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First-principles investigation of the lattice vibrations in the alkali feldspar solid solution.

Benisek A, Dachs E, Grodzicki M - Phys Chem Miner (2014)

Bottom Line: This produces an increasing excess vibrational entropy that reaches a constant value above ~200 K.The softening of the lowest optical mode is, however, not reflected by thoroughly measured literature IR data.Comparing calculated and measured IR spectra suggests that the resolution of the measured spectra was insufficient for detecting the lowest IR-active modes.

View Article: PubMed Central - PubMed

Affiliation: Materialforschung und Physik, Universität Salzburg, Hellbrunnerstr. 34, 5020 Salzburg, Austria.

ABSTRACT

The heat capacities of Al, Si ordered alkali feldspars of different Na, K compositions were calculated using the density functional theory. The effect of the Na, K distribution, if random, ordered or clustered, on the resulting heat capacity was investigated on different cells with Ab50Or50 composition. For all compositions and distributions studied, the excess heat capacity of mixing is positive at low temperatures with a maximum at ~60 K. This produces an increasing excess vibrational entropy that reaches a constant value above ~200 K. The amount of the excess heat capacity of Ab50Or50, however, depends on the Na, K distribution. Best agreement with measured excess heat capacities is achieved, if the distribution of Na and K is either ordered or clustered. The positive excess heat capacities can be attributed to a strong softening of the acoustic and the lowest optical modes related to a strong increase of Na-O bond lengths in samples with intermediate compositions. The softening of the lowest optical mode is, however, not reflected by thoroughly measured literature IR data. Comparing calculated and measured IR spectra suggests that the resolution of the measured spectra was insufficient for detecting the lowest IR-active modes.

No MeSH data available.


Related in: MedlinePlus

IR spectra in the low-frequency region. The abscissa is shown in units of wavenumber (w) as well as frequency (ν). Solid line measured by Zhang et al. (1996); Vertical bars DFT calculations
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Fig9: IR spectra in the low-frequency region. The abscissa is shown in units of wavenumber (w) as well as frequency (ν). Solid line measured by Zhang et al. (1996); Vertical bars DFT calculations

Mentions: On the other hand, IR spectra (Zhang et al. 1996) do not exhibit any phonon softening of the lowest frequency mode, which is visible in the IR spectra at ~100 and ~90 cm−1 for low microcline and low albite, respectively (Zhang et al. 1996, their Fig. 1). From their figure, a slight shift to even higher frequencies in samples with intermediate composition may be derived suggesting a small stiffening by the substitution process at variance with the positive excess heat capacities measured by calorimetry (Benisek et al. 2014a) and derived from the DFT calculations of this study. In order to resolve this discrepancy, we used the DFT methods to calculate the IR spectra of the end-member and Ab50Or50 compositions. According to these calculations, the lowest IR-active modes have low intensities and low wavenumbers of 71, 73, and 60 cm−1 for Ab, Or and Ab50Or50 compositions, respectively. Note the softening (by 12 cm−1) of this mode with the Na–K substitution. In Fig. 9, the measured low-frequency IR spectra of Zhang et al. (1996) are compared to the calculated IR modes. Some calculated modes have slightly different frequencies, however, in general, good agreement is observed. Even the lowest IR-active mode at 60 cm−1 of the Ab50Or50 sample, as calculated by the DFT methods of this study, might be identified in the observed data by a small shoulder. The resolution of the measured IR data, however, is not sufficient to assign an IR band unequivocally to these low frequencies.Fig. 9


First-principles investigation of the lattice vibrations in the alkali feldspar solid solution.

Benisek A, Dachs E, Grodzicki M - Phys Chem Miner (2014)

IR spectra in the low-frequency region. The abscissa is shown in units of wavenumber (w) as well as frequency (ν). Solid line measured by Zhang et al. (1996); Vertical bars DFT calculations
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC4509561&req=5

Fig9: IR spectra in the low-frequency region. The abscissa is shown in units of wavenumber (w) as well as frequency (ν). Solid line measured by Zhang et al. (1996); Vertical bars DFT calculations
Mentions: On the other hand, IR spectra (Zhang et al. 1996) do not exhibit any phonon softening of the lowest frequency mode, which is visible in the IR spectra at ~100 and ~90 cm−1 for low microcline and low albite, respectively (Zhang et al. 1996, their Fig. 1). From their figure, a slight shift to even higher frequencies in samples with intermediate composition may be derived suggesting a small stiffening by the substitution process at variance with the positive excess heat capacities measured by calorimetry (Benisek et al. 2014a) and derived from the DFT calculations of this study. In order to resolve this discrepancy, we used the DFT methods to calculate the IR spectra of the end-member and Ab50Or50 compositions. According to these calculations, the lowest IR-active modes have low intensities and low wavenumbers of 71, 73, and 60 cm−1 for Ab, Or and Ab50Or50 compositions, respectively. Note the softening (by 12 cm−1) of this mode with the Na–K substitution. In Fig. 9, the measured low-frequency IR spectra of Zhang et al. (1996) are compared to the calculated IR modes. Some calculated modes have slightly different frequencies, however, in general, good agreement is observed. Even the lowest IR-active mode at 60 cm−1 of the Ab50Or50 sample, as calculated by the DFT methods of this study, might be identified in the observed data by a small shoulder. The resolution of the measured IR data, however, is not sufficient to assign an IR band unequivocally to these low frequencies.Fig. 9

Bottom Line: This produces an increasing excess vibrational entropy that reaches a constant value above ~200 K.The softening of the lowest optical mode is, however, not reflected by thoroughly measured literature IR data.Comparing calculated and measured IR spectra suggests that the resolution of the measured spectra was insufficient for detecting the lowest IR-active modes.

View Article: PubMed Central - PubMed

Affiliation: Materialforschung und Physik, Universität Salzburg, Hellbrunnerstr. 34, 5020 Salzburg, Austria.

ABSTRACT

The heat capacities of Al, Si ordered alkali feldspars of different Na, K compositions were calculated using the density functional theory. The effect of the Na, K distribution, if random, ordered or clustered, on the resulting heat capacity was investigated on different cells with Ab50Or50 composition. For all compositions and distributions studied, the excess heat capacity of mixing is positive at low temperatures with a maximum at ~60 K. This produces an increasing excess vibrational entropy that reaches a constant value above ~200 K. The amount of the excess heat capacity of Ab50Or50, however, depends on the Na, K distribution. Best agreement with measured excess heat capacities is achieved, if the distribution of Na and K is either ordered or clustered. The positive excess heat capacities can be attributed to a strong softening of the acoustic and the lowest optical modes related to a strong increase of Na-O bond lengths in samples with intermediate compositions. The softening of the lowest optical mode is, however, not reflected by thoroughly measured literature IR data. Comparing calculated and measured IR spectra suggests that the resolution of the measured spectra was insufficient for detecting the lowest IR-active modes.

No MeSH data available.


Related in: MedlinePlus