**7. References**

Blair, H.C. (1998). How the osteoclast degrades bone. Bioessays, Vol.20, pp.837-46


A macroscopic model of bone external remodeling has been developed, basing on the thermodynamics of surfaces and with the identified configurational driving forces promoting surface evolution. The interactions between the surface diffusion of minerals and the mechanical driving factors have been quantified, resulting in a relatively rich model in terms of physical and mechanical parameters. Applications of the developed formalism to

Works accounting for the multiscale aspect of bone remodeling have emerged in the literature since the late nineteen's considering cell-scale (a few microns) up to bone-scale (a few centimeters) remodeling, showing adaptation of the 3D trabeculae architecture in response to mechanical stimulation, see the recent contributions (Tsubota et al., 2009; Coelho et al., 2009) and the references therein. It is likely that one has in the future to combine models at both micro and macro scales in a hierarchical approach to get deeper insight into

The present modeling framework shall serve as a convenient platform for the simulation of bone remodeling with the consideration of real geometries extracted from CT scans. The predictive aspect of those simulations is interesting in a medical context, since it will help doctors in adapting the medical treatment according to short and long term predictions of

Carter, D.R. ; Orr, T.E. & Fyrhie, D.P. (1989). Relationships between loading history and femoral cancellous bone architecture. *J. Biomech*., Vol.22, No.3, pp.231-244 Couchman, P.R. & Linford, R.G. (1980). Aspects of solid surface thermodynamics:

Eshelby, J. D. (1951). The force on an elastic singularity. *Phil. Trans. R. Soc.,* Vol.A244, pp.87–

Ganghoffer, J.F. & Haussy, B. (2005). Mechanical modeling of growth considering domain

Ganghoffer, J.F. (2010a). Mechanical modeling of growth considering domain variation—

Ganghoffer, J.F. (2010b). On Eshelby tensors in the context of the thermodynamics of open

Garikipati., K. (2009). The kinematics of biological growth. *Appl. Mech. Rev.* 62 (3), 030801,

Gurtin, M.E. & Murdoch, A.I. (1975). A continuum theory of elastic material Surfaces.

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relationships of the Shuttleworth type. *Jnal of Electroanalytical Chemistry*. Vol.115,

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Part II: Volumetric and surface growth involving Eshelby tensors*. J. Mech. Phys.* 

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real geometries

the simulations.

**7. References** 

the mechanisms of Wolff's law.

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pp.4311-4337

112

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doi:10.1115/1.3090829


**15** 

*Russia* 

**Thermodynamic Aspects of CVD** 

*Frumkin Institute of Physical Chemistry and Electrochemistry,* 

The low-temperature chemical vapor deposition (CVD) of refractory metals by the hydrogen reduction of their fluorides is known as one of the perspective technique for the production of high quality metallic coatings [1]. The CVD of tungsten has been more extensively studied due to unique combination of its features such as low deposition temperature (750- 900 K), high growth rate (up to 5 mm/h), a good purity and high density of tungsten deposit [2, 3]. Up to now there is a great interest to CVD tungsten alloys due to their

The thermodynamic analysis of the CVD processes is useful to define the optimal deposition conditions. The understanding of the gas phase phenomena controlling the metals and alloys deposition requires the knowledge of the gaseous mixture composition and surface reaction kinetics which lead to the deposit growth. This chapter contains the calculated and known thermochemical parameters of V, Nb, Ta, Mo, W, Re fluorides, the compositions of gas and solid phases as result of the equilibrium of the hydrogen and fluorides for the metals VB group (V, Nb, Ta ), VIB group (Mo, W), VII group (Re). A particular attention is

The accuracy of thermodynamic analysis depends on the completeness and reliability of thermochemical data. Unfortunately, a limited number of the transition metal fluorides have been characterized thermochemically or have been studied by a spectroscopic technique. The experimental data were completed with the evaluated thermochemical constants for fluorides in different valent and structural states. The calculated data were obtained by the interpolation procedure based on the periodic law. The interpolation was performed on properties of a number of the compounds that represent the electron-nuclei analogies [6]. The unknown enthalpy of the fluorides formation was calculating via energy of halids

Ω (МХn) = Δf Н (Мat) + n Δf Н (Хat) - Δf Н (МХn ), (1)

**1. Introduction** 

physical-mechanical properties [4, 5].

paid to the theoretical aspects of tungsten alloys crystallization.

**2. Estimation of thermochemical constants** 

atomization as following:

**Crystallization of Refractory** 

**Metals and Their Alloys** 

*Russian Academy of Sciences, Moscow,* 

Yu. V. Lakhotkin

Taber, L. (1995). Biomechanics of growth, remodeling and morphogenesis. *Appl. Mech. Rev*., Vol.48, pp.487-545

Thompson, D.W. (1992). On Growth and Form. Dover reprint of 1942. 2nd edition

Vidal, C.; Dewel, P. & Borckmans, P. (1994). *Au-delà de l'équilibre*. Hermann

