Lesson plan
hexatic phase
The hexatic phase is a state of matter that is between the solid and the isotropic liquid phases in two dimensional systems of particles. It is characterized by two order parameters: a short-range positional and a quasi-long-range orientational (sixfold) order. More generally, a hexatic is any phase that contains sixfold orientational order, in analogy with the nematic phase (with twofold orientational order). It is a fluid phase, since the shear modulus and the Young's modulus vanish due to the dissociation of dislocations. It is an anisotropic phase, since there exists a director field with sixfold symmetry. The existence of the director field implies that an elastic modulus against drilling or torsion exists within the plane, that is usually called Frank's constant after Charles Frank in analogy to liquid crystals. The ensemble becomes an isotropic liquid (and Frank's constant becomes zero) after the dissociation of disclinations at a higher temperature (or lower density). Therefore, the hexatic phase contains disclinations but no dislocations. The KTHNY theory of two-step melting by i) destroying positional order and ii) destroying orientational order was developed by John Michael Kosterlitz, David J. Thouless, Bertrand Halperin, David Robert Nelson and A. P. Young in theoretical studies about topological defect unbinding two dimensions.…
Article summary
The hexatic phase is a state of matter that is between the solid and the isotropic liquid phases in two dimensional systems of particles. It is characterized by two order parameters: a short-range positional and a quasi-long-range orientational (sixfold) order. More generally, a hexatic is any phase that contains sixfold orientational order, in analogy with the nematic phase (with twofold orientational order). It is a fluid phase, since the shear modulus and the Young's modulus vanish due to the dissociation of dislocations. It is an anisotropic phase, since there exists a director field with sixfold symmetry. The existence of the director field implies that an elastic modulus against drilling or torsion exists within the plane, that is usually called Frank's constant after Charles Frank in analogy to liquid crystals. The ensemble becomes an isotropic liquid (and Frank's constant becomes zero) after the dissociation of disclinations at a higher temperature (or lower density). Therefore, the hexatic phase contains disclinations but no dislocations. The KTHNY theory of two-step melting by i) destroying positional order and ii) destroying orientational order was developed by John Michael Kosterlitz, David J. Thouless, Bertrand Halperin, David Robert Nelson and A. P. Young in theoretical studies about topological defect unbinding two dimensions.…
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Discussion questions
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