A representation of the Mayer expansion coefficients and virial coefficients

1990 ◽  
Vol 84 (2) ◽  
pp. 869-877 ◽  
Author(s):  
G. I. Kalmykov
Keyword(s):  
Virial Coefficients ◽  
Mayer Expansion ◽  
Expansion Coefficients

RELATIONS BETWEEN INTERMEDIATE STATISTICS AND QUANTUM STATISTICS

2012 ◽  
Vol 26 (32) ◽  
pp. 1250212
Author(s):  
PENG-FEI MA ◽  
CHI-CHUN ZHOU ◽  
YU-ZHU CHEN ◽  
HAI PANG
Keyword(s):  
High Temperature ◽  
Occupation Number ◽  
Virial Coefficients ◽  
Degenerate State ◽  
State Expansion ◽  
Bose Statistics ◽  
Fermi Statistics ◽  
Single State ◽  
Classical Behavior ◽  
Expansion Coefficients

We provide the relations among intermediate, Bose and Fermi statistics through a simplified quantum dot model. We show that the high-temperature (near-classical) behavior of the intermediate statistics is like the Bose statistics: We develop the virial expansion of the intermediate statistics, and find that the first n (maximum occupation number on a single state) expansion coefficients are the same as the corresponding Bose virial coefficients. We also show that under low-temperature (near-quantum) conditions, the n-intermediate statistics on a single state behaves more like the Fermi statistics on an n-degenerate state.

Defects in β-SiC thin films grown on α-SiC substrates

1988 ◽  
Vol 46 ◽  
pp. 568-569
Author(s):  
Karren L. More
Keyword(s):  
Thin Films ◽  
Semiconductor Device ◽  
Lattice Mismatch ◽  
Chemical Vapor ◽  
Substrate Material ◽  
Growth Interface ◽  
Si Substrates ◽  
Thermal Expansion Coefficients ◽  
Device Applications ◽  
Expansion Coefficients

Beta-SiC is an ideal candidate material for use in semiconductor device applications. Currently, monocrystalline β-SiC thin films are epitaxially grown on {100} Si substrates by chemical vapor deposition (CVD). These films, however, contain a high density of defects such as stacking faults, microtwins, and antiphase boundaries (APBs) as a result of the 20% lattice mismatch across the growth interface and an 8% difference in thermal expansion coefficients between Si and SiC. An ideal substrate material for the growth of β-SiC is α-SiC. Unfortunately, high purity, bulk α-SiC single crystals are very difficult to grow. The major source of SiC suitable for use as a substrate material is the random growth of {0001} 6H α-SiC crystals in an Acheson furnace used to make SiC grit for abrasive applications. To prepare clean, atomically smooth surfaces, the substrates are oxidized at 1473 K in flowing 02 for 1.5 h which removes ∽50 nm of the as-grown surface. The natural {0001} surface can terminate as either a Si (0001) layer or as a C (0001) layer.

Critical consolute point in hard-sphere binary mixtures: Effect of the value of the eighth and higher virial coefficients on its location

2010 ◽  
Vol 75 (3) ◽  
pp. 359-369 ◽  
Author(s):  
Mariano López De Haro ◽  
Anatol Malijevský ◽  
Stanislav Labík
Keyword(s):  
Equation Of State ◽  
Binary Mixtures ◽  
Hard Sphere ◽  
Hard Spheres ◽  
Virial Coefficients ◽  
Fluid Mixture ◽  
Binary Fluid ◽  
Virial Series ◽  
Consolute Point ◽  
Critical Constants

Various truncations for the virial series of a binary fluid mixture of additive hard spheres are used to analyze the location of the critical consolute point of this system for different size asymmetries. The effect of uncertainties in the values of the eighth virial coefficients on the resulting critical constants is assessed. It is also shown that a replacement of the exact virial coefficients in lieu of the corresponding coefficients in the virial expansion of the analytical Boublík–Mansoori–Carnahan–Starling–Leland equation of state, which still leads to an analytical equation of state, may lead to a critical consolute point in the system.

The Bender Equation of State and Virial Coefficients

2000 ◽  
Vol 65 (9) ◽  
pp. 1464-1470 ◽  
Author(s):  
Anatol Malijevský ◽  
Tomáš Hujo
Keyword(s):  
Equation Of State ◽  
Virial Coefficient ◽  
Virial Coefficients ◽  
Low Density ◽  
Second Virial Coefficients ◽  
The Third ◽  
Temperature Dependences ◽  
Experimental Values

The second and third virial coefficients calculated from the Bender equation of state (BEOS) are tested against experimental virial coefficient data. It is shown that the temperature dependences of the second and third virial coefficients as predicted by the BEOS are sufficiently accurate. We conclude that experimental second virial coefficients should be used to determine independently five of twenty constants of the Bender equation. This would improve the performance of the equation in a region of low-density gas, and also suppress correlations among the BEOS constants, which is even more important. The third virial coefficients cannot be used for the same purpose because of large uncertainties in their experimental values.

scholarly journals On Using the BMCSL Equation of State to Renormalize the Onsager Theory Approach to Modeling Hard Prolate Spheroidal Liquid Crystal Mixtures

Entropy ◽  
2021 ◽  
Vol 23 (7) ◽  
pp. 846
Author(s):  
Donya Ohadi ◽  
David S. Corti ◽  
Mark J. Uline
Keyword(s):  
Equation Of State ◽  
Second Virial Coefficient ◽  
Virial Coefficients ◽  
Pure Component ◽  
Excluded Volume ◽  
Theory Approach ◽  
Prolate Spheroidal ◽  
Empirical Correction ◽  
Prolate Spheroids ◽  
Onsager Theory

Modifications to the traditional Onsager theory for modeling isotropic–nematic phase transitions in hard prolate spheroidal systems are presented. Pure component systems are used to identify the need to update the Lee–Parsons resummation term. The Lee–Parsons resummation term uses the Carnahan–Starling equation of state to approximate higher-order virial coefficients beyond the second virial coefficient employed in Onsager’s original theoretical approach. As more exact ways of calculating the excluded volume of two hard prolate spheroids of a given orientation are used, the division of the excluded volume by eight, which is an empirical correction used in the original Lee–Parsons resummation term, must be replaced by six to yield a better match between the theoretical and simulation results. These modifications are also extended to binary mixtures of hard prolate spheroids using the Boublík–Mansoori–Carnahan–Starling–Leland (BMCSL) equation of state.

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