We propose a new frustrated Heisenberg antiferromagnetic model with spatially anisotropic exchange parameters J c , J a , and J ac , extending along the c, a, and a ± c (c-a-ca model) lattice directions, and apply it to describe the fascinating physics of copper carbodiimide, CuNCN, assuming the resonating valence bond (RVB) type of its phases. This explains within a unified picture the intriguing absence of magnetic order in CuNCN. We further present a parameters-temperature phase diagram of the c-a-ca-RVB model in the high-temperature approximation. Eight different phases including Curie and Pauli paramagnets (respectively, in disordered and 1D-or Q1D-RVB phases) and (pseudo)gapped (quasi-Arrhenius) paramagnets (2D-RVB phases) are possible. By adding magnetostriction and elastic terms to the model, we derive possible structural manifestations of RVB phase transitions. Assuming a sequence of RVB phase transitions to occur in CuNCN with decreasing temperature, several anomalies observed in the temperature course of the lattice constants are explained.

We derived the analytical formula of the motional capacitance C a of a quartz-crystal tuning-fork tactile sensor by use of the conservation law of energy that the electrostatic energy in C a is equal to the sum of the strain energy of its arm and the elastic energy of the material in contact with its base. In this analysis, the strain energy of the arm and the elastic energy of the material in contact with its base were obtained by applying the torsion spring model to the joint of the arm and the base, which were depicted as an L-shaped bar, and the elastic foundation to the materials in contact with its base, and the electrostatic energy of the arm was derived by applying the bimorph flexural model to the arm treated as a piezoelectric material. As a result of calculation, we found that the calculated value of the change in reciprocal motional capacitance Áð1=C a Þ of the quartz-crystal tuning-fork tactile sensor by our model is closer to the measured one for plastics than that given by the theoretical formula of motional capacitance of only one arm and Áð1=C a Þ is affected by the Young's moduli of materials in contact with the sensor's base.

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