A viscoplastic constitutive model, the Anand model, in which plasticity and creep are unified and described by the same set of flow and evolutionary relations, was applied to represent the inelastic deformation behavior for solder alloys. After conducting creep tests and constant strain rate tests, the material parameters for the Anand model of the Pb‐rich content solder 92.5Pb5Sn2.5Ag were determined from the experimental data using a nonlinear fitting method. The material parameters for 60Sn40Pb, 62Sn36Pb2Ag and 96.5Sn3.5Ag solders were fitted from the conventional model in the literature where plasticity and creep are artificially separated. Model simulations and verifications reveal that there is good agreement between the model predictions and experimental data. Some discussion on this unified model is also presented. This viscoplastic constitutive model for solder alloys possesses some advantages over the separated model. The achieved Anand model has been applied in finite element simulation of stress/strain responses in solder joints for chip component, thin quad flat pack and flip‐chip assembly. The simulation results are in good agreement with the results in the literature. It is concluded that the Anand model could be recommended as a useful material model for solder alloys and can be used in the finite element simulation of solder joint reliability in electronic packaging and surface mount technology.
Precise detection of spin resonance is of paramount importance to achieve coherent spin control in quantum computing. We present a novel setup for spin resonance measurements, which uses a dc-SQUID flux detector coupled to an antenna from a coplanar waveguide. The SQUID and the waveguide are fabricated from 20 nm Nb thin film, allowing high magnetic field operation with the field applied parallel to the chip. We observe a resonance signal between the first and third excited states of Gd spins S = 7/2 in a CaWO 4 crystal, relevant for state control in multi-level systems.Solid state spin-based qubits are studied for quantum computing due to their relatively long coherence time 1,2 . Typical implementations of these qubits are molecule-based magnets 3-6 , nitrogen-vacancy (NV) centers in diamond 7 and quantum spins in crystals 8-11 . These spin-based qubits are designed such that the spins are well separated in the crystal, leading to an increased decoherence time due to weak spin dipolar interactions.Among the rare-earth ions, S-state lanthanide ions doped in a crystal have a rich energy level structure due to their large spin. Multi-level systems are promising for implementing few-qubits algorithms 12 or as quantum memories [13][14][15][16] . For quantum technology applications, a higher sensitivity electron spin resonance (ESR) measurement is needed to be able to manipulate spins in mesoscopic crystals placed on superconducting chips [17][18][19][20][21] .Compared to other ultra-high sensitivity ESR measurements 22,23 , the use of Josephson junctions can increase significantly the spatial resolution of the magnetic detection while allowing an on-chip implementation. For instance, the magnetic signal of one nanoparticle is detectable if placed on the junction of a micrometer sized superconducting quantum interference device (micro-SQUID) 24 . We present a novel setup for ESR measurements, which combines the high spin sensitivity of an on-chip micro-SQUID and the flexibility of a coplanar waveguide for microwave excitation. Different dc-SQUID implementations were also used to detect molecular 25,26 and diluted 27 spins. In our case, the coupling of the two devices generates a cavity effect, which amplifies the microwave power seen by the spins. When using micro-SQUIDs, the samples are positioned close to their loop for increased sensitivity since the device a) Electronic mail: gy10c@my.fsu.edu b) Electronic mail: ic@magnet.fsu. edu FIG. 1. (color online) Scanning electron micrograph of the device and of the micro-SQUID (inset). The darker (blue) area is the coplanar waveguide with the two Ω-loop shortcircuits between the central line and the lateral ground planes. The microwave excitation is depicted by the curvy arrow and an in-plane field B0 is generated by an external coil. The SQUIDs share a common ground (sketched as a white rectangle). Each SQUID has one I − V line shown in green for clarity in their narrowest region.can work under in-plane magnetic fields in the range of ∼Tesla [28][29][30] .Using this s...
We designed and fabricated a new type of superconducting quantum interference device (SQUID) susceptometers for magnetic imaging of quantum materials. The 2-junction SQUID sensors employ 3D Nb nano-bridges fabricated using electron beam lithography. The two counter-wound balanced pickup loops of the SQUID enable gradiometric measurement and they are surrounded by a one-turn field coil for susceptibility measurements. The smallest pickup loop of the SQUIDs were 1 μm in diameter and the flux noise was around 1 μФ0/√Hz at 100 Hz. We demonstrate scanning magnetometry, susceptometry and current magnetometry on some test samples using these nano-SQUIDs.
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