By Y. A. Tatarchenko (auth.)
ISBN-10: 9048143071
ISBN-13: 9789048143078
ISBN-10: 9401729883
ISBN-13: 9789401729888
The monograph "Shaped Crystal development" through V. A. Tatarchenko is the 1st systematic of the macroscopic crystallization conception. the speculation is predicated at the solid assertion progress belief, which means self-stabilization is found in the approach, with progress parameter deviations taking place below the motion of exterior perturbations attenuating with time. The crystallization cost is without doubt one of the parameters liable for crystal disorder formation. Steady-state crystal development signifies that crystallization price inner stabilization is current, therefore permitting extra ideal crystals to develop. most crucial is the truth that the crystal form (an simply saw parameter) is among the stable-growth features while turning out to be crystals with none touch with the crucible partitions. which means constant-cross-section crystal development is to a definite quantity facts of crystallization method balance. the rules of the sturdy crystal development concept have been constructed via the writer of the monograph within the early Seventies. because of the efforts during the last twenty years of V. A. Tatarchenko, his disciples (V. A. Borodin, S. ok. Brantov, E. A. Brener, G. I. Romanova, G. A. Satunkin et al) and his fans (B. L. Timan, zero. V. Kolotiy et al) the idea has been accomplished, that's confirmed via this monograph. The attribute function of the idea is its development in the direction of fixing sensible difficulties that ensue within the technique of crystal growth.
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Additional info for Shaped Crystal Growth
Sample text
Calculation of the growth angle '1/;o from the crystallized melted disk shape: disk thickness is constant, 'lj; L = '1/;o (a); decreasing disk thickness, 'lj; L < '1/;o (b); increasing disk thickness, 'lj; L > '1/;o (c): 1 - crystal; 2 - crystallization front; 3 - melt. 3. Boundary Conditions of the Capillary Problem As the Laplace capillary equation is a second-order differential equation, formulation of the boundary problem for melt column shape calculation requires assignment of two boundary conditions.
For this approximation to be applied, the temperature in the system should reach the stationary value much faster than the crystallization front relaxes. 40). 46) for most of the cases will be given below. 40) with the left side equal to zero for corresponding boundary conditions) results in calculation of liquid- and solid-phase temperature distribution. Then the temperature is a function of the boundary conditions, the crystallization front position, h0 , being one of them. 44) should be satisfied at the crystallization front; then V = Vc as the crystallization front displacement rate is equal to zero due to the stationary process.
For a plate it is its half-thickness. 8). 36) Here Vc denotes the crystallization rate. 3) near the stationary state, the deviations of 8a 0 and dhjdt can be regarded as negligible. 38) Shaped Crystal Growth 38 c v e d. J t Crystal growth for the case of capillary shaping: O'O = O'e-growth of crystal of constant Fig. 8. cross-sections (a, d); O'O < O'e-growth of crystal of widening cross-sections (b, e); O'O > O'e-growth of crystals of narrowing cross-sections (c, f); V is crystal displacement rate.
Shaped Crystal Growth by Y. A. Tatarchenko (auth.)
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