Abstract
This chapter provides tables of the physical and physicochemical properties of the elements . Emphasis is given to properties of the elements in the condensed state. The tables are structured according to the Periodic Table of the Elements. Most of the tables deal with the properties of elements of one particular group (column) of the Periodic Table. Only the elements of the first period (hydrogen and helium), the lanthanides, and the actinides are arranged according to the periods (rows) of the Periodic Table. This synoptic representation is intended to provide an immediate overview of the trends in the data for chemically related elements.
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1 How to Use this Chapter
To find properties of a specific element or group of elements, start from one of Tables 4.1–4.5 and proceed in one of the following ways:
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1.
If the name of the element is known, refer to Table 4.1, where an alphabetical list of the elements is given, together with the numbers of the pages where the properties of these elements can be found.
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2.
If you know the chemical symbol of the element, refer to Table 4.2, where an alphabetical list of element symbols is given, together with the numbers of the pages where the properties of the corresponding elements will be found.
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3.
If the atomic number Z of the element is known, refer to Table 4.3, where a list of the elements in order of atomic number is given, together with the numbers of the pages where the properties of these elements will be found.
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4.
If you know the group of the Periodic Table that contains the element of interest, refer to Table 4.4, which gives the numbers of the pages where the properties of the elements of each group will be found.
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5.
To look up the element in the Periodic Table, refer to Table 4.5, where the element symbol and the atomic number will be found. Then use Table 4.2 or Table 4.3 to find the numbers of the pages where the properties of the element of interest are tabulated.
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6.
Alternatively, one may also find the name and the chemical symbol of the element you are looking for in the alphabetic index at the end of the volume. The index again will give you the first number of those pages on which the properties of the element are described.
The data-tables corresponding to the Periodes and Groups of the Periodic Table are subdivided in the following way:
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A.
Atomic, ionic, and molecular properties
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B.
Materials data:
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(a)
Crystallographic properties
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(b)
Mechanical properties
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(c)
Thermal and thermodynamic properties
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(d)
Electronic, electromagnetic, and optical properties .
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(a)
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C.
Allotropic and high-pressure modifications
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D.
Ionic radii .
2 Description of Properties Tabulated
2.1 Parts A of the Tables
The properties tabulated in parts A of the tables concern the atomic, ionic, and molecular properties of the elements:
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The relative atomic mass, or atomic weight, A.
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The abundance in the lithosphere and in the sea.
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The atomic radius: the radius rcov for single covalent bonding (after Pauling) , the radius rmet for metallic bonding with a coordination number of 12 (after Pauling), the radius rvdW for van der Waals bonding (after Bondi) , and, for some elements, the radius ros of the outer-shell orbital are given.
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The completely and partially occupied electron shells in the atom.
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The symbol for the electronic ground state.
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The electronic configuration.
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The oxidation states.
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The electron affinity.
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The electronegativity XA (after Allred and Rochow).
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The first, second, third, and fourth ionization energies and the standard electrode potential E0.
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The internuclear distance in the molecule.
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The dissociation energy of the molecule .
2.2 Parts B of the Tables
Parts B of the tables contain data on the macroscopic properties of the elements. Most of the data concern the condensed phases. If not indicated otherwise, the data in this section apply to the standard state of the element, that is, they are valid at standard temperature and pressure (GlossaryTerm
STP
, T = 298.15 K and \(p={\mathrm{100}}\,{\mathrm{kPa}}={\mathrm{1}}\,{\mathrm{bar}}\)). For those elements which are stable in the gas phase at STP, data are given for the macroscopic properties in the gas phase.The quantities describing the physical and physicochemical properties of materials can be divided into two classes. The first class contains all those quantities which are not directly connected with external (generalized) forces, these quantities have well-defined values even in the absence of external forces . Some examples are the electronic ground-state configuration of the atom, the coordination number in the crystallized state and the surface tension in the liquid state. The second class contains those quantities which describe the response of the material to externally applied (generalized) forces F. Such a force might be a mechanical stress field, an electric or magnetic field, a field gradient, or a temperature gradient. The response of the material to the external force might be observed via a suitable observable O, such as a mechanical strain, an electric current density, a dielectric polarization, a magnetization, or a heat current density. Assuming homogeneous conditions, the dependence of the observable O on the force F can be used to define material-specific parameters χ, which are also called physical properties of the material. Some examples are the elastic moduli or compliance constants, the electrical conductivity, the dielectric constant, the magnetic susceptibility, and the thermal conductivity.
In the linear-response regime, that is, under weak external forces F, these parameters χ are considered as being independent of the strength of the forces. The dependence of an observable O on a force F is then the simple proportionality
For strong external fields , the dependence of the response on the strength of the forces can be expressed by a power expansion in the forces, which then – in addition to the linear parameters χ – defines nonlinear field-dependent materials properties χ(nl)(F), where
In general, the class of materials properties that describe the response to externally applied forces have tensor character. The rank of the property tensor χ depends on the rank of the external force F and that of the observable O considered. In the case of Ohm's law, j = σE, in which the current density j and the electric field strength E are vectors, the conductivity tensor σ is of rank 2; in the case of the generalized Hooke's law, ε = sσ, the strain tensor ε and the stress tensor σ both are of rank 2, so that the elastic compliance tensor s is of rank 4. A vector can be considered as a tensor of rank 1, and a scalar, correspondingly, as a tensor of rank 0. A second-rank tensor, such as the electrical conductivity σ, in general has nine components in three-dimensional (GlossaryTerm
3-D
) space; a tensor of rank n in general has 3n components in three-dimensional space. Symmetry, however, of both the underlying crystal lattice and the physical phenomenon (for example, action = reaction), may reduce the number of independent nonvanishing components in the tensor. The tensor components reflect the crystal symmetry by being invariant under those orthogonal transformations which are elements of the point group of the crystal. In cubic crystals, for example, physical properties described by tensors of rank 2 are characterized by only one nonvanishing tensor component. Therefore cubic crystals are isotropic with respect to their electrical conductivity, their heat conductivity, and their dielectric properties.2.2.1 Subdivisions B(a) of the Tables
These parts deal with the crystallographic properties . Here you will find the crystal system and the Bravais lattice in which the element is stable in its standard state; the structure type in which the element crystallizes; the lattice constants \(a,b,c,\alpha,\beta,\gamma\) (symmetry reduces the number of independent lattice constants); the space group; the Schoenflies symbol; the Strukturbericht type; the Pearson symbol; the number A of atoms per cell; the coordination number; and the shortest interatomic distance between atoms in the solid state and in the liquid state.
Basic concepts of crystallography are explained in Chap. 3.
2.2.2 Subdivisions B(b) of the Tables
These parts cover the mechanical properties . At the top of the table, you will find the density of the material in the solid state (ϱs) and in the liquid state (ϱl), and the molar volume Vmol in the solid state. Here, one mole is the amount of substance which contains as many elementary particles (atoms or molecules) as there are atoms in 0.012 kg of the carbon isotope with a relative atomic mass of 12. This number of particles is called Avogadro's number and is approximately equal to 6.022 × 1023. The next three rows present the viscosity η , the surface tension, and its temperature dependence, in the liquid state. The next properties are the coefficient of linear thermal expansion α and the sound velocity , both in the solid and in the liquid state. A number of quantities are tabulated for the presentation of the elastic properties. For isotropic materials, we list the volume compressibility \(\kappa=-(1/V)(\mathrm{d}{V}/\mathrm{d}{P})\), and in some cases also its reciprocal value, the bulk modulus (or compression modulus); the elastic modulus (or Young's modulus) E; the shear modulus G; and the Poisson number (or Poisson's ratio) μ. Hooke's law, which expresses the linear relation between the strain ε and the stress σ in terms of Young's modulus, reads σ = Eε. For monocrystalline materials, the components of the elastic compliance tensor s and the components of the elastic stiffness tensor c are given. The elastic compliance tensor s and the elastic stiffness tensor c are both defined by the generalized forms of Hooke's law, σ = cε and ε = sσ. At the end of the list, the tensile strength, the Vickers hardness, and the Mohs hardness are given for some elements.
2.2.3 Subdivisions B(c) of the Tables
The thermal and thermodynamic properties are tabulated in these subdivisions of the tables. The properties tabulated are:
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The thermal conductivity, λ.
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The molar heat capacity at constant pressure, cp.
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The standard entropy S0, that is, the molar entropy of the element at 298.15 K and 100 kPa.
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The enthalpy difference H298 − H0, that is, the difference between the molar enthalpies of the element at 298.15 and at 0 K.
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The melting temperature, Tm.
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The molar enthalpy change ΔHm and molar entropy change ΔSm at the melting temperature.
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The relative volume change \(\Updelta V_{\mathrm{m}}=(V_{\mathrm{l}}-V_{\mathrm{s}})/V_{\mathrm{l}}\) on melting.
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The boiling temperature, Tb.
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The molar enthalpy change ΔHb of boiling, and, for some elements, the molar enthalpy of sublimation.
In addition, the critical temperature Tc, the critical pressure pc, the critical density ϱc, the triple-point temperature Ttr, and the triple-point pressure ptr are given for some elements. For the element helium, the table also contains data for the λ point, at which liquid helium passes from the normal-fluid phase helium I (above the λ point) to the superfluid phase helium II (below the λ point), for 4He and 3He.
Throughout the chapter, temperature is measured in units of Kelvin (K), the unit of thermodynamic temperature. 1 K is defined as the fraction 1 ∕ 273.16 of the thermodynamic temperature of the triple point of water. To convert data given in kelvin into degrees Celsius (∘C), the following equation can be used
This can be expressed in words as follows: the Celsius scale is shifted towards higher temperatures by 273.15 K relative to the kelvin scale, such that the temperature 273.15 K becomes 0∘C and the temperature 0 K becomes \(-{\mathrm{273.15}}\,{\mathrm{{}^{\circ}\mathrm{C}}}\). To convert data given in kelvin into degrees fahrenheit (∘F), the following equation can be used
This can be expressed approximately in words as follows: the Fahrenheit scale is shifted relative to the kelvin scale and also differs by a scaling so that its degrees are smaller than those of the kelvin scale by nearly a factor of 2.
2.2.4 Subdivisions B(d) of the Tables
These subdivisions of the tables present data on the electronic, electromagnetic, and optical properties of the elements. Data are given for:
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The electrical resistivity ρs in the solid state, and its temperature and pressure dependence.
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The electrical resistivity ρl in the liquid state, and the resistivity ratio ρl ∕ ρs at the melting temperature.
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The critical temperature Tcr and critical field strength Hcr for superconductivity.
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The electronic band gap ΔE.
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The Hall coefficient R, together with the range of magnetic field strength B over which it was measured.
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The thermoelectric coefficient.
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The electronic work function.
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The thermal work function.
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The intrinsic charge carrier concentration.
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The electron and hole mobilities.
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The static dielectric constant ε of the element in the solid state, and in some cases also in the liquid state.
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The molar magnetic susceptibility χmol and the mass magnetic susceptibility χmass of the element in the solid state, and in some cases also in the liquid state. The susceptibilities are given in the definitions of both the SI system and the cgs system (see below).
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The refractive index n in the solid and liquid states.
The magnetic susceptibility is the parameter that describes the response of the material to an externally applied magnetic field H, as measured by the observable magnetization M, in the linear regime, via M = χH. Three different forms of the term magnetization are in use, depending on the specific application:
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The volume magnetization Mvol, equal to the magnetic dipole moment divided by the volume of the sample.
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The molar magnetization, or magnetization related to the number of particles, Mmol, equal to the magnetic dipole moment divided by the number of particles measures in moles.
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The mass magnetization Mmass, equal to the magnetic dipole moment divided by the mass of the sample.
Correspondingly, there are three different magnetic susceptibilities. The volume susceptibility χvol is a dimensionless number because in this case M and H are both measured in the same units, namely A ∕ m in the SI system and gauss in the cgs system. The dimensionless character of χvol might be the reason why, in physics textbooks, mostly only this susceptibility is mentioned. The other two susceptibilities, the molar susceptibility χmol and the mass susceptibility χmass, are more useful for practical applications. In both the SI system and the cgs system, the molar susceptibility is measured in units of cm3 ∕ mol, and the mass susceptibility is measured in units of cm3 ∕ g. In this Handbook, data are given for the molar and mass susceptibilities.
Although susceptibilities have the same dimensions in the SI and cgs systems, the numerical values in the cgs system are smaller than those in the SI system by a factor of 4π. This is due to the different definitions of the quantities dipole moment and magnetization in the two systems. The difference can be seen most clearly in the general relations between the magnetization M and the field strengths B and H in the two systems. In the SI system, this relation reads \(B=\mu_{0}(H+M)\), whereas in the cgs system, it reads \(B=H+4\uppi M\). Because of this difference, the magnetic-susceptibility data in Sect. 4.5 are given for both the SI and the cgs definitions.
2.3 Parts C of the Tables
Parts C of the tables present crystallographic data for allotropic and high-pressure modifications of the elements. The left-hand columns contain data for allotropic modifications that are stable at a pressure of 100 kPa over the temperature ranges indicated, and the right-hand columns contain data for modifications stable at higher pressures as indicated. The modifications stable at 100 kPa are denoted by Greek letters in front of the chemical symbol of the element (normally starting with α for the modification stable over the lowest temperature range), and the high-pressure modifications are denoted by Roman numerals after the chemical symbol. In these parts of the tables, GlossaryTerm
RT
stands for room temperature, and GlossaryTermRTP
stands for room temperature and standard pressure, i. e., 100 kPa.2.4 Parts D of the Tables
Parts D of the tables contain data on ionic radii determined from crystal structures. The first row lists the elements, and the second row lists the positive and negative ions for which data are given. The remaining rows give the ionic radii of these ions for the most common coordination numbers.
4 Tables of the Elements in Different Orders
5 Data
5.1 Elements of the First Period
5.2 Elements of the Main Groups and Subgroup I to IV
5.3 Elements of the Main Groups and Subgroup V to VIII
5.4 Elements of the Lanthanides Period
5.5 Elements of the Actinides Period
References
W. Martienssen (Ed.): Numerical Data and Functional Relationships in Science and Technology, Landolt–Börnstein, New Series, Vol. III and IV (Springer, Berlin, Heidelberg 1970–2003)
K. Schäfer, C. Synowietz (Eds.): Elemente, anorganische Verbindungen und Materialien, Minerale, D’Ans-Lax, Taschenbuch für Chemiker und Physiker, Vol. 3, 4th edn. (Springer, Berlin, Heidelberg 1998)
W.M. Haynes (Ed.): CRC Handbook of Chemistry and Physics, 97th edn. (CRC, Boca Raton 2016)
Lehrstuhl für Werkstoffchemie, T.H. Aachen (Ed.): Thermodynamic Properties of Inorganic Materials, Landolt–Börnstein, New Series, Vol. IV/19 (Springer, Berlin, Heidelberg 1999)
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Martienssen, W. (2018). The Elements. In: Warlimont, H., Martienssen, W. (eds) Springer Handbook of Materials Data. Springer Handbooks. Springer, Cham. https://doi.org/10.1007/978-3-319-69743-7_4
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DOI: https://doi.org/10.1007/978-3-319-69743-7_4
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