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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

Excess heat capacities (CP, Vexc) plotted against temperature (T). Points measurements from Benisek et al. (2014a), lines represent the DFT results. a Data of Ab50Or50 of cell 1 (solid), cell 2 (dashed-dotted), cell 3 (dotted) and cell 4 (dashed). b Measured data of Ab70Or30, calculated ones of Ab75Or25. c Data of Ab25Or75. Error bars as shown in a represent 1 SD
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Fig3: Excess heat capacities (CP, Vexc) plotted against temperature (T). Points measurements from Benisek et al. (2014a), lines represent the DFT results. a Data of Ab50Or50 of cell 1 (solid), cell 2 (dashed-dotted), cell 3 (dotted) and cell 4 (dashed). b Measured data of Ab70Or30, calculated ones of Ab75Or25. c Data of Ab25Or75. Error bars as shown in a represent 1 SD

Mentions: In the second step, the heat capacities of the solid solutions with intermediate compositions (Ab75Or25, Ab50Or50 and Ab25Or75) were calculated. The calculated heat capacities of all solid solution compositions and cells deviate positively from the linear combination of the end-member heat capacities (i.e. CVlinear = XACVA + XBCVB) at low temperatures. The behaviour of the resulting excess heat capacity as a function of temperature is characterised by a distinct positive peak at ~60 K for all cells. The calculated excess heat capacities (CVexc) of Ab50Or50 are compared with measured ones (CPexc) in Fig. 3a. The structure with a quasi-random Na, K distribution (cell 3) results in large excess heat capacities, whereas the other configurations agree more or less with the measured data. The calculated excess heat capacities do not exhibit the negative peak of the measured data at ~320 K. This negative peak, however, may not be significant taking into account the uncertainty of the experimental data (error bars in Fig. 3a represent one standard deviation). The calculated excess heat capacities of Ab75Or25 and Ab25Or75 are in accordance with the calorimetrically derived values as shown in Fig. 3b, c.Fig. 3


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

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

Excess heat capacities (CP, Vexc) plotted against temperature (T). Points measurements from Benisek et al. (2014a), lines represent the DFT results. a Data of Ab50Or50 of cell 1 (solid), cell 2 (dashed-dotted), cell 3 (dotted) and cell 4 (dashed). b Measured data of Ab70Or30, calculated ones of Ab75Or25. c Data of Ab25Or75. Error bars as shown in a represent 1 SD
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

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getmorefigures.php?uid=PMC4509561&req=5

Fig3: Excess heat capacities (CP, Vexc) plotted against temperature (T). Points measurements from Benisek et al. (2014a), lines represent the DFT results. a Data of Ab50Or50 of cell 1 (solid), cell 2 (dashed-dotted), cell 3 (dotted) and cell 4 (dashed). b Measured data of Ab70Or30, calculated ones of Ab75Or25. c Data of Ab25Or75. Error bars as shown in a represent 1 SD
Mentions: In the second step, the heat capacities of the solid solutions with intermediate compositions (Ab75Or25, Ab50Or50 and Ab25Or75) were calculated. The calculated heat capacities of all solid solution compositions and cells deviate positively from the linear combination of the end-member heat capacities (i.e. CVlinear = XACVA + XBCVB) at low temperatures. The behaviour of the resulting excess heat capacity as a function of temperature is characterised by a distinct positive peak at ~60 K for all cells. The calculated excess heat capacities (CVexc) of Ab50Or50 are compared with measured ones (CPexc) in Fig. 3a. The structure with a quasi-random Na, K distribution (cell 3) results in large excess heat capacities, whereas the other configurations agree more or less with the measured data. The calculated excess heat capacities do not exhibit the negative peak of the measured data at ~320 K. This negative peak, however, may not be significant taking into account the uncertainty of the experimental data (error bars in Fig. 3a represent one standard deviation). The calculated excess heat capacities of Ab75Or25 and Ab25Or75 are in accordance with the calorimetrically derived values as shown in Fig. 3b, c.Fig. 3

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