Mathematical modeling of solid phase diffusion under mechanical alloying within Ni-Cr system

Ball milling has been used as a solid-state mechanical alloying technique in two binary systems of plastic crystals: neopentylglycol/pentaglycerin (NPG/PG), showing a partial solubility in the ordered phase, and 2-amino-2-methyl-1,3-propanediol/tris(hydroxymethyl) (AMP/TRIS) whose immiscibility in this ordered solid phase is almost total. For the AMP/TRIS system the stable state at room temperature was reached by milling. Contrarily, for NPG/PG, DSC measurements reveal that an annealing period is required after milling. These results have been compared with those of the pentaglycerin/pentaerythritol (PG/PE) binary system, previously studied, whose miscibility is total at room temperature.

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Mathematical Modeling of a Solid–Liquid Mixture with Mass Exchange Between Constituents

Mathematics and Mechanics of Solids ◽

10.1177/1081286505052339 ◽

2006 ◽

Vol 11 (6) ◽

pp. 575-595 ◽

Cited By ~ 2

Author(s):

L. Fusi ◽

A. Farina ◽

D. Ambrosi

Keyword(s):

Mathematical Modeling ◽

Liquid Mixture ◽

Solid Phase ◽

Deformation Gradient ◽

Elastic Solid ◽

Solid Deformation ◽

Solid Stress ◽

Phase Deformation ◽

Mass Conversion ◽

Solid Liquid

The mechanical behavior of a mixture composed by an elastic solid and a fluid that exchange mass is investigated. Both the liquid flow and the solid deformation depend on how the solid phase has increased (diminished) its mass, i.e. on the mass conversion between constituents. The model is developed introducing a decomposition of the solid phase deformation gradient. In particular, exploiting the criterion of maximization of the rate of entropy production, we determine an explicit evolution equation for the so-called growth tensor which involves directly the solid stress tensor. An example of a possible choice of the constitutive functions is also presented.

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Barrier Properties of Electroless Ni-B UBM for Solder Joining

International Symposium on Microelectronics ◽

10.4071/isom-2015-thp45 ◽

2015 ◽

Vol 2015 (1) ◽

pp. 000862-000867

Author(s):

Masaru Morita ◽

Toshiya Akamatsu ◽

Nobuhiro Imaizumi ◽

Seiki Sakuyama

Keyword(s):

Integrated Circuits ◽

High Speed ◽

Solid Phase ◽

Barrier Properties ◽

Electrode Structure ◽

Phase Diffusion ◽

3D Ics ◽

The Difference ◽

Electroless Ni ◽

Plating Layer

As demands accelerate for high density, high speed transmission and low power integrated circuits, 3D-ICs with through-silicon via (TSV) is pursued. In the structure of 3D-ICs, the first die is attached to the second die with micro bump, and the second die is attached to the circuit substrate with a C4 solder bump. The electrode structure of the second die is Cu/Ni UBM. The stress of the Ni-B layer is less than that of the Ni-P layer, and the Ni-B layer can suppress stress and die warpage. The purposes of our study are to clarify the difference in the barrier properties of the Ni-B UBM and Ni-P under bump metal (UBM) and the relevance of the barrier properties of Ni UBM and intermetallic compound (IMC) growth. It was found that an electroless Ni-B plating layer is superior to a Ni-P plating layer for UBM in liquid phase diffusion and in solid phase diffusion, and that a segregated B layer is formed under the IMC layer of a Ni-B land due to reflow soldering. It was estimated that this B layer plays the role of being a barrier layer for solder diffusion.

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