We use Monte Carlo simulations to investigate the ground state of electrorheological (ER) fiuids in a strong electric field. Our results suggest a body-centered tetragonal (bct) lattice with conventional Bravais vectors a~=J6ax, a2= J6ay", and a3 =2az where a is the radius of dielectric spheres and the z axis is the direction of the applied electric field. This bct lattice can be regarded as a compound of chains of class A and class B where chains of class B are obtained from chains of class A by shifting a distance of a in the z direction. For typical ER systems, this bct structure can be formed at room temperature. PACS number(s): 61.90.+d, 62.20. -x, 02.50.+s An electrorheological (ER) fluid consists of a suspension of fine dielectric particles in a liquid of low dielectric constant [1][2][3][4][5][6][7]. Its viscosity increases dramatically in the presence of an applied electric field. If the field exceeds a critical value, the ER Auid turns into a solid whose yield stress increases as the field is further strengthened. The phenomenon is completely reversible and the time scale for the transition is of the order of millisecond. This unique property makes ER fluids attractive for futuristic technology. Indeed, there has been an enormous resurgence of interest about ER Auids during the last couple ofThe nature of ER fluids lies in electric-field-induced solidification. At a fixed temperature, there is a critical electric field E,. As the applied electric field exceeds E" the phase transition occurs and ER Auids turn into a solid [3,4].The question about the structure of an induced ER solid has recently attracted great attention for its relationship to the properties of ER fluids. Halsey and Toor [4] showed that dielectric particles in ER Auids form columns, spreading between two electrodes. Each column has a width -a(L/a) I where a is the radius of the dielectric particle and L is the distance between two parallel electrodes. In our recent work [7], we suggest that the thick columns in the induced ER solid have a structure of body-centered tetragonal (bct) lattice. As shown in Fig. l(a), the bct lattice has three conventional Bravais vectors, ai =&6ax, a2= J6ay", and a3=2az. In the z direction, the structure has chains. We can regard the bct structure as a compound of chains of class 2 and class 8 where chains of class 8 are obtained from chains of class A by shifting a distance of a in the z direction. Figure 1(b) is a projection of the bct lattice onto the x-y plane in which 0 represents A chains and x represents 8 chains. Figure 1(b) can be viewed as a two-dimensional crystal in which an A (or 8) chain has four 8 (or A) chains as its nearest neighbor at p= J3a, while the four next-nearestneighbor A (or 8) chains are at p = J6a. Though our suggestion of the bct lattice is based on analytical argument and calculations, as is usual in many-body problems, we can hardly call them a rigorous proof. Therefore, it would be significant if we can show -I-Ci , 0, ) cJ FIG. I. (a) Three-dimensional body-centered tetr...
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