A Quantitative Study on the Effect of Heat Treatment on the Microstructure and Orientation of Titanium Hydride in Electrochemically Hydrogenated Pure Titanium

The electrochemical hydrogen charging of pure titanium and its alloys has been investigated previously, while how a subsequent annealing treatment affects the type of hydride and its orientation relationship with matrix is not clear. In the present study, a quantitative study on the microstructure and orientation of titanium hydrides during electrochemical hydrogen charging and subsequent annealing treatment was carried out using scanning electron microscopy, transmission electron microscopy and electron backscatter diffraction. The results show that δ-hydride is the main in both the electrochemically hydrogenated sample and the subsequent annealing treated sample. After electrochemical hydrogen charging for 48 h, the surface is mainly composed of dense δ-hydride with a thickness of approximately 42 μm, the orientation relationship between α-matrix and δ-hydride follows only the orientation relationship of OR2, {0001}_α//{1$\overline{1}$1}_δ, $\langle 1\overline{2}10\rangle_{\alpha }$//$\langle 110\rangle_{\delta }$ and an interface plane $\{ 10\overline{1}3\}_{\alpha }$//$\{ 1\overline{1}0\}_{\delta }$. Besides OR2, a part of hydrides show an orientation relationship of OR1 with the matrix after annealing, {0001}_α//{001}_δ, $\langle 1\overline{2}10\rangle_{\alpha }$//$\langle 110\rangle_{\delta }$ and an interface plane of $\{ 10\overline{1}0\}_{\alpha }$//$\{ 1\overline{1}0\}_{\delta }$. It is further found that the relative frequency of OR1and OR2 is closely related to annealing duration. Under an argon atmosphere at 450 °C, the frequencies of OR1 and OR2 are nearly balance with an annealing time of 12 h, while OR1 becomes to be the predominant one with a relative frequency of 96.5% after annealing for 96 h. The mechanism for the evolution of orientation relationship of hydrides with annealing time was discussed.     

Improving the Mechanical Properties of Mg-Gd-Y-Ag-Zr Alloy via Pre-Strain and Two-Stage Ageing

In this study, we investigated the effects of single-stage ageing (SSA), two-stage ageing (TSA), 2% pre-strain + single-stage ageing (P2%SSA) and 2% pre-strain + two-stage ageing (P2%TSA) on the mechanical properties of as-extruded Mg–8Gd–3Y–0.5Ag–0.5Zr alloy (E alloy). Compared with the SSA treatment, the TSA treatment increased the number density of $\beta ^{\prime}$ phase. The P2%SSA and P2%TSA treatments generated the $\gamma ^{\prime}$ phase and chain-like precipitates in addition to the $\beta ^{\prime}$ phase. The contributions of these ageing treatments to the alloy strengthening can be ranked as P2%TSA > P2%SSA > TSA > SSA, because the increments in the tensile yield strength were estimated to be 199 MPa > 148 MPa > 144 MPa > 110 MPa. Different from the traditional strengthening of $\beta ^{\prime}$ phase in the E + SSA and E + TSA alloys, the composite precipitates comprising the $\beta ^{\prime}$ phase, $\gamma ^{\prime}$ phase and chain-like precipitates in the E + P2%SSA and E + P2%TSA alloys provided better combined strengthening effect. The $\beta ^{\prime}$ phase was still dominated in the strengthening effect of the composite precipitates. Owing to the higher number density of $\beta ^{\prime}$ phase in the composite precipitates, the E + P2%TSA alloy exhibited the better mechanical performance as compared with the E + P2%SSA alloy. Finally, the E + P2%TSA alloy had the ultimate tensile strength of 452 MPa, the tensile yield strength of 401 MPa and elongation to failure of 3.3%.     

Surface Structures and Their Relative Stabilities of Orthorhombic YAlO3: A First-Principles Study

First-principles energetics calculations were performed to investigate the structures and relative stabilities of six low miller-index surfaces of orthorhombic YAlO₃ (YAP). The stoichiometric YAP (100) and (001) were predicted to have the lowest surface energies of 1.91 and 1.96 J/m², respectively. Using a thermodynamic defect model, non-stoichiometric YAP surface energies were further predicted as a function of ${P}_{{\text{O}}_{2}}$(${P}_{{\text{O}}_{2}}<1\ \mathrm{atm}$) and temperature (T). All the results were combined to construct the surface phase diagrams at T = 300 and 1400 K, revealing the strong correlation of the surface stabilities of YAP with its surface stoichiometry.     

Interfacial Oxides Evolution of High-Speed Steel Joints by Hot-Compression Bonding

The interfacial oxidation behavior of Cr4Mo4V high-speed steel (HSS) joints undergoing hot-compression bonding was investigated by using optical microscopy (OM), scanning electron microscopy (SEM), and transmission electron microscopy (TEM). In the heating and holding processes, dispersed rod-like and granular $\delta - {\text{Al}}_{{2}} {\text{O}}_{{3}}$ oxides were formed at the interface and in the matrix near the interface due to the selective oxidation and internal oxidation of Al, while irregular Si–Al–O compounds and spheroidal SiO₂ particles were formed at the interface. After the post-holding treatment, SiO₂ oxides and Si–Al–O compounds were dissolved into the matrix, and $\delta - {\text{Al}}_{{2}} {\text{O}}_{{3}}$ oxides were transformed into nanoscale $\alpha - {\text{Al}}_{{2}} {\text{O}}_{{3}}$ particles, which did not deteriorate the mechanical properties of the joints. The formation and migration of newly-formed grain boundaries by plastic deformation and post-holding treatment were the main mechanism for interface healing. The tensile test results showed that the strength of the healed joints was comparable to that of the base material, and the in-situ tensile observations proved that the fracture was initiated at the grain boundary of the matrix rather than at the interface. The clarification of interfacial oxides and microstructure is essential for the application of hot-compression bonding of HSSs.     

Formation of Face-Centered Cubic Phase in Ti35 Alloy Under In Situ Heating Transmission Electron Microscopy

A thermally induced hexagonal close-packed (HCP) to face-centered cubic (FCC) phase transition was investigated in an α-type Ti35 alloy with twinned structure by in situ heating transmission electron microscopy (TEM) and ab initio calculations. TEM observations indicated that the HCP to FCC phase transition occurred both within matrix/twin and at the twin boundaries in the thinner region of the TEM film, and the FCC-Ti precipitated as plates within the matrix/twin, while as equiaxed cells at twin boundaries. The crystallographic orientation relationship between HCP-Ti and FCC-Ti can be described as: $\left\{ {111} \right\}_{{{\text{FCC}}}} //\left\{ {0002} \right\}_{{{\text{HCP}}}} \;{\text{and}}\; < 110 >\,_{{{\text{FCC}}}} //\, <1\overline{2} 10>\,_{{{\text{HCP}}}}$. The HCP to FCC phase transition was accomplished by forming an intermediate state with a BB stacking sequence through the slip of partial dislocations. The formation of such FCC-Ti may be related to the thermal stress and temperature. Ab initio calculations showed that the formation of FCC-Ti may also be related to the contamination of interstitial atoms such as oxygen.     

Effect of Forging on Microstructure,Texture, and Uniaxial Properties of Cast AZ31B Alloy

The effect of open-die hot forging on cast AZ31B magnesium alloy was investigated in terms of the evolution of microstructure, texture, and mechanical properties. A refined microstructure with strong basal texture was developed in forged material. A significant increase in tensile yield and ultimate strengths by 143 and 23%, respectively, was determined as well. When tested in compression at room temperature, the forged alloy displayed significant in-plane asymmetry and unchanged yield strength compared to the cast alloy owing to the activation of \(\left\{ {10\bar{1}2} \right\}\left\langle {10\bar{1}1} \right\rangle\) extension twins in both the cast and forged conditions. However, the ultimate compressive strength for the forged material increased by 22 percent compared to the as-cast material. Microstructure and texture analysis of the fracture samples confirmed that the deformation of the forged samples was dominated by slip during tension and twin in compression. In comparison, both slip and twin were observed in the cast samples for similar testing conditions. The increase in strength of forging was attributed to the refinement of grains and the formation of strong basal texture, which activated the non-basal slip on the prismatic and pyramidal slip systems instead of extension twin.     

Detailed Structures and Formation Mechanisms of Well-Known Al_(10)RE_2Mn_7 Phase in Die-Cast Mg-4Al-4RE-0.3Mn Alloy

The detailed structures and the corresponding formation mechanisms of the well-known Al_(10)RE_2Mn_7 phase in the conventional die-cast Mg–4Al–4RE–0.3Mn alloy were thoroughly investigated using transmission electron microscopy(TEM). The results indicate that the Al_(10)RE_2Mn_7 phase ordinarily contains both normal (111) twins and orientation twins.Both detailed TEM observations and density functional theory calculations indicate that the Al_(10)RE_2Mn_7 phase is transferred from the Al_8REMn_4 phase following an orientation relationship as [010]_(Al_8REMn_4)//[101]_(Al_(10)RE_2Mn_7) and (101)_(Al_8REMn_4)//(110)_(Al_(10)RE_2Mn_7). Moreover, forming orientation twins in the Al_(10)RE_2Mn_7 phase is attributed to the blurry regions at incoherent twin boundaries in the Al_8REMn_4 phase. Finally, these formed orientation twins result in the (111) twins in the Al_(10)RE_2Mn_7 phase.     

Effect of Ag Addition on Microstructure,Mechanical and Corrosion Properties of Mg-Nd-Zn-Zr Alloy for Orthopedic Application

The as-extruded Mg–3Nd–0.2Zn–0.4Zr–xAg (x = 0, 0.2, 0.5, 1 wt%) alloys were prepared for biomedical applications. Scanning electron microscope, electron backscattered diffraction, X-ray diffraction, tensile test machine, electrochemical workstation, and immersion experiments were used to study microstructures, mechanical properties, and corrosion behavior of the as-extruded alloys. The results indicate that the microstructures of all the as-extruded alloys are composed of coarse undynamic recrystallized grains, fine equiaxed recrystallized grains, and precipitated phases. Ag element plays a positive role in promoting dynamic recrystallization and grain refinement. And during the extrusion, all the four alloys generate a $\left\langle {10\overline{1}0} \right\rangle$//ED fiber texture. With the increase of Ag element, the volume fraction of Mg₁₂Nd phase increases and then decreases slightly. By increasing Ag addition, both yield strength and ultimate tensile strength of the as-extruded alloys reduce first and then improve, and the elongation improves gradually from 9.4 to 12.7%. More importantly, the addition of Ag accelerates corrosion of the as-extruded alloys in simulated body fluid, and all the as-extruded alloys show uniform corrosion mode.     

Effect of Zn and Y Additions on Grain Boundary Movement of Mg Binary Alloys During Static Recrystallization

Texture evolution in rolled Mg–1 wt% Zn and Mg–1 wt% Y binary alloys was analyzed by quasi-in situ electron backscatter diffraction (EBSD) during static recrystallization. Mg–1 wt% Zn and Mg–1 wt% Y alloys exhibited strong basal texture at the initial recrystallization state. After grain growth annealing, the basal texture component {0001} < $11\overline{2}0$ > was increased in Mg–1 wt% Zn alloy and that of Mg–1 wt% Y alloy was decreased to be a random texture. Zn and Y atoms segregated strongly to the recrystallized grain boundaries in Mg–1 wt% Zn alloy and Mg–1 wt% Y alloy, respectively. Thus, Zn and Y elements facilitated the grain boundary movements along contrary directions during grain growth. In Mg–1 wt% Zn alloy, due to the Zn element segregation on grain boundaries, the grains consisted of a strong texture grew more easily because the grain boundary migration tended to move from the orientation close to normal direction to the orientation near to transverse direction or rolling direction. Therefore, after grain growth, the volume fraction of texture component {0001} < $11\overline{2}0$ > was increased by consuming the neighboring grains, leading to a stronger basal texture. On the contrary, in the Mg–1 wt% Y alloy, the Y element segregation caused the opposite direction of grain boundary migration, resulting in a random texture.     

Tension-compression asymmetry of a rolled Mg-Y-Nd alloy

In this work, tension and compression deformation behaviors of rolled and aged Mg-Y-Nd alloys were investigated. The microstructure evolution and plastic deformation mechanism during tension and compression were analyzed by combined use of electron backscatter diffraction and a visco-plastic self-consistent crystal plasticity model. The results show that both rolled and aged Mg-Y-Nd sheets show an extremely low yield asymmetry. Elimination of yield asymmetry can be ascribed to the tilted basal texture and suppression of {10-12} twinning. The rolled sheet has almost no yield asymmetry, however exhibits a remarkable strain-hardening behavior asymmetry. Compressed sample shows lower initial strain hardening rate and keeps higher strain hardening rate at the later stage compared with tension. The strain-hardening asymmetry can be aggravated by aging at 280 C. It is considered the limited amount of twins in compression plays the critical role in the strain hardening asymmetry. Finally, the relevant mechanism was analyzed and discussed.     

Dependence of Microstructure Evolution and Mechanical Properties on Loading Direction for AZ31 Magnesium Alloy Sheet with Non-basal Texture During In-Plane Uniaxial Tension

In-plane uniaxial tension of AZ31 magnesium alloy sheet with non-basal texture has been conducted in order to demonstrate the effects of loading direction on the microstructure evolution and mechanical properties at ambient temperature. Loading axes are chosen to be along five directions distributed between rolling direction (RD) and transverse direction (TD), allowing various activities in involved slip and twinning modes to take place. As for twinning modes, electron backscattered diffraction observations confirm that the contribution of ${{\{ 10\overline{1}1\} }}$ compression twinning is minimal to the plastic deformation of all deformed samples. By comparison, ${{\{ 10\overline{1}2\} }}$ extension twinning (ET) not only serves as an important carrier on sustaining and accommodating plastic strain but also contributes to the emergence of TD-component texture with the progression of plastic strain. In terms of slip modes, analysis on Schmid factor demonstrates that the increasing tilted angle between loading direction and RD of sheet is unfavorable to the activation of basal <a> slip, whereas it contributes to the activation of prismatic <a> slip. These observations consequently explain the increasing tendency of 0.2% proof yield stress. Moreover, the activations of basal <a> slip and ${{\{ 10\overline{1}2\} }}$ ET collectively contribute to the concentration of two tilted basal poles toward normal direction. With increasing angle between loading direction and RD, the activations of basal <a> slip and ${{\{ 10\overline{1}2\} }}$ ET are gradually weakened. This leads to a weakening tendency about concentration of two tilted basal poles, a generally increasing tendency about Lankford value (r-value) and a generally decreasing tendency about strain-hardening exponent (n-value).     

The Effect of Texture on the Corrosion Behavior of AZ31?Mg Alloy

Magnesium (Mg) grains show anisotropic corrosion behavior, which implies that the single-phase, hot-rolled Mg alloy AZ31 sheet, if highly textured, will have different corrosion performance depending on its crystallographic orientation of the grains. Its rolling surface, dominated by (0001) basal crystallographic planes, is more corrosion resistant than its cross-section surface, which is mainly composed of $ \{ 10\overline{1} 0\} $ and $ \{ 11\overline{2} 0\} $ prismatic crystallographic planes. Furthermore, grain refinement by hot rolling is beneficial to the overall corrosion resistance of AZ31 because of the dissolution of AlMn(Fe) intermetallic precipitates in the alloy. Surface compressive deformation machining can lead to refined grains and an expected preferred grain orientation, thus improving the corrosion resistance of AZ31 alloy.     

First-Principles Studies on Twinnability of Magnesium Alloys: Effects of Yttrium and Lithium on $$\left( {10\bar{1}1} \right)\left[ {\bar{1}012} \right]$$ Compression Twinning Deformation Processes

We investigate the energetics involved in the \(\left( {10\bar{1}2} \right)\left[ {\bar{1}011} \right]\) tension and \(\left( {10\bar{1}1} \right)\left[ {\bar{1}012} \right]\) compression twinning deformation processes in magnesium via first-principles studies. Through identification of structural changes associated with each deformation process, we study the energetics of each deformation process and the local instability in the twin boundary region. We observe that the energy barrier in the \(\left( {10\bar{1}1} \right)\left[ {\bar{1}012} \right]\) compression twinning deformation pathway is higher than that in the \(\left( {10\bar{1}2} \right)\left[ {\bar{1}011} \right]\) tension twinning deformation pathway, even though the \(\left( {10\bar{1}1} \right)\) compression twin boundary is more stable than the \(\left( {10\bar{1}2} \right)\) tension twin boundary. We extend our study to examine the effects of Y and Li as alloying elements on each twinning deformation process. Our calculations predict that the addition of Y causes a reduction in the probability of fracture by an order of magnitude when the twinning deformation occurs and weakening of the resistivity to twinning deformation. However, the effect of Li addition on the twinning deformations is weaker than that of Y addition.     

熔剂中添加LaCl3对Mg合金显微组织与性能的影响

测试分析了含有不同量LaCl3的熔剂对Mg合金的力学性能、组织、断口形貌以及腐蚀行为的影响．结果表明，LaCl3以熔剂形式加入Mg合金中，合金内会形成粒状细小的Al10La2Mn7稀土相，该稀土相起到γ相形核核心的作用，使γ相得到细化．LaCl3可以提高合金的抗拉强度σb和延伸率δ当熔剂中含有5％的LaCl3时，σb和δ分别从161MPa和2．1％上升到最大值203MPa和4．2％．分别提高了26％和100％．之后，随着LaCl3加入量的进一步提高，在精炼过程中会造成熔剂结团，并增加Mg熔体内的夹杂，合金的力学性能反而下降．LaCl3不改变Mg合金的断裂机理，断口形貌仍为准解理断裂．研究还表明，含5％LaCl3的熔剂能明显改善Mg合金的耐蚀性，在5％Nacl溶液中腐蚀速率从1.10mg／(cm^2-d)下降到0．17mg／(cm^3-d)，降低了84％．     

初始取向对AZ31镁合金微观织构演化的影响

将从挤压棒材中截取的长轴与挤压方向分别成0°,45°和90°的AZ31镁合金长方体试样在中、高温度(523-723 K)下沿长轴方向压缩变形,利用OM和SEM/EBSD技术观察和分析了初始取向对其微观织构演化的影响.结果表明,随着变形温度的降低,初始取向对变形行为的影响显著增加,在523 K时,长轴平行挤压方向的0°试...     

Tailoring Texture to Highly Strengthen AZ31 Alloy Plate in the Thickness Direction via Pre-tension and Rolling-Annealing

Conventional wrought Mg alloys, such as AZ31 and ZK60 rolled plates, usually exhibit significantly low tensile yield strength in the thickness direction. This can be attributed to the high activity of {10-12} tension twinning due to the strong basal texture (< 0001 > //ND, normal direction). In this work, the tensile yield strength in the ND of the as-rolled (AR) AZ31 plate increased from 50 to 150 MPa (increased by 200%) via simple processing, i.e., pre-tension and rolling-annealing (PTRA) treatment. The strong basal texture (< 0001 > //ND) of the AR plate was changed into a weakened fiber texture (< 0001 > ⊥ND). The evolution of microstructures during PTRA treatment and the activated deformation modes during uniaxial tension were studied quantitatively and statistically by the means of intergranular misorientation (IM) and in-grain misorientation axes (IGMA) analysis. The results indicate that various twin variants, as well as {10-12}-{10-12} secondary twins, were activated during pre-tension and rolling, and most residual matrix was consumed by twins after annealing. The dominated deformation modes in tension changed from {10-12} tension twinning (the AR sample) to prismatic slip (the PTRA sample) in the early tensile deformation. The underlying formation mechanism of the fiber texture and corresponding strengthening mechanism were discussed.     

AZ31镁合金中拉伸孪晶静态再结晶的分析

基于前期工作对压缩孪晶静态再结晶的分析,主要利用XRD和EBSD技术进一步研究AZ31镁合金中拉伸孪晶静态再结晶过程中组织和织构的演变规律,以及再结晶初期新晶粒的取向特征,结果表明:拉伸孪晶不能有效地促进再结晶形核,其细化晶粒的效果不显著,其再结晶速率显著延迟于压缩孪晶;退火过程中并没有生成新的再结晶织构组分,表现为初始基面织构的减弱;新晶粒优先在拉伸孪晶的变体交叉处,或拉伸孪晶与压缩孪晶的交叉处形核,但其取向规律性不强,没有遵循初始拉伸或压缩孪晶内的取向规律,同时还对拉伸与压缩孪晶的再结晶行为进行了比较。     

Crystallographic analysis of the martensitic transformation in medium-carbon steel with packet martensite

Based on X-ray diffraction studies of the martensite texture in a single martensite packet, exact orientation relationships between the orientations of martensite crystallites and the original austenite single crystal in medium-carbon steel 37KhN3A have been determined to be as follows: (011)_α||(1; 0.990; 1.009)_γ to an accuracy of \( \pm 0.15^\circ ,{\left[ {01\overline 1 } \right]_\alpha }||{\left[ {1;1.163; - 2.133} \right]_\gamma }\) to an accuracy of ±0.15°. It has been shown that the orientation relationships proved to be almost the same as in the Fe–31% Ni alloy with a twinned martensite with close lattice parameters. Therefore, the conclusion has been drawn that the mechanism of the lattice deformation upon the martensitic transformation is the same in both alloys. It is described as follows. The lattice deformation occurs by shear on the (111) plane in the \({\left[ {11\overline 2 } \right]_{_\gamma }}\) direction and is accompanied by an additional change in the dimensions in the mutually perpendicular directions \({\left[ {11\overline 2 } \right]_{_\gamma }},\left[ {111} \right],\;and{\left[ {1\overline 1 0} \right]_{_\gamma }}\). The invariantlattice deformation is implemented by slip in martensite on the planes of the (112)_α type in the direction \({\left[ {\overline 1 \overline 1 1} \right]_\alpha }\). One of the 24 crystallographically equivalent variants of the transformation mechanism has been considered. Apart from this type of deformation, an additional deformation of martensite is possible that does not change its orientation. It has been shown that the orientation of the martensite crystallite calculated via the phenomenological theory of the martensitic transformations (PTMT) differs by approximately 1° from the experimentally determined orientation. This refers to both the lath and twinned martensite. In the twinned martensite, the invariant plane obtained in the PTMT calculations and the habit plane coincide. In lath martensite of 37KhN3A steel, the invariant plane of the martensite crystal obtained in PTMT calculations deviates by ~25° from the orientation of the surface of the martensite plate (habit plane), which is close to the (111)_γ plane. An explanation of this phenomenon is given.     

Microstructural Evolution and Biodegradation Response of Mg-2Zn-0.SNd Alloy During Tensile and Compressive Deformation

The effect of deformation behavior on the in vitro corrosion rate of Mg-2Zn-0.5Nd alloy was investigated experimentally after uniaxial tensile and compressive stress.The microstructure and texture were characterized using electron backscattered diffraction and X-ray diffraction,while potentiodynamic polarization and immersion tests were used to investigate the cor-rosion response after deformation.The result reveals that applied compressive stress has more dominant effect on the corro-sion rate of Mg-2Zn-0.5Nd alloy as compared to tensile stress.Both tensile and compressive strains introduce dislocation slip and deformation twins in the alloy,thereby accelerating the corrosion rate due to the increased stress corrosion related to dislocation slips and deformation twins.The { 10(1)2} tension twinning and prismatic slip were the major contributors to tensile deformation while basal slip,and { 10(1)2} tension twin were obtainable during compressive deformation.The twinning activity after deformation increases with the plastic strain and this correlates with the degradation rate.     

Reequilibrium kinetics of NiO-Cr2O3 solid solutions

Electrical conductivity has been measured to monitor the reequilibration kinetics for single crystals of NiO-Cr₂O₃ solid solutions. It has been found that the rate for the reduction process is higher than that for the oxidation runs, thus indicating that the obtained kinetic data are not purely bulk controlled. The following expressions for the apparent chemical diffusion coefficient have been obtained within the temperature range 900–1200°C and oxygen partial pressure range 1–10^?5 atm: $$\begin{gathered} \tilde D_{1 red} = 1.22 \times 10^{ - 2} exp \left( {\frac{{24,420 \pm 1210 cal/mole \cdot ^\circ K}}{{RT}}} \right) \hfill \\ \tilde D_{1 oxid}^* = 1.44 \times 10^{ - 2} exp \left( {\frac{{27,340 \pm 700 cal/mole \cdot ^\circ K}}{{RT}}} \right) \hfill \\ \tilde D_{2 red} = 2.29 \times 10^{ - 2} exp \left( {\frac{{25,340 \pm 2230 calmole \cdot ^\circ K}}{{RT}}} \right) \hfill \\ \tilde D_{2 oxid}^* = 0.109 exp \left( {\frac{{29,610 \pm 3200 cal/mole \cdot ^\circ K}}{{RT}}} \right) \hfill \\ \tilde D_{3 red} = 3.16 \times 10^{ - 2} exp \left( {\frac{{26,020 \pm 2430 cal/mole \cdot ^\circ K}}{{RT}}} \right) \hfill \\ \tilde D_{3 oxid}^* = 0.202 exp \left( {\frac{{31,500 \pm 2640 cal/mole \cdot ^\circ K}}{{RT}}} \right) \hfill \\ \end{gathered} $$ .