Elastic Moduli and Related Thermodynamic Properties of Cryocrystalline Argon
Detail examination is carried out of elastic moduli and related thermodynamic properties entire the whole range of solid state of cryocrystalline Argon. It is shown that tight correlation Κ(V) exists between isothermal compressibility Κ(T) and molar volume V (T) of the solid. With high value of squared linear correlation coefficient R2 dependence Κ(V) is linear below premelting range. At higher temperatures – up to the melting point of Ar – correlation dependence Κ(V) increases monotonically with larger slope. The compressibility of solid Argon was thoroughly studied in the premelting range; the results are interpreted in terms of vacancy model.
Argon (Ar), Bulk modulus, Compressibility, Cryocrystals, Correlation, Molar Volume, Rare gas solids, Vacancies
[1]
D. L. Anderson and O. L. Anderson. The Bulk Modulus-Volume Relationship for Oxides. J. Geophys. Res. 1970; 75(17): 3494–3500.
[2]
R. Grover, I. C. Getting, and G. C. Kennedy. Simple Compressibility Relation for Solids. Phys. Rev. B. 1973; 7 (2): 567–571.
[3]
R. E. Newnham. Elastic Properties of Oxides. Am. Ceram. Soc. Bull. 1974; 53 (11): 821–829.
[4]
R. M. Hazen and L. W. Finger. Bulk Modulus-Volume Relationship for Cation-Anion Polyhedra. J. Geophys. Res. B. 1979; 84 (12): 6723–6728.
[5]
M. L. Cohen. Calculation of Bulk Moduli of Diamond and Zinc-blende Solids. Phys. Rev. B. 1985; 32 (12) 7988–7991.
[6]
I. V. Aleksandrov, A. F. Goncharov, A. N. Zisman, and S. M. Stishov. Diamond at High Pressures: Raman Scattering of Light, Equation of State, and High-pressure Scale. Sov. Phys. JETP. 1987; 66 (2): 384–390.
[7]
P. K. Lam, M. L. Cohen, and G. Martinez. Analytic Relation between Bulk Moduli and Lattice constants. Phys. Rev. B. 1987; 35 (17: 9190–9194.
[8]
M. L. Cohen. Theory of Bulk Moduli of Hard Solids // Mat. Sci. Eng. A. 1988. 105–106 (1): 11–18.
[9]
D. L. Anderson Chapter 5. “Thermodynamics and Equations of State” in: “Theory of the Earth”. Boston: Blackwell Scientific Publications, 1989.
[10]
S. Tanabe, K. Hirao, and N. Soga Elastic Properties and Molar Volume of Rare-Earth Aluminosilicate Glasses. J. Am. Ceram. Soc. 1992; 75 (3): 503–506.
[11]
D. J. Green. An Introduction to the Mechanical Properties of Ceramics. Cambridge: Cambridge Univ. Press, 1998.
[12]
M. H. G. Jacobs and H. A. J. Oonk. A new equation of state based on Grover, Getting and Kennedy’s empirical relation between volume and bulk modulus. The high-pressure thermodynamics of MgO. Phys. Chem. Chem. Phys. 2000; 2 (11): 2641–2646.
[13]
M. Bengisu. Chapter “Properties of Ceramic Materials and Their Evaluation” in: “Engineering Ceramics” – part of the series “Engineering Materials”. Berlin–Heidelberg: Springer-Verlag, 2001.
[14]
V. V. Brazhkin and A. G. Lyapin. Harder than Diamond: Dreams and Reality. Phil. Mag. A. 2002; 82 (2): 231–253.
[15]
C. Li, Y. L. Chin, and P. Wu. Correlation between Bulk Modulus of Ternary Intermetallic Compounds and Atomic Properties of Their Constituent Elements. Intermetallics. 2004; 12 (1): 103–109.
[16]
K. Sushil. Volume Dependence of Isothermal Bulk Modulus and Thermal Expansivity of MgO. Physica B: Condensed Matter. 2005; 367 (1–4): 114–123.
[17]
J. Garai and A. Laugier. The Temperature Dependence of the Isothermal Bulk Modulus at 1 bar Pressure. J. Appl. Phys. 2007; 101 (2): 023514.
[18]
T. Rouxel. Elastic Properties and Short to Medium Range Order in Glasses. J. Am. Ceram. Soc. 2007; 90 (10): 3019–3039.
[19]
J. Wang, W.-H. Wang, H.-B. Yu, H. Y. Bai. Correlations between Elastic Moduli and Molar Volume in Metallic Glasses. Appl. Phys. Lett. 2009; 94 (12): 121904.
[20]
T. Song, X. W. Sun, R. F. Wang, H. W. Lu, J. H. Tian, and P. Guo. Effects of Pressure and Temperature on the Isothermal Bulk Modulus of CaO. Physica B. 2011; 406 (2): 293–296.
[21]
S. Wacke, T. Górecki, Cz. Górecki, and K. Książek. Relations between the Cohesive Energy, Atomic Volume, Bulk Modulus and Sound Velocity in Metals. J. Phys.: Conf. Series. 2011; 289: 012020.
[22]
W.-H. Wang. The Elastic Properties, Elastic Models and Elastic Perspectives of Metallic Glasses. Progress Mater. Sci. 2012; 57 (3): 487–656.
[23]
M. Q. Jiang, G. Wilde, J. B. Gao, and L. H. Dai. A universal power law for metallic glasses. Scr. Mater. 2013; 69 (10): 760–763.
[24]
B. Xu, Q. Wang, and Y. Tian. Bulk Modulus for Polar Covalent Crystals. Sci. Rep. 2013; 3: 3068.
[25]
V. Yu. Bodryakov. Correlation of Temperature Dependencies of Thermal Expansion and Heat Capacity of Refractory Metal up to the Melting Point: Molybdenum. High Temp. 2014; 52 (6): 840–845.
[26]
V. Yu. Bodryakov. On the Correlation between Thermal Expansion Coefficient and Heat Capacity of Argon Cryocrystals. Phys. Solid State. 2014; 56 (11): 2359–2365.
[27]
V. Yu. Bodryakov. On Correlation between Heat Capacity and Thermal Expansivity of Cubic Pt-Metals (Following to the John Arblaster’s Evaluations). Open Sci. J. Mod. Phys. 2015; 2 (1): 10–13.
[28]
V. Yu. Bodryakov and A. A. Bykov. Correlation Characteristics of the Volumetric Thermal Expansion Coefficient and Specific Heat of Corundum. Glass and Ceramics. 2015; 72 (1-2): 67–70.
[29]
V. Yu. Bodryakov. Correlation between the Thermal Expansion Coefficient and Heat Capacity of Solid Xenon. Inorg. Mater. 2015: 51 (2): 172–176.
[30]
V. Yu. Bodryakov. Correlation between the Thermal Expansion Coefficient and Heat Capacity of an Inert-gas Single Crystal: Krypton. Tech. Phys. 2015; 60 (3): 381–384.
[31]
V. Yu. Bodryakov and Yu. N. Babintsev. Correlation Analysis of the Heat Capacity and Thermal Expansion of Solid Mercury. Phys. Solid State. 2015; 57 (6): 1264–1269.
[32]
V. Yu. Bodryakov. Specific Heat and Thermal Expansion of Refractory Nonmetal: CaO. Open Sci. J. Mod. Phys. 2015; 2 (4): 50–54.
[33]
V. Yu. Bodryakov. Correlation of Temperature Dependences of Thermal Expansion and the Heat Capacity of Refractory Metal up to the Melting Point: Tungsten. High Temp. 2015; 53 (5): 643–648.
[34]
G. L. Pollack. The Solid State of Rare Gases. Rev. Mod. Phys. 1964; 36 (3): 748 – 792.
[35]
N. R. Werthamer. Self–Consistent Phonon Theory of Rare Gas Solids. Rare Gas Solids. 1976; 1: 265-300.
[36]
M. L. Klein and J. A. Venables, eds. Rare Gas Solids. Vol. 1. London – New York – San Francisco: Academic Press, 1976.
[37]
M. L. Klein and J. A. Venables, eds. Rare Gas Solids. Vol. 2. London – New York – San Francisco: Academic Press, 1977.
[38]
P. C. Trivedi. Lattice Anharmonicity of Rare-gas Solids, Copper and Sodium. J. Phys. F: Metal Phys. 1971; 1 (3): 262–271.
[39]
S. Lehri and M. P. Verma. Phonon Dispersion in Rare Gas Solids. Phys. Stat. Sol. (b). 1979; 92 (2): 363–370.
[40]
E. R. Cowley and G. K. Horton. Phonons in Rare-gas Solids Close to Melting. Phys. Rev. Lett. 1987; 58 (8): 789–791.
[41]
B. M. Smirnov. Mechanisms of Melting of Rare Gas Solids. Phys. Scr. 1993; 48 (4): 483–486.
[42]
C. Malinowska-Adamska, P. Słoma and J. Tomaszewski. Self-Consistent Calculations of the Thermodynamic and Elastic Properties of Heavier Rare Gas Solids near the Lattice Instability Point. Phys. Stat. Sol. (b). 2000; 219 (2): 229–240.
[43]
W. B. Holzapfel, M. Hartwig, and G. Reiß. Equations of State for Rare Gas Solids under Strong Compression. J. Low Temp. Phys. 2001; 122 (3-4): 401-412.
[44]
T. Tsuchiya and K. Kawamura. First-principles Study of Systematics of High-pressure Elasticity in Rare Gas Solids, Ne, Ar, Kr, and Xe. J. Chem. Phys. 2002; 117 (12): 5859 – 5865.
[45]
A. I. Karasevskii and W. B. Holzapfel. Equations of State and Thermodynamic Properties of Rare-gas Solids under Pressure Calculated Using a Self-consistent Statistical Method. Phys. Rev. B. 2003; 67 (22): 224301.
[46]
S. Gupta and S. C. Goyal. Effect of Temperature on Elastic Properties of Rare Gas Solids. Physica B: Condensed Matter. 2004; 352 (1-4): 24–35.
[47]
R. J. Magyar, A. Fleszar, and E. K. U. Gross. Exact-exchange Density-functional Calculations for Noble-gas Solids. Phys. Rev. B. 2004; 69 (4): 045111.
[48]
R. Ramírez and C. P. Herrero. Anharmonic Phonon Energies in Rare-gas Solids Derived by Path-integral Simulations. Phys. Rev. B. 2005. V. 72. Issue 2. P. 024303.
[49]
S. Galamić-Mulaomerović and C. H. Patterson. Band Structures of Rare-gas Solids within the GW Approximation. Phys. Rev. B. 2005; 71 (19): 195103.
[50]
P. Schwerdtfeger, N. Gaston, R. P. Krawczyk, R. Tonner, and G. E. Moyano. Extension of the Lennard-Jones Potential: Theoretical Investigations into Rare-gas Clusters and Crystal Lattices of He, Ne, Ar, and Kr Using Many-body Interaction Expansions. Phys. Rev. B. 2006. V. 73. Issue 6. P. 064112.
[51]
G. E. Moyano, P. Schwerdtfeger and K. Rosciszewski. Lattice Dynamics for fcc Rare Gas Solids Ne, Ar, and Kr from ab initio Potentials. Phys. Rev. B. 2007; 75 (2): 024101.
[52]
Yu. A. Freiman and S. M. Tretyak. Many-body Interactions and High-pressure Equations of State in Rare-gas Solids. Low Temp. Phys. 2007. V. 33. Issue 6. P. 545–552.
[53]
E. P. Troitskaya, V. V. Chabanenko, E. A. Pilipenko, I. V. Zhikharev, and I. I. Gorbenko. Elastic Properties of Heavy Rare-Gas Crystals under Pressure in the Model of Deformable Atoms // Phys. Solid State. 2013; 55 (11): 2335–2344.
[54]
E. Aprile, A. E. Bolotnikov, A. I. Bolozdynya, and T. Doke. Noble Gas Detectors. Weinheim (Germany): Wiley-VCH, 2006.
[55]
V. Yu. Bodryakov and V. M. Zamyatin. Computation of Thermodynamic Functions during Calorimetric Investigations (Using Aluminium as an Example). High Temp. 1998; 36 (3): 497–499.
[56]
V. Yu. Bodryakov and V. M. Zamyatin. Calculation of Thermodynamic Functions upon Calorimetric Studies (with Lead as an Example). Phys. Met. Metallogr. 1998; 85 (4): 387-391.
[57]
V. Yu. Bodryakov, A. A. Povzner, and O. G. Zelyukova. Effect of Thermal Expansion on the Elastic Moduli and Debye Temperature of Paramagnetic Lutetium. Phys. Solid State. 1998; 40 (9): 1433-1435.
[58]
V. Yu. Bodryakov, A. A. Povzner, and O. G. Zelyukova. Magnetic Contribution to the Debye Temperature and the Lattice Heat Capacity of Ferromagnetic Rare-earth Metals (Using Gadolinium as an Example). Phys. Solid State. 1999; 41 (7): 1138–1143.
[59]
V. Yu. Bodryakov and A. A. Povzner. Description of the Thermodynamic Properties of a Nonmetallic Solid (Germanium): A Self-consistent Thermodynamic Approach. Phys. Solid State. 2003; 45 (7): 1254-1259.
[60]
V. Yu. Bodryakov and A. A. Povzner. Self-consistent Thermodynamic Approach to Calculating the Grüneisen Parameters of the Crystal Lattice in Solids. Tech. Phys. 2003; 48 (7): 931–933.
[61]
V. Yu. Bodryakov and A. A. Povzner. Thermodynamic Grounds for the Invar and Ellinvar Effects in Ferromagnets. Tech. Phys. 2004; 49 (2): 207-213.
[62]
V. Yu. Bodryakov and A. A. Povzner. Self-consistent Thermodynamic Description of a Nonmetallic Nonferromagnetic Solid (Using Silicon as an Example). High Temp. 2004; 42 (4): 565–573.
[63]
V. Yu. Bodryakov and A. A. Povzner. Effect of the Interaction between the Magnetic and Phonon Subsystems on the Magnetic Properties of a Ferromagnet: Model Calculations. Phys. Solid State. 2004; 46 (5): 872-876.
[64]
V. Yu. Bodryakov. A Comprehensive Study of the Effect of Lattice and Magnetic Anharmonicity on Thermodynamic Properties of Solids (Doctoral Dissertation). Yekaterinburg: Ural State Technical University – UPI, 2005.
[65]
V. Yu. Bodryakov, A. A. Povzner, and I. V. Safonov. The Magnetic Dependence of the Debye Temperature of a Ferromagnet. High Temp. 2005; 43 (3): 391–395.
[66]
V. Yu. Bodryakov, A. A. Povzner, and I. V. Safonov. The Effect of Phonon Anharmonicity on the Thermodynamic Properties of Nonmetallic Solid. High Temp. 2005; 43 (6): 859–869.
[67]
O. V. Anoshina, V. Yu. Bodryakov, A. A. Povzner and I. V. Safonov. A Self-consistent Thermodynamic Model of a Metal Solid (Using Aluminum as an Example). Russian Phys. J. 2005; 48 (12): 1235-1244.
[68]
V. Yu. Bodryakov, A. A. Povzner, and I. V. Safonov. Thermodynamic Description of Metallic Solids. Tech. Phys. 2006; 51 (2): 216-225.
[69]
V. Yu. Bodryakov. Thermodynamic Simulation of the Kovar and Invar Behavior of Ferromagnets. Phys. Met. Metallogr. 2007; 104 (1): 19-28.
[70]
V. Yu. Bodryakov and A. N. Bashkatov. Physical Statistical Analysis of Thermodynamic Properties of Ferromagnets with Allowance for Magnetophonon Interaction (by the Example of Nickel). Tech. Phys. 2007; 52 (3): 313–319.
[71]
V. Yu. Bodryakov. Ellinvar Behavior of Simple Ferromagnets: Thermodynamic Simulation. Tech. Physics. 2007; 52 (8): 1016–1023.
[72]
V. Yu. Bodryakov. Invar and Covar Behavior of Ferromagnets with Allowance for Magnetophonon Interaction: A Thermodynamic Simulation // Tech. Phys. 2007; V. 52 (12): 1569–1575.
[73]
V. Yu. Bodryakov. The Part Played by Magnetoelastic Interaction in the Forming of Thermodynamic Functions of Ferromagnets: Thermodynamic Potential and its First Thermodynamic Derivatives. High Temp. 2008; 46 (4): 474–483.
[74]
V. Yu. Bodryakov. The Part Played by Magnetoelastic Interaction in the Forming of Thermodynamic Functions of Ferromagnets: Second Thermodynamic Derivatives of Thermodynamic Potential. High Temp. 2009; 47 (1): 33–44.
[75]
A. N. Filanovich, A. A. Povzner, V. Yu. Bodryakov, Yu. Yu. Tsiovkin and V. V. Dremov. Effect of Phonon Anharmonicity on the Thermal and Elastic Properties of Stabilized δ-Plutonium. Tech. Phys. Letters. 2009; 35 (10): 929–932.
[76]
V. Yu. Bodryakov. Heat Capacity of Solid Tantalum: Self-consistent Calculation. High Temp. 2013; 51 (2): 206–214.
[77]
L. D. Landau and E. M. Lifshitz. Course of Theoretical Physics. V. 5. Statistical Physics. Part 1. 3rd Edition, Oxford–Burlington: Butterworth–Heinemann, 1980.
[78]
L. D. Landau and E. M. Lifshitz. Course of Theoretical Physics. Theory of Elasticity. V. 7. 2nd Edition. Oxford – New York –Toronto – Sydney – Paris – Brawnsweig: Pergamon Press, 1970.
[79]
Frenkel’ Ya. I. Vvedenie v Teoriyu Metallov (Introduction to the Theory of Metals). Moscow: GONTI, 1958.
[80]
A. J. E. Foreman and A. B. Lidiard. Vacancy Contribution to the Specific Heat of Solid Argon. Phil. Mag. 1963; 8 (85): 97–103.
[81]
L. Jansen. Contribution of Three-body Interactions to the Energy of Vacancy Formation in Solid Argon. Phil. Mag. 1963; 8 (92): 1305–1311.
[82]
O. G. Peterson, D. N. Batchelder, and R. O. Simmons. Observations on the Thermal Defect Structure of Solid Argon. Phil. Mag. 1965; 12 (120): 1193–1201.
[83]
H. R. Glyde. Vacancies in Solid Argon. J. Phys. Chem. Solids. 1966; 27 (10): 1659–1665.
[84]
J. J. Burton. Many-Body Contribution to Self-Diffusion in Rare-Gas Solids. Phys. Rev. 1969; 182 (3): 885–890.
[85]
R. G. Pritchard and D. Gugan. Bulk Expansivity and Vacancies in Solid Argon. Phys. Lett. A. 1970; 32 (2): 124–125.
[86]
J. H. Crawford and L. M. Slifkin. Point Defects in Solids. V. 1. General and Ionic Crystals. New York – London: Plenum Press, 1972.
[87]
A. Seeger. Investigation of Point Defects in Equilibrium Concentrations with Particular Reference to Positron Annihilation Techniques. J. Phys. F: Met. Phys. 1973; 3 (2): 248–294.
[88]
C. L. Reynolds, Jr. and P. R. Couchman. On Vacancies and Melting. Scripta Metallurgica. 1976; 10 (7): 605–606.
[89]
N. F. Uvarov, W. Bollmann, and E. F. Hairetdinov. Estimation of Point Defect Parameters of Solids on the Basis of a Defect Formation Model of Melting (III). Formation Entropy and Concentration of Schottky Defects (Vacancies). Crystal Research and Technology. 1989; 24 (5): 543–550.
[90]
R. LeSar, R. Najafabadi, and D. J. Srolovitz. Finite-temperature Defect Properties from Free-energy Minimization. Phys. Rev. Lett. 1989; 63 (6): 624–627.
[91]
J. D. McCoy, R. McRae, A. D. J. Haymet. Equilibrium Vacancy Concentration at Melting: The Density Functional Theory. Chem. Phys. Letters. 1990; 169 (6): 549–554.
[92]
W. Schilling. Properties of Frenkel defects. J. Nucl. Mater. 1994; 216: 45–48.
[93]
J. G. Dash. History of the Search for Continuous Melting. Rev. Mod. Phys. 1999; 71 (5): 1737–1743.
[94]
Z. H. Jin, P. Gumbsch, K. Lu, and E. Ma. Melting Mechanisms at the Limit of Superheating. Phys. Rev. Lett. 2001; 87 (5): 055703.
[95]
P. Varotsos. Comparison of Models that Interconnect Point Defect Parameters in Solids with Bulk Properties. J. Appl. Phys. 2007; 101 (12): 123503.
[96]
V. Yu. Bodryakov. Heat Capacity and Thermal Expansion of Cryocystalline Xenon at Elevated Temperatures. Tech. Phys. 2013; 58 (5): 722–729.
[97]
J. R. Barker and E. R. Dobbs. Measurement of the Elasticity of Solid Argon with an Ultrasonic Interferometer. Phil. Mag. Series 7. 1955; 46 (381): 1069–1080.
[98]
R. H. Beaumont, H. Chihara, and J. A. Morrison. Thermodynamic Properties of Krypton. Vibrational and other Properties of Solid Argon and Solid Krypton. Proc. Phys. Soc. (London). 1961; 78 (6): 1462–1481.
[99]
B. L. Smith and C. J. Pings. Optical Determination of the Compressibility of Solid Argon. J. Chem. Phys. 1963; 38 (4): 825–827.
[100]
O. K. Rice. The Thermodynamic Properties and Interatomic Potential Energy of Solid Argon. J. Mitchell Soc. 1964; 12: 120–129.
[101]
O. G. Peterson, D. N. Batchelder, and R. O. Simmons. Measurements of X-ray Lattice Constant, Thermal Expansivity and Isothermal Conductivity of Argon Crystals. Phys. Rev. 1966; 150 (2): 703–711.
[102]
H. R. Moeller and C. H. Squire. Ultrasonic Velocities in Solid Argon. Phys. Rev. 1966; 151 (2): 689–693.
[103]
V. G. Manzhelii, V. G. Gavrilko, and E. I. Voitovich. Thermal Expansion of Solidified Inert Gases. Sov. Phys. – Solid State. 1967; 9 (5): 1483–1489.
[104]
A. O. Urvas, D. L. Losee, and R. O. Simmons. The compressibility of krypton, argon, and other noble gas solids. J. Phys. Chem. Solids. 1967; 28 (11): 2269–2281.
[105]
M. Gsänger, H. Egger, and E. Lüsher. Determination of the Elastic Constants of Argon. Phys. Lett. A. 1968; 27 (10): 695–696.
[106]
G. J. Keeler and D. N. Batchelder. Measurement of the Elastic Constants of Argon from 3 to 77 Degrees K. J. Phys. C: Solid State Phys. 1970; 3 (3): 510–522.
[107]
E. I. Voitovich, A. M. Tolkachev, and V. G. Manzhelii. Adiabatic Compressibility of Solid Gases. J. Low Temp. Phys. 1971; 5 (4): 435-446.
[108]
H. Meixner, P. Leiderer, P. Berberich and E. Lüscher. The Elastic Constants of Solid Argon Determined by Stimulated Brillouin Scattering. Phys. Lett. A. 1972; 40 (3): 257–258.
[109]
S. Gewurtz and B. P. Stoicheff. Elastic Constants of Argon Single Crystals Determined by Brillouin Scattering. Phys. Rev. B. 1974; 10 (8): 3487–3499.
[110]
M. S. Anderson and C. A. Swenson. Experimental Equations of State for the Rare Gas Solids. J. Phys. Chem. Solids. 1975; 36 (2): 145–161.
[111]
V. A. Rabinovich, A. A. Vasserman, V. I. Nedostup, and L. S. Veksler. Thermophysical Properties of Neon, Argon, Krypton, and Xenon. Moscow: Izd. Standartov, 1976; London: Taylor and Francis, 1988.
[112]
F. Birch. Isotherms of the Rare Gas Solids. J. Phys. Chem. Solids. 1977; 38 (2): 175–177.
[113]
G. Raghurama and R. Narayan. Estimation of Properties of Rare-gas Solids from Compression Characteristics of Closed-shell Ions. J. Phys. C: Solid State Phys. 1985; 18 (4): 721–729.
[114]
S. Gupta and S. C. Goyal. Effect of Temperature on Elastic Properties of Rare Gas Solids. Physica B: Condensed Matter. 2004; 352 (1-4): 24–35.
[115]
K. Devlal and B. R. K. Gupta. Equation of State for Inert Gas Solids. Pramana. 2007; 69 (2): 307–312.
[116]
K. Clusius. Atomwärmen und Schmelzwärmen von Neon, Argon und Krypton. Z. phys. Chem. B. 1936; 31: 459-474.
[117]
H. Fenichel and B. Serin. Low-Temperature Specific Heats of Solid Neon and Solid Xenon. Phys. Rev. 1966; 142 (2): 490–495.
[118]
L. Finegold and N. E. Phillips. Low-Temperature Heat Capacities of Solid Argon and Krypton. Phys. Rev. 1969; 177 (3): 1383–1391.
[119]
O. I. Pursky and V. A. Konstantinov. Contribution of Thermal Expansion and “Diffusive” Modes to Isobaric Thermal Conductivity of Rare Gas Solids. IBM Journal of Research and Development. 1976; 20 (3): 222–227.
[120]
G. E. Moyano, P. Schwerdtfeger, and K. Rosciszewski. Lattice Dynamics for fcc Rare Gas Solids Ne, Ar, and Kr from ab initio Potentials. Phys. Rev. B. 2007; 75 (2): 024101.
[121]
E. R. Dobbs, B. F. Figgins, G. O. Jones, D. C. Piercey, and D. P. Riley. Density and Expansivity of Solid Argon. Nature. 1956; 178 (4531): 483.