Isomorphism among commensurate and incommensurate high-temperature phases of A<sub>2</sub>BO<sub>4</sub>compounds

Tuinstra, F.; Berg, A. J. van den

doi:10.1080/01411598308244074

Cited by 22 publications

(9 citation statements)

References 8 publications

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“…It is interesting to observe that the dipolardipolar interaction between two NN out-plane BX 4 tetrahedra changes its sign exactly at c/a = 1.63. The value of the modulation vector q b in molybdates and tungstates is correlated with the ratio c/a in the following way: the smaller the ratio c/a the more q b deviates from the lock-in value 2π/b of the p hase P mcn [22]. This behavior is consistent with our calculations (12).…”

Section: Application Tosupporting

confidence: 88%

“…The modulation wave vec-tor associated with the vertical tetrahedra orientation has the incommensurate component directed in the basal plane of the hcp structure. This phase occurs in alkali molybdates and tungstates K 2 M oO 4 , K 2 W O 4 , Rb 2 W O 4 in the temperature interval of 590 − 750K [20][21][22]. There is no consistent explanation of this kind of incommensurate phase although several ideas were proposed in [14].…”

Section: Commensurate and Incommensurate Phases Inmentioning

confidence: 99%

“…(iii) Located in the upper part of Table II the alkali molybdates and tungstates [20][21][22] that have the intermediate incommensurate phase modulated along crystallographical direction b. The actual transition sequence there is: P mcn − (0, q b , 2π/c) − P 6 3 /mmc.…”

Section: Application Tomentioning

confidence: 99%

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Basal-plane incommensurate phases in hexagonal-close-packed structures

1998

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An Ising model with competing interactions is used to study the appearance of incommensurate phases in the basal plane of a hexagonal-close-packed structure. The calculated mean-field phase diagram reveals various 1q-incommensurate and lock-in phases. The results are applied to explain the basal-plane incommensurate phase in some compounds of the AЈAЉBX 4 family, like K 2 MoO 4 , K 2 WO 4 , Rb 2 WO 4 , and to describe the sequence of high-temperature phase transitions in other compounds of this family. ͓S0163-1829͑98͒03909-5͔

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Section: Application Tosupporting

confidence: 88%

Section: Commensurate and Incommensurate Phases Inmentioning

confidence: 99%

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Basal-plane incommensurate phases in hexagonal-close-packed structures

1998

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“…In between an incommensurable, orthorhombic modification (Ccmm) exists according to literature. [23,24] Due to the low exposure time and high heating rate it cannot be clearly identified in the XRPD data. While K 2 MoO 4 was treated with hydrogen for 4.5 h no reaction occurred (Figure S15).…”

Section: The Effect Of Potassium On the Reduction Of Moomentioning

confidence: 99%

In situ studies on the industrial production process for molybdenum dioxide, MoO₂

Keilholz

Uhlenhut

Gabke

et al. 2023

Zeitschrift anorg allge chemie

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In the industrial production of molybdenum the reduction of molybdenum trioxide with hydrogen is a two‐step process. In order to get a deeper understanding of the chemistry involved, in situ studies were performed on the thermal behavior of molybdenum trioxide and the first reduction step to molybdenum dioxide. MoO3 shows a very strong anisotropy for thermal expansion (linear expansion coefficients α in 10−4 K−1: 1.32(4) for a, 5.5(1) for b, −0.246(5) for c). Upon heating in air, preferred orientation in XRPD patterns decreases and the color changes from grey to yellow, probably caused by decreasing oxygen vacancy concentration. The reduction of MoO3 by hydrogen was investigated via in situ X‐ray powder diffraction for varying heating rate, hydrogen flow and potassium content. The formation of the intermediate γ‐Mo4O11 shows a higher rate for increasing potassium content; it does not play a role whether potassium is present in the starting material MoO3 or in MoO2 formed in the reaction. The high‐temperature modification of K2MoO4 was found to crystallize in the α‐K2SO4 type (P63/mmc, a=6.3463(2) Å, c= 8.1331(2) Å). Heating up MoO3 in vacuum (1 Pa) with the same T,t protocol as above yields MoO2 even without the presence of hydrogen.

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“…was relatively poorly studied because of the high hygroscopic nature of these compounds [10,11]. It is known that the Inc − P 6 3 /mmc transition reveals a substantial discontinuity of the lattice parameter (∼ 0.2 − 0.7%) [10].…”

Section: Introductionmentioning

confidence: 99%

Thermodynamics of the incommensurate state inRb2WO4:The Lifshitz point in
Luk’yanchuk
¹
,
Jório
²
,
Saint‐Grégoire
³

2000
Phys. Rev. B
11
0
3
0
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We consider the evolution of the phase transition from the parent hexagonal phase P 6 3 /mmc to the orthorhombic phase P mcn that occurs in several compounds of A ′ A ′′ BX 4 family as a function of the hcp lattice parameter c/a. For compounds of K 2 SO 4 type with c/a larger than the threshold value 1.26 the direct first-order transition P mcn−P 6 3 /mmc is characterized by the large entropy jump ∼ R ln 2. For compoundswith c/a < 1.26 this transition occurs via an intermediate incommensurate (Inc) phase. DSC measurements were performed in Rb 2 W O 4 to characterize the thermodynamics of the P mcn − Inc − P 6 3 /mmc transitions. It was 1 found that both transitions are again of the first order with entropy jumps 0.2 · R ln 2 and 0.3 · R ln 2. Therefore, at c/a ∼ 1.26 the A ′ A ′′ BX 4 compounds reveal an unusual Lifshitz point where three first order transition lines meet.We propose the coupling of crystal elasticity with BX 4 tetrahedra orientation as a possible source of the transitions discontinuity.

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Isomorphism among commensurate and incommensurate high-temperature phases of A₂BO₄compounds

Cited by 22 publications

References 8 publications

Basal-plane incommensurate phases in hexagonal-close-packed structures

Basal-plane incommensurate phases in hexagonal-close-packed structures

In situ studies on the industrial production process for molybdenum dioxide, MoO₂

Thermodynamics of the incommensurate state inRb2WO4:The Lifshitz point in
Luk’yanchuk
¹
,
Jório
²
,
Saint‐Grégoire
³

2000
Phys. Rev. B
11
0
3
0
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Isomorphism among commensurate and incommensurate high-temperature phases of A2BO4compounds

Cited by 22 publications

References 8 publications

Basal-plane incommensurate phases in hexagonal-close-packed structures

Basal-plane incommensurate phases in hexagonal-close-packed structures

In situ studies on the industrial production process for molybdenum dioxide, MoO2

Thermodynamics of the incommensurate state inRb2WO4:The Lifshitz point inLuk’yanchuk1, Jório2, Saint‐Grégoire3 2000Phys. Rev. B11030View full textAdd to dashboardCite

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Isomorphism among commensurate and incommensurate high-temperature phases of A₂BO₄compounds

In situ studies on the industrial production process for molybdenum dioxide, MoO₂

Thermodynamics of the incommensurate state inRb2WO4:The Lifshitz point in
Luk’yanchuk
¹
,
Jório
²
,
Saint‐Grégoire
³

2000
Phys. Rev. B
11
0
3
0
View full text Add to dashboard Cite