electronic solders: The potential of combining solute with nucleant particles

Grain refinement of electronic solders: The potential of combining solute with nucleant particles

Nonuniformity in lattice contraction of bismuth nanoclusters heated near its melting point

Multi-scale plasticity homogenization of Sn–3Ag-0.5Cu: From β-Sn micropillars to polycrystals with intermetallics

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