W.M.B. Duval

Characterization of directionally solidified lead chloride

Abstract A complete analysis has been carried out on directionally solidified lead(II) chloride material. Purification by directional freezing consistently produced high purity material suitable for subsequent growth of single crystals. It was observed that silicon, magnesium, halogens, sulfur and phosphorous were the hardest impurities to remove from the supplied material. Direct photographic observations of the solid-liquid interface were taken at several values of G / v ratios (denoting the temperature gradient and the translation velocity, respectively) to study the morphology of the interface and optimize the growth conditions. The solid-liquid interface morphology varied from a smooth convex shape to dendritic as the G / v ratio decreased. Single crystals subsequently grown from the material purified by the present method showed no optical distortion, exhibited a transmission range from 0.30 to 20 μm, and displayed extremely low beam scattering.

Growth and characterization of lead bromide crystals

Lead(II) bromide was purified by a combination of directional freezing and zone-refining methods. Differential thermal analysis of the lead bromide showed that a destructive phase transformation occurs below the melting temperature. This transformation causes extensive cracking, making it very difficult to grow a large single crystal. Energy of phase transformation for pure lead bromide was determined to be 24.67 cal/g. To circumvent this limitation, crystals were doped by silver bromide which decreased the energy of phase transformation. The addition of silver helped in achieving the size, but enhanced the inhomogeneity in the crystal. The acoustic attenuation constant was almost identical for the pure and doped (below 3000 ppm) crystals.

Direct observations of interface instabilities

Single crystals of lead bromide doped with silver bromide were grown by the vertical Bridgman method. Direct observations were made in order to understand the interfacial instabilities. Numerical studies were carried out to provide a framework for interpreting the observed convective and morphological instabilities. Observations on interfacial instabilities in lead bromide with 500 and 5000 ppm silver bromide impurities supported the numerical results predicted for 1-g conditions. X-ray rocking curves, X-ray contour scans, and etch-pit studies showed that increasing solutal convection deteriorated the crystal quality of the crystals.

Identification and control of a multizone crystal growth furnace

Abstract This paper presents an intelligent adaptive control system for the control of a solid-liquid interface of a crystal while it is growing via directional solidification inside a multizone transparent furnace. The task of the process controller is to establish a user-specified axial temperature profile and to maintain a desirable interface shape. Both single-input-single-output and multi-input-multi-output adaptive pole placement algorithms have been used to control the temperature. We also describe an intelligent measurement system to assess the shape of the crystal while it is growing inside a multizone transparent furnace. A color video imaging system observes the crystal in real time, and determines the position and the shape of the interface. This information is used to evaluate the crystal growth rate, and to analyze the effects of translational velocity and temperature profiles on the shape of the interface. Creation of this knowledge base is the first step to incorporate image processing into furnace control.

On-line control of solid–liquid interface by state feedback

Abstract This paper deals with the problem of controlling the solid–liquid interface shape during directional solidification of a molten material inside a Bridgman–Stockbarger furnace. The necessary convective boundary conditions that would achieve the desired interface shape are found using feedback controls. A state-space model of the solidification process is determined by employing a modified finite-element technique to the governing conduction equation developed using the apparent heat capacity (AHC) formulation. This model is used to design a dynamic controller that would set up a desired interface shape at the desired location and translate it at the desired velocity. The proposed controller is implemented on a multizone transparent Bridgman crystal growth furnace.

Physical Vapor Transport of Mercurous Chloride Crystals: Design of a Microgravity Experiment

Abstract Flow field characteristics predicted from a computational model show that the dynamical state of the flow, for practical crystal growth conditions of mercurous chloride, can range from steady to unsteady. Evidence that the flow field can be strongly dominated by convection for ground-based conditions is provided by the prediction of asymmetric velocity profiles by the model which show reasonable agreement with laser Doppler velocimetry experiments in both magnitude and planform. Unsteady flow is shown to be correlated with a degradation of crystal quality as quantified by light scattering pattern measurements. A microgravity experiment is designed to show that an experiment performed with parameters which yield an unsteady flow becomes steady (diffusive-advective) in a microgravity environment of 10 −3 g 0 as predicted by the model, and hence yields crystals with optimal quality.

Control of crystal growth in bridgman furnace

Control of crystal quality during crystal growth requires accurate implementation of thermal boundary conditions. We identify this problem as the furnace temperature control problem. The thermal boundary conditions, in turn, dictate the interface shape between the solid and the liquid region of the material. Determination of the boundary conditions for a given desired interface shape is considered as the material temperature control problem in this paper. We outline the current efforts for the solution of the furnace temperature control and the material temperature control problems. We restrict our review to Bridgman growth control techniques.

Projective control design for multi-zone crystal growth furnace

This paper addresses the problem of controlling the temperature profile inside a multi-Zone crystal growth furnace. A minimal discrete-time state-space model of the furnace is determined by Least Squares identification of a Multi Input / Multi-Output (MIMO) input-output model. An integral control structure for the discrete-time model is derived to allow reference tracking, and a state-feedback control is designed for the system by solving a Discrete Linear Quadratic Regulator (DLQR) problem with a suitably chosen cost. This state-feedback controller serves as a reference for designing an output-feedback controller through the projective control approach. The resulting projective controller has structure similar to a MIMO Proportional-plus-Integral controller. The projective controller is used to control a simulated and an actual furnace. The resulting control system achieves the necessary control objective; i.e., it maintains the required temperature with no steady-state error and a reasonable transient behavior inspite of the uncertainties associated with the identified model.

Active control of interface shape during the crystal growth of lead bromide

A thermal model for predicting and designing the furnace temperature profile was developed and used for the crystal growth of lead bromide. The model gives the ampoule temperature as a function of the furnace temperature, thermal conductivity, heat transfer coefficients, and dimensions as variable parameters. Crystal interface curvature was derived from the model and it was compared with the predicted curvature for a particular furnace temperature and growth parameters. Large crystals of lead bromide were grown and it was observed that interface shape was in agreement with the shape predicted by this model.

Effect of growth conditions on the quality of lead bromide crystals

Single crystals of pure and doped lead bromide were grown by the Bridgman method in different convective conditions. The convection level was varied by changing the thermal and solutal Rayleigh number. The homogeneity in refractive index, and hence the optical quality, was estimated by examining the optical distortion, birefringence interferograms, and laser scattering through the crystal. The optical quality of the crystal varied significantly with the variation of convection level during the crystal growth. The critical concentration of the solute was estimated for several values of growth velocity by numerical analysis at the thermal gradient of 20 K/cm.