Thermal Vibrations of Atoms in Cubic Crystals I. The Temperature Variation of Thermal Diffuse Scattering of X-rays by Lead Single Crystals

Cartz, L.

doi:10.1088/0370-1301/68/11/320

Cited by 23 publications

(6 citation statements)

References 22 publications

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“…The calculated bulk moduli B T , second cumulants (mean square relative displacement), and Lindemann ratios LR are presented in tables 1. The Lindemann ratios are calculated as a function of temperature, and take values of about 0.069 at the experimental melting temperature 1685 K. This theoretical finding is in good agreement with the previous studies: Cartz [32] and Gilvarry [33] reformulated the Lindemann criterion utilizing the Debye and Waller theory of the temperature dependence of the mean-square amplitude of vibration, and showed that the amplitude attains a value of less than 10% of interatomic distances at melting. However, it must be noted that the Lindemann 'constant' is not strictly constant from one lattice type to another, and in spite of the partial success the physical relation between lattice instability and melting has not yet been clarified.…”

Section: Resultssupporting

confidence: 86%

Application of the statistical moment method to thermodynamic quantities of silicon

Hùng¹,

Masuda‐Jindo²,

Hanh³

2005

J. Phys.: Condens. Matter

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The lattice constants, thermal expansion coefficients, specific heats at constant volume and those at constant pressure, C v and C p , second cumulants, and Lindemann ratio are derived analytically for diamond cubic semiconductors, using the statistical moment method. The calculated thermodynamic quantities of the Si crystal are in good agreement with the experimental results. We also find the characteristic negative thermal expansion in the Si crystal at low temperatures.

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Section: Resultssupporting

confidence: 86%

Application of the statistical moment method to thermodynamic quantities of silicon

Hùng¹,

Masuda‐Jindo²,

Hanh³

2005

J. Phys.: Condens. Matter

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“…As noted before, real condensed materials normally exhibit significant deviations from the idealized Debye theory arising from the inherently anharmonic nature of interparticle interactions in the strongly condensed state . The practical consequences of these interactions are apparent in observations of the thermal and electrical conductivity, as well as in many other thermodynamic and dynamic properties of condensed materials. , Grüneisen introduced a widely utilized measure of anharmonicity based on a consideration of the thermal expansion coefficient α P , the property that perhaps best provides the physical expression of these anharmonic interactions. Note that crystalline materials composed of particles interacting through ideal harmonic interactions exhibit no thermal expansion upon heating, and moreover, their stiffness is independent of T .…”

Section: Introductionmentioning

confidence: 99%

“…38 The practical consequences of these interactions are apparent in observations of the thermal and electrical conductivity, as well as in many other thermodynamic and dynamic properties of condensed materials. 39,40 Gruneisen 27 introduced a widely utilized measure of anharmonicity based on a consideration of the thermal expansion coefficient α P , the property that perhaps best provides the physical expression of these anharmonic interactions. Note that crystalline materials composed of particles interacting through ideal harmonic interactions exhibit no thermal expansion upon heating, and moreover, their stiffness is independent of T. 41 In particular, Gruneisen introduced his famous anharmonicity parameter γ G through the relationship 27…”

Section: Introductionmentioning

confidence: 99%

Equation of State and Entropy Theory Approach to Thermodynamic Scaling in Polymeric Glass-Forming Liquids

Douglas

2021

Macromolecules

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Numerous experimental and computational studies have established that most liquids seem to exhibit a remarkable, yet poorly understood, property termed "thermodynamic scaling", in which the structural relaxation time τ α , and many other dynamic properties, can be expressed in terms of a "universal" reduced variable, TV γ , where T is the temperature, V is the material volume, and γ is a scaling exponent describing how T and V are linked to each other when either quantity is varied. Here, we show that this scaling relation can be derived by combining the Murnaghan equation of state (EOS) with the generalized entropy theory (GET) of glass formation. In our theory, thermodynamic scaling arises in the non-Arrhenius relaxation regime as a scaling property of the fluid configurational entropy density s c , normalized by its value s c * at the onset temperature T A of glass formation, s c /s c *, so that a constant value of TV γ corresponds to a reduced isoentropic fluid condition. Molecular dynamics simulations on a coarse-grained polymer melt are utilized to confirm that the predicted thermodynamic scaling of τ α by the GET holds both above and below T A and to test whether the extent L of stringlike collective motion, normalized its value L A at T A , also obeys thermodynamic scaling, as required for consistency with thermodynamic scaling. While the predicted thermodynamic scaling of both τ α and L/L A is confirmed by simulation, we find that the isothermal compressibility κ T and the long-wavelength limit S(0) of the static structure factor do not exhibit thermodynamic scaling, an observation that would appear to eliminate some proposed models of glass formation emphasizing fluid "structure" over configurational entropy. It is found, however, that by defining a low-temperature hyperuniform reference state, we may define compressibility relative to this condition, δκ T , a transformed dimensionless variable that exhibits thermodynamic scaling and which can be directly related to s c /s c *. Further, the Murnaghan EOS allows us to interpret γ as a measure of intrinsic anharmonicity of intermolecular interactions that may be directly determined from the pressure derivative of the material bulk modulus. Finally, we show that many phenomenological relationships related to the glass formation and melting of materials can be understood based on the Murnaghan EOS and thermodynamic scaling.

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“…At the outset, we note that melting in crystalline materials and the “softening” in glass materials have often been correlated with critical values of 〈 u 2 〉, i.e., the empirical Lindemann criterion, [ 56 , 62 , 63 ] so we might hope that critical values of H might have a similar interpretation. The phenomenological Hansen-Verlet condition for freezing in terms of a critical value of S p also points in this direction.…”

Section: Resultsmentioning

confidence: 97%

Approach to hyperuniformity in a metallic glass-forming material exhibiting a fragile to strong glass transition

et al. 2023

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We investigate a metallic glass-forming (GF) material (Al90Sm10) exhibiting a fragile-strong (FS) glass-formation by molecular dynamics simulation to better understand this highly distinctive pattern of glass-formation in which many of the usual phenomenological relations describing relaxation times and diffusion of ordinary GF liquids no longer apply, and where instead genuine thermodynamic features are observed in response functions and little thermodynamic signature is exhibited at the glass transition temperature, Tg. Given the many unexpected similarities between the thermodynamics and dynamics of this metallic GF material with water, we first focus on the anomalous static scattering in this liquid, following recent studies on water, silicon and other FS GF liquids. We quantify the “hyperuniformity index” H of our liquid, which provides a quantitative measure of molecular “jamming”. To gain insight into the T-dependence and magnitude of H, we also estimate another more familiar measure of particle localization, the Debye–Waller parameter 〈u2〉 describing the mean-square particle displacement on a timescale on the order of the fast relaxation time, and we also calculate H and 〈u2〉 for heated crystalline Cu. This comparative analysis between H and 〈u2〉 for crystalline and metallic glass materials allows us to understand the critical value of H on the order of 10–3 as being analogous to the Lindemann criterion for both the melting of crystals and the “softening” of glasses. We further interpret the emergence of FS GF and liquid–liquid phase separation in this class of liquids to arise from a cooperative self-assembly process in the GF liquid. Graphical abstract

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Thermal Vibrations of Atoms in Cubic Crystals I. The Temperature Variation of Thermal Diffuse Scattering of X-rays by Lead Single Crystals

Cited by 23 publications

References 22 publications

Application of the statistical moment method to thermodynamic quantities of silicon

Application of the statistical moment method to thermodynamic quantities of silicon

Equation of State and Entropy Theory Approach to Thermodynamic Scaling in Polymeric Glass-Forming Liquids

Approach to hyperuniformity in a metallic glass-forming material exhibiting a fragile to strong glass transition

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