Correlation Functions and the Coexistence of Phases

1965 ◽  
Vol 6 (11) ◽  
pp. 1643-1653 ◽  
Author(s):  
Michael E. Fisher
Keyword(s):  
Correlation Functions ◽  
Coexistence Of Phases

Microstructural observations of the “Wustite-Spinel” coexistence following quenching of cation-excess spinels, Ni2(1+x)Ti1-xO4

1990 ◽  
Vol 48 (4) ◽  
pp. 1058-1059
Author(s):  
Ian M. Anderson ◽  
Arnulf Muan ◽  
C. Barry Carter
Keyword(s):  
Film Growth ◽  
Spinel Phase ◽  
Model Systems ◽  
Ion Milling ◽  
Coexistence Of Phases ◽  
Nonequilibrium Conditions ◽  
Diffraction Patterns ◽  
Spinel Structures ◽  
Highly Porous ◽  
Standard Techniques

Oxide mixtures which feature a coexistence of phases with the wüstite and spinel structures are considered model systems for the study of solid-state reaction kinetics, phase boundaries, and thin-film growth, and such systems are especially suited to TEM studies. (In this paper, the terms “wüstite” and “spinel” will refer to phases of those structure types.) The study of wüstite-spinel coexistence has been limited mostly to systems near their equilibrium condition, where the assumptions of local thermodynamic equilibrium are valid. The cation-excess spinels of the type Ni2(1+x)Ti1-xO4, which reportedly exist only above 1375°C4, provide an excellent system for the study of wüstite-spinel coexistence under highly nonequilibrium conditions. The nature of these compounds has been debated in the literature. X-ray and neutron powder diffraction patterns have been used to advocate the existence of a single-phase, non- stoichiometric spinel. TEM studies of the microstructure have been used to suggest equilibrium coexistence of a stoichiometric spinel, Ni2TiO4, and a wüstite phase; this latter study has shown a coexistence of wüstite and spinel phases in specimens thought to have been composed of a single, non- stoichiometric spinel phase. The microstructure and nature of this phase coexistence is the focus of this study. Specimens were prepared by ball-milling a mixture of NiO and TiO2 powders with 10 wt.% TiO2. The mixture was fired in air at 1483°C for 5 days, and then quenched to room temperature. The aggregate thus produced was highly porous, and needed to be infiltrated prior to TEM sample preparation, which was performed using the standard techniques of lapping, dimpling, and ion milling.

FIDDLE. Simultaneous Indexing and Structure Solution from Powder Diffraction Data using a Genetic Algorithm and Correlation Functions

2019 ◽  
Author(s):  
Carmen Guguta ◽  
Jan M.M. Smits ◽  
Rene de Gelder
Keyword(s):  
Genetic Algorithm ◽  
Powder Diffraction ◽  
Diffraction Data ◽  
Correlation Functions ◽  
Cross Correlation ◽  
Simultaneous Optimization ◽  
Powder Diffraction Data ◽  
Structure Solution ◽  
Matching Technique

A method for the determination of crystal structures from powder diffraction data is presented that circumvents the difficulties associated with separate indexing. For the simultaneous optimization of the parameters that describe a crystal structure a genetic algorithm is used together with a pattern matching technique based on auto and cross correlation functions.<br>

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