Using Carrier Fringes to Study the High Temperature Deformation Behavior of a BGA Package Under Extended Dwell Times

There is a compelling need to experimentally understand solder joint deformation behavior at high temperatures over an extended period of time. Accordingly, the deformation behavior of solder joints in a Ceramic Ball Grid Array (CBGA) package mounted on an organic FR4 board under extended dwell time at a high temperature has been studied using laser moiré interferometry. The warpage and the in-plane horizontal deformation of the ceramic substrate and the organic board as a function of time were determined. The variation of the normal strains and shear strains in the solder joints with time were also investigated. It was found that increased sensitivity was necessary to accurately determine the strains in the small sized solder joints. A new method utilizing carrier fringes to increase the sensitivity of the moiré interferometry system is proposed and has been used to determine the strains in the small sized solder joints. Increased sensitivity can be obtained merely by changing the incident angle of the laser light on the surface of the specimen, thereby making it unnecessary to use expensive phase shifting apparatus with the traditional laser moiré system.     

Anti-biofouling properties of comblike block copolymers with amphiphilic side chains

Surfaces of novel block copolymers with amphiphilic side chains were studied for their ability to influence the adhesion of marine organisms. The surface-active polymer, obtained by grafting fluorinated molecules with hydrophobic and hydrophilic blocks to a block copolymer precursor, showed interesting bioadhesion properties. Two different algal species, one of which adhered strongly to hydrophobic surfaces, and the other, to hydrophilic surfaces, showed notably weak adhesion to the amphiphilic surfaces. Both organisms are known to secrete adhesive macromolecules, with apparently different wetting characteristics, to attach to underwater surfaces. The ability of the amphiphilic surface to undergo an environment-dependent transformation in surface chemistry when in contact with the extracellular polymeric substances is a possible reason for its antifouling nature. Near-edge X-ray absorption fine structure spectroscopy (NEXAFS) was used, in a new approach based on angle-resolved X-ray photoelectron spectroscopy (XPS), to determine the variation in chemical composition within the top few nanometers of the surface and also to study the surface segregation of the amphiphilic block. A mathematical model to extract depth-profile information from the normalized NEXAFS partial electron yield is developed.     

Surfaces of fluorinated pyridinium block copolymers with enhanced antibacterial activity

Polystyrene-b-poly(4-vinylpyridine) copolymers were quaternized with 1-bromohexane and 6-perfluorooctyl-1-bromohexane. Surfaces prepared from these polymers were characterized by contact angle measurements, near-edge X-ray absorption fine structure spectroscopy and X-ray photoelectron spectroscopy. The fluorinated pyridinium surfaces showed enhanced antibacterial activity compared to their nonfluorinated counterparts. Even a polymer with a relatively low molecular weight pyridinium block showed high antimicrobial activity. The bactericidal effect was found to be related to the molecular composition and organization in the top 2-3 nm of the surface and increased with increasing hydrophilicity and pyridinium concentration of the surface.     

Note on a Fermat-type diophantine equation

Let p>5 be a prime number and ζ a pth root of unity. Let c be an integer divisible only by primes of the form kp−1,(k,p)=1.Let C_p⁽ⁱ⁾ be the eigenspace of the p-Sylow subgroup of ideal class group C of corresponding to ωi,ω being the Teichmuller character.In this article we extend the main theorem in Sitaraman (J. Number Theory 80 (2000) 174) and get the following: For any fixed odd positive integer n<p−4, assume:

(a)

At least one of C_p⁽³⁾,C_p⁽⁵⁾,…,C_p⁽ⁿ⁾ is non-trivial.

(b)

C_p⁽ⁱ⁾=0 for p−n−1?i?p−2.

(c)

for 1?i?n+1.

Let q be an odd prime such that , and such that there is a prime ideal Q over q in whose ideal class is of the form I^pJ where J is non-trivial, not a pth power and J∈C_p⁽³⁾⊕C_p⁽⁵⁾⊕?⊕C_p⁽ⁿ⁾.For such p and q, if x^p+y^p=pcz^p has a non-trivial solution , with (x,y,z)=1, then .Let t(n)=n²²⁴ⁿ⁴. If , then applying a result of Soulé (J. Reine Angew. Math. 517 (1999) 209), we show that the above result holds with only condition (a) because the others are automatically satisfied.We also make a remark about the effect of Soulé's result on the p-divisibility of h_p⁺ (the class number of the maximal real subgroup of ) which is relevant to the existence of integral solutions to x^p+y^p=pcz^p.