The α-inc-β transitions of quartz: A century of research on displacive phase transitions

Quartz and Cristobalite: high‐temperature cell parameters and volumes of fusion

“…Recently, much interest has been paid to the mechanisms of these a-13 transitions [Dolino, 1990], the dynamic nature of the high-temperature 13-phases [Hatch and Ghose, 1991 …”

Liftings and stresses for planar periodic frameworks

“…There is an equivalent form for the periodic stress conditions (21), which refers directly to the periods λ β = Λc β implicated in the edge descriptions (18). It can be given in terms of tensor products, namely: …”

“…An edge representative β originates in one of the chosen vertex representatives i = i(β) and ends at some other vertex representative j = j(β) plus some period Λc β , where c β is a column vector with two integer entries. The edge vectors e β , β ∈ E/Γ thus have the form: (18) By taking the squared length of the m edge representatives, we obtain a map: (19) and the differential of this map at the point under consideration (i.e. the point of (ℝ 2 ) n × GL(2) ⊂ ℝ 2n+4 corresponding to the framework (p, π)), seen as a matrix with m rows and 2n +4 columns is called the rigidity matrix R = R(G, Γ, p, π) of the framework.…”

“…Definition 1-A periodic stress for the framework (G, Γ, p, π) is a stress induced from an element in the kernel of the transposed rigidity matrix R t , that is, a Γ-invariant equilibrium stress s satisfying the conditions (21) with integer coefficients as given in the edge description (18).…”

Difusión Selectiva de Hidrocarburos en Zeolitas de Poro Pequeño a Partir de Técnicas de Simulación Molecular

“…Esta característica convierte a la coesita en un especimen excelente para evaluar la transferabilidad de los campos de fuerza, especialmente aquellos parametrizados a partir de la estructura del cuarzo α. 131 La coesita tiene una celda unidad e tipo monoclínico-beta, compuesta por 48átomos, con simetría de grupo C2/c. La tabla 3.2 sumariza los parámetros estructurales para estas tres estructuras, y la figura 3.1 muestra el diagrama de fases del cuarzo.…”